Table of contents

  1. December 2007
  2. November 2007
  3. October 2007
  4. September 2007
  5. August 2007
  6. July 2007
  7. June 2007
  8. May 2007
  9. April 2007
  10. March 2007
  11. February 2007
  12. January 2007

December 2007

Dec 31, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(2·10166+7)/9 = (2)1653<166> = 32 · 13 · 19 · 2203 · 92591638837<11> · C148

C148 = P62 · P87

P62 = 10579117484643669985321526488483937482639067300717328050482541<62>

P87 = 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651<87>

Number: n
N=4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191
  ( 148 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Dec 31 10:05:46 2007  prp62 factor: 10579117484643669985321526488483937482639067300717328050482541
Mon Dec 31 10:05:46 2007  prp87 factor: 463246679702034732206614919683068341832261226156838899536755186335885948793861377955651
Mon Dec 31 10:05:46 2007  elapsed time 01:19:50 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 48.46 hours.
Scaled time: 63.48 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_165_3
n: 4900741048938921529386312376049753422014062526470395527666102273448608728036064841441443726000645540939103525055300397035584580148478781490647789191
skew: 0.81
deg: 5
c5: 20
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:230209, AFBsize:229397, largePrimes:7279611 encountered
Relations: rels:6773272, finalFF:518245
Max relations in full relation-set: 28
Initial matrix: 459672 x 518245 with sparse part having weight 38557490.
Pruned matrix : 415223 x 417585 with weight 27293794.
Total sieving time: 45.28 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 48.46 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10154-9 = 6(9)1531<155> = 24187568437147<14> · 357505542381274647193<21> · C121

C121 = P35 · P86

P35 = 87307807817705591131142443529365687<35>

P86 = 92719261960991305708767306625668063796197431975684064005420378748486361040936361668683<86>

7·10165-9 = 6(9)1641<166> = 449 · 96293 · 193732283 · C150

C150 = P60 · P91

P60 = 119720935477183205712026361015748167111027951799849560997421<60>

P91 = 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341<91>

Number: n
N=835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Dec 31 23:17:09 2007  prp60 factor: 119720935477183205712026361015748167111027951799849560997421
Mon Dec 31 23:17:09 2007  prp91 factor: 6980473515066820668028752248342210383473908035017528053560574089914810233581451339796380341
Mon Dec 31 23:17:09 2007  elapsed time 02:16:22 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 58.35 hours.
Scaled time: 102.75 units (timescale=1.761).
Factorization parameters were as follows:
name: KA_6_9_164_1
n: 835708819297501087161209256684919312616575197394475766671782482860339428847159691345411763978143923133144396640238950619922829764501373132545436100561
type: snfs
skew: 1.05
deg: 5
c5: 7
c0: -9
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:230209, AFBsize:230717, largePrimes:7456900 encountered
Relations: rels:6921697, finalFF:489538
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 58.10 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 58.35 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(7·10164-61)/9 = (7)1631<164> = 67 · 16943 · 608743 · 4855817 · 723493411 · 103466618887166809<18> · C120

C120 = P39 · P40 · P43

P39 = 200987859740178940829671987628842189511<39>

P40 = 1524315768672965057529391990531835488823<40>

P43 = 1010681974438265260089808346426272470700763<43>

Tue Jan 01 00:33:37 2008  
Tue Jan 01 00:33:37 2008  
Tue Jan 01 00:33:37 2008  Msieve v. 1.32
Tue Jan 01 00:33:37 2008  random seeds: 670f8060 b722816b
Tue Jan 01 00:33:37 2008  factoring 203134806920325175654885525513483664774580080235041609363980893235812401418296893 (81 digits)
Tue Jan 01 00:33:37 2008  searching for 15-digit factors
Tue Jan 01 00:33:38 2008  commencing quadratic sieve (80-digit input)
Tue Jan 01 00:33:38 2008  using multiplier of 5
Tue Jan 01 00:33:38 2008  using 64kb Opteron sieve core
Tue Jan 01 00:33:38 2008  sieve interval: 6 blocks of size 65536
Tue Jan 01 00:33:38 2008  processing polynomials in batches of 17
Tue Jan 01 00:33:38 2008  using a sieve bound of 1305691 (50294 primes)
Tue Jan 01 00:33:38 2008  using large prime bound of 129263409 (26 bits)
Tue Jan 01 00:33:38 2008  using trial factoring cutoff of 27 bits
Tue Jan 01 00:33:38 2008  polynomial 'A' values have 10 factors
Tue Jan 01 00:51:33 2008  50454 relations (25765 full + 24689 combined from 273397 partial), need 50390
Tue Jan 01 00:51:34 2008  begin with 299162 relations
Tue Jan 01 00:51:34 2008  reduce to 72049 relations in 2 passes
Tue Jan 01 00:51:34 2008  attempting to read 72049 relations
Tue Jan 01 00:51:35 2008  recovered 72049 relations
Tue Jan 01 00:51:35 2008  recovered 62785 polynomials
Tue Jan 01 00:51:35 2008  attempting to build 50454 cycles
Tue Jan 01 00:51:35 2008  found 50454 cycles in 1 passes
Tue Jan 01 00:51:35 2008  distribution of cycle lengths:
Tue Jan 01 00:51:35 2008     length 1 : 25765
Tue Jan 01 00:51:35 2008     length 2 : 24689
Tue Jan 01 00:51:35 2008  largest cycle: 2 relations
Tue Jan 01 00:51:35 2008  matrix is 50294 x 50454 with weight 1538986 (avg 30.50/col)
Tue Jan 01 00:51:35 2008  filtering completed in 4 passes
Tue Jan 01 00:51:35 2008  matrix is 42992 x 43056 with weight 1286275 (avg 29.87/col)
Tue Jan 01 00:51:35 2008  saving the first 48 matrix rows for later
Tue Jan 01 00:51:35 2008  matrix is 42944 x 43056 with weight 1002106 (avg 23.27/col)
Tue Jan 01 00:51:35 2008  matrix includes 64 packed rows
Tue Jan 01 00:51:35 2008  commencing Lanczos iteration
Tue Jan 01 00:52:18 2008  lanczos halted after 680 iterations (dim = 42920)
Tue Jan 01 00:52:18 2008  recovered 6 nontrivial dependencies
Tue Jan 01 00:52:18 2008  prp39 factor: 200987859740178940829671987628842189511
Tue Jan 01 00:52:18 2008  prp43 factor: 1010681974438265260089808346426272470700763
Tue Jan 01 00:52:18 2008  elapsed time 00:18:41

Dec 30, 2007 (2nd)

By Sinkiti Sibata / PFGW

(2·102442+7)/9 is prime.

Dec 30, 2007

By Robert Backstrom / GGNFS, Msieve

(28·10163+17)/9 = 3(1)1623<164> = 3 · 11 · 113 · 5227723 · 5474506657<10> · C144

C144 = P54 · P90

P54 = 568254104215421080733918790780653788490645701320935561<54>

P90 = 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507<90>

Number: n
N=291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427
  ( 144 digits)
SNFS difficulty: 164 digits.
Divisors found:

Sun Dec 30 22:22:57 2007  prp54 factor: 568254104215421080733918790780653788490645701320935561
Sun Dec 30 22:22:57 2007  prp90 factor: 513006657969163357232705769402175646798527021065255936378677850134407454699737691808031507
Sun Dec 30 22:22:57 2007  elapsed time 00:55:31 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.78 hours.
Scaled time: 54.81 units (timescale=1.532).
Factorization parameters were as follows:
name: KA_3_1_162_3
n: 291518138880813831877316139677912045506082513260025572748734915030214053671271873482644565087545343430540161717571420952814494855357103004720427
skew: 0.45
deg: 5
c5: 875
c0: 17
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:7351213 encountered
Relations: rels:6806772, finalFF:496921
Max relations in full relation-set: 28
Initial matrix: 433413 x 496921 with sparse part having weight 48938966.
Pruned matrix : 
Total sieving time: 35.60 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

(89·10161+1)/9 = 9(8)1609<162> = 11 · 151 · 54497 · 4734857424467<13> · 29333719355391524558753<23> · C119

C119 = P50 · P70

P50 = 24068764486818214538179925119843116225195355366201<50>

P70 = 3267965275130364758731306727795381662655553549388276194815369559709367<70>

Number: n
N=78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767
  ( 119 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Dec 30 22:54:11 2007  prp50 factor: 24068764486818214538179925119843116225195355366201
Sun Dec 30 22:54:11 2007  prp70 factor: 3267965275130364758731306727795381662655553549388276194815369559709367
Sun Dec 30 22:54:11 2007  elapsed time 01:13:42 (Msieve 1.32)

Version: GGNFS-0.77.1-20050930-k8
Total time: 37.56 hours.
Scaled time: 31.47 units (timescale=0.838).
Factorization parameters were as follows:
name: KA_9_8_160_9
n: 78655886558212839023556857120942142003924560409165078599494695301264178096244478079634342453626033940099746525414904767
type: snfs
deg: 5
c5: 890
c0: 1
skew: 0.22
m: 100000000000000000000000000000000
rlim: 3000000
alim: 3000000
lbpr: 28
lbpa: 28
mbpr: 48
mbpa: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:216816, AFBsize:217061, largePrimes:5646354 encountered
Relations: rels:5529662, finalFF:441875
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.45 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000
total time: 37.56 hours.
 --------- CPU info (if available) ----------
CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03
Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM)
Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888)
Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848)
Total of 2 processors activated (12009.47 BogoMIPS).

Dec 29, 2007 (2nd)

By Robert Backstrom / GMP-ECM

2·10163+3 = 2(0)1623<164> = 166140237444137244767<21> · C144

C144 = P39 · P105

P39 = 190635692847477990579123632346869310511<39>

P105 = 631467424737264651495425260061946168071504561817690296672097889180937084893277408137330615731353547645619<105>

7·10153-9 = 6(9)1521<154> = 137945979054044323691<21> · C134

C134 = P33 · P101

P33 = 772167558584103691869638283989203<33>

P101 = 65716956589780721844302884925214520835046088468765165698360498247128407329527151604691722545317100967<101>

Dec 29, 2007

By Jo Yeong Uk / GGNFS

7·10148-9 = 6(9)1471<149> = 7354479179<10> · 18371504286793171<17> · C123

C123 = P55 · P69

P55 = 2814258676699625279171724231993155814622006129842908123<55>

P69 = 184093046599172102452699913165893938014185229449403497478166109476613<69>

Number: 69991_148
N=518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399
  ( 123 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=2814258676699625279171724231993155814622006129842908123 (pp55)
 r2=184093046599172102452699913165893938014185229449403497478166109476613 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 15.54 hours.
Scaled time: 33.21 units (timescale=2.137).
Factorization parameters were as follows:
n: 518085453711788532865190630641573477595982123762441212022596337954685562506751479459950679549038087281476496982221376227399
m: 1000000000000000000000000000000
c5: 7
c0: -900
skew: 2.64
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175703, largePrimes:5573819 encountered
Relations: rels:5511681, finalFF:495649
Max relations in full relation-set: 28
Initial matrix: 352073 x 495649 with sparse part having weight 44562981.
Pruned matrix : 293821 x 295645 with weight 24414844.
Total sieving time: 15.02 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.40 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 15.54 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (4th)

By Sinkiti Sibata / GGNFS

3·10171+1 = 3(0)1701<172> = 59 · 2421821 · 1600388452377973<16> · 19226964394318121967711782431<29> · C120

C120 = P42 · P79

P42 = 454231567465961238949597490091615349190531<42>

P79 = 1502151578223577638654775137097332901436078950967469661170957656557872845681903<79>

Number: 30001_171
N=682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493
  ( 120 digits)
Divisors found:
 r1=454231567465961238949597490091615349190531 (pp42)
 r2=1502151578223577638654775137097332901436078950967469661170957656557872845681903 (pp79)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 72.45 hours.
Scaled time: 143.38 units (timescale=1.979).
Factorization parameters were as follows:
name: 30001_171
n: 682324665947963157631469728271325158696221411931460030747532541936673539403173263878033566456941819939868757489765660493
skew: 44071.04
# norm 1.16e+16
c5: 49080
c4: -8193826874
c3: -490521821772937
c2: 13679562189223828075
c1: 268407340291989159886011
c0: -3575626527912292763955712170
# alpha -5.23
Y1: 1376995663549
Y0: -106811371197497656583221
# Murphy_E 2.89e-10
# M 516601066594921290271387127147345628955044795772215321251305996854853784465683210678704718808492261730386730080006420124
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316211, largePrimes:7704182 encountered
Relations: rels:7780725, finalFF:757685
Max relations in full relation-set: 32
Initial matrix: 632244 x 757685 with sparse part having weight 71595438.
Pruned matrix : 531677 x 534902 with weight 46827802.
Total sieving time: 67.50 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.05 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 72.45 hours.
 --------- CPU info (if available) ----------

Dec 28, 2007 (3rd)

By Jo Yeong Uk / GGNFS

7·10140-9 = 6(9)1391<141> = 26003 · 49967046113187701<17> · C120

C120 = P49 · P72

P49 = 3072384756632832193294930209979933326902287322161<49>

P72 = 175353850256855514724412620180648233024414774451978568104314670271200777<72>

Number: 70009_140
N=538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097
  ( 120 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=3072384756632832193294930209979933326902287322161 (pp49)
 r2=175353850256855514724412620180648233024414774451978568104314670271200777 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.12 hours.
Scaled time: 13.11 units (timescale=2.144).
Factorization parameters were as follows:
n: 538754496546039129594575511841279608916142932610183608764794445522735349555460282454684421134028742368503726717312519097
m: 10000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368951 encountered
Relations: rels:3483950, finalFF:405792
Max relations in full relation-set: 28
Initial matrix: 228213 x 405792 with sparse part having weight 35387880.
Pruned matrix : 168806 x 170011 with weight 13391873.
Total sieving time: 5.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.12 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10144-9 = 6(9)1431<145> = 1487 · 3084617 · 6753139867<10> · C126

C126 = P55 · P72

P55 = 2066420873807475272508154570496764559275489805725499291<55>

P72 = 109360704402145490620976185805347880615820804660378980898198273592328057<72>

Number: 69991_144
N=225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587
  ( 126 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=2066420873807475272508154570496764559275489805725499291 (pp55)
 r2=109360704402145490620976185805347880615820804660378980898198273592328057 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.14 hours.
Scaled time: 21.75 units (timescale=2.144).
Factorization parameters were as follows:
n: 225985242350882492390817091181539241057870132922821577330562232474083020570409647436082746217322496695164359587616913392907587
m: 100000000000000000000000000000
c5: 7
c0: -90
skew: 1.67
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114352, largePrimes:3482197 encountered
Relations: rels:3539168, finalFF:329576
Max relations in full relation-set: 28
Initial matrix: 228573 x 329576 with sparse part having weight 32251907.
Pruned matrix : 200812 x 202018 with weight 16980012.
Total sieving time: 9.89 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.14 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

7·10186-9 = 6(9)1851<187> = 1882873212211<13> · 5833979226117373<16> · 47533639674475314086029<23> · 22494947546032604356359491<26> · C111

C111 = P43 · P69

P43 = 2515472027805282686708792675704535850836383<43>

P69 = 236922626264959098658721156310440198919184175106191358028227502394681<69>

Number: n
N=595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823
  ( 111 digits)
Divisors found:
 r1=2515472027805282686708792675704535850836383 (pp43)
 r2=236922626264959098658721156310440198919184175106191358028227502394681 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.07 hours.
Scaled time: 33.44 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_6_9_185_1
n: 595972239123669791995895721145326920898097780541200339694452957278131466762170631342974085756411616949220478823
skew: 7691.60
# norm 7.39e+14
c5: 65280
c4: -3707517143
c3: -59981266406565
c2: 195444948138712791
c1: 464656384627185252258
c0: -666305598531814435117600
# alpha -4.72
Y1: 299854219969
Y0: -1556288568485250579843
# Murphy_E 8.93e-10
# M 261347015577692975215738963466108609772390237867217698520093975466862424241959027489401092781747038850578899133
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 100000)
Primes: RFBsize:230209, AFBsize:229965, largePrimes:7449706 encountered
Relations: rels:7280948, finalFF:562779
Max relations in full relation-set: 28
Initial matrix: 460254 x 562779 with sparse part having weight 47426767.
Pruned matrix : 375082 x 377447 with weight 27995113.
Total sieving time: 16.82 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.45 hours.
Total square root time: 0.65 hours, sqrts: 4.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 19.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10158-9 = 6(9)1571<159> = 665507 · 4787893769<10> · C144

C144 = P34 · P110

P34 = 4551229532797823713440523924237357<34>

P110 = 48269429654485286004700435874371392955763120608188765913835335149678303496468383067863156974558912669025897961<110>

5·10167+3 = 5(0)1663<168> = 7 · 773 · 8329 · C161

C161 = P68 · P93

P68 = 66986389608208370945649030468786635518218514529828739674619854324867<68>

P93 = 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811<93>

Number: n
N=11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137
  ( 161 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Dec 28 08:58:01 2007  prp68 factor: 66986389608208370945649030468786635518218514529828739674619854324867
Fri Dec 28 08:58:01 2007  prp93 factor: 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811
Fri Dec 28 08:58:01 2007  elapsed time 01:10:29 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.34 hours.
Scaled time: 84.62 units (timescale=1.826).
Factorization parameters were as follows:
name: KA_5_0_166_3
n: 11094292410356841480689529799258319926065860290596351278048063092974674681508936485819419666883219858321891974475405828661656232743521548965580379379979492866137
skew: 0.36
deg: 5
c5: 500
c0: 3
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:250150, AFBsize:249916, largePrimes:7647488 encountered
Relations: rels:7156043, finalFF:585019
Max relations in full relation-set: 28
Initial matrix: 500132 x 585019 with sparse part having weight 52070590.
Pruned matrix : 452893 x 455457 with weight 34748113.
Total sieving time: 46.16 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 46.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 28, 2007

By Sinkiti Sibata / PFGW

7·1012755-9 and 7·1015142-9 are PRPs.

Dec 27, 2007 (5th)

By Yousuke Koide

(101809-1)/9 is divisible by 23016857713231589991096649713043507<35>

(101863-1)/9 is divisible by 7506789884668978259450285467<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 27, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

7·10137-9 = 6(9)1361<138> = 9041 · 162129560783<12> · C123

C123 = P50 · P73

P50 = 63195768153342995547599618615921084920365446753767<50>

P73 = 7556685842419476053247753995520570438772601000514461987314342496480958991<73>

Number: 69991_137
N=477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097
  ( 123 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=63195768153342995547599618615921084920365446753767 (pp50)
 r2=7556685842419476053247753995520570438772601000514461987314342496480958991 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.07 hours.
Scaled time: 8.67 units (timescale=2.130).
Factorization parameters were as follows:
n: 477550566505190610831339497667016508356659514844638240871039919937869611141038512390547786684479527858687496804388001769097
m: 1000000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1450001)
Primes: RFBsize:107126, AFBsize:107093, largePrimes:2316731 encountered
Relations: rels:2429777, finalFF:264060
Max relations in full relation-set: 28
Initial matrix: 214287 x 264060 with sparse part having weight 22014166.
Pruned matrix : 198204 x 199339 with weight 13643617.
Total sieving time: 3.87 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.07 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10162-9 = 6(9)1611<163> = 859 · 118247 · 2662639391<10> · 68628329971<11> · C135

C135 = P30 · P105

P30 = 436977788659416077831566216483<30>

P105 = 863057237779628902143622988929371538585971609219344275040457451654589439284920068001169478963439353329509<105>

Dec 27, 2007 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

5·10171-9 = 4(9)1701<172> = 7 · 41 · C170

C170 = P43 · P128

P43 = 1363684689367687199660001585916252959225073<43>

P128 = 12775389298778802140820274185385735600606854567622114532762344954306460995067145385939039085787137146377153359945100703455866041<128>

7·10143-9 = 6(9)1421<144> = 97 · 317 · 571 · C137

C137 = P68 · P70

P68 = 11669963674208858774803484401760836297661604636382205067928038771673<68>

P70 = 3416342715437805134104596866257027736379971208960481691857755728114273<70>

Number: n
N=39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729
  ( 137 digits)
SNFS difficulty: 143 digits.
Divisors found:

Thu Dec 27 16:03:21 2007  prp68 factor: 11669963674208858774803484401760836297661604636382205067928038771673
Thu Dec 27 16:03:21 2007  prp70 factor: 3416342715437805134104596866257027736379971208960481691857755728114273
Thu Dec 27 16:03:21 2007  elapsed time 00:58:19 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 10.12 hours.
Scaled time: 13.24 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_6_9_142_1
n: 39868595387807238075146492882117277574103046308113959709594872989761346018457223189921629162943461946194596677613254006978940667499388729
skew: 0.26
deg: 5
c5: 7000
c0: -9
m: 10000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1100001)
Primes: RFBsize:203362, AFBsize:202857, largePrimes:6879960 encountered
Relations: rels:6390626, finalFF:531267
Max relations in full relation-set: 28
Initial matrix: 406287 x 531267 with sparse part having weight 31643740.
Pruned matrix : 
Total sieving time: 9.91 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 10.12 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10194-9 = 6(9)1931<195> = 59 · 503 · 19009 · 4546319117<10> · 3201890183553739545421<22> · 3663534177803835316717<22> · 5453825411908180414535101<25> · C109

C109 = P47 · P62

P47 = 52063286361231377503035962252713421659616793211<47>

P62 = 81944416344344076297954674797070896167668217005498046483209993<62>

Number: n
N=4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523
  ( 109 digits)
Divisors found:

Thu Dec 27 21:14:40 2007  prp47 factor: 52063286361231377503035962252713421659616793211
Thu Dec 27 21:14:40 2007  prp62 factor: 81944416344344076297954674797070896167668217005498046483209993
Thu Dec 27 21:14:40 2007  elapsed time 01:21:04 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.97 hours.
Scaled time: 28.00 units (timescale=1.753).
Factorization parameters were as follows:
name: KA_6_9_193_1
n: 4266295613839554521455940618914223009809176846224270626203668901679911671717662492929960969596044736169757523
skew: 20303.21
# norm 3.02e+15
c5: 64260
c4: -5524240892
c3: 33370301956429
c2: 2960552805759545129
c1: 13268125763144698600299
c0: -427943730192357035630844
# alpha -6.40
Y1: 410046852743
Y0: -581336125346552761433
# Murphy_E 1.18e-09
# M 835049287715849898352208609708011149328452835128639575533350171456753898162996679714302558410477726301170271
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:230209, AFBsize:229921, largePrimes:6992043 encountered
Relations: rels:6742934, finalFF:579789
Max relations in full relation-set: 28
Initial matrix: 460216 x 579789 with sparse part having weight 39572835.
Pruned matrix : 350884 x 353249 with weight 18553288.
Total sieving time: 15.64 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 15.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10108-9 = 6(9)1071<109> = 404321 · 378807857 · C95

C95 = P46 · P50

P46 = 2663967441313171836581746263544242756268412123<46>

P50 = 17156308633252668896929507566790813539577265672261<50>

Number: n
N=45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103
  ( 95 digits)
Divisors found:
 r1=2663967441313171836581746263544242756268412123 (pp46)
 r2=17156308633252668896929507566790813539577265672261 (pp50)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.81 hours.
Scaled time: 8.43 units (timescale=1.754).
Factorization parameters were as follows:
name: KA_6_9_107_1
n:  45703847612105192551412600444051943138121632548159102877835632289400552214113597792942597220103
m:  5492465041505502450157
deg: 4
c4: 50220792
c3: 473490998762
c2: -150320131923816106
c1: -1840155014132418213
c0: 240325391527681110358680
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.908
# E(F1,F2) = 4.085225e-05
# GGNFS version 0.77.1-20050930-k8 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198729570.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved  special-q in [100000, 100000)
Primes: RFBsize:92938, AFBsize:92993, largePrimes:1857627 encountered
Relations: rels:1908164, finalFF:212612
Max relations in full relation-set: 28
Initial matrix: 186005 x 212612 with sparse part having weight 16282353.
Pruned matrix : 174218 x 175212 with weight 11293718.
Total sieving time: 4.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.30 hours.
Total square root time: 0.04 hours, sqrts: 14.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 4.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10145-9 = 6(9)1441<146> = 94261 · C141

C141 = P34 · P108

P34 = 1021695068102849396044532089064863<34>

P108 = 726849841772289840962937682508573633040889067399121266108989206433699098743911136797514039693842951036128037<108>

Dec 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS

7·10113-9 = 6(9)1121<114> = 491 · 2423 · 4003873 · C102

C102 = P48 · P54

P48 = 184432465107840005841929350652158018855881137453<48>

P54 = 796792925041443202307060294296189274485989498333919823<54>

Number: 69991_113
N=146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819
  ( 102 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=184432465107840005841929350652158018855881137453 (pp48)
 r2=796792925041443202307060294296189274485989498333919823 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.40 hours.
Scaled time: 1.62 units (timescale=0.675).
Factorization parameters were as follows:
name: 69991_113
n: 146954483345879750650262027109056915485927149646071893433452883477538598863216027684838960521344430819
m: 10000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2223893 encountered
Relations: rels:2457553, finalFF:359535
Max relations in full relation-set: 28
Initial matrix: 112989 x 359535 with sparse part having weight 31384555.
Pruned matrix : 71414 x 72042 with weight 5203701.
Total sieving time: 2.19 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.40 hours.
 --------- CPU info (if available) ----------

7·10135-9 = 6(9)1341<136> = 3673 · 255019 · 84498497 · 15088353311<11> · C109

C109 = P37 · P73

P37 = 2619090469168430611738435623980583053<37>

P73 = 2238016293251830424874207565385593578321653128229251831899397482529153343<73>

Number: 69991_135
N=5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179
  ( 109 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2619090469168430611738435623980583053 (pp37)
 r2=2238016293251830424874207565385593578321653128229251831899397482529153343 (pp73)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.83 hours.
Scaled time: 13.67 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_135
n: 5861567143499528535945249491745181774451528037501922335500468042836092047603598088439983509779689035584096179
m: 1000000000000000000000000000
c5: 7
c0: -9
skew: 1.05
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63908, largePrimes:1579365 encountered
Relations: rels:1604122, finalFF:195607
Max relations in full relation-set: 28
Initial matrix: 142472 x 195607 with sparse part having weight 16386599.
Pruned matrix : 126424 x 127200 with weight 8919279.
Total sieving time: 6.60 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.83 hours.
 --------- CPU info (if available) ----------

7·10147-9 = 6(9)1461<148> = 44253346650419<14> · 640263926981563<15> · 2384930862846177191492797<25> · C96

C96 = P36 · P60

P36 = 345533806013666402094028972113839143<36>

P60 = 299796493353162488095487968396822078060268288441471385866693<60>

Number: 69991_147
N=103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099
  ( 96 digits)
Divisors found:
 r1=345533806013666402094028972113839143 (pp36)
 r2=299796493353162488095487968396822078060268288441471385866693 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 11.00 hours.
Scaled time: 7.42 units (timescale=0.675).
Factorization parameters were as follows:
name: 69991_147
n:  103589823377869076072607851794326081481578050618794143412322232850520425835300380055682643364099
m:  7455843658268344282957
deg: 4
c4: 33522000
c3: 140814788
c2: 77276617925738599
c1: 69424401729227304416
c0: 2357246899800669557952
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.016
# E(F1,F2) = 2.812171e-05
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1198709841.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1500001)
Primes: RFBsize:92938, AFBsize:92936, largePrimes:1911524 encountered
Relations: rels:2002935, finalFF:233843
Max relations in full relation-set: 28
Initial matrix: 185950 x 233843 with sparse part having weight 21496159.
Pruned matrix : 166071 x 167064 with weight 13108251.
Polynomial selection time: 0.17 hours.
Total sieving time: 9.92 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.72 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 11.00 hours.
 --------- CPU info (if available) ----------

Dec 27, 2007

By Sinkiti Sibata / GGNFS

7·10133-9 = 6(9)1321<134> = 449 · 1493 · 90917 · 94389114492319<14> · C110

C110 = P44 · P66

P44 = 85173022756831337810382828011673697322037311<44>

P66 = 142864005459473961587757841830261127716190760624346731496837517471<66>

Number: 69991_133
N=12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481
  ( 110 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=85173022756831337810382828011673697322037311 (pp44)
 r2=142864005459473961587757841830261127716190760624346731496837517471 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.35 hours.
Scaled time: 16.72 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_133
n: 12168159188131852215584768023354461103145336764833774484034596076561291835579447472592128168069219417276360481
m: 100000000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63823, largePrimes:1568311 encountered
Relations: rels:1565951, finalFF:168189
Max relations in full relation-set: 28
Initial matrix: 142389 x 168189 with sparse part having weight 15197800.
Pruned matrix : 134600 x 135375 with weight 10638770.
Total sieving time: 8.08 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.35 hours.
 --------- CPU info (if available) ----------

Dec 26, 2007 (6th)

By Sinkiti Sibata / PRIMO

(2·102978-17)/3 is prime.

Dec 26, 2007 (5th)

By Sinkiti Sibata / GGNFS

7·10118-9 = 6(9)1171<119> = 29 · 281 · 479 · 564899 · C107

C107 = P34 · P74

P34 = 1984136958064167375045366373528421<34>

P74 = 15999844291278446970836451631567805232288393575182670206207520554418064299<74>

Number: 69991_118
N=31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879
  ( 107 digits)
SNFS difficulty: 118 digits.
Divisors found:
 r1=1984136958064167375045366373528421 (pp34)
 r2=15999844291278446970836451631567805232288393575182670206207520554418064299 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.24 hours.
Scaled time: 4.45 units (timescale=1.991).
Factorization parameters were as follows:
name: 69991_118
n: 31745882381597551712985680104483070892222684616727431250512197757342182638804213346559326046812565481941879
m: 100000000000000000000000
c5: 7000
c0: -9
skew: 0.26
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2167506 encountered
Relations: rels:2281489, finalFF:242097
Max relations in full relation-set: 28
Initial matrix: 112989 x 242097 with sparse part having weight 22238741.
Pruned matrix : 87145 x 87773 with weight 5534433.
Total sieving time: 2.10 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.24 hours.
 --------- CPU info (if available) ----------

7·10122-9 = 6(9)1211<123> = 83 · 13523 · 244861 · 1071691642724939<16> · C97

C97 = P44 · P53

P44 = 82895830946665960950649287503567133316049651<44>

P53 = 28669805558837951631417683899953649248910278323675131<53>

Number: 69991_122
N=2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281
  ( 97 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=82895830946665960950649287503567133316049651 (pp44)
 r2=28669805558837951631417683899953649248910278323675131 (pp53)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.38 hours.
Scaled time: 6.77 units (timescale=2.003).
Factorization parameters were as follows:
name: 69991_122
n: 2376607354879214865611819176528989671083739593311572594941837848584100495761234335579813189929281
m: 1000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63803, largePrimes:2446192 encountered
Relations: rels:2891407, finalFF:532620
Max relations in full relation-set: 28
Initial matrix: 112969 x 532620 with sparse part having weight 52760048.
Pruned matrix : 76482 x 77110 with weight 9438717.
Total sieving time: 3.23 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.38 hours.
 --------- CPU info (if available) ----------

7·10132-9 = 6(9)1311<133> = 1292567 · 190646486287<12> · C116

C116 = P41 · P76

P41 = 10653299394346279999189253853948866948741<41>

P76 = 2666441366915221621544897168193843156735547511317187784920639757035112567619<76>

Number: 69991_132
N=28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679
  ( 116 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=10653299394346279999189253853948866948741 (pp41)
 r2=2666441366915221621544897168193843156735547511317187784920639757035112567619 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.77 hours.
Scaled time: 11.49 units (timescale=1.991).
Factorization parameters were as follows:
name: 69991_132
n: 28406398199217797464553546226922521246087029329926717717175210835294924586217098258316437679183181636843102569417679
m: 100000000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:63951, AFBsize:63803, largePrimes:1538473 encountered
Relations: rels:1545151, finalFF:170046
Max relations in full relation-set: 28
Initial matrix: 127822 x 170046 with sparse part having weight 14925657.
Pruned matrix : 117194 x 117897 with weight 8533990.
Total sieving time: 5.57 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.77 hours.
 --------- CPU info (if available) ----------

Dec 26, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

7·10117-9 = 6(9)1161<118> = C118

C118 = P48 · P70

P48 = 965127703405741647531200158987421082342396773977<48>

P70 = 7252926193392239386243000349720048960099140101219877063658000208088783<70>

Number: 69991_117
N=6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 118 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=965127703405741647531200158987421082342396773977 (pp48)
 r2=7252926193392239386243000349720048960099140101219877063658000208088783 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.05 hours.
Scaled time: 2.25 units (timescale=2.145).
Factorization parameters were as follows:
n: 6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 100000000000000000000000
c5: 700
c0: -9
skew: 0.42
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49186, largePrimes:1878131 encountered
Relations: rels:1929377, finalFF:194599
Max relations in full relation-set: 28
Initial matrix: 98352 x 194599 with sparse part having weight 16935639.
Pruned matrix : 78199 x 78754 with weight 4525630.
Total sieving time: 1.00 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

7·10152-9 = 6(9)1511<153> = 642738965504016239<18> · C136

C136 = P32 · P104

P32 = 12499425996572633795685838286539<32>

P104 = 87131128901653143200613872829832683606052695848751370614553206443217691319643034696885938619060585421771<104>

Dec 26, 2007 (3rd)

By matsui / GGNFS

2·10167+9 = 2(0)1669<168> = 47 · 184481867 · 10008810089<11> · 118729587401<12> · 10440234088181<14> · C124

C124 = P61 · P63

P61 = 6290280740566369228935563961231140837620944228695383054749943<61>

P63 = 295567569227359507343672924451640185453395509237894904088703543<63>

N=1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049
  ( 124 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=6290280740566369228935563961231140837620944228695383054749943 (pp61)
 r2=295567569227359507343672924451640185453395509237894904088703543 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 127.80 hours.
Scaled time: 166.65 units (timescale=1.304).
Factorization parameters were as follows:
n: 1859202988246876566381452884068131590659953240147645274080909534187043414526270082207047941221587915349634178688954923148049
m: 1000000000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 5450001)
Primes: RFBsize:380800, AFBsize:380082, largePrimes:5892464 encountered
Relations: rels:6135246, finalFF:894339
Max relations in full relation-set: 28
Initial matrix: 760947 x 894339 with sparse part having weight 44957251.
Pruned matrix : 648054 x 651922 with weight 30819584.
Total sieving time: 114.05 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 13.26 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 127.80 hours.

Dec 26, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(22·10166-1)/3 = 7(3)166<167> = 13 · 2501184977<10> · C157

C157 = P47 · P111

P47 = 20970006021949093438264942952242363969867903567<47>

P111 = 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399<111>

Number: n
N=2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233
  ( 157 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Dec 26 05:26:18 2007  prp47 factor: 20970006021949093438264942952242363969867903567
Wed Dec 26 05:26:18 2007  prp111 factor: 107550815343039437975417504676624224363468612606306698519306645404641567204160857189344675377069667152654245399
Wed Dec 26 05:26:18 2007  elapsed time 02:18:47 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 78.83 hours.
Scaled time: 138.12 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_7_3_166
n: 2255341245409071967907084403148340605774006950236708152769712418205381307006397248573287358922524681798311083347365571924927256446185523776892981730485438233
type: snfs
skew: 0.34
deg: 5
c5: 220
c0: -1
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500001)
Primes: RFBsize:230209, AFBsize:230048, largePrimes:7684784 encountered
Relations: rels:7152361, finalFF:475660
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.54 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000
total time: 78.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10120-9 = 6(9)1191<121> = 197 · 419 · C116

C116 = P52 · P65

P52 = 1323129079639263647678527821934298050401138159281717<52>

P65 = 64093734415499366088944419295581630353010019359658087508532919861<65>

Number: n
N=84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337
  ( 116 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=1323129079639263647678527821934298050401138159281717 (pp52)
 r2=64093734415499366088944419295581630353010019359658087508532919861 (pp65)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.47 hours.
Scaled time: 2.59 units (timescale=1.755).
Factorization parameters were as follows:
name: KA_6_9_119_1
n: 84804283827823074034139781689543631804029414971590564917679270198563173134002883345650145984517160752577444483481337
type: snfs
skew: 1.05
deg: 5
c5: 7
c0: -9
m: 1000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:78498, AFBsize:78361, largePrimes:4117883 encountered
Relations: rels:3508482, finalFF:209284
Max relations in full relation-set: 28
Initial matrix: 156925 x 209284 with sparse part having weight 9419779.
Pruned matrix : 113353 x 114201 with weight 3874739.
Total sieving time: 1.28 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 1.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10166-17)/9 = (8)1657<166> = 4083907 · 43094378617<11> · C149

C149 = P41 · P51 · P58

P41 = 38584081030692973979026508694832853174717<41>

P51 = 418114217260780904751406897239535819468897448269121<51>

P58 = 3130746579328069205359019081831876161205414051790095798089<58>

Number: n
N=1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769
  ( 109 digits)
Divisors found:

Thu Dec 27 01:08:55 2007  prp51 factor: 418114217260780904751406897239535819468897448269121
Thu Dec 27 01:08:55 2007  prp58 factor: 3130746579328069205359019081831876161205414051790095798089
Thu Dec 27 01:08:55 2007  elapsed time 00:56:09 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.81 hours.
Scaled time: 19.34 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_165_7
n: 1309009655457622967425044640452475241525607022021852781211536044491653424923374629964185236322257748149509769
skew: 17293.45
# norm 1.67e+15
c5: 69840
c4: 7463998242
c3: -78994172254267
c2: -2236017190191479429
c1: 14571241816633004474387
c0: 2943605098409076728592987
# alpha -6.80
Y1: 379170613327
Y0: -451398307899860421580
# Murphy_E 1.27e-09
# M 913262407536112418797141648337235351640361187128809490900940893449426725706506274192425043867981484896313502
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:230209, AFBsize:230668, largePrimes:6776674 encountered
Relations: rels:6460557, finalFF:550004
Max relations in full relation-set: 28
Initial matrix: 460957 x 550004 with sparse part having weight 33437232.
Pruned matrix : 373838 x 376206 with weight 17048281.
Total sieving time: 13.36 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 14.81 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 26, 2007

By Yousuke Koide

(101791-1)/9 is divisible by 430713366297695220680641963<27>

(101827-1)/9 is divisible by 223755556979749662730993077361<30>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (6th)

By Bruce Dodson

(10301-1)/9 is divisible by 1141240390081433457327371568501745249133720840602413587<55>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (5th)

By Yousuke Koide

(101707-1)/9 is divisible by 75920820144562528214807220511<29>

(101713-1)/9 is divisible by 21378384423167366346901350575839<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(4·10167-13)/9 = (4)1663<167> = 7 · 199 · 178417 · C159

C159 = P73 · P87

P73 = 1485476151933583531111398308948380526129750464603540854114915552692816459<73>

P87 = 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017<87>

Number: n
N=178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

prp73 factor: 1485476151933583531111398308948380526129750464603540854114915552692816459
prp87 factor: 120382802341518563935422558643399557108880046309548748111160170924304751890414156384017
elapsed time 02:46:27 (Msieve 1.32)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 82.93 hours.
Scaled time: 108.55 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_4_166_3
n: 178825781981260185544919324400362315519182373617989035689700410480589420542722308843419223897366923093762619358223783664573201072908733661591929401830902135803
skew: 1.01
deg: 5
c5: 25
c0: -26
m: 2000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3900397)
Primes: RFBsize:230209, AFBsize:230867, largePrimes:7730813 encountered
Relations: rels:7172093, finalFF:452321
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 82.63 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 82.93 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 25, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(4·10161+41)/9 = (4)1609<161> = 18094688609<11> · 26999490049546734407<20> · C131

C131 = P57 · P75

P57 = 661800895912546464100385070921509481515371228023099756833<57>

P75 = 137462252416217059157918563636603097318468429817984026396850545706670319831<75>

Number: 44449_161
N=90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223
  ( 131 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=661800895912546464100385070921509481515371228023099756833 (pp57)
 r2=137462252416217059157918563636603097318468429817984026396850545706670319831 (pp75)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 83.42 hours.
Scaled time: 166.08 units (timescale=1.991).
Factorization parameters were as follows:
name: 44449_161
n: 90972641803209054654671943300688174982440708379689549892031878497530778160414254242799972773189906368931128996322659002194437655223
m: 100000000000000000000000000000000
c5: 40
c0: 41
skew: 1
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4950001)
Primes: RFBsize:315948, AFBsize:314247, largePrimes:6029218 encountered
Relations: rels:6254224, finalFF:838574
Max relations in full relation-set: 32
Initial matrix: 630261 x 838574 with sparse part having weight 63869247.
Pruned matrix : 474489 x 477704 with weight 46325545.
Total sieving time: 79.60 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.37 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 83.42 hours.
 --------- CPU info (if available) ----------

Dec 25, 2007 (2nd)

By Jo Yeong Uk / GGNFS

9·10181-7 = 8(9)1803<182> = 3613 · 3761 · 17011 · 2340581 · 730684027 · 15300750882422633<17> · 979400478501517858241<21> · C119

C119 = P53 · P66

P53 = 16940272774462961564775996098870506033529998386074873<53>

P66 = 896797988999442350354441292775914106811664777578919757946243069497<66>

Number: 89993_181
N=15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881
  ( 119 digits)
Divisors found:
 r1=16940272774462961564775996098870506033529998386074873 (pp53)
 r2=896797988999442350354441292775914106811664777578919757946243069497 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 38.34 hours.
Scaled time: 82.16 units (timescale=2.143).
Factorization parameters were as follows:
name: 89993_181
n: 15192002557240387749167059448579590970166470920242453316132075745911229316132758666921505340614262736034804889184448881
skew: 98114.36
# norm 2.21e+16
c5: 31560
c4: -1924665624
c3: -412313060325580
c2: 47672706443648087839
c1: 1442560992222373548243522
c0: -146358796049818815151457984880
# alpha -6.24
Y1: 3744248581117
Y0: -54512483709568246234133
# Murphy_E 3.34e-10
# M 5312090155304946753032180946674168126337529924282533139667763695347823533748345268463219266442595271493810276031748175
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4125001)
Primes: RFBsize:315948, AFBsize:316143, largePrimes:7687286 encountered
Relations: rels:7809081, finalFF:793940
Max relations in full relation-set: 28
Initial matrix: 632175 x 793940 with sparse part having weight 66592823.
Pruned matrix : 496253 x 499477 with weight 40203065.
Polynomial selection time: 2.37 hours.
Total sieving time: 34.05 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.57 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 38.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 25, 2007

The factor table of 699...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Dec 24, 2007

By Robert Backstrom / GGNFS, Msieve

(64·10169-1)/9 = 7(1)169<170> = 191 · 227 · 23599 · C161

C161 = P68 · P94

P68 = 11931889546918933708321958997600760626322617766055953766899623909449<68>

P94 = 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373<94>

Number: n
N=69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477
  ( 161 digits)
SNFS difficulty: 171 digits.
Divisors found:

Mon Dec 24 19:01:19 2007  prp68 factor: 11931889546918933708321958997600760626322617766055953766899623909449
Mon Dec 24 19:01:19 2007  prp94 factor: 5824724856908681664958265245672136436260835730449256750908837269949436735995268697884565220373
Mon Dec 24 19:01:19 2007  elapsed time 01:27:33 (Msieve 1.32)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 72.40 hours.
Scaled time: 131.56 units (timescale=1.817).
Factorization parameters were as follows:
name: KA_7_1_169
n: 69499973633827580647471586447132751857395021337483909114981344631924934491933816608111087357431841283281168537224630080843910275596154330028617514385574482004477
skew: 0.35
deg: 5
c5: 1
c0: -5
m: 20000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4900001)
Primes: RFBsize:250150, AFBsize:249616, largePrimes:7898818 encountered
Relations: rels:7354029, finalFF:555685
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 72.21 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 72.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 23, 2007 (5th)

By matsui / GGNFS

3·10166+1 = 3(0)1651<167> = 192 · 31 · 373 · 193939 · 23755628747941<14> · 447212374355192497<18> · C124

C124 = P45 · P79

P45 = 625649191871122082626948379908529671729699051<45>

P79 = 5575285937796913330137969587393113913079322142661733106598322245299860531890319<79>

N=3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269
  ( 124 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=625649191871122082626948379908529671729699051 (pp45)
 r2=5575285937796913330137969587393113913079322142661733106598322245299860531890319 (pp79)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 108.27 hours.
Scaled time: 184.28 units (timescale=1.702).
Factorization parameters were as follows:
n: 3488173141433069844672322710287029279310821431486754226005972594141095952219346638593373912893212468814594969707770010387269
m: 1000000000000000000000000000000000
c5: 30
c0: 1
skew: 0.51
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 5200001)
Primes: RFBsize:348513, AFBsize:347321, largePrimes:5907563 encountered
Relations: rels:6145608, finalFF:870306
Max relations in full relation-set: 28
Initial matrix: 695901 x 870306 with sparse part having weight 52151957.
Pruned matrix : 553239 x 556782 with weight 35119544.
Total sieving time: 103.81 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 4.08 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 108.27 hours.

Dec 23, 2007 (4th)

By Sinkiti Sibata / GGNFS

(22·10161-1)/3 = 7(3)161<162> = 73 · 34653533 · 22935196665910109914667553700279<32> · C122

C122 = P53 · P69

P53 = 15456307151502000419816734779747252856782558221670037<53>

P69 = 817754305715924564199835791161046377202886980231427415903294669859419<69>

Number: 73333_161
N=12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503
  ( 122 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=15456307151502000419816734779747252856782558221670037 (pp53)
 r2=817754305715924564199835791161046377202886980231427415903294669859419 (pp69)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 94.57 hours.
Scaled time: 64.40 units (timescale=0.681).
Factorization parameters were as follows:
name: 73333_161
n: 12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503
m: 100000000000000000000000000000000
c5: 220
c0: -1
skew: 0.34
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315952, largePrimes:5839234 encountered
Relations: rels:5995706, finalFF:784221
Max relations in full relation-set: 32
Initial matrix: 631967 x 784221 with sparse part having weight 49430510.
Pruned matrix : 512955 x 516178 with weight 33232195.
Total sieving time: 82.14 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 11.76 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 94.57 hours.
 --------- CPU info (if available) ----------

5·10167+9 = 5(0)1669<168> = 17 · 1989241 · 4503242489106295715733929<25> · 13375753468061863141381463203<29> · C108

C108 = P33 · P75

P33 = 247594231851496673861477854899257<33>

P75 = 991401494836260862208699840210242066186026283682422229091025681417922365483<75>

Number: 50009_167
N=245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131
  ( 108 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=247594231851496673861477854899257 (pp33)
 r2=991401494836260862208699840210242066186026283682422229091025681417922365483 (pp75)
Version: GGNFS-0.77.1-20060722-nocona
Total time: 148.51 hours.
Scaled time: 295.68 units (timescale=1.991).
Factorization parameters were as follows:
name: 50009_167
n: 245465291570409554408333235492955931297544893177855395881640586610749416809020286506572455808735126099146131
m: 1000000000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7250001)
Primes: RFBsize:380800, AFBsize:380707, largePrimes:6144009 encountered
Relations: rels:6397329, finalFF:900175
Max relations in full relation-set: 32
Initial matrix: 761574 x 900175 with sparse part having weight 67509735.
Pruned matrix : 652300 x 656171 with weight 49587514.
Total sieving time: 142.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 5.80 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 148.51 hours.
 --------- CPU info (if available) ----------

Dec 23, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10187+9 = 2(0)1869<188> = 61 · 149 · 283 · 70663 · 2939271579080203<16> · 4012670006992512529<19> · 5937247290902120471857247<25> · C118

C118 = P48 · P70

P48 = 875378053458562890900671686629987206094799966703<48>

P70 = 1795070177818256857278501924746661172178297270528928854534971402770967<70>

Number: 20009_187
N=1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801
  ( 118 digits)
Divisors found:
 r1=875378053458562890900671686629987206094799966703 (pp48)
 r2=1795070177818256857278501924746661172178297270528928854534971402770967 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 33.41 hours.
Scaled time: 71.01 units (timescale=2.125).
Factorization parameters were as follows:
name: 20009_187
n: 1571365038080062045688276537552192603928436205005459284020038961717757775228192637376787221670115377779946873535111801
skew: 86841.90
# norm 2.08e+16
c5: 18720
c4: 8005758744
c3: -417143604761414
c2: -54242084718394161427
c1: 1422581424753045528714126
c0: 43918391624543280113635161840
# alpha -6.35
Y1: 1252807503029
Y0: -38440854919115622102169
# Murphy_E 3.88e-10
# M 1529114244625491084620152441929551187310300433953474676067635486861415835076684651925957412555777624572292435341208442
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 100
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3975001)
Primes: RFBsize:315948, AFBsize:316044, largePrimes:7583161 encountered
Relations: rels:7616240, finalFF:734012
Max relations in full relation-set: 28
Initial matrix: 632072 x 734011 with sparse part having weight 59496583.
Pruned matrix : 544994 x 548218 with weight 38635632.
Total sieving time: 31.36 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000
total time: 33.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407681)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405133)
Total of 4 processors activated (19246.11 BogoMIPS).

Dec 23, 2007 (2nd)

By Robert Backstrom / GMP-ECM

(13·10165-31)/9 = 1(4)1641<166> = 11 · 499 · 1319876500333999<16> · C147

C147 = P40 · P107

P40 = 1994429019434361543756357833325269071763<40>

P107 = 99966786327320553004552683264048083299808115979086757765172472797852861187379110833799751735350193567159837<107>

Dec 23, 2007

By Yousuke Koide

(101465-1)/9 is divisible by 750351062900043426795315702791<30>

(101547-1)/9 is divisible by 223088287829064817231566124802627<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 22, 2007

By Robert Backstrom / GGNFS, Msieve

5·10153+9 = 5(0)1529<154> = 113 · 283 · C150

C150 = P64 · P86

P64 = 9652395741655011049538026702985684108326820233080272800634433481<64>

P86 = 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891<86>

Number: n
N=156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571
  ( 150 digits)
SNFS difficulty: 154 digits.
Divisors found:

Sat Dec 22 17:46:28 2007  prp64 factor: 9652395741655011049538026702985684108326820233080272800634433481
Sat Dec 22 17:46:28 2007  prp86 factor: 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891
Sat Dec 22 17:46:28 2007  elapsed time 00:41:58 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.36 hours.
Scaled time: 35.68 units (timescale=1.752).
Factorization parameters were as follows:
name: KA_5_0_152_9
n: 156352606397948653804058913662090747052753369398667875793489477469589418055598986835110541292723349698239469651959098158166296632164858188185997060571
type: snfs
skew: 1.41
deg: 5
c5: 8
c0: 45
m: 5000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:216816, AFBsize:215956, largePrimes:6188331 encountered
Relations: rels:5704176, finalFF:531554
Max relations in full relation-set: 28
Initial matrix: 432837 x 531554 with sparse part having weight 24767036.
Pruned matrix : 
Total sieving time: 20.20 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 20.36 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 21, 2007 (3rd)

By Yousuke Koide

(101339-1)/9 is divisible by 5775107139441156343356533814929<31>

(101351-1)/9 is divisible by 1782854636817021657923017573<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 21, 2007 (2nd)

By NFSNet

(10239-1)/9 = (1)239<239> = 479 · 142847911 · C228

C228 = P54 · P81 · P94

P54 = 383155477843726029783939406113226468701730728790004161<54>

P81 = 128780300340244872385688233345188210841783983757299260103530718169486826135819357<81>

P94 = 3290967632861131703281828943635774383301940171982919699073443165222894023742681701403432993547<94>

Reference: NFSNet current status

Dec 21, 2007

By Robert Backstrom / GGNFS, Msieve

5·10163+9 = 5(0)1629<164> = 470209 · 29802628633<11> · C148

C148 = P39 · P44 · P66

P39 = 994274499440732115855225384785607465089<39>

P44 = 20388243227799757288129029804812187656347787<44>

P66 = 176010423833552850724204320884474640196768850687932515195507552179<66>

Number: n
N=3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697
  ( 148 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Dec 21 19:06:29 2007  prp39 factor: 994274499440732115855225384785607465089
Fri Dec 21 19:06:29 2007  prp44 factor: 20388243227799757288129029804812187656347787
Fri Dec 21 19:06:29 2007  prp66 factor: 176010423833552850724204320884474640196768850687932515195507552179
Fri Dec 21 19:06:29 2007  elapsed time 01:29:29 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 46.82 hours.
Scaled time: 61.47 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_5_0_162_9
n: 3567997124893726715042848190931992165491965877318560254922568110615225565901811932175902351214161088571608357164392386147216979036661072219279275697
skew: 1.41
deg: 5
c5: 8
c0: 45
m: 500000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:230209, AFBsize:229217, largePrimes:7357077 encountered
Relations: rels:6869781, finalFF:531314
Max relations in full relation-set: 28
Initial matrix: 459491 x 531314 with sparse part having weight 41024110.
Pruned matrix : 405664 x 408025 with weight 28167530.
Total sieving time: 46.52 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 46.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 20, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10157+9 = 5(0)1569<158> = 1097 · 14897 · 26348627 · 158905115827<12> · 230706227803<12> · C121

C121 = P59 · P63

P59 = 25360542995799645970199393340105446955335067305527210019419<59>

P63 = 124896659843040259553684977555818906011332891068066978344194417<63>

Number: 50009_157
N=3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723
  ( 121 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=25360542995799645970199393340105446955335067305527210019419 (pp59)
 r2=124896659843040259553684977555818906011332891068066978344194417 (pp63)
Version: GGNFS-0.77.1-20060513-k8
Total time: 49.75 hours.
Scaled time: 99.65 units (timescale=2.003).
Factorization parameters were as follows:
name: 50009_157
n: 3167447111981185564662038922263931214905167097009116697762326586042626329656257920880146946528001824003871576052481383723
m: 10000000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3200001)
Primes: RFBsize:216816, AFBsize:216721, largePrimes:5704293 encountered
Relations: rels:5645688, finalFF:500017
Max relations in full relation-set: 28
Initial matrix: 433604 x 500017 with sparse part having weight 46100082.
Pruned matrix : 406183 x 408415 with weight 34369135.
Total sieving time: 46.98 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.40 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 49.75 hours.
 --------- CPU info (if available) ----------

Dec 20, 2007

By Robert Backstrom / GGNFS, Msieve

5·10159+9 = 5(0)1589<160> = 158855819 · C152

C152 = P51 · P101

P51 = 595062504831659452988979151082530531460782679178587<51>

P101 = 52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753<101>

Number: n
N=31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011
  ( 152 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=595062504831659452988979151082530531460782679178587 (pp51)
 r2=52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753 (pp101)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 20.39 hours.
Scaled time: 37.07 units (timescale=1.818).
Factorization parameters were as follows:
name: KA_5_0_158_9
n: 31475082445673582785154379519455941365295532548291479331959504738066913368782543622150851143828731889261167071254720609258890289690930364974543362494011
skew: 1.78
deg: 5
c5: 1
c0: 18
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6939749 encountered
Relations: rels:6405566, finalFF:494197
Max relations in full relation-set: 48
Initial matrix: 433819 x 494197 with sparse part having weight 37620448.
Pruned matrix : 385615 x 387848 with weight 23915069.
Total sieving time: 19.02 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.08 hours.
Total square root time: 0.14 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 20.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

8·10163-7 = 7(9)1623<164> = 1511 · 9661 · 321227 · 564463 · C146

C146 = P42 · P104

P42 = 725182024346650930487852356735252779350207<42>

P104 = 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569<104>

Number: n
N=30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783
  ( 146 digits)
SNFS difficulty: 165 digits.
Divisors found:

Thu Dec 20 18:40:55 2007  prp42 factor: 725182024346650930487852356735252779350207
Thu Dec 20 18:40:55 2007  prp104 factor: 41678193707764674563769995598226622228791564423366352341260784993112394124120101447997247395973034963569
Thu Dec 20 18:40:55 2007  elapsed time 02:14:03 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 113.19 hours.
Scaled time: 198.19 units (timescale=1.751).
Factorization parameters were as follows:
name: KA_7_9_162_3
n: 30224276884108635845705620161872665740218373338594605309453520593775179206533817870115077142218894679107820860767648488655970203393799663737608783
type: snfs
skew: 0.49
deg: 5
c5: 2
c0: -175
m: 1000000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 4400001)
Primes: RFBsize:230209, AFBsize:231247, largePrimes:7814161 encountered
Relations: rels:7249012, finalFF:516556
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 112.81 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 113.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 19, 2007 (5th)

By Yousuke Koide

(101249-1)/9 is divisible by 3859327619352771895471324837<28>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 19, 2007 (4th)

By Jo Yeong Uk / GMP-ECM

5·10162+9 = 5(0)1619<163> = 7 · 292 · 271229879065601402201623<24> · C136

C136 = P35 · P101

P35 = 64374435181365818315554180691915647<35>

P101 = 48643521375868913517679138570941692047144478517809618044912143356711058007954967110653981808106775647<101>

Dec 19, 2007 (3rd)

By matsui / GGNFS

(7·10166+11)/9 = (7)1659<166> = 3 · 40361 · 205111360920457<15> · 12389475956090072848518619<26> · C122

C122 = P47 · P75

P47 = 55943227542338151602426973986475076889992624589<47>

P75 = 451837410354294038053223198387566184140151017305302109616973764868158183999<75>

N=25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411
  ( 122 
digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=55943227542338151602426973986475076889992624589 (pp47)
 r2=451837410354294038053223198387566184140151017305302109616973764868158183999 (pp75)
Version: GGNFS-0.77.1-20060513-prescott
Total time: 10.74 hours.
Scaled time: 18.27 units (timescale=1.701).
Factorization parameters were as follows:
n: 25277243059591087751933230830792917038072519013701850924280163483893165455099071542202433152586138066004172655689993751411
m: 1000000000000000000000000000000000
c5: 70
c0: 11
skew: 0.69
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6000001)
Primes: , , largePrimes:5871705 encountered
Relations: rels:5969485, finalFF:743203
Max relations in full relation-set: 28
Initial matrix: 696897 x 743203 with sparse part having weight 52810271.
Pruned matrix : 665688 x 669236 with weight 44065470.
Total sieving time: 2.91 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 7.59 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 10.74 hours.

Dec 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10156+9 = 5(0)1559<157> = 7 · 37447 · 28194483512088014904108943<26> · C126

C126 = P62 · P64

P62 = 74881270812473695723895111402915691073452855235176557355117707<62>

P64 = 9034780048660293802053456177468412100175147936351538480358818021<64>

Number: 50009_156
N=676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847
  ( 126 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=74881270812473695723895111402915691073452855235176557355117707 (pp62)
 r2=9034780048660293802053456177468412100175147936351538480358818021 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.37 hours.
Scaled time: 64.84 units (timescale=2.003).
Factorization parameters were as follows:
name: 50009_156
n: 676535811554865734658433221423933641105523804759318323019495315982034160190227630983735165481246914074639192835621689847797847
m: 10000000000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:5559380 encountered
Relations: rels:5479029, finalFF:518470
Max relations in full relation-set: 28
Initial matrix: 432702 x 518470 with sparse part having weight 40228570.
Pruned matrix : 380168 x 382395 with weight 26863487.
Total sieving time: 30.33 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.72 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.37 hours.
 --------- CPU info (if available) ----------

Dec 19, 2007

By Robert Backstrom / GGNFS, Msieve

5·10147+9 = 5(0)1469<148> = C148

C148 = P40 · P108

P40 = 5849697884884838262743075248501338289883<40>

P108 = 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923<108>

Number: n
N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 148 digits)
SNFS difficulty: 149 digits.
Divisors found:

Wed Dec 19 02:59:00 2007  prp40 factor: 5849697884884838262743075248501338289883
Wed Dec 19 02:59:00 2007  prp108 factor: 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923
Wed Dec 19 02:59:00 2007  elapsed time 00:54:34 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 12.29 hours.
Scaled time: 16.07 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_5_0_146_9
n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
skew: 2.24
deg: 5
c5: 4
c0: 225
m: 500000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500001)
Primes: RFBsize:203362, AFBsize:203297, largePrimes:6971350 encountered
Relations: rels:6423924, finalFF:479679
Max relations in full relation-set: 28
Initial matrix: 406723 x 479679 with sparse part having weight 30923173.
Pruned matrix : 
Total sieving time: 12.09 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 12.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 18, 2007 (4th)

By Jo Yeong Uk / GGNFS, GMP-ECM

5·10164+9 = 5(0)1639<165> = C165

C165 = P79 · P86

P79 = 6673964901781837641922867159706054031558290898862034367879686441388466755506249<79>

P86 = 74917984640061309718805919117074967560324362619058281263115508699855177428830489506241<86>

Number: 50009_164
N=500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 165 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=6673964901781837641922867159706054031558290898862034367879686441388466755506249 (pp79)
 r2=74917984640061309718805919117074967560324362619058281263115508699855177428830489506241 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 39.42 hours.
Scaled time: 84.59 units (timescale=2.146).
Factorization parameters were as follows:
n: 500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2500000, 4600001)
Primes: RFBsize:348513, AFBsize:348406, largePrimes:6566352 encountered
Relations: rels:6735729, finalFF:809660
Max relations in full relation-set: 28
Initial matrix: 696986 x 809660 with sparse part having weight 54958042.
Pruned matrix : 606950 x 610498 with weight 38013089.
Total sieving time: 37.13 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 2.13 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000
total time: 39.42 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10185+9 = 5(0)1849<186> = C186

C186 = P42 · C144

P42 = 862676558302067280404855791214660371447819<42>

C144 = [579591499488646557153454224836516440632324855138225561082733176963781513205559091433257936622764264592554118739834167338788722441133338317646011<144>]

Dec 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS

5·10154+9 = 5(0)1539<155>= 829 · 15683 · 56596823 · 44630287349<11> · C130

C130 = P58 · P72

P58 = 6547416756766895807011708792092633881889587619560266369321<58>

P72 = 232538362293215384924110022839616818354212477256510811617282792627275661<72>

Number: 50009_154
N=1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181
  ( 130 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=6547416756766895807011708792092633881889587619560266369321 (pp58)
 r2=232538362293215384924110022839616818354212477256510811617282792627275661 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.09 hours.
Scaled time: 64.08 units (timescale=1.997).
Factorization parameters were as follows:
name: 50009_154
n: 1522525569869729691381144278511493679974899677541911790344380065429203883992934588841549407329972980911637269126252640383900396181
m: 10000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5911757 encountered
Relations: rels:6144438, finalFF:787955
Max relations in full relation-set: 28
Initial matrix: 433819 x 787955 with sparse part having weight 63391684.
Pruned matrix : 273376 x 275609 with weight 35731953.
Total sieving time: 30.69 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.09 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.09 hours.
 --------- CPU info (if available) ----------

Dec 18, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

5·10163+3 = 5(0)1623<164> = 29 · 227 · 1372379 · 3452401427<10> · C145

C145 = P58 · P87

P58 = 1652368488234263596749387089016071429414818510198454291329<58>

P87 = 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013<87>

Number: n
N=1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:

Tue Dec 18 13:14:30 2007  prp58 factor: 1652368488234263596749387089016071429414818510198454291329
Tue Dec 18 13:14:30 2007  prp87 factor: 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013
Tue Dec 18 13:14:30 2007  elapsed time 01:41:34 (Msieve 1.31)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.55 hours.
Scaled time: 85.80 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_5_0_162_3
n: 1603063766031098986258777513442487052832641665579047108880335847996162488378285630331639750683924926169543565709805927302627011252569149775992277
skew: 1.13
deg: 5
c5: 8
c0: 15
m: 500000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:230209, AFBsize:229672, largePrimes:7196433 encountered
Relations: rels:6672971, finalFF:503221
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 65.18 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

5·10145+9 = 5(0)1449<146> = 480587 · 664114531 · 173304257326374916002763<24> · C108

C108 = P40 · P69

P40 = 8011859098238196250376857716817447795633<40>

P69 = 112826851275727796887800559483225541997057785219800577879840211604843<69>

Number: n
N=903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619
  ( 108 digits)
SNFS difficulty: 145 digits.
Divisors found:

Tue Dec 18 15:02:49 2007  prp40 factor: 8011859098238196250376857716817447795633
Tue Dec 18 15:02:49 2007  prp69 factor: 112826851275727796887800559483225541997057785219800577879840211604843
Tue Dec 18 15:02:49 2007  elapsed time 00:24:54 (Msieve 1.31)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.79 hours.
Scaled time: 8.75 units (timescale=1.829).
Factorization parameters were as follows:
name: KA_5_0_144_9
n: 903952834919007588982726744512079025688319216306952508354097362135326614270017939800842749245239175617050619
skew: 1.12
deg: 5
c5: 5
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:183072, AFBsize:182621, largePrimes:6411156 encountered
Relations: rels:5849768, finalFF:448390
Max relations in full relation-set: 28
Initial matrix: 365759 x 448390 with sparse part having weight 26854576.
Pruned matrix : 294774 x 296666 with weight 13333677.
Total sieving time: 4.67 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 4.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 X2 6000+

Dec 18, 2007

By Yousuke Koide

(101171-1)/9 is divisible by 822720687271610738727673132529<30>, cofactor is prime

(101193-1)/9 is divisible by 14202873041760299228830573<26>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (3rd)

By Yousuke Koide

(101509-1)/9 is divisible by 276617318087890951973712854116609<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

5·10116+9 = 5(0)1159<117> = 5647 · 14738747 · C106

C106 = P37 · P70

P37 = 1770527491110016131038045568525078001<37>

P70 = 3393039989462346591698405537211579666741526697212892785900831616289301<70>

Number: 50009_116
N=6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301
  ( 106 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=1770527491110016131038045568525078001 (pp37)
 r2=3393039989462346591698405537211579666741526697212892785900831616289301 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.65 hours.
Scaled time: 1.11 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_116
n: 6007470579778724082070197662126840225249465868554753560298389981872307218603794018676645158186753206767301
m: 100000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:1928320 encountered
Relations: rels:1872426, finalFF:132412
Max relations in full relation-set: 28
Initial matrix: 113221 x 132412 with sparse part having weight 9758667.
Pruned matrix : 104806 x 105436 with weight 6199905.
Total sieving time: 1.39 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.65 hours.
 --------- CPU info (if available) ----------

5·10137+9 = 5(0)1369<138> = 97 · 1506773568889<13> · 226074463554510734010057673<27> · C98

C98 = P38 · P60

P38 = 54141127725421474038977984368371957931<38>

P60 = 279493344149482372551112704180571406141518303948937390507771<60>

Number: 50009_137
N=15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801
  ( 98 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=54141127725421474038977984368371957931 (pp38)
 r2=279493344149482372551112704180571406141518303948937390507771 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 12.19 hours.
Scaled time: 24.20 units (timescale=1.985).
Factorization parameters were as follows:
name: 50009_137
n: 15132084844002305813551973140721593577879529754928485014234706791511561393412085501945537540581801
m: 1000000000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1975001)
Primes: RFBsize:78498, AFBsize:64083, largePrimes:1684652 encountered
Relations: rels:1727895, finalFF:191071
Max relations in full relation-set: 28
Initial matrix: 142648 x 191071 with sparse part having weight 20882416.
Pruned matrix : 131206 x 131983 with weight 12913225.
Total sieving time: 11.87 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 12.19 hours.
 --------- CPU info (if available) ----------

5·10151+9 = 5(0)1509<152> = 17 · 43 · 107 · C147

C147 = P48 · P100

P48 = 334673882571236023305008947620488003064113918729<48>

P100 = 1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513<100>

Number: 50009_151
N=639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977
  ( 147 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=334673882571236023305008947620488003064113918729 (pp48)
 r2=1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513 (pp100)
Version: GGNFS-0.77.1-20060513-k8
Total time: 20.92 hours.
Scaled time: 41.16 units (timescale=1.967).
Factorization parameters were as follows:
name 50009_151
n: 639247222470818364294207141669969443982765894882186736898628175460577623790224631473976245573212984389582827262615543935461600419346177940856846977
m: 1000000000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175768, largePrimes:5442675 encountered
Relations: rels:5368300, finalFF:498395
Max relations in full relation-set: 28
Initial matrix: 352135 x 498395 with sparse part having weight 42380181.
Pruned matrix : 282161 x 283985 with weight 22301234.
Total sieving time: 19.66 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 1.00 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.92 hours.
 --------- CPU info (if available) ----------

Dec 17, 2007

By Jo Yeong Uk / GGNFS

5·10138+9 = 5(0)1379<139> = 7 · 67 · 24062444319260058179401<23> · C114

C114 = P45 · P69

P45 = 946212734975879332729540202137182929419049849<45>

P69 = 468240129107916666081642626977725725851067323112806555638980157404389<69>

Number: 50009_138
N=443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261
  ( 114 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=946212734975879332729540202137182929419049849 (pp45)
 r2=468240129107916666081642626977725725851067323112806555638980157404389 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.63 hours.
Scaled time: 9.87 units (timescale=2.129).
Factorization parameters were as follows:
n: 443054773188660674408303607729086637392367280159933140054775228028741936788471173247150308418917853949686442387261
m: 10000000000000000000000000000
c5: 1
c0: 180
skew: 2.83
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1000001)
Primes: RFBsize:107126, AFBsize:107118, largePrimes:2193538 encountered
Relations: rels:2294860, finalFF:267501
Max relations in full relation-set: 28
Initial matrix: 214308 x 267501 with sparse part having weight 20336589.
Pruned matrix : 188484 x 189619 with weight 11495582.
Total sieving time: 4.48 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.63 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10149+9 = 5(0)1489<150> = 614655261608425773017<21> · C129

C129 = P43 · P87

P43 = 1292831320258423031896200514838978324604313<43>

P87 = 629211332393361618328576188689966621539549657057208953485058442782747222654866355168729<87>

Number: 50009_149
N=813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177
  ( 129 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1292831320258423031896200514838978324604313 (pp43)
 r2=629211332393361618328576188689966621539549657057208953485058442782747222654866355168729 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.28 hours.
Scaled time: 24.19 units (timescale=2.145).
Factorization parameters were as follows:
n: 813464117579671160481609861465604632683977337341874220218641873074098242561055665721518223145604420413125413994385245321276128177
m: 1000000000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:134903, largePrimes:3896038 encountered
Relations: rels:4055635, finalFF:434303
Max relations in full relation-set: 28
Initial matrix: 270042 x 434303 with sparse part having weight 42347910.
Pruned matrix : 218215 x 219629 with weight 20005906.
Total sieving time: 10.98 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007 (4th)

By Sinkiti Sibata / GGNFS

5·10121+9 = 5(0)1209<122> = 401 · C120

C120 = P39 · P81

P39 = 234394740470022334833839226247804877881<39>

P81 = 531958520279564508033197824266783726238632647326464705045488524626649705389905089<81>

Number: 50009_121
N=124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409
  ( 120 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=234394740470022334833839226247804877881 (pp39)
 r2=531958520279564508033197824266783726238632647326464705045488524626649705389905089 (pp81)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.07 hours.
Scaled time: 4.13 units (timescale=1.992).
Factorization parameters were as follows:
name: 50009_121
n: 124688279301745635910224438902743142144638403990024937655860349127182044887780548628428927680798004987531172069825436409
m: 1000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64058, largePrimes:2256398 encountered
Relations: rels:2489942, finalFF:350248
Max relations in full relation-set: 28
Initial matrix: 113221 x 350248 with sparse part having weight 32201932.
Pruned matrix : 75006 x 75636 with weight 5986172.
Total sieving time: 1.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.07 hours.
 --------- CPU info (if available) ----------

5·10107+9 = 5(0)1069<108> = 19 · C107

C107 = P35 · P73

P35 = 22161612064368328651072431710802457<35>

P73 = 1187449243189082427047892522175799526276103441537325771419337450292326123<73>

Number: 50009_107
N=26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211
  ( 107 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=22161612064368328651072431710802457 (pp35)
 r2=1187449243189082427047892522175799526276103441537325771419337450292326123 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.95 hours.
Scaled time: 1.31 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_107
n: 26315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211
m: 1000000000000000000000
c5: 500
c0: 9
skew: 0.45
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2414537 encountered
Relations: rels:2970085, finalFF:672208
Max relations in full relation-set: 28
Initial matrix: 113248 x 672208 with sparse part having weight 51031416.
Pruned matrix : 58155 x 58785 with weight 4968824.
Total sieving time: 1.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.95 hours.
 --------- CPU info (if available) ----------

5·10114+9 = 5(0)1139<115> = 7 · 83 · 463 · 48623 · C105

C105 = P38 · P67

P38 = 70541614319082877066125526339209355501<38>

P67 = 5419082164403195929289385747756719945734828037540124137574223619561<67>

Number: 50009_114
N=382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061
  ( 105 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=70541614319082877066125526339209355501 (pp38)
 r2=5419082164403195929289385747756719945734828037540124137574223619561 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.67 hours.
Scaled time: 1.13 units (timescale=0.674).
Factorization parameters were as follows:
name: 50009_114
n: 382270804004751115685801549224284849574629336415081490606549481511433152190319400016180865627738226555061
m: 100000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63888, largePrimes:2196933 encountered
Relations: rels:2439165, finalFF:379789
Max relations in full relation-set: 28
Initial matrix: 113053 x 379789 with sparse part having weight 30408564.
Pruned matrix : 65611 x 66240 with weight 4277422.
Total sieving time: 1.50 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.67 hours.
 --------- CPU info (if available) ----------

Dec 16, 2007 (3rd)

By Robert Backstrom / GMP-ECM

5·10102+9 = 5(0)1019<103> = 7 · 23 · 7001 · C97

C97 = P41 · P57

P41 = 31854706908327006451053849450780933259103<41>

P57 = 139254884403520782870512217316445103008038584589836414223<57>

Dec 16, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10133+9 = 5(0)1329<134> = C134

C134 = P55 · P80

P55 = 1808856091842673778141469519200801928271629226769243833<55>

P80 = 27641778815618891492508230793764960546620767858028425576294203682615206075499473<80>

Number: 50009_133
N=50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 134 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1808856091842673778141469519200801928271629226769243833 (pp55)
 r2=27641778815618891492508230793764960546620767858028425576294203682615206075499473 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.70 hours.
Scaled time: 5.79 units (timescale=2.145).
Factorization parameters were as follows:
n: 50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000
c5: 1
c0: 180
skew: 2.83
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1150001)
Primes: RFBsize:92938, AFBsize:92784, largePrimes:1635992 encountered
Relations: rels:1676140, finalFF:218361
Max relations in full relation-set: 28
Initial matrix: 185786 x 218361 with sparse part having weight 11337457.
Pruned matrix : 170705 x 171697 with weight 7105532.
Total sieving time: 2.59 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 2.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10126+9 = 5(0)1259<127> = 7 · 541 · C124

C124 = P62 · P62

P62 = 18583998288422002372740046473239078846323774567438627504014367<62>

P62 = 71045331073170059497410700220270620432737612295639886159776421<62>

Number: 50009_126
N=1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507
  ( 124 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=18583998288422002372740046473239078846323774567438627504014367 (pp62)
 r2=71045331073170059497410700220270620432737612295639886159776421 (pp62)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.52 hours.
Scaled time: 3.25 units (timescale=2.136).
Factorization parameters were as follows:
n: 1320306311064166886717718510694481119619751782413519936625297068919989437549511486664906258251914444151043041985740691840507
m: 10000000000000000000000000
c5: 50
c0: 9
skew: 0.71
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:64058, largePrimes:1387334 encountered
Relations: rels:1376239, finalFF:164736
Max relations in full relation-set: 28
Initial matrix: 128074 x 164736 with sparse part having weight 7959278.
Pruned matrix : 112535 x 113239 with weight 4175510.
Total sieving time: 1.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

5·10129+9 = 5(0)1289<130> = 1283 · 6673 · 421483 · C118

C118 = P35 · P36 · P48

P35 = 55851141761388119444538473036013289<35>

P36 = 188165401070611685235607528162110379<36>

P48 = 131847024827184141097638546699400890537611235187<48>

Number: 50009_129
N=1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297
  ( 118 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=55851141761388119444538473036013289 (pp35)
 r2=188165401070611685235607528162110379 (pp36)
 r3=131847024827184141097638546699400890537611235187 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.96 hours.
Scaled time: 4.16 units (timescale=2.127).
Factorization parameters were as follows:
n: 1385613673935590348953591613436489741829549505362287644707221680889335587698736375275354448321494087870618987366346297
m: 100000000000000000000000000
c5: 1
c0: 18
skew: 1.78
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78486, largePrimes:1556493 encountered
Relations: rels:1609896, finalFF:225323
Max relations in full relation-set: 28
Initial matrix: 157051 x 225323 with sparse part having weight 11609462.
Pruned matrix : 126069 x 126918 with weight 5246803.
Total sieving time: 1.89 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

Dec 16, 2007

By Sinkiti Sibata / PRIMO

(2·102403+1)/3 is prime.

Dec 15, 2007 (4th)

By matsui / GGNFS

(5·10166+7)/3 = 1(6)1659<167> = 38609 · 75787 · 156630091583671031730558418871436461<36> · C122

C122 = P52 · P71

P52 = 2264388869748319451290164995673979200391552839732379<52>

P71 = 16059767993409165566619664888931389674520944070045699328877175122292297<71>

N=36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563
  ( 122 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=2264388869748319451290164995673979200391552839732379 (pp52)
 r2=16059767993409165566619664888931389674520944070045699328877175122292297 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 125.39 hours.
Scaled time: 238.73 units (timescale=1.904).
Factorization parameters were as follows:
n: 36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563
m: 1000000000000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:349596, largePrimes:6068375 encountered
Relations: rels:6296703, finalFF:852370
Max relations in full relation-set: 28
Initial matrix: 698174 x 852370 with sparse part having weight 63956552.
Pruned matrix : 581570 x 585124 with weight 46821531.
Total sieving time: 110.75 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 14.13 hours.
Time per square root: 0.35 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 125.39 hours.

Dec 15, 2007 (3rd)

By Yousuke Koide

(101375-1)/9 is divisible by 584213416911071661540509773751<30>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 15, 2007 (2nd)

The factor table of 500...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Dec 15, 2007

By Alfred Reich

101813+1 is divisible by 1341949101412826358472947603971939<34>

101966+1 is divisible by 4955902500081447124888466401899581<34>

Reference: Factorizations of numbers of the form 10n+1 (Alfred Reich)

Dec 14, 2007 (4th)

By Yousuke Koide

(101315-1)/9 is divisible by 155872807295141767753013971998423271<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 14, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(2·102362+43)/9 is prime.

Dec 14, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(5·10163+31)/9 = (5)1629<163> = 32 · 11503 · 2014594707737<13> · C146

C146 = P35 · P44 · P68

P35 = 30188843843595259209660847329747917<35>

P44 = 35971250079769021640351453407071430175983319<44>

P68 = 24529244107054551003240215672832228187869914838761899129142536396667<68>

Number: n
N=882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773
  ( 111 digits)
Divisors found:

Fri Dec 14 06:00:23 2007  prp44 factor: 35971250079769021640351453407071430175983319
Fri Dec 14 06:00:23 2007  prp68 factor: 24529244107054551003240215672832228187869914838761899129142536396667
Fri Dec 14 06:00:23 2007  elapsed time 01:21:20 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 23.38 hours.
Scaled time: 40.42 units (timescale=1.729).
Factorization parameters were as follows:
name: KA_5_162_9
n: 882347574042559821772402450073629885235585583487871518473855136881851884014580940306573631458996102973759197773
skew: 19044.42
# norm 6.38e+15
c5: 111600
c4: 14885090508
c3: 145705138135436
c2: -5337155657782209549
c1: 9745908703860354342290
c0: 107907444208141710319877800
# alpha -6.45
Y1: 212966576537
Y0: -1512145107533754160601
# Murphy_E 8.60e-10
# M 496213671955529285371696094504443999209726698467323627075527118570036745236814734332119703037015817317104508841
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved  special-q in [100000, 1200001)
Primes: RFBsize:230209, AFBsize:230305, largePrimes:6818981 encountered
Relations: rels:6507373, finalFF:543771
Max relations in full relation-set: 28
Initial matrix: 460599 x 543771 with sparse part having weight 35789432.
Pruned matrix : 
Total sieving time: 23.12 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 23.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(4·10161+23)/9 = (4)1607<161> = 133 · 132253376785665958621<21> · C138

C138 = P39 · P99

P39 = 208122669820059734018270507907490349851<39>

P99 = 734955876882058340201805409936009321630527412736093444708338848258488834565508219522142315629339181<99>

5·10152-9 = 4(9)1511<153> = 19 · 199 · 1451 · 94201 · C141

C141 = P52 · P90

P52 = 2456042554669170698593684758425118153245909492210089<52>

P90 = 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649<90>

Number: n
N=967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761
  ( 141 digits)
SNFS difficulty: 152 digits.
Divisors found:

Fri Dec 14 22:19:20 2007  prp52 factor: 2456042554669170698593684758425118153245909492210089
Fri Dec 14 22:19:20 2007  prp90 factor: 393916809814646016551948100067256455621282070935459752206741992118247884075792950119651649
Fri Dec 14 22:19:20 2007  elapsed time 01:04:26 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 22.64 hours.
Scaled time: 29.75 units (timescale=1.314).
Factorization parameters were as follows:
name: KA_4_9_151_1
n: 967476447904293055909635216958020112332090895404733428215992995669631565708561959491679428666082918940760232731437093604988438320239803286761
skew: 0.45
deg: 5
c5: 500
c0: -9
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1100000)
Primes: RFBsize:203362, AFBsize:203297, largePrimes:6755039 encountered
Relations: rels:6230916, finalFF:474146
Max relations in full relation-set: 28
Initial matrix: 406726 x 474146 with sparse part having weight 31631044.
Pruned matrix : 349533 x 351630 with weight 19468857.
Total sieving time: 22.45 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 22.64 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 14, 2007

By Jo Yeong Uk / GGNFS

5·10158-9 = 4(9)1571<159> = 192370543578919<15> · 255761895497279<15> · 6553146809446631<16> · C115

C115 = P36 · P79

P36 = 916954738515527411860196269384889891<36>

P79 = 1691210995646724198680462578472437912581425581533448011756847939729769453981971<79>

Number: 49991_158
N=1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161
  ( 115 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=916954738515527411860196269384889891 (pp36)
 r2=1691210995646724198680462578472437912581425581533448011756847939729769453981971 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.62 hours.
Scaled time: 54.41 units (timescale=2.124).
Factorization parameters were as follows:
n: 1550763936287826755654564895336804649264066034246143513988755304298815619485742512321951624878705182064449334155161
m: 100000000000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282037, largePrimes:5639108 encountered
Relations: rels:5690607, finalFF:673567
Max relations in full relation-set: 28
Initial matrix: 565247 x 673567 with sparse part having weight 41646735.
Pruned matrix : 476541 x 479431 with weight 26834784.
Total sieving time: 24.40 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.62 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407682)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405112)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405126)
Total of 4 processors activated (19246.09 BogoMIPS).

(67·10161+23)/9 = 7(4)1607<162> = 3 · 11 · 1399 · 1523 · 87433 · 21320365267<11> · 40377356857463<14> · C126

C126 = P37 · P89

P37 = 6578288242353527353007952811929293213<37>

P89 = 21383556043195314533903891888116589234987504067784812619439791414098469151797015018035563<89>

Dec 13, 2007

By Sinkiti Sibata / PRIMO

(2·102175-17)/3 is prime.

Dec 12, 2007

By Sinkiti Sibata / PFGW

2·1012984-7 and 2·1013614-7 are PRP.

Dec 11, 2007 (2nd)

By Yousuke Koide

101121+1 is divisible by 69849282640264627005884025897913761023<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 11, 2007

By Robert Backstrom / GGNFS, Msieve

5·10155-9 = 4(9)1541<156> = 52249831 · C148

C148 = P68 · P81

P68 = 12577330540482969770037590027834896246509937898150565038352486568081<68>

P81 = 760845786107138460535930299805308106874138122028043088814610693093595148504742881<81>

Number: n
N=9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361
  ( 148 digits)
SNFS difficulty: 155 digits.
Divisors found:

Tue Dec 11 14:10:53 2007  prp68 factor: 12577330540482969770037590027834896246509937898150565038352486568081
Tue Dec 11 14:10:53 2007  prp81 factor: 760845786107138460535930299805308106874138122028043088814610693093595148504742881
Tue Dec 11 14:10:53 2007  elapsed time 01:06:58 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 25.92 hours.
Scaled time: 44.94 units (timescale=1.734).
Factorization parameters were as follows:
name: KA_4_9_154_1
n: 9569408942203085786057374998973680890948719049445346531360072724445749881946986584511632200303193325161185688811127446517482515876462834875006581361
type: snfs
skew: 1.12
deg: 5
c5: 5
c0: -9
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:6390484 encountered
Relations: rels:5934433, finalFF:556300
Max relations in full relation-set: 28
Initial matrix: 433373 x 556300 with sparse part having weight 28717637.
Pruned matrix : 323054 x 325284 with weight 14040928.
Total sieving time: 25.73 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 25.92 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 10, 2007 (5th)

By Sinkiti Sibata / PFGW

(8·1010717-11)/3, (8·1014673-11)/3, (8·1016754-11)/3 and (8·1017606-11)/3 are PRP.

Dec 10, 2007 (4th)

By suberi / GMP-ECM

(16·10176-61)/9 = 1(7)1751<177> = 3 · 5261 · C173

C173 = P36 · C137

P36 = 817155339792930387676948727914630841<36>

C137 = [13784254841763201401763506838527012403768451779816402753683122065119425484587917320413953839479488490114718629521019279324075409499402757<137>]

Dec 10, 2007 (3rd)

By Jo Yeong Uk / GGNFS

5·10166-9 = 4(9)1651<167> = 41 · 89 · 809 · 16811 · 1289694079831<13> · 47803986587156910009154269051461<32> · C113

C113 = P48 · P65

P48 = 423642819486377500810088159556192139680472557229<48>

P65 = 38574774798609590656685912133706632252046886635615382500322326219<65>

Number: 49991_166
N=16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151
  ( 113 digits)
Divisors found:
 r1=423642819486377500810088159556192139680472557229 (pp48)
 r2=38574774798609590656685912133706632252046886635615382500322326219 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.00 hours.
Scaled time: 42.48 units (timescale=2.124).
Factorization parameters were as follows:
name: 49991_166
n: 16341926356735026827094185515432260422814688809284832362536839593066759444529868046049647268284701680004884687151
skew: 27295.93
# norm 2.18e+15
c5: 33120
c4: 4441313622
c3: -62567391423243
c2: -2850563779112809232
c1: 20403393653491258023492
c0: 412100355487556686774922021
# alpha -5.81
Y1: 642727557923
Y0: -3456530699039931079782
# Murphy_E 7.71e-10
# M 1551685654449727006542580819033466558148370987093910726938703232431161248973769563550852895364742766086059152787
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2380001)
Primes: RFBsize:203362, AFBsize:203153, largePrimes:7633589 encountered
Relations: rels:7513780, finalFF:534371
Max relations in full relation-set: 28
Initial matrix: 406594 x 534371 with sparse part having weight 51341064.
Pruned matrix : 315342 x 317438 with weight 31467716.
Polynomial selection time: 1.06 hours.
Total sieving time: 18.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 20.00 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 10, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10179+9 = 4(0)1789<180> = C180

C180 = P45 · P135

P45 = 921163045658547580756150590548571589420901651<45>

P135 = 434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659<135>

Number: 40009_179
N=400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 180 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=921163045658547580756150590548571589420901651 (pp45)
 r2=434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659 (pp135)
Version: GGNFS-0.77.1-20060513-k8
Total time: 514.08 hours.
Scaled time: 1025.58 units (timescale=1.995).
Factorization parameters were as follows:
name: 40009_179
n: 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000000000
c5: 2
c0: 45
skew: 1.86
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9400001)
Primes: RFBsize:501962, AFBsize:502481, largePrimes:6588779 encountered
Relations: rels:7085432, finalFF:1174582
Max relations in full relation-set: 28
Initial matrix: 1004508 x 1174582 with sparse part having weight 72170055.
Pruned matrix : 861753 x 866839 with weight 54190298.
Total sieving time: 503.52 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 9.74 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 514.08 hours.
 --------- CPU info (if available) ----------

Dec 10, 2007

By Robert Backstrom / GGNFS, Msieve

5·10146-9 = 4(9)1451<147> = 41 · 59 · 5970268730389741<16> · C128

C128 = P59 · P69

P59 = 89514634314987140562070529941642327551603414368208045052321<59>

P69 = 386764152467374483050690533716910166621405836972248541038074724385249<69>

Number: n
N=34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929
  ( 128 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=89514634314987140562070529941642327551603414368208045052321 (pp59)
 r2=386764152467374483050690533716910166621405836972248541038074724385249 (pp69)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.86 hours.
Scaled time: 12.82 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_4_9_145_1
n: 34621051674262958248832730437816687088862152041094871343262841750725698980225021240368058000790564138392180385545468782765612929
skew: 0.71
deg: 5
c5: 50
c0: -9
m: 100000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:135072, AFBsize:134503, largePrimes:6508918 encountered
Relations: rels:5845525, finalFF:310973
Max relations in full relation-set: 28
Initial matrix: 269640 x 310973 with sparse part having weight 24290713.
Pruned matrix : 244308 x 245720 with weight 16377793.
Total sieving time: 7.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.51 hours.
Total square root time: 0.05 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 8.86 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

4·10154+9 = 4(0)1539<155> = 17 · 13913 · 1396989572897<13> · 61059519554988608394921409<26> · C112

C112 = P56 · P56

P56 = 42618868918024524866536599051397923694814520254443166653<56>

P56 = 46520226216352324323002797548303105981922548494168073941<56>

Number: n
N=1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473
  ( 112 digits)
SNFS difficulty: 155 digits.
Divisors found:

Mon Dec 10 21:43:43 2007  prp56 factor: 42618868918024524866536599051397923694814520254443166653
Mon Dec 10 21:43:43 2007  prp56 factor: 46520226216352324323002797548303105981922548494168073941
Mon Dec 10 21:43:43 2007  elapsed time 01:00:47 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 24.01 hours.
Scaled time: 31.77 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_0_153_9
n: 1982639423151567720765887757879743509716301779332394742489381947815103365988434494345777849480504756361889489473
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:203362, AFBsize:203302, largePrimes:6863368 encountered
Relations: rels:6330906, finalFF:483438
Max relations in full relation-set: 28
Initial matrix: 406729 x 483438 with sparse part having weight 36996653.
Pruned matrix : 344289 x 346386 with weight 21435247.
Total sieving time: 23.83 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 24.01 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 9, 2007 (2nd)

By Yousuke Koide

(101177-1)/9 is divisible by 15112598396753272691345143612337643317<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 9, 2007

By Jo Yeong Uk / GGNFS

5·10154-9 = 4(9)1531<155> = 20431 · 52699109 · 32997845429069<14> · 307535008641326161<18> · C112

C112 = P35 · P78

P35 = 29858758013316752254424575775237339<35>

P78 = 153258730444147188544171970047926818140030968120876657797177159787574781970379<78>

Number: 49991_154
N=4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481
  ( 112 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=29858758013316752254424575775237339 (pp35)
 r2=153258730444147188544171970047926818140030968120876657797177159787574781970379 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 16.32 hours.
Scaled time: 34.73 units (timescale=2.128).
Factorization parameters were as follows:
n: 4576115345759931963273148602487874485867641118618536902522504884305530749801301398793635737836618902146792781481
m: 10000000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:5614449 encountered
Relations: rels:5616644, finalFF:590726
Max relations in full relation-set: 28
Initial matrix: 433819 x 590726 with sparse part having weight 45178149.
Pruned matrix : 324617 x 326850 with weight 28243374.
Total sieving time: 15.65 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.55 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 16.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

4·10166+9 = 4(0)1659<167> = 95273 · 8165188054910845523309<22> · 14974400622659504557368769453<29> · C112

C112 = P50 · P63

P50 = 16787178947577077116058498947766265186683375867777<50>

P63 = 204548731765952768246248790510940164302339098214505480636361977<63>

Number: 40009_166
N=3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129
  ( 112 digits)
Divisors found:
 r1=16787178947577077116058498947766265186683375867777 (pp50)
 r2=204548731765952768246248790510940164302339098214505480636361977 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.28 hours.
Scaled time: 37.04 units (timescale=2.144).
Factorization parameters were as follows:
name: 40009_166
n: 3433796163654992834720717303856461988726115533311254786924829579654454831482818646616432841788029058212662315129
skew: 32399.49
# norm 4.04e+15
c5: 43260
c4: -2582623147
c3: -129295358935911
c2: -427069562025293841
c1: 24893025188825634820574
c0: -213047928497871312783824304
# alpha -6.19
Y1: 8847912799
Y0: -2398488377529493938175
# Murphy_E 7.74e-10
# M 1450873548697470902964069406047257719289617562836590192062108198415984904995949699924035264821588859357326623899
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2240001)
Primes: RFBsize:203362, AFBsize:203291, largePrimes:7436972 encountered
Relations: rels:7186524, finalFF:474824
Max relations in full relation-set: 28
Initial matrix: 406739 x 474824 with sparse part having weight 42851975.
Pruned matrix : 354327 x 356424 with weight 28562696.
Polynomial selection time: 0.94 hours.
Total sieving time: 15.41 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.68 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007 (3rd)

By matsui / GMP-ECM

(37·10178-1)/9 = 4(1)178<179> = 7 · 137 · C176

C176 = P33 · C144

P33 = 256606801414902925624321820940911<33>

C144 = [167059987357085613333034797110824057589025658340318711449285988164500386196628719375549643795216399404461119111310119558935462349796606422281239<144>]

Dec 8, 2007 (2nd)

By Jo Yeong Uk / GGNFS

5·10162-9 = 4(9)1611<163> = C163

C163 = P44 · P56 · P64

P44 = 68385977371361886229008858431010504877885471<44>

P56 = 10358845079111018892823016494495871163939965326959587059<56>

P64 = 7058161771042422170571387133040680162138563583374078964992316019<64>

Number: 49991_162
N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 163 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=68385977371361886229008858431010504877885471 (pp44)
 r2=10358845079111018892823016494495871163939965326959587059 (pp56)
 r3=7058161771042422170571387133040680162138563583374078964992316019 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 48.82 hours.
Scaled time: 104.66 units (timescale=2.144).
Factorization parameters were as follows:
n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 500000000000000000000000000000000
c5: 4
c0: -225
skew: 2.24
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2500000, 5100001)
Primes: RFBsize:348513, AFBsize:348286, largePrimes:6727746 encountered
Relations: rels:6971731, finalFF:855302
Max relations in full relation-set: 28
Initial matrix: 696863 x 855302 with sparse part having weight 63866792.
Pruned matrix : 578415 x 581963 with weight 45564381.
Total sieving time: 46.21 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 2.42 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,49,49,2.5,2.5,100000
total time: 48.82 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

5·10151-9 = 4(9)1501<152> = 41 · 71 · 5849 · 301673 · 2377056670405894456247259031<28> · C112

C112 = P34 · P78

P34 = 7216593624182899656979319751461431<34>

P78 = 567463522224990994815587976391783657930851218965846028456860191438113244343673<78>

Number: 49991_151
N=4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063
  ( 112 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=7216593624182899656979319751461431 (pp34)
 r2=567463522224990994815587976391783657930851218965846028456860191438113244343673 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.78 hours.
Scaled time: 27.42 units (timescale=2.146).
Factorization parameters were as follows:
n: 4095153636445241190206816689343683703674815019630873708328681246983802788485970229898316586832416033236168376063
m: 1000000000000000000000000000000
c5: 50
c0: -9
skew: 0.71
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:175768, largePrimes:5401564 encountered
Relations: rels:5292212, finalFF:469027
Max relations in full relation-set: 28
Initial matrix: 352135 x 469027 with sparse part having weight 39728717.
Pruned matrix : 293297 x 295121 with weight 22323023.
Total sieving time: 12.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 8, 2007

By Robert Backstrom / GMP-ECM

5·10157-9 = 4(9)1561<158> = 23 · 47 · 32993 · C151

C151 = P41 · P110

P41 = 64414577002263313514982818321328963237311<41>

P110 = 21763981302826500962913776820417810329105314486317929333032864905086682541577240814547337472885523445053489457<110>

Dec 7, 2007 (4th)

By Jo Yeong Uk / GGNFS

5·10148-9 = 4(9)1471<149> = 29 · 792 · 109 · 752100379 · C133

C133 = P34 · P99

P34 = 3528305141284807144178302848697901<34>

P99 = 955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729<99>

Number: 49991_148
N=3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3528305141284807144178302848697901 (pp34)
 r2=955101178320483387652564653901091192062550077009781733001890240341202021273986351553940732976675729 (pp99)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.19 hours.
Scaled time: 21.63 units (timescale=2.123).
Factorization parameters were as follows:
n: 3369888397915338921258428641420141674023216060199260547003287810058336759881465047437666734012844616469309629039403567538331159944829
m: 1000000000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:134763, largePrimes:3725528 encountered
Relations: rels:3800513, finalFF:378509
Max relations in full relation-set: 28
Initial matrix: 269899 x 378509 with sparse part having weight 33652982.
Pruned matrix : 230441 x 231854 with weight 17271651.
Total sieving time: 9.90 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (3rd)

By Jo Yeong Uk / GGNFS

8·10186-7 = 7(9)1853<187> = C187

C187 = P59 · P129

P59 = 23673718891878340687652156651068165346397873316066209701723<59>

P129 = 337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491<129>

Number: 79993_186
N=7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 187 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=23673718891878340687652156651068165346397873316066209701723 (pp59)
 r2=337927472930521778199552160468265760927553690616358987625083967033589270515553679435711873302636879244937694756967161283401298491 (pp129)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 403.36 hours.
Scaled time: 859.97 units (timescale=2.132).
Factorization parameters were as follows:
n: 7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 20000000000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [6000000, 12600001)
Primes: RFBsize:788060, AFBsize:788254, largePrimes:11493077 encountered
Relations: rels:12030057, finalFF:1799960
Max relations in full relation-set: 28
Initial matrix: 1576379 x 1799960 with sparse part having weight 101413617.
Pruned matrix : 1375471 x 1383416 with weight 74538419.
Total sieving time: 389.01 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 13.95 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000
total time: 403.36 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 7, 2007 (2nd)

By Sinkiti Sibata / PFGW

5·1010820-9 and 5·1014592-9 are PRP.

Dec 7, 2007

By Yousuke Koide

(101093-1)/9 is divisible by 199506195135220536755902065305293<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 6, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

5·10199-9 = 4(9)1981<200> = C200

C200 = P34 · P167

P34 = 1224112416041742410052808832168959<34>

P167 = 40845921783620723265274965609618243098936302659169196754666765677273901878095642440080026040452661066087357309697423682859960350348666458327845592281510888305426519049<167>

Dec 6, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(16·10162-7)/9 = 1(7)162<163>= 149 · 12918999672424547147<20> · C141

C141 = P53 · P89

P53 = 42410911175907381021122531054551380413053150932223867<53>

P89 = 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477<89>

Number: n
N=923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559
  ( 141 digits)
SNFS difficulty: 163 digits.
Divisors found:

Thu Dec 06 08:21:53 2007  prp53 factor: 42410911175907381021122531054551380413053150932223867
Thu Dec 06 08:21:53 2007  prp89 factor: 21776331263493214068135261250146977053996751440377507135716102961789622007528024777905477
Thu Dec 06 08:21:53 2007  elapsed time 02:06:15 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.27 hours.
Scaled time: 88.59 units (timescale=1.317).
Factorization parameters were as follows:
name: KA_1_7_162
n: 923554050953145651757115932207095054219542878393925009149107585156454700784480736260600830105563687523730018039673296026246046433409929419559
skew: 0.67
deg: 5
c5: 50
c0: -7
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:217591, largePrimes:7393862 encountered
Relations: rels:6850636, finalFF:494540
Max relations in full relation-set: 28
Initial matrix: 434472 x 494540 with sparse part having weight 50632783.
Pruned matrix : 
Total sieving time: 67.01 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 67.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10152+9 = 4(0)1519<153> = 26713 · 1234873 · 1996467668952176494127953<25> · C118

C118 = P41 · P78

P41 = 35974049014171230767387935670841612478177<41>

P78 = 168835367899724431687288680957130059518243845115630566914418157002167566445961<78>

Number: n
N=6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097
  ( 118 digits)
SNFS difficulty: 152 digits.
Divisors found:

Thu Dec 06 16:08:51 2007  prp41 factor: 35974049014171230767387935670841612478177
Thu Dec 06 16:08:51 2007  prp78 factor: 168835367899724431687288680957130059518243845115630566914418157002167566445961
Thu Dec 06 16:08:51 2007  elapsed time 00:47:53 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 22.03 hours.
Scaled time: 31.99 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_4_0_151_9
n: 6073691800150318752219511984753628781476739145121835518994745689916081064629478208333175321810209710086068549562293097
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 2000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:148933, AFBsize:148625, largePrimes:7017509 encountered
Relations: rels:6462685, finalFF:361511
Max relations in full relation-set: 28
Initial matrix: 297622 x 361511 with sparse part having weight 34777349.
Pruned matrix : 266133 x 267685 with weight 22914288.
Total sieving time: 21.83 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 22.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(34·10161-7)/9 = 3(7)161<162> = 197 · 9371 · 110183 · 694182710171<12> · C139

C139 = P58 · P82

P58 = 2616862112205494779410765284481436663033222318232195981387<58>

P82 = 1022386293766035950048848925429858897403553614981437089485799152210536157188516281<82>

Number: n
N=2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747
  ( 139 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Dec 06 23:56:31 2007  prp58 factor: 2616862112205494779410765284481436663033222318232195981387
Thu Dec 06 23:56:31 2007  prp82 factor: 1022386293766035950048848925429858897403553614981437089485799152210536157188516281
Thu Dec 06 23:56:31 2007  elapsed time 02:44:21 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 69.26 hours.
Scaled time: 83.04 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_3_7_161
n: 2675443956194536316022798734239381743434700299393259205203764910786567960718170468410719273526054038360896452757923210295394590633222461747
type: snfs
skew: 0.46
deg: 5
c5: 340
c0: -7
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3000001)
Primes: RFBsize:230209, AFBsize:229397, largePrimes:7454855 encountered
Relations: rels:6893700, finalFF:514080
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.95 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 69.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Dec 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS

5·10143-9 = 4(9)1421<144> = 17 · C143

C143 = P60 · P84

P60 = 285720265191441664337755675562698371459936363289423581013937<60>

P84 = 102939022145228428989427304065983196665834399279521532082685405829806319911074359479<84>

Number: 49991_143
N=29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823
  ( 143 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=285720265191441664337755675562698371459936363289423581013937 (pp60)
 r2=102939022145228428989427304065983196665834399279521532082685405829806319911074359479 (pp84)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.80 hours.
Scaled time: 23.49 units (timescale=1.991).
Factorization parameters were as follows:
name: 49991_143
n: 29411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823
m: 50000000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:99898, largePrimes:2740628 encountered
Relations: rels:2726242, finalFF:266126
Max relations in full relation-set: 28
Initial matrix: 199984 x 266126 with sparse part having weight 25911863.
Pruned matrix : 180593 x 181656 with weight 15619042.
Total sieving time: 11.27 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.36 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.80 hours.
 --------- CPU info (if available) ----------

5·10135-9 = 4(9)1341<136> = 7 · 23 · 79 · 17536644897128650802233<23> · C110

C110 = P46 · P65

P46 = 1719936531432379284578110469620659745107108719<46>

P65 = 13033411521941582112132234407177385128654436282436915981843640207<65>

Number: 49991_135
N=22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833
  ( 110 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1719936531432379284578110469620659745107108719 (pp46)
 r2=13033411521941582112132234407177385128654436282436915981843640207 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.81 hours.
Scaled time: 11.61 units (timescale=2.000).
Factorization parameters were as follows:
name: 49991_135
n: 22416640605779012272061571478739422204655514974373750892597086537285582773909365228492465712874266775868664833
m: 1000000000000000000000000000
c5: 5
c0: -9
skew: 1.12
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63763, largePrimes:1597471 encountered
Relations: rels:1658522, finalFF:230632
Max relations in full relation-set: 28
Initial matrix: 142327 x 230632 with sparse part having weight 17325623.
Pruned matrix : 115642 x 116417 with weight 7445126.
Total sieving time: 5.63 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.81 hours.
 --------- CPU info (if available) ----------

5·10142-9 = 4(9)1411<143> = 2339 · 7678802901535212851801<22> · C118

C118 = P30 · P44 · P46

P30 = 117630389300918643864328074179<30>

P44 = 13290764272933581140590846123083681578082559<44>

P46 = 1780642654590329845797643787582718386220435529<46>

Number: 49991_142
N=2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=117630389300918643864328074179 (pp30)
 r2=13290764272933581140590846123083681578082559 (pp44)
 r3=1780642654590329845797643787582718386220435529 (pp46)
Version: GGNFS-0.77.1-20060513-k8
Total time: 15.52 hours.
Scaled time: 30.95 units (timescale=1.994).
Factorization parameters were as follows:
name: 49991_142
n: 2783852765203771242392062028278372201075337622567765162596504687226524568762724852814366472811671739409898543364743269
m: 10000000000000000000000000000
c5: 500
c0: -9
skew: 0.45
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2350001)
Primes: RFBsize:100021, AFBsize:99988, largePrimes:2795102 encountered
Relations: rels:2767439, finalFF:225205
Max relations in full relation-set: 28
Initial matrix: 200076 x 225205 with sparse part having weight 24651803.
Pruned matrix : 193526 x 194590 with weight 19788059.
Total sieving time: 14.86 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 15.52 hours.
 --------- CPU info (if available) ----------

Dec 6, 2007 (2nd)

By Sinkiti Sibata / PFGW

(22·1011431-7)/3 and (22·1012927-7)/3 are PRP.

Dec 6, 2007

By Robert Backstrom / GGNFS, Msieve 1.30

9·10161+7 = 9(0)1607<162> = 32742491009<11> · 15305913553837<14> · C139

C139 = P61 · P78

P61 = 2871374186022696036738055549847702632759229312163023359543043<61>

P78 = 625434371370412843235342091358846490870084281799111208724718685614180061274753<78>

Number: n
N=1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Dec 06 02:15:29 2007  prp61 factor: 2871374186022696036738055549847702632759229312163023359543043
Thu Dec 06 02:15:29 2007  prp78 factor: 625434371370412843235342091358846490870084281799111208724718685614180061274753
Thu Dec 06 02:15:29 2007  elapsed time 01:54:10 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.06 hours.
Scaled time: 84.97 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_9_0_160_7
n: 1795856109004335763698691572087419453798364220434114608269312678179761222742470512062548832927933855893213113194030583971753238970152693379
skew: 0.60
deg: 5
c5: 90
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:230209, AFBsize:230767, largePrimes:7363359 encountered
Relations: rels:6836918, finalFF:495414
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 64.81 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 65.06 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 5, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM

5·10153-9 = 4(9)1521<154> = 72 · 31 · 233 · 367 · 190668767 · 15049933389679<14> · C125

C125 = P36 · P89

P36 = 394436722224962502210435443374249441<36>

P89 = 34009384186180731129927406696605787600972387399376193654041569409619395347174902797719823<89>

Dec 5, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS

5·10123-9 = 4(9)1221<124> = 7 · 31 · 103668634195146479<18> · C105

C105 = P33 · P72

P33 = 529652772019323584350569475910017<33>

P72 = 419634942345057429532843777824194673588852290057980851002408093562224161<72>

5·10124-9 = 4(9)1231<125> = 112834510063289823811<21> · C105

C105 = P45 · P60

P45 = 449489779543195000651111258759942012797389869<45>

P60 = 985844086264210902762592892891295128151928079697441377159249<60>

Number: n
N=443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381
  ( 105 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=449489779543195000651111258759942012797389869 (pp45)
 r2=985844086264210902762592892891295128151928079697441377159249 (pp60)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.96 hours.
Scaled time: 2.60 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_9_123_1
n: 443126840998862673372330594167340785125969505774279345379238258715809495060385177703056868837181152248381
skew: 1.78
deg: 5
c5: 1
c0: -18
m: 10000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:63951, AFBsize:63888, largePrimes:4613515 encountered
Relations: rels:4003172, finalFF:210650
Max relations in full relation-set: 48
Initial matrix: 127906 x 210650 with sparse part having weight 17161578.
Pruned matrix : 98518 x 99221 with weight 4907911.
Total sieving time: 1.71 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.06 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 5, 2007

By Sinkiti Sibata / GGNFS

5·10128-9 = 4(9)1271<129> = 17981 · 3843931457165509<16> · C109

C109 = P45 · P64

P45 = 942477006562110761447064968719904363145782491<45>

P64 = 7675554588296651640866311850875593032012524032228064348193639269<64>

Number: 49991_128
N=7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079
  ( 109 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=942477006562110761447064968719904363145782491 (pp45)
 r2=7675554588296651640866311850875593032012524032228064348193639269 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.04 hours.
Scaled time: 6.11 units (timescale=2.010).
Factorization parameters were as follows:
name: 49991_128
n: 7234033712081902712464612958999569631054058842077060936513763588440193920136568538523951971389190729990239079
m: 50000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63928, largePrimes:1408145 encountered
Relations: rels:1391646, finalFF:160862
Max relations in full relation-set: 28
Initial matrix: 127944 x 160862 with sparse part having weight 8338899.
Pruned matrix : 116420 x 117123 with weight 4694100.
Total sieving time: 2.90 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.04 hours.
 --------- CPU info (if available) ----------

5·10129-9 = 4(9)1281<130> = 7 · 399271 · C124

C124 = P37 · P88

P37 = 1719378230348833617587044366277777273<37>

P88 = 1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311<88>

Number: 49991_129
N=1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903
  ( 124 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=1719378230348833617587044366277777273 (pp37)
 r2=1040477691594168476615746126692780490295108691699389255395317590980581957687501917021311 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.02 hours.
Scaled time: 6.07 units (timescale=2.010).
Factorization parameters were as follows:
name: 49991_129
n: 1788974692090620870822788818335702532150558678906592979991749248720078056543765297969835739921721623372882793176278052464903
m: 100000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:63951, AFBsize:63888, largePrimes:1400726 encountered
Relations: rels:1379152, finalFF:155356
Max relations in full relation-set: 28
Initial matrix: 127906 x 155356 with sparse part having weight 8163928.
Pruned matrix : 118614 x 119317 with weight 4886712.
Total sieving time: 2.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.02 hours.
 --------- CPU info (if available) ----------

5·10131-9 = 4(9)1301<132> = 41 · 5547391 · C124

C124 = P60 · P64

P60 = 331708005539959846200945699830264904120183676134446346135329<60>

P64 = 6627373043733457754101972925473022695394088807721914419175039809<64>

Number: 49991_131
N=2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161
  ( 124 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=331708005539959846200945699830264904120183676134446346135329 (pp60)
 r2=6627373043733457754101972925473022695394088807721914419175039809 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.40 hours.
Scaled time: 8.73 units (timescale=1.985).
Factorization parameters were as follows:
name: 49991_131
n: 2198352694306118352775557233934329691552518925057765344324838864814459845991060504289533496412119129734953277157126876312161
m: 100000000000000000000000000
c5: 50
c0: -9
skew: 0.71
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64058, largePrimes:1540929 encountered
Relations: rels:1578173, finalFF:205413
Max relations in full relation-set: 28
Initial matrix: 128074 x 205413 with sparse part having weight 14981903.
Pruned matrix : 107027 x 107731 with weight 6295031.
Total sieving time: 4.24 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

5·10133-9 = 4(9)1321<134> = 1388981393<10> · C125

C125 = P46 · P79

P46 = 4580943858133272901234098370518760018593679951<46>

P79 = 7858119105566310646465581070947787541968136461241464994014105774627915529998537<79>

Number: 49991_133
N=35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687
  ( 125 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=4580943858133272901234098370518760018593679951 (pp46)
 r2=7858119105566310646465581070947787541968136461241464994014105774627915529998537 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.68 hours.
Scaled time: 9.29 units (timescale=1.985).
Factorization parameters were as follows:
name: 49991_133
n: 35997602453123718699088433361036392227609920185590275938275294088118860783040021616761859674530571627319128529175336476231687
m: 500000000000000000000000000
c5: 8
c0: -45
skew: 1.41
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 925001)
Primes: RFBsize:78498, AFBsize:63928, largePrimes:1457680 encountered
Relations: rels:1439431, finalFF:160358
Max relations in full relation-set: 28
Initial matrix: 142491 x 160358 with sparse part having weight 10506246.
Pruned matrix : 136383 x 137159 with weight 7567068.
Total sieving time: 4.48 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 4.68 hours.
 --------- CPU info (if available) ----------

5·10134-9 = 4(9)1331<135> = 19 · 4294946301634720547509<22> · C112

C112 = P40 · P72

P40 = 7661951585715267309757814664269644345249<40>

P72 = 799685573994862057768981025766325851378881906722550433228529476184746329<72>

Number: 49991_134
N=6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=7661951585715267309757814664269644345249 (pp40)
 r2=799685573994862057768981025766325851378881906722550433228529476184746329 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.82 hours.
Scaled time: 11.55 units (timescale=1.986).
Factorization parameters were as follows:
name: 49991_134
n: 6127152151743557074542844552870042019610302481794247517939862406771161342106351861871786326029301318444361340921
m: 1000000000000000000000000000
c5: 1
c0: -18
skew: 1.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63888, largePrimes:1619441 encountered
Relations: rels:1697010, finalFF:245323
Max relations in full relation-set: 28
Initial matrix: 142453 x 245323 with sparse part having weight 18456007.
Pruned matrix : 112751 x 113527 with weight 7450413.
Total sieving time: 5.64 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

Dec 4, 2007 (5th)

By Jo Yeong Uk / GGNFS

5·10118-9 = 4(9)1171<119> = C119

C119 = P60 · P60

P60 = 113451761893099661361741916560523265424931846016438394824059<60>

P60 = 440715940992725025596348804318707127294139212236448645152949<60>

Number: 49991_118
N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:

r1=113451761893099661361741916560523265424931846016438394824059
(pp60)

r2=440715940992725025596348804318707127294139212236448645152949
(pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.74 hours.
Scaled time: 1.58 units (timescale=2.145).
Factorization parameters were as follows:
n:
49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 1000000000000000000000000
c5: 1
c0: -180
skew: 2.83
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49121,
largePrimes:1721640 encountered
Relations: rels:1663175, finalFF:113797
Max relations in full relation-set: 28
Initial matrix: 98283 x 113797 with sparse part having
weight 8423002.
Pruned matrix : 92995 x 93550 with weight 5618322.
Total sieving time: 0.68 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz
stepping 07
Memory: 8167512k/8912896k available (2114k kernel
code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine..
4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine..
4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine..
4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine..
4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Dec 4, 2007 (4th)

By Robert Backstrom / GMP-ECM

5·10113-9 = 4(9)1121<114> = 23 · 263 · 200041 · 2035289 · C99

C99 = P30 · P69

P30 = 443952373522730358003023095039<30>

P69 = 457303931730390724716183370178707280616570660476664818059347925723369<69>

Dec 4, 2007 (3rd)

By matsui / GMP-ECM

(4·10185-13)/9 = (4)1843<185> = 7 · 1451 · C181

C181 = P33 · C149

P33 = 164277524510786827843488693745099<33>

C149 = [26636298892028694012587941153238062628591187075841112023861911522751253412947765247273184353075516238787560153594780836262462832930974948643067577301<149>]

Dec 4, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

4·10161+9 = 4(0)1609<162> = 4051 · 127235411 · 1969369859<10> · C141

C141 = P40 · P102

P40 = 3315928709727846416041854024938819789689<40>

P102 = 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619<102>

Number: n
N=394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Dec 04 13:47:12 2007  prp40 factor: 3315928709727846416041854024938819789689
Tue Dec 04 13:47:12 2007  prp102 factor: 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619
Tue Dec 04 13:47:12 2007  elapsed time 01:05:12 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.49 hours.
Scaled time: 45.35 units (timescale=1.440).
Factorization parameters were as follows:
name: KA_4_0_160_9
n: 394060101005733730854944506185225543063987154654543968918320787847903391279563079348777846305919632986249125213107544098370152142181416420491
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:203362, AFBsize:203082, largePrimes:7092138 encountered
Relations: rels:6575017, finalFF:473191
Max relations in full relation-set: 28
Initial matrix: 406511 x 473191 with sparse part having weight 37652625.
Pruned matrix : 356677 x 358773 with weight 25275013.
Total sieving time: 31.28 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 31.49 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Dec 4, 2007

The factor table of 499...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Dec 3, 2007 (3rd)

By Yousuke Koide

(101019-1)/9 is divisible by 1164875952920329463736875905335015089<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 3, 2007 (2nd)

By Robert Backstrom / GMP-ECM

(64·10234+53)/9 = 7(1)2337<235> = 13 · 1181 · 7451 · 1471598307214747<16> · 3052073285905649<16> · 172548225862787861<18> · 2699321912890730492306803<25> · C155

C155 = P47 · P109

P47 = 26652891282185821045577962549160542412294508503<47>

P109 = 1114899980065870331232905973592925067977812491581216317251152807767466063464285258166500582274270472922906037<109>

Dec 3, 2007

By Jo Yeong Uk / GGNFS

(4·10187-1)/3 = 1(3)187<188> = 132 · 71 · 641 · 4354373 · C174

C174 = P52 · P122

P52 = 5361712371792973170896785910460906141853462256912209<52>

P122 = 74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791<122>

Number: 13333_187
N=398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319
  ( 174 digits)
SNFS difficulty: 187 digits.
Divisors found:
 r1=5361712371792973170896785910460906141853462256912209 (pp52)
 r2=74251719049861199442807051707488431927072858194646024738993713156188070400742301801156540569317981596338173399436320309791 (pp122)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 361.56 hours.
Scaled time: 773.01 units (timescale=2.138).
Factorization parameters were as follows:
n: 398116360656536779984902594959659524762886894764740907788961498125477543559005946143561502786041981375439529374284451922273986560056748206834695296451854204990252061970138319
m: 20000000000000000000000000000000000000
c5: 25
c0: -2
skew: 0.6
type: snfs
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [6000000, 11900001)
Primes: RFBsize:788060, AFBsize:788149, largePrimes:11393019 encountered
Relations: rels:11956011, finalFF:1824015
Max relations in full relation-set: 28
Initial matrix: 1576273 x 1824015 with sparse part having weight 91057329.
Pruned matrix : 1349070 x 1357015 with weight 64635248.
Total sieving time: 348.71 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 12.46 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,187,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,50,50,2.6,2.6,100000
total time: 361.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Jo Yeong Uk completed factorizations up to n=200 of 133...33. Congratulations!

Dec 2, 2007

By Sinkiti Sibata / PFGW

2·1013561+9, 2·1015955+9, (23·1013092-11)/3, (17·1011046+7)/3, (17·1015448+7)/3, (17·1016628+7)/3, (17·1016918+7)/3 and (17·1018734+7)/3 are PRP.

Dec 1, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10160+9 = 4(0)1599<161> = 277 · 138637 · 247609 · 15173733529<11> · C138

C138 = P62 · P76

P62 = 60797126856307127135595444344471160234256633836042739865882569<62>

P76 = 4559940072470123498850798447077277366305328269178339465898539108054593612449<76>

Number: n
N=277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:

Sat Dec 01 14:19:53 2007  prp62 factor: 60797126856307127135595444344471160234256633836042739865882569
Sat Dec 01 14:19:53 2007  prp76 factor: 4559940072470123498850798447077277366305328269178339465898539108054593612449
Sat Dec 01 14:19:53 2007  elapsed time 01:19:11

Version: GGNFS-0.77.1-20051202-athlon
Total time: 27.74 hours.
Scaled time: 40.22 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_4_0_159_9
n: 277231255043124412962563195334423003572989349824918726484343257938458321577544020345163333731927265082665578558503965730046567209330501481
skew: 1.18
deg: 5
c5: 4
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1500000)
Primes: RFBsize:203362, AFBsize:203477, largePrimes:7032527 encountered
Relations: rels:6512477, finalFF:474011
Max relations in full relation-set: 28
Initial matrix: 406903 x 474011 with sparse part having weight 35734018.
Pruned matrix : 354822 x 356920 with weight 23455777.
Total sieving time: 27.55 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 27.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 3400+

4·10151+9 = 4(0)1509<152> = 7 · 131 · 197 · 1531 · 47933 · 2296496011<10> · 1404598779340570579<19> · C111

C111 = P31 · P81

P31 = 6104431168415592413869608635611<31>

P81 = 153232696611883288817148088275635599149717352290249536018399392505789557880036813<81>

4·10157+9 = 4(0)1569<158> = 7 · 87972114341735599736283329579<29> · C128

C128 = P53 · P76

P53 = 22156740177008454467142813185853133375535106690625343<53>

P76 = 2931642819433829612544003364072511581602586787125479620745479951967818422771<76>

Number: n
N=64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453
  ( 128 digits)
SNFS difficulty: 157 digits.
Divisors found:

Sat Dec 01 21:40:37 2007  prp53 factor: 22156740177008454467142813185853133375535106690625343
Sat Dec 01 21:40:37 2007  prp76 factor: 2931642819433829612544003364072511581602586787125479620745479951967818422771
Sat Dec 01 21:40:37 2007  elapsed time 01:33:31 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 37.39 hours.
Scaled time: 48.71 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_4_0_156_9
n: 64955648241987874447117430039138259202002854155007541960018688539768478636343303641089348405672723770075499054458421913940885453
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600001)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7116928 encountered
Relations: rels:6581195, finalFF:473861
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 37.16 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10162+9 = 4(0)1619<163> = 13 · C162

C162 = P77 · P86

P77 = 14484959608208348655122569360348676482871487639034491862149522347733039174529<77>

P86 = 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317<86>

Number: n
N=307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
  ( 162 digits)
SNFS difficulty: 162 digits.
Divisors found:

Sun Dec 02 00:56:26 2007  prp77 factor: 14484959608208348655122569360348676482871487639034491862149522347733039174529
Sun Dec 02 00:56:26 2007  prp86 factor: 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317
Sun Dec 02 00:56:26 2007  elapsed time 01:38:38 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.08 hours.
Scaled time: 75.52 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_4_0_161_9
n: 307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800000)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7515407 encountered
Relations: rels:6986522, finalFF:507662
Max relations in full relation-set: 28
Initial matrix: 433431 x 507662 with sparse part having weight 54891344.
Pruned matrix : 403528 x 405759 with weight 36508693.
Total sieving time: 56.79 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 57.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Dec 1, 2007 (4th)

By Yousuke Koide

101497+1 is divisible by 7016092401376747085885131800303253<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 1, 2007 (3rd)

By Robert Backstrom / GGNFS

4·10155+9 = 4(0)1549<156> = 1975423 · 3095912878954409<16> · C134

C134 = P65 · P70

P65 = 34448312105302906122201979845692525321041884536529688865372252369<65>

P70 = 1898642540091341888277141518857734481586769553402869501770427156234223<70>

Number: n
N=65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=34448312105302906122201979845692525321041884536529688865372252369 (pp65)
 r2=1898642540091341888277141518857734481586769553402869501770427156234223 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.75 hours.
Scaled time: 32.02 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_154_9
n: 65405030797471631024897797203292080268700559470205742591870217011703486438834669678697175888566047633668436172058302458077017630624287
type: snfs
skew: 1.17
deg: 5
c5: 4
c0: 9
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:216816, AFBsize:216936, largePrimes:6166954 encountered
Relations: rels:5660881, finalFF:507771
Max relations in full relation-set: 28
Initial matrix: 433816 x 507771 with sparse part having weight 24265495.
Pruned matrix : 362409 x 364642 with weight 13836447.
Total sieving time: 24.20 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 2.29 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 26.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Dec 1, 2007 (2nd)

By Sinkiti Sibata / Msieve

4·10172+9 = 4(0)1719<173> = 379417 · 2183353693<10> · 369214042069<12> · 10392906827609765461<20> · 1432364659536702101368956541<28> · C100

C100 = P45 · P56

P45 = 521485688834094616003641826229481656646415453<45>

P56 = 16846429736694498814138730507079319979241737624177166277<56>

Thu Nov 29 14:35:06 2007  Msieve v. 1.30
Thu Nov 29 14:35:06 2007  random seeds: 5e6160f2 130a07ab
Thu Nov 29 14:35:06 2007  factoring 8785172015635305902166850873310561627369223602890592020277003775916249170381081979472941403203278481 (100 digits)
Thu Nov 29 14:35:06 2007  commencing quadratic sieve (100-digit input)
Thu Nov 29 14:35:07 2007  using multiplier of 1
Thu Nov 29 14:35:07 2007  using 64kb Pentium 4 sieve core
Thu Nov 29 14:35:07 2007  sieve interval: 18 blocks of size 65536
Thu Nov 29 14:35:07 2007  processing polynomials in batches of 6
Thu Nov 29 14:35:07 2007  using a sieve bound of 2825051 (102331 primes)
Thu Nov 29 14:35:07 2007  using large prime bound of 423757650 (28 bits)
Thu Nov 29 14:35:07 2007  using double large prime bound of 3379182069851550 (43-52 bits)
Thu Nov 29 14:35:07 2007  using trial factoring cutoff of 52 bits
Thu Nov 29 14:35:07 2007  polynomial 'A' values have 13 factors
Sat Dec  1 08:30:49 2007  102586 relations (23428 full + 79158 combined from 1560356 partial), need 102427
Sat Dec  1 08:30:56 2007  begin with 1583784 relations
Sat Dec  1 08:30:59 2007  reduce to 275743 relations in 14 passes
Sat Dec  1 08:30:59 2007  attempting to read 275743 relations
Sat Dec  1 08:31:11 2007  recovered 275743 relations
Sat Dec  1 08:31:11 2007  recovered 267629 polynomials
Sat Dec  1 08:31:11 2007  attempting to build 102586 cycles
Sat Dec  1 08:31:11 2007  found 102586 cycles in 5 passes
Sat Dec  1 08:31:11 2007  distribution of cycle lengths:
Sat Dec  1 08:31:11 2007     length 1 : 23428
Sat Dec  1 08:31:11 2007     length 2 : 17036
Sat Dec  1 08:31:11 2007     length 3 : 16856
Sat Dec  1 08:31:11 2007     length 4 : 14145
Sat Dec  1 08:31:11 2007     length 5 : 11048
Sat Dec  1 08:31:11 2007     length 6 : 7584
Sat Dec  1 08:31:11 2007     length 7 : 5024
Sat Dec  1 08:31:11 2007     length 9+: 7465
Sat Dec  1 08:31:11 2007  largest cycle: 20 relations
Sat Dec  1 08:31:12 2007  matrix is 102331 x 102586 with weight 6915312 (avg 67.41/col)
Sat Dec  1 08:31:15 2007  filtering completed in 3 passes
Sat Dec  1 08:31:15 2007  matrix is 98799 x 98863 with weight 6691681 (avg 67.69/col)
Sat Dec  1 08:31:16 2007  saving the first 48 matrix rows for later
Sat Dec  1 08:31:16 2007  matrix is 98751 x 98863 with weight 5212412 (avg 52.72/col)
Sat Dec  1 08:31:16 2007  matrix includes 64 packed rows
Sat Dec  1 08:31:16 2007  using block size 21845 for processor cache size 512 kB
Sat Dec  1 08:31:17 2007  commencing Lanczos iteration
Sat Dec  1 08:32:59 2007  lanczos halted after 1563 iterations (dim = 98750)
Sat Dec  1 08:32:59 2007  recovered 16 nontrivial dependencies
Sat Dec  1 08:33:01 2007  prp45 factor: 521485688834094616003641826229481656646415453
Sat Dec  1 08:33:01 2007  prp56 factor: 16846429736694498814138730507079319979241737624177166277
Sat Dec  1 08:33:01 2007  elapsed time 41:57:55

Dec 1, 2007

By Sinitiki Sibata / PFGW

4·1019679-9 is PRP.

November 2007

Nov 30, 2007 (3rd)

By Alfred Reich

101655+1 is divisible by 18802215938788787651629737655497612041<38>

101813+1 is divisible by 1341949101412826358472947603971939<34>

Reference: Factorizations of numbers of the form 10n+1 (Alfred Reich)

Nov 30, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

(19·10161-1)/9 = 2(1)161<162> = 727717 · 384816673 · 674074250329<12> · C136

C136 = P35 · P101

P35 = 14467529402478870760723338650411987<35>

P101 = 77302329134119121600032539311233102902267933504106572342606708487422816772928441334860645111491619777<101>

Nov 30, 2007

By Bruce Dodson

10242+1 is divisible by 209363088773816814667969748813613304559806235889961<51> and cofactor is prime.

Reference: Factoring and Prime Identification (Torbjörn Granlund)

Nov 29, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10158+9 = 4(0)1579<159> = 29 · 617 · C155

C155 = P59 · P97

P59 = 16694516335098246170350962150521377733606416852014894432101<59>

P97 = 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513<97>

Number: n
N=22355110937238026043704241882300340915441792879897166489688705080198960487341418431788967752752473034147431956631084781758229475213770748337338624042921813
  ( 155 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu Nov 29 08:24:10 2007  prp59 factor: 16694516335098246170350962150521377733606416852014894432101
Thu Nov 29 08:24:10 2007  prp97 factor: 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513
Thu Nov 29 08:24:10 2007  elapsed time 01:05:46 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 33.00 hours.
Scaled time: 43.14 units (timescale=1.307).
Factorization parameters were as follows:
name: KA_4_0_157_9
n: 22355110937238026043704241882300340915441792879897166489688705080198960487341418431788967752752473034147431956631084781758229475213770748337338624042921813
skew: 2.95
deg: 5
c5: 1
c0: 225
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1450000)
Primes: RFBsize:216816, AFBsize:216371, largePrimes:7014483 encountered
Relations: rels:6490308, finalFF:490288
Max relations in full relation-set: 28
Initial matrix: 433251 x 490288 with sparse part having weight 34015211.
Pruned matrix : 387237 x 389467 with weight 22902473.
Total sieving time: 31.53 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.22 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10153+9 = 4(0)1529<154> = 211 · 499 · 823 · 7213 · 5983931 · 20484293 · C128

C128 = P34 · P95

P34 = 1674567153955540249123309372823653<34>

P95 = 31178204285060110569074580607563260199102302136786304734413870091585370032227633400052324234081<95>

Nov 28, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

4·10171+9 = 4(0)1709<172> = 4727579 · 42758299609<11> · 70786206663533<14> · 52842317195285609<17> · 1749706642519018677552131<25> · C100

C100 = P44 · P57

P44 = 13309174465738976322573197980572388901369971<44>

P57 = 227171538029579664285228640378502521594404174584065064527<57>

Number: n
N=30234656332859324703546336715738054258309704996708157961949684440936332
94526234496732144750815118717
  ( 100 digits)
Divisors found:

Wed Nov 28 06:36:31 2007  recovered 43 nontrivial dependencies
...
Wed Nov 28 07:11:14 2007  reading relations for dependency 7
...
Wed Nov 28 07:16:43 2007  prp44 factor: 
13309174465738976322573197980572388901369971
Wed Nov 28 07:16:43 2007  prp57 factor: 
227171538029579664285228640378502521594404174584065064527
Wed Nov 28 07:16:43 2007  elapsed time 00:53:58 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.30 hours.
Scaled time: 7.53 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_0_170_9
n: 
3023465633285932470354633671573805425830970499670815796194968444093633294
526234496732144750815118717
skew: 13066.21
# norm 1.20e+14
c5: 13380
c4: -91502224
c3: -7858450792205
c2: -14686422473786386
c1: -36147477295763868464
c0: 769155274794014273908275
# alpha -6.05
Y1: 15220904303
Y0: -11770923922825153852
# Murphy_E 3.35e-09
# M 
9956905416872819849530372527310632673808913467304665376913463743595106352
33511921121477064551418045
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved  special-q in [100000, 800000)
Primes: RFBsize:135072, AFBsize:134812, largePrimes:3453555 encountered
Relations: rels:3414232, finalFF:377182
Max relations in full relation-set: 28
Initial matrix: 269962 x 377182 with sparse part having weight 19839270.
Pruned matrix : 171344 x 172757 with weight 6919700.
Total sieving time: 6.15 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,
26,48,48,2.5,2.5,100000
total time: 6.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(2·10167+7)/9 = (2)1663<167> = 17 · 22549 · 56437 · 85331 · C152

C152 = P58 · P94

P58 = 2871978723164024191549374139558544135462013900057318167591<58>

P94 = 4191401889447764303388864665063780609861896939555630361153238115797687072530286019054001194603<94>

Number: n
N=12037617046723468605626924896371158078923549938485194482958855970507181664139302569091093571951782614912001181491026391397577812391492441451368958711373
  ( 152 digits)
SNFS difficulty: 167 digits.
Divisors found:

Wed Nov 28 16:26:47 2007  prp58 factor: 2871978723164024191549374139558544135462013900057318167591
Wed Nov 28 16:26:47 2007  prp94 factor: 4191401889447764303388864665063780609861896939555630361153238115797687072530286019054001194603
Wed Nov 28 16:26:47 2007  elapsed time 01:44:43 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.04 hours.
Scaled time: 106.55 units (timescale=1.439).
Factorization parameters were as follows:
name: KA_2_166_3
n: 12037617046723468605626924896371158078923549938485194482958855970507181664139302569091093571951782614912001181491026391397577812391492441451368958711373
skew: 0.51
deg: 5
c5: 200
c0: 7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3700001)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:7734112 encountered
Relations: rels:7208772, finalFF:447988
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 73.76 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 74.04 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Nov 28, 2007

By JMB / GMP-ECM

4·10165+9 = 4(0)1649<166> = 19 · 1877 · 8893 · 11427643437022285783<20> · 128867463506675408316022657357<30> · C109

C109 = P39 · P71

P39 = 467807742471873906594101709631462254293<39>

P71 = 18307391061578173853638901084078048550027933080852242492899530687116597<71>

Nov 27, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(5·10162-23)/9 = (5)1613<162> = 916781 · 51222224362217<14> · C143

C143 = P53 · P90

P53 = 88251067479212923009474772487688631800999197025093157<53>

P90 = 134055145824349829678858500491427751894659830463832718793400933405117679808822762144065977<90>

Number: n
N=11830509720080425325375598472836094119415647645200888882018736825250641
682747740385363305803723965653576539279961713632444852447675173179219389
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Wed Nov 28 01:46:13 2007  prp53 factor: 
88251067479212923009474772487688631800999197025093157
Wed Nov 28 01:46:13 2007  prp90 factor: 
1340551458243498296788585004914277518946598304638327187934009334051176798
08822762144065977
Wed Nov 28 01:46:13 2007  elapsed time 01:49:31 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 57.66 hours.
Scaled time: 76.39 units (timescale=1.325).
Factorization parameters were as follows:
name: KA_5_161_3
n: 
1183050972008042532537559847283609411941564764520088888201873682525064168
2747740385363305803723965653576539279961713632444852447675173179219389
skew: 0.54
deg: 5
c5: 500
c0: -23
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:216816, AFBsize:216551, largePrimes:7434136 encountered
Relations: rels:6877587, finalFF:488281
Max relations in full relation-set: 28
Initial matrix: 433433 x 488281 with sparse part having weight 51570740.
Pruned matrix : 409705 x 411936 with weight 36845788.
Total sieving time: 57.40 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 57.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 27, 2007 (3rd)

By Sinkiti Sibata / GGNFS

4·10141+9 = 4(0)1409<142> = 3264208176022063<16> · 1989887208412614157281179<25> · C102

C102 = P38 · P65

P38 = 12560245906602427344287633654384461339<38>

P65 = 49029282824428429410597115467691293631272803877265436025347251103<65>

Number: 40009_141
N=615819848899179877938710121407036005167041262827473023425282772740726134822493088078335262461028606917
  ( 102 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=12560245906602427344287633654384461339 (pp38)
 r2=49029282824428429410597115467691293631272803877265436025347251103 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 8.54 hours.
Scaled time: 17.10 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_141
n: 615819848899179877938710121407036005167041262827473023425282772740726134822493088078335262461028606917
m: 10000000000000000000000000000
c5: 40
c0: 9
skew: 0.74
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1550001)
Primes: RFBsize:100021, AFBsize:99568, largePrimes:2682501 encountered
Relations: rels:2667799, finalFF:280425
Max relations in full relation-set: 28
Initial matrix: 199656 x 280425 with sparse part having weight 23554506.
Pruned matrix : 173823 x 174885 with weight 12458201.
Total sieving time: 8.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 8.54 hours.
 --------- CPU info (if available) ----------

4·10135+9 = 4(0)1349<136> = 4432543729<10> · 350104414826237<15> · C112

C112 = P32 · P34 · P47

P32 = 50076108520827966913691944342129<32>

P34 = 4390119913201648970056724078503841<34>

P47 = 11724718391352138352586053521568560187634367997<47>

Number: 40009_135
N=25775635121078719114580793852241494535899517591251721059647750320822687095
16545156309460784839303831716228099533
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=50076108520827966913691944342129 (pp32)
 r2=4390119913201648970056724078503841 (pp34)
 r3=11724718391352138352586053521568560187634367997 (pp47)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.32 hours.
Scaled time: 12.66 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_135
n:
2577563512107871911458079385224149453589951759125172105964775032082268709516
545156309460784839303831716228099533
m: 1000000000000000000000000000
c5: 4
c0: 9
skew: 1.18
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64053, largePrimes:1576550 encountered
Relations: rels:1619234, finalFF:212791
Max relations in full relation-set: 28
Initial matrix: 142615 x 212791 with sparse part having weight 15765979.
Pruned matrix : 120857 x 121634 with weight 7446674.
Total sieving time: 6.12 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.32 hours.
 --------- CPU info (if available) ----------

Nov 27, 2007 (2nd)

By Sinkiti Sibata / GGNFS

4·10145+9 = 4(0)1449<146> = 7 · 23 · 16196138573250129419<20> · 270390616492056889150461299<27> · C98

C98 = P40 · P59

P40 = 1605173021880918410125104138533069730893<40>

P59 = 35343468163557001022907513872788192718182385124531802470493<59>

Number: 40009_145
N=56732381595848825220588411669623668386053143977130622031227669941751645504214351435599936083040249
  ( 98 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=1605173021880918410125104138533069730893 (pp40)
 r2=35343468163557001022907513872788192718182385124531802470493 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 11.67 hours.
Scaled time: 23.46 units (timescale=2.010).
Factorization parameters were as follows:
name: 40009_145
n: 56732381595848825220588411669623668386053143977130622031227669941751645504214351435599936083040249
m: 100000000000000000000000000000
c5: 4
c0: 9
skew: 1.18
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1950001)
Primes: RFBsize:100021, AFBsize:100078, largePrimes:2670477 encountered
Relations: rels:2616911, finalFF:229148
Max relations in full relation-set: 28
Initial matrix: 200163 x 229148 with sparse part having weight 21999475.
Pruned matrix : 191898 x 192962 with weight 16653697.
Total sieving time: 11.09 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 11.67 hours.
 --------- CPU info (if available) ----------

Nov 27, 2007

By Robert Backstrom / GGNFS, Msieve

4·10137+9 = 4(0)1369<138> = 47 · 210996161 · 27663076039007<14> · C115

C115 = P48 · P68

P48 = 144128879329630272184991648078450696106391196441<48>

P68 = 10116635425360137333667412655105196323996222926944429943963917753921<68>

Number: n
N=1458099326443594054045323972411079454526604785894103274387642346249087765340142012336087436548886974989376608995161
  ( 115 digits)
SNFS difficulty: 137 digits.
Divisors found:

Tue Nov 27 03:12:55 2007  prp48 factor: 144128879329630272184991648078450696106391196441
Tue Nov 27 03:12:55 2007  prp68 factor: 10116635425360137333667412655105196323996222926944429943963917753921
Tue Nov 27 03:12:55 2007  elapsed time 00:26:19 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 6.20 hours.
Scaled time: 8.01 units (timescale=1.293).
Factorization parameters were as follows:
name: KA_4_0_136_9
n: 1458099326443594054045323972411079454526604785894103274387642346249087765340142012336087436548886974989376608995161
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 2000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 800000)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:6288087 encountered
Relations: rels:5665178, finalFF:314490
Max relations in full relation-set: 28
Initial matrix: 228211 x 314490 with sparse part having weight 25079773.
Pruned matrix : 185311 x 186516 with weight 11952601.
Total sieving time: 6.00 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.20 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10146+9 = 4(0)1459<147> = 220681 · 486209806553<12> · C130

C130 = P39 · P91

P39 = 764412203911204700836054966106935734613<39>

P91 = 4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501<91>

Number: n
N=3727960774017682077509562283847137837199147716353152979632032702775892834651891935886292568866270350371012428874815801170002379113
  ( 130 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=764412203911204700836054966106935734613 (pp39)
 r2=4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501 (pp91)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 10.26 hours.
Scaled time: 12.27 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_0_145_9
n: 3727960774017682077509562283847137837199147716353152979632032702775892834651891935886292568866270350371012428874815801170002379113
type: snfs
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1150001)
Primes: RFBsize:148933, AFBsize:148405, largePrimes:5927738 encountered
Relations: rels:5289921, finalFF:359602
Max relations in full relation-set: 28
Initial matrix: 297405 x 359602 with sparse part having weight 20581544.
Pruned matrix : 247886 x 249437 with weight 11630633.
Total sieving time: 8.79 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.21 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 10.26 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 26, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(102153+53)/9 is prime.

Nov 26, 2007 (2nd)

By Sinkiti Sibata / GGNFS, Msieve

4·10126+9 = 4(0)1259<127> = 132 · 1093 · 157478185310284045321<21> · C102

C102 = P32 · P70

P32 = 51219530045909995936125110786993<32>

P70 = 2684708475243401264102954877320619544959453611256556529626076156285909<70>

Number: 40009_126
N=137509506412238603536864415063538192494400116628332569921903945385237808208535294351993306538906381637
  ( 102 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=51219530045909995936125110786993 (pp32)
 r2=2684708475243401264102954877320619544959453611256556529626076156285909 (pp70)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.80 hours.
Scaled time: 5.61 units (timescale=2.003).
Factorization parameters were as follows:
name: 40009_126
n: 137509506412238603536864415063538192494400116628332569921903945385237808208535294351993306538906381637
m: 10000000000000000000000000
c5: 40
c0: 9
skew: 0.74
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63733, largePrimes:2383131 encountered
Relations: rels:2755788, finalFF:468753
Max relations in full relation-set: 28
Initial matrix: 112898 x 468753 with sparse part having weight 45593086.
Pruned matrix : 76412 x 77040 with weight 8664530.
Total sieving time: 2.66 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.80 hours.
 --------- CPU info (if available) ----------

4·10128+9 = 4(0)1279<129> = 1993 · 51913 · 1430797079340329352472921<25> · C97

C97 = P48 · P50

P48 = 181803558476376236283955641729897094029004670893<48>

P50 = 14862646249026576411818998493115073085499220973317<50>

Number: 40009_128
N=2702081976448597109558698566520468643612755318410534419392185730772033180107476795736942719562081
  ( 97 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=181803558476376236283955641729897094029004670893 (pp48)
 r2=14862646249026576411818998493115073085499220973317 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.78 hours.
Scaled time: 7.55 units (timescale=1.997).
Factorization parameters were as follows:
name: 40009_128
n: 2702081976448597109558698566520468643612755318410534419392185730772033180107476795736942719562081
m: 20000000000000000000000000
c5: 125
c0: 9
skew: 0.59
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:1557590 encountered
Relations: rels:1625431, finalFF:234022
Max relations in full relation-set: 28
Initial matrix: 128110 x 234022 with sparse part having weight 14826718.
Pruned matrix : 98552 x 99256 with weight 5347992.
Total sieving time: 3.66 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.78 hours.
 --------- CPU info (if available) ----------

4·10129+9 = 4(0)1289<130> = 19 · 13921 · 42456366769<11> · 1961107985919825167<19> · C96

C96 = P32 · P64

P32 = 90496029963707513725625363116699<32>

P64 = 2007068038467510110982557191892561779029831762757164209225700983<64>

Number: 40009_129
N=181631689348355459790962688701929834427428033812142412776081374439007954060590809771261908015117
  ( 96 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=90496029963707513725625363116699 (pp32)
 r2=2007068038467510110982557191892561779029831762757164209225700983 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.35 hours.
Scaled time: 8.78 units (timescale=2.016).
Factorization parameters were as follows:
name: 40009_129
n: 181631689348355459790962688701929834427428033812142412776081374439007954060590809771261908015117
m: 100000000000000000000000000
c5: 2
c0: 45
skew: 1.86
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:1536620 encountered
Relations: rels:1564442, finalFF:196332
Max relations in full relation-set: 28
Initial matrix: 128109 x 196332 with sparse part having weight 14524685.
Pruned matrix : 109268 x 109972 with weight 6465733.
Total sieving time: 4.20 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.35 hours.
 --------- CPU info (if available) ----------

4·10133+9 = 4(0)1329<134> = 7 · 14039910954930703<17> · C117

C117 = P54 · P64

P54 = 212045331507039776360742002829387808898620546351104409<54>

P64 = 1919414992157459171757261776221197366678153779688615271444343881<64>

Number: 40009_133
N=407002988311610582561227888701054777787770001367652789611232968795378225157190752222575768698744823864819960731271329
  ( 117 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=212045331507039776360742002829387808898620546351104409 (pp54)
 r2=1919414992157459171757261776221197366678153779688615271444343881 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.87 hours.
Scaled time: 11.73 units (timescale=1.997).
Factorization parameters were as follows:
name: 40009_133
n: 407002988311610582561227888701054777787770001367652789611232968795378225157190752222575768698744823864819960731271329
m: 200000000000000000000000000
c5: 125
c0: 9
skew: 0.59
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64093, largePrimes:1612445 encountered
Relations: rels:1679680, finalFF:236889
Max relations in full relation-set: 28
Initial matrix: 142657 x 236889 with sparse part having weight 18018688.
Pruned matrix : 114736 x 115513 with weight 7558893.
Total sieving time: 5.69 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.87 hours.
 --------- CPU info (if available) ----------

4·10147+9 = 4(0)1469<148> = 19 · 4057594903<10> · 44338326960703<14> · 256008644002393841860575255628769<33> · C91

C91 = P39 · P53

P39 = 404664799012214157417672549706061106703<39>

P53 = 11295575051062064761509401409725052595688718501423797<53>

Mon Nov 26 07:03:06 2007  Msieve v. 1.28
Mon Nov 26 07:03:06 2007  random seeds: 806018b8 fde7d0ee
Mon Nov 26 07:03:06 2007  factoring 4570921607765411105037991565791212407235592613498883380616910429784125813855670791040411291 (91 digits)
Mon Nov 26 07:03:07 2007  commencing quadratic sieve (91-digit input)
Mon Nov 26 07:03:07 2007  using multiplier of 3
Mon Nov 26 07:03:07 2007  using 64kb Pentium 2 sieve core
Mon Nov 26 07:03:07 2007  sieve interval: 18 blocks of size 65536
Mon Nov 26 07:03:07 2007  processing polynomials in batches of 6
Mon Nov 26 07:03:07 2007  using a sieve bound of 1719869 (64508 primes)
Mon Nov 26 07:03:07 2007  using large prime bound of 165107424 (27 bits)
Mon Nov 26 07:03:07 2007  using double large prime bound of 619412223763104 (42-50 bits)
Mon Nov 26 07:03:07 2007  using trial factoring cutoff of 50 bits
Mon Nov 26 07:03:07 2007  polynomial 'A' values have 12 factors
Mon Nov 26 18:54:49 2007  64777 relations (16555 full + 48222 combined from 769817 partial), need 64604
Mon Nov 26 18:54:55 2007  begin with 786372 relations
Mon Nov 26 18:55:11 2007  reduce to 163091 relations in 10 passes
Mon Nov 26 18:55:11 2007  attempting to read 163091 relations
Mon Nov 26 18:55:23 2007  recovered 163091 relations
Mon Nov 26 18:55:23 2007  recovered 145695 polynomials
Mon Nov 26 18:55:45 2007  attempting to build 64777 cycles
Mon Nov 26 18:55:45 2007  found 64777 cycles in 6 passes
Mon Nov 26 18:55:48 2007  distribution of cycle lengths:
Mon Nov 26 18:55:48 2007     length 1 : 16555
Mon Nov 26 18:55:48 2007     length 2 : 11833
Mon Nov 26 18:55:48 2007     length 3 : 11147
Mon Nov 26 18:55:48 2007     length 4 : 8679
Mon Nov 26 18:55:48 2007     length 5 : 6323
Mon Nov 26 18:55:48 2007     length 6 : 4272
Mon Nov 26 18:55:48 2007     length 7 : 2648
Mon Nov 26 18:55:48 2007     length 9+: 3320
Mon Nov 26 18:55:48 2007  largest cycle: 18 relations
Mon Nov 26 18:55:49 2007  matrix is 64508 x 64777 with weight 4021806 (avg 62.09/col)
Mon Nov 26 18:55:53 2007  filtering completed in 3 passes
Mon Nov 26 18:55:53 2007  matrix is 61073 x 61137 with weight 3812110 (avg 62.35/col)
Mon Nov 26 18:55:56 2007  saving the first 48 matrix rows for later
Mon Nov 26 18:55:56 2007  matrix is 61025 x 61137 with weight 3042466 (avg 49.76/col)
Mon Nov 26 18:55:56 2007  matrix includes 64 packed rows
Mon Nov 26 18:55:56 2007  using block size 10922 for processor cache size 256 kB
Mon Nov 26 18:55:58 2007  commencing Lanczos iteration
Mon Nov 26 18:59:10 2007  lanczos halted after 966 iterations
Mon Nov 26 18:59:11 2007  recovered 16 nontrivial dependencies
Mon Nov 26 18:59:37 2007  prp39 factor: 404664799012214157417672549706061106703
Mon Nov 26 18:59:37 2007  prp53 factor: 11295575051062064761509401409725052595688718501423797
Mon Nov 26 18:59:37 2007  elapsed time 11:56:31

Nov 26, 2007

By Robert Backstrom / GGNFS, Msieve

4·10110+9 = 4(0)1099<111> = 113 · 2393 · 251419167001<12> · C94

C94 = P36 · P59

P36 = 165181848872234857617062189249532241<36>

P59 = 35618706443028798016568330143685321380313564206887456692761<59>

Number: n
N=5883563784696880916434650652243177524072887965464968204171469084560963632896817817164100807401
  ( 94 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=165181848872234857617062189249532241 (pp36)
 r2=35618706443028798016568330143685321380313564206887456692761 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.95 hours.
Scaled time: 1.13 units (timescale=1.193).
Factorization parameters were as follows:
name: KA_4_0_109_9
n: 5883563784696880916434650652243177524072887965464968204171469084560963632896817817164100807401
type: snfs
skew: 1.18
deg: 5
c5: 4
c0: 9
m: 10000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:64053, largePrimes:3675896 encountered
Relations: rels:3189891, finalFF:232392
Max relations in full relation-set: 28
Initial matrix: 128068 x 232392 with sparse part having weight 9272010.
Pruned matrix : 64275 x 64979 with weight 2367167.
Total sieving time: 0.80 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.4,2.4,50000
total time: 0.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10119+9 = 4(0)1189<120> = 59011 · C115

C115 = P44 · P72

P44 = 10299709529696676595537272509874674618354731<44>

P72 = 658115379703367141596436109463234164314654145602057711013672694021719049<72>

Number: n
N=6778397247970717323888766501160800528714985341715951263323787090542441239768856653844198539255393062310416701970819
  ( 115 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=10299709529696676595537272509874674618354731 (pp44)
 r2=658115379703367141596436109463234164314654145602057711013672694021719049 (pp72)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.09 hours.
Scaled time: 2.49 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_4_0_118_9
n: 6778397247970717323888766501160800528714985341715951263323787090542441239768856653844198539255393062310416701970819
type: snfs
skew: 1.86
deg: 5
c5: 2
c0: 45
m: 1000000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 240001)
Primes: RFBsize:78498, AFBsize:78531, largePrimes:4067301 encountered
Relations: rels:3437845, finalFF:191917
Max relations in full relation-set: 28
Initial matrix: 157094 x 191917 with sparse part having weight 8634183.
Pruned matrix : 126308 x 127157 with weight 4290229.
Total sieving time: 1.70 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.17 hours.
Total square root time: 0.12 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(52·10164-7)/9 = 5(7)164<165> = 29 · 7019 · 6320886474787<13> · C147

C147 = P52 · P96

P52 = 1253831070899856312688601931720582966577047750139261<52>

P96 = 358154634908081150423440098044503617839531497495445248785010282856127665013429077944232929344361<96>

Number: n
N=449065409434546449622971187681183740755523201415900451788832840460807324862141335905611317885561982939064087542226259352648468932390312211175057221
  ( 147 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Nov 26 16:37:58 2007  prp52 factor: 1253831070899856312688601931720582966577047750139261
Mon Nov 26 16:37:58 2007  prp96 factor: 358154634908081150423440098044503617839531497495445248785010282856127665013429077944232929344361
Mon Nov 26 16:37:58 2007  elapsed time 02:02:22 (Msieve 1.30)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 108.78 hours.
Scaled time: 140.77 units (timescale=1.294).
Factorization parameters were as follows:
name: KA_5_7_164
n: 449065409434546449622971187681183740755523201415900451788832840460807324862141335905611317885561982939064087542226259352648468932390312211175057221
skew: 1.06
deg: 5
c5: 26
c0: -35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3600001)
Primes: RFBsize:230209, AFBsize:230477, largePrimes:7720364 encountered
Relations: rels:7181991, finalFF:477241
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 108.43 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 108.78 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

4·10131+9 = 4(0)1309<132> = 619 · 194167 · 14543527 · C117

C117 = P44 · P73

P44 = 80094272947449979071432758202536808045156517<44>

P73 = 2857082077051308573674020837361541499660528541802562865615658481450429087<73>

Number: n
N=228835911712614820963407007506081825552432657431830205371716856226255647416792245683256227303671261195144781724409979
  ( 117 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=80094272947449979071432758202536808045156517 (pp44)
 r2=2857082077051308573674020837361541499660528541802562865615658481450429087 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 3.68 hours.
Scaled time: 4.40 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_130_9
n: 228835911712614820963407007506081825552432657431830205371716856226255647416792245683256227303671261195144781724409979
type: snfs
skew: 0.74
deg: 5
c5: 40
c0: 9
m: 100000000000000000000000000
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 460001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:4179030 encountered
Relations: rels:3531412, finalFF:259869
Max relations in full relation-set: 28
Initial matrix: 227794 x 259869 with sparse part having weight 7780095.
Pruned matrix : 168810 x 170012 with weight 4136104.
Total sieving time: 3.28 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.26 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.2,2.2,50000
total time: 3.68 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10117+9 = 4(0)1169<118> = 163890451 · 119008224119929<15> · C96

C96 = P34 · P63

P34 = 1049848161996414833607686052033851<34>

P63 = 195345258444219449654150537877637812726731604913236518703820721<63>

Number: n
N=205082860532378423488589379837991228596967004928112301824211634341274075328421533654926527226571
  ( 96 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=1049848161996414833607686052033851 (pp34)
 r2=195345258444219449654150537877637812726731604913236518703820721 (pp63)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.75 hours.
Scaled time: 2.09 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_4_0_116_9
n: 205082860532378423488589379837991228596967004928112301824211634341274075328421533654926527226571
type: snfs
skew: 0.94
deg: 5
c5: 25
c0: 18
m: 200000000000000000000000
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 220001)
Primes: RFBsize:78498, AFBsize:78241, largePrimes:3946046 encountered
Relations: rels:3317892, finalFF:182434
Max relations in full relation-set: 28
Initial matrix: 156803 x 182434 with sparse part having weight 7590913.
Pruned matrix : 131548 x 132396 with weight 4205854.
Total sieving time: 1.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.18 hours.
Total square root time: 0.11 hours, sqrts: 5.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.4,2.4,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 25, 2007 (5th)

By Jo Yeong Uk / GGNFS

4·10118+9 = 4(0)1179<119> = C119

C119 = P52 · P68

P52 = 3728574790867178284745181738866780429302431068160529<52>

P68 = 10727959674558907354142285722781332734722136495462711094331511744121<68>

Number: 40009_118
N=40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=3728574790867178284745181738866780429302431068160529 (pp52)
 r2=10727959674558907354142285722781332734722136495462711094331511744121 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.90 hours.
Scaled time: 1.93 units (timescale=2.144).
Factorization parameters were as follows:
n: 40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000
c5: 1
c0: 225
skew: 2.95
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49111, largePrimes:1886445 encountered
Relations: rels:1942478, finalFF:199895
Max relations in full relation-set: 28
Initial matrix: 98273 x 199895 with sparse part having weight 17093793.
Pruned matrix : 77103 x 77658 with weight 4340439.
Total sieving time: 0.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407675)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.08 BogoMIPS).

Nov 25, 2007 (4th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(4·10164-7)/3 = 1(3)1631<165> = 983 · 6424123 · 8002014907<10> · C145

C145 = P41 · P44 · P61

P41 = 38845079894049413226636666173926767146741<41>

P44 = 37241278615967782300259863150917251444291063<44>

P61 = 1823943632731313508599180109626448102079347834135801509470639<61>

Number: n
N=67925993006367260173084306432034998810393910129667030593595794518859702769290352728359242093103768599257
  ( 104 digits)
Divisors found:

Mon Nov 26 00:08:03 2007  prp44 factor: 37241278615967782300259863150917251444291063
Mon Nov 26 00:08:03 2007  prp61 factor: 1823943632731313508599180109626448102079347834135801509470639
Mon Nov 26 00:08:03 2007  elapsed time 01:07:26 (Msieve 1.30)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 18.97 hours.
Scaled time: 22.69 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_1_3_163_1
n: 67925993006367260173084306432034998810393910129667030593595794518859702769290352728359242093103768599257
skew: 14548.83
# norm 4.31e+14
c5: 15540
c4: 662881441
c3: -30284510564936
c2: -70420841882984262
c1: 1380105811745476751310
c0: 213375504826872901606500
# alpha -5.63
Y1: 56183257309
Y0: -84745088989414396159
# Murphy_E 1.94e-09
# M 35605800172212779601640616997983630603863264454095218451097658761114576612953147801228187028086397273557
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1200000)
Primes: RFBsize:169511, AFBsize:169993, largePrimes:4092500 encountered
Relations: rels:4001895, finalFF:381407
Max relations in full relation-set: 28
Initial matrix: 339591 x 381407 with sparse part having weight 23210863.
Pruned matrix : 297455 x 299216 with weight 14265146.
Total sieving time: 18.76 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 18.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 25, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(22·102159-31)/9 is prime.

Nov 25, 2007 (2nd)

By matsui / GMP-ECM

(5·10187-23)/9 = (5)1863<187> = 3 · C187

C187 = P34 · C154

P34 = 1249569676018218532056891295863517<34>

C154 = [1481991670726852801036337564124989580909663768841067210637083024250974479404992726846367777814579781927851301822010278319654383652691909116064846052888903<154>]

Nov 25, 2007

The factor table of 400...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Nov 24, 2007 (4th)

By matsui / GMP-ECM

(2·10189+61)/9 = (2)1889<189> = 31 · 107 · C185

C185 = P36 · C149

P36 = 927349548463379812942637190276565777<36>

C149 = [72243462018069324109887983093635000589160560432323063168326829250562665832911989665414796383191130798805708121654081515508917870686847094978760612881<149>]

Nov 24, 2007 (3rd)

By Sinkiti Sibata / GGNFS

4·10159-9 = 3(9)1581<160> = 13 · 199 · 2130173 · 64929089 · 24131072597<11> · 952589489681209<15> · C117

C117 = P44 · P73

P44 = 74079493501806378527450601403663790436099271<44>

P73 = 6564912794659200412500871081575072082513907943647734630671406825808638043<73>

Number: 39991_159
N=486325414711881789179913696860213450928824568538724820830782157801328627106326427776063177946853247455134006055166653
  ( 117 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=74079493501806378527450601403663790436099271 (pp44)
 r2=6564912794659200412500871081575072082513907943647734630671406825808638043 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 77.01 hours.
Scaled time: 51.98 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_159
n: 486325414711881789179913696860213450928824568538724820830782157801328627106326427776063177946853247455134006055166653
m: 100000000000000000000000000000000
c5: 2
c0: -45
skew: 1.86
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:283407, largePrimes:5742291 encountered
Relations: rels:5806571, finalFF:681486
Max relations in full relation-set: 28
Initial matrix: 566618 x 681486 with sparse part having weight 45436461.
Pruned matrix : 483086 x 485983 with weight 31035378.
Total sieving time: 66.61 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 9.87 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 77.01 hours.
 --------- CPU info (if available) ----------

Nov 24, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(32·10162-23)/9 = 3(5)1613<163> = 79 · 353 · 10831 · 2304545063<10> · C145

C145 = P59 · P87

P59 = 11418294572176870102030727526262175468766886077048774464453<59>

P87 = 447353324129822631187220179321823753744991839539223628912706731724334093004388243879691<87>

Number: n
N=5108012032756833801090420940354909442473568947558897114792618109230650012286452899825548147198860702329357055515312908368542021336328083488124023
  ( 145 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sat Nov 24 02:02:22 2007  prp59 factor: 11418294572176870102030727526262175468766886077048774464453
Sat Nov 24 02:02:22 2007  prp87 factor: 447353324129822631187220179321823753744991839539223628912706731724334093004388243879691
Sat Nov 24 02:02:22 2007  elapsed time 01:45:11 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.69 hours.
Scaled time: 59.13 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_3_5_161_3
n: 5108012032756833801090420940354909442473568947558897114792618109230650012286452899825548147198860702329357055515312908368542021336328083488124023
skew: 0.75
deg: 5
c5: 100
c0: -23
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:216816, AFBsize:217116, largePrimes:7231197 encountered
Relations: rels:6696431, finalFF:498681
Max relations in full relation-set: 28
Initial matrix: 433996 x 498681 with sparse part having weight 44598884.
Pruned matrix : 388932 x 391165 with weight 29632951.
Total sieving time: 44.45 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.69 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 24, 2007

By Yousuke Koide

101749+1 is divisible by 1107787169378395599401257233239538397<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 22, 2007 (3rd)

By Robert Backstrom / GGNFS

(5·10161-41)/9 = (5)1601<161> = 32 · 68196269 · 15233617008611<14> · C139

C139 = P50 · P90

P50 = 16440538531421432078827696011643851667074412930711<50>

P90 = 361414271751827151353177663968973256352972286750998069364546030733668065300904591141591911<90>

Number: n
N=5941845260541530719336256541742219880917628765154081949520232045063493647492461579811333302877434609513809414777144042637306700263481078721
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Nov 22 18:28:14 2007  prp50 factor: 16440538531421432078827696011643851667074412930711
Thu Nov 22 18:28:14 2007  prp90 factor: 361414271751827151353177663968973256352972286750998069364546030733668065300904591141591911
Thu Nov 22 18:28:14 2007  elapsed time 02:27:05 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 48.96 hours.
Scaled time: 58.56 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_5_160_1
n: 5941845260541530719336256541742219880917628765154081949520232045063493647492461579811333302877434609513809414777144042637306700263481078721
type: snfs
skew: 0.96
deg: 5
c5: 50
c0: -41
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:250567, largePrimes:7178290 encountered
Relations: rels:6709445, finalFF:607497
Max relations in full relation-set: 28
Initial matrix: 500782 x 607497 with sparse part having weight 34954359.
Pruned matrix : 408203 x 410770 with weight 20239156.
Total sieving time: 48.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 48.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 22, 2007 (2nd)

By Jo Yeong Uk / GGNFS

8·10181-7 = 7(9)1803<182> = C182

C182 = P48 · P135

P48 = 216148982655435929699114314027715477553384103519<48>

P135 = 370115089218478356758654535607364677329573694364240237802979699121028544430300307143621280593966654455367748978194923424449434078433447<135>

Number: 79993_181
N=79999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 182 digits)
SNFS difficulty: 182 digits.
Divisors found:
 r1=216148982655435929699114314027715477553384103519 (pp48)
 r2=370115089218478356758654535607364677329573694364240237802979699121028544430300307143621280593966654455367748978194923424449434078433447 (pp135)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 248.23 hours.
Scaled time: 529.98 units (timescale=2.135).
Factorization parameters were as follows:
n: 79999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 2000000000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 9100001)
Primes: RFBsize:664579, AFBsize:665480, largePrimes:11067378 encountered
Relations: rels:11387297, finalFF:1536217
Max relations in full relation-set: 28
Initial matrix: 1330124 x 1536217 with sparse part having weight 93212688.
Pruned matrix : 1143509 x 1150223 with weight 64319333.
Total sieving time: 238.30 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 9.59 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,182,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 248.23 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 22, 2007

By Yousuke Koide

101079+1 is divisible by 12872791513686398145408033283561<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 21, 2007 (2nd)

By Robert Backstrom / GGNFS

2·10162+9 = 2(0)1619<163> = 11 · 113 · 2081 · 2657 · C153

C153 = P47 · P107

P47 = 27122851242050836906551105038309233622985323233<47>

P107 = 10729015936115722072912979992395528159519097329221924474233456905349010539193520511048503243582233656097483<107>

Number: n
N=291001503208859535061564265651302436861094295924708253361979542649323701281159624158760359646784825637743314939558512723565886104522114020560808112722539
  ( 153 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=27122851242050836906551105038309233622985323233 (pp47)
 r2=10729015936115722072912979992395528159519097329221924474233456905349010539193520511048503243582233656097483 (pp107)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 36.87 hours.
Scaled time: 48.12 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_2_0_161_9
n: 291001503208859535061564265651302436861094295924708253361979542649323701281159624158760359646784825637743314939558512723565886104522114020560808112722539
skew: 1.08
deg: 5
c5: 25
c0: 36
m: 200000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1550001)
Primes: RFBsize:230209, AFBsize:230472, largePrimes:7089581 encountered
Relations: rels:6599696, finalFF:530658
Max relations in full relation-set: 28
Initial matrix: 460745 x 530658 with sparse part having weight 35163360.
Pruned matrix : 401897 x 404264 with weight 22662170.
Total sieving time: 33.35 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.15 hours.
Total square root time: 0.12 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 36.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 21, 2007

By Sinkiti Sibata / GGNFS

4·10151-9 = 3(9)1501<152> = 31 · 5519 · 371213 · 1158569 · 54827975693<11> · 85431185431<11> · C114

C114 = P48 · P66

P48 = 683451293547552766493247508223331705485919834283<48>

P66 = 169811308556460662649467994337463527761352643619555931552038754243<66>

Number: 39991_151
N=116057758491915655173344214309582763419377248961382375191490426117901521122776418083702863212981536767552323112769
  ( 114 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=683451293547552766493247508223331705485919834283 (pp48)
 r2=169811308556460662649467994337463527761352643619555931552038754243 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 27.46 hours.
Scaled time: 18.54 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_151
n: 116057758491915655173344214309582763419377248961382375191490426117901521122776418083702863212981536767552323112769
m: 1000000000000000000000000000000
c5: 40
c0: -9
skew: 0.74
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175758, largePrimes:5240539 encountered
Relations: rels:5083135, finalFF:433587
Max relations in full relation-set: 28
Initial matrix: 352127 x 433587 with sparse part having weight 34832429.
Pruned matrix : 302527 x 304351 with weight 21729699.
Total sieving time: 23.97 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.16 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 27.46 hours.
 --------- CPU info (if available) ----------

4·10185+3 = 4(0)1843<186> = 59 · C184

C184 = P68 · P117

P68 = 11020580464970018963281153740355391062570795450373519356122648057289<68>

P117 = 615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353<117>

Number: 40003_185
N=6779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661017
  ( 184 digits)
SNFS difficulty: 185 digits.
Divisors found:
 r1=11020580464970018963281153740355391062570795450373519356122648057289 (pp68)
 r2=615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353 (pp117)
Version: GGNFS-0.77.1-20060513-k8
Total time: 676.35 hours.
Scaled time: 1350.68 units (timescale=1.997).
Factorization parameters were as follows:
name: 40003_185
n: 6779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661017
m: 10000000000000000000000000000000000000
c5: 4
c0: 3
skew: 0.94
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11400001)
Primes: RFBsize:501962, AFBsize:502056, largePrimes:6651477 encountered
Relations: rels:7134496, finalFF:1151991
Max relations in full relation-set: 28
Initial matrix: 1004085 x 1151991 with sparse part having weight 85952580.
Pruned matrix : 882609 x 887693 with weight 67545486.
Total sieving time: 663.68 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 11.72 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 676.35 hours.
 --------- CPU info (if available) ----------

Nov 20, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

4·10161-9 = 3(9)1601<162> = 53 · C160

C160 = P41 · P120

P41 = 21806825430466113390135407080568754712841<41>

P120 = 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267<120>

Number: n
N=7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Nov 20 21:05:11 2007  prp41 factor: 21806825430466113390135407080568754712841
Tue Nov 20 21:05:11 2007  prp120 factor: 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267
Tue Nov 20 21:05:11 2007  elapsed time 01:33:02 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 32.27 hours.
Scaled time: 42.73 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_3_9_160_1
n: 7547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
skew: 0.74
deg: 5
c5: 40
c0: -9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:216816, AFBsize:216336, largePrimes:7059026 encountered
Relations: rels:6542964, finalFF:512046
Max relations in full relation-set: 28
Initial matrix: 433219 x 512046 with sparse part having weight 41365043.
Pruned matrix : 370773 x 373003 with weight 24932021.
Total sieving time: 32.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 32.27 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 20, 2007 (2nd)

By matsui / GMP-ECM

(2·10186-17)/3 = (6)1851<186> = 577 · C184

C184 = P35 · C149

P35 = 56045655546039900196398563598407527<35>

C149 = [20615362435591879186624607699826768353984778680961983009624827499187120028491903918962048793936194257434728540858949740169821440639266289814167775059<149>]

Nov 20, 2007

By JMB / GMP-ECM

9·10200+7 = 9(0)1997<201> = 16363 · 1185871 · 11041256557141927631<20> · C172

C172 = P40 · P133

P40 = 1129520353150946514870638937980393951891<40>

P133 = 3719029026601584878459985815308542356310526920113885973087730339593263375620616238307141131837874615521876099561714963205165591240279<133>

Nov 19, 2007 (2nd)

By Robert Backstrom / GGNFS, GMP-ECM, Msieve

4·10147-9 = 3(9)1461<148> = 13 · 89 · 6167403400563579766175239<25> · C120

C120 = P43 · P77

P43 = 9859117276170965916528849893551257536137453<43>

P77 = 56857301497661450675385390309929156870609092238968154609890852061865551467889<77>

Number: n
N=560562803472055342614818809179881640621418269258805647401713026165934061851143305328751575837660941339806278907419746717
  ( 120 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=9859117276170965916528849893551257536137453 (pp43)
 r2=56857301497661450675385390309929156870609092238968154609890852061865551467889 (pp77)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 16.03 hours.
Scaled time: 19.11 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_3_9_146_1
n: 560562803472055342614818809179881640621418269258805647401713026165934061851143305328751575837660941339806278907419746717
type: snfs
skew: 0.94
deg: 5
c5: 25
c0: -18
m: 200000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1800001)
Primes: RFBsize:148933, AFBsize:148625, largePrimes:6504113 encountered
Relations: rels:5821520, finalFF:335213
Max relations in full relation-set: 28
Initial matrix: 297622 x 335213 with sparse part having weight 24954157.
Pruned matrix : 280576 x 282128 with weight 18024050.
Total sieving time: 13.38 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.30 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 16.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

2·10158+9 = 2(0)1579<159> = 11 · 41 · 97 · 4773739 · 7061641 · C141

C141 = P34 · P107

P34 = 3675342336556885802003207981173427<34>

P107 = 36899426515186775228625677333483856599631170454625200580800988523050776047130897857948345990003506238466139<107>

(14·10166-41)/9 = 1(5)1651<167> = 17 · 2011 · C162

C162 = P32 · P40 · P45 · P47

P32 = 35081134283933574559653611257097<32>

P40 = 2728630078335383137189177941861782066861<40>

P45 = 126411714129835466690844912764467931579339687<45>

P47 = 37602690897693034145575177417896418231525935887<47>

Number: n
N=12970326457624057370940093292765884024967210652070161540053382611780691229396033766335056809054710948583510049684525069811157738709
  ( 131 digits)
SNFS difficulty: 167 digits.
Divisors found:

Mon Nov 19 08:29:02 2007  prp40 factor: 2728630078335383137189177941861782066861
Mon Nov 19 08:29:02 2007  prp45 factor: 126411714129835466690844912764467931579339687
Mon Nov 19 08:29:02 2007  prp47 factor: 37602690897693034145575177417896418231525935887
Mon Nov 19 08:29:02 2007  elapsed time 03:38:46 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 212.15 hours.
Scaled time: 254.37 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_1_5_165_1

n: 12970326457624057370940093292765884024967210652070161540053382611780691229396033766335056809054710948583510049684525069811157738709

# n: 455013764166366032572485317680859846010341812839838405111754630577574971642892197488974041464754308817841739712626306945785109999577487218988374398325549347867773

type: snfs
skew: 0.78
deg: 5
c5: 140
c0: -41
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3400001)
Primes: RFBsize:250150, AFBsize:250097, largePrimes:7703762 encountered
Relations: rels:7182168, finalFF:528137
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 211.32 hours.
Total relation processing time: 0.83 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 212.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 19, 2007

By Jo Yeong Uk / GGNFS

2·10153+9 = 2(0)1529<154> = 7 · 23 · 41 · 83 · 3482753797249<13> · 36236576853259787647<20> · C116

C116 = P52 · P64

P52 = 2959271181514799226974060568985564239580538542286449<52>

P64 = 9774340558371489481440431760860958181256487808303078991400909109<64>

Number: 20009_153
N=28924924332700020078102154409371603648546043054508471127824139389385626667861861974281623089899076036621178091363941
  ( 116 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2959271181514799226974060568985564239580538542286449 (pp52)
 r2=9774340558371489481440431760860958181256487808303078991400909109 (pp64)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.75 hours.
Scaled time: 29.35 units (timescale=2.134).
Factorization parameters were as follows:
n: 28924924332700020078102154409371603648546043054508471127824139389385626667861861974281623089899076036621178091363941
m: 10000000000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2300001)
Primes: RFBsize:216816, AFBsize:216826, largePrimes:5458908 encountered
Relations: rels:5374729, finalFF:530472
Max relations in full relation-set: 28
Initial matrix: 433706 x 530472 with sparse part having weight 36351069.
Pruned matrix : 358650 x 360882 with weight 22220315.
Total sieving time: 13.03 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 13.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 18, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

2·10161+9 = 2(0)1609<162> = 89 · C160

C160 = P74 · P86

P74 = 34658477847360659014058595102069167012530568460007500101714626375633760287<74>

P86 = 64838133432541527475079803698431770081537553848180889286332859833318730119895305215663<86>

Number: n
N=2247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
  ( 160 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=34658477847360659014058595102069167012530568460007500101714626375633760287 (pp74)
 r2=64838133432541527475079803698431770081537553848180889286332859833318730119895305215663 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.07 hours.
Scaled time: 58.35 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_2_0_160_9
n: 2247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
skew: 0.85
deg: 5
c5: 20
c0: 9
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:216816, AFBsize:216651, largePrimes:7001649 encountered
Relations: rels:6463003, finalFF:491333
Max relations in full relation-set: 48
Initial matrix: 433534 x 491333 with sparse part having weight 39251584.
Pruned matrix : 388274 x 390505 with weight 25421104.
Total sieving time: 39.34 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.37 hours.
Total square root time: 0.08 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 44.07 hours.
 --------- CPU info (if available) ----------

2·10154+9 = 2(0)1539<155> = 11 · 139 · 123307 · C147

C147 = P57 · P90

P57 = 830079215274331883817516423026643554541585944243418276953<57>

P90 = 127795405115706014236248092068937621366157768320616692605819506501989361071666161673603051<90>

Number: n
N=106080309594110586696617947039119018304385493129409072262824490186120714311071268289763648455730854269029413911116146625540532880538725457703783603
  ( 147 digits)
SNFS difficulty: 155 digits.
Divisors found:

Sun Nov 18 21:03:15 2007  prp57 factor: 830079215274331883817516423026643554541585944243418276953
Sun Nov 18 21:03:15 2007  prp90 factor: 127795405115706014236248092068937621366157768320616692605819506501989361071666161673603051
Sun Nov 18 21:03:15 2007  elapsed time 00:52:25 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 17.88 hours.
Scaled time: 23.42 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_2_0_153_9
n: 106080309594110586696617947039119018304385493129409072262824490186120714311071268289763648455730854269029413911116146625540532880538725457703783603
skew: 2.14
deg: 5
c5: 1
c0: 45
m: 10000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 750000)
Primes: RFBsize:203362, AFBsize:203572, largePrimes:6377392 encountered
Relations: rels:5863802, finalFF:471912
Max relations in full relation-set: 28
Initial matrix: 406998 x 471912 with sparse part having weight 26578410.
Pruned matrix : 347290 x 349388 with weight 15627841.
Total sieving time: 17.71 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 17.88 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 18, 2007 (4th)

By Jo Yeong Uk / GGNFS

4·10141-9 = 3(9)1401<142> = 13 · 191 · 20359 · 195319 · 12420177806754397<17> · C113

C113 = P36 · P78

P36 = 163736308730108767707475962968700893<36>

P78 = 199209262950089812594969876563503547961581096151892699792833892052250192212997<78>

Number: 39991_141
N=32617789380293323671116887710598264533701832802595148777896193264079821368295646222589206276954325334265840106321
  ( 113 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=163736308730108767707475962968700893 (pp36)
 r2=199209262950089812594969876563503547961581096151892699792833892052250192212997 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.44 hours.
Scaled time: 11.55 units (timescale=2.123).
Factorization parameters were as follows:
n: 32617789380293323671116887710598264533701832802595148777896193264079821368295646222589206276954325334265840106321
m: 20000000000000000000000000000
c5: 5
c0: -36
skew: 1.48
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:113572, largePrimes:3187730 encountered
Relations: rels:3200509, finalFF:325241
Max relations in full relation-set: 28
Initial matrix: 227794 x 325241 with sparse part having weight 26244758.
Pruned matrix : 187279 x 188481 with weight 12048136.
Total sieving time: 5.27 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 18, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

2·10148+9 = 2(0)1479<149> = 11 · 17 · 41 · 89819 · C140

C140 = P33 · P45 · P63

P33 = 609146353706828448793174289718131<33>

P45 = 150327116082360350342458857196514705709372161<45>

P63 = 317159220689745360562169219217954642762236170568071499368229363<63>

Number: 20009_148
N=29042655068025427477641936744710994528214215510409132260749261322213369262621494629040875043696308199191832070407911191359581261140499285033
  ( 140 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=609146353706828448793174289718131 (pp33)
 r2=150327116082360350342458857196514705709372161 (pp45)
 r3=317159220689745360562169219217954642762236170568071499368229363 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 20.82 hours.
Scaled time: 14.06 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_148
n: 29042655068025427477641936744710994528214215510409132260749261322213369262621494629040875043696308199191832070407911191359581261140499285033
m: 200000000000000000000000000000
c5: 125
c0: 18
skew: 0.68
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2650001)
Primes: RFBsize:114155, AFBsize:113727, largePrimes:2759008 encountered
Relations: rels:2717014, finalFF:256815
Max relations in full relation-set: 28
Initial matrix: 227948 x 256815 with sparse part having weight 24576686.
Pruned matrix : 218819 x 220022 with weight 19196213.
Total sieving time: 19.03 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.53 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 20.82 hours.
 --------- CPU info (if available) ----------

4·10117-9 = 3(9)1161<118> = 13 · 9973 · 214363 · 581922332049027043<18> · C90

C90 = P42 · P48

P42 = 531991308851942132115845825480210110671439<42>

P48 = 464912723832181683082293085018597257414298049209<48>

Sat Nov 17 15:56:48 2007  Msieve v. 1.28
Sat Nov 17 15:56:48 2007  random seeds: 515dd9e0 50f90094
Sat Nov 17 15:56:48 2007  factoring 247329528453403843265964841503467900787215031507298040842564825634927508129438170852841751 (90 digits)
Sat Nov 17 15:56:49 2007  commencing quadratic sieve (89-digit input)
Sat Nov 17 15:56:49 2007  using multiplier of 1
Sat Nov 17 15:56:49 2007  using 64kb Pentium 2 sieve core
Sat Nov 17 15:56:49 2007  sieve interval: 18 blocks of size 65536
Sat Nov 17 15:56:49 2007  processing polynomials in batches of 6
Sat Nov 17 15:56:49 2007  using a sieve bound of 1575281 (59464 primes)
Sat Nov 17 15:56:49 2007  using large prime bound of 126022480 (26 bits)
Sat Nov 17 15:56:49 2007  using double large prime bound of 380896014563600 (42-49 bits)
Sat Nov 17 15:56:49 2007  using trial factoring cutoff of 49 bits
Sat Nov 17 15:56:49 2007  polynomial 'A' values have 11 factors
Sat Nov 17 23:25:48 2007  59782 relations (15877 full + 43905 combined from 635165 partial), need 59560
Sat Nov 17 23:25:52 2007  begin with 651042 relations
Sat Nov 17 23:25:54 2007  reduce to 146575 relations in 9 passes
Sat Nov 17 23:25:54 2007  attempting to read 146575 relations
Sat Nov 17 23:26:02 2007  recovered 146575 relations
Sat Nov 17 23:26:02 2007  recovered 123038 polynomials
Sat Nov 17 23:26:14 2007  attempting to build 59782 cycles
Sat Nov 17 23:26:14 2007  found 59782 cycles in 5 passes
Sat Nov 17 23:26:16 2007  distribution of cycle lengths:
Sat Nov 17 23:26:16 2007     length 1 : 15877
Sat Nov 17 23:26:16 2007     length 2 : 11295
Sat Nov 17 23:26:17 2007     length 3 : 10499
Sat Nov 17 23:26:17 2007     length 4 : 7977
Sat Nov 17 23:26:17 2007     length 5 : 5541
Sat Nov 17 23:26:17 2007     length 6 : 3771
Sat Nov 17 23:26:17 2007     length 7 : 2219
Sat Nov 17 23:26:17 2007     length 9+: 2603
Sat Nov 17 23:26:17 2007  largest cycle: 19 relations
Sat Nov 17 23:26:18 2007  matrix is 59464 x 59782 with weight 3654625 (avg 61.13/col)
Sat Nov 17 23:26:21 2007  filtering completed in 3 passes
Sat Nov 17 23:26:21 2007  matrix is 55555 x 55619 with weight 3417406 (avg 61.44/col)
Sat Nov 17 23:26:23 2007  saving the first 48 matrix rows for later
Sat Nov 17 23:26:23 2007  matrix is 55507 x 55619 with weight 2798607 (avg 50.32/col)
Sat Nov 17 23:26:23 2007  matrix includes 64 packed rows
Sat Nov 17 23:26:23 2007  using block size 10922 for processor cache size 256 kB
Sat Nov 17 23:26:26 2007  commencing Lanczos iteration
Sat Nov 17 23:29:02 2007  lanczos halted after 879 iterations
Sat Nov 17 23:29:03 2007  recovered 17 nontrivial dependencies
Sat Nov 17 23:29:33 2007  prp42 factor: 531991308851942132115845825480210110671439
Sat Nov 17 23:29:33 2007  prp48 factor: 464912723832181683082293085018597257414298049209
Sat Nov 17 23:29:33 2007  elapsed time 07:32:45

4·10105-9 = 3(9)1041<106> = 13 · 4049 · 230177683 · C93

C93 = P34 · P59

P34 = 5089468623085822110371775885182959<34>

P59 = 64868403116863325702101470038639463824085108816719708634719<59>

Number: 39991_105
N=330145702292958441592211172106378607837842790909434221456259170903001863735703019123414553521
  ( 93 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=5089468623085822110371775885182959 (pp34)
 r2=64868403116863325702101470038639463824085108816719708634719 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.24 hours.
Scaled time: 0.84 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_105
n: 330145702292958441592211172106378607837842790909434221456259170903001863735703019123414553521
m: 1000000000000000000000
c5: 4
c0: -9
skew: 1.18
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64053, largePrimes:2165320 encountered
Relations: rels:2447143, finalFF:427386
Max relations in full relation-set: 28
Initial matrix: 113215 x 427386 with sparse part having weight 29087007.
Pruned matrix : 55181 x 55811 with weight 3194505.
Total sieving time: 1.11 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.24 hours.
 --------- CPU info (if available) ----------

4·10123-9 = 3(9)1221<124> = 13 · 15601 · 14877774143167099699747<23> · C97

C97 = P48 · P49

P48 = 470762130228440485791543763322013994572073144603<48>

P49 = 2815948587112211304623095233966680241651606098227<49>

Number: 39991_123
N=1325641955482711805978372001349693249395454462809784497501309555808926827572054827616211192918881
  ( 97 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=470762130228440485791543763322013994572073144603 (pp48)
 r2=2815948587112211304623095233966680241651606098227 (pp49)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.60 hours.
Scaled time: 1.75 units (timescale=0.675).
Factorization parameters were as follows:
name: 39991_123
n: 1325641955482711805978372001349693249395454462809784497501309555808926827572054827616211192918881
m: 2000000000000000000000000
c5: 125
c0: -9
skew: 0.59
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:64093, largePrimes:2072753 encountered
Relations: rels:2079058, finalFF:159271
Max relations in full relation-set: 28
Initial matrix: 113257 x 159271 with sparse part having weight 13679756.
Pruned matrix : 100109 x 100739 with weight 6360731.
Total sieving time: 2.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.60 hours.
 --------- CPU info (if available) ----------

Nov 18, 2007 (2nd)

By Yousuke Koide

(101683-1)/9 is divisible by 2597072697640403933361917807092159369<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 18, 2007

By Robert Backstrom / GGNFS

4·10109-9 = 3(9)1081<110> = 53 · C108

C108 = P49 · P59

P49 = 7969641884935205730310904257533114365615152149547<49>

P59 = 94698982969196667127271104615127284069462500623071914214001<59>

Number: n
N=754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
  ( 108 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=7969641884935205730310904257533114365615152149547 (pp49)
 r2=94698982969196667127271104615127284069462500623071914214001 (pp59)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.96 hours.
Scaled time: 1.15 units (timescale=1.192).
Factorization parameters were as follows:
name: KA_3_9_108_1
n: 754716981132075471698113207547169811320754716981132075471698113207547169811320754716981132075471698113207547
type: snfs
skew: 1.86
deg: 5
c5: 2
c0: -45
m: 10000000000000000000000
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 160001)
Primes: RFBsize:63951, AFBsize:64093, largePrimes:3342545 encountered
Relations: rels:2790483, finalFF:160806
Max relations in full relation-set: 28
Initial matrix: 128109 x 160806 with sparse part having weight 5905277.
Pruned matrix : 96382 x 97086 with weight 2618908.
Total sieving time: 0.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.4,2.4,50000
total time: 0.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

4·10121-9 = 3(9)1201<122> = 31 · C121

C121 = P48 · P73

P48 = 207550763771542349075740138245104441965655783933<48>

P73 = 6216901143594248208194826668257714111385850652570251799400319368993225117<73>

Number: n
N=1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=207550763771542349075740138245104441965655783933 (pp48)
 r2=6216901143594248208194826668257714111385850652570251799400319368993225117 (pp73)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.05 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_3_9_120_1
n: 1290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161
skew: 0.74
deg: 5
c5: 40
c0: -9
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:63733, largePrimes:4298910 encountered
Relations: rels:3675690, finalFF:181805
Max relations in full relation-set: 48
Initial matrix: 127751 x 181805 with sparse part having weight 12806423.
Pruned matrix : 102487 x 103189 with weight 4549576.
Total sieving time: 1.36 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.10 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 17, 2007 (4th)

By Jo Yeong Uk / GGNFS

(4·10195-1)/3 = 1(3)195<196> = 919 · 2815092622300365139319<22> · 1616772208578912506305058572743036521<37> · C135

C135 = P49 · P86

P49 = 9750955237361634372618257316599424244951087381213<49>

P86 = 32691476708214933835165765723715218661077209696240370449876399876944717064876363130561<86>

Number: 13333_195
N=318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493
  ( 135 digits)
Divisors found:
 r1=9750955237361634372618257316599424244951087381213 (pp49)
 r2=32691476708214933835165765723715218661077209696240370449876399876944717064876363130561 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 386.78 hours.
Scaled time: 823.45 units (timescale=2.129).
Factorization parameters were as follows:
name: 13333_195
n: 318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493
skew: 131671.97
# norm 3.05e+18
c5: 197280
c4: -307423178886
c3: -58612697870847169
c2: 3978958100881520574793
c1: 213561147801238145597164433
c0: -11098269473779960898804283038595
# alpha -5.90
Y1: 773059969233563
Y0: -69451436841457195078837658
# Murphy_E 4.23e-11
# M 56576599863178588454020620146065243601482425869774777937223046811868572601341632692068072510368265616104157355536434726657596047407882
type: gnfs
rlim: 12000000
alim: 12000000
lpbr: 28
lpba: 28
mfbr: 51
mfba: 51
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 12000000/12000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6000000, 11600001)
Primes: RFBsize:788060, AFBsize:788407, largePrimes:12637468 encountered
Relations: rels:13248927, finalFF:1826316
Max relations in full relation-set: 28
Initial matrix: 1576544 x 1826316 with sparse part having weight 125344949.
Pruned matrix : 1341143 x 1349089 with weight 79768099.
Polynomial selection time: 23.32 hours.
Total sieving time: 349.55 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 13.52 hours.
Time per square root: 0.67 hours.
Prototype def-par.txt line would be:
gnfs,134,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,28,28,51,51,2.6,2.6,100000
total time: 386.78 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

4·10131-9 = 3(9)1301<132> = 83 · 157 · 43427 · 89517934664444970329<20> · C103

C103 = P37 · P67

P37 = 2706709430006427754108248781033420387<37>

P67 = 2917230383237813120633073932480522042054906957099018520221291471441<67>

Number: 39991_131
N=7896094987811053945775833802148765097844972873029553301959921686999250192636341021809147450036357667667
  ( 103 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=2706709430006427754108248781033420387 (pp37)
 r2=2917230383237813120633073932480522042054906957099018520221291471441 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.06 hours.
Scaled time: 4.43 units (timescale=2.145).
Factorization parameters were as follows:
n: 7896094987811053945775833802148765097844972873029553301959921686999250192636341021809147450036357667667
m: 200000000000000000000000000
c5: 5
c0: -36
skew: 1.48
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1000001)
Primes: RFBsize:92938, AFBsize:92554, largePrimes:1605182 encountered
Relations: rels:1657757, finalFF:229082
Max relations in full relation-set: 28
Initial matrix: 185559 x 229082 with sparse part having weight 10774169.
Pruned matrix : 157627 x 158618 with weight 5983307.
Total sieving time: 1.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 2.06 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 17, 2007 (3rd)

By Robert Backstrom / GGNFS

2·10152+9 = 2(0)1519<153> = 11 · 5689 · C148

C148 = P69 · P80

P69 = 246315360411796404596074328483957549191621049813614560388841748191993<69>

P80 = 12975075126577197804004996961447593348172069718738575880540661517804485822477547<80>

Number: n
N=3195960306172997331373144345547228303424471468064366640566324166253855127119321178030968855366816344141005768708352642260183128525543712747087681171
  ( 148 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=246315360411796404596074328483957549191621049813614560388841748191993 (pp69)
 r2=12975075126577197804004996961447593348172069718738575880540661517804485822477547 (pp80)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.67 hours.
Scaled time: 14.62 units (timescale=0.877).
Factorization parameters were as follows:
name: KA_2_0_151_9
n: 3195960306172997331373144345547228303424471468064366640566324166253855127119321178030968855366816344141005768708352642260183128525543712747087681171
skew: 0.54
deg: 5
c5: 200
c0: 9
m: 1000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 650001)
Primes: RFBsize:203362, AFBsize:203482, largePrimes:6183842 encountered
Relations: rels:5700058, finalFF:479667
Max relations in full relation-set: 28
Initial matrix: 406909 x 479667 with sparse part having weight 26262880.
Pruned matrix : 339138 x 341236 with weight 14609906.
Total sieving time: 14.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.47 hours.
Total square root time: 0.32 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 16.67 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

2·10147+9 = 2(0)1469<148> = 7 · 188393823755666606087<21> · C127

C127 = P35 · P92

P35 = 48974472633629490212445941599538267<35>

P92 = 30966742771240142891864085906864765198542074244953818306582481386219016872212029624089901403<92>

Number: 20009_147
N=1516579896402744219014433937457116142826101612462661029810181639049330302450011786700883958686428599152590539537076162355488601
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=48974472633629490212445941599538267 (pp35)
 r2=30966742771240142891864085906864765198542074244953818306582481386219016872212029624089901403 (pp92)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 17.87 hours.
Scaled time: 12.06 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_147
n: 1516579896402744219014433937457116142826101612462661029810181639049330302450011786700883958686428599152590539537076162355488601
m: 100000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2350001)
Primes: RFBsize:114155, AFBsize:114287, largePrimes:2723540 encountered
Relations: rels:2681399, finalFF:265609
Max relations in full relation-set: 28
Initial matrix: 228507 x 265609 with sparse part having weight 23794062.
Pruned matrix : 215996 x 217202 with weight 17271817.
Total sieving time: 16.25 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.37 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 17.87 hours.
 --------- CPU info (if available) ----------

Nov 17, 2007

The factor table of 399...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Nov 16, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

2·10149+9 = 2(0)1489<150> = 467 · 1867 · 4621 · 108421 · C135

C135 = P40 · P96

P40 = 1863452397272640607861076350654167212689<40>

P96 = 245697714723845525541313190866322224591579633478192557941408979790414184607140661966923663278569<96>

Number: 20009_149
N=457845995506559311920071361063861840226353200596349254744820183599147637255647440000439776818147406947190006280979032862128666078562041
  ( 135 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1863452397272640607861076350654167212689 (pp40)
 r2=245697714723845525541313190866322224591579633478192557941408979790414184607140661966923663278569 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.32 hours.
Scaled time: 19.79 units (timescale=2.123).
Factorization parameters were as follows:
n: 457845995506559311920071361063861840226353200596349254744820183599147637255647440000439776818147406947190006280979032862128666078562041
m: 1000000000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1500001)
Primes: RFBsize:135072, AFBsize:135163, largePrimes:3697267 encountered
Relations: rels:3741082, finalFF:354567
Max relations in full relation-set: 28
Initial matrix: 270299 x 354567 with sparse part having weight 30900567.
Pruned matrix : 237134 x 238549 with weight 17237573.
Total sieving time: 9.00 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 9.32 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10191+9 = 2(0)1909<192> = C192

C192 = P45 · C148

P45 = 139787422364207720750158040677389843257571643<45>

C148 = [1430743886806296706788516093667434949145159858014350886258366962866810355411884866166709798529837275207436439253831768696683312353651987615427655563<148>]

Nov 16, 2007 (2nd)

By Sinkiti Sibata / GGNFS

2·10137+9 = 2(0)1369<138> = 1747 · 187546628295101<15> · 17157672728274349<17> · 1099656391248576163177704783751416330647<40> · 32352842794331493715586477085068987078828228518142150588757859949<65>

C104 = P40 · P65

P40 = 1099656391248576163177704783751416330647<40>

P65 = 32352842794331493715586477085068987078828228518142150588757859949<65>

Number: 20009_137
N=35577010353847071166627381630160508224933719406788362654288006111043429068247910493731177879457902557003
  ( 104 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=1099656391248576163177704783751416330647 (pp40)
 r2=32352842794331493715586477085068987078828228518142150588757859949 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.22 hours.
Scaled time: 5.55 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_137
n: 35577010353847071166627381630160508224933719406788362654288006111043429068247910493731177879457902557003
m: 1000000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63988, largePrimes:1552634 encountered
Relations: rels:1574611, finalFF:193594
Max relations in full relation-set: 28
Initial matrix: 142551 x 193594 with sparse part having weight 15125767.
Pruned matrix : 126553 x 127329 with weight 8216971.
Total sieving time: 7.78 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.22 hours.
 --------- CPU info (if available) ----------

Nov 16, 2007

By Robert Backstrom / GGNFS, Msieve

2·10146+9 = 2(0)1459<147> = 11 · 19 · 443 · C142

C142 = P43 · P99

P43 = 5697591929599718777554446090898432894508443<43>

P99 = 379130428884937776481991873307188799908650024737963391395977785501700705423478684413792248504210049<99>

Number: n
N=2160130471880501582295570652467409031505502932377115577780897966237160724507760268720230701934396837568989166945683519284564787713177875943707
  ( 142 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=5697591929599718777554446090898432894508443 (pp43)
 r2=379130428884937776481991873307188799908650024737963391395977785501700705423478684413792248504210049 (pp99)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.11 hours.
Scaled time: 10.69 units (timescale=1.318).
Factorization parameters were as follows:
name: KA_2_0_145_9
n: 2160130471880501582295570652467409031505502932377115577780897966237160724507760268720230701934396837568989166945683519284564787713177875943707
skew: 0.85
deg: 5
c5: 20
c0: 9
m: 100000000000000000000000000000
type: snfs
rlim: 2200000
alim: 2200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2200000/2200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:162662, AFBsize:162600, largePrimes:6215071 encountered
Relations: rels:5583240, finalFF:372600
Max relations in full relation-set: 48
Initial matrix: 325329 x 372600 with sparse part having weight 24152920.
Pruned matrix : 286219 x 287909 with weight 14211438.
Total sieving time: 6.19 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.66 hours.
Total square root time: 0.10 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,100000
total time: 8.11 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

2·10167-9 = 1(9)1661<168> = 11 · 25693999 · C159

C159 = P51 · P54 · P56

P51 = 213778048882883699682952867750597400299228114685941<51>

P54 = 253294029617274149322595661355934135791715095080163601<54>

P56 = 13068253350533572176578369071664035808002504957074122959<56>

Number: n
N=707628975225622987615972826254806883824577800513582250010277426328933141866387485335318251478947211830209140203586766770644842719181945240138828454917359567819
  ( 159 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Nov 16 05:59:23 2007  prp51 factor: 213778048882883699682952867750597400299228114685941
Fri Nov 16 05:59:23 2007  prp54 factor: 253294029617274149322595661355934135791715095080163601
Fri Nov 16 05:59:23 2007  prp56 factor: 13068253350533572176578369071664035808002504957074122959
Fri Nov 16 05:59:23 2007  elapsed time 01:49:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 62.94 hours.
Scaled time: 82.45 units (timescale=1.310).
Factorization parameters were as follows:
name: KA_1_9_166_1
n: 707628975225622987615972826254806883824577800513582250010277426328933141866387485335318251478947211830209140203586766770644842719181945240138828454917359567819
skew: 0.54
deg: 5
c5: 200
c0: -9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600001)
Primes: RFBsize:230209, AFBsize:230472, largePrimes:7397646 encountered
Relations: rels:6871280, finalFF:499906
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 62.61 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000
total time: 62.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 15, 2007 (4th)

By Sinkiti Sibata / GGNFS

2·10133+9 = 2(0)1329<134> = 41 · 106261 · 138657907177600053240515967083<30> · C98

C98 = P30 · P68

P30 = 337482959187671618348715804443<30>

P68 = 98101523251692854700293015379351134705420468393200528633582388590261<68>

Number: 20009_133
N=33107592367799477994531315875696566699102396778630104307460969147141634839210559134468289330329623
  ( 98 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=337482959187671618348715804443 (pp30)
 r2=98101523251692854700293015379351134705420468393200528633582388590261 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.55 hours.
Scaled time: 3.75 units (timescale=0.676).
Factorization parameters were as follows:
name: 20009_133
n: 33107592367799477994531315875696566699102396778630104307460969147141634839210559134468289330329623
m: 200000000000000000000000000
c5: 125
c0: 18
skew: 0.68
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 925001)
Primes: RFBsize:78498, AFBsize:63828, largePrimes:1467588 encountered
Relations: rels:1461357, finalFF:170545
Max relations in full relation-set: 28
Initial matrix: 142392 x 170545 with sparse part having weight 10197756.
Pruned matrix : 131765 x 132540 with weight 6330275.
Total sieving time: 5.15 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.55 hours.
 --------- CPU info (if available) ----------

2·10136+9 = 2(0)1359<137> = 11 · 626113 · 1638117457<10> · 14068805453502347862038393<26> · C96

C96 = P37 · P59

P37 = 7479989621822215707304648726870274177<37>

P59 = 16845400134770192015265810071674311005731257071385123440419<59>

Number: 20009_136
N=126003418183523590081005231307316729274954208236469757844274078817776161403684503808348053760163
  ( 96 digits)
SNFS difficulty: 136 digits.
Divisors found:
 r1=7479989621822215707304648726870274177 (pp37)
 r2=16845400134770192015265810071674311005731257071385123440419 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.86 hours.
Scaled time: 5.31 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_136
n: 126003418183523590081005231307316729274954208236469757844274078817776161403684503808348053760163
m: 1000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1150001)
Primes: RFBsize:78498, AFBsize:63843, largePrimes:1536871 encountered
Relations: rels:1552675, finalFF:189444
Max relations in full relation-set: 28
Initial matrix: 142408 x 189444 with sparse part having weight 14166681.
Pruned matrix : 126873 x 127649 with weight 7809355.
Total sieving time: 7.43 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.86 hours.
 --------- CPU info (if available) ----------

Nov 15, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(2·10167+1)/3 = (6)1667<167> = 67 · 163 · 154247 · 105057409 · C150

C150 = P44 · P45 · P62

P44 = 35110383512037779258731687752743501077616849<44>

P45 = 144490044053633250534088853071686157579676183<45>

P62 = 74255636529996781604025069037975869335914287473493040697234147<62>

Number: n
N=376706333569452881833796963898895894903820904576725150866190626909505248384898760572288876235614404361232252029198354520001692450611622477750149560949
  ( 150 digits)
SNFS difficulty: 167 digits.
Divisors found:

Thu Nov 15 11:40:38 2007  prp44 factor: 35110383512037779258731687752743501077616849
Thu Nov 15 11:40:38 2007  prp45 factor: 144490044053633250534088853071686157579676183
Thu Nov 15 11:40:38 2007  prp62 factor: 74255636529996781604025069037975869335914287473493040697234147
Thu Nov 15 11:40:38 2007  elapsed time 03:04:59 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 61.61 hours.
Scaled time: 81.70 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_6_166_7
n: 376706333569452881833796963898895894903820904576725150866190626909505248384898760572288876235614404361232252029198354520001692450611622477750149560949
skew: 0.35
deg: 5
c5: 200
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2850000)
Primes: RFBsize:250150, AFBsize:249566, largePrimes:7551318 encountered
Relations: rels:7059925, finalFF:577979
Max relations in full relation-set: 28
Initial matrix: 499781 x 577979 with sparse part having weight 49191823.
Pruned matrix : 444384 x 446946 with weight 33215771.
Total sieving time: 61.30 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 61.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 15, 2007 (2nd)

By Jo Yeong Uk / GGNFS

2·10138+9 = 2(0)1379<139> = 112 · 41 · 9034909729<10> · C125

C125 = P30 · P38 · P58

P30 = 799755820751262322119275375033<30>

P38 = 20766309102022228980253099855875658537<38>

P58 = 2686706507069958673687375702336773298121688744721734859241<58>

Number: 20009_138
N=44620758746381241841688897721867317475788276748995108314229042673027347676487429597124584059980824714622578162566104956058761
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=799755820751262322119275375033 (pp30)
 r2=20766309102022228980253099855875658537 (pp38)
 r3=2686706507069958673687375702336773298121688744721734859241 (pp58)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.74 hours.
Scaled time: 10.09 units (timescale=2.126).
Factorization parameters were as follows:
n: 44620758746381241841688897721867317475788276748995108314229042673027347676487429597124584059980824714622578162566104956058761
m: 10000000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1000001)
Primes: RFBsize:107126, AFBsize:106598, largePrimes:2324281 encountered
Relations: rels:2569529, finalFF:387303
Max relations in full relation-set: 28
Initial matrix: 213788 x 387303 with sparse part having weight 31262275.
Pruned matrix : 152381 x 153513 with weight 10650969.
Total sieving time: 4.62 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10141+9 = 2(0)1409<142> = 7 · 29 · 84089 · 1843241 · C128

C128 = P39 · P45 · P45

P39 = 193589288637298059074525377001965216949<39>

P45 = 468214580957084640590379178323139739604088747<45>

P45 = 701271823576894703710295051061370970173632749<45>

Number: 20009_141
N=63564209137520160828475746211489351888520291688068698024161891639200326972468705608592258442484833328985146148995415235418800347
  ( 128 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=193589288637298059074525377001965216949 (pp39)
 r2=468214580957084640590379178323139739604088747 (pp45)
 r3=701271823576894703710295051061370970173632749 (pp45)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.50 hours.
Scaled time: 11.67 units (timescale=2.123).
Factorization parameters were as follows:
n: 63564209137520160828475746211489351888520291688068698024161891639200326972468705608592258442484833328985146148995415235418800347
m: 10000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:113962, largePrimes:3318316 encountered
Relations: rels:3434745, finalFF:413798
Max relations in full relation-set: 28
Initial matrix: 228184 x 413798 with sparse part having weight 34667463.
Pruned matrix : 162968 x 164172 with weight 12380892.
Total sieving time: 5.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 15, 2007

By JMB / GMP-ECM

9·10178+7 = 9(0)1777<179> = 149 · C177

C177 = P35 · C143

P35 = 34477381911603229695013790339605181<35>

C143 = [17519510245477803843772234672206519263441432562534062592219996721821259842723144120268391140425192935308257597913633559158414046764815248848903<143>]

Nov 14, 2007 (3rd)

By Jo Yeong Uk / GGNFS, Msieve

2·10151+9 = 2(0)1509<152> = C152

C152 = P64 · P88

P64 = 5361545627942898041009151470006806437953024698709373565545033283<64>

P88 = 3730267610848168946728870898319835513379653329283710892077298113553792162530729021571523<88>

Number: 20009_151
N=20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
  ( 152 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=5361545627942898041009151470006806437953024698709373565545033283 (pp64)
 r2=3730267610848168946728870898319835513379653329283710892077298113553792162530729021571523 (pp88)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.44 hours.
Scaled time: 24.53 units (timescale=2.145).
Factorization parameters were as follows:
n: 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009
m: 1000000000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176393, largePrimes:5255231 encountered
Relations: rels:5101022, finalFF:437517
Max relations in full relation-set: 28
Initial matrix: 352762 x 437517 with sparse part having weight 35441926.
Pruned matrix : 301643 x 303470 with weight 21914347.
Total sieving time: 10.89 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 11.44 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10115+9 = 2(0)1149<116> = 2549 · C112

C112 = P34 · P36 · P43

P34 = 3610985855871191931623417922834769<34>

P36 = 347349964829672312277520077897474727<36>

P43 = 6255573247015228068683536228478645049008707<43>

Number: 20009_115
N=7846214201647704982346018046292663789721459395841506473126716359356610435464888191447626520204001569242840329541
  ( 112 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=3610985855871191931623417922834769 (pp34)
 r2=347349964829672312277520077897474727 (pp36)
 r3=6255573247015228068683536228478645049008707 (pp43)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.64 hours.
Scaled time: 1.37 units (timescale=2.143).
Factorization parameters were as follows:
n: 7846214201647704982346018046292663789721459395841506473126716359356610435464888191447626520204001569242840329541
m: 100000000000000000000000
c5: 2
c0: 9
skew: 1.35
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:48886, largePrimes:1863902 encountered
Relations: rels:1959876, finalFF:245084
Max relations in full relation-set: 28
Initial matrix: 98049 x 245084 with sparse part having weight 19250215.
Pruned matrix : 66805 x 67359 with weight 3521221.
Total sieving time: 0.60 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.64 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10128+9 = 2(0)1279<129> = 11 · 19 · 41 · 3628268961937<13> · C112

C112 = P30 · P82

P30 = 838738174203331430476288994347<30>

P82 = 7669622162401410990558076424963758890890607406854931844023679051213111668308932099<82>

Number: 20009_128
N=6432804889321966154737940019106072881085761416381139523418545975573334342986996964229572138342044269550217844353
  ( 112 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=838738174203331430476288994347 (pp30)
 r2=7669622162401410990558076424963758890890607406854931844023679051213111668308932099 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.75 hours.
Scaled time: 3.75 units (timescale=2.146).
Factorization parameters were as follows:
n: 6432804889321966154737940019106072881085761416381139523418545975573334342986996964229572138342044269550217844353
m: 100000000000000000000000000
c5: 1
c0: 450
skew: 3.39
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1572335 encountered
Relations: rels:1653001, finalFF:250088
Max relations in full relation-set: 28
Initial matrix: 156973 x 250088 with sparse part having weight 11746162.
Pruned matrix : 112238 x 113086 with weight 4590998.
Total sieving time: 1.69 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10129+9 = 2(0)1289<130> = 73 · 163 · 4507 · C121

C121 = P41 · P80

P41 = 82003635083982433094568610504258544735069<41>

P80 = 96789357905979190059916421135822880484975096215801511141201084498141280349953947<80>

Number: 20009_129
N=7937079185734887593874167046697325195980474197859232432137387602376763124415823530918175646633742048331470586833465867343
  ( 121 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=82003635083982433094568610504258544735069 (pp41)
 r2=96789357905979190059916421135822880484975096215801511141201084498141280349953947 (pp80)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.72 hours.
Scaled time: 3.68 units (timescale=2.139).
Factorization parameters were as follows:
n: 7937079185734887593874167046697325195980474197859232432137387602376763124415823530918175646633742048331470586833465867343
m: 100000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 850001)
Primes: RFBsize:78498, AFBsize:78411, largePrimes:1567044 encountered
Relations: rels:1646980, finalFF:248901
Max relations in full relation-set: 28
Initial matrix: 156973 x 248901 with sparse part having weight 11659733.
Pruned matrix : 112684 x 113532 with weight 4605631.
Total sieving time: 1.66 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.72 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

2·10143+9 = 2(0)1429<144> = 41 · 67 · 3331649 · 14935649 · 82226933119967<14> · 1277854822563168097967<22> · C92

C92 = P39 · P53

P39 = 378442673724566134246810453283328526129<39>

P53 = 36795294718689337041099821264332695452995703051552587<53>

Wed Nov 14 21:20:40 2007  
Wed Nov 14 21:20:40 2007  
Wed Nov 14 21:20:40 2007  Msieve v. 1.28
Wed Nov 14 21:20:40 2007  random seeds: 3b93c2a8 eb1b55fc
Wed Nov 14 21:20:40 2007  factoring 13924909713824200219224541074202380892627126993472216666474137256898926894158453179847045723 (92 digits)
Wed Nov 14 21:20:41 2007  commencing quadratic sieve (91-digit input)
Wed Nov 14 21:20:41 2007  using multiplier of 3
Wed Nov 14 21:20:41 2007  using 32kb Intel Core sieve core
Wed Nov 14 21:20:41 2007  sieve interval: 36 blocks of size 32768
Wed Nov 14 21:20:41 2007  processing polynomials in batches of 6
Wed Nov 14 21:20:41 2007  using a sieve bound of 1753547 (65732 primes)
Wed Nov 14 21:20:41 2007  using large prime bound of 177108247 (27 bits)
Wed Nov 14 21:20:41 2007  using double large prime bound of 702796695147472 (42-50 bits)
Wed Nov 14 21:20:41 2007  using trial factoring cutoff of 50 bits
Wed Nov 14 21:20:41 2007  polynomial 'A' values have 12 factors
Wed Nov 14 22:27:23 2007  66322 relations (17638 full + 48684 combined from 795835 partial), need 65828
Wed Nov 14 22:27:23 2007  begin with 813473 relations
Wed Nov 14 22:27:24 2007  reduce to 163711 relations in 11 passes
Wed Nov 14 22:27:24 2007  attempting to read 163711 relations
Wed Nov 14 22:27:25 2007  recovered 163711 relations
Wed Nov 14 22:27:25 2007  recovered 140908 polynomials
Wed Nov 14 22:27:25 2007  attempting to build 66322 cycles
Wed Nov 14 22:27:25 2007  found 66322 cycles in 5 passes
Wed Nov 14 22:27:25 2007  distribution of cycle lengths:
Wed Nov 14 22:27:25 2007     length 1 : 17638
Wed Nov 14 22:27:25 2007     length 2 : 12531
Wed Nov 14 22:27:25 2007     length 3 : 11404
Wed Nov 14 22:27:25 2007     length 4 : 8950
Wed Nov 14 22:27:25 2007     length 5 : 6342
Wed Nov 14 22:27:25 2007     length 6 : 4034
Wed Nov 14 22:27:25 2007     length 7 : 2526
Wed Nov 14 22:27:25 2007     length 9+: 2897
Wed Nov 14 22:27:25 2007  largest cycle: 17 relations
Wed Nov 14 22:27:25 2007  matrix is 65732 x 66322 with weight 3973198 (avg 59.91/col)
Wed Nov 14 22:27:26 2007  filtering completed in 3 passes
Wed Nov 14 22:27:26 2007  matrix is 61414 x 61478 with weight 3685100 (avg 59.94/col)
Wed Nov 14 22:27:27 2007  saving the first 48 matrix rows for later
Wed Nov 14 22:27:27 2007  matrix is 61366 x 61478 with weight 2818330 (avg 45.84/col)
Wed Nov 14 22:27:27 2007  matrix includes 64 packed rows
Wed Nov 14 22:27:27 2007  using block size 24591 for processor cache size 4096 kB
Wed Nov 14 22:27:28 2007  commencing Lanczos iteration
Wed Nov 14 22:27:44 2007  lanczos halted after 972 iterations
Wed Nov 14 22:27:44 2007  recovered 16 nontrivial dependencies
Wed Nov 14 22:27:45 2007  prp39 factor: 378442673724566134246810453283328526129
Wed Nov 14 22:27:45 2007  prp53 factor: 36795294718689337041099821264332695452995703051552587
Wed Nov 14 22:27:45 2007  elapsed time 01:07:05

Nov 14, 2007 (2nd)

By matsuix / GMP-ECM

(79·10188-7)/9 = 8(7)188<189> = 17 · 293 · C186

C186 = P32 · C154

P32 = 21765125120660595551469602307679<32>

C154 = [8096678074753473185944039706917079992623437626274897607442886516416138091715794569583278042469134900566577085836441842147205791368296429713363394770501523<154>]

Nov 14, 2007

By Sinkiti Sibata / Msieve, GGNFS

2·10113+9 = 2(0)1129<114> = 29 · 41 · 43 · 66063586712481298029647<23> · C86

C86 = P30 · P57

P30 = 126503094686428494316629112361<30>

P57 = 468076014118751200598434885891146498395685059990909881001<57>

Tue Nov 13 19:16:24 2007  
Tue Nov 13 19:16:24 2007  Msieve v. 1.28
Tue Nov 13 19:16:24 2007  random seeds: 79b93950 914c419f
Tue Nov 13 19:16:24 2007  factoring 59213064334510423889180281278137633024927225091119261905297311496666472844090768153361 (86 digits)
Tue Nov 13 19:16:25 2007  commencing quadratic sieve (86-digit input)
Tue Nov 13 19:16:25 2007  using multiplier of 1
Tue Nov 13 19:16:25 2007  using 64kb Pentium 2 sieve core
Tue Nov 13 19:16:25 2007  sieve interval: 8 blocks of size 65536
Tue Nov 13 19:16:25 2007  processing polynomials in batches of 13
Tue Nov 13 19:16:25 2007  using a sieve bound of 1450331 (55667 primes)
Tue Nov 13 19:16:25 2007  using large prime bound of 116026480 (26 bits)
Tue Nov 13 19:16:25 2007  using double large prime bound of 328248542117840 (41-49 bits)
Tue Nov 13 19:16:25 2007  using trial factoring cutoff of 49 bits
Tue Nov 13 19:16:25 2007  polynomial 'A' values have 11 factors
Wed Nov 14 00:52:54 2007  55802 relations (15557 full + 40245 combined from 585823 partial), need 55763
Wed Nov 14 00:52:57 2007  begin with 601380 relations
Wed Nov 14 00:52:59 2007  reduce to 134103 relations in 9 passes
Wed Nov 14 00:52:59 2007  attempting to read 134103 relations
Wed Nov 14 00:53:05 2007  recovered 134103 relations
Wed Nov 14 00:53:05 2007  recovered 113504 polynomials
Wed Nov 14 00:53:06 2007  attempting to build 55802 cycles
Wed Nov 14 00:53:06 2007  found 55802 cycles in 5 passes
Wed Nov 14 00:53:09 2007  distribution of cycle lengths:
Wed Nov 14 00:53:09 2007     length 1 : 15557
Wed Nov 14 00:53:09 2007     length 2 : 10981
Wed Nov 14 00:53:09 2007     length 3 : 9922
Wed Nov 14 00:53:09 2007     length 4 : 7142
Wed Nov 14 00:53:09 2007     length 5 : 4933
Wed Nov 14 00:53:09 2007     length 6 : 3153
Wed Nov 14 00:53:09 2007     length 7 : 1922
Wed Nov 14 00:53:09 2007     length 9+: 2192
Wed Nov 14 00:53:09 2007  largest cycle: 17 relations
Wed Nov 14 00:53:10 2007  matrix is 55667 x 55802 with weight 2940878 (avg 52.70/col)
Wed Nov 14 00:53:15 2007  filtering completed in 3 passes
Wed Nov 14 00:53:15 2007  matrix is 51377 x 51441 with weight 2736176 (avg 53.19/col)
Wed Nov 14 00:53:17 2007  saving the first 48 matrix rows for later
Wed Nov 14 00:53:17 2007  matrix is 51329 x 51441 with weight 2040428 (avg 39.67/col)
Wed Nov 14 00:53:17 2007  matrix includes 64 packed rows
Wed Nov 14 00:53:17 2007  using block size 5461 for processor cache size 128 kB
Wed Nov 14 00:53:18 2007  commencing Lanczos iteration
Wed Nov 14 00:55:31 2007  lanczos halted after 813 iterations
Wed Nov 14 00:55:32 2007  recovered 17 nontrivial dependencies
Wed Nov 14 00:55:33 2007  prp30 factor: 126503094686428494316629112361
Wed Nov 14 00:55:33 2007  prp57 factor: 468076014118751200598434885891146498395685059990909881001
Wed Nov 14 00:55:33 2007  elapsed time 05:39:09

2·10124+9 = 2(0)1239<125> = 11 · 7699 · 530843 · C114

C114 = P50 · P65

P50 = 12933342699273453806862343859989698555609089656801<50>

P65 = 34397439116451164611055979433447141435329163111083759614363162267<65>

Number: 20009_124
N=444873868070456791285157294883334653826114223009391544914693262254988985036803067248867103876557666800384103127867
  ( 114 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=12933342699273453806862343859989698555609089656801 (pp50)
 r2=34397439116451164611055979433447141435329163111083759614363162267 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.57 hours.
Scaled time: 1.74 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_124
n: 444873868070456791285157294883334653826114223009391544914693262254988985036803067248867103876557666800384103127867
m: 10000000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:2172125 encountered
Relations: rels:2319136, finalFF:277481
Max relations in full relation-set: 28
Initial matrix: 113080 x 277481 with sparse part having weight 24656124.
Pruned matrix : 81390 x 82019 with weight 5386144.
Total sieving time: 2.35 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.57 hours.
 --------- CPU info (if available) ----------

2·10131+9 = 2(0)1309<132> = 23 · 5816239007<10> · 74887441003<11> · C110

C110 = P50 · P60

P50 = 57062021722090451670266439953685372616833385097687<50>

P60 = 349867635331476129784259517594411816903548623239985088658229<60>

Number: 20009_131
N=19964154607141111700061809502715420631256369551377576495671386457041725733903887371073728671212925530921416323
  ( 110 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=57062021722090451670266439953685372616833385097687 (pp50)
 r2=349867635331476129784259517594411816903548623239985088658229 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.46 hours.
Scaled time: 3.01 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_131
n: 19964154607141111700061809502715420631256369551377576495671386457041725733903887371073728671212925530921416323
m: 100000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs

Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63843, largePrimes:1417127 encountered
Relations: rels:1397458, finalFF:156815
Max relations in full relation-set: 28
Initial matrix: 127861 x 156815 with sparse part having weight 9252290.
Pruned matrix : 118504 x 119207 with weight 5490939.
Total sieving time: 4.16 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.46 hours.
 --------- CPU info (if available) ----------

2·10132+9 = 2(0)1319<133> = 11 · 17 · 338993 · 2059033 · 22755127841<11> · 113606374765035095179<21> · C88

C88 = P41 · P47

P41 = 64553585691076468757776709697760029089923<41>

P47 = 91818881868322405255423164024086685058772234099<47>

Number: 20009_132
N=5927238058745577841908105029284969199323891268952962791663876711778527940853004477884377
  ( 88 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=64553585691076468757776709697760029089923 (pp41)
 r2=91818881868322405255423164024086685058772234099 (pp47)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 4.49 hours.
Scaled time: 3.03 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_132
n: 5927238058745577841908105029284969199323891268952962791663876711778527940853004477884377
m: 100000000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:63988, largePrimes:1398569 encountered
Relations: rels:1367313, finalFF:147644
Max relations in full relation-set: 28
Initial matrix: 128004 x 147644 with sparse part having weight 8145619.
Pruned matrix : 122053 x 122757 with weight 5454428.
Total sieving time: 4.18 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.49 hours.
 --------- CPU info (if available) ----------

2·10121+9 = 2(0)1209<122> = 47 · 25022303 · 6042247621<10> · C103

C103 = P50 · P54

P50 = 23276367811865773221842316006407580116078609884723<50>

P54 = 120918048180665503779004167358585435298916357823336103<54>

Number: 20009_121
N=2814532964546077252871970629316708556510168734465584891122419326288554907143692044303039418256114054469
  ( 103 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=23276367811865773221842316006407580116078609884723 (pp50)
 r2=120918048180665503779004167358585435298916357823336103 (pp54)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.13 hours.
Scaled time: 1.44 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_121
n: 2814532964546077252871970629316708556510168734465584891122419326288554907143692044303039418256114054469
m: 1000000000000000000000000
c5: 20
c0: 9
skew: 0.85
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63843, largePrimes:2088965 encountered
Relations: rels:2160713, finalFF:219066
Max relations in full relation-set: 28
Initial matrix: 113008 x 219066 with sparse part having weight 18684530.
Pruned matrix : 87485 x 88114 with weight 4996495.
Total sieving time: 1.91 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.13 hours.
 --------- CPU info (if available) ----------

Nov 13, 2007 (5th)

By Jo Yeong Uk / GMP-ECM

2·10144+9 = 2(0)1439<145> = 11 · 42923 · C139

C139 = P33 · P107

P33 = 128461577505546794238270375795409<33>

P107 = 32974179012994192473352789524852599153449785137428491442089586166492685253837254412846376457647278813227617<107>

Nov 13, 2007 (4th)

By Sinkiti Sibata / GGNFS

2·10109+9 = 2(0)1089<110> = 23 · 95905845140127483764287<23> · C85

C85 = P42 · P44

P42 = 748402279230484392743519946043122325419467<42>

P44 = 12114959912210466897728207722918366529921027<44>

Number: 20009_109
N=9066863611084262532391767761617834512428564112384343014130227238186317203834158432609
  ( 85 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=748402279230484392743519946043122325419467 (pp42)
 r2=12114959912210466897728207722918366529921027 (pp44)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.20 hours.
Scaled time: 0.81 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_109
n: 9066863611084262532391767761617834512428564112384343014130227238186317203834158432609
m: 10000000000000000000000
c5: 1
c0: 45
skew: 2.14
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:1920083 encountered
Relations: rels:1935524, finalFF:195943
Max relations in full relation-set: 28
Initial matrix: 113080 x 195943 with sparse part having weight 13085661.
Pruned matrix : 82364 x 82993 with weight 3462543.
Total sieving time: 1.04 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.20 hours.
 --------- CPU info (if available) ----------

2·10112+9 = 2(0)1119<113> = 11 · 83 · 10859 · 4136577279787441<16> · C90

C90 = P31 · P59

P31 = 9206018018107001474355735891329<31>

P59 = 52973226058227628382351941365777895979723862883622018652443<59>

Number: 20009_112
N=487672473569298877322950209283462946924937198672763413701237098246837153702239074068366747
  ( 90 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=9206018018107001474355735891329 (pp31)
 r2=52973226058227628382351941365777895979723862883622018652443 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.05 hours.
Scaled time: 1.38 units (timescale=0.675).
Factorization parameters were as follows:
name: 20009_112
n: 487672473569298877322950209283462946924937198672763413701237098246837153702239074068366747
m: 10000000000000000000000
c5: 200
c0: 9
skew: 0.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63988, largePrimes:2409465 encountered
Relations: rels:3030076, finalFF:735233
Max relations in full relation-set: 28
Initial matrix: 113151 x 735233 with sparse part having weight 52489673.
Pruned matrix : 56354 x 56983 with weight 4802576.
Total sieving time: 1.89 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.05 hours.
 --------- CPU info (if available) ----------

2·10142+9 = 2(0)1419<143> = 11 · 449 · 183695312580749129<18> · 470754046684836857<18> · 237679956825681386323<21> · C84

C84 = P35 · P49

P35 = 36136781193374500273671200283243499<35>

P49 = 5452012051103151492998305179171168472959562758251<49>

Tue Nov 13 17:25:38 2007  Msieve v. 1.28
Tue Nov 13 17:25:38 2007  random seeds: 101e150d 418d085c
Tue Nov 13 17:25:38 2007  factoring 197018166554355499780407837997782804306340474278893940041682769225414512357104360249 (84 digits)
Tue Nov 13 17:25:39 2007  commencing quadratic sieve (83-digit input)
Tue Nov 13 17:25:40 2007  using multiplier of 29
Tue Nov 13 17:25:40 2007  using 64kb Pentium 2 sieve core
Tue Nov 13 17:25:40 2007  sieve interval: 6 blocks of size 65536
Tue Nov 13 17:25:40 2007  processing polynomials in batches of 17
Tue Nov 13 17:25:40 2007  using a sieve bound of 1392707 (53151 primes)
Tue Nov 13 17:25:40 2007  using large prime bound of 121165509 (26 bits)
Tue Nov 13 17:25:40 2007  using double large prime bound of 354880447655010 (41-49 bits)
Tue Nov 13 17:25:40 2007  using trial factoring cutoff of 49 bits
Tue Nov 13 17:25:40 2007  polynomial 'A' values have 11 factors
Tue Nov 13 21:04:22 2007  53343 relations (15805 full + 37538 combined from 575786 partial), need 53247
Tue Nov 13 21:04:28 2007  begin with 591591 relations
Tue Nov 13 21:04:31 2007  reduce to 124728 relations in 11 passes
Tue Nov 13 21:04:31 2007  attempting to read 124728 relations
Tue Nov 13 21:04:40 2007  recovered 124728 relations
Tue Nov 13 21:04:40 2007  recovered 100888 polynomials
Tue Nov 13 21:04:54 2007  attempting to build 53343 cycles
Tue Nov 13 21:04:55 2007  found 53343 cycles in 5 passes
Tue Nov 13 21:04:57 2007  distribution of cycle lengths:
Tue Nov 13 21:04:57 2007     length 1 : 15805
Tue Nov 13 21:04:57 2007     length 2 : 10899
Tue Nov 13 21:04:57 2007     length 3 : 9489
Tue Nov 13 21:04:57 2007     length 4 : 6716
Tue Nov 13 21:04:57 2007     length 5 : 4439
Tue Nov 13 21:04:57 2007     length 6 : 2729
Tue Nov 13 21:04:57 2007     length 7 : 1532
Tue Nov 13 21:04:57 2007     length 9+: 1734
Tue Nov 13 21:04:57 2007  largest cycle: 17 relations
Tue Nov 13 21:04:57 2007  matrix is 53151 x 53343 with weight 2794558 (avg 52.39/col)
Tue Nov 13 21:04:59 2007  filtering completed in 3 passes
Tue Nov 13 21:04:59 2007  matrix is 48275 x 48339 with weight 2547868 (avg 52.71/col)
Tue Nov 13 21:05:01 2007  saving the first 48 matrix rows for later
Tue Nov 13 21:05:01 2007  matrix is 48227 x 48339 with weight 1924721 (avg 39.82/col)
Tue Nov 13 21:05:01 2007  matrix includes 64 packed rows
Tue Nov 13 21:05:02 2007  commencing Lanczos iteration
Tue Nov 13 21:09:26 2007  lanczos halted after 764 iterations
Tue Nov 13 21:09:27 2007  recovered 17 nontrivial dependencies
Tue Nov 13 21:09:49 2007  prp35 factor: 36136781193374500273671200283243499
Tue Nov 13 21:09:49 2007  prp49 factor: 5452012051103151492998305179171168472959562758251
Tue Nov 13 21:09:49 2007  elapsed time 03:44:11

Nov 13, 2007 (3rd)

By matsuix / GMP-ECM

2·10177+3 = 2(0)1763<178> = 19 · 23 · 107 · C173

C173 = P30 · C144

P30 = 221303620588838744540899263379<30>

C144 = [193275258075082552732257542798544930147975742565477273667881259410088142299640908729176984976444019569373369657540183408799360677960504958362823<144>]

Nov 13, 2007 (2nd)

By JMB / GMP-ECM

9·10179+7 = 9(0)1787<180> = 367699 · 313009111137872717<18> · C157

C157 = P34 · P124

P34 = 1707358559977705545311234918697001<34>

P124 = 4580030236511827524816894288626065240922568714998170751384355667293248449614016116415020750898340461128531874477462326513929<124>

Nov 13, 2007

The factor table of 200...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Nov 12, 2007 (5th)

By Yousuke Koide

(101309-1)/9 is divisible by 1163807225003295831984120638730881<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 12, 2007 (4th)

By matsuix / GMP-ECM

6·10194-1 = 5(9)194<195> = 19 · C194

C194 = P30 · P164

P30 = 552558220648518327302187386107<30>

P164 = 57150443497805430547760194830899991379283534240795388543593799035627131426642721828037543684764910233345763252213386580962086660768427630404724977220097501462854303<164>

Nov 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(8·10178+7)/3 = 2(6)1779<179> = C179

C179 = P78 · P101

P78 = 767662720421063505818715038954728721321787934050897941208611795952414246856909<78>

P101 = 34737477745486953572334913721147854658092970596516908814796404141305652988617311793270855849086732641<101>

Number: 26669_178
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=767662720421063505818715038954728721321787934050897941208611795952414246856909 (pp78)
 r2=34737477745486953572334913721147854658092970596516908814796404141305652988617311793270855849086732641 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 229.96 hours.
Scaled time: 491.89 units (timescale=2.139).
Factorization parameters were as follows:
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 1000000000000000000000000000000000000
c5: 2
c0: 175
skew: 2.45
type: snfs
Factor base limits: 10000000/10000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 50/50
Sieved algebraic special-q in [5000000, 8800001)
Primes: RFBsize:664579, AFBsize:665250, largePrimes:11139695 encountered
Relations: rels:11517589, finalFF:1584544
Max relations in full relation-set: 28
Initial matrix: 1329894 x 1584544 with sparse part having weight 95324120.
Pruned matrix : 1095649 x 1102362 with weight 62665643.
Total sieving time: 220.70 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 8.91 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000
total time: 229.96 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 12, 2007 (2nd)

By Robert Backstrom / GMP-ECM

2·10165+3 = 2(0)1643<166> = 94136405394950299<17> · C149

C149 = P36 · P113

P36 = 838305023383274289860418539450587157<36>

P113 = 25343717347214324824522098723663613215893017202640604427624247481323908812513490062007103784101162836271292998421<113>

Nov 12, 2007

By JMB / GMP-ECM, Msieve

9·10177+7 = 9(0)1767<178> = 153438528657199<15> · 32667044190772508911<20> · C145

C145 = P33 · P112

P33 = 231363885166211856645528826109773<33>

P112 = 7760731807961019750154843183467424612751080704744319434512584619725381829268383039969389480897051376995338032131<112>

9·10182+7 = 9(0)1817<183> = 681997 · 5371290194501118001753<22> · 15159963126712966411921<23> · C134

C134 = P37 · P41 · P57

P37 = 6744944339966240521048365048076011509<37>

P41 = 19234654468418325743668292529120757280653<41>

P57 = 124916706233941797813783021695951936693773474351449547931<57>

9·10191+7 = 9(0)1907<192> = 192 · 71 · 223 · 5348430907<10> · 7081217033400011183081<22> · 4467601201156530952852184773<28> · C126

C126 = P32 · P38 · P58

P32 = 16211565179348756515840607697259<32>

P38 = 21676057655573837315308075461982724731<38>

P58 = 2648244977702149059480307274983753320329588866774945947601<58>

Nov 11, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(17·10165-71)/9 = 1(8)1641<166> = 32 · 11 · 19 · 239 · 2301857 · C154

C154 = P52 · P103

P52 = 1104452615085621808528281839929327507501092871162291<52>

P103 = 1652700990864867075451213479344319367803780935121458431710865579015107058129083254411956069524400585357<103>

Number: n
N=1825329931315300800903828355172001996656416128933119005508117804769257585582659512383777143680106332212925711617403703267839837227789771348804185345172887
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Nov 12 01:18:09 2007  prp52 factor: 1104452615085621808528281839929327507501092871162291
Mon Nov 12 01:18:09 2007  prp103 factor: 1652700990864867075451213479344319367803780935121458431710865579015107058129083254411956069524400585357
Mon Nov 12 01:18:09 2007  elapsed time 01:38:44 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.96 hours.
Scaled time: 60.94 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_1_8_164_1
n: 1825329931315300800903828355172001996656416128933119005508117804769257585582659512383777143680106332212925711617403703267839837227789771348804185345172887
skew: 1.33
deg: 5
c5: 17
c0: -71
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:249087, largePrimes:7336079 encountered
Relations: rels:6862148, finalFF:583606
Max relations in full relation-set: 28
Initial matrix: 499302 x 583606 with sparse part having weight 42516043.
Pruned matrix : 429944 x 432504 with weight 26149440.
Total sieving time: 45.69 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.96 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 11, 2007 (3rd)

By matsuix / GMP-ECM

4·10176+7 = 4(0)1757<177> = 11 · 37 · C174

C174 = P37 · C138

P37 = 7135210354090040619550238567081980993<37>

C138 = [137739594774192223139709541988016487305378968971069153072936288397790444184230544651923302551708474913403317389091953092751175896905333457<138>]

(14·10196-41)/9 = 1(5)1951<197> = 43 · C195

C195 = P29 · C167

P29 = 12991941439670998826484083573<29>

C167 = [27844730337109139843652566781414443973010019917901912124608905800374293093913322511112990355973246182909621326436655829024147474787381586660026718061075677175452115209<167>]

Nov 11, 2007 (2nd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

9·10163+7 = 9(0)1627<164> = 47 · 349 · 859 · 58211 · C153

C153 = P33 · P42 · P78

P33 = 818470811192938112676337938572201<33>

P42 = 873583190755642325776044428797599382814221<42>

P78 = 153466481365034760327052932409167822889494591377902353931701362171082781011161<78>

Number: n
N=134065738464908389294733191862713080806437886653151154389264336165712868499470848705785633116618319074552541740190520581
  ( 120 digits)
SNFS difficulty: 163 digits.
Divisors found:

Sun Nov 11 08:08:38 2007  prp42 factor: 873583190755642325776044428797599382814221
Sun Nov 11 08:08:38 2007  prp78 factor: 153466481365034760327052932409167822889494591377902353931701362171082781011161
Sun Nov 11 08:08:38 2007  elapsed time 01:40:59 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.94 hours.
Scaled time: 83.51 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_9_0_162_7

n: 134065738464908389294733191862713080806437886653151154389264336165712868499470848705785633116618319074552541740190520581

# n: 109728893714553854980742941642496184479539542626049635609986238428007354105418652745423356276793313693697545479480233833467867898192710425178858044968781

skew: 0.16
deg: 5
c5: 9000
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2950001)
Primes: RFBsize:216816, AFBsize:217011, largePrimes:7516572 encountered
Relations: rels:6969287, finalFF:457940
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 63.56 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.94 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 11, 2007

By JMB / GMP-ECM

9·10183+7 = 9(0)1827<184> = 59 · 5879009045374855927<19> · C164

C164 = P35 · P129

P35 = 81464545498575947436007410472506863<35>

P129 = 318506082558980426195556346049653444619519149682263511747011957601975589600934055977483795167502851069663481908650764978825371373<129>

9·10164+7 = 9(0)1637<165> = 883 · 24573393591862132649<20> · C143

C143 = P34 · P110

P34 = 2564993881968404917452325855647781<34>

P110 = 16170756423913671663934778083625100661998605305949217253030068605305369307115708420697061171260255444165225841<110>

9·10173+7 = 9(0)1727<174> = 19 · 647 · 224401 · C165

C165 = P31 · P134

P31 = 4204449134966651726234511502249<31>

P134 = 77598037366254001837116882823105292830227805356149887771917581121716866409828186604482406682111147355193961123945624774784312354859251<134>

9·10169+7 = 9(0)1687<170> = 2111 · 1429958609<10> · C158

C158 = P32 · P126

P32 = 56769904881370799699375018291651<32>

P126 = 525185398197314224568248713026766256427182001005757531713576174925963787257959304880282840700874560113146274753741218461103843<126>

Nov 10, 2007 (2nd)

By Sinkiti Sibata / PFGW

(23·1010598+7)/3, (23·1012465+7)/3, (23·1015875+7)/3 and (23·1018895+7)/3 are PRPs. There is no other PRP of the form (23·10n+7)/3 (10001≤n≤20000).

Nov 10, 2007

By matsuix / GMP-ECM

6·10166-1 = 5(9)166<167> = 1415744095201<13> · C155

C155 = P26 · C130

P26 = 12712979409464320156621733<26>

C130 = [3333643448967159954626524687734330724615407100378702091659234658746271899362005594705868470962976554854259399799326518042378430003<130>]

Nov 9, 2007

By matsuix / GMP-ECM

(55·10180-1)/9 = 6(1)180<181> = 3 · 23 · C179

C179 = P30 · P150

P30 = 101498619902504222710961733499<30>

P150 = 872591447867335155263871338215982008049920291961559255672354899684344056901549523294371067281499223907198249217989811855244487724718971598186664829281<150>

Nov 8, 2007 (2nd)

By matsuix / GMP-ECM

(8·10174-53)/9 = (8)1733<174> = 2309 · C171

C171 = P29 · C143

P29 = 28200513448768426338019164149<29>

C143 = [13651064825355236966422593727849148145450828300351719858603135500864608496173059635187685618753649483887590160393912399962653031892990513454363<143>]

Nov 8, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

9·10153+7 = 9(0)1527<154> = 907 · 1567 · 51635332541907318461<20> · C129

C129 = P61 · P68

P61 = 4772486568530653705948719675085861919871051034726502704647793<61>

P68 = 25696533054533355691086868666739471157508323084478430890473067987511<68>

Number: n
N=122636358860564412039100336767082272939485086621808173675665794174642554988798630986018211854909258720752103550308799860577713223
  ( 129 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=4772486568530653705948719675085861919871051034726502704647793 (pp61)
 r2=25696533054533355691086868666739471157508323084478430890473067987511 (pp68)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 26.78 hours.
Scaled time: 35.54 units (timescale=1.327).
Factorization parameters were as follows:
name: KA_9_0_152_7
n: 122636358860564412039100336767082272939485086621808173675665794174642554988798630986018211854909258720752103550308799860577713223
skew: 0.24
deg: 5
c5: 9000
c0: 7
m: 1000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1100001)
Primes: RFBsize:183072, AFBsize:183101, largePrimes:6782121 encountered
Relations: rels:6200134, finalFF:427533
Max relations in full relation-set: 48
Initial matrix: 366240 x 427533 with sparse part having weight 38208097.
Pruned matrix : 321175 x 323070 with weight 23509586.
Total sieving time: 23.39 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 3.08 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 26.78 hours.
 --------- CPU info (if available) ----------

Cywin on AMD 64 3200+

(67·10165+23)/9 = 7(4)1647<166> = 11 · 17 · 113417 · C159

C159 = P76 · P84

P76 = 3436383816970356938534318813689175226044935882855602276600499748816862981373<76>

P84 = 102143530795393078870771512077719961217354103402463760765008945031833455587257908841<84>

Number: n
N=351004376233502067423634322257777917760418568213229144337614952819956323425302295053639519584815678512598105002812461856105588319194641309439952033732715018693
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Nov 08 15:26:03 2007  prp76 factor: 3436383816970356938534318813689175226044935882855602276600499748816862981373
Thu Nov 08 15:26:03 2007  prp84 factor: 102143530795393078870771512077719961217354103402463760765008945031833455587257908841
Thu Nov 08 15:26:03 2007  elapsed time 02:17:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 81.97 hours.
Scaled time: 98.04 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_7_4_164_7
n: 351004376233502067423634322257777917760418568213229144337614952819956323425302295053639519584815678512598105002812461856105588319194641309439952033732715018693
type: snfs
skew: 0.81
deg: 5
c5: 67
c0: 23
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:250150, AFBsize:249876, largePrimes:7471694 encountered
Relations: rels:6998321, finalFF:574667
Max relations in full relation-set: 28
Initial matrix: 500091 x 574667 with sparse part having weight 41672522.
Pruned matrix : 442380 x 444944 with weight 28636697.
Total sieving time: 81.66 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 81.97 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(71·10165-17)/9 = 7(8)1647<166> = 3 · 11 · 79 · 467 · 1619 · 377387 · C152

C152 = P31 · P41 · P81

P31 = 1719997418393992940622623083871<31>

P41 = 38022766744779558259291504973562443163143<41>

P81 = 162163322041498669991056527746571842965333158652283809975565132898038976089503147<81>

Nov 7, 2007 (4th)

By Jo Yeong Uk / GGNFS

9·10160+7 = 9(0)1597<161> = 193 · 233 · 43499 · 1514405906081012721338467999<28> · C125

C125 = P58 · P67

P58 = 9539345889759064940903674568760087065552798466254478738629<58>

P67 = 3184850972645850020285709503660847208668237617514389096861847478007<67>

Number: 90007_160
N=30381395035404349559261482175363386501616068379879041925147514635035093035613293267212425275525857274850151785739806178832403
  ( 125 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=9539345889759064940903674568760087065552798466254478738629 (pp58)
 r2=3184850972645850020285709503660847208668237617514389096861847478007 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 30.91 hours.
Scaled time: 66.06 units (timescale=2.137).
Factorization parameters were as follows:
n: 30381395035404349559261482175363386501616068379879041925147514635035093035613293267212425275525857274850151785739806178832403
m: 100000000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283337, largePrimes:5671469 encountered
Relations: rels:5709779, finalFF:661423
Max relations in full relation-set: 28
Initial matrix: 566547 x 661423 with sparse part having weight 42662144.
Pruned matrix : 495804 x 498700 with weight 29440637.
Total sieving time: 29.54 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.24 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 30.91 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 7, 2007 (3rd)

By Sinkiti Sibata / PFGW

9·1015710+7, 9·1016453+7, 9·1017488+7 and 9·1018109+7 are PRPs. There is no other PRP of the form 9·10n+7 (10001≤n≤20000).

Nov 7, 2007 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

9·10121+7 = 9(0)1207<122> = 71 · 10733 · 14298301 · 13437563210843<14> · C96

C96 = P47 · P50

P47 = 46754707307478264058557236237372093839004268587<47>

P50 = 13147183761460396406902731745730328931732164333889<50>

Mon Nov 05 07:44:28 2007  
Mon Nov 05 07:44:28 2007  Msieve v. 1.28
Mon Nov 05 07:44:28 2007  random seeds: cd76d0a4 bee9a5b5
Mon Nov 05 07:44:28 2007  factoring 614692728684711966341285537593488278848176917343378079725035602868779219670052351614028502244843 (96 digits)
Mon Nov 05 07:44:29 2007  commencing quadratic sieve (96-digit input)
Mon Nov 05 07:44:30 2007  using multiplier of 11
Mon Nov 05 07:44:30 2007  using 64kb Pentium 2 sieve core
Mon Nov 05 07:44:30 2007  sieve interval: 18 blocks of size 65536
Mon Nov 05 07:44:30 2007  processing polynomials in batches of 6
Mon Nov 05 07:44:30 2007  using a sieve bound of 2297747 (84706 primes)
Mon Nov 05 07:44:30 2007  using large prime bound of 344662050 (28 bits)
Mon Nov 05 07:44:30 2007  using double large prime bound of 2329744160961150 (43-52 bits)
Mon Nov 05 07:44:30 2007  using trial factoring cutoff of 52 bits
Mon Nov 05 07:44:30 2007  polynomial 'A' values have 13 factors
Tue Nov 06 21:50:05 2007  85254 relations (21080 full + 64174 combined from 1274004 partial), need 84802
Tue Nov 06 21:50:26 2007  begin with 1295084 relations
Tue Nov 06 21:53:11 2007  reduce to 222278 relations in 12 passes
Tue Nov 06 21:53:12 2007  attempting to read 222278 relations
Tue Nov 06 21:53:48 2007  recovered 222278 relations
Tue Nov 06 21:53:48 2007  recovered 207893 polynomials
Tue Nov 06 21:56:08 2007  attempting to build 85254 cycles
Tue Nov 06 21:56:15 2007  found 85254 cycles in 6 passes
Tue Nov 06 21:56:21 2007  distribution of cycle lengths:
Tue Nov 06 21:56:21 2007     length 1 : 21080
Tue Nov 06 21:56:21 2007     length 2 : 14945
Tue Nov 06 21:56:21 2007     length 3 : 14297
Tue Nov 06 21:56:21 2007     length 4 : 11531
Tue Nov 06 21:56:21 2007     length 5 : 8635
Tue Nov 06 21:56:21 2007     length 6 : 5795
Tue Nov 06 21:56:21 2007     length 7 : 3728
Tue Nov 06 21:56:21 2007     length 9+: 5243
Tue Nov 06 21:56:21 2007  largest cycle: 20 relations
Tue Nov 06 21:56:42 2007  matrix is 84706 x 85254 with weight 5719147 (avg 67.08/col)
Tue Nov 06 21:57:55 2007  filtering completed in 3 passes
Tue Nov 06 21:57:55 2007  matrix is 80583 x 80647 with weight 5410769 (avg 67.09/col)
Tue Nov 06 21:57:59 2007  saving the first 48 matrix rows for later
Tue Nov 06 21:58:00 2007  matrix is 80535 x 80647 with weight 4352733 (avg 53.97/col)
Tue Nov 06 21:58:00 2007  matrix includes 64 packed rows
Tue Nov 06 21:58:00 2007  using block size 10922 for processor cache size 256 kB
Tue Nov 06 21:58:03 2007  commencing Lanczos iteration
Tue Nov 06 22:04:03 2007  lanczos halted after 1275 iterations
Tue Nov 06 22:04:05 2007  recovered 15 nontrivial dependencies
Tue Nov 06 23:20:29 2007  prp47 factor: 46754707307478264058557236237372093839004268587
Tue Nov 06 23:20:29 2007  prp50 factor: 13147183761460396406902731745730328931732164333889
Tue Nov 06 23:20:29 2007  elapsed time 39:36:01

9·10166-7 = 8(9)1653<167> = 42709 · 1578482099<10> · C154

C154 = P39 · P115

P39 = 326236852168633890020751838911718198217<39>

P115 = 4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519<115>

Number: 89993_166
N=1335006700623134276833509278792951544459029456753960978279183880064673180289547757171082237750647795330058324252033450827327369675772426590179731812393623
  ( 154 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=326236852168633890020751838911718198217 (pp39)
 r2=4092139473970466337231565660348581447470351547418909019180227591362356350317132972423887166170348215102482040007519 (pp115)
Version: GGNFS-0.77.1-20060513-k8
Total time: 124.14 hours.
Scaled time: 248.65 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_166
n: 1335006700623134276833509278792951544459029456753960978279183880064673180289547757171082237750647795330058324252033450827327369675772426590179731812393623
m: 1000000000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:349111, largePrimes:5986344 encountered
Relations: rels:6137431, finalFF:783376
Max relations in full relation-set: 28
Initial matrix: 697691 x 783376 with sparse part having weight 60293050.
Pruned matrix : 635609 x 639161 with weight 46938360.
Total sieving time: 117.98 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.62 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 124.14 hours.
 --------- CPU info (if available) ----------

Nov 7, 2007

By Robert Backstrom / GGNFS, Msieve

9·10154+7 = 9(0)1537<155> = C155

C155 = P75 · P81

P75 = 342774283579171568600971909894532466448184589420657720323497289127488139607<75>

P81 = 262563454469922156375323276959104849917481523961677799993943153957816466910677201<81>

Number: n
N=90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 155 digits)
SNFS difficulty: 155 digits.
Divisors found:

Wed Nov 07 02:43:42 2007  prp75 factor: 342774283579171568600971909894532466448184589420657720323497289127488139607
Wed Nov 07 02:43:42 2007  prp81 factor: 262563454469922156375323276959104849917481523961677799993943153957816466910677201
Wed Nov 07 02:43:42 2007  elapsed time 01:08:12 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 31.83 hours.
Scaled time: 38.16 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_9_0_153_7
n: 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
type: snfs
skew: 1.51
deg: 5
c5: 9
c0: 70
m: 10000000000000000000000000000000
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1350000)
Primes: RFBsize:216816, AFBsize:217291, largePrimes:6508656 encountered
Relations: rels:6015638, finalFF:533595
Max relations in full relation-set: 28
Initial matrix: 434171 x 533595 with sparse part having weight 29453920.
Pruned matrix : 345128 x 347362 with weight 15856430.
Total sieving time: 31.59 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000
total time: 31.83 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Nov 6, 2007 (7th)

By JMB / GGNFS

9·10152+7 = 9(0)1517<153> = 4761397 · 170458908643<12> · 49688519499466733076979<23> · C113

C113 = P39 · P74

P39 = 703840987201156095759020645169329337871<39>

P74 = 31707193373284828223436939712373236806907701314756561688871528206762760813<74>

Nov 6, 2007 (6th)

By Jo Yeong Uk / GGNFS, GMP-ECM

9·10150+7 = 9(0)1497<151> = 19732343 · 326052556279<12> · C133

C133 = P39 · P94

P39 = 589499724724831441087810448027951375963<39>

P94 = 2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237<94>

Number: 90007_150
N=1398866416610448089159839440560263500294515545943113810621260052431416451996375989188510257329362504846021037950153661991966102374231
  ( 133 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=589499724724831441087810448027951375963 (pp39)
 r2=2372972128635709558872684003447910854760650370032899324921933688620430554494554451055042317237 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.90 hours.
Scaled time: 27.68 units (timescale=2.146).
Factorization parameters were as follows:
n: 1398866416610448089159839440560263500294515545943113810621260052431416451996375989188510257329362504846021037950153661991966102374231
m: 1000000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5458981 encountered
Relations: rels:5399088, finalFF:508783
Max relations in full relation-set: 28
Initial matrix: 352824 x 508783 with sparse part having weight 43914106.
Pruned matrix : 281114 x 282942 with weight 22700108.
Total sieving time: 12.40 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.39 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10162+7 = 9(0)1617<163> = 5675476123<10> · 19653188594940718862107501<26> · C128

C128 = P36 · P93

P36 = 688903506523745903246622831283151599<36>

P93 = 117124780898551182812517761055884645674869174813318998257172923202640159324081908982573296791<93>

Nov 6, 2007 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

9·10164-7 = 8(9)1633<165> = 19 · 1847353 · C158

C158 = P40 · P56 · P63

P40 = 5195304037384876588643582502770703788863<40>

P56 = 44521045988937219971985542168110282187182538753337627749<56>

P63 = 110856890051938744122912238100452821884732080214861054731598977<63>

Number: n
N=4935464700192921827044022834990668957767855479530538704420183216532608252538248713711246307900524500214451242775212773
  ( 118 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Nov 06 10:24:21 2007  prp56 factor: 44521045988937219971985542168110282187182538753337627749
Tue Nov 06 10:24:21 2007  prp63 factor: 110856890051938744122912238100452821884732080214861054731598977
Tue Nov 06 10:24:21 2007  elapsed time 01:29:30 (Msieve 1.29)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 64.39 hours.
Scaled time: 84.09 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_8_9_163_3
n: 4935464700192921827044022834990668957767855479530538704420183216532608252538248713711246307900524500214451242775212773

# n: 25641239683282826264048301029977258784524896461386415561816513169184004869328396388038224934470250706081392645243448898305618334648776412862933585172092747099

skew: 1.51
deg: 5
c5: 9
c0: -70
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3200000)
Primes: RFBsize:216816, AFBsize:217291, largePrimes:7651039 encountered
Relations: rels:7167373, finalFF:504847
Max relations in full relation-set: 28
Initial matrix: 434171 x 504847 with sparse part having weight 46676546.
Pruned matrix : 406046 x 408280 with weight 34115092.
Total sieving time: 64.06 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 64.39 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(2·10166+1)/3 = (6)1657<166> = 132420593 · C158

C158 = P36 · P123

P36 = 472608263478122255214913213813840403<36>

P123 = 106525087996081326022960925559747436760122308821013875848798824526842994763515192581889447596719018370039169071680038462873<123>

Nov 6, 2007 (4th)

By matsuix / GMP-ECM

(19·10165-1)/9 = 2(1)165<166> = 97 · 28030207 · 678175727 · 28933389748066579<17> · C131

C131 = P40 · P92

P40 = 1004850910964957079601987123021515538751<40>

P92 = 39379469642482560582795123873781476067047647244625665707647850841194751914774629866823998323<92>

Nov 6, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10133+7 = 9(0)1327<134> = 5881 · 26930082287<11> · 176964956297383872307<21> · C100

C100 = P44 · P57

P44 = 25264976655443100325796147326226279933324489<44>

P57 = 127100563245798676374051740186784449244832505678728530547<57>

Number: 90007_133
N=3211192763298772886403404485557143401237610375947392799399813124253179761582114633674548555499665483
  ( 100 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=25264976655443100325796147326226279933324489 (pp44)
 r2=127100563245798676374051740186784449244832505678728530547 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.81 hours.
Scaled time: 5.96 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_133
n: 3211192763298772886403404485557143401237610375947392799399813124253179761582114633674548555499665483
m: 100000000000000000000000000
c5: 9000
c0: 7
skew: 0.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:78498, AFBsize:63803, largePrimes:1571280 encountered
Relations: rels:1590409, finalFF:190659
Max relations in full relation-set: 28
Initial matrix: 142368 x 190659 with sparse part having weight 15771459.
Pruned matrix : 127262 x 128037 with weight 8863354.
Total sieving time: 8.34 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.81 hours.
 --------- CPU info (if available) ----------

9·10117+7 = 9(0)1167<118> = 47 · 443867 · C111

C111 = P41 · P71

P41 = 17471857037357853190634584935442902072067<41>

P71 = 24691798610564857752888526692177153472802870226100236461016311059115929<71>

Number: 90007_117
N=431411575319020471390006657639299562083696817558297724701797533850110074663442648073275160198696667283265655243
  ( 111 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=17471857037357853190634584935442902072067 (pp41)
 r2=24691798610564857752888526692177153472802870226100236461016311059115929 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.78 hours.
Scaled time: 1.88 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_117
n: 431411575319020471390006657639299562083696817558297724701797533850110074663442648073275160198696667283265655243
m: 100000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2291621 encountered
Relations: rels:2546258, finalFF:364912
Max relations in full relation-set: 28
Initial matrix: 112985 x 364912 with sparse part having weight 33871287.
Pruned matrix : 74587 x 75215 with weight 6217223.
Total sieving time: 2.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

Nov 6, 2007 (2nd)

By JMB / GGNFS

9·10184+7 = 9(0)1837<185> = 617 · 3725507 · 159746791 · 1198459567<10> · 80746431532206891622049<23> · 666062407088402900138543<24> · C112

C112 = P53 · P60

P53 = 11636058351571852705216457129789359016330456971195199<53>

P60 = 326792650541123463809952364790176505238645003791330917413293<60>

Nov 6, 2007

By Torbjörn Granlund

(10843-1)/9 is divisible by 769166959867961874063651865987632601<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 5, 2007 (5th)

By JMB / GMP-ECM, Msieve

9·10147+7 = 9(0)1467<148> = 25951 · 1738969 · 197021917 · 92978880982634662097<20> · C110

C110 = P30 · P40 · P41

P30 = 102931531869565976194616134711<30>

P40 = 2005256885602141410291462050850625780121<40>

P41 = 52744753108364828721861464937342277420987<41>

9·10151+7 = 9(0)1507<152> = 269 · 21613 · 67791928153<11> · 44970969250703<14> · 383031576676808952277813<24> · C98

C98 = P40 · P58

P40 = 6810025963958582438251862479127272552967<40>

P58 = 1946621858651143417424307752923064400610721325684111628979<58>

Nov 5, 2007 (4th)

By Sinkiti Sibata / GGNFS

9·10120+7 = 9(0)1197<121> = 29 · 281 · 386471 · 142583653 · C104

C104 = P33 · P71

P33 = 266099299493114096677875328801409<33>

P71 = 75319566589929176165358361692126958829966221213822132241587381268023129<71>

Number: 90007_120
N=20042483907705114278411372506196732936640720090441885904393246630974136265348532459246920117086459788761
  ( 104 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=266099299493114096677875328801409 (pp33)
 r2=75319566589929176165358361692126958829966221213822132241587381268023129 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.09 hours.
Scaled time: 1.41 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_120
n: 20042483907705114278411372506196732936640720090441885904393246630974136265348532459246920117086459788761
m: 1000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:2006815 encountered
Relations: rels:1988282, finalFF:148363
Max relations in full relation-set: 28
Initial matrix: 113070 x 148363 with sparse part having weight 12012483.
Pruned matrix : 101019 x 101648 with weight 6176663.
Total sieving time: 1.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.09 hours.
 --------- CPU info (if available) ----------

9·10126+7 = 9(0)1257<127> = 18386461 · 1742218293047<13> · C108

C108 = P32 · P77

P32 = 13822662893206118250744627949841<32>

P77 = 20325913755563927082639117313372686004914219990075373791674260136282142256981<77>

Number: 90007_126
N=280958253839541308962636479299682207592405666050712699120756569825329538777009922534463258852005274600090021
  ( 108 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=13822662893206118250744627949841 (pp32)
 r2=20325913755563927082639117313372686004914219990075373791674260136282142256981 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.97 hours.
Scaled time: 2.69 units (timescale=0.676).
Factorization parameters were as follows:
name: 90007_126
n: 280958253839541308962636479299682207592405666050712699120756569825329538777009922534463258852005274600090021
m: 10000000000000000000000000
c5: 90
c0: 7
skew: 0.6
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 750001)
Primes: RFBsize:49098, AFBsize:64083, largePrimes:2196928 encountered
Relations: rels:2262442, finalFF:171270
Max relations in full relation-set: 28
Initial matrix: 113248 x 171270 with sparse part having weight 16894508.
Pruned matrix : 103160 x 103790 with weight 7851326.
Total sieving time: 3.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.22 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.97 hours.
 --------- CPU info (if available) ----------

Nov 5, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

4·10161-3 = 3(9)1607<162> = 13 · 71 · 738953 · 17948851 · 743599950371757358081470341<27> · C119

C119 = P43 · P77

P43 = 2846805213519635781879812334100609838888539<43>

P77 = 15435038486874269067278126927452408807037060575563649377214970000125309743587<77>

Number: n
N=43940548035309899548763925751595996999472868799993550808813202591598052489814547810338118021293899624001452203163049393
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Nov 05 02:38:02 2007  prp43 factor: 2846805213519635781879812334100609838888539
Mon Nov 05 02:38:02 2007  prp77 factor: 15435038486874269067278126927452408807037060575563649377214970000125309743587
Mon Nov 05 02:38:02 2007  elapsed time 01:17:03 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 33.21 hours.
Scaled time: 43.87 units (timescale=1.321).
Factorization parameters were as follows:
name: KA_3_9_160_7
n: 43940548035309899548763925751595996999472868799993550808813202591598052489814547810338118021293899624001452203163049393
skew: 0.60
deg: 5
c5: 40
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:215821, largePrimes:7042289 encountered
Relations: rels:6514886, finalFF:501112
Max relations in full relation-set: 28
Initial matrix: 432703 x 501112 with sparse part having weight 40819259.
Pruned matrix : 378693 x 380920 with weight 25477509.
Total sieving time: 33.00 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 33.21 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10111+7 = 9(0)1107<112> = 131 · 859 · C107

C107 = P33 · P35 · P40

P33 = 682916690512923260407060455419117<33>

P35 = 51118310350528656363520883890560151<35>

P40 = 2291046123805509364111583138403788910949<40>

9·10127+7 = 9(0)1267<128> = 344206321 · C120

C120 = P35 · P85

P35 = 33157853781215682395478284485540807<35>

P85 = 7885645618034098004254139912968642957732499669205257892740457352566043261860258601681<85>

9·10135+7 = 9(0)1347<136> = 1002121 · 14760091 · C123

C123 = P54 · P70

P54 = 588447254183867044277609191468715934421424931568990421<54>

P70 = 1034012456449314522976535796820781617144073180839915839118262268905897<70>

Number: n
N=608461790789514535341427955241331643019831322889419400572308896788480722510373845551247628493647294880837405891288543412637
  ( 123 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=588447254183867044277609191468715934421424931568990421 (pp54)
 r2=1034012456449314522976535796820781617144073180839915839118262268905897 (pp70)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.84 hours.
Scaled time: 6.28 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_9_0_134_7
n: 608461790789514535341427955241331643019831322889419400572308896788480722510373845551247628493647294880837405891288543412637
skew: 0.95
deg: 5
c5: 9
c0: 7
m: 1000000000000000000000000000
type: snfs
rlim: 2400000
alim: 2400000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 440001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5339208 encountered
Relations: rels:4827042, finalFF:398527
Max relations in full relation-set: 48
Initial matrix: 352824 x 398527 with sparse part having weight 16282983.
Pruned matrix : 297861 x 299689 with weight 9125460.
Total sieving time: 3.68 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.99 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,2400000,2400000,28,28,48,48,2.5,2.5,75000
total time: 4.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10143+7 = 9(0)1427<144> = 67 · 14449 · C138

C138 = P32 · P107

P32 = 16764671435106466291549252481783<32>

P107 = 55454254267525152340965490394347806129765919513362592966669387843539324159605808600050322487693263291392363<107>

Nov 5, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM

9·10108+7 = 9(0)1077<109> = 37871 · 3406331833<10> · 88079868587<11> · C84

C84 = P33 · P52

P33 = 144064331776620889004606685503461<33>

P52 = 5498138252554114429604456503865744400402842973430807<52>

Mon Nov  5 01:24:55 2007  
Mon Nov  5 01:24:55 2007  
Mon Nov  5 01:24:55 2007  Msieve v. 1.28
Mon Nov  5 01:24:55 2007  random seeds: 152d9442 e6816ec9
Mon Nov  5 01:24:55 2007  factoring 792085613369686554167223683559223742655367466905587896034275024581697823391242523027 (84 digits)
Mon Nov  5 01:24:55 2007  commencing quadratic sieve (84-digit input)
Mon Nov  5 01:24:55 2007  using multiplier of 43
Mon Nov  5 01:24:55 2007  using 32kb Intel Core sieve core
Mon Nov  5 01:24:55 2007  sieve interval: 12 blocks of size 32768
Mon Nov  5 01:24:55 2007  processing polynomials in batches of 17
Mon Nov  5 01:24:55 2007  using a sieve bound of 1401067 (53824 primes)
Mon Nov  5 01:24:55 2007  using large prime bound of 119090695 (26 bits)
Mon Nov  5 01:24:55 2007  using double large prime bound of 344017052465110 (41-49 bits)
Mon Nov  5 01:24:55 2007  using trial factoring cutoff of 49 bits
Mon Nov  5 01:24:55 2007  polynomial 'A' values have 11 factors
Mon Nov  5 01:43:23 2007  54205 relations (16445 full + 37760 combined from 563337 partial), need 53920
Mon Nov  5 01:43:23 2007  begin with 579782 relations
Mon Nov  5 01:43:24 2007  reduce to 124756 relations in 9 passes
Mon Nov  5 01:43:24 2007  attempting to read 124756 relations
Mon Nov  5 01:43:25 2007  recovered 124756 relations
Mon Nov  5 01:43:25 2007  recovered 99117 polynomials
Mon Nov  5 01:43:25 2007  attempting to build 54205 cycles
Mon Nov  5 01:43:25 2007  found 54205 cycles in 5 passes
Mon Nov  5 01:43:25 2007  distribution of cycle lengths:
Mon Nov  5 01:43:25 2007     length 1 : 16445
Mon Nov  5 01:43:25 2007     length 2 : 11224
Mon Nov  5 01:43:25 2007     length 3 : 9837
Mon Nov  5 01:43:25 2007     length 4 : 6662
Mon Nov  5 01:43:25 2007     length 5 : 4386
Mon Nov  5 01:43:25 2007     length 6 : 2611
Mon Nov  5 01:43:25 2007     length 7 : 1468
Mon Nov  5 01:43:25 2007     length 9+: 1572
Mon Nov  5 01:43:25 2007  largest cycle: 15 relations
Mon Nov  5 01:43:25 2007  matrix is 53824 x 54205 with weight 2718225 (avg 50.15/col)
Mon Nov  5 01:43:25 2007  filtering completed in 3 passes
Mon Nov  5 01:43:25 2007  matrix is 48768 x 48832 with weight 2453195 (avg 50.24/col)
Mon Nov  5 01:43:26 2007  saving the first 48 matrix rows for later
Mon Nov  5 01:43:26 2007  matrix is 48720 x 48832 with weight 1746320 (avg 35.76/col)
Mon Nov  5 01:43:26 2007  matrix includes 64 packed rows
Mon Nov  5 01:43:26 2007  commencing Lanczos iteration
Mon Nov  5 01:44:06 2007  lanczos halted after 771 iterations
Mon Nov  5 01:44:07 2007  recovered 17 nontrivial dependencies
Mon Nov  5 01:44:07 2007  prp33 factor: 144064331776620889004606685503461
Mon Nov  5 01:44:07 2007  prp52 factor: 5498138252554114429604456503865744400402842973430807
Mon Nov  5 01:44:07 2007  elapsed time 00:19:12

9·10131+7 = 9(0)1307<132> = 38921 · 632971 · 968437 · 83275116371<11> · 274255609394142444443<21> C85

C85 = P40 · P45

P40 = 2288057282169860293574275141471863042313<40>

P45 = 721881101657780564083407600404226856588479089<45>

Mon Nov  5 01:45:50 2007  
Mon Nov  5 01:45:50 2007  
Mon Nov  5 01:45:50 2007  Msieve v. 1.28
Mon Nov  5 01:45:50 2007  random seeds: 72177c0e 693b4483
Mon Nov  5 01:45:50 2007  factoring 1651705311508886027462420179604336574242886949428131140156014177945487040201122692857 (85 digits)
Mon Nov  5 01:45:50 2007  commencing quadratic sieve (84-digit input)
Mon Nov  5 01:45:50 2007  using multiplier of 5
Mon Nov  5 01:45:50 2007  using 32kb Intel Core sieve core
Mon Nov  5 01:45:50 2007  sieve interval: 12 blocks of size 32768
Mon Nov  5 01:45:50 2007  processing polynomials in batches of 17
Mon Nov  5 01:45:50 2007  using a sieve bound of 1413031 (54118 primes)
Mon Nov  5 01:45:50 2007  using large prime bound of 118694604 (26 bits)
Mon Nov  5 01:45:50 2007  using double large prime bound of 341960341070040 (41-49 bits)
Mon Nov  5 01:45:50 2007  using trial factoring cutoff of 49 bits
Mon Nov  5 01:45:50 2007  polynomial 'A' values have 11 factors
Mon Nov  5 02:05:58 2007  54588 relations (16316 full + 38272 combined from 571175 partial), need 54214
Mon Nov  5 02:05:58 2007  begin with 587491 relations
Mon Nov  5 02:05:58 2007  reduce to 126754 relations in 10 passes
Mon Nov  5 02:05:58 2007  attempting to read 126754 relations
Mon Nov  5 02:05:59 2007  recovered 126754 relations
Mon Nov  5 02:05:59 2007  recovered 102596 polynomials
Mon Nov  5 02:05:59 2007  attempting to build 54588 cycles
Mon Nov  5 02:05:59 2007  found 54588 cycles in 5 passes
Mon Nov  5 02:05:59 2007  distribution of cycle lengths:
Mon Nov  5 02:05:59 2007     length 1 : 16316
Mon Nov  5 02:05:59 2007     length 2 : 11199
Mon Nov  5 02:05:59 2007     length 3 : 9830
Mon Nov  5 02:05:59 2007     length 4 : 6838
Mon Nov  5 02:05:59 2007     length 5 : 4545
Mon Nov  5 02:05:59 2007     length 6 : 2670
Mon Nov  5 02:05:59 2007     length 7 : 1519
Mon Nov  5 02:05:59 2007     length 9+: 1671
Mon Nov  5 02:05:59 2007  largest cycle: 18 relations
Mon Nov  5 02:05:59 2007  matrix is 54118 x 54588 with weight 2840617 (avg 52.04/col)
Mon Nov  5 02:06:00 2007  filtering completed in 3 passes
Mon Nov  5 02:06:00 2007  matrix is 49044 x 49108 with weight 2553112 (avg 51.99/col)
Mon Nov  5 02:06:00 2007  saving the first 48 matrix rows for later
Mon Nov  5 02:06:00 2007  matrix is 48996 x 49108 with weight 1908309 (avg 38.86/col)
Mon Nov  5 02:06:00 2007  matrix includes 64 packed rows
Mon Nov  5 02:06:00 2007  commencing Lanczos iteration
Mon Nov  5 02:06:41 2007  lanczos halted after 776 iterations
Mon Nov  5 02:06:42 2007  recovered 16 nontrivial dependencies
Mon Nov  5 02:06:42 2007  prp40 factor: 2288057282169860293574275141471863042313
Mon Nov  5 02:06:42 2007  prp45 factor: 721881101657780564083407600404226856588479089
Mon Nov  5 02:06:42 2007  elapsed time 00:20:52

9·10112+7 = 9(0)1117<113> = 1706363 · 6132851 · 14021233 · C93

C93 = P45 · P49

P45 = 366287276724937330096345104351579811913585089<45>

P49 = 1674559682769946750885495255184227109771029382647<49>

Number: 90007_112
N=613369905915178755561126474140880398319161319784569225022227103519115609390857587884174550583
  ( 93 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=366287276724937330096345104351579811913585089 (pp45)
 r2=1674559682769946750885495255184227109771029382647 (pp49)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.89 hours.
Scaled time: 1.90 units (timescale=2.119).
Factorization parameters were as follows:
n: 613369905915178755561126474140880398319161319784569225022227103519115609390857587884174550583
m: 10000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 360001)
Primes: RFBsize:30757, AFBsize:30859, largePrimes:1047627 encountered
Relations: rels:958703, finalFF:81871
Max relations in full relation-set: 28
Initial matrix: 61680 x 81871 with sparse part having weight 4265106.
Pruned matrix : 57019 x 57391 with weight 2165245.
Total sieving time: 0.86 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10114+7 = 9(0)1137<115> = 653 · 4287299 · 249763385813<12> · C95

C95 = P42 · P54

P42 = 115630510169949718409527011290812428381853<42>

P54 = 111312603505914666012718121697883345483669372301240129<54>

Number: 90007_114
N=12871133131734246468791789551870388883140990287398533490691419410177257253759609146868658979037
  ( 95 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=115630510169949718409527011290812428381853 (pp42)
 r2=111312603505914666012718121697883345483669372301240129 (pp54)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.90 hours.
Scaled time: 1.93 units (timescale=2.145).
Factorization parameters were as follows:
n: 12871133131734246468791789551870388883140990287398533490691419410177257253759609146868658979037
m: 100000000000000000000000
c5: 9
c0: 70
skew: 1.51
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 420001)
Primes: RFBsize:49098, AFBsize:49341, largePrimes:1898932 encountered
Relations: rels:2001615, finalFF:245554
Max relations in full relation-set: 28
Initial matrix: 98503 x 245554 with sparse part having weight 19808415.
Pruned matrix : 69060 x 69616 with weight 3831506.
Total sieving time: 0.85 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.90 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10146+7 = 9(0)1457<147> = 23 · 4271 · 437543 · 5421833 · 8849681 · C123

C123 = P35 · P89

P35 = 23988971368700909013664451648647553<35>

P89 = 18191938657561789126660465345836496511300044062263632583171015546703249344891910371448337<89>

9·10132+7 = 9(0)1317<133> = 491 · 85117573 · C123

C123 = P51 · P73

P51 = 139221663158686554389864242499707408798312738177711<51>

P73 = 1546802865177850881667388439251649501422697254868710734255734319160698559<73>

Number: 90007_132
N=215348467468682007507192912246188645535589219763134333352082775267400780424803384796810560313123800212289002220311443618449
  ( 123 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=139221663158686554389864242499707408798312738177711 (pp51)
 r2=1546802865177850881667388439251649501422697254868710734255734319160698559 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.77 hours.
Scaled time: 8.02 units (timescale=2.125).
Factorization parameters were as follows:
n: 215348467468682007507192912246188645535589219763134333352082775267400780424803384796810560313123800212289002220311443618449
m: 100000000000000000000000000
c5: 900
c0: 7
skew: 0.38
type: snfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [600000, 1350001)
Primes: RFBsize:92938, AFBsize:92634, largePrimes:1721351 encountered
Relations: rels:1789708, finalFF:239139
Max relations in full relation-set: 28
Initial matrix: 185636 x 239139 with sparse part having weight 15179814.
Pruned matrix : 164618 x 165610 with weight 8472390.
Total sieving time: 3.64 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000
total time: 3.77 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10140+7 = 9(0)1397<141> = 151 · 160910339138441<15> · C125

C125 = P33 · P46 · P48

P33 = 119266962910373522768317901849023<33>

P46 = 1073502048919627741496999269090973341811523617<46>

P48 = 289306754986378993892936910082750693641415226647<48>

Number: 90007_140
N=37040906958342008436196962352631290237631464821269784853671653578621103961679404648708146669704204687383872089120977255061577
  ( 125 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=119266962910373522768317901849023 (pp33)
 r2=1073502048919627741496999269090973341811523617 (pp46)
 r3=289306754986378993892936910082750693641415226647 (pp48)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.15 hours.
Scaled time: 13.17 units (timescale=2.142).
Factorization parameters were as follows:
n: 37040906958342008436196962352631290237631464821269784853671653578621103961679404648708146669704204687383872089120977255061577
m: 10000000000000000000000000000
c5: 9
c0: 7
skew: 0.95
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:113992, largePrimes:3368728 encountered
Relations: rels:3487641, finalFF:407793
Max relations in full relation-set: 28
Initial matrix: 228211 x 407793 with sparse part having weight 35263251.
Pruned matrix : 168183 x 169388 with weight 13199446.
Total sieving time: 5.98 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.15 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 5, 2007

The factor table of 900...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Nov 4, 2007 (3rd)

By Sinkiti Sibata / PFGW

9·1010855-7 is PRP. It is the only PRP of the form 9·10n-7 (10001≤n≤20000).

Nov 4, 2007 (2nd)

By Jo Yeong Uk / GGNFS

9·10160+1 = 9(0)1591<161> = 196668336511615844317373683402996797341833<42> · C120

C120 = P52 · P69

P52 = 1739150909232723432175836807853304310816643860207313<52>

P69 = 263130261241924464291801141224892605010946153371020043305094966475369<69>

Number: 90001_160
N=457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497
  ( 120 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1739150909232723432175836807853304310816643860207313 (pp52)
 r2=263130261241924464291801141224892605010946153371020043305094966475369 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.70 hours.
Scaled time: 59.42 units (timescale=2.145).
Factorization parameters were as follows:
n: 457623233085536978487969224809644797039838287759370817200669676684400841774026444495529209155367065867115087869248173497
m: 100000000000000000000000000000000
c5: 9
c0: 1
skew: 0.64
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282992, largePrimes:5669639 encountered
Relations: rels:5735722, finalFF:684749
Max relations in full relation-set: 28
Initial matrix: 566202 x 684749 with sparse part having weight 43062449.
Pruned matrix : 470596 x 473491 with weight 28108258.
Total sieving time: 26.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.17 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.70 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 4, 2007

By Sinkiti Sibata / GGNFS

9·10161-7 = 8(9)1603<162> = 53 · 710382599 · 3193863019<10> · 14169121763<11> · C132

C132 = P39 · P93

P39 = 637003641965194182950788890954509239897<39>

P93 = 829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291<93>

Number: 89993_161
N=528220323458424440646483477713402912362372432295144177626701835540702260229176792484870656015751898878654984062057672951330199945027
  ( 132 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=637003641965194182950788890954509239897 (pp39)
 r2=829226536019218470577471928756725407087718463007725782007729866451066972588969963334914455291 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 72.73 hours.
Scaled time: 146.18 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_161
n: 528220323458424440646483477713402912362372432295144177626701835540702260229176792484870656015751898878654984062057672951330199945027
m: 100000000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316641, largePrimes:5828768 encountered
Relations: rels:5947621, finalFF:747210
Max relations in full relation-set: 28
Initial matrix: 632656 x 747210 with sparse part having weight 48277826.
Pruned matrix : 546815 x 550042 with weight 33888020.
Total sieving time: 68.82 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.49 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 72.73 hours.
 --------- CPU info (if available) ----------

Nov 3, 2007 (2nd)

By suberi / GGNFS

3·10158-7 = 2(9)1573<159> = 17 · 41 · 47 · 3041 · 841123744137979613<18> · C133

C133 = P51 · P83

P51 = 263885431718243596975433066048441779693678318105769<51>

P83 = 13567470651611743221749122292261888185172901056388384006891037144978168857382893251<83>

Number: 29993_158
N=3580257850225164627404836853606844290357386870515998826943797062408011849614535981097388373034324355416498626742076743203763054265019
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=263885431718243596975433066048441779693678318105769 (pp51)
 r2=13567470651611743221749122292261888185172901056388384006891037144978168857382893251 (pp83)
Version: GGNFS-0.77.1-20060722-k8
Total time: 49.54 hours.
Scaled time: 72.72 units (timescale=1.468).
Factorization parameters were as follows:
n: 3580257850225164627404836853606844290357386870515998826943797062408011849614535981097388373034324355416498626742076743203763054265019
m: 10000000000000000000000000000000
c5: 3000
c0: -7
skew: 0.3
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283037, largePrimes:5584207 encountered
Relations: rels:5598336, finalFF:647691
Max relations in full relation-set: 32
Initial matrix: 566250 x 647691 with sparse part having weight 39597994.
Pruned matrix : 499206 x 502101 with weight 26364073.
Total sieving time: 45.55 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.63 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 49.54 hours.
 --------- CPU info (if available) ----------

Nov 3, 2007

By Jo Yeong Uk / GGNFS

(8·10160+1)/9 = (8)1599<160> = 3 · 825027643337<12> · 4496569364490716593<19> · C129

C129 = P45 · P85

P45 = 584055110117804933562252574038305701305028939<45>

P85 = 1367485081849265048121060885327005302341443223828135540212293179914394095612984131937<85>

Number: 88889_160
N=798686650063927990314125701018237249713184766388387794727385204591609598499027731309396698824991490472673979526416377225579124843
  ( 129 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=584055110117804933562252574038305701305028939 (pp45)
 r2=1367485081849265048121060885327005302341443223828135540212293179914394095612984131937 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.65 hours.
Scaled time: 59.31 units (timescale=2.145).
Factorization parameters were as follows:
n: 798686650063927990314125701018237249713184766388387794727385204591609598499027731309396698824991490472673979526416377225579124843
m: 200000000000000000000000000000000
c5: 1
c0: 4
skew: 1.32
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282707, largePrimes:5654427 encountered
Relations: rels:5714441, finalFF:680834
Max relations in full relation-set: 28
Initial matrix: 565917 x 680834 with sparse part having weight 42328056.
Pruned matrix : 473624 x 476517 with weight 27571459.
Total sieving time: 26.35 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.16 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Nov 2, 2007 (6th)

By Sinkiti Sibata / GGNFS

9·10159-7 = 8(9)1583<160> = 18104666690449826252281753693<29> · C132

C132 = P56 · P77

P56 = 22392329597836817510288640646341074175512979619336814351<56>

P77 = 22199985850784836127380389132731731977501124190563051137404670084573603137251<77>

Number: 89993_159
N=497109400238087848582031566032851660055020853947195342757531373490526734611539481118145584113295135923191327086633995939773759489101
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=22392329597836817510288640646341074175512979619336814351 (pp56)
 r2=22199985850784836127380389132731731977501124190563051137404670084573603137251 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.23 hours.
Scaled time: 118.63 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_159
n: 497109400238087848582031566032851660055020853947195342757531373490526734611539481118145584113295135923191327086633995939773759489101
m: 100000000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:284062, largePrimes:5877832 encountered
Relations: rels:6049555, finalFF:771663
Max relations in full relation-set: 28
Initial matrix: 567272 x 771663 with sparse part having weight 50943228.
Pruned matrix : 418651 x 421551 with weight 36252838.
Total sieving time: 56.43 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.23 hours.
 --------- CPU info (if available) ----------

Nov 2, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

6·10167+7 = 6(0)1667<168> = 157 · C166

C166 = P47 · P120

P47 = 30141491732912660764138607233343720887304110987<47>

P120 = 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073<120>

Number: n
N=3821656050955414012738853503184713375796178343949044585987261146496815286624203821656050955414012738853503184713375796178343949044585987261146496815286624203821656051
  ( 166 digits)
SNFS difficulty: 168 digits.
Divisors found:

Fri Nov 02 11:53:15 2007  prp47 factor: 30141491732912660764138607233343720887304110987
Fri Nov 02 11:53:15 2007  prp120 factor: 126790541251891655395868197515952259522258968043055404184000880238481113593670765322134091338218303304135490412872342073
Fri Nov 02 11:53:15 2007  elapsed time 05:00:20 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 142.75 hours.
Scaled time: 170.45 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_6_0_166_7
n: 3821656050955414012738853503184713375796178343949044585987261146496815286624203821656050955414012738853503184713375796178343949044585987261146496815286624203821656051
type: snfs
skew: 0.82
deg: 5
c5: 75
c0: 28
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 5000213)
Primes: RFBsize:250150, AFBsize:250046, largePrimes:8066210 encountered
Relations: rels:7523828, finalFF:472612
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 142.32 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 142.75 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

3·10160-1 = 2(9)160<161> = 3119 · 62171 · 716003 · 80479894854409<14> · C133

C133 = P59 · P75

P59 = 22773127470380768369771978355584433053642892841637684786821<59>

P75 = 117894381311324651726376382743763178993218466198694259251340381195966953253<75>

Number: n
N=2684823773644472499695314004905933113030245860446596390581560505765323424678107700978354714731235290256104741769394425383100177478713
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Nov 02 21:39:00 2007  prp59 factor: 22773127470380768369771978355584433053642892841637684786821
Fri Nov 02 21:39:00 2007  prp75 factor: 117894381311324651726376382743763178993218466198694259251340381195966953253
Fri Nov 02 21:39:00 2007  elapsed time 01:07:33 (Msieve 1.29)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 28.18 hours.
Scaled time: 37.37 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_2_9_160
n: 2684823773644472499695314004905933113030245860446596390581560505765323424678107700978354714731235290256104741769394425383100177478713
skew: 0.95
deg: 5
c5: 3
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1400000)
Primes: RFBsize:216816, AFBsize:216846, largePrimes:7002342 encountered
Relations: rels:6502743, finalFF:523807
Max relations in full relation-set: 28
Initial matrix: 433727 x 523807 with sparse part having weight 39790411.
Pruned matrix : 360363 x 362595 with weight 22732739.
Total sieving time: 27.98 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 28.18 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 2, 2007 (4th)

By matsui / GMP-ECM

(5·10166+7)/3 = 1(6)1659<167> = 38609 · 75787 · C157

C157 = P36 · C122

P36 = 156630091583671031730558418871436461<36>

C122 = [36365559895016016644306948036519971789440001831406469011965021801985852343260659678682774063764231328439857717070493184563<122>]

Nov 2, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

2·10160-3 = 1(9)1597<161> = 15073 · 1023361 · 2269267633<10> · 51894756337<11> · C131

C131 = P49 · P82

P49 = 1244702530203678363132386159041482385491409469399<49>

P82 = 8845587159376599603050287573778844195307606321990000300773593282138846596884883531<82>

Number: 19997_160
N=11010124718413221462280367876462346322453582439931705506709272261862462870251427913507922600641649990825847478334158897252623567869
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=1244702530203678363132386159041482385491409469399 (pp49)
 r2=8845587159376599603050287573778844195307606321990000300773593282138846596884883531 (pp82)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 25.76 hours.
Scaled time: 54.81 units (timescale=2.128).
Factorization parameters were as follows:
n: 11010124718413221462280367876462346322453582439931705506709272261862462870251427913507922600641649990825847478334158897252623567869
m: 100000000000000000000000000000000
c5: 2
c0: -3
skew: 1.08
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283187, largePrimes:5679964 encountered
Relations: rels:5762216, finalFF:699117
Max relations in full relation-set: 28
Initial matrix: 566398 x 699117 with sparse part having weight 43937665.
Pruned matrix : 457329 x 460224 with weight 27759676.
Total sieving time: 24.56 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 25.76 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

(7·10161+11)/9 = (7)1609<161> = 13 · 1181 · 188695951 · 13069034534977941833<20> · C130

C130 = P34 · P96

P34 = 6012553105775282745767182262190667<34>

P96 = 341662463922226905047290637587563518265187529653427259070665961826179127070588201628147242777463<96>

Nov 2, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

9·10160-7 = 8(9)1593<161> = 619 · 31247 · 201823 · C149

C149 = P44 · P44 · P61

P44 = 44832592826645189491277561661890927333335849<44>

P44 = 58928729369518409469720209631759471783420671<44>

P61 = 8726738097012509717654043907256703264726239277870739541104253<61>

Number: n
N=23055411367586615082003261341128857444920360386517972549304906315835176876756217183769848071125522085298104115328957218756792728520856138498005089787
  ( 149 digits)
SNFS difficulty: 160 digits.
Divisors found:

Fri Nov 02 05:43:45 2007  prp44 factor: 44832592826645189491277561661890927333335849
Fri Nov 02 05:43:45 2007  prp44 factor: 58928729369518409469720209631759471783420671
Fri Nov 02 05:43:45 2007  prp61 factor: 8726738097012509717654043907256703264726239277870739541104253
Fri Nov 02 05:43:45 2007  elapsed time 01:21:01 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 35.14 hours.
Scaled time: 50.08 units (timescale=1.425).
Factorization parameters were as follows:
name: KA_8_9_159_3
n: 23055411367586615082003261341128857444920360386517972549304906315835176876756217183769848071125522085298104115328957218756792728520856138498005089787
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800179)
Primes: RFBsize:203362, AFBsize:203517, largePrimes:7126574 encountered
Relations: rels:6588475, finalFF:452122
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 34.95 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 35.14 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Nov 2, 2007

By Jo Yeong Uk / GGNFS, GMP-ECM

(4·10190-31)/9 = (4)1891<190> = C190

C190 = P89 · P101

P89 = 56633002372177889917787382603024134082794402810604184699423290284260806567232850743196879<89>

P101 = 78477994425170505252478126430623716163551522942533133685072386085630247384183834818134344179505629079<101>

Number: 44441_190
N=4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 190 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=56633002372177889917787382603024134082794402810604184699423290284260806567232850743196879 (pp89)
 r2=78477994425170505252478126430623716163551522942533133685072386085630247384183834818134344179505629079 (pp101)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 506.30 hours.
Scaled time: 1086.00 units (timescale=2.145).
Factorization parameters were as follows:
n: 4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 100000000000000000000000000000000000000
c5: 4
c0: -31
skew: 1.51
type: snfs
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6500000, 14600001)
Primes: RFBsize:849252, AFBsize:849764, largePrimes:12825340 encountered
Relations: rels:13582667, finalFF:1936815
Max relations in full relation-set: 28
Initial matrix: 1699080 x 1936815 with sparse part having weight 144996551.
Pruned matrix : 1492822 x 1501381 with weight 111522440.
Total sieving time: 485.19 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 20.54 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000
total time: 506.30 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific ro2utine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

P89 is the biggest factor which was found in our tables so far. Congratulations!

I was surprized that two P89s had been found continuously from the same near-repdigit sequence.

(5·10160-23)/9 = (5)1593<160> = 3 · 47 · 36583 · 391183217 · 13416202562095777<17> · C129

C129 = P36 · P93

P36 = 557467334877805199211719058269920279<36>

P93 = 368128820889923730632432710032916764064373628070399222255862045362828218454119475627959989141<93>

Nov 1, 2007 (5th)

By matsui / Msieve

(5·10173+7)/3 = 1(6)1729<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077<12> · 1862230537518772176753410725489813<34> · C104

C104 = P43 · P61

P43 = 5917523119420196943705339866721088586618339<43>

P61 = 6239425363430810864236794554166498878991514867897846161057107<61>

Nov 1, 2007 (4th)

By Robert Backstrom / GMP-ECM, GGNFS

9·10154-7 = 8(9)1533<155> = 31 · 59 · 3116155837<10> · C143

C143 = P34 · P47 · P63

P34 = 3792154237087773328323098510929643<34>

P47 = 13515254733080096925398066307959108515533417271<47>

P63 = 308105468835983009135964692963347948427570307230290780677274397<63>

prp34 factors: 3792154237087773328323098510929643
prp47 factor:  13515254733080096925398066307959108515533417271 (pp47)
prp63 factor:  308105468835983009135964692963347948427570307230290780677274397 (pp63)

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 15791000075873905536643005674835499743042023035608132996665252198463383016350684288596800392658129485982981128379660782197197761083905185830441 (143 digits)
Using B1=1030000, B2=875663603, polynomial Dickson(3), sigma=1277051764
Step 1 took 15188ms
Step 2 took 8703ms
********** Factor found in step 2: 3792154237087773328323098510929643
Found probable prime factor of 34 digits: 3792154237087773328323098510929643
Composite cofactor 4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587 has 109 digits

Number: n
N=4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587
  ( 109 digits)
Divisors found:
 r1=13515254733080096925398066307959108515533417271 (pp47)
 r2=308105468835983009135964692963347948427570307230290780677274397 (pp63)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 15.47 hours.
Scaled time: 20.19 units (timescale=1.305).
Factorization parameters were as follows:
name: KA_8_9_153_3
n: 4164123895973381665684521031919367758331000757893159498628020621881612855280700051156426496919521695565910587
skew: 13433.88
# norm 5.58e+14
c5: 62340
c4: -1730045296
c3: -31252455735533
c2: 59780409705258362
c1: 594864083607926757768
c0: 4226538018654160771217904
# alpha -5.88
Y1: 54837503413
Y0: -582038343536829418255
# Murphy_E 1.28e-09
# M 775188593700025757374907442535572328332511394125380113220895912641476417303724565829169862375221504000062036
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:230209, AFBsize:230238, largePrimes:6848426 encountered
Relations: rels:6590432, finalFF:586768
Max relations in full relation-set: 28
Initial matrix: 460530 x 586768 with sparse part having weight 36842357.
Pruned matrix : 341921 x 344287 with weight 16084571.
Total sieving time: 13.36 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 1.49 hours.
Total square root time: 0.31 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 15.47 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Nov 1, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(85·102960-31)/9 is prime.

Nov 1, 2007 (2nd)

By Sinkiti Sibata / GGNFS

9·10152-7 = 8(9)1513<153> = 27487 · 2387449 · 5618769997<10> · C133

C133 = P44 · P89

P44 = 75820868126956676281536230696860571433120407<44>

P89 = 32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109<89>

Number: 89993_152
N=2440842795357990826312342895539487490184328387705207959270387795925092533977126288036775251949678234292518146093908937568969876062363
  ( 133 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=75820868126956676281536230696860571433120407 (pp44)
 r2=32192229601894986931087007258474395061004652068487123300133829248970334366365297350334109 (pp89)
Version: GGNFS-0.77.1-20060513-k8
Total time: 37.53 hours.
Scaled time: 72.25 units (timescale=1.925).
Factorization parameters were as follows:
name: 89993_152
n: 2440842795357990826312342895539487490184328387705207959270387795925092533977126288036775251949678234292518146093908937568969876062363
m: 1000000000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175703, largePrimes:5892665 encountered
Relations: rels:5985872, finalFF:583936
Max relations in full relation-set: 28
Initial matrix: 352069 x 583936 with sparse part having weight 61282735.
Pruned matrix : 277434 x 279258 with weight 33988858.
Total sieving time: 35.96 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.27 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.53 hours.
 --------- CPU info (if available) ----------

Nov 1, 2007

By Yousuke Koide

(101265-1)/9 is divisible by 7973059286225484515918622191263721<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

October 2007

Oct 31, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

9·10157-7 = 8(9)1563<158> = 23 · 64057787 · C149

C149 = P73 · P76

P73 = 8547312778918799179387612593474476828728823510172134540253167241939987973<73>

P76 = 7146824962215572093535969278319248184705372720242480746696150650147917691641<76>

Number: n
N=61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693
  ( 149 digits)
SNFS difficulty: 157 digits.
Divisors found:

Thu Nov 01 00:37:53 2007  prp73 factor: 8547312778918799179387612593474476828728823510172134540253167241939987973
Thu Nov 01 00:37:53 2007  prp76 factor: 7146824962215572093535969278319248184705372720242480746696150650147917691641
Thu Nov 01 00:37:53 2007  elapsed time 01:22:09 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 37.30 hours.
Scaled time: 49.46 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_9_156_3
n: 61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693
skew: 0.38
deg: 5
c5: 900
c0: -7
m: 10000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:216816, AFBsize:216321, largePrimes:7229719 encountered
Relations: rels:6721021, finalFF:520151
Max relations in full relation-set: 28
Initial matrix: 433201 x 520151 with sparse part having weight 46044664.
Pruned matrix : 368182 x 370412 with weight 28093041.
Total sieving time: 37.05 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 37.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 31, 2007 (4th)

By Jo Yeong Uk / GGNFS, Msieve

9·10150-7 = 8(9)1493<151> = 859 · 352963277 · 18139634852382632412042997<26> · C115

C115 = P41 · P74

P41 = 55504280314514112186236174411054189440309<41>

P74 = 29482533885016913889484106257918099812603456906714576053691076225565509087<74>

Number: 89993_150
N=1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883
  ( 115 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=55504280314514112186236174411054189440309 (pp41)
 r2=29482533885016913889484106257918099812603456906714576053691076225565509087 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.99 hours.
Scaled time: 27.87 units (timescale=2.146).
Factorization parameters were as follows:
n: 1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883
m: 1000000000000000000000000000000
c5: 9
c0: -7
skew: 0.95
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176458, largePrimes:5472027 encountered
Relations: rels:5419693, finalFF:513988
Max relations in full relation-set: 28
Initial matrix: 352824 x 513988 with sparse part having weight 44556647.
Pruned matrix : 279117 x 280945 with weight 22936374.
Total sieving time: 12.50 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.99 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10153-7 = 8(9)1523<154> = 235483 · 15771126802857831503737789<26> · 2469438507084583723424410362013<31> · C93

C93 = P35 · P59

P35 = 29916323560200857306637278521712341<35>

P59 = 32803016936544339453376593485631195739277624165372655627383<59>

Wed Oct 31 08:32:17 2007  
Wed Oct 31 08:32:17 2007  
Wed Oct 31 08:32:17 2007  Msieve v. 1.28
Wed Oct 31 08:32:17 2007  random seeds: 78b84c31 5c438943
Wed Oct 31 08:32:17 2007  factoring 981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603 (93 digits)
Wed Oct 31 08:32:17 2007  commencing quadratic sieve (93-digit input)
Wed Oct 31 08:32:18 2007  using multiplier of 3
Wed Oct 31 08:32:18 2007  using 32kb Intel Core sieve core
Wed Oct 31 08:32:18 2007  sieve interval: 36 blocks of size 32768
Wed Oct 31 08:32:18 2007  processing polynomials in batches of 6
Wed Oct 31 08:32:18 2007  using a sieve bound of 1953863 (72941 primes)
Wed Oct 31 08:32:18 2007  using large prime bound of 244232875 (27 bits)
Wed Oct 31 08:32:18 2007  using double large prime bound of 1253277823035125 (42-51 bits)
Wed Oct 31 08:32:18 2007  using trial factoring cutoff of 51 bits
Wed Oct 31 08:32:18 2007  polynomial 'A' values have 12 factors
Wed Oct 31 09:57:24 2007  73505 relations (19333 full + 54172 combined from 979953 partial), need 73037
Wed Oct 31 09:57:24 2007  begin with 999286 relations
Wed Oct 31 09:57:24 2007  reduce to 184209 relations in 11 passes
Wed Oct 31 09:57:24 2007  attempting to read 184209 relations
Wed Oct 31 09:57:26 2007  recovered 184209 relations
Wed Oct 31 09:57:26 2007  recovered 160186 polynomials
Wed Oct 31 09:57:26 2007  attempting to build 73505 cycles
Wed Oct 31 09:57:26 2007  found 73505 cycles in 6 passes
Wed Oct 31 09:57:26 2007  distribution of cycle lengths:
Wed Oct 31 09:57:26 2007     length 1 : 19333
Wed Oct 31 09:57:26 2007     length 2 : 13661
Wed Oct 31 09:57:26 2007     length 3 : 12554
Wed Oct 31 09:57:26 2007     length 4 : 9800
Wed Oct 31 09:57:26 2007     length 5 : 7114
Wed Oct 31 09:57:26 2007     length 6 : 4591
Wed Oct 31 09:57:26 2007     length 7 : 2825
Wed Oct 31 09:57:26 2007     length 9+: 3627
Wed Oct 31 09:57:26 2007  largest cycle: 18 relations
Wed Oct 31 09:57:26 2007  matrix is 72941 x 73505 with weight 4546757 (avg 61.86/col)
Wed Oct 31 09:57:27 2007  filtering completed in 3 passes
Wed Oct 31 09:57:27 2007  matrix is 68316 x 68380 with weight 4231949 (avg 61.89/col)
Wed Oct 31 09:57:28 2007  saving the first 48 matrix rows for later
Wed Oct 31 09:57:28 2007  matrix is 68268 x 68380 with weight 3299116 (avg 48.25/col)
Wed Oct 31 09:57:28 2007  matrix includes 64 packed rows
Wed Oct 31 09:57:28 2007  using block size 27352 for processor cache size 4096 kB
Wed Oct 31 09:57:29 2007  commencing Lanczos iteration
Wed Oct 31 09:57:50 2007  lanczos halted after 1081 iterations
Wed Oct 31 09:57:50 2007  recovered 15 nontrivial dependencies
Wed Oct 31 09:57:50 2007  prp35 factor: 29916323560200857306637278521712341
Wed Oct 31 09:57:50 2007  prp59 factor: 32803016936544339453376593485631195739277624165372655627383
Wed Oct 31 09:57:50 2007  elapsed time 01:25:33

Oct 31, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10148-7 = 8(9)1473<149> = 53 · 839 · 3833 · 5333122741489<13> · 380397540317863012963011373<27> · C102

C102 = P48 · P55

P48 = 185048077381378285528736195447051909587258335893<48>

P55 = 1406572115111896750750738223467919885903244947129739803<55>

Number: 89993_148
N=260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079
  ( 102 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=185048077381378285528736195447051909587258335893 (pp48)
 r2=1406572115111896750750738223467919885903244947129739803 (pp55)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.10 hours.
Scaled time: 59.93 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_148
n: 260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079
m: 100000000000000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4250001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3049998 encountered
Relations: rels:3108836, finalFF:263510
Max relations in full relation-set: 28
Initial matrix: 228304 x 263510 with sparse part having weight 32994625.
Pruned matrix : 218898 x 220103 with weight 26198623.
Total sieving time: 29.21 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.62 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 30.10 hours.
 --------- CPU info (if available) ----------

Oct 31, 2007 (2nd)

By matsui / GMP-ECM, Msieve

(5·10198+7)/3 = 1(6)1979<199> = 2671 · 2222089 · 43446912661062564370891697<26> · 151432609261393100562428907767<30> · C134

C134 = P38 · P43 · P53

P38 = 78356711420850326025452572618724188949<38>

P43 = 5527668366912659164266442169275274462403349<43>

P53 = 98540986433720343595658132228977073747961703420580549<53>

(5·10173+7)/3 = 1(6)1729<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077<12> · C137

C137 = P34 · C104

P34 = 1862230537518772176753410725489813<34>

C104 = [36921943839998587914228808236155511843378747795412617433005313650028624835179704262350945849262592485273<104>]

Oct 31, 2007

By Womack

(10309-1)/9 is divisible by 5294796903161592416528456780680376286484870226446771978908657527791<67> and the cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 30, 2007 (5th)

By Tyler Cadigan / Msieve, GGNFS

(64·10163-1)/9 = 7(1)163<164> = 637330387763<12> · 10957735036324101653<20> · C134

C134 = P61 · P73

P61 = 5153208161696653721426359516088698419315495201808470280932923<61>

P73 = 1975942751788253995617036939102852461531533982770011785041254696010379563<73>

Mon Oct 29 19:58:09 2007  
Mon Oct 29 19:58:09 2007  
Mon Oct 29 19:58:09 2007  Msieve v. 1.29
Mon Oct 29 19:58:09 2007  random seeds: 79db1e80 385338a0
Mon Oct 29 19:58:09 2007  factoring 10182444315560575705513301530834416904561566048028307675788338594283441380448622210798637965512347107701350195485846065970978973052649 (134 digits)
Mon Oct 29 19:58:10 2007  commencing number field sieve (133-digit input)
Mon Oct 29 19:58:10 2007  R0: -400000000000000000000000000000000
Mon Oct 29 19:58:10 2007  R1:  1
Mon Oct 29 19:58:10 2007  A0: -2
Mon Oct 29 19:58:10 2007  A1:  0
Mon Oct 29 19:58:10 2007  A2:  0
Mon Oct 29 19:58:10 2007  A3:  0
Mon Oct 29 19:58:10 2007  A4:  0
Mon Oct 29 19:58:10 2007  A5:  125
Mon Oct 29 19:58:10 2007  size score = 2.442337e-011, Murphy alpha = 0.284179, combined = 2.221603e-011
Mon Oct 29 20:01:42 2007  restarting with 5837456 relations
Mon Oct 29 20:01:48 2007  factor base loaded:
Mon Oct 29 20:01:48 2007  348513 rational ideals (max prime = 4999999)
Mon Oct 29 20:01:48 2007  316326 algebraic ideals (max prime = 4499969)
Mon Oct 29 20:01:48 2007  added 15854 free relations
Mon Oct 29 20:01:48 2007  
Mon Oct 29 20:01:48 2007  commencing relation filtering
Mon Oct 29 20:01:48 2007  commencing duplicate removal, pass 1
Mon Oct 29 20:01:52 2007  error -14 reading relation 62058
Mon Oct 29 20:06:03 2007  found 79763 hash collisions in 5853309 relations
Mon Oct 29 20:06:03 2007  commencing duplicate removal, pass 2
Mon Oct 29 20:09:59 2007  found 17169 duplicates and 5836140 unique relations
Mon Oct 29 20:09:59 2007  memory use: 37.8 MB
Mon Oct 29 20:10:05 2007  ignoring smallest 282973 rational and 283029 algebraic ideals
Mon Oct 29 20:10:05 2007  filtering ideals above 3997355
Mon Oct 29 20:10:05 2007  need 962203 more relations than ideals
Mon Oct 29 20:10:05 2007  commencing singleton removal, pass 1
Mon Oct 29 20:14:14 2007  relations with 0 large ideals: 103993
Mon Oct 29 20:14:14 2007  relations with 1 large ideals: 760328
Mon Oct 29 20:14:14 2007  relations with 2 large ideals: 2000058
Mon Oct 29 20:14:14 2007  relations with 3 large ideals: 1934872
Mon Oct 29 20:14:14 2007  relations with 4 large ideals: 844689
Mon Oct 29 20:14:14 2007  relations with 5 large ideals: 173568
Mon Oct 29 20:14:14 2007  relations with 6 large ideals: 17913
Mon Oct 29 20:14:14 2007  relations with 7+ large ideals: 719
Mon Oct 29 20:14:14 2007  5836140 relations and about 5716455 large ideals
Mon Oct 29 20:14:14 2007  commencing singleton removal, pass 2
Mon Oct 29 20:18:32 2007  found 3032525 singletons
Mon Oct 29 20:18:32 2007  current dataset: 2803615 relations and about 2113481 large ideals
Mon Oct 29 20:18:32 2007  commencing singleton removal, pass 3
Mon Oct 29 20:22:13 2007  found 448303 singletons
Mon Oct 29 20:22:13 2007  current dataset: 2355312 relations and about 1639581 large ideals
Mon Oct 29 20:22:13 2007  commencing singleton removal, final pass
Mon Oct 29 20:26:10 2007  memory use: 77.5 MB
Mon Oct 29 20:26:10 2007  commencing in-memory singleton removal
Mon Oct 29 20:26:11 2007  begin with 2355312 relations and 1708927 unique ideals
Mon Oct 29 20:26:17 2007  reduce to 2069330 relations and 1416639 ideals in 11 passes
Mon Oct 29 20:26:17 2007  max relations containing the same ideal: 35
Mon Oct 29 20:26:18 2007  dataset has 15.3% excess relations
Mon Oct 29 20:26:22 2007  ignoring smallest 256574 rational and 256498 algebraic ideals
Mon Oct 29 20:26:22 2007  filtering ideals above 3597619
Mon Oct 29 20:26:22 2007  need 611282 more relations than ideals
Mon Oct 29 20:26:22 2007  commencing singleton removal, final pass
Mon Oct 29 20:29:45 2007  memory use: 93.6 MB
Mon Oct 29 20:29:45 2007  commencing in-memory singleton removal
Mon Oct 29 20:29:46 2007  begin with 2355312 relations and 1761848 unique ideals
Mon Oct 29 20:29:53 2007  reduce to 2068928 relations and 1469137 ideals in 11 passes
Mon Oct 29 20:29:53 2007  max relations containing the same ideal: 35
Mon Oct 29 20:29:54 2007  dataset has 6.0% excess relations
Mon Oct 29 20:29:54 2007  relations with 0 large ideals: 68851
Mon Oct 29 20:29:54 2007  relations with 1 large ideals: 298085
Mon Oct 29 20:29:54 2007  relations with 2 large ideals: 616837
Mon Oct 29 20:29:54 2007  relations with 3 large ideals: 631687
Mon Oct 29 20:29:54 2007  relations with 4 large ideals: 341963
Mon Oct 29 20:29:54 2007  relations with 5 large ideals: 94801
Mon Oct 29 20:29:54 2007  relations with 6 large ideals: 15793
Mon Oct 29 20:29:54 2007  relations with 7+ large ideals: 911
Mon Oct 29 20:29:54 2007  commencing 2-way merge
Mon Oct 29 20:30:00 2007  reduce to 1298002 relation sets and 698213 unique ideals
Mon Oct 29 20:30:00 2007  ignored 2 oversize relation sets
Mon Oct 29 20:30:00 2007  commencing full merge
Mon Oct 29 20:30:59 2007  found 664054 cycles, need 590413
Mon Oct 29 20:31:00 2007  weight of 590413 cycles is about 38798316 (65.71/cycle)
Mon Oct 29 20:31:00 2007  distribution of cycle lengths:
Mon Oct 29 20:31:00 2007  1 relations: 100601
Mon Oct 29 20:31:00 2007  2 relations: 68982
Mon Oct 29 20:31:00 2007  3 relations: 62992
Mon Oct 29 20:31:00 2007  4 relations: 55520
Mon Oct 29 20:31:00 2007  5 relations: 50346
Mon Oct 29 20:31:00 2007  6 relations: 44152
Mon Oct 29 20:31:00 2007  7 relations: 39232
Mon Oct 29 20:31:00 2007  8 relations: 34235
Mon Oct 29 20:31:00 2007  9 relations: 30168
Mon Oct 29 20:31:00 2007  10+ relations: 104185
Mon Oct 29 20:31:00 2007  heaviest cycle: 17 relations
Mon Oct 29 20:31:00 2007  commencing cycle optimization
Mon Oct 29 20:31:02 2007  start with 3228434 relations
Mon Oct 29 20:31:22 2007  pruned 92753 relations
Mon Oct 29 20:31:22 2007  distribution of cycle lengths:
Mon Oct 29 20:31:22 2007  1 relations: 100601
Mon Oct 29 20:31:22 2007  2 relations: 70333
Mon Oct 29 20:31:22 2007  3 relations: 65309
Mon Oct 29 20:31:22 2007  4 relations: 56690
Mon Oct 29 20:31:22 2007  5 relations: 52216
Mon Oct 29 20:31:22 2007  6 relations: 45474
Mon Oct 29 20:31:22 2007  7 relations: 40433
Mon Oct 29 20:31:22 2007  8 relations: 35072
Mon Oct 29 20:31:22 2007  9 relations: 30464
Mon Oct 29 20:31:22 2007  10+ relations: 93821
Mon Oct 29 20:31:22 2007  heaviest cycle: 17 relations
Mon Oct 29 20:31:25 2007  
Mon Oct 29 20:31:25 2007  commencing linear algebra
Mon Oct 29 20:31:27 2007  read 590413 cycles
Mon Oct 29 20:31:31 2007  cycles contain 1626805 unique relations
Mon Oct 29 20:35:42 2007  read 1626805 relations
Mon Oct 29 20:35:52 2007  using 32 quadratic characters above 134216228
Mon Oct 29 20:38:40 2007  read 590413 cycles
Mon Oct 29 20:40:52 2007  filtering completed in 3 passes
Mon Oct 29 20:40:53 2007  matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col)
Mon Oct 29 20:42:11 2007  read 585316 cycles
Mon Oct 29 20:44:43 2007  matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col)
Mon Oct 29 20:44:43 2007  saving the first 48 matrix rows for later
Mon Oct 29 20:44:44 2007  matrix is 585068 x 585316 with weight 39821171 (avg 68.03/col)
Mon Oct 29 20:44:44 2007  matrix includes 64 packed rows
Mon Oct 29 20:44:44 2007  using block size 21845 for processor cache size 512 kB
Mon Oct 29 20:44:55 2007  commencing Lanczos iteration
Mon Oct 29 23:39:22 2007  lanczos halted after 9254 iterations (dim = 585068)
Mon Oct 29 23:39:40 2007  recovered 51 nontrivial dependencies
Mon Oct 29 23:39:49 2007  
Mon Oct 29 23:39:49 2007  commencing square root phase
Mon Oct 29 23:39:49 2007  reading relations for dependency 1
Mon Oct 29 23:40:38 2007  read 292046 cycles
Mon Oct 29 23:40:40 2007  cycles contain 983974 unique relations
Mon Oct 29 23:45:16 2007  read 983974 relations
Mon Oct 29 23:45:37 2007  multiplying 1554024 relations
Mon Oct 29 23:58:13 2007  multiply complete, coefficients have about 43.64 million bits
Mon Oct 29 23:58:15 2007  initial square root is modulo 1843111
Tue Oct 30 00:16:39 2007  prp61 factor: 5153208161696653721426359516088698419315495201808470280932923
Tue Oct 30 00:16:39 2007  prp73 factor: 1975942751788253995617036939102852461531533982770011785041254696010379563
Tue Oct 30 00:16:39 2007  elapsed time 04:18:30

Oct 30, 2007 (4th)

By Sinkiti Sibata / GGNFS

(8·10169+7)/3 = 2(6)1689<170> = 29 · 2731 · 3853 · 6101 · C158

C158 = P39 · P119

P39 = 662045957785193703483721009542997210001<39>

P119 = 21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827<119>

Number: 26669_169
N=14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827
  ( 158 digits)
SNFS difficulty: 170 digits.
Divisors found:
 r1=662045957785193703483721009542997210001 (pp39)
 r2=21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827 (pp119)
Version: GGNFS-0.77.1-20060513-k8
Total time: 139.76 hours.
Scaled time: 279.94 units (timescale=2.003).
Factorization parameters were as follows:
name: 26669_169
n: 14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827
m: 10000000000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 7100001)
Primes: RFBsize:412849, AFBsize:412831, largePrimes:6055936 encountered
Relations: rels:6345700, finalFF:951274
Max relations in full relation-set: 28
Initial matrix: 825744 x 951274 with sparse part having weight 56560583.
Pruned matrix : 721298 x 725490 with weight 40805496.
Total sieving time: 133.63 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 5.58 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 139.76 hours.
 --------- CPU info (if available) ----------

Oct 30, 2007 (3rd)

By Jo Yeong Uk / GGNFS

9·10143-7 = 8(9)1423<144> = 1777 · 1725179 · 133421887 · C127

C127 = P39 · P89

P39 = 156872632499525723095280260098133461577<39>

P89 = 14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429<89>

Number: 89993_143
N=2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533
  ( 127 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=156872632499525723095280260098133461577 (pp39)
 r2=14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 9.59 hours.
Scaled time: 20.58 units (timescale=2.146).
Factorization parameters were as follows:
n: 2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533
m: 100000000000000000000000000000
c5: 9
c0: -700
skew: 2.39
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1400001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3411338 encountered
Relations: rels:3448077, finalFF:323928
Max relations in full relation-set: 28
Initial matrix: 228301 x 323928 with sparse part having weight 30228512.
Pruned matrix : 199683 x 200888 with weight 15655341.
Total sieving time: 9.35 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 9.59 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10144-7 = 8(9)1433<145> = 30380069764762946805547503800941<32> · C114

C114 = P40 · P74

P40 = 5793759319832245415885975057146558926953<40>

P74 = 51132060310818176689028811056072205332653270314035794978186101297841513141<74>

Number: 89993_144
N=296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373
  ( 114 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=5793759319832245415885975057146558926953 (pp40)
 r2=51132060310818176689028811056072205332653270314035794978186101297841513141 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.87 hours.
Scaled time: 19.03 units (timescale=2.146).
Factorization parameters were as follows:
n: 296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373
m: 100000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1350001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3343512 encountered
Relations: rels:3328593, finalFF:281277
Max relations in full relation-set: 28
Initial matrix: 228636 x 281277 with sparse part having weight 25879845.
Pruned matrix : 211599 x 212806 with weight 16431801.
Total sieving time: 8.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.87 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10153-7 = 8(9)1523<154> = 235483 · 15771126802857831503737789<26> · C124

C124 = P31 · C93

P31 = 2469438507084583723424410362013<31>

C93 = [981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603<93>]

9·10146-7 = 8(9)1453<147> = 19 · 307 · 2243 · 17371526793899<14> · 28598478520519<14> · C114

C114 = P44 · P70

P44 = 64299853807288749095977974116352073454267827<44>

P70 = 2153427995281495420234041605616327252058426335937525315582533212837981<70>

Number: 89993_146
N=138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287
  ( 114 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=64299853807288749095977974116352073454267827 (pp44)
 r2=2153427995281495420234041605616327252058426335937525315582533212837981 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.37 hours.
Scaled time: 22.21 units (timescale=2.143).
Factorization parameters were as follows:
n: 138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287
m: 100000000000000000000000000000
c5: 90
c0: -7
skew: 0.6
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1575001)
Primes: RFBsize:135072, AFBsize:135493, largePrimes:3715295 encountered
Relations: rels:3729829, finalFF:320257
Max relations in full relation-set: 28
Initial matrix: 270632 x 320257 with sparse part having weight 29075311.
Pruned matrix : 251639 x 253056 with weight 19777051.
Total sieving time: 10.00 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.28 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 10.37 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

8·10167-7 = 7(9)1663<168> = 15137 · C164

C164 = P41 · P123

P41 = 70835644003123593484318087394932806885707<41>

P123 = 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227<123>

Number: n
N=52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489
  ( 164 digits)
SNFS difficulty: 167 digits.
Divisors found:

Tue Oct 30 07:24:05 2007  prp41 factor: 70835644003123593484318087394932806885707
Tue Oct 30 07:24:05 2007  prp123 factor: 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227
Tue Oct 30 07:24:05 2007  elapsed time 02:09:23 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 78.72 hours.
Scaled time: 102.80 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_7_9_166_3
n: 52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489
skew: 0.78
deg: 5
c5: 25
c0: -7
m: 2000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3100001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:7450046 encountered
Relations: rels:6889776, finalFF:446877
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 78.46 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 78.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10141-7 = 8(9)1403<142> = 2467639565737<13> · C130

C130 = P62 · P68

P62 = 53727058137272382231521263461791395461691665958866250660772681<62>

P68 = 67884046657300958448660911774042029705347021611364740350454114167369<68>

Number: n
N=3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289
  ( 130 digits)
SNFS difficulty: 141 digits.
Divisors found:

Tue Oct 30 09:24:32 2007  prp62 factor: 53727058137272382231521263461791395461691665958866250660772681
Tue Oct 30 09:24:32 2007  prp68 factor: 67884046657300958448660911774042029705347021611364740350454114167369
Tue Oct 30 09:24:32 2007  elapsed time 00:50:42 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.66 hours.
Scaled time: 9.64 units (timescale=1.447).
Factorization parameters were as follows:
name: KA_8_9_140_3
n: 3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289
skew: 0.60
deg: 5
c5: 90
c0: -7
m: 10000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 9500000)
Primes: RFBsize:148933, AFBsize:149225, largePrimes:6523890 encountered
Relations: rels:5928439, finalFF:382643
Max relations in full relation-set: 28
Initial matrix: 298225 x 382643 with sparse part having weight 26922338.
Pruned matrix : 236427 x 237982 with weight 14528939.
Total sieving time: 6.49 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 6.66 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 30, 2007

By matsui / GMP-ECM

(5·10181+7)/3 = 1(6)1809<182> = 19 · 167393 · C175

C175 = P38 · P138

P38 = 15723245803923831841763637804116393807<38>

P138 = 333284910953414496865344254925662573105861000375900329621890909608385992777196180707248922993978075855583628204941899412869920935091825201<138>

Oct 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve 1.28, GMP-ECM

9·10184-7 = 8(9)1833<185> = 31 · 311 · 22091 · 37100458201<11> · 1275537910469<13> · 282209150413571<15> · 480434327015263<15> · 14873984820428774119490711269<29> · C97

C97 = P39 · P58

P39 = 593474640229445793717454630072648349617<39>

P58 = 7461012807353624814862644671648910980191120545663272451503<58>

Number: n
N=4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351
  ( 97 digits)
Divisors found:
 r1=593474640229445793717454630072648349617 (pp39)
 r2=7461012807353624814862644671648910980191120545663272451503 (pp58)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.00 hours.
Scaled time: 11.63 units (timescale=1.453).
Factorization parameters were as follows:
name: n
n:  4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351
m:  13069795307958322129988
deg: 4
c4: 151748640
c3: 1255715867918
c2: -263120823138764827
c1: -4731771597968022768
c0: 240860015889048958069487
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.565
# E(F1,F2) = 2.428134e-05
# GGNFS version 0.77.1-20051202-athlon polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1193586766.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [100000, 1180001)
Primes: RFBsize:92938, AFBsize:92740, largePrimes:1863035 encountered
Relations: rels:1930390, finalFF:234741
Max relations in full relation-set: 28
Initial matrix: 185753 x 234741 with sparse part having weight 16859853.
Pruned matrix : 163671 x 164663 with weight 9437558.
Polynomial selection time: 0.17 hours.
Total sieving time: 7.24 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.44 hours.
Total square root time: 0.06 hours, sqrts: 2.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 8.00 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

9·10140-7 = 8(9)1393<141> = 47 · 109 · 167 · 617 · C133

C133 = P33 · P101

P33 = 153337616869490449763658859895879<33>

P101 = 11119053224090329768606633153477332542273472771580149117582678104067239138069306589653736225297573611<101>

(89·10164+1)/9 = 9(8)1639<165> = 17 · 19597 · 7888299157<10> · C150

C150 = P42 · P109

P42 = 270666531521708051044165587427652002648199<42>

P109 = 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927<109>

Number: n
N=376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473
  ( 150 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Oct 29 21:17:16 2007  prp42 factor: 270666531521708051044165587427652002648199
Mon Oct 29 21:17:16 2007  prp109 factor: 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927
Mon Oct 29 21:17:16 2007  elapsed time 02:10:55 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.57 hours.
Scaled time: 98.88 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_9_8_163_9
n: 376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473
skew: 0.65
deg: 5
c5: 89
c0: 10
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3500000)
Primes: RFBsize:250150, AFBsize:249266, largePrimes:7709961 encountered
Relations: rels:7186570, finalFF:561747
Max relations in full relation-set: 28
Initial matrix: 499481 x 561747 with sparse part having weight 51822639.
Pruned matrix : 473183 x 475744 with weight 37331802.
Total sieving time: 74.27 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 74.57 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

9·10145-7 = 8(9)1443<146> = 97 · 3307 · 3767 · C137

C137 = P29 · P108

P29 = 88689612345000909646591931059<29>

P108 = 839785174596700619416492075514766572936766799231731694119293012984478206119418982501449042954689673043155839<108>

Oct 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

9·10138-7 = 8(9)1373<139> = 113 · 1039 · 21012038995387387919<20> · C115

C115 = P55 · P60

P55 = 8324111480329451493669984302302012442668075809611357389<55>

P60 = 438270694932342412379485394874876095508458992349269934992589<60>

Number: 89993_138
N=3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121
  ( 115 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=8324111480329451493669984302302012442668075809611357389 (pp55)
 r2=438270694932342412379485394874876095508458992349269934992589 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.25 hours.
Scaled time: 13.42 units (timescale=2.146).
Factorization parameters were as follows:
n: 3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121
m: 10000000000000000000000000000
c5: 9
c0: -700
skew: 2.39
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114082, largePrimes:3249074 encountered
Relations: rels:3266483, finalFF:322988
Max relations in full relation-set: 28
Initial matrix: 228301 x 322988 with sparse part having weight 26878127.
Pruned matrix : 191188 x 192393 with weight 12738220.
Total sieving time: 6.06 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.25 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10149-7 = 8(9)1483<150> = C150

C150 = P38 · P42 · P72

P38 = 35794409962129142828512220689799871821<38>

P42 = 123028439265110134626156384131454479013793<42>

P72 = 204372184460583650412981392697490828081020379007054396748321776875537981<72>

Number: 89993_149
N=899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 150 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=35794409962129142828512220689799871821 (pp38)
 r2=123028439265110134626156384131454479013793 (pp42)
 r3=204372184460583650412981392697490828081020379007054396748321776875537981 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 12.84 hours.
Scaled time: 27.54 units (timescale=2.146).
Factorization parameters were as follows:
n: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 1000000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176833, largePrimes:5402800 encountered
Relations: rels:5281314, finalFF:455491
Max relations in full relation-set: 28
Initial matrix: 353199 x 455491 with sparse part having weight 38566153.
Pruned matrix : 301756 x 303585 with weight 22658433.
Total sieving time: 12.29 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.44 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 12.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10139-7 = 8(9)1383<140> = 31 · 34319 · C134

C134 = P41 · P93

P41 = 95880034599375142177521603584056943225357<41>

P93 = 882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941<93>

Number: 89993_139
N=84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937
  ( 134 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=95880034599375142177521603584056943225357 (pp41)
 r2=882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.16 hours.
Scaled time: 13.12 units (timescale=2.129).
Factorization parameters were as follows:
n: 84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937
m: 10000000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114417, largePrimes:3350084 encountered
Relations: rels:3437732, finalFF:383556
Max relations in full relation-set: 28
Initial matrix: 228636 x 383556 with sparse part having weight 32672853.
Pruned matrix : 174534 x 175741 with weight 12890921.
Total sieving time: 5.98 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.16 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122)
Total of 4 processors activated (19246.09 BogoMIPS).

9·10197-7 = 8(9)1963<198> = C198

C198 = P33 · C166

P33 = 104572749495411191273052631155941<33>

C166 = [8606448662225270711938618675616267002791985751466136050473524371365139986511632740091624538638242280156899111248894398265050813422371895877062117828590480106511274373<166>]

Oct 29, 2007

By Sinkiti Sibata / GGNFS

9·10137-7 = 8(9)1363<138> = 227 · 2521 · C133

C133 = P39 · P94

P39 = 221091843902924979644001926922716807503<39>

P94 = 7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093<94>

Number: 89993_137
N=1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779
  ( 133 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=221091843902924979644001926922716807503 (pp39)
 r2=7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093 (pp94)
Version: GGNFS-0.77.1-20060513-k8
Total time: 13.09 hours.
Scaled time: 26.31 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_137
n: 1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779
m: 1000000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 2125001)
Primes: RFBsize:78498, AFBsize:63823, largePrimes:1683910 encountered
Relations: rels:1718050, finalFF:173211
Max relations in full relation-set: 28
Initial matrix: 142385 x 173211 with sparse part having weight 19269917.
Pruned matrix : 135154 x 135929 with weight 13734266.
Total sieving time: 12.78 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 13.09 hours.
 --------- CPU info (if available) ----------

Oct 28, 2007 (5th)

By JMB / GMP-ECM

(2·10164+43)/9 = (2)1637<164> = 33 · 172 · 2309 · 631311078642593<15> · C142

C142 = P36 · P106

P36 = 212146409889374522698249183584805409<36>

P106 = 9209220022038251514752208083059669039690403032046144718649809261395595313649005423325208968370329688568373<106>

Oct 28, 2007 (4th)

By Robert Backstrom / GGNFS, GMP-ECM

9·10120-7 = 8(9)1193<121> = C121

C121 = P56 · P66

P56 = 20354029401725849662526304753223971301497103511422609997<56>

P66 = 442172889817918611600780346173978409068598975005735222119428696669<66>

Number: n
N=8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 121 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=20354029401725849662526304753223971301497103511422609997 (pp56)
 r2=442172889817918611600780346173978409068598975005735222119428696669 (pp66)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.55 hours.
Scaled time: 2.24 units (timescale=1.442).
Factorization parameters were as follows:
name: KA_8_9_119_3
n: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
skew: 0.95
deg: 5
c5: 9
c0: -7
m: 1000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 250001)
Primes: RFBsize:78498, AFBsize:78361, largePrimes:4232731 encountered
Relations: rels:3638568, finalFF:200786
Max relations in full relation-set: 28
Initial matrix: 156923 x 200786 with sparse part having weight 10194178.
Pruned matrix : 122805 x 123653 with weight 4620848.
Total sieving time: 1.31 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.13 hours.
Total square root time: 0.05 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 1.55 hours.
 --------- CPU info (if available) ----------

9·10124-7 = 8(9)1233<125> = 31 · 83 · 859 · C119

C119 = P39 · P80

P39 = 514997239710717504843060243797163586321<39>

P80 = 79068710858248681348102914984733040362741538735234491408794076224567905858038519<80>

Number: n
N=40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599
  ( 119 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=514997239710717504843060243797163586321 (pp39)
 r2=79068710858248681348102914984733040362741538735234491408794076224567905858038519 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 2.17 hours.
Scaled time: 3.15 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_8_9_123_3
n: 40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599
skew: 1.51
deg: 5
c5: 9
c0: -70
m: 10000000000000000000000000
type: snfs
rlim: 1000000
alim: 1000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 350001)
Primes: RFBsize:78498, AFBsize:78806, largePrimes:4616754 encountered
Relations: rels:3996538, finalFF:211076
Max relations in full relation-set: 28
Initial matrix: 157368 x 211076 with sparse part having weight 12304449.
Pruned matrix : 125655 x 126505 with weight 5315318.
Total sieving time: 1.90 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.16 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

9·10123-7 = 8(9)1223<124> = 283 · 449 · 18553 · C115

C115 = P33 · P83

P33 = 335087805245091568482853093222231<33>

P83 = 11392970303565490307790042441076114728020253883982388272289002974166360045042039653<83>

Oct 28, 2007 (3rd)

By Sinkiti Sibata / GGNFS

9·10103-7 = 8(9)1023<104> = 8969263 · 22129553 · C90

C90 = P34 · P57

P34 = 3138341068996635669510657500009591<34>

P57 = 144481741911394492878214372456463812416287949515103488657<57>

Number: 89993_103
N=453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287
  ( 90 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=3138341068996635669510657500009591 (pp34)
 r2=144481741911394492878214372456463812416287949515103488657 (pp57)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.16 hours.
Scaled time: 2.33 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_103
n: 453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287
m: 100000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 350001)
Primes: RFBsize:37706, AFBsize:41552, largePrimes:1383872 encountered
Relations: rels:1489916, finalFF:267931
Max relations in full relation-set: 28
Initial matrix: 79325 x 267931 with sparse part having weight 10896930.
Pruned matrix : 39729 x 40189 with weight 1773397.
Total sieving time: 1.10 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.16 hours.
 --------- CPU info (if available) ----------

9·10110-7 = 8(9)1093<111> = 19 · 41551595117<11> · C100

C100 = P29 · P71

P29 = 41281949109330068117018801413<29>

P71 = 27614743514922133541815936402538216668321370424896711617313719193012707<71>

Number: 89993_110
N=1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991
  ( 100 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=41281949109330068117018801413 (pp29)
 r2=27614743514922133541815936402538216668321370424896711617313719193012707 (pp71)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.60 hours.
Scaled time: 3.20 units (timescale=2.003).
Factorization parameters were as follows:
name: 89993_110
n: 1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991
m: 10000000000000000000000
c5: 9
c0: -7
skew: 0.95
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63908, largePrimes:2384591 encountered
Relations: rels:2925739, finalFF:659504
Max relations in full relation-set: 28
Initial matrix: 113070 x 659504 with sparse part having weight 48577546.
Pruned matrix : 58429 x 59058 with weight 4920438.
Total sieving time: 1.50 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

9·10133-7 = 8(9)1323<134> = 264101 · 534617 · C123

C123 = P39 · P85

P39 = 182955127132944612210518087078849494903<39>

P85 = 3484055901363921062151806188107621607898929991774539197434850631713521731052250641243<85>

Number: 89993_133
N=637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429
  ( 123 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=182955127132944612210518087078849494903 (pp39)
 r2=3484055901363921062151806188107621607898929991774539197434850631713521731052250641243 (pp85)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.85 hours.
Scaled time: 13.77 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_133
n: 637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429
m: 100000000000000000000000000
c5: 9000
c0: -7
skew: 0.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63803, largePrimes:1569153 encountered
Relations: rels:1588445, finalFF:190481
Max relations in full relation-set: 28
Initial matrix: 142368 x 190481 with sparse part having weight 15782385.
Pruned matrix : 127348 x 128123 with weight 8890552.
Total sieving time: 6.62 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.85 hours.
 --------- CPU info (if available) ----------

9·10122-7 = 8(9)1213<123> = 53 · 4483 · 916879 · 2468335253078521<16> · C97

C97 = P38 · P59

P38 = 21496643135387952418448986201888231937<38>

P59 = 77859405334185056592558073314508609031087592802266287870129<59>

Number: 89993_122
N=1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873
  ( 97 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=21496643135387952418448986201888231937 (pp38)
 r2=77859405334185056592558073314508609031087592802266287870129 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.78 hours.
Scaled time: 5.54 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_122
n: 1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873
m: 1000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:63823, largePrimes:2113012 encountered
Relations: rels:2116801, finalFF:142981
Max relations in full relation-set: 28
Initial matrix: 112985 x 142981 with sparse part having weight 12791337.
Pruned matrix : 105117 x 105745 with weight 7557577.
Total sieving time: 2.61 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.78 hours.
 --------- CPU info (if available) ----------

9·10127-7 = 8(9)1263<128> = 16927 · 2815289 · 34549727 · C110

C110 = P53 · P58

P53 = 18928495665651195086151678397725759673977330546366127<53>

P58 = 2887877797068484257309586094965034801453924030197429437839<58>

Number: 89993_127
N=54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553
  ( 110 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=18928495665651195086151678397725759673977330546366127 (pp53)
 r2=2887877797068484257309586094965034801453924030197429437839 (pp58)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.41 hours.
Scaled time: 8.86 units (timescale=2.010).
Factorization parameters were as follows:
name: 89993_127
n: 54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553
m: 10000000000000000000000000
c5: 900
c0: -7
skew: 0.38
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63823, largePrimes:1546280 encountered
Relations: rels:1577253, finalFF:198015
Max relations in full relation-set: 28
Initial matrix: 127838 x 198015 with sparse part having weight 14562521.
Pruned matrix : 108690 x 109393 with weight 6383787.
Total sieving time: 4.25 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.41 hours.
 --------- CPU info (if available) ----------

9·10119-7 = 8(9)1183<120> = 61 · 823 · 1004981 · 1446682233738538319<19> · C92

C92 = P41 · P51

P41 = 45567990874948473844291875103339917072403<41>

P51 = 270596365668481699029128282701225154281973286874043<51>

Number: 89993_119
N=12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329
  ( 92 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=45567990874948473844291875103339917072403 (pp41)
 r2=270596365668481699029128282701225154281973286874043 (pp51)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.11 hours.
Scaled time: 4.20 units (timescale=1.991).
Factorization parameters were as follows:
name: 89993_119
n: 12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329
m: 1000000000000000000000000
c5: 9
c0: -70
skew: 1.51
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:1981105 encountered
Relations: rels:1934715, finalFF:128846
Max relations in full relation-set: 28
Initial matrix: 113390 x 128846 with sparse part having weight 9933260.
Pruned matrix : 107064 x 107694 with weight 6957791.
Total sieving time: 1.96 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.11 hours.
 --------- CPU info (if available) ----------

Oct 28, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(5·102847+1)/3 is prime.

Oct 28, 2007

The factor table of 899...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Oct 27, 2007

By Yousuke Koide

101121+1 is divisible by 162578197086018239450239785966343<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 26, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(8·10163+7)/3 = 2(6)1629<164> = 17 · 9672675193889<13> · 2132690377238720580097964644733<31> · C119

C119 = P32 · P88

P32 = 16241366780245493793149978382913<32>

P88 = 4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897<88>

Number: 26669_163
N=76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961
  ( 119 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=16241366780245493793149978382913 (pp32)
 r2=4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 89.67 hours.
Scaled time: 179.08 units (timescale=1.997).
Factorization parameters were as follows:
name: 26669_163
n: 76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961
m: 200000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5150001)
Primes: RFBsize:315948, AFBsize:316791, largePrimes:5926048 encountered
Relations: rels:6075527, finalFF:765961
Max relations in full relation-set: 28
Initial matrix: 632805 x 765961 with sparse part having weight 56904865.
Pruned matrix : 534793 x 538021 with weight 40888773.
Total sieving time: 85.28 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.92 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 89.67 hours.
 --------- CPU info (if available) ----------

Oct 26, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS

(82·10161+71)/9 = 9(1)1609<162> = 11 · 23 · 3748991 · 2671832954149<13> · 5966029856099<13> · 302592140766530934908888222616061079<36> · C93

C93 = P40 · P53

P40 = 3850694069121437110112555389391787483611<40>

P53 = 51718395086698620503380784735167544390948057134540087<53>

Fri Oct 26 00:04:24 2007  
Fri Oct 26 00:04:24 2007  
Fri Oct 26 00:04:24 2007  Msieve v. 1.28
Fri Oct 26 00:04:24 2007  random seeds: bb05f469 520cf979
Fri Oct 26 00:04:24 2007  factoring 199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157 (93 digits)
Fri Oct 26 00:04:24 2007  commencing quadratic sieve (92-digit input)
Fri Oct 26 00:04:24 2007  using multiplier of 53
Fri Oct 26 00:04:24 2007  using 32kb Intel Core sieve core
Fri Oct 26 00:04:24 2007  sieve interval: 36 blocks of size 32768
Fri Oct 26 00:04:24 2007  processing polynomials in batches of 6
Fri Oct 26 00:04:24 2007  using a sieve bound of 1879931 (70588 primes)
Fri Oct 26 00:04:24 2007  using large prime bound of 219951927 (27 bits)
Fri Oct 26 00:04:24 2007  using double large prime bound of 1037982177167364 (42-50 bits)
Fri Oct 26 00:04:24 2007  using trial factoring cutoff of 50 bits
Fri Oct 26 00:04:24 2007  polynomial 'A' values have 12 factors
Fri Oct 26 01:38:35 2007  70852 relations (18438 full + 52414 combined from 913373 partial), need 70684
Fri Oct 26 01:38:35 2007  begin with 931811 relations
Fri Oct 26 01:38:36 2007  reduce to 176982 relations in 10 passes
Fri Oct 26 01:38:36 2007  attempting to read 176982 relations
Fri Oct 26 01:38:37 2007  recovered 176982 relations
Fri Oct 26 01:38:37 2007  recovered 157867 polynomials
Fri Oct 26 01:38:38 2007  attempting to build 70852 cycles
Fri Oct 26 01:38:38 2007  found 70852 cycles in 5 passes
Fri Oct 26 01:38:38 2007  distribution of cycle lengths:
Fri Oct 26 01:38:38 2007     length 1 : 18438
Fri Oct 26 01:38:38 2007     length 2 : 13138
Fri Oct 26 01:38:38 2007     length 3 : 12424
Fri Oct 26 01:38:38 2007     length 4 : 9444
Fri Oct 26 01:38:38 2007     length 5 : 6893
Fri Oct 26 01:38:38 2007     length 6 : 4449
Fri Oct 26 01:38:38 2007     length 7 : 2721
Fri Oct 26 01:38:38 2007     length 9+: 3345
Fri Oct 26 01:38:38 2007  largest cycle: 17 relations
Fri Oct 26 01:38:38 2007  matrix is 70588 x 70852 with weight 4361172 (avg 61.55/col)
Fri Oct 26 01:38:38 2007  filtering completed in 3 passes
Fri Oct 26 01:38:38 2007  matrix is 66408 x 66472 with weight 4123761 (avg 62.04/col)
Fri Oct 26 01:38:39 2007  saving the first 48 matrix rows for later
Fri Oct 26 01:38:39 2007  matrix is 66360 x 66472 with weight 3167656 (avg 47.65/col)
Fri Oct 26 01:38:39 2007  matrix includes 64 packed rows
Fri Oct 26 01:38:39 2007  using block size 26588 for processor cache size 4096 kB
Fri Oct 26 01:38:41 2007  commencing Lanczos iteration
Fri Oct 26 01:39:01 2007  lanczos halted after 1051 iterations
Fri Oct 26 01:39:01 2007  recovered 17 nontrivial dependencies
Fri Oct 26 01:39:01 2007  prp40 factor: 3850694069121437110112555389391787483611
Fri Oct 26 01:39:01 2007  prp53 factor: 51718395086698620503380784735167544390948057134540087
Fri Oct 26 01:39:01 2007  elapsed time 01:34:37

10160-3 = (9)1597<160> = 13 · 383 · 52771123082243438120761219452533939<35> · C122

C122 = P55 · P68

P55 = 3104829324566476660204837376960208819056316254480075411<55>

P68 = 12258118210972106300910696745912453876036288591144435630300652094167<68>

Number: 99997_160
N=38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637
  ( 122 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=3104829324566476660204837376960208819056316254480075411 (pp55)
 r2=12258118210972106300910696745912453876036288591144435630300652094167 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.28 hours.
Scaled time: 51.72 units (timescale=2.130).
Factorization parameters were as follows:
n: 38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637
m: 100000000000000000000000000000000
c5: 1
c0: -3
skew: 1.25
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:282992, largePrimes:5668831 encountered
Relations: rels:5757196, finalFF:705905
Max relations in full relation-set: 28
Initial matrix: 566202 x 705905 with sparse part having weight 43019303.
Pruned matrix : 449468 x 452363 with weight 26383924.
Total sieving time: 23.17 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.99 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.28 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 26, 2007

By Robert Backstrom / GGNFS, Msieve

(68·10159+13)/9 = 7(5)1587<160> = 3 · 11 · 4815673 · 4744027650700422249483517<25> · C128

C128 = P43 · P85

P43 = 1817556499049832315979311388016701905830557<43>

P85 = 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717<85>

Number: n
N=10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369
  ( 128 digits)
SNFS difficulty: 161 digits.
Divisors found:

Fri Oct 26 04:07:36 2007  prp43 factor: 1817556499049832315979311388016701905830557
Fri Oct 26 04:07:36 2007  prp85 factor: 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717
Fri Oct 26 04:07:36 2007  elapsed time 01:12:41 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 35.05 hours.
Scaled time: 45.84 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_5_158_7
n: 10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369
skew: 1.14
deg: 5
c5: 34
c0: 65
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:216756, largePrimes:7052915 encountered
Relations: rels:6510490, finalFF:471406
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 34.83 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 35.05 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 25, 2007 (4th)

By Robert Backstrom / GGNFS, Msieve

(8·10167+7)/3 = 2(6)1669<168> = 13 · C167

C167 = P41 · P127

P41 = 13118854935330807737302880871625861715191<41>

P127 = 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343<127>

Number: n
N=20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
  ( 167 digits)
SNFS difficulty: 167 digits.
Divisors found:

Fri Oct 26 00:52:24 2007  prp41 factor: 13118854935330807737302880871625861715191
Fri Oct 26 00:52:24 2007  prp127 factor: 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343
Fri Oct 26 00:52:24 2007  elapsed time 02:20:14 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 68.58 hours.
Scaled time: 82.23 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_2_6_166_9
n: 20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513
type: snfs
skew: 0.78
deg: 5
c5: 25
c0: 7
m: 2000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:250196, largePrimes:7501352 encountered
Relations: rels:7006091, finalFF:549114
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.27 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 68.58 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 25, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(26·102688-11)/3 is prime.

Oct 25, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

(46·10161-1)/9 = 5(1)161<162> = 17 · 29 · 47 · 724447 · 855857254801063<15> · 3172216729960337<16> · C122

C122 = P31 · P91

P31 = 8979918563026048055214325630447<31>

P91 = 1248899066404055568679090185969582597135314562972683825422549780576518206214842043840714379<91>

(82·10161+71)/9 = 9(1)1609<162> = 11 · 23 · 3748991 · 2671832954149<13> · 5966029856099<13> · C128

C128 = P36 · C93

P36 = 302592140766530934908888222616061079<36>

C93 = [199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157<93>]

Oct 25, 2007

By Robert Backstrom / GGNFS, Msieve

10166+9 = 1(0)1659<167> = 6841 · 3298055297<10> · C153

C153 = P47 · P106

P47 = 96175707342105206747325741564689382490429756801<47>

P106 = 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817<106>

Number: n
N=443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417
  ( 153 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Oct 25 15:40:05 2007  prp47 factor: 96175707342105206747325741564689382490429756801
Thu Oct 25 15:40:05 2007  prp106 factor: 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817
Thu Oct 25 15:40:05 2007  elapsed time 01:54:23 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 62.44 hours.
Scaled time: 82.79 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_1_0_165_9
n: 443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417
skew: 0.98
deg: 5
c5: 10
c0: 9
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:250150, AFBsize:250021, largePrimes:7553576 encountered
Relations: rels:7043754, finalFF:563405
Max relations in full relation-set: 28
Initial matrix: 500238 x 563405 with sparse part having weight 49550458.
Pruned matrix : 457419 x 459984 with weight 35024031.
Total sieving time: 62.12 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 62.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 24, 2007 (5th)

By Jo Yeong Uk / GGNFS, GMP-ECM

(10160+11)/3 = (3)1597<160> = 2357 · 3547 · 6483784428566166293003<22> · C131

C131 = P65 · P66

P65 = 98546042989459507145454598033560826513496496641717463749658701161<65>

P66 = 624008085251487858816186117499534910163524917199921025095545919941<66>

Number: 33337_160
N=61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=98546042989459507145454598033560826513496496641717463749658701161 (pp65)
 r2=624008085251487858816186117499534910163524917199921025095545919941 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.41 hours.
Scaled time: 51.96 units (timescale=2.129).
Factorization parameters were as follows:
n: 61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501
m: 100000000000000000000000000000000
c5: 1
c0: 11
skew: 1.62
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283048, largePrimes:5715875 encountered
Relations: rels:5844133, finalFF:739067
Max relations in full relation-set: 28
Initial matrix: 566258 x 739067 with sparse part having weight 45560931.
Pruned matrix : 423383 x 426278 with weight 27548907.
Total sieving time: 23.43 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.85 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.41 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(28·10159-1)/9 = 3(1)159<160> = 33 · 97 · 717667 · 31119047 · 4319493713<10> · C134

C134 = P51 · P83

P51 = 691407189640250229701631872793975317289967702892453<51>

P83 = 17810004148297787657731990085303963501623195591076357396769870762158063825273702029<83>

Number: 31111_159
N=12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137
  ( 134 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=691407189640250229701631872793975317289967702892453 (pp51)
 r2=17810004148297787657731990085303963501623195591076357396769870762158063825273702029 (pp83)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.18 hours.
Scaled time: 66.89 units (timescale=2.145).
Factorization parameters were as follows:
n: 12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137
m: 100000000000000000000000000000000
c5: 14
c0: -5
skew: 0.81
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:284317, largePrimes:5680047 encountered
Relations: rels:5727480, finalFF:670051
Max relations in full relation-set: 28
Initial matrix: 567529 x 670051 with sparse part having weight 43786702.
Pruned matrix : 489700 x 492601 with weight 29899843.
Total sieving time: 29.75 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(2·10162+43)/9 = (2)1617<162> = 79 · 3074539183721<13> · 92026938157876922867<20> · C127

C127 = P31 · P97

P31 = 7374950638373593966200740279443<31>

P97 = 1348050841856743517595672702299157137569123136816328878609841055467622001119053294651183847225613<97>

(4·10162-13)/9 = (4)1613<162> = 4795407827859115566133901<25> · C137

C137 = P30 · P108

P30 = 732132950352080637131122456739<30>

P108 = 126590752328295613964062194725925454032813432338962666501971716450553063422318328708874925852644810865626637<108>

(5·10162-41)/9 = (5)1611<162> = 17 · 7802477 · 1221834755184846949<19> · C136

C136 = P29 · P107

P29 = 74150969555284684198040824859<29>

P107 = 46229241501927787031803827366761897615314009076339630433468603502437500587889723061122144734719131912055229<107>

3·10163-7 = 2(9)1623<164> = 41 · 43 · 73 · 433163734125755498123<21> · C138

C138 = P33 · P105

P33 = 984803325251956195887249668731139<33>

P105 = 546442521935781460110773913223987286991730594097092602213887622250012599971203648826978554376441175284731<105>

Oct 24, 2007 (4th)

By Sinkiti Sibata / GGNFS

(8·10158+7)/3 = 2(6)1579<159> = 453968096244493<15> · C144

C144 = P56 · P88

P56 = 77025991204399032295102167879033530984020107406191788251<56>

P88 = 7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083<88>

Number: 26669_158
N=587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833
  ( 144 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=77025991204399032295102167879033530984020107406191788251 (pp56)
 r2=7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083 (pp88)
Version: GGNFS-0.77.1-20060513-k8
Total time: 59.71 hours.
Scaled time: 118.95 units (timescale=1.992).
Factorization parameters were as follows:
name: 26669_158
n: 587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833
m: 20000000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3900001)
Primes: RFBsize:283146, AFBsize:284107, largePrimes:5971981 encountered
Relations: rels:6202849, finalFF:822675
Max relations in full relation-set: 28
Initial matrix: 567319 x 822675 with sparse part having weight 58139262.
Pruned matrix : 388038 x 390938 with weight 44121525.
Total sieving time: 56.94 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 2.38 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 59.71 hours.
 --------- CPU info (if available) ----------

Oct 24, 2007 (3rd)

By Robert Backstrom / GGNFS

(8·10152+7)/3 = 2(6)1519<153> = 61 · C151

C151 = P39 · P113

P39 = 421869844046731851658147807645650077819<39>

P113 = 10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691<113>

Number: n
N=4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929
  ( 151 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=421869844046731851658147807645650077819 (pp39)
 r2=10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691 (pp113)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 16.95 hours.
Scaled time: 22.10 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_2_6_151_9
n: 4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929
skew: 0.78
deg: 5
c5: 25
c0: 7
m: 2000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:203362, AFBsize:203182, largePrimes:6399966 encountered
Relations: rels:5939023, finalFF:511751
Max relations in full relation-set: 28
Initial matrix: 406608 x 511751 with sparse part having weight 27504928.
Pruned matrix : 311614 x 313711 with weight 13508229.
Total sieving time: 15.13 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.56 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 16.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 24, 2007 (2nd)

By Kurt Beschorner

10753+1 is divisible by 1756473376297178637489284481878718601<37>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 24, 2007

By Yousuke Koide

101371+1 is divisible by 127539278618607069275328998039143<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 23, 2007

By Sinkiti Sibata / GGNFS

(8·10146+7)/3 = 2(6)1459<147> = 2167165829<10> · C138

C138 = P64 · P74

P64 = 4143397241869544226241437570296544113990642586158773224155313511<64>

P74 = 29697508503653602939343659106341885529158177653874575739404674525553127951<74>

Number: 26669_146
N=123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961
  ( 138 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=4143397241869544226241437570296544113990642586158773224155313511 (pp64)
 r2=29697508503653602939343659106341885529158177653874575739404674525553127951 (pp74)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.70 hours.
Scaled time: 39.37 units (timescale=1.998).
Factorization parameters were as follows:
name: 26669_146
n: 123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961
m: 200000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2877121 encountered
Relations: rels:2886374, finalFF:288594
Max relations in full relation-set: 28
Initial matrix: 228612 x 288594 with sparse part having weight 30123579.
Pruned matrix : 210472 x 211679 with weight 20270448.
Total sieving time: 18.98 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.51 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.70 hours.
 --------- CPU info (if available) ----------

Oct 23, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10165+7)/3 = 2(6)1649<166> = 73 · 9803 · 19961 · 3844331 · 12325751 · 106692540971<12> · 5524900734469672569379<22> · C109

C109 = P33 · P36 · P42

P33 = 161800001655869356136898432615667<33>

P36 = 226209579099872731684276944664364189<36>

P42 = 182609076402191723318653867302508477992533<42>

Number: 26669_165
N=6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579
  ( 109 digits)
Divisors found:
 r1=161800001655869356136898432615667 (pp33)
 r2=226209579099872731684276944664364189 (pp36)
 r3=182609076402191723318653867302508477992533 (pp42)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 14.55 hours.
Scaled time: 30.77 units (timescale=2.114).
Factorization parameters were as follows:
name: 26669_165
n: 6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579
skew: 30844.34
# norm 3.88e+15
c5: 32640
c4: -6377134016
c3: 10966983900756
c2: 6023277967525827220
c1: 20338186144994372135593
c0: -322736910701913843682752030
# alpha -6.58
Y1: 391238345143
Y0: -728218088733067565453
# Murphy_E 1.05e-09
# M 2458195276530130644457672644483945265068481024582090432931298737948038172243268879673145326804447368387365992
type: gnfs
rlim: 2400000
alim: 2400000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1200000, 1920001)
Primes: RFBsize:176302, AFBsize:175803, largePrimes:7512919 encountered
Relations: rels:7327983, finalFF:490794
Max relations in full relation-set: 28
Initial matrix: 352190 x 490794 with sparse part having weight 47989971.
Pruned matrix : 258659 x 260483 with weight 27043110.
Polynomial selection time: 0.68 hours.
Total sieving time: 13.24 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.38 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000
total time: 14.55 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 23, 2007

By Robert Backstrom / GGNFS, Msieve

(64·10160+53)/9 = 7(1)1597<161> = 23 · 191 · 114769 · 748180586440778137<18> · C135

C135 = P43 · P92

P43 = 2272678914182122391159400004256881975433059<43>

P92 = 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647<92>

Number: n
N=188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173
  ( 135 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 23 03:14:29 2007  prp43 factor: 2272678914182122391159400004256881975433059
Tue Oct 23 03:14:29 2007  prp92 factor: 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647
Tue Oct 23 03:14:29 2007  elapsed time 01:10:32 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 38.03 hours.
Scaled time: 49.78 units (timescale=1.309).
Factorization parameters were as follows:
name: KA_7_1_159_7
n: 188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173
skew: 1.93
deg: 5
c5: 2
c0: 53
m: 200000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:216946, largePrimes:7083358 encountered
Relations: rels:6573818, finalFF:499435
Max relations in full relation-set: 28
Initial matrix: 433827 x 499435 with sparse part having weight 36087703.
Pruned matrix : 381360 x 383593 with weight 23854377.
Total sieving time: 37.83 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 38.03 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(8·10160+7)/3 = 2(6)1599<161> = 49843 · C156

C156 = P70 · P86

P70 = 8206529381083043352109674031409945933677801693490815409442456291123149<70>

P86 = 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067<86>

Number: n
N=535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983
  ( 156 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 23 23:09:38 2007  prp70 factor: 8206529381083043352109674031409945933677801693490815409442456291123149
Tue Oct 23 23:09:38 2007  prp86 factor: 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067
Tue Oct 23 23:09:38 2007  elapsed time 01:04:53 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.34 hours.
Scaled time: 52.83 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_2_6_159_9
n: 535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983
skew: 1.95
deg: 5
c5: 1
c0: 28
m: 200000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800000)
Primes: RFBsize:203362, AFBsize:203227, largePrimes:7259162 encountered
Relations: rels:6779635, finalFF:504684
Max relations in full relation-set: 28
Initial matrix: 406653 x 504684 with sparse part having weight 41751576.
Pruned matrix : 337714 x 339811 with weight 26445618.
Total sieving time: 36.12 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 36.34 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 22, 2007 (4th)

By Sinkiti Sibata / PRIMO

(85·102580-13)/9 is prime.

Oct 22, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(8·10154+7)/3 = 2(6)1539<155> = 17224619 · 55682718131<11> · 46415095754141034190321569677<29> · C108

C108 = P35 · P73

P35 = 63976167233321490585818587278762619<35>

P73 = 9363133420441845598841194850047950471022696892436041111098985547200676067<73>

Number: 26669_154
N=599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473
  ( 108 digits)
Divisors found:
 r1=63976167233321490585818587278762619 (pp35)
 r2=9363133420441845598841194850047950471022696892436041111098985547200676067 (pp73)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.65 hours.
Scaled time: 22.83 units (timescale=2.144).
Factorization parameters were as follows:
name: 26669_154
n: 599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473
skew: 21354.62
# norm 6.78e+14
c5: 32400
c4: 104238510
c3: -63159803819065
c2: 42231149150739894
c1: 10386860579266260178521
c0: 1573011234854712440644311
# alpha -5.93
Y1: 268163654693
Y0: -450172247251438281950
# Murphy_E 1.31e-09
# M 353372238522770296188352642033280019967747150736232710020604793608863613888916745569090484185353683588909139
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:135004, largePrimes:4543413 encountered
Relations: rels:4565506, finalFF:355041
Max relations in full relation-set: 28
Initial matrix: 270157 x 355041 with sparse part having weight 33355043.
Pruned matrix : 221309 x 222723 with weight 18208925.
Polynomial selection time: 0.60 hours.
Total sieving time: 9.69 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 10.65 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10157+7)/3 = 2(6)1569<158>= 71 · 73 · 4423 · 17761 · 463849 · 131698991 · C133

C133 = P48 · P85

P48 = 272730925941823417805548362043843409679870198107<48>

P85 = 3931060343889521523931450002903303012283257053146040409429479768292617881055891882137<85>

Number: 26669_157
N=1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659
  ( 133 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=272730925941823417805548362043843409679870198107 (pp48)
 r2=3931060343889521523931450002903303012283257053146040409429479768292617881055891882137 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 19.84 hours.
Scaled time: 42.45 units (timescale=2.140).
Factorization parameters were as follows:
n: 1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659
m: 20000000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5656803 encountered
Relations: rels:5671985, finalFF:600758
Max relations in full relation-set: 28
Initial matrix: 433786 x 600758 with sparse part having weight 46380712.
Pruned matrix : 331528 x 333760 with weight 28777533.
Total sieving time: 19.11 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.61 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 19.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 22, 2007 (2nd)

By Sinkiti Sibata / GGNFS

(8·10150+7)/3 = 2(6)1499<151> = 19 · 19173023 · 221211127 · C134

C134 = P52 · P83

P52 = 3153611510488812690844381411841100171038865591531757<52>

P83 = 10493234479791580568317662070396265616908097303633122206670593944661297064473922083<83>

Number: 26669_150
N=33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831
  ( 134 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=3153611510488812690844381411841100171038865591531757 (pp52)
 r2=10493234479791580568317662070396265616908097303633122206670593944661297064473922083 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.11 hours.
Scaled time: 42.22 units (timescale=2.000).
Factorization parameters were as follows:
name: 26669_150
n: 33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831
m: 1000000000000000000000000000000
c5: 8
c0: 7
skew: 0.97
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:176343, largePrimes:5664697 encountered
Relations: rels:5756890, finalFF:642726
Max relations in full relation-set: 28
Initial matrix: 352710 x 642726 with sparse part having weight 56826393.
Pruned matrix : 241016 x 242843 with weight 25378288.
Total sieving time: 20.10 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.75 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.11 hours.
 --------- CPU info (if available) ----------

(8·10143+7)/3 = 2(6)1429<144> = 132 · 3517 · 62776679931694823<17> · C121

C121 = P47 · P75

P47 = 20021116406067209554446200468334668005750140859<47>

P75 = 356962853960238997946851914156890231498548267914175830313090442617598040829<75>

Number: 26669_143
N=7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111
  ( 121 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=20021116406067209554446200468334668005750140859 (pp47)
 r2=356962853960238997946851914156890231498548267914175830313090442617598040829 (pp75)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.14 hours.
Scaled time: 34.23 units (timescale=1.997).
Factorization parameters were as follows:
nama: 26669_143
n: 7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111
m: 20000000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:100373, largePrimes:2900939 encountered
Relations: rels:2943333, finalFF:278741
Max relations in full relation-set: 28
Initial matrix: 200460 x 278741 with sparse part having weight 32014645.
Pruned matrix : 180795 x 181861 with weight 19476116.
Total sieving time: 16.50 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.43 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.14 hours.
 --------- CPU info (if available) ----------

Oct 22, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(13·10165-1)/3 = 4(3)165<166> = 7 · 801331 · C159

C159 = P77 · P83

P77 = 20581230672475861430727158263255086663302501457153191742856250309416063163917<77>

P83 = 37535376232092446430954426168419670162044288493908322073297750728833564783295676597<83>

Number: n
N=772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449
  ( 159 digits)
SNFS difficulty: 166 digits.
Divisors found:

Mon Oct 22 02:26:02 2007  prp77 factor: 20581230672475861430727158263255086663302501457153191742856250309416063163917
Mon Oct 22 02:26:02 2007  prp83 factor: 37535376232092446430954426168419670162044288493908322073297750728833564783295676597
Mon Oct 22 02:26:02 2007  elapsed time 02:07:00 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 54.52 hours.
Scaled time: 65.37 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_4_3_165
n: 772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449
type: snfs
skew: 0.60
deg: 5
c5: 13
c0: -1
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:250150, AFBsize:249271, largePrimes:7324010 encountered
Relations: rels:6828395, finalFF:550183
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 54.23 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 54.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

(8·10162+7)/3 = 2(6)1619<163> = 23 · 2417 · C158

C158 = P38 · P121

P38 = 13758431094795674099921153836784941879<38>

P121 = 3486545464024582803252161746345501308393073883180459970373351716778246003294776444321266822336985947908508412928696412621<121>

Oct 21, 2007 (5th)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve

(2·10165+1)/3 = (6)1647<165> = 1907 · 25763 · 1950089 · C151

C151 = P38 · P54 · P61

P38 = 11159480313913593484408359509139419441<38>

P54 = 145144015245287700460200196670856548838130894793891909<54>

P61 = 4295998076553065365533511361350566844970496455322403010819807<61>

prp38 factor: 11159480313913593484408359509139419441
prp54 factor: 145144015245287700460200196670856548838130894793891909
prp61 factor: 4295998076553065365533511361350566844970496455322403010819807

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283 (151 digits)
Using B1=1361500, B2=1303162716, polynomial Dickson(6), sigma=52991453
Step 1 took 19547ms
Step 2 took 9719ms
********** Factor found in step 2: 11159480313913593484408359509139419441
Found probable prime factor of 38 digits: 11159480313913593484408359509139419441
Composite cofactor 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563 has 114 digits

Number: n
N=623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563
  ( 114 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Oct 21 14:25:53 2007  prp54 factor: 145144015245287700460200196670856548838130894793891909
Sun Oct 21 14:25:53 2007  prp61 factor: 4295998076553065365533511361350566844970496455322403010819807
Sun Oct 21 14:25:53 2007  elapsed time 01:41:00 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.08 hours.
Scaled time: 62.64 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_6_164_7

n: 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563

# n: 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283

skew: 0.87
deg: 5
c5: 2
c0: 1
m: 1000000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300001)
Primes: RFBsize:203362, AFBsize:203032, largePrimes:7214058 encountered
Relations: rels:6650540, finalFF:426929
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 42.87 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 43.08 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(8·10165-53)/9 = (8)1643<165> = 6403993 · C159

C159 = P45 · P114

P45 = 350982021485651168585060151283338980210340619<45>

P114 = 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649<114>

Number: n
N=138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731
  ( 159 digits)
SNFS difficulty: 165 digits.
Divisors found:

Sun Oct 21 20:17:38 2007  prp45 factor: 350982021485651168585060151283338980210340619
Sun Oct 21 20:17:38 2007  prp114 factor: 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649
Sun Oct 21 20:17:38 2007  elapsed time 01:35:15 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 47.74 hours.
Scaled time: 63.31 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_164_3
n: 138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731
skew: 1.46
deg: 5
c5: 8
c0: -53
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:250150, AFBsize:250051, largePrimes:7311231 encountered
Relations: rels:6818524, finalFF:565781
Max relations in full relation-set: 28
Initial matrix: 500266 x 565781 with sparse part having weight 42203089.
Pruned matrix : 447352 x 449917 with weight 27775961.
Total sieving time: 47.50 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 47.74 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 21, 2007 (4th)

By anonymous / GMP-ECM

(5·10190+7)/3 = 1(6)1899<191> = 983 · 3110537 · 4168826771<10> · 54213944958939972267302651<26> · C146

C146 = P29 · P117

P29 = 95241712200343898401070633893<29>

P117 = 253225715089880357003437152506851618536597279889801230013665252373632182359449182088181293413579341092522759275175463<117>

Oct 21, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(8·10130+7)/3 = 2(6)1299<131> = 359 · C128

C128 = P33 · P96

P33 = 682633639211723545834566164085833<33>

P96 = 108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227<96>

Number: 26669_130
N=74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091
  ( 128 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=682633639211723545834566164085833 (pp33)
 r2=108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.74 hours.
Scaled time: 7.43 units (timescale=1.987).
Factorization parameters were as follows:
name: 26669_130
n: 74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091
m: 100000000000000000000000000
c5: 8
c0: 7
skew: 0.97
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:63951, AFBsize:64073, largePrimes:1455357 encountered
Relations: rels:1452260, finalFF:170662
Max relations in full relation-set: 28
Initial matrix: 128089 x 170662 with sparse part having weight 10762332.
Pruned matrix : 114592 x 115296 with weight 5636879.
Total sieving time: 3.59 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 3.74 hours.
 --------- CPU info (if available) ----------

(8·10133+7)/3 = 2(6)1329<134> = 73 · 523 · 30253 · 694831 · 1145213 · C113

C113 = P42 · P72

P42 = 133271547249140168413145147446888048704353<42>

P72 = 217707224173432323868406589757746873580273750494054826756936569259268393<72>

Number: 26669_133
N=29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729
  ( 113 digits)
SNFS difficulty: 133 digits.
Divisors found:
 r1=133271547249140168413145147446888048704353 (pp42)
 r2=217707224173432323868406589757746873580273750494054826756936569259268393 (pp72)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.92 hours.
Scaled time: 13.77 units (timescale=1.988).
Factorization parameters were as follows:
name: 26669_133
n: 29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729
m: 200000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:64168, largePrimes:1593511 encountered
Relations: rels:1626248, finalFF:203055
Max relations in full relation-set: 28
Initial matrix: 142732 x 203055 with sparse part having weight 17060245.
Pruned matrix : 124557 x 125334 with weight 8832672.
Total sieving time: 6.72 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.92 hours.
 --------- CPU info (if available) ----------

(8·10103+7)/3 = 2(6)1029<104> = 6641346161<10> · C94

C94 = P44 · P50

P44 = 50628118279694776375171982905395943152916717<44>

P50 = 79308699618830633011348707020263138933756280563537<50>

Number: 26669_103
N=4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029
  ( 94 digits)
SNFS difficulty: 103 digits.
Divisors found:
 r1=50628118279694776375171982905395943152916717 (pp44)
 r2=79308699618830633011348707020263138933756280563537 (pp50)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.18 hours.
Scaled time: 2.36 units (timescale=1.995).
Factorization parameters were as follows:
name: 26669_103
n: 4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029
m: 200000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 350001)
Primes: RFBsize:37706, AFBsize:41542, largePrimes:1391765 encountered
Relations: rels:1503988, finalFF:273193
Max relations in full relation-set: 28
Initial matrix: 79314 x 273193 with sparse part having weight 11183859.
Pruned matrix : 40266 x 40726 with weight 1829275.
Total sieving time: 1.13 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 1.18 hours.
 --------- CPU info (if available) ----------

(8·10104+7)/3 = 2(6)1039<105> = 76561 · C100

C100 = P33 · P67

P33 = 733945223005884153559250475665329<33>

P67 = 4745669469153279016048570235521763800475125498182552663288629329901<67>

Number: 26669_104
N=3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429
  ( 100 digits)
SNFS difficulty: 105 digits.
Divisors found:
 r1=733945223005884153559250475665329 (pp33)
 r2=4745669469153279016048570235521763800475125498182552663288629329901 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.96 hours.
Scaled time: 3.87 units (timescale=1.977).
Factorization parameters were as follows:
name: 26669_104
n: 3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429
m: 1000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:64193, largePrimes:2081424 encountered
Relations: rels:2253638, finalFF:328853
Max relations in full relation-set: 28
Initial matrix: 113355 x 328853 with sparse part having weight 22829670.
Pruned matrix : 62492 x 63122 with weight 3004338.
Total sieving time: 1.88 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

(8·10134+7)/3 = 2(6)1339<135> = 148654243 · 1262823917<10> · C118

C118 = P41 · P77

P41 = 37620956682884538589371868827603031738343<41>

P77 = 37758852612331776616795032844299692308607656131997210191374930427924942519293<77>

Number: 26669_134
N=1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499
  ( 118 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=37620956682884538589371868827603031738343 (pp41)
 r2=37758852612331776616795032844299692308607656131997210191374930427924942519293 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.82 hours.
Scaled time: 11.68 units (timescale=2.007).
Factorization parameters were as follows:
name: 26669_134
n: 1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499
m: 1000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64193, largePrimes:1541556 encountered
Relations: rels:1560889, finalFF:192289
Max relations in full relation-set: 28
Initial matrix: 142755 x 192289 with sparse part having weight 14621950.
Pruned matrix : 126409 x 127186 with weight 7901050.
Total sieving time: 5.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.82 hours.
 --------- CPU info (if available) ----------

(8·10142+7)/3 = 2(6)1419<143> = 3064708476607<13> · 4187678852923<13> · C118

C118 = P40 · P78

P40 = 9788973638568650061780766529522450169529<40>

P78 = 212260427653808834797575069001986356489959724932965465429439372027648665816401<78>

Number: 26669_142
N=2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129
  ( 118 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=9788973638568650061780766529522450169529 (pp40)
 r2=212260427653808834797575069001986356489959724932965465429439372027648665816401 (pp78)
Version: GGNFS-0.77.1-20060513-k8
Total time: 10.11 hours.
Scaled time: 20.14 units (timescale=1.992).
Factorization parameters were as follows:
name: 26669_142
n: 2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129
m: 20000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1750001)
Primes: RFBsize:100021, AFBsize:99418, largePrimes:2798512 encountered
Relations: rels:2847765, finalFF:330698
Max relations in full relation-set: 28
Initial matrix: 199503 x 330698 with sparse part having weight 30315932.
Pruned matrix : 162985 x 164046 with weight 13847017.
Total sieving time: 9.75 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 10.11 hours.
 --------- CPU info (if available) ----------

Oct 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10139+7)/3 = 2(6)1389<140> = 1768103158425827<16> · 27452760668249467<17> · C108

C108 = P40 · P69

P40 = 1241873230306512944129120625376444423573<40>

P69 = 442382402449578672496474001239726150208458221956431612701743308645417<69>

Number: 26669_139
N=549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941
  ( 108 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=1241873230306512944129120625376444423573 (pp40)
 r2=442382402449578672496474001239726150208458221956431612701743308645417 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.56 hours.
Scaled time: 11.90 units (timescale=2.140).
Factorization parameters were as follows:
n: 549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941
m: 10000000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1100001)
Primes: RFBsize:114155, AFBsize:114442, largePrimes:3315311 encountered
Relations: rels:3411950, finalFF:393858
Max relations in full relation-set: 28
Initial matrix: 228661 x 393858 with sparse part having weight 33230335.
Pruned matrix : 169036 x 170243 with weight 12385404.
Total sieving time: 5.40 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 5.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10141+7)/3 = 2(6)1409<142> = 29 · 73 · 1339806917806153<16> · 92415619460291259403<20> · C104

C104 = P39 · P65

P39 = 502212812269744236328154953897511547463<39>

P65 = 20256877015611825323436706422598519488570631957881652952297498821<65>

Number: 26669_141
N=10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123
  ( 104 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=502212812269744236328154953897511547463 (pp39)
 r2=20256877015611825323436706422598519488570631957881652952297498821 (pp65)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.21 hours.
Scaled time: 13.22 units (timescale=2.127).
Factorization parameters were as follows:
n: 10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123
m: 20000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:3261056 encountered
Relations: rels:3266559, finalFF:311634
Max relations in full relation-set: 28
Initial matrix: 228612 x 311634 with sparse part having weight 26294993.
Pruned matrix : 196110 x 197317 with weight 13252279.
Total sieving time: 6.01 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10151+7)/3 = 2(6)1509<152> = 83 · 191 · 222531925376261959597<21> · 87151965549522581150273<23> · C104

C104 = P37 · P68

P37 = 2151824979439633304570135127360335431<37>

P68 = 40307031630293129082698941368209006104445744505208908458146567077043<68>

Number: 26669_151
N=86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533
  ( 104 digits)
Divisors found:
 r1=2151824979439633304570135127360335431 (pp37)
 r2=40307031630293129082698941368209006104445744505208908458146567077043 (pp68)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 5.74 hours.
Scaled time: 12.28 units (timescale=2.138).
Factorization parameters were as follows:
name: 26669_151
n: 86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533
skew: 11778.21
# norm 6.95e+14
c5: 62160
c4: 1496130332
c3: -45556222412128
c2: -74626143902162469
c1: 113505084408824096690
c0: -1919290235623806504596725
# alpha -6.68
Y1: 4648483103
Y0: -67442740130436131592
# Murphy_E 2.11e-09
# M 56184838726415761082613399246235419642783909465629485767916514734753284656665661743230574578593360749961
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 60000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [900000, 1620001)
Primes: RFBsize:135072, AFBsize:135343, largePrimes:4346551 encountered
Relations: rels:4257071, finalFF:317428
Max relations in full relation-set: 28
Initial matrix: 270499 x 317428 with sparse part having weight 25317400.
Pruned matrix : 238627 x 240043 with weight 16192467.
Polynomial selection time: 0.39 hours.
Total sieving time: 5.00 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.21 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000
total time: 5.74 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 21, 2007

By Yousuke Koide

101073+1 is divisible by 588831771788611721102815421599303<33>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 20, 2007 (5th)

By Jo Yeong Uk / GGNFS

(8·10137+7)/3 = 2(6)1369<138> = 13 · 773 · 56401 · 23192382931<11> · 887752643993<12> · C107

C107 = P36 · P72

P36 = 225827415705440762247969188163076931<36>

P72 = 101191741405873712462631199841067741763362688081142783407044807587961997<72>

Number: 26669_137
N=22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207
  ( 107 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=225827415705440762247969188163076931 (pp36)
 r2=101191741405873712462631199841067741763362688081142783407044807587961997 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.05 hours.
Scaled time: 6.48 units (timescale=2.122).
Factorization parameters were as follows:
n: 22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207
m: 2000000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1250001)
Primes: RFBsize:107126, AFBsize:106423, largePrimes:2289110 encountered
Relations: rels:2432530, finalFF:305349
Max relations in full relation-set: 28
Initial matrix: 213613 x 305349 with sparse part having weight 22381011.
Pruned matrix : 177541 x 178673 with weight 10158100.
Total sieving time: 2.91 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 20, 2007 (4th)

By Sinkiti Sibata / GGNFS

8·10162-7 = 7(9)1613<163> = 494213 · 388509891553534266757079<24> · C134

C134 = P59 · P76

P59 = 16147676136454049333700128338546853224145331776821755134693<59>

P76 = 2580261432154997404112328929704725753375527855692727120431726388111826233063<76>

Number: 79993_162
N=41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659
  ( 134 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=16147676136454049333700128338546853224145331776821755134693 (pp59)
 r2=2580261432154997404112328929704725753375527855692727120431726388111826233063 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 61.95 hours.
Scaled time: 124.03 units (timescale=2.002).
Factorization parameters were as follows:
name: 79993_162
n: 41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659
m: 200000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4150001)
Primes: RFBsize:315948, AFBsize:315706, largePrimes:5839925 encountered
Relations: rels:6045274, finalFF:823077
Max relations in full relation-set: 28
Initial matrix: 631718 x 823077 with sparse part having weight 47717456.
Pruned matrix : 473657 x 476879 with weight 31143738.
Total sieving time: 59.04 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.51 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 61.95 hours.
 --------- CPU info (if available) ----------

(8·10111+7)/3 = 2(6)1109<112> = 2145389 · 1377179399<10> · C96

C96 = P35 · P62

P35 = 18106717789925267749261242702101927<35>

P62 = 49846243240205443718855673321344571054539531011124970246880177<62>

Number: 26669_111
N=902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079
  ( 96 digits)
SNFS difficulty: 112 digits.
Divisors found:
 r1=18106717789925267749261242702101927 (pp35)
 r2=49846243240205443718855673321344571054539531011124970246880177 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 1.44 hours.
Scaled time: 2.88 units (timescale=2.004).
Factorization parameters were as follows:
name: 26669_111
n: 902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079
m: 20000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63943, largePrimes:2241963 encountered
Relations: rels:2551561, finalFF:441249
Max relations in full relation-set: 28
Initial matrix: 113106 x 441249 with sparse part having weight 35014615.
Pruned matrix : 62074 x 62703 with weight 4765126.
Total sieving time: 1.35 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.44 hours.
 --------- CPU info (if available) ----------

(8·10123+7)/3 = 2(6)1229<124> = 1229019557<10> · 379092951201193<15> · C100

C100 = P49 · P52

P49 = 2898545393005568842248882069535618909163031509171<49>

P52 = 1974622690311058776335153117537051940589078496100539<52>

Number: 26669_123
N=5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169
  ( 100 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=2898545393005568842248882069535618909163031509171 (pp49)
 r2=1974622690311058776335153117537051940589078496100539 (pp52)
Version: GGNFS-0.77.1-20060513-k8
Total time: 2.84 hours.
Scaled time: 5.61 units (timescale=1.980).
Factorization parameters were as follows:
name: 26669_123
n: 5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169
m: 2000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64168, largePrimes:2114570 encountered
Relations: rels:2123330, finalFF:147078
Max relations in full relation-set: 28
Initial matrix: 113332 x 147078 with sparse part having weight 13374411.
Pruned matrix : 104524 x 105154 with weight 7551198.
Total sieving time: 2.67 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------

(8·10128+7)/3 = 2(6)1279<129> = 419 · 16311689 · 7428034067<10> · C109

C109 = P45 · P65

P45 = 351941064731415296526137239470932854807364819<45>

P65 = 14924917745215309816252937894497602188907340265178654448165423583<65>

Number: 26669_128
N=5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477
  ( 109 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=351941064731415296526137239470932854807364819 (pp45)
 r2=14924917745215309816252937894497602188907340265178654448165423583 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.50 hours.
Scaled time: 8.89 units (timescale=1.977).
Factorization parameters were as follows:
name: 26669_128
n: 5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477
m: 20000000000000000000000000
c5: 250
c0: 7
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64168, largePrimes:1486278 encountered
Relations: rels:1489312, finalFF:175012
Max relations in full relation-set: 28
Initial matrix: 128185 x 175012 with sparse part having weight 12253287.
Pruned matrix : 114089 x 114793 with weight 6318497.
Total sieving time: 4.34 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Oct 20, 2007 (3rd)

By Jo Yeong Uk / GGNFS

6·10157+7 = 6(0)1567<158> = 29575545858739133328361799<26> · C133

C133 = P54 · P79

P54 = 909973554507637615273149646490856241896005712528152743<54>

P79 = 2229408796486527839879415799102804165173602971152320543487096830961582839982551<79>

Number: 60007_157
N=2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393
  ( 133 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=909973554507637615273149646490856241896005712528152743 (pp54)
 r2=2229408796486527839879415799102804165173602971152320543487096830961582839982551 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.18 hours.
Scaled time: 66.81 units (timescale=2.143).
Factorization parameters were as follows:
n: 2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393
m: 20000000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5685473 encountered
Relations: rels:5694522, finalFF:634310
Max relations in full relation-set: 28
Initial matrix: 566304 x 634310 with sparse part having weight 42093593.
Pruned matrix : 518113 x 521008 with weight 30976126.
Total sieving time: 29.55 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.48 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.18 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10120+7)/3 = 2(6)1199<121> = C121

C121 = P61 · P61

P61 = 1060471105842071452080239329331029536565351505210275149416401<61>

P61 = 2514605680415204721631917533968366670395835407292136222935069<61>

Number: 26669_120
N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 121 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=1060471105842071452080239329331029536565351505210275149416401 (pp61)
 r2=2514605680415204721631917533968366670395835407292136222935069 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.89 hours.
Scaled time: 1.88 units (timescale=2.115).
Factorization parameters were as follows:
n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 2000000000000000000000000
c5: 1
c0: 28
skew: 1.95
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 450001)
Primes: RFBsize:49098, AFBsize:49156, largePrimes:1800198 encountered
Relations: rels:1786914, finalFF:141902
Max relations in full relation-set: 28
Initial matrix: 98318 x 141902 with sparse part having weight 11624596.
Pruned matrix : 86828 x 87383 with weight 5098835.
Total sieving time: 0.84 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.89 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10129+7)/3 = 2(6)1289<130> = C130

C130 = P34 · P97

P34 = 1638212584355948805449002823879881<34>

P97 = 1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549<97>

Number: 26669_129
N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 130 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=1638212584355948805449002823879881 (pp34)
 r2=1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.97 hours.
Scaled time: 4.23 units (timescale=2.142).
Factorization parameters were as follows:
n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 100000000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 900001)
Primes: RFBsize:78498, AFBsize:78746, largePrimes:1495528 encountered
Relations: rels:1503818, finalFF:187166
Max relations in full relation-set: 28
Initial matrix: 157308 x 187166 with sparse part having weight 9227172.
Pruned matrix : 142970 x 143820 with weight 5564851.
Total sieving time: 1.90 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 1.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(16·10159-61)/9 = 1(7)1581<160> = 7 · 11 · 139 · 283 · 1123 · 5563 · 11321 · 1123247 · 11160628967<11> · C126

C126 = P48 · P79

P48 = 188771796820566483431209728112718047569192774367<48>

P79 = 3506798873133264834251861643109592173565728384191166286258478470759285819773297<79>

Number: 17771_159
N=661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=188771796820566483431209728112718047569192774367 (pp48)
 r2=3506798873133264834251861643109592173565728384191166286258478470759285819773297 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 29.47 hours.
Scaled time: 63.21 units (timescale=2.145).
Factorization parameters were as follows:
n: 661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999
m: 200000000000000000000000000000000
c5: 1
c0: -1220
skew: 4.14
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:282548, largePrimes:5712059 encountered
Relations: rels:5803604, finalFF:708737
Max relations in full relation-set: 28
Initial matrix: 565758 x 708737 with sparse part having weight 44615649.
Pruned matrix : 451837 x 454729 with weight 28540403.
Total sieving time: 28.30 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 1.04 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 29.47 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10106+7)/3 = 2(6)1059<107> = 38933 · C102

C102 = P31 · P72

P31 = 4246217137079532440315775172579<31>

P72 = 161305309862279566253022081601447659781689908478972816016415808296252467<72>

Number: 26669_106
N=684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393
  ( 102 digits)
SNFS difficulty: 107 digits.
Divisors found:
 r1=4246217137079532440315775172579 (pp31)
 r2=161305309862279566253022081601447659781689908478972816016415808296252467 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.46 hours.
Scaled time: 0.97 units (timescale=2.131).
Factorization parameters were as follows:
n: 684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393
m: 2000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 260001)
Primes: RFBsize:30757, AFBsize:30719, largePrimes:1032267 encountered
Relations: rels:965725, finalFF:100183
Max relations in full relation-set: 28
Initial matrix: 61541 x 100183 with sparse part having weight 4259001.
Pruned matrix : 47943 x 48314 with weight 1440203.
Total sieving time: 0.43 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.46 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10114+7)/3 = 2(6)1139<115> = 19 · 59 · 131 · 1613 · 172841183 · C98

C98 = P38 · P61

P38 = 15049466556427553742046054404910545751<38>

P61 = 4328018617649452918247261765466850080785970021940189130656211<61>

Number: 26669_114
N=65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461
  ( 98 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=15049466556427553742046054404910545751 (pp38)
 r2=4328018617649452918247261765466850080785970021940189130656211 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.67 hours.
Scaled time: 1.44 units (timescale=2.143).
Factorization parameters were as follows:
n: 65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461
m: 100000000000000000000000
c5: 4
c0: 35
skew: 1.54
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 390001)
Primes: RFBsize:49098, AFBsize:49236, largePrimes:1810475 encountered
Relations: rels:1862920, finalFF:208249
Max relations in full relation-set: 28
Initial matrix: 98398 x 208249 with sparse part having weight 15809065.
Pruned matrix : 71479 x 72034 with weight 3436955.
Total sieving time: 0.63 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 0.67 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10121+7)/3 = 2(6)1209<122> = 1201 · 130987 · 356098343 · C105

C105 = P34 · P72

P34 = 2613842632420286549810407132723579<34>

P72 = 182116015280402325835265886158642537928794970041065896876634298939239171<72>

Number: 26669_121
N=476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009
  ( 105 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=2613842632420286549810407132723579 (pp34)
 r2=182116015280402325835265886158642537928794970041065896876634298939239171 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.03 hours.
Scaled time: 2.21 units (timescale=2.145).
Factorization parameters were as follows:
n: 476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009
m: 2000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 600000/600000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [300000, 480001)
Primes: RFBsize:49098, AFBsize:49101, largePrimes:1853503 encountered
Relations: rels:1867932, finalFF:158603
Max relations in full relation-set: 28
Initial matrix: 98264 x 158603 with sparse part having weight 13988463.
Pruned matrix : 85087 x 85642 with weight 5253077.
Total sieving time: 0.97 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000
total time: 1.03 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10122+7)/3 = 2(6)1219<123> = 71 · C121

C121 = P32 · P89

P32 = 41145387625225226433684691675373<32>

P89 = 91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343<89>

Number: 26669_122
N=3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
  ( 121 digits)
SNFS difficulty: 122 digits.
Divisors found:
 r1=41145387625225226433684691675373 (pp32)
 r2=91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343 (pp89)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.01 hours.
Scaled time: 2.16 units (timescale=2.140).
Factorization parameters were as follows:
n: 3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
m: 2000000000000000000000000
c5: 25
c0: 7
skew: 0.78
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:63951, AFBsize:63568, largePrimes:1347942 encountered
Relations: rels:1344158, finalFF:170026
Max relations in full relation-set: 28
Initial matrix: 127582 x 170026 with sparse part having weight 7333871.
Pruned matrix : 103697 x 104398 with weight 3449577.
Total sieving time: 0.96 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,122,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.01 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

(8·10136+7)/3 = 2(6)1359<137> = C137

C137 = P58 · P79

P58 = 5964796989232317289442216128587619639536748687234582636411<58>

P79 = 4470674645726497105263584854203238916337233478995531171674915681021609495628279<79>

Number: 26669_136
N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 137 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=5964796989232317289442216128587619639536748687234582636411 (pp58)
 r2=4470674645726497105263584854203238916337233478995531171674915681021609495628279 (pp79)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.34 hours.
Scaled time: 7.05 units (timescale=2.115).
Factorization parameters were as follows:
n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
m: 2000000000000000000000000000
c5: 5
c0: 14
skew: 1.23
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1300001)
Primes: RFBsize:107126, AFBsize:107483, largePrimes:2282771 encountered
Relations: rels:2388130, finalFF:269548
Max relations in full relation-set: 28
Initial matrix: 214674 x 269548 with sparse part having weight 20402502.
Pruned matrix : 193656 x 194793 with weight 11687881.
Total sieving time: 3.16 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.34 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 20, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(19·102450-1)/9 is prime.

Oct 20, 2007

The factor table of 266...669 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Oct 19, 2007 (4th)

By anonymous / GMP-ECM

(5·10197+7)/3 = 1(6)1969<198> = 83 · C196

C196 = P32 · P165

P32 = 15064399083367851403807447165139<32>

P165 = 133296530276542123994572514856391958946944378887295148756651456417065116602615650106241786028692598529148978098311741021285646641176103363192439421156437978817430437<165>

Oct 19, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(7·10165-61)/9 = (7)1641<165> = 3 · 24320321 · C158

C158 = P43 · P56 · P60

P43 = 2761925283898534955675154755036172189749839<43>

P56 = 31324884696363766525451707222706492435165921240617655521<56>

P60 = 123214995686345230412614529840111656059539641564894743216343<60>

Number: n
N=10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817
  ( 158 digits)
SNFS difficulty: 165 digits.
Divisors found:

Fri Oct 19 11:07:36 2007  prp43 factor: 2761925283898534955675154755036172189749839
Fri Oct 19 11:07:36 2007  prp56 factor: 31324884696363766525451707222706492435165921240617655521
Fri Oct 19 11:07:36 2007  prp60 factor: 123214995686345230412614529840111656059539641564894743216343
Fri Oct 19 11:07:36 2007  elapsed time 01:47:49 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 68.73 hours.
Scaled time: 89.90 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_7_164_1
n: 10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817
skew: 1.54
deg: 5
c5: 7
c0: -61
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700000)
Primes: RFBsize:216816, AFBsize:217077, largePrimes:7393191 encountered
Relations: rels:6842637, finalFF:458263
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 68.48 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 68.73 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 19, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10157-7 = 7(9)1563<158> = 857 · 3270705001345087307<19> · C137

C137 = P45 · P92

P45 = 578713235026034382304696193140789480917763057<45>

P92 = 49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451<92>

Number: 79993_157
N=28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707
  ( 137 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=578713235026034382304696193140789480917763057 (pp45)
 r2=49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451 (pp92)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.59 hours.
Scaled time: 64.80 units (timescale=1.988).
Factorization parameters were as follows:
name: 79993_157
n: 28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707
m: 20000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5533011 encountered
Relations: rels:5442369, finalFF:511459
Max relations in full relation-set: 28
Initial matrix: 433786 x 511459 with sparse part having weight 38990519.
Pruned matrix : 385864 x 388096 with weight 26569740.
Total sieving time: 30.52 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 1.78 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.59 hours.
 --------- CPU info (if available) ----------

Oct 19, 2007

By Yousuke Koide

101240+1 is divisible by 15595203791066837732161767737921<32>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 17, 2007 (5th)

By suberi / PRIMO

(49·102340+23)/9 is prime.

(49·102454+23)/9 is prime.

Oct 17, 2007 (4th)

By Jo Yeong Uk / GGNFS

6·10147+7 = 6(0)1467<148> = 31 · 74460874157397706814885857<26> · C121

C121 = P34 · P87

P34 = 3757810852757300286714196049398151<34>

P87 = 691713910870677076891814665811219671401933953308716939722566516154829814248796350852671<87>

Number: 60007_147
N=2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321
  ( 121 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=3757810852757300286714196049398151 (pp34)
 r2=691713910870677076891814665811219671401933953308716939722566516154829814248796350852671 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 13.31 hours.
Scaled time: 28.42 units (timescale=2.135).
Factorization parameters were as follows:
n: 2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321
m: 200000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1800001)
Primes: RFBsize:135072, AFBsize:134748, largePrimes:3940451 encountered
Relations: rels:4092560, finalFF:408421
Max relations in full relation-set: 28
Initial matrix: 269886 x 408421 with sparse part having weight 41102101.
Pruned matrix : 230332 x 231745 with weight 21474737.
Total sieving time: 12.95 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 13.31 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

6·10149+7 = 6(0)1487<150> = 25747 · 436150417 · 2488433141<10> · 314768938357<12> · C116

C116 = P45 · P72

P45 = 288204824127944521231161772400113432086544229<45>

P72 = 236684181525452140035337569045008331845614114346156387833169766487401841<72>

Number: 60007_149
N=68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589
  ( 116 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=288204824127944521231161772400113432086544229 (pp45)
 r2=236684181525452140035337569045008331845614114346156387833169766487401841 (pp72)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 11.33 hours.
Scaled time: 24.17 units (timescale=2.133).
Factorization parameters were as follows:
n: 68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589
m: 1000000000000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1650001)
Primes: RFBsize:135072, AFBsize:135283, largePrimes:3745970 encountered
Relations: rels:3742941, finalFF:304925
Max relations in full relation-set: 28
Initial matrix: 270420 x 304925 with sparse part having weight 27971216.
Pruned matrix : 258210 x 259626 with weight 21031729.
Total sieving time: 10.95 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000
total time: 11.33 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 17, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

8·10160-7 = 7(9)1593<161> = 179 · 2341 · C156

C156 = P74 · P83

P74 = 16454596943744503209146711864636020997566170732129357607128813577870908913<74>

P83 = 11602412280012005744956049762841701654854199246869403531853864740606458920710587799<83>

Number: n
N=190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487
  ( 156 digits)
SNFS difficulty: 160 digits.
Divisors found:

Thu Oct 18 14:19:06 2007  prp74 factor: 16454596943744503209146711864636020997566170732129357607128813577870908913
Thu Oct 18 14:19:06 2007  prp83 factor: 11602412280012005744956049762841701654854199246869403531853864740606458920710587799
Thu Oct 18 14:19:06 2007  elapsed time 01:30:26 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.43 hours.
Scaled time: 53.27 units (timescale=1.199).
Factorization parameters were as follows:
name: KA_7_9_159_3
n: 190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487
type: snfs
skew: 0.97
deg: 5
c5: 8
c0: -7
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:230209, AFBsize:229842, largePrimes:6910058 encountered
Relations: rels:6394628, finalFF:542880
Max relations in full relation-set: 28
Initial matrix: 460116 x 542880 with sparse part having weight 33147572.
Pruned matrix : 389747 x 392111 with weight 20148312.
Total sieving time: 44.19 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 44.43 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 17, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10156-7 = 7(9)1553<157> = 181 · 909281 · C149

C149 = P41 · P49 · P61

P41 = 10904285406759073728471842840772332558593<41>

P49 = 1088070887339914750056094304772577853777226365141<49>

P61 = 4096933317053668078876000501612735226248308616390449901334401<61>

Number: 79993_156
N=48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813
  ( 149 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=10904285406759073728471842840772332558593 (pp41)
 r2=1088070887339914750056094304772577853777226365141 (pp49)
 r3=4096933317053668078876000501612735226248308616390449901334401 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.39 hours.
Scaled time: 80.67 units (timescale=1.997).
Factorization parameters were as follows:
name: 79993_156
n: 48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813
m: 20000000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2800001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:5747043 encountered
Relations: rels:5780210, finalFF:606107
Max relations in full relation-set: 28
Initial matrix: 434262 x 606107 with sparse part having weight 50764657.
Pruned matrix : 345539 x 347774 with weight 31579083.
Total sieving time: 38.37 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.68 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 40.39 hours.
 --------- CPU info (if available) ----------

Oct 18, 2007

By Sinkiti Sibata / PRIMO

(8·102308+7)/3 is prime.

Oct 17, 2007 (3rd)

By Jo Yeong Uk / GGNFS

(4·10188-31)/9 = (4)1871<188> = C188

C188 = P89 · P100

P89 = 13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861<89>

P100 = 3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781<100>

Number: 44441_188
N=44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
  ( 188 digits)
SNFS difficulty: 190 digits.
Divisors found:
 r1=13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861 (pp89)
 r2=3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781 (pp100)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 506.97 hours.
Scaled time: 1079.34 units (timescale=2.129).
Factorization parameters were as follows:
n: 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441
m: 100000000000000000000000000000000000000
c5: 1
c0: -775
skew: 3.78
type: snfs
Factor base limits: 13000000/13000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 51/51
Sieved algebraic special-q in [6500000, 14600001)
Primes: RFBsize:849252, AFBsize:849399, largePrimes:12866508 encountered
Relations: rels:13641443, finalFF:1950967
Max relations in full relation-set: 28
Initial matrix: 1698715 x 1950967 with sparse part having weight 145829012.
Pruned matrix : 1480381 x 1488938 with weight 111459556.
Total sieving time: 484.73 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 21.67 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000
total time: 506.97 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

P89 is the largest factor found by GGNFS in our tables so far. Congratulations!

Oct 17, 2007 (2nd)

By Robert Backstrom / GGNFS

8·10158-7 = 7(9)1573<159> = 13 · 67 · C156

C156 = P75 · P82

P75 = 346176468096559273822741304052813207109273708583996031665987163333529663757<75>

P82 = 2653226273941471985206044635089360508906271929143252016829426314360757542050928219<82>

Number: n
N=918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=346176468096559273822741304052813207109273708583996031665987163333529663757 (pp75)
 r2=2653226273941471985206044635089360508906271929143252016829426314360757542050928219 (pp82)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 41.09 hours.
Scaled time: 53.30 units (timescale=1.297).
Factorization parameters were as follows:
name: KA_7_9_157_3
n: 918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783
skew: 0.49
deg: 5
c5: 250
c0: -7
m: 20000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:216816, AFBsize:217701, largePrimes:7120715 encountered
Relations: rels:6580353, finalFF:493138
Max relations in full relation-set: 48
Initial matrix: 434583 x 493138 with sparse part having weight 42370582.
Pruned matrix : 389862 x 392098 with weight 27989624.
Total sieving time: 36.05 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 4.66 hours.
Total square root time: 0.16 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 41.09 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 17, 2007

By Sinkiti Sibata / GGNFS

8·10155-7 = 7(9)1543<156> = 17 · 29 · 43 · 671189 · 25898947 · C139

C139 = P33 · P107

P33 = 152487428057225842444645257923753<33>

P107 = 14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193<107>

Number: 79993_155
N=2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329
  ( 139 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=152487428057225842444645257923753 (pp33)
 r2=14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193 (pp107)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.46 hours.
Scaled time: 64.57 units (timescale=1.989).
Factorization parameters were as follows:
name: 79993_155
n: 2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329
m: 10000000000000000000000000000000
c5: 8
c0: -7
skew: 0.97
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:5864311 encountered
Relations: rels:6046107, finalFF:741412
Max relations in full relation-set: 28
Initial matrix: 433412 x 741412 with sparse part having weight 59974965.
Pruned matrix : 286069 x 288300 with weight 35055031.
Total sieving time: 30.74 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.41 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.46 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007 (5th)

By Sinkiti Sibata / PRIMO

(13·102215+23)/9 is prime.

Oct 16, 2007 (4th)

By suberi / PRIMO

(32·102488-41)/9 is prime.

6·102749+7 is prime.

(55·102684+17)/9 is prime.

Oct 16, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

8·10154-7 = 7(9)1533<155> = 2356867 · 603555989507<12> · C137

C137 = P33 · P105

P33 = 113351694760778508277044308809837<33>

P105 = 496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581<105>

Number: 79993_154
N=56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297
  ( 137 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=113351694760778508277044308809837 (pp33)
 r2=496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581 (pp105)
Version: GGNFS-0.77.1-20060513-k8
Total time: 32.35 hours.
Scaled time: 64.79 units (timescale=2.003).
Factorization parameters were as follows:
name: 79993_154
n: 56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297
m: 10000000000000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216906, largePrimes:5878753 encountered
Relations: rels:6079432, finalFF:757874
Max relations in full relation-set: 28
Initial matrix: 433786 x 757874 with sparse part having weight 61304584.
Pruned matrix : 284596 x 286828 with weight 35456047.
Total sieving time: 30.84 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 32.35 hours.
 --------- CPU info (if available) ----------

8·10151-7 = 7(9)1503<152> = 23 · 107 · 5569 · 6029 · 5676941659286357<16> · 21788576409750498214905595223<29> · C97

C97 = P31 · P67

P31 = 5423671886025109442120246388749<31>

P67 = 1443175595670302296287530288340641513337370692964945259930652789367<67>

Sun Oct 14 13:22:15 2007  Msieve v. 1.28
Sun Oct 14 13:22:15 2007  random seeds: bb320d00 c465a215
Sun Oct 14 13:22:15 2007  factoring 7827310904834559223584755757587750335344461821449169367211160089090463613553875031305565495631883 (97 digits)
Sun Oct 14 13:22:16 2007  commencing quadratic sieve (97-digit input)
Sun Oct 14 13:22:17 2007  using multiplier of 2
Sun Oct 14 13:22:17 2007  using 64kb Pentium 2 sieve core
Sun Oct 14 13:22:17 2007  sieve interval: 18 blocks of size 65536
Sun Oct 14 13:22:17 2007  processing polynomials in batches of 6
Sun Oct 14 13:22:17 2007  using a sieve bound of 2395621 (88235 primes)
Sun Oct 14 13:22:17 2007  using large prime bound of 359343150 (28 bits)
Sun Oct 14 13:22:17 2007  using double large prime bound of 2511405435485700 (43-52 bits)
Sun Oct 14 13:22:17 2007  using trial factoring cutoff of 52 bits
Sun Oct 14 13:22:17 2007  polynomial 'A' values have 13 factors
Tue Oct 16 05:45:50 2007  88486 relations (21837 full + 66649 combined from 1318373 partial), need 88331
Tue Oct 16 05:46:24 2007  begin with 1340210 relations
Tue Oct 16 05:49:03 2007  reduce to 229420 relations in 11 passes
Tue Oct 16 05:49:04 2007  attempting to read 229420 relations
Tue Oct 16 05:49:50 2007  recovered 229420 relations
Tue Oct 16 05:49:51 2007  recovered 215053 polynomials
Tue Oct 16 05:51:40 2007  attempting to build 88486 cycles
Tue Oct 16 05:51:49 2007  found 88486 cycles in 6 passes
Tue Oct 16 05:51:55 2007  distribution of cycle lengths:
Tue Oct 16 05:51:55 2007     length 1 : 21837
Tue Oct 16 05:51:55 2007     length 2 : 15474
Tue Oct 16 05:51:55 2007     length 3 : 15081
Tue Oct 16 05:51:55 2007     length 4 : 12029
Tue Oct 16 05:51:55 2007     length 5 : 8894
Tue Oct 16 05:51:55 2007     length 6 : 6072
Tue Oct 16 05:51:55 2007     length 7 : 3868
Tue Oct 16 05:51:55 2007     length 9+: 5231
Tue Oct 16 05:51:55 2007  largest cycle: 19 relations
Tue Oct 16 05:52:26 2007  matrix is 88235 x 88486 with weight 5849695 (avg 66.11/col)
Tue Oct 16 05:53:30 2007  filtering completed in 3 passes
Tue Oct 16 05:53:30 2007  matrix is 83979 x 84043 with weight 5585692 (avg 66.46/col)
Tue Oct 16 05:53:34 2007  saving the first 48 matrix rows for later
Tue Oct 16 05:53:35 2007  matrix is 83931 x 84043 with weight 4343397 (avg 51.68/col)
Tue Oct 16 05:53:35 2007  matrix includes 64 packed rows
Tue Oct 16 05:53:35 2007  using block size 10922 for processor cache size 256 kB
Tue Oct 16 05:53:38 2007  commencing Lanczos iteration
Tue Oct 16 05:59:52 2007  lanczos halted after 1329 iterations
Tue Oct 16 05:59:53 2007  recovered 18 nontrivial dependencies
Tue Oct 16 06:24:18 2007  prp31 factor: 5423671886025109442120246388749
Tue Oct 16 06:24:18 2007  prp67 factor: 1443175595670302296287530288340641513337370692964945259930652789367
Tue Oct 16 06:24:18 2007  elapsed time 41:02:03

8·10152-7 = 7(9)1513<153> = 13 · 18307 · 4639298979169<13> · 238372349228810543<18> · C118

C118 = P33 · P86

P33 = 132196018950577432404812799228403<33>

P86 = 22993381145741293920904930229003616713749210764279783545611429634014833752788402278923<86>

Number: 79993_152
N=3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969
  ( 118 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=132196018950577432404812799228403 (pp33)
 r2=22993381145741293920904930229003616713749210764279783545611429634014833752788402278923 (pp86)
Version: GGNFS-0.77.1-20060513-k8
Total time: 21.25 hours.
Scaled time: 42.02 units (timescale=1.978).
Factorization parameters were as follows:
name: 79993_152
n: 3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969
m: 2000000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1900001)
Primes: RFBsize:176302, AFBsize:175903, largePrimes:5420804 encountered
Relations: rels:5333741, finalFF:489141
Max relations in full relation-set: 28
Initial matrix: 352269 x 489141 with sparse part having weight 41279494.
Pruned matrix : 285474 x 287299 with weight 22202017.
Total sieving time: 20.13 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.86 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 21.25 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007 (2nd)

By Bryan Koen / GGNFS

(23·10170+1)/3 = 7(6)1697<171> = 13 · 461 · 1289 · 10909069 · 3428780111<10> · 5783988689<10> · 1475103520971674381<19> · C120

C120 = P50 · P71

P50 = 28622256358095202962667644344453285032065134088263<50>

P71 = 10864963237661550249466184242559236733294008124794269198135353057048507<71>

Number: 76667_170
N=310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341
  ( 120 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=28622256358095202962667644344453285032065134088263 (pp50)
 r2=10864963237661550249466184242559236733294008124794269198135353057048507 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 96.07 hours.
Scaled time: 214.23 units (timescale=2.230).
Factorization parameters were as follows:
n: 310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341
m: 10000000000000000000000000000000000
c5: 23
c0: 1
skew: 0.53
type: snfs

Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6700001)
Primes: RFBsize:412849, AFBsize:412891, largePrimes:5994447 encountered
Relations: rels:6291016, finalFF:958381
Max relations in full relation-set: 28
Initial matrix: 825805 x 958381 with sparse part having weight 51452736.
Pruned matrix : 711926 x 716119 with weight 36381718.
Total sieving time: 83.92 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 11.78 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 96.07 hours.
 --------- CPU info (if available) ----------

Oct 16, 2007

By Robert Backstrom / GGNFS, Msieve

6·10164+7 = 6(0)1637<165> = 29 · 127031 · C159

C159 = P61 · P98

P61 = 1770843922137685855971883220866292296403759900031873711559753<61>

P98 = 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981<98>

Number: n
N=162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693
  ( 159 digits)
SNFS difficulty: 165 digits.
Divisors found:

Tue Oct 16 01:56:00 2007  prp61 factor: 1770843922137685855971883220866292296403759900031873711559753
Tue Oct 16 01:56:00 2007  prp98 factor: 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981
Tue Oct 16 01:56:00 2007  elapsed time 01:28:26 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.90 hours.
Scaled time: 70.50 units (timescale=1.308).
Factorization parameters were as follows:
name: KA_6_0_163_7
n: 162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693
skew: 1.63
deg: 5
c5: 3
c0: 35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2700001)
Primes: RFBsize:216816, AFBsize:216606, largePrimes:7411428 encountered
Relations: rels:6890615, finalFF:484135
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 53.63 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 53.90 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10185+7 = 6(0)1847<186> = 9109 · 486119 · 10533650783<11> · 7198232528923<13> · 6020878659975871147<19> · 57715737637649789572192595701<29> · C106

C106 = P44 · P63

P44 = 15856940822896359383771402356889784989979289<44>

P63 = 324309472250677628769264887001027044666888119049640084725461111<63>

Number: n
N=5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079
  ( 106 digits)
Divisors found:

Wed Oct 17 00:32:49 2007  prp44 factor: 15856940822896359383771402356889784989979289
Wed Oct 17 00:32:49 2007  prp63 factor: 324309472250677628769264887001027044666888119049640084725461111
Wed Oct 17 00:32:49 2007  elapsed time 00:52:18 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 8.70 hours.
Scaled time: 12.65 units (timescale=1.454).
Factorization parameters were as follows:
name: n
n: 5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079
skew: 21313.42
# norm 5.43e+14
c5: 9000
c4: -76048988
c3: 12119061025586
c2: -340898511045832731
c1: -5046737451005388060230
c0: -9154601256957836199856000
# alpha -6.42
Y1: 5525266307
Y0: -224588401435796917287
# Murphy_E 1.76e-09
# M 241119437529606858479298978826451053129591147004948447723988093141534466268833497155997142159084665980338
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved  special-q in [100000, 1300000)
Primes: RFBsize:183072, AFBsize:182920, largePrimes:4087871 encountered
Relations: rels:4028528, finalFF:410738
Max relations in full relation-set: 28
Initial matrix: 366075 x 410738 with sparse part having weight 23343007.
Pruned matrix : 317878 x 319772 with weight 13914370.
Total sieving time: 8.54 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 8.70 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 15, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(86·102107+13)/9 is prime.

Oct 15, 2007 (2nd)

By Sinkiti Sibata / GGNFS

8·10146-7 = 7(9)1453<147> = 13 · 1046365087<10> · 19154907071<11> · C127

C127 = P52 · P76

P52 = 1580183000642280038370796123881094831961607470495009<52>

P76 = 1943014132025684712297993803987711508705879519397502794606730636362479155677<76>

Number: 79993_146
N=3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093
  ( 127 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=1580183000642280038370796123881094831961607470495009 (pp52)
 r2=1943014132025684712297993803987711508705879519397502794606730636362479155677 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 19.55 hours.
Scaled time: 39.02 units (timescale=1.996).
Factorization parameters were as follows:
name: 79993_146
n: 3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093
m: 200000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 2850001)
Primes: RFBsize:114155, AFBsize:114392, largePrimes:2881812 encountered
Relations: rels:2895290, finalFF:293370
Max relations in full relation-set: 28
Initial matrix: 228612 x 293370 with sparse part having weight 30568649.
Pruned matrix : 209081 x 210288 with weight 20114196.
Total sieving time: 18.83 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.52 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 19.55 hours.
 --------- CPU info (if available) ----------

Oct 15, 2007

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

6·10188+7 = 6(0)1877<189> = 17 · 199 · 257 · 3463 · 16649 · 96059 · 61883693 · 90624285000529213<17> · 454041790607190733<18> · 517371257791985827755390629<27> · C101

C101 = P49 · P53

P49 = 3525119596170058088736272803183372325772469391249<49>

P53 = 26831479803562967544394299568098567920660248574603957<53>

Number: n
N=94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293
  ( 101 digits)
Divisors found:
 r1=3525119596170058088736272803183372325772469391249 (pp49)
 r2=26831479803562967544394299568098567920660248574603957 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.98 hours.
Scaled time: 9.14 units (timescale=1.309).
Factorization parameters were as follows:
name: n
n: 94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293
skew: 7737.01
# norm 9.79e+13
c5: 78000
c4: -297470066
c3: -15863340244548
c2: 7080761517578508
c1: 414301049080350364575
c0: -367453236957540790697550
# alpha -5.80
Y1: 14831016739
Y0: -16471952224750940243
# Murphy_E 2.86e-09
# M 1155531281704554954285740779202815785221773336456573589977276941683087980735395064780088119878136440
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:135072, AFBsize:135064, largePrimes:3586849 encountered
Relations: rels:3583146, finalFF:407778
Max relations in full relation-set: 48
Initial matrix: 270216 x 407778 with sparse part having weight 25913894.
Pruned matrix : 153604 x 155019 with weight 8586650.
Total sieving time: 6.41 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.35 hours.
Total square root time: 0.06 hours, sqrts: 1.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 6.98 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10142-7 = 7(9)1413<143> = 2857 · C140

C140 = P66 · P75

P66 = 170295424162300840230361627660073534692518109605861209895558110069<66>

P75 = 164428376204146486985826323441216525770957734599964780155385367813374589421<75>

Number: n
N=28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049
  ( 140 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=170295424162300840230361627660073534692518109605861209895558110069 (pp66)
 r2=164428376204146486985826323441216525770957734599964780155385367813374589421 (pp75)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.72 hours.
Scaled time: 9.22 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_7_9_141_3
n: 28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049
type: snfs
skew: 0.65
deg: 5
c5: 25
c0: -7
m: 20000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:148933, AFBsize:148500, largePrimes:5611558 encountered
Relations: rels:4989427, finalFF:361392
Max relations in full relation-set: 28
Initial matrix: 297497 x 361392 with sparse part having weight 17904087.
Pruned matrix : 240103 x 241654 with weight 9277622.
Total sieving time: 6.20 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.13 hours.
Total square root time: 0.19 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 7.72 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10165-1 = 4(9)165<166> = 428440364567<12> · C155

C155 = P67 · P88

P67 = 4418255297469253568147847349351285035723609901981851222353873612047<67>

P88 = 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151<88>

Number: n
N=11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Oct 15 22:21:57 2007  prp67 factor: 4418255297469253568147847349351285035723609901981851222353873612047
Mon Oct 15 22:21:57 2007  prp88 factor: 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151
Mon Oct 15 22:21:57 2007  elapsed time 01:18:34 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 44.16 hours.
Scaled time: 64.21 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_4_9_165
n: 11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097
skew: 0.72
deg: 5
c5: 5
c0: -1
m: 1000000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2400000)
Primes: RFBsize:203362, AFBsize:203387, largePrimes:7325021 encountered
Relations: rels:6796373, finalFF:457305
Max relations in full relation-set: 28
Initial matrix: 406814 x 457305 with sparse part having weight 40727776.
Pruned matrix : 379736 x 381834 with weight 30695175.
Total sieving time: 43.93 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 44.16 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

8·10168-7 = 7(9)1673<169> = 889051 · 3504811485997<13> · 212811322817407<15> · 15345355832599422733596083704019<32> · C105

C105 = P33 · P73

P33 = 350969010395558715534644431751677<33>

P73 = 2240052427411472440287076912394101922396296096003376631991190413937458559<73>

Oct 14, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

6·10146+7 = 6(0)1457<147> = 4357 · C144

C144 = P62 · P83

P62 = 11418173072097254220419104341228272288444055633023768296587371<62>

P83 = 12060548760877474653322042621937488929340653264886088872424357570501388208759630481<83>

Number: n
N=137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451
  ( 144 digits)
SNFS difficulty: 146 digits.
Divisors found:
 r1=11418173072097254220419104341228272288444055633023768296587371 (pp62)
 r2=12060548760877474653322042621937488929340653264886088872424357570501388208759630481 (pp83)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 14.29 hours.
Scaled time: 17.06 units (timescale=1.194).
Factorization parameters were as follows:
name: KA_6_0_145_7
n: 137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: 7
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1500001)
Primes: RFBsize:148933, AFBsize:148615, largePrimes:6235655 encountered
Relations: rels:5562121, finalFF:337505
Max relations in full relation-set: 28
Initial matrix: 297615 x 337505 with sparse part having weight 22977078.
Pruned matrix : 271076 x 272628 with weight 15819578.
Total sieving time: 11.99 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.85 hours.
Total square root time: 0.22 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 14.29 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

6·10148+7 = 6(0)1477<149> = 4549 · 787609 · 12956873023<11> · C130

C130 = P40 · P90

P40 = 9540749344069170990484839035782631826167<40>

P90 = 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347<90>

Number: n
N=1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949
  ( 130 digits)
SNFS difficulty: 149 digits.
Divisors found:

Sun Oct 14 07:28:32 2007  prp40 factor: 9540749344069170990484839035782631826167
Sun Oct 14 07:28:32 2007  prp90 factor: 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347
Sun Oct 14 07:28:32 2007  elapsed time 00:56:42 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 15.17 hours.
Scaled time: 17.95 units (timescale=1.183).
Factorization parameters were as follows:
name: KA_6_0_147_7
n: 1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949
skew: 0.52
deg: 5
c5: 375
c0: 14
m: 200000000000000000000000000000
type: snfs
rlim: 1800000
alim: 1800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1850000)
Primes: RFBsize:135072, AFBsize:135288, largePrimes:6951878 encountered
Relations: rels:6272499, finalFF:315014
Max relations in full relation-set: 28
Initial matrix: 270426 x 315014 with sparse part having weight 39437700.
Pruned matrix : 259998 x 261414 with weight 27086460.
Total sieving time: 14.94 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000
total time: 15.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

8·10153-7 = 7(9)1523<154> = 73 · 246833 · 540901 · C141

C141 = P38 · P104

P38 = 45503821118476645834178831665898714663<38>

P104 = 18038409980107755666629933064361219737535695629711907649346771548449394176944215804284623352754129419979<104>

Oct 14, 2007

By Sinkiti Sibata / GGNFS, Msieve

8·10137-7 = 7(9)1363<138> = 73 · 9964781 · C130

C130 = P48 · P82

P48 = 141316153943199860951746141560760739245162925887<48>

P82 = 7782292667443130880016248231198064453618474981570509859512503079754219269452839403<82>

Number: 79993_137
N=1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461
  ( 130 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=141316153943199860951746141560760739245162925887 (pp48)
 r2=7782292667443130880016248231198064453618474981570509859512503079754219269452839403 (pp82)
Version: GGNFS-0.77.1-20060513-k8
Total time: 6.78 hours.
Scaled time: 13.49 units (timescale=1.990).
Factorization parameters were as follows:
name: 79993_137
n: 1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461
m: 2000000000000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1225001)
Primes: RFBsize:78498, AFBsize:63568, largePrimes:1548308 encountered
Relations: rels:1559004, finalFF:182026
Max relations in full relation-set: 28
Initial matrix: 142130 x 182026 with sparse part having weight 14809823.
Pruned matrix : 129678 x 130452 with weight 8882231.
Total sieving time: 6.56 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 6.78 hours.
 --------- CPU info (if available) ----------

8·10165-7 = 7(9)1643<166> = 2381 · 5443 · 9170957 · 1193913161057723<16> · 18720100338778545677<20> · 221092714624829016465471979<27> · C92

C92 = P38 · P54

P38 = 14107017695779960660551276385083916411<38>

P54 = 965577295039246891714130651139286441420217189730013597<54>

Sat Oct 13 14:10:21 2007  Msieve v. 1.28
Sat Oct 13 14:10:21 2007  random seeds: d891a068 1d65775f
Sat Oct 13 14:10:21 2007  factoring 13621415987762003925737115669456429853506846533116955465249119119459261411157655645041440367 (92 digits)
Sat Oct 13 14:10:22 2007  commencing quadratic sieve (91-digit input)
Sat Oct 13 14:10:22 2007  using multiplier of 7
Sat Oct 13 14:10:22 2007  using 64kb Pentium 2 sieve core
Sat Oct 13 14:10:22 2007  sieve interval: 18 blocks of size 65536
Sat Oct 13 14:10:22 2007  processing polynomials in batches of 6
Sat Oct 13 14:10:22 2007  using a sieve bound of 1753547 (65651 primes)
Sat Oct 13 14:10:22 2007  using large prime bound of 177108247 (27 bits)
Sat Oct 13 14:10:22 2007  using double large prime bound of 702796695147472 (42-50 bits)
Sat Oct 13 14:10:22 2007  using trial factoring cutoff of 50 bits
Sat Oct 13 14:10:22 2007  polynomial 'A' values have 12 factors
Sun Oct 14 04:42:53 2007  66323 relations (17390 full + 48933 combined from 797713 partial), need 65747
Sun Oct 14 04:43:12 2007  begin with 815103 relations
Sun Oct 14 04:43:18 2007  reduce to 165651 relations in 10 passes
Sun Oct 14 04:43:18 2007  attempting to read 165651 relations
Sun Oct 14 04:43:40 2007  recovered 165651 relations
Sun Oct 14 04:43:40 2007  recovered 143802 polynomials
Sun Oct 14 04:44:26 2007  attempting to build 66323 cycles
Sun Oct 14 04:44:27 2007  found 66323 cycles in 5 passes
Sun Oct 14 04:44:31 2007  distribution of cycle lengths:
Sun Oct 14 04:44:31 2007     length 1 : 17390
Sun Oct 14 04:44:31 2007     length 2 : 12238
Sun Oct 14 04:44:31 2007     length 3 : 11622
Sun Oct 14 04:44:31 2007     length 4 : 8894
Sun Oct 14 04:44:31 2007     length 5 : 6300
Sun Oct 14 04:44:31 2007     length 6 : 4157
Sun Oct 14 04:44:31 2007     length 7 : 2532
Sun Oct 14 04:44:31 2007     length 9+: 3190
Sun Oct 14 04:44:32 2007  largest cycle: 19 relations
Sun Oct 14 04:44:33 2007  matrix is 65651 x 66323 with weight 3988888 (avg 60.14/col)
Sun Oct 14 04:44:40 2007  filtering completed in 4 passes
Sun Oct 14 04:44:40 2007  matrix is 61409 x 61473 with weight 3690038 (avg 60.03/col)
Sun Oct 14 04:44:44 2007  saving the first 48 matrix rows for later
Sun Oct 14 04:44:44 2007  matrix is 61361 x 61473 with weight 2824181 (avg 45.94/col)
Sun Oct 14 04:44:44 2007  matrix includes 64 packed rows
Sun Oct 14 04:44:44 2007  using block size 10922 for processor cache size 256 kB
Sun Oct 14 04:44:47 2007  commencing Lanczos iteration
Sun Oct 14 04:49:15 2007  lanczos halted after 972 iterations
Sun Oct 14 04:49:16 2007  recovered 17 nontrivial dependencies
Sun Oct 14 04:50:10 2007  prp38 factor: 14107017695779960660551276385083916411
Sun Oct 14 04:50:10 2007  prp54 factor: 965577295039246891714130651139286441420217189730013597
Sun Oct 14 04:50:10 2007  elapsed time 14:39:49

8·10131-7 = 7(9)1303<132> = 149 · 281 · 376313501619021334931<21> · C107

C107 = P44 · P64

P44 = 37274544353516647698335148848851846484864657<44>

P64 = 1362182369130717145175925548652388406862572932354777517395196191<64>

Number: 79993_131
N=50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487
  ( 107 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=37274544353516647698335148848851846484864657 (pp44)
 r2=1362182369130717145175925548652388406862572932354777517395196191 (pp64)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.40 hours.
Scaled time: 8.79 units (timescale=1.999).
Factorization parameters were as follows:
name: 79993_131
n: 50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487
m: 200000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63943, largePrimes:1469981 encountered
Relations: rels:1455868, finalFF:158326
Max relations in full relation-set: 28
Initial matrix: 127959 x 158326 with sparse part having weight 11756685.
Pruned matrix : 119410 x 120113 with weight 7188237.
Total sieving time: 4.24 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.07 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 4.40 hours.
 --------- CPU info (if available) ----------

6·10150+7 = 6(0)1497<151> = 13 · 1021 · 51377866217<11> · 38690659722181<14> · 13553397374370467<17> · C107

C107 = P44 · P63

P44 = 75896163172818350563639937211446513525782697<44>

P63 = 221071096062905112755419151133504653865878416206951105384644033<63>

Number: 60007_150
N=16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001
  ( 107 digits)
Divisors found:
 r1=75896163172818350563639937211446513525782697 (pp44)
 r2=221071096062905112755419151133504653865878416206951105384644033 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 19.13 hours.
Scaled time: 12.93 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_150
n: 16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001
skew: 36403.92
# norm 2.09e+14
c5: 2100
c4: -112214840
c3: -13116197646990
c2: 123037965666033289
c1: 5760329507112287712094
c0: 1238462310613528311780792
# alpha -5.17
Y1: 120696764773
Y0: -380634342801918434537
# Murphy_E 1.56e-09
# M 13741135059811030920870521422422840200370178162132655706061264578222105542413703524686047496399343377873432
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:183420, largePrimes:4395571 encountered
Relations: rels:4422833, finalFF:421465
Max relations in full relation-set: 28
Initial matrix: 366571 x 421465 with sparse part having weight 30675596.
Pruned matrix : 323362 x 325258 with weight 19810409.
Total sieving time: 15.47 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.20 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 19.13 hours.
 --------- CPU info (if available) ----------

8·10134-7 = 7(9)1333<135> = 13 · 31 · 43 · 379 · 398471 · 16515812627621261<17> · C107

C107 = P41 · P66

P41 = 48003731369287073342189922196135629754309<41>

P66 = 385572109653783210030204978859579938448033879962204411809558451037<66>

Number: 79993_134
N=18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=48003731369287073342189922196135629754309 (pp41)
 r2=385572109653783210030204978859579938448033879962204411809558451037 (pp66)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.87 hours.
Scaled time: 11.71 units (timescale=1.996).
Factorization parameters were as follows:
name: 79993_134
n: 18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433
m: 1000000000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:64193, largePrimes:1523402 encountered
Relations: rels:1537466, finalFF:188576
Max relations in full relation-set: 28
Initial matrix: 142755 x 188576 with sparse part having weight 13498820.
Pruned matrix : 126954 x 127731 with weight 7386006.
Total sieving time: 5.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.87 hours.
 --------- CPU info (if available) ----------

8·10136-7 = 7(9)1353<137> = 163 · 269 · 22407799279<11> · 81876428270723<14> · C108

C108 = P42 · P67

P42 = 110918576820312746668279691257635716599183<42>

P67 = 8965772596523034939022478706473281787255547555025279231551238868629<67>

Number: 79993_136
N=994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107
  ( 108 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=110918576820312746668279691257635716599183 (pp42)
 r2=8965772596523034939022478706473281787255547555025279231551238868629 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.91 hours.
Scaled time: 15.72 units (timescale=1.988).
Factorization parameters were as follows:
name: 79993_136
n: 994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107
m: 2000000000000000000000000000
c5: 5
c0: -14
skew: 1.23
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63943, largePrimes:1589559 encountered
Relations: rels:1610836, finalFF:189841
Max relations in full relation-set: 28
Initial matrix: 142506 x 189841 with sparse part having weight 16890095.
Pruned matrix : 128981 x 129757 with weight 9843551.
Total sieving time: 7.67 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.91 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007 (6th)

By Robert Backstrom / Msieve, GGNFS

8·10110-7 = 7(9)1093<111> = 13 · 30197 · 69511273067394199277<20> · C86

C86 = P43 · P43

P43 = 3412752588243064179197971634430268240789861<43>

P43 = 8590585972779452282610598329176427275489929<43>

Sat Oct 13 14:21:54 2007  Msieve v. 1.28
Sat Oct 13 14:21:54 2007  random seeds: 71c0a470 a1018f8f
Sat Oct 13 14:21:54 2007  factoring 29317544513127637059005073107012633156477405810349541305000972214868654912800710809869 (86 digits)
Sat Oct 13 14:21:54 2007  commencing quadratic sieve (85-digit input)
Sat Oct 13 14:21:54 2007  using multiplier of 1
Sat Oct 13 14:21:54 2007  using 64kb Opteron sieve core
Sat Oct 13 14:21:54 2007  sieve interval: 7 blocks of size 65536
Sat Oct 13 14:21:54 2007  processing polynomials in batches of 15
Sat Oct 13 14:21:54 2007  using a sieve bound of 1442579 (55333 primes)
Sat Oct 13 14:21:54 2007  using large prime bound of 115406320 (26 bits)
Sat Oct 13 14:21:54 2007  using double large prime bound of 325097179907280 (41-49 bits)
Sat Oct 13 14:21:54 2007  using trial factoring cutoff of 49 bits
Sat Oct 13 14:21:54 2007  polynomial 'A' values have 11 factors
Sat Oct 13 14:54:41 2007  55598 relations (16566 full + 39032 combined from 566706 partial), need 55429
Sat Oct 13 14:54:42 2007  begin with 583272 relations
Sat Oct 13 14:54:43 2007  reduce to 129047 relations in 9 passes
Sat Oct 13 14:54:43 2007  attempting to read 129047 relations
Sat Oct 13 14:54:44 2007  recovered 129047 relations
Sat Oct 13 14:54:44 2007  recovered 103401 polynomials
Sat Oct 13 14:54:45 2007  attempting to build 55598 cycles
Sat Oct 13 14:54:45 2007  found 55598 cycles in 5 passes
Sat Oct 13 14:54:45 2007  distribution of cycle lengths:
Sat Oct 13 14:54:45 2007     length 1 : 16566
Sat Oct 13 14:54:46 2007     length 2 : 11426
Sat Oct 13 14:54:46 2007     length 3 : 9845
Sat Oct 13 14:54:46 2007     length 4 : 7055
Sat Oct 13 14:54:46 2007     length 5 : 4727
Sat Oct 13 14:54:46 2007     length 6 : 2766
Sat Oct 13 14:54:46 2007     length 7 : 1568
Sat Oct 13 14:54:46 2007     length 9+: 1645
Sat Oct 13 14:54:46 2007  largest cycle: 19 relations
Sat Oct 13 14:54:46 2007  matrix is 55333 x 55598 with weight 2843187 (avg 51.14/col)
Sat Oct 13 14:54:47 2007  filtering completed in 3 passes
Sat Oct 13 14:54:47 2007  matrix is 49684 x 49748 with weight 2566866 (avg 51.60/col)
Sat Oct 13 14:54:48 2007  saving the first 48 matrix rows for later
Sat Oct 13 14:54:48 2007  matrix is 49636 x 49748 with weight 1895227 (avg 38.10/col)
Sat Oct 13 14:54:48 2007  matrix includes 64 packed rows
Sat Oct 13 14:54:48 2007  commencing Lanczos iteration
Sat Oct 13 14:56:13 2007  lanczos halted after 786 iterations
Sat Oct 13 14:56:13 2007  recovered 16 nontrivial dependencies
Sat Oct 13 14:56:14 2007  prp43 factor: 3412752588243064179197971634430268240789861
Sat Oct 13 14:56:14 2007  prp43 factor: 8590585972779452282610598329176427275489929
Sat Oct 13 14:56:14 2007  elapsed time 00:34:20

8·10103-7 = 7(9)1023<104> = 281 · 9903493 · 76751663 · C87

C87 = P35 · P53

P35 = 11645958539351398837968999925860551<35>

P53 = 32161199219947116795810535309580815458905862060506117<53>

Sat Oct 13 14:18:15 2007  Msieve v. 1.28
Sat Oct 13 14:18:15 2007  random seeds: fd6310c0 0e9f8101
Sat Oct 13 14:18:15 2007  factoring 374547992691324672010178946818039861713393421705423703090741037387853600337071824490467 (87 digits)
Sat Oct 13 14:18:15 2007  commencing quadratic sieve (87-digit input)
Sat Oct 13 14:18:15 2007  using multiplier of 7
Sat Oct 13 14:18:15 2007  using 64kb Athlon XP sieve core
Sat Oct 13 14:18:15 2007  sieve interval: 10 blocks of size 65536
Sat Oct 13 14:18:15 2007  processing polynomials in batches of 11
Sat Oct 13 14:18:15 2007  using a sieve bound of 1483429 (56667 primes)
Sat Oct 13 14:18:15 2007  using large prime bound of 118674320 (26 bits)
Sat Oct 13 14:18:15 2007  using double large prime bound of 341855144981120 (42-49 bits)
Sat Oct 13 14:18:15 2007  using trial factoring cutoff of 49 bits
Sat Oct 13 14:18:15 2007  polynomial 'A' values have 11 factors
Sat Oct 13 15:27:24 2007  56771 relations (15604 full + 41167 combined from 595942 partial), need 56763
Sat Oct 13 15:27:25 2007  begin with 611546 relations
Sat Oct 13 15:27:25 2007  reduce to 136916 relations in 9 passes
Sat Oct 13 15:27:25 2007  attempting to read 136916 relations
Sat Oct 13 15:27:27 2007  recovered 136916 relations
Sat Oct 13 15:27:27 2007  recovered 116979 polynomials
Sat Oct 13 15:27:28 2007  attempting to build 56771 cycles
Sat Oct 13 15:27:28 2007  found 56771 cycles in 6 passes
Sat Oct 13 15:27:28 2007  distribution of cycle lengths:
Sat Oct 13 15:27:28 2007     length 1 : 15604
Sat Oct 13 15:27:28 2007     length 2 : 10981
Sat Oct 13 15:27:28 2007     length 3 : 9938
Sat Oct 13 15:27:28 2007     length 4 : 7431
Sat Oct 13 15:27:28 2007     length 5 : 5307
Sat Oct 13 15:27:28 2007     length 6 : 3290
Sat Oct 13 15:27:28 2007     length 7 : 1927
Sat Oct 13 15:27:28 2007     length 9+: 2293
Sat Oct 13 15:27:28 2007  largest cycle: 20 relations
Sat Oct 13 15:27:29 2007  matrix is 56667 x 56771 with weight 3278330 (avg 57.75/col)
Sat Oct 13 15:27:30 2007  filtering completed in 4 passes
Sat Oct 13 15:27:30 2007  matrix is 52445 x 52509 with weight 3068265 (avg 58.43/col)
Sat Oct 13 15:27:31 2007  saving the first 48 matrix rows for later
Sat Oct 13 15:27:31 2007  matrix is 52397 x 52509 with weight 2467820 (avg 47.00/col)
Sat Oct 13 15:27:31 2007  matrix includes 64 packed rows
Sat Oct 13 15:27:31 2007  using block size 10922 for processor cache size 256 kB
Sat Oct 13 15:27:32 2007  commencing Lanczos iteration
Sat Oct 13 15:28:04 2007  lanczos halted after 830 iterations
Sat Oct 13 15:28:04 2007  recovered 18 nontrivial dependencies
Sat Oct 13 15:28:05 2007  prp35 factor: 11645958539351398837968999925860551
Sat Oct 13 15:28:05 2007  prp53 factor: 32161199219947116795810535309580815458905862060506117
Sat Oct 13 15:28:05 2007  elapsed time 01:09:50

8·10119-7 = 7(9)1183<120> = 31 · C119

C119 = P41 · P78

P41 = 65850038351296212647890397578950381287521<41>

P78 = 391897290556327270259798161999635360467060860906617319029511693859070848809543<78>

Number: n
N=25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903
  ( 119 digits)
SNFS difficulty: 120 digits.
Divisors found:
 r1=65850038351296212647890397578950381287521 (pp41)
 r2=391897290556327270259798161999635360467060860906617319029511693859070848809543 (pp78)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 1.48 hours.
Scaled time: 1.94 units (timescale=1.313).
Factorization parameters were as follows:
name: KA_7_9_118_3
n: 25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903
skew: 1.54
deg: 5
c5: 4
c0: -35
m: 1000000000000000000000000
type: snfs
rlim: 800000
alim: 800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:63951, AFBsize:64193, largePrimes:4027991 encountered
Relations: rels:3391987, finalFF:155362
Max relations in full relation-set: 48
Initial matrix: 128208 x 155362 with sparse part having weight 9403022.
Pruned matrix : 112183 x 112888 with weight 4664374.
Total sieving time: 1.28 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.12 hours.
Total square root time: 0.02 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,120,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000
total time: 1.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 13, 2007 (5th)

By Sinkiti Sibata / GGNFS

6·10134+7 = 6(0)1337<135> = 193 · 863 · 23603 · 100586824269101<15> · C112

C112 = P35 · P77

P35 = 16080745011300179212403283434151191<35>

P77 = 94355816472667095064977591820097467102390568492729306979142286831385089101801<77>

Number: 60007_134
N=1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991
  ( 112 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=16080745011300179212403283434151191 (pp35)
 r2=94355816472667095064977591820097467102390568492729306979142286831385089101801 (pp77)
Version: GGNFS-0.77.1-20060513-k8
Total time: 5.83 hours.
Scaled time: 11.61 units (timescale=1.992).
Factorization parameters were as follows:
name: 60007_134
n: 1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991
m: 1000000000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1075001)
Primes: RFBsize:78498, AFBsize:63993, largePrimes:1532434 encountered
Relations: rels:1543630, finalFF:184907
Max relations in full relation-set: 28
Initial matrix: 142556 x 184907 with sparse part having weight 13770867.
Pruned matrix : 128299 x 129075 with weight 7860258.
Total sieving time: 5.62 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.11 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.83 hours.
 --------- CPU info (if available) ----------

8·10102-7 = 7(9)1013<103> = 2599231 · C97

C97 = P36 · P62

P36 = 123290814675728514277867589716453613<36>

P62 = 24964012229434350382875423100742889170251821341837628816240131<62>

Number: 79993_102
N=3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303
  ( 97 digits)
SNFS difficulty: 102 digits.
Divisors found:
 r1=123290814675728514277867589716453613 (pp36)
 r2=24964012229434350382875423100742889170251821341837628816240131 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 0.89 hours.
Scaled time: 1.79 units (timescale=1.999).
Factorization parameters were as follows:
name: 79993_102
n: 3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303
m: 200000000000000000000
c5: 25
c0: -7
skew: 0.78
type: snfs
Factor base limits: 450000/500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [250000, 310001)
Primes: RFBsize:37706, AFBsize:41317, largePrimes:1576393 encountered
Relations: rels:1849951, finalFF:427438
Max relations in full relation-set: 28
Initial matrix: 79087 x 427438 with sparse part having weight 15779526.
Pruned matrix : 37970 x 38429 with weight 2534723.
Total sieving time: 0.84 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.01 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000
total time: 0.89 hours.
 --------- CPU info (if available) ----------

8·10113-7 = 7(9)1123<114> = 43 · 73 · 947 · 138185209 · C100

C100 = P34 · P67

P34 = 1766907794190056087078782907983423<34>

P67 = 1102232585621228023273179280338960623464028098584925315433259382103<67>

Number: 79993_113
N=1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
  ( 100 digits)
SNFS difficulty: 113 digits.
Divisors found:
 r1=1766907794190056087078782907983423 (pp34)
 r2=1102232585621228023273179280338960623464028098584925315433259382103 (pp67)
Version: GGNFS-0.77.1-20060513-k8
Total time: 4.01 hours.
Scaled time: 7.94 units (timescale=1.983).
Factorization parameters were as follows:
name: 79993_113
n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
m: 20000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569
m: 20000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64168, largePrimes:2727503 encountered
Relations: rels:3846323, finalFF:1205129
Max relations in full relation-set: 28
Initial matrix: 113332 x 1205129 with sparse part having weight 90876931.
Pruned matrix : 49293 x 49923 with weight 10051860.
Total sieving time: 3.88 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 4.01 hours.
 --------- CPU info (if available) ----------

8·10128-7 = 7(9)1273<129> = 13 · 4458931 · 28353751 · 344697087446640263047<21> · C94

C94 = P39 · P55

P39 = 212705206095827642161365792695450030873<39>

P55 = 6638800655743115255251905310435410068403132728886029351<55>

Number: 79993_128
N=1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423
  ( 94 digits)
SNFS difficulty: 128 digits.
Divisors found:
 r1=212705206095827642161365792695450030873 (pp39)
 r2=6638800655743115255251905310435410068403132728886029351 (pp55)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.28 hours.
Scaled time: 3.57 units (timescale=0.676).
Factorization parameters were as follows:
name: 79993_128
n: 1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423
m: 20000000000000000000000000
c5: 250
c0: -7
skew: 0.49
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64168, largePrimes:1487851 encountered
Relations: rels:1489577, finalFF:174328
Max relations in full relation-set: 28
Initial matrix: 128185 x 174328 with sparse part having weight 12264098.
Pruned matrix : 114449 x 115153 with weight 6368258.
Total sieving time: 4.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.28 hours.
 --------- CPU info (if available) ----------

8·10114-7 = 7(9)1133<115> = 230904677 · C107

C107 = P48 · P59

P48 = 587132704218609332602624273840988912804671457773<48>

P59 = 59009370997911180303851532975515874983963222792974758349433<59>

Number: 79993_114
N=34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709
  ( 107 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=587132704218609332602624273840988912804671457773 (pp48)
 r2=59009370997911180303851532975515874983963222792974758349433 (pp59)
Version: GGNFS-0.77.1-20060513-k8
Total time: 3.32 hours.
Scaled time: 6.61 units (timescale=1.994).
Factorization parameters were as follows:
name: 79993_114
n: 34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709
m: 100000000000000000000000
c5: 4
c0: -35
skew: 1.54
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:64193, largePrimes:2486912 encountered
Relations: rels:3148089, finalFF:767372
Max relations in full relation-set: 28
Initial matrix: 113355 x 767372 with sparse part having weight 60310023.
Pruned matrix : 62081 x 62711 with weight 6647029.
Total sieving time: 3.20 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.02 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.32 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007 (4th)

The factor table of 799...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Oct 13, 2007 (3rd)

By Robert Backstrom / GGNFS

6·10144+7 = 6(0)1437<145> = 13 · 61 · 6217 · C139

C139 = P47 · P92

P47 = 17996214744046724344420417956846958165765495333<47>

P92 = 67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259<92>

Number: n
N=1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247
  ( 139 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=17996214744046724344420417956846958165765495333 (pp47)
 r2=67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259 (pp92)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.95 hours.
Scaled time: 11.51 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_0_143_7
n: 1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247
skew: 1.63
deg: 5
c5: 3
c0: 35
m: 100000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 900001)
Primes: RFBsize:148933, AFBsize:148840, largePrimes:6333809 encountered
Relations: rels:5693227, finalFF:347656
Max relations in full relation-set: 28
Initial matrix: 297838 x 347656 with sparse part having weight 22955213.
Pruned matrix : 259683 x 261236 with weight 14197561.
Total sieving time: 6.15 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.51 hours.
Total square root time: 0.13 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 7.95 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 13, 2007 (2nd)

By Sinkiti Sibata / GGNFS

6·10132+7 = 6(0)1317<133> = 13 · 31 · 59 · 2090009 · 148913261947<12> · C111

C111 = P55 · P57

P55 = 1983329501828473727548585254782922572449329984672734213<55>

P57 = 408806495210391060163003461145989705978462625906890077609<57>

Number: 60007_132
N=810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717
  ( 111 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=1983329501828473727548585254782922572449329984672734213 (pp55)
 r2=408806495210391060163003461145989705978462625906890077609 (pp57)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.78 hours.
Scaled time: 5.26 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_132
n: 810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717
m: 100000000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1250001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1533110 encountered
Relations: rels:1528629, finalFF:158241
Max relations in full relation-set: 28
Initial matrix: 127540 x 158241 with sparse part having weight 14199593.
Pruned matrix : 119830 x 120531 with weight 9182188.
Total sieving time: 7.35 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.29 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 7.78 hours.
 --------- CPU info (if available) ----------

6·10167-7 = 5(9)1663<168> = 86004929922823687<17> · 117124643630091042473553137641<30> · C122

C122 = P55 · P68

P55 = 1422924018199617086667469983408773956446337923324187259<55>

P68 = 41859873490837916408900575837828799444368507615420908476733092182981<68>

Number: 59993_167
N=59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079
  ( 122 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=1422924018199617086667469983408773956446337923324187259 (pp55)
 r2=41859873490837916408900575837828799444368507615420908476733092182981 (pp68)
Version: GGNFS-0.77.1-20060513-k8
Total time: 154.80 hours.
Scaled time: 308.82 units (timescale=1.995).
Factorization parameters were as follows:
name: 59993_167
n: 59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079
m: 1000000000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7450001)
Primes: RFBsize:380800, AFBsize:380567, largePrimes:6136257 encountered
Relations: rels:6361592, finalFF:867619
Max relations in full relation-set: 28
Initial matrix: 761433 x 867619 with sparse part having weight 66909828.
Pruned matrix : 680057 x 683928 with weight 51296332.
Total sieving time: 147.94 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 6.30 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 154.80 hours.
 --------- CPU info (if available) ----------

Oct 13, 2007

By Jo Yeong Uk / GMP-ECM, GGNFS

6·10193+7 = 6(0)1927<194> = C194

C194 = P37 · C157

P37 = 9431867921209970677263227064224760463<37>

C157 = [6361412235753920282712594389572541485300199982510262458997768914548898435588007324833733189857362507423842664895526461468007039663923961796686299905053607689<157>]

6·10140+7 = 6(0)1397<141> = 17 · 25765322537<11> · 29151135776457323<17> · C113

C113 = P52 · P61

P52 = 6123908191785128062611453979386707666992816396823857<52>

P61 = 7673307351852464227438937019759901799643665911557369118867853<61>

Number: 60007_140
N=46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021
  ( 113 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=6123908191785128062611453979386707666992816396823857 (pp52)
 r2=7673307351852464227438937019759901799643665911557369118867853 (pp61)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.19 hours.
Scaled time: 13.10 units (timescale=2.117).
Factorization parameters were as follows:
n: 46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021
m: 10000000000000000000000000000
c5: 6
c0: 7
skew: 1.03
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1150001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:3206977 encountered
Relations: rels:3155190, finalFF:262058
Max relations in full relation-set: 28
Initial matrix: 228633 x 262058 with sparse part having weight 22384343.
Pruned matrix : 214081 x 215288 with weight 15710541.
Total sieving time: 5.95 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.19 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

6·10183+7 = 6(0)1827<184> = C184

C184 = P37 · P148

P37 = 4646109535270935651861373920553944113<37>

P148 = 1291403044730436574664225203953221354301912479271324672689780038042977651172600578097674193944368819808698887156719580132180993397271065994090189239<148>

6·10160+7 = 6(0)1597<161> = 4229 · 482513 · 19099104039013<14> · C139

C139 = P34 · P105

P34 = 2891475901086594031773677024975431<34>

P105 = 532441594081401683367165802963920698884830621397625778059323292338660459693626121501287829706854904467897<105>

Oct 12, 2007 (3rd)

By Jo Yeong Uk / GGNFS

6·10152+7 = 6(0)1517<153> = C153

C153 = P43 · P111

P43 = 1840685266806508095129806305318544351784701<43>

P111 = 325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107<111>

Number: 60007_152
N=600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 153 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1840685266806508095129806305318544351784701 (pp43)
 r2=325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107 (pp111)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 20.05 hours.
Scaled time: 42.60 units (timescale=2.125).
Factorization parameters were as follows:
n: 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
m: 2000000000000000000000000000000
c5: 75
c0: 28
skew: 0.82
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2500001)
Primes: RFBsize:176302, AFBsize:175743, largePrimes:5716294 encountered
Relations: rels:5680786, finalFF:487419
Max relations in full relation-set: 28
Initial matrix: 352111 x 487419 with sparse part having weight 48790712.
Pruned matrix : 305178 x 307002 with weight 29072127.
Total sieving time: 19.36 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 20.05 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 12, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(89·10163+1)/9 = 9(8)1629<164> = 32 · 11 · 191 · 44453 · 169823791 · C147

C147 = P71 · P77

P71 = 53555495404586983124284868689499027110767249977749056417262621184569457<71>

P77 = 12935263718227109600388586097547759844207588321745878007455274683392359947511<77>

Number: n
N=692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527
  ( 147 digits)
SNFS difficulty: 164 digits.
Divisors found:

Fri Oct 12 07:40:24 2007  prp71 factor: 53555495404586983124284868689499027110767249977749056417262621184569457
Fri Oct 12 07:40:24 2007  prp77 factor: 12935263718227109600388586097547759844207588321745878007455274683392359947511
Fri Oct 12 07:40:24 2007  elapsed time 01:36:36 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.85 hours.
Scaled time: 58.50 units (timescale=1.432).
Factorization parameters were as follows:
name: KA_9_8_162_9
n: 692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527
skew: 0.10
deg: 5
c5: 89000
c0: 1
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100001)
Primes: RFBsize:203362, AFBsize:202807, largePrimes:7209972 encountered
Relations: rels:6664266, finalFF:448066
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 40.59 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 40.85 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

6·10145+7 = 6(0)1447<146> = 163 · C144

C144 = P64 · P80

P64 = 3919572055477532086753025839329335485817252963822084748594102007<64>

P80 = 93912844131744392068992466757974562467028071947951869170587151041083038337579227<80>

Number: n
N=368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589
  ( 144 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=3919572055477532086753025839329335485817252963822084748594102007 (pp64)
 r2=93912844131744392068992466757974562467028071947951869170587151041083038337579227 (pp80)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 11.95 hours.
Scaled time: 14.29 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_6_0_144_7
n: 368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589
type: snfs
skew: 1.03
deg: 5
c5: 6
c0: 7
m: 100000000000000000000000000000
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1400001)
Primes: RFBsize:148933, AFBsize:149160, largePrimes:6126432 encountered
Relations: rels:5452417, finalFF:336584
Max relations in full relation-set: 28
Initial matrix: 298159 x 336584 with sparse part having weight 21730162.
Pruned matrix : 270315 x 271869 with weight 14890622.
Total sieving time: 9.92 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.75 hours.
Total square root time: 0.07 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000
total time: 11.95 hours.
 --------- CPU info (if available) ----------

6·10138+7 = 6(0)1377<139> = 13 · C138

C138 = P52 · P86

P52 = 8786475728072227386487041599685529123701731718444931<52>

P86 = 52528280487235138475680678891847720293425922478509734700005290994634833797311729822369<86>

Number: n
N=461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=8786475728072227386487041599685529123701731718444931 (pp52)
 r2=52528280487235138475680678891847720293425922478509734700005290994634833797311729822369 (pp86)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 6.79 hours.
Scaled time: 8.84 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_6_0_137_3
n: 461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539
skew: 0.26
deg: 5
c5: 6000
c0: 7
m: 1000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 750001)
Primes: RFBsize:114155, AFBsize:114432, largePrimes:6211466 encountered
Relations: rels:5545647, finalFF:312486
Max relations in full relation-set: 48
Initial matrix: 228654 x 312486 with sparse part having weight 29654727.
Pruned matrix : 190499 x 191706 with weight 12900013.
Total sieving time: 5.71 hours.
Total relation processing time: 0.17 hours.
Matrix solve time: 0.83 hours.
Total square root time: 0.08 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000
total time: 6.79 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(25·10164-7)/9 = 2(7)164<165> = 109 · 233 · 98429 · 3605093 · C149

C149 = P69 · P81

P69 = 202665523211650989063300380086943340369476928178393708116016987186139<69>

P81 = 152088249235178053009249905689353519859990659090201830262384603581442406000454727<81>

Number: n
N=30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053
  ( 149 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=202665523211650989063300380086943340369476928178393708116016987186139 (pp69)
 r2=152088249235178053009249905689353519859990659090201830262384603581442406000454727 (pp81)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 63.84 hours.
Scaled time: 83.38 units (timescale=1.306).
Factorization parameters were as follows:
name: KA_2_7_164
n: 30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053
skew: 1.23
deg: 5
c5: 5
c0: -14
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:216816, AFBsize:217381, largePrimes:7523615 encountered
Relations: rels:7019729, finalFF:495769
Max relations in full relation-set: 28
Initial matrix: 434262 x 495769 with sparse part having weight 44468095.
Pruned matrix : 406710 x 408945 with weight 32940913.
Total sieving time: 58.95 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 4.48 hours.
Total square root time: 0.14 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 12, 2007

By Sinkiti Sibata / GGNFS

6·10114+7 = 6(0)1137<115> = 13 · 23 · 294199 · 314707 · 2354837 · C95

C95 = P32 · P64

P32 = 13963735493801662655038504422019<32>

P64 = 6591283660858015718799436869882276779748116589270476529805242367<64>

Number: 60007_114
N=92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973
  ( 95 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=13963735493801662655038504422019 (pp32)
 r2=6591283660858015718799436869882276779748116589270476529805242367 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.60 hours.
Scaled time: 1.08 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_114
n: 92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973
m: 100000000000000000000000
c5: 3
c0: 35
skew: 1.63
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63993, largePrimes:2069865 encountered
Relations: rels:2160911, finalFF:246690
Max relations in full relation-set: 28
Initial matrix: 113156 x 246690 with sparse part having weight 18938825.
Pruned matrix : 79136 x 79765 with weight 3921681.
Total sieving time: 1.41 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.60 hours.
 --------- CPU info (if available) ----------

6·10116+7 = 6(0)1157<117> = 1433 · C114

C114 = P46 · P68

P46 = 4260569836341526184189932091009434032922764443<46>

P68 = 98273714505283129560284285927238795172266087521311216860992588389453<68>

Number: 60007_116
N=418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679
  ( 114 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=4260569836341526184189932091009434032922764443 (pp46)
 r2=98273714505283129560284285927238795172266087521311216860992588389453 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.17 hours.
Scaled time: 1.47 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_116
n: 418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679
m: 100000000000000000000000
c5: 60
c0: 7
skew: 0.65
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63883, largePrimes:2216313 encountered
Relations: rels:2423409, finalFF:333688
Max relations in full relation-set: 28
Initial matrix: 113048 x 333688 with sparse part having weight 30159400.
Pruned matrix : 73820 x 74449 with weight 5302920.
Total sieving time: 1.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.17 hours.
 --------- CPU info (if available) ----------

6·10117+7 = 6(0)1167<118> = 31 · 2602909783189<13> · C104

C104 = P39 · P65

P39 = 761007481197519851161967935908199514911<39>

P65 = 97710562768479463816800500502385687103003804418987111582005841643<65>

Number: 60007_117
N=74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773
  ( 104 digits)
SNFS difficulty: 117 digits.
Divisors found:
 r1=761007481197519851161967935908199514911 (pp39)
 r2=97710562768479463816800500502385687103003804418987111582005841643 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.20 hours.
Scaled time: 1.49 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_117
n: 74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773
m: 100000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63523, largePrimes:1980594 encountered
Relations: rels:1938172, finalFF:128803
Max relations in full relation-set: 28
Initial matrix: 112687 x 128803 with sparse part having weight 10218920.
Pruned matrix : 106545 x 107172 with weight 7132342.
Total sieving time: 1.89 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.20 hours.
 --------- CPU info (if available) ----------

6·10127+7 = 6(0)1267<128> = 197 · 9720031 · 266168660299<12> · C108

C108 = P43 · P65

P43 = 3583617409332378966987419272264607655669797<43>

P65 = 32850260496263134596383389203484134247046587543608521946389524867<65>

Number: 60007_127
N=117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999
  ( 108 digits)
SNFS difficulty: 127 digits.
Divisors found:
 r1=3583617409332378966987419272264607655669797 (pp43)
 r2=32850260496263134596383389203484134247046587543608521946389524867 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.28 hours.
Scaled time: 3.57 units (timescale=0.676).
Factorization parameters were as follows:
name: 60007_127
n: 117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999
m: 10000000000000000000000000
c5: 600
c0: 7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1506649 encountered
Relations: rels:1516333, finalFF:181202
Max relations in full relation-set: 28
Initial matrix: 127540 x 181202 with sparse part having weight 12751877.
Pruned matrix : 111515 x 112216 with weight 6223089.
Total sieving time: 4.97 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.19 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.28 hours.
 --------- CPU info (if available) ----------

Oct 11, 2007 (4th)

By Sinkiti Sibata / Msieve

6·10155+7 = 6(0)1547<156> = 30253 · 8290186057<10> · 93174093649657<14> · 47369174977499761<17> · 7846580404504329797862521<25> · C86

C86 = P41 · P46

P41 = 11519704348754539604022205034624081555611<41>

P46 = 5996609457515185443760101854342559834794121041<46>

Thu Oct 11 07:46:13 2007  Msieve v. 1.28
Thu Oct 11 07:46:13 2007  random seeds: a4efa528 11c3b45d
Thu Oct 11 07:46:13 2007  factoring 69079168045520282358058872569745380341436008514853935086936756082097682617184706711051 (86 digits)
Thu Oct 11 07:46:14 2007  commencing quadratic sieve (86-digit input)
Thu Oct 11 07:46:14 2007  using multiplier of 11
Thu Oct 11 07:46:14 2007  using 64kb Pentium 2 sieve core
Thu Oct 11 07:46:14 2007  sieve interval: 9 blocks of size 65536
Thu Oct 11 07:46:14 2007  processing polynomials in batches of 12
Thu Oct 11 07:46:14 2007  using a sieve bound of 1470947 (55891 primes)
Thu Oct 11 07:46:14 2007  using large prime bound of 117675760 (26 bits)
Thu Oct 11 07:46:14 2007  using double large prime bound of 336694943593840 (41-49 bits)
Thu Oct 11 07:46:14 2007  using trial factoring cutoff of 49 bits
Thu Oct 11 07:46:14 2007  polynomial 'A' values have 11 factors
Thu Oct 11 13:23:21 2007  56030 relations (15871 full + 40159 combined from 586780 partial), need 55987
Thu Oct 11 13:23:28 2007  begin with 602651 relations
Thu Oct 11 13:23:29 2007  reduce to 133601 relations in 10 passes
Thu Oct 11 13:23:29 2007  attempting to read 133601 relations
Thu Oct 11 13:23:38 2007  recovered 133601 relations
Thu Oct 11 13:23:38 2007  recovered 112180 polynomials
Thu Oct 11 13:23:39 2007  attempting to build 56030 cycles
Thu Oct 11 13:23:39 2007  found 56030 cycles in 6 passes
Thu Oct 11 13:23:42 2007  distribution of cycle lengths:
Thu Oct 11 13:23:42 2007     length 1 : 15871
Thu Oct 11 13:23:42 2007     length 2 : 11072
Thu Oct 11 13:23:42 2007     length 3 : 9884
Thu Oct 11 13:23:42 2007     length 4 : 7361
Thu Oct 11 13:23:42 2007     length 5 : 4850
Thu Oct 11 13:23:42 2007     length 6 : 3171
Thu Oct 11 13:23:42 2007     length 7 : 1783
Thu Oct 11 13:23:42 2007     length 9+: 2038
Thu Oct 11 13:23:42 2007  largest cycle: 20 relations
Thu Oct 11 13:23:42 2007  matrix is 55891 x 56030 with weight 3116041 (avg 55.61/col)
Thu Oct 11 13:23:47 2007  filtering completed in 3 passes
Thu Oct 11 13:23:47 2007  matrix is 51400 x 51464 with weight 2897239 (avg 56.30/col)
Thu Oct 11 13:23:49 2007  saving the first 48 matrix rows for later
Thu Oct 11 13:23:49 2007  matrix is 51352 x 51464 with weight 2270531 (avg 44.12/col)
Thu Oct 11 13:23:49 2007  matrix includes 64 packed rows
Thu Oct 11 13:23:49 2007  using block size 5461 for processor cache size 128 kB
Thu Oct 11 13:23:51 2007  commencing Lanczos iteration
Thu Oct 11 13:26:11 2007  lanczos halted after 814 iterations
Thu Oct 11 13:26:12 2007  recovered 16 nontrivial dependencies
Thu Oct 11 13:26:13 2007  prp41 factor: 11519704348754539604022205034624081555611
Thu Oct 11 13:26:13 2007  prp46 factor: 5996609457515185443760101854342559834794121041
Thu Oct 11 13:26:13 2007  elapsed time 05:40:00

6·10104+7 = 6(0)1037<105> = 8629566092175419113<19> · C86

C86 = P39 · P48

P39 = 312703414298744945585964596618843105759<39>

P48 = 222346177668355476515021026054869613681073668721<48>

Thu Oct 11 08:00:35 2007  Msieve v. 1.26
Thu Oct 11 08:00:35 2007  random seeds: 35251e1c b1bd4346
Thu Oct 11 08:00:35 2007  factoring 69528408913170114020623970508248965547977728760224458789292141359530747384979933264239 (86 digits)
Thu Oct 11 08:00:36 2007  commencing quadratic sieve (86-digit input)
Thu Oct 11 08:00:36 2007  using multiplier of 31
Thu Oct 11 08:00:36 2007  using 64kb Pentium 2 sieve core
Thu Oct 11 08:00:36 2007  sieve interval: 9 blocks of size 65536
Thu Oct 11 08:00:36 2007  processing polynomials in batches of 12
Thu Oct 11 08:00:36 2007  using a sieve bound of 1470947 (55662 primes)
Thu Oct 11 08:00:36 2007  using large prime bound of 117675760 (26 bits)
Thu Oct 11 08:00:36 2007  using double large prime bound of 336694943593840 (41-49 bits)
Thu Oct 11 08:00:36 2007  using trial factoring cutoff of 49 bits
Thu Oct 11 08:00:36 2007  polynomial 'A' values have 11 factors
Thu Oct 11 13:29:42 2007  55839 relations (15809 full + 40030 combined from 583377 partial), need 55758
Thu Oct 11 13:29:51 2007  begin with 599186 relations
Thu Oct 11 13:29:54 2007  reduce to 132538 relations in 10 passes
Thu Oct 11 13:29:54 2007  attempting to read 132538 relations
Thu Oct 11 13:30:03 2007  recovered 132538 relations
Thu Oct 11 13:30:03 2007  recovered 110467 polynomials
Thu Oct 11 13:30:16 2007  attempting to build 55839 cycles
Thu Oct 11 13:30:16 2007  found 55838 cycles in 5 passes
Thu Oct 11 13:30:18 2007  distribution of cycle lengths:
Thu Oct 11 13:30:18 2007     length 1 : 15809
Thu Oct 11 13:30:18 2007     length 2 : 11217
Thu Oct 11 13:30:18 2007     length 3 : 9985
Thu Oct 11 13:30:18 2007     length 4 : 7192
Thu Oct 11 13:30:18 2007     length 5 : 4922
Thu Oct 11 13:30:18 2007     length 6 : 3106
Thu Oct 11 13:30:18 2007     length 7 : 1762
Thu Oct 11 13:30:18 2007     length 9+: 1845
Thu Oct 11 13:30:18 2007  largest cycle: 18 relations
Thu Oct 11 13:30:19 2007  matrix is 55662 x 55838 with weight 3139688 (avg 56.23/col)
Thu Oct 11 13:30:22 2007  filtering completed in 3 passes
Thu Oct 11 13:30:22 2007  matrix is 50880 x 50944 with weight 2899893 (avg 56.92/col)
Thu Oct 11 13:30:24 2007  saving the first 48 matrix rows for later
Thu Oct 11 13:30:24 2007  matrix is 50832 x 50944 with weight 2295297 (avg 45.06/col)
Thu Oct 11 13:30:24 2007  matrix includes 64 packed rows
Thu Oct 11 13:30:24 2007  using block size 10922 for processor cache size 256 kB
Thu Oct 11 13:30:25 2007  commencing Lanczos iteration
Thu Oct 11 13:33:05 2007  lanczos halted after 805 iterations
Thu Oct 11 13:33:06 2007  recovered 17 nontrivial dependencies
Thu Oct 11 13:33:21 2007  prp39 factor: 312703414298744945585964596618843105759
Thu Oct 11 13:33:21 2007  prp48 factor: 222346177668355476515021026054869613681073668721
Thu Oct 11 13:33:21 2007  elapsed time 05:32:46

Oct 11, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM

(4·10162+23)/9 = (4)1617<162> = 3 · 191537 · 36201871247<11> · C146

C146 = P68 · P79

P68 = 14267717847005813507700165288034158445726684150241889062913896709923<68>

P79 = 1497469599792136047698907928447361359099204601762726546842329109356470216353817<79>

Number: n
N=21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091
  ( 146 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Oct 11 07:49:06 2007  prp68 factor: 14267717847005813507700165288034158445726684150241889062913896709923
Thu Oct 11 07:49:06 2007  prp79 factor: 1497469599792136047698907928447361359099204601762726546842329109356470216353817
Thu Oct 11 07:49:06 2007  elapsed time 02:07:31 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 67.17 hours.
Scaled time: 80.33 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_4_161_7
n: 21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091
type: snfs
skew: 1.13
deg: 5
c5: 25
c0: 46
m: 200000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2900000)
Primes: RFBsize:230209, AFBsize:229862, largePrimes:7394863 encountered
Relations: rels:6833492, finalFF:510861
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 66.85 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 67.17 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

6·10106+7 = 6(0)1057<107> = C107

C107 = P33 · P74

P33 = 660354883413107731466749453206421<33>

P74 = 90860235166103760559298389079671871752970399872818769276787670766575373867<74>

Number: n
N=60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
  ( 107 digits)
SNFS difficulty: 106 digits.
Divisors found:
 r1=660354883413107731466749453206421 (pp33)
 r2=90860235166103760559298389079671871752970399872818769276787670766575373867 (pp74)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 0.81 hours.
Scaled time: 0.97 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_6_0_105_7
n: 60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007
type: snfs
skew: 0.65
deg: 5
c5: 60
c0: 7
m: 1000000000000000000000
rlim: 500000
alim: 500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 50000
Factor base limits: 500000/500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 200001)
Primes: RFBsize:41538, AFBsize:41547, largePrimes:2680462 encountered
Relations: rels:2220524, finalFF:111084
Max relations in full relation-set: 28
Initial matrix: 83152 x 111084 with sparse part having weight 5499964.
Pruned matrix : 67479 x 67958 with weight 2313666.
Total sieving time: 0.68 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.04 hours.
Total square root time: 0.04 hours, sqrts: 3.
Prototype def-par.txt line would be:
snfs,106,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.4,2.4,50000
total time: 0.81 hours.
 --------- CPU info (if available) ----------

6·10112+7 = 6(0)1117<113> = 43 · C112

C112 = P29 · P32 · P52

P29 = 42037675529382231904791550999<29>

P32 = 14936485810428385363892834492251<32>

P52 = 2222264100043128899370105966054617650050692155163401<52>

N = 6*10^112+7 : c112

prp29 factor: 42037675529382231904791550999
prp32 factor: 14936485810428385363892834492251
prp52 factor: 2222264100043128899370105966054617650050692155163401

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM]
Input number is 1395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395349 (112 digits)
Using B1=87500, B2=26096911, polynomial x^2, sigma=730686625
Step 1 took 1203ms
Step 2 took 953ms
********** Factor found in step 2: 42037675529382231904791550999
Found probable prime factor of 29 digits: 42037675529382231904791550999
Composite cofactor 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 has 83 digits

Thu Oct 11 14:51:32 2007  
Thu Oct 11 14:51:32 2007  
Thu Oct 11 14:51:32 2007  Msieve v. 1.28
Thu Oct 11 14:51:32 2007  random seeds: 409cfc00 e37a735e
Thu Oct 11 14:51:32 2007  factoring 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 (83 digits)
Thu Oct 11 14:51:32 2007  commencing quadratic sieve (83-digit input)
Thu Oct 11 14:51:33 2007  using multiplier of 1
Thu Oct 11 14:51:33 2007  using 64kb Athlon XP sieve core
Thu Oct 11 14:51:33 2007  sieve interval: 6 blocks of size 65536
Thu Oct 11 14:51:33 2007  processing polynomials in batches of 17
Thu Oct 11 14:51:33 2007  using a sieve bound of 1369321 (52647 primes)
Thu Oct 11 14:51:33 2007  using large prime bound of 121869569 (26 bits)
Thu Oct 11 14:51:33 2007  using trial factoring cutoff of 27 bits
Thu Oct 11 14:51:33 2007  polynomial 'A' values have 10 factors
Thu Oct 11 15:25:57 2007  52751 relations (26020 full + 26731 combined from 283185 partial), need 52743
Thu Oct 11 15:25:58 2007  begin with 309205 relations
Thu Oct 11 15:25:58 2007  reduce to 76065 relations in 2 passes
Thu Oct 11 15:25:58 2007  attempting to read 76065 relations
Thu Oct 11 15:25:59 2007  recovered 76065 relations
Thu Oct 11 15:25:59 2007  recovered 69714 polynomials
Thu Oct 11 15:25:59 2007  attempting to build 52751 cycles
Thu Oct 11 15:25:59 2007  found 52751 cycles in 1 passes
Thu Oct 11 15:25:59 2007  distribution of cycle lengths:
Thu Oct 11 15:25:59 2007     length 1 : 26020
Thu Oct 11 15:25:59 2007     length 2 : 26731
Thu Oct 11 15:25:59 2007  largest cycle: 2 relations
Thu Oct 11 15:25:59 2007  matrix is 52647 x 52751 with weight 1646722 (avg 31.22/col)
Thu Oct 11 15:26:00 2007  filtering completed in 4 passes
Thu Oct 11 15:26:00 2007  matrix is 46089 x 46153 with weight 1415834 (avg 30.68/col)
Thu Oct 11 15:26:00 2007  saving the first 48 matrix rows for later
Thu Oct 11 15:26:01 2007  matrix is 46041 x 46153 with weight 1132687 (avg 24.54/col)
Thu Oct 11 15:26:01 2007  matrix includes 64 packed rows
Thu Oct 11 15:26:01 2007  commencing Lanczos iteration
Thu Oct 11 15:27:17 2007  lanczos halted after 730 iterations
Thu Oct 11 15:27:18 2007  recovered 10 nontrivial dependencies
Thu Oct 11 15:27:18 2007  prp32 factor: 14936485810428385363892834492251
Thu Oct 11 15:27:18 2007  prp52 factor: 2222264100043128899370105966054617650050692155163401
Thu Oct 11 15:27:18 2007  elapsed time 00:35:46

(55·10164-1)/9 = 6(1)164<165> = 13 · 863 · 19751 · C157

C157 = P46 · P112

P46 = 2039347963490980778560349082035680167389362879<46>

P112 = 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861<112>

Number: n
N=2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819
  ( 157 digits)
SNFS difficulty: 166 digits.
Divisors found:

Thu Oct 11 23:37:55 2007  prp46 factor: 2039347963490980778560349082035680167389362879
Thu Oct 11 23:37:55 2007  prp112 factor: 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861
Thu Oct 11 23:37:55 2007  elapsed time 01:27:35 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 46.45 hours.
Scaled time: 61.40 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_6_1_164
n: 2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819
skew: 0.71
deg: 5
c5: 11
c0: -2
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2200000)
Primes: RFBsize:250150, AFBsize:250187, largePrimes:7389826 encountered
Relations: rels:6945502, finalFF:606876
Max relations in full relation-set: 28
Initial matrix: 500404 x 606876 with sparse part having weight 45655180.
Pruned matrix : 414282 x 416848 with weight 26923583.
Total sieving time: 46.18 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 46.45 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 11, 2007 (2nd)

By Yousuke Koide

101009+1 is divisible by 873234964696345278371172272680705837<36>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 11, 2007

The factor table of 600...007 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Oct 10, 2007 (2nd)

By Sinkiti Sibata / PRIMO

(28·102207+53)/9 is prime.

Oct 10, 2007

By Jo Yeong Uk / GGNFS

(8·10159-53)/9 = (8)1583<159> = 480451 · 4208429 · 104033087 · 13728238483<11> · C129

C129 = P42 · P87

P42 = 316712295015730221860570435349138324870013<42>

P87 = 971912454296354051931961805793739631984439234627451326067513307017004518364331228609949<87>

Number: 88883_159
N=307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337
  ( 129 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=316712295015730221860570435349138324870013 (pp42)
 r2=971912454296354051931961805793739631984439234627451326067513307017004518364331228609949 (pp87)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.09 hours.
Scaled time: 76.93 units (timescale=2.132).
Factorization parameters were as follows:
n: 307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337
m: 100000000000000000000000000000000
c5: 4
c0: -265
skew: 2.31
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282842, largePrimes:5712676 encountered
Relations: rels:5728756, finalFF:637907
Max relations in full relation-set: 28
Initial matrix: 566052 x 637907 with sparse part having weight 44270840.
Pruned matrix : 519131 x 522025 with weight 33004800.
Total sieving time: 34.34 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.60 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.09 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 9, 2007 (5th)

By Sinkiti Sibata / GGNFS

6·10163-7 = 5(9)1623<164> = 30339296027748931253<20> · C145

C145 = P50 · P96

P50 = 15909833358959093262353180001154624082529476187767<50>

P96 = 124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843<96>

Number: 59993_163
N=1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=15909833358959093262353180001154624082529476187767 (pp50)
 r2=124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843 (pp96)
Version: GGNFS-0.77.1-20060513-k8
Total time: 95.21 hours.
Scaled time: 190.23 units (timescale=1.998).
Factorization parameters were as follows:
name: 59993_163
n: 1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581
m: 200000000000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5350001)
Primes: RFBsize:315948, AFBsize:315866, largePrimes:5944123 encountered
Relations: rels:6092944, finalFF:763528
Max relations in full relation-set: 28
Initial matrix: 631880 x 763528 with sparse part having weight 59643557.
Pruned matrix : 535995 x 539218 with weight 43398744.
Total sieving time: 90.70 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 4.03 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 95.21 hours.
 --------- CPU info (if available) ----------

Oct 9, 2007 (4th)

By Sinkiti Sibata / PRIMO

(8·102073-11)/3 is prime.

Oct 9, 2007 (3rd)

By suberi / PRIMO

5·102733+9 is prime.

Oct 9, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(8·10159-17)/9 = (8)1587<159> = 229 · 800509 · 4884721 · 262148354051<12> · C133

C133 = P41 · P93

P41 = 31689588497279916590736503849012575753313<41>

P93 = 119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029<93>

Number: 88887_159
N=3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=31689588497279916590736503849012575753313 (pp41)
 r2=119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029 (pp93)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 31.11 hours.
Scaled time: 66.71 units (timescale=2.144).
Factorization parameters were as follows:
n: 3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077
m: 100000000000000000000000000000000
c5: 4
c0: -85
skew: 1.84
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283447, largePrimes:5649191 encountered
Relations: rels:5661375, finalFF:639116
Max relations in full relation-set: 28
Initial matrix: 566657 x 639116 with sparse part having weight 40954229.
Pruned matrix : 512428 x 515325 with weight 29660434.
Total sieving time: 29.57 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.40 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 31.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115)
Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125)
Total of 4 processors activated (19246.09 BogoMIPS).

Oct 9, 2007

By Robert Backstrom / GGNFS, Msieve

4·10162+3 = 4(0)1613<163> = 7 · 16111 · 898857769272037<15> · C143

C143 = P47 · P96

P47 = 52633384675921297349532423419308829377260438229<47>

P96 = 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643<96>

Number: n
N=39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247
  ( 143 digits)
SNFS difficulty: 162 digits.
Divisors found:

Tue Oct 09 03:46:58 2007  prp47 factor: 52633384675921297349532423419308829377260438229
Tue Oct 09 03:46:58 2007  prp96 factor: 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643
Tue Oct 09 03:46:58 2007  elapsed time 01:16:25 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.15 hours.
Scaled time: 52.53 units (timescale=1.453).
Factorization parameters were as follows:
name: KA_4_0_161_3
n: 39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247
skew: 0.75
deg: 5
c5: 25
c0: 6
m: 200000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:203362, AFBsize:202562, largePrimes:7139160 encountered
Relations: rels:6577562, finalFF:434257
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 35.92 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 36.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Oct 8, 2007 (4th)

By Bryan Koen / GMP-ECM

(23·10173+1)/3 = 7(6)1727<174> = 11 · 19 · 41 · C170

C170 = P30 · P141

P30 = 357911945978650040346202809163<30>

P141 = 249977110919930838083661846538618118461822803550100409862996457896163981755684629971850878837293997356705743192000800069352481784564014480361<141>

Oct 8, 2007 (3rd)

By Sinkiti Sibata / PRIMO

(31·102177+23)/9 is prime.

Oct 8, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(73·10159-1)/9 = 8(1)159<160> = 2657 · 105091757 · 340002075499<12> · C137

C137 = P68 · P69

P68 = 85748085121300963152030695599342054561573492952495448497507158243159<68>

P69 = 996355092269813964638397829269428609707014906515819237429532829639679<69>

Number: n
N=85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Mon Oct 08 11:11:00 2007  prp68 factor: 85748085121300963152030695599342054561573492952495448497507158243159
Mon Oct 08 11:11:00 2007  prp69 factor: 996355092269813964638397829269428609707014906515819237429532829639679
Mon Oct 08 11:11:01 2007  elapsed time 01:25:31 (Msieve 1.28)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 45.89 hours.
Scaled time: 60.85 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_8_1_159
n: 85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961
skew: 0.67
deg: 5
c5: 73
c0: -10
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:250150, AFBsize:250101, largePrimes:7499050 encountered
Relations: rels:7084336, finalFF:634136
Max relations in full relation-set: 28
Initial matrix: 500316 x 634136 with sparse part having weight 48027068.
Pruned matrix : 392586 x 395151 with weight 27479275.
Total sieving time: 45.64 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 45.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10164-7 = 5(9)1633<165> = 17 · 302404974167609<15> · C150

C150 = P51 · P99

P51 = 604857162810389628774661784293336029351376392407791<51>

P99 = 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991<99>

Number: n
N=116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881
  ( 150 digits)
SNFS difficulty: 165 digits.
Divisors found:

Mon Oct 08 17:31:28 2007  prp51 factor: 604857162810389628774661784293336029351376392407791
Mon Oct 08 17:31:28 2007  prp99 factor: 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991
Mon Oct 08 17:31:28 2007  elapsed time 01:42:50 (Msieve 1.28)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 53.19 hours.
Scaled time: 63.34 units (timescale=1.191).
Factorization parameters were as follows:
name: KA_5_9_163_3
n: 116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881
skew: 1.63
deg: 5
c5: 3
c0: -35
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2600000)
Primes: RFBsize:216816, AFBsize:216606, largePrimes:7376363 encountered
Relations: rels:6846162, finalFF:475104
Max relations in full relation-set: 28
Initial matrix: 
Pruned matrix : 
Total sieving time: 52.94 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 53.19 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 8, 2007

By Jo Yeong Uk / GGNFS

(5·10159-41)/9 = (5)1581<159> = 203232471011<12> · 30634761442301959<17> · C131

C131 = P66 · P66

P66 = 140302918730839359783997803266247889954113331203299846460516096197<66>

P66 = 635994249340914371879827621457572197377938193794948288296614712167<66>

Number: 55551_159
N=89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899
  ( 131 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=140302918730839359783997803266247889954113331203299846460516096197 (pp66)
 r2=635994249340914371879827621457572197377938193794948288296614712167 (pp66)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.76 hours.
Scaled time: 59.39 units (timescale=2.139).
Factorization parameters were as follows:
n: 89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899
m: 100000000000000000000000000000000
c5: 1
c0: -82
skew: 2.41
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282833, largePrimes:5618340 encountered
Relations: rels:5637592, finalFF:646613
Max relations in full relation-set: 28
Initial matrix: 566045 x 646613 with sparse part having weight 40570327.
Pruned matrix : 501999 x 504893 with weight 27943297.
Total sieving time: 26.39 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.23 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.76 hours.
 --------- CPU info (if available) ----------

Oct 7, 2007 (5th)

By Sinkiti Sibata / PRIMO

(17·102068-53)/9 is prime.

Oct 7, 2007 (4th)

By Yousuke Koide

101007+1 is divisible by 80130271534233515728987750894609<32>

101054+1 is divisible by 111276132074930025328712302045364981<36>

101605+1 is divisible by 4298338634928851216299618775086771<34>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 7, 2007 (3rd)

By Sinkiti Sibata / GGNFS

6·10161-7 = 5(9)1603<162> = 59 · 4889 · 22063 · 61949 · 56338169 · 5137570679<10> · C130

C130 = P32 · P99

P32 = 25632208522320555148392302355173<32>

P99 = 205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443<99>

Number: 59993_161
N=5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639
  ( 130 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=25632208522320555148392302355173 (pp32)
 r2=205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443 (pp99)
Version: GGNFS-0.77.1-20060513-k8
Total time: 67.83 hours.
Scaled time: 134.98 units (timescale=1.990).
Factorization parameters were as follows:
name: 59993_161
n: 5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639
m: 100000000000000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316366, largePrimes:5776158 encountered
Relations: rels:5879966, finalFF:735887
Max relations in full relation-set: 28
Initial matrix: 632381 x 735887 with sparse part having weight 44476895.
Pruned matrix : 553498 x 556723 with weight 31162467.
Total sieving time: 64.08 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 3.36 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 67.83 hours.
 --------- CPU info (if available) ----------

Oct 7, 2007 (2nd)

By Jo Yeong Uk / GMP-ECM

10192+9 = 1(0)1919<193> = C193

C193 = P48 · P145

P48 = 325208379747671632800443572929049811907718391209<48>

P145 = 3074951515012920315894112276452006313835272802228418099697777887803931547784516799444634005241238767287033369894773351997005678938044816110863201<145>

Oct 7, 2007

By suberi / PRIMO

(13·102079-7)/3 is prime.

(13·102120-7)/3 is prime.

(13·102260-7)/3 is prime.

(13·102423-7)/3 is prime.

Oct 6, 2007 (4th)

By Jo Yeong Uk / GGNFS

(4·10159+41)/9 = (4)1589<159> = 3709 · 3456197 · 40995079027450649<17> · C132

C132 = P48 · P85

P48 = 218551920024031168927773697661809538745109102567<48>

P85 = 3869686706115428835860198962763376764473465747888783930870949253002451781545174371711<85>

Number: 44449_159
N=845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137
  ( 132 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=218551920024031168927773697661809538745109102567 (pp48)
 r2=3869686706115428835860198962763376764473465747888783930870949253002451781545174371711 (pp85)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 27.95 hours.
Scaled time: 59.92 units (timescale=2.144).
Factorization parameters were as follows:
n: 845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137
m: 100000000000000000000000000000000
c5: 2
c0: 205
skew: 2.52
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:283793, largePrimes:5629726 encountered
Relations: rels:5660465, finalFF:657003
Max relations in full relation-set: 28
Initial matrix: 567004 x 657003 with sparse part having weight 41479342.
Pruned matrix : 495662 x 498561 with weight 28049677.
Total sieving time: 26.61 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 27.95 hours.
 --------- CPU info (if available) ----------

Oct 6, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

2·10161+3 = 2(0)1603<162> = 1645747984609139286241<22> · C141

C141 = P44 · P97

P44 = 23143371269685496536153160328427093498540901<44>

P97 = 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383<97>

Number: n
N=121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083
  ( 141 digits)
SNFS difficulty: 161 digits.
Divisors found:

Sat Oct 06 11:57:55 2007  prp44 factor: 23143371269685496536153160328427093498540901
Sat Oct 06 11:57:55 2007  prp97 factor: 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383
Sat Oct 06 11:57:55 2007  elapsed time 01:40:44 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 43.82 hours.
Scaled time: 63.63 units (timescale=1.452).
Factorization parameters were as follows:
name: KA_2_0_160_3
n: 121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083
skew: 0.68
deg: 5
c5: 20
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:203362, AFBsize:203062, largePrimes:7438144 encountered
Relations: rels:6924431, finalFF:458969
Max relations in full relation-set: 28
Initial matrix: 406490 x 458969 with sparse part having weight 41917861.
Pruned matrix : 379962 x 382058 with weight 31649775.
Total sieving time: 43.56 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 43.82 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

2·10160-9 = 1(9)1591<161> = 158642813009799873789292199<27> · C135

C135 = P48 · P87

P48 = 514829968216555250825419476063055331353216130401<48>

P87 = 244875747315362559771904473968778705005860870814895857896156971504755878896463497536209<87>

Number: n
N=126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809
  ( 135 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=514829968216555250825419476063055331353216130401 (pp48)
 r2=244875747315362559771904473968778705005860870814895857896156971504755878896463497536209 (pp87)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 39.32 hours.
Scaled time: 46.99 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_1_9_159_1
n: 126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809
type: snfs
skew: 1.35
deg: 5
c5: 2
c0: -9
m: 100000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1600001)
Primes: RFBsize:230209, AFBsize:230337, largePrimes:6544960 encountered
Relations: rels:6024747, finalFF:519640
Max relations in full relation-set: 28
Initial matrix: 460611 x 519640 with sparse part having weight 28682777.
Pruned matrix : 405415 x 407782 with weight 18445497.
Total sieving time: 35.33 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.68 hours.
Total square root time: 0.09 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 39.32 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 6, 2007 (2nd)

By Sinkiti Sibata / GGNFS

6·10160-7 = 5(9)1593<161> = 110893837864780114169227<24> · 53482456690377432712639319435401<32> · C107

C107 = P51 · P56

P51 = 125543951754463483312651367167081146619879782542807<51>

P56 = 80581749745901679359607613279455998414547734638470247237<56>

Number: 59993_160
N=10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259
  ( 107 digits)
Divisors found:
 r1=125543951754463483312651367167081146619879782542807 (pp51)
 r2=80581749745901679359607613279455998414547734638470247237 (pp56)
Version: GGNFS-0.77.1-20060513-k8
Total time: 16.09 hours.
Scaled time: 31.66 units (timescale=1.968).
Factorization parameters were as follows:
name: 59993_160
n: 10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259
skew: 8717.48
# norm 7.18e+14
c5: 34200
c4: 3446830450
c3: -49450344917839
c2: -282207816974048745
c1: 293743109705688382953
c0: -105852972657943776101076
# alpha -6.04
Y1: 1982489113
Y0: -196879813041941649923
# Murphy_E 1.63e-09
# M 8200850302644055184453131829831345367830490194178486463399401491964831823878780279463907218481306105711361
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2300001)
Primes: RFBsize:183072, AFBsize:182207, largePrimes:4770558 encountered
Relations: rels:5287342, finalFF:797494
Max relations in full relation-set: 28
Initial matrix: 365359 x 797494 with sparse part having weight 66842766.
Pruned matrix : 198399 x 200289 with weight 27225588.
Total sieving time: 15.17 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.58 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 16.09 hours.
 --------- CPU info (if available) ----------

6·10148-7 = 5(9)1473<149> = 17 · 5261 · 7069 · 20877877 · 4124979457<10> · C124

C124 = P46 · P78

P46 = 2202754157836179317307651152968047629805882079<46>

P78 = 500267040879752050179524392513061490125276212618093746534715313369595549802451<78>

Number: 59993_148
N=1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629
  ( 124 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=2202754157836179317307651152968047629805882079 (pp46)
 r2=500267040879752050179524392513061490125276212618093746534715313369595549802451 (pp78)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 38.13 hours.
Scaled time: 25.82 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_148
n: 1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629
m: 200000000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 4550001)
Primes: RFBsize:114155, AFBsize:114432, largePrimes:3074783 encountered
Relations: rels:3142613, finalFF:260671
Max relations in full relation-set: 28
Initial matrix: 228653 x 260671 with sparse part having weight 33256669.
Pruned matrix : 220290 x 221497 with weight 26947508.
Total sieving time: 35.67 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 2.06 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 38.13 hours.
 --------- CPU info (if available) ----------

Oct 6, 2007

By Bryan Koen / GGNFS

(61·10169-7)/9 = 6(7)169<170> = 679517 · 2099650316119<13> · 462133680259364512974037301324911<33> · C120

C120 = P38 · P82

P38 = 56540095809527061398275309610361450221<38>

P82 = 1818092044741429958746153841013907596909769895723120119363711217697392274661650529<82>

Number: 67777_169
N=102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909
  ( 120 digits)
Divisors found:
 r1=56540095809527061398275309610361450221 (pp38)
 r2=1818092044741429958746153841013907596909769895723120119363711217697392274661650529 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 57.70 hours.
Scaled time: 129.60 units (timescale=2.246).
Factorization parameters were as follows:
name: 67777_169
n: 102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909
skew: 105558.47
# norm 5.86e+015
c5: 3420
c4: -855817826
c3: -172975041238792
c2: 10097144255620342185
c1: 454824918396171751978112
c0: 4817673992078805183239899869
# alpha -4.79
Y1: 1203809206333
Y0: -124620494456053891335838
# Murphy_E 3.13e-010
# M 19860790920966959294374370574608201829699352757127470678651745225926909610626249915480516469649586859101696560082650191
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4350001)
Primes: RFBsize:315948, AFBsize:316478, largePrimes:7651281 encountered
Relations: rels:7683310, finalFF:711142
Max relations in full relation-set: 28
Initial matrix: 632504 x 711142 with sparse part having weight 59334766.
Pruned matrix : 568876 x 572102 with weight 42656010.
Total sieving time: 48.21 hours.
Total relation processing time: 0.50 hours.
Matrix solve time: 8.60 hours.
Time per square root: 0.39 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 57.70 hours.
 --------- CPU info (if available) ----------

Oct 5, 2007 (4th)

By Jo Yeong Uk / PRIMO

(55·102015+17)/9 is prime.

Oct 5, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

6·10151-7 = 5(9)1503<152> = 38049083 · C145

C145 = P45 · P100

P45 = 163890451242523530323685961374784914589069397<45>

P100 = 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143<100>

Number: n
N=1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771
  ( 145 digits)
SNFS difficulty: 151 digits.
Divisors found:

Fri Oct 05 09:28:44 2007  prp45 factor: 163890451242523530323685961374784914589069397
Fri Oct 05 09:28:44 2007  prp100 factor: 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143
Fri Oct 05 09:28:44 2007  elapsed time 00:54:09 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 19.99 hours.
Scaled time: 26.51 units (timescale=1.326).
Factorization parameters were as follows:
name: KA_5_9_150_3
n: 1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771
skew: 0.65
deg: 5
c5: 60
c0: -7
m: 1000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 900000)
Primes: RFBsize:216816, AFBsize:216901, largePrimes:6806958 encountered
Relations: rels:6383461, finalFF:576223
Max relations in full relation-set: 28
Initial matrix: 433784 x 576223 with sparse part having weight 36816750.
Pruned matrix : 309229 x 311461 with weight 17215851.
Total sieving time: 19.80 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 19.99 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 5, 2007 (2nd)

By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM

6·10159-7 = 5(9)1583<160> = 13 · 46099251251888935727327<23> · 24879066220185916328457524320554279793687<41> · C96

C96 = P41 · P56

P41 = 17014311483120697384989356382969398497597<41>

P56 = 23651874787979709585009977994193399030605069949949286937<56>

Thu Oct  4 21:37:14 2007  
Thu Oct  4 21:37:14 2007  
Thu Oct  4 21:37:14 2007  Msieve v. 1.28
Thu Oct  4 21:37:14 2007  random seeds: 1a77d3d5 9d0329b9
Thu Oct  4 21:37:14 2007  factoring 402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389 (96 digits)
Thu Oct  4 21:37:14 2007  commencing quadratic sieve (96-digit input)
Thu Oct  4 21:37:14 2007  using multiplier of 1
Thu Oct  4 21:37:14 2007  using 32kb Intel Core sieve core
Thu Oct  4 21:37:14 2007  sieve interval: 36 blocks of size 32768
Thu Oct  4 21:37:14 2007  processing polynomials in batches of 6
Thu Oct  4 21:37:14 2007  using a sieve bound of 2248781 (83529 primes)
Thu Oct  4 21:37:14 2007  using large prime bound of 337317150 (28 bits)
Thu Oct  4 21:37:14 2007  using double large prime bound of 2241140878991550 (43-51 bits)
Thu Oct  4 21:37:14 2007  using trial factoring cutoff of 51 bits
Thu Oct  4 21:37:14 2007  polynomial 'A' values have 12 factors
Fri Oct  5 02:05:05 2007  83793 relations (19127 full + 64666 combined from 1276886 partial), need 83625
Fri Oct  5 02:05:06 2007  begin with 1296013 relations
Fri Oct  5 02:05:07 2007  reduce to 225145 relations in 12 passes
Fri Oct  5 02:05:07 2007  attempting to read 225145 relations
Fri Oct  5 02:05:08 2007  recovered 225145 relations
Fri Oct  5 02:05:08 2007  recovered 213597 polynomials
Fri Oct  5 02:05:09 2007  attempting to build 83793 cycles
Fri Oct  5 02:05:09 2007  found 83793 cycles in 6 passes
Fri Oct  5 02:05:09 2007  distribution of cycle lengths:
Fri Oct  5 02:05:09 2007     length 1 : 19127
Fri Oct  5 02:05:09 2007     length 2 : 13665
Fri Oct  5 02:05:09 2007     length 3 : 13753
Fri Oct  5 02:05:09 2007     length 4 : 11694
Fri Oct  5 02:05:09 2007     length 5 : 8929
Fri Oct  5 02:05:09 2007     length 6 : 6357
Fri Oct  5 02:05:09 2007     length 7 : 4300
Fri Oct  5 02:05:09 2007     length 9+: 5968
Fri Oct  5 02:05:09 2007  largest cycle: 20 relations
Fri Oct  5 02:05:09 2007  matrix is 83529 x 83793 with weight 5817253 (avg 69.42/col)
Fri Oct  5 02:05:10 2007  filtering completed in 4 passes
Fri Oct  5 02:05:10 2007  matrix is 80599 x 80663 with weight 5617583 (avg 69.64/col)
Fri Oct  5 02:05:11 2007  saving the first 48 matrix rows for later
Fri Oct  5 02:05:11 2007  matrix is 80551 x 80663 with weight 4705622 (avg 58.34/col)
Fri Oct  5 02:05:11 2007  matrix includes 64 packed rows
Fri Oct  5 02:05:11 2007  using block size 32265 for processor cache size 4096 kB
Fri Oct  5 02:05:14 2007  commencing Lanczos iteration
Fri Oct  5 02:05:49 2007  lanczos halted after 1276 iterations
Fri Oct  5 02:05:49 2007  recovered 17 nontrivial dependencies
Fri Oct  5 02:05:50 2007  prp41 factor: 17014311483120697384989356382969398497597
Fri Oct  5 02:05:50 2007  prp56 factor: 23651874787979709585009977994193399030605069949949286937
Fri Oct  5 02:05:50 2007  elapsed time 04:28:36

(5·10161-23)/9 = (5)1603<161> = 181 · 9377 · 59980747 · 1556391950309252260727<22> · C126

C126 = P30 · P97

P30 = 204200339305081254682089876323<30>

P97 = 1717108343637436044836379289726170911481645229487158423846189656851215623920488863042590355402187<97>

6·10185-7 = 5(9)1843<186> = 1259 · 105094819 · 18234595094684519<17> · 496645177774564607081<21> · 91097916289552225379407273<26> · C112

C112 = P43 · P70

P43 = 1567828725851495950483147060696472797473131<43>

P70 = 3505861909643653215337674382799814173297028903124851463841838321295469<70>

Number: 59993_185
N=5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439
  ( 112 digits)
Divisors found:
 r1=1567828725851495950483147060696472797473131 (pp43)
 r2=3505861909643653215337674382799814173297028903124851463841838321295469 (pp70)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 17.45 hours.
Scaled time: 37.14 units (timescale=2.129).
Factorization parameters were as follows:
name: 59993_185
n: 5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439
skew: 31918.14
# norm 4.35e+15
c5: 49500
c4: 1148015948
c3: -102222124732255
c2: -6099585714717477637
c1: 33741417547897847981555
c0: 598316031826581667570223049
# alpha -6.53
Y1: 598253464301
Y0: -2565057913790794214018
# Murphy_E 7.81e-10
# M 3628664822376311219602672466853507363069765951502221673628741042021637214537904922189021557595578069943077896990
type: gnfs
rlim: 2800000
alim: 2800000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 70000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1400000, 2240001)
Primes: RFBsize:203362, AFBsize:203437, largePrimes:7582629 encountered
Relations: rels:7467623, finalFF:565840
Max relations in full relation-set: 28
Initial matrix: 406880 x 565840 with sparse part having weight 52660477.
Pruned matrix : 291699 x 293797 with weight 29738311.
Polynomial selection time: 0.94 hours.
Total sieving time: 15.79 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000
total time: 17.45 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 5, 2007

By Sinkiti Sibata / GGNFS

6·10142-7 = 5(9)1413<143> = 353 · 85223 · 1064743 · 17170804432778660568577<23> · C108

C108 = P32 · P76

P32 = 42191759522915775604583057626823<32>

P76 = 2585572109501371476246882696300039865583164290410873961325438433783561473999<76>

Number: 59993_142
N=109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177
  ( 108 digits)
SNFS difficulty: 142 digits.
Divisors found:
 r1=42191759522915775604583057626823 (pp32)
 r2=2585572109501371476246882696300039865583164290410873961325438433783561473999 (pp76)
Version: GGNFS-0.77.1-20060513-k8
Total time: 17.01 hours.
Scaled time: 34.09 units (timescale=2.004).
Factorization parameters were as follows:
name: 59993_142
n: 109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177
m: 10000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 2550001)
Primes: RFBsize:100021, AFBsize:99733, largePrimes:2907987 encountered
Relations: rels:2943976, finalFF:268434
Max relations in full relation-set: 28
Initial matrix: 199820 x 268434 with sparse part having weight 31091401.
Pruned matrix : 182446 x 183509 with weight 19802614.
Total sieving time: 16.40 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 0.42 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 17.01 hours.
 --------- CPU info (if available) ----------

6·10152-7 = 5(9)1513<153> = 19 · 79 · 317 · 683 · 194723 · C139

C139 = P61 · P79

P61 = 2422519199645591483038400362598333261141854085321449290981587<61>

P79 = 3913867442685506786621678329983313608259562954908441460080566565534765765237163<79>

Number: 59993_152
N=9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681
  ( 139 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2422519199645591483038400362598333261141854085321449290981587 (pp61)
 r2=3913867442685506786621678329983313608259562954908441460080566565534765765237163 (pp79)
Version: GGNFS-0.77.1-20060513-k8
Total time: 30.48 hours.
Scaled time: 59.79 units (timescale=1.962).
Factorization parameters were as follows:
name: 59993_152
n: 9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681
m: 1000000000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:175743, largePrimes:5726784 encountered
Relations: rels:5711566, finalFF:522112
Max relations in full relation-set: 28
Initial matrix: 352111 x 522112 with sparse part having weight 50262752.
Pruned matrix : 292470 x 294294 with weight 27860308.
Total sieving time: 28.94 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 30.48 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (10th)

By Jo Yeong Uk / GGNFS

6·10145-7 = 5(9)1443<146> = 1766550377<10> · 157012037513<12> · 4348276733443<13> · C113

C113 = P36 · P78

P36 = 208622310195879907337278472254444759<36>

P78 = 238459345830976112102219160803088310324167412809493635059788300420093626611189<78>

Number: 59993_145
N=49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451
  ( 113 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=208622310195879907337278472254444759 (pp36)
 r2=238459345830976112102219160803088310324167412809493635059788300420093626611189 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 10.31 hours.
Scaled time: 21.94 units (timescale=2.128).
Factorization parameters were as follows:
n: 49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451
m: 100000000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1450001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:3499162 encountered
Relations: rels:3558668, finalFF:328093
Max relations in full relation-set: 28
Initial matrix: 228633 x 328093 with sparse part having weight 33496163.
Pruned matrix : 202020 x 203227 with weight 17855809.
Total sieving time: 10.03 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 10.31 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 4, 2007 (9th)

By Robert Backstrom / GGNFS, Msieve

(17·10161-71)/9 = 1(8)1601<162> = 7 · 11 · 523 · 12553 · 892039002817<12> · C141

C141 = P70 · P71

P70 = 5517382888130356012700422947230695246102802588279510829603153154612691<70>

P71 = 75918829205014441614543498027493064480460216213141344861042989326442621<71>

Number: n
N=418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111
  ( 141 digits)
SNFS difficulty: 162 digits.
Divisors found:

Thu Oct 04 19:17:06 2007  prp70 factor: 5517382888130356012700422947230695246102802588279510829603153154612691
Thu Oct 04 19:17:06 2007  prp71 factor: 75918829205014441614543498027493064480460216213141344861042989326442621
Thu Oct 04 19:17:06 2007  elapsed time 01:24:27 (Msieve 1.26)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 56.52 hours.
Scaled time: 73.71 units (timescale=1.304).
Factorization parameters were as follows:
name: KA_1_8_160_1
n: 418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111
skew: 0.84
deg: 5
c5: 170
c0: -71
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2300000)
Primes: RFBsize:216816, AFBsize:216842, largePrimes:7378545 encountered
Relations: rels:6867652, finalFF:491420
Max relations in full relation-set: 28
Initial matrix: 433725 x 491420 with sparse part having weight 41722542.
Pruned matrix : 394644 x 396876 with weight 30589920.
Total sieving time: 55.53 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.74 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 56.52 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 4, 2007 (8th)

By Sinkiti Sibata / GGNFS

6·10132-7 = 5(9)1313<133> = 17 · 31397 · 60607 · 17658261422573<14> · C110

C110 = P45 · P65

P45 = 157220545256202605499721340161299887750890477<45>

P65 = 66808873437291415726408144788722762650560407722248850407211168531<65>

Number: 59993_132
N=10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287
  ( 110 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=157220545256202605499721340161299887750890477 (pp45)
 r2=66808873437291415726408144788722762650560407722248850407211168531 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.23 hours.
Scaled time: 5.57 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_132
n: 10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287
m: 100000000000000000000000000
c5: 600
c0: -7
skew: 0.41
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1300001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1546399 encountered
Relations: rels:1543966, finalFF:157068
Max relations in full relation-set: 28
Initial matrix: 127540 x 157068 with sparse part having weight 14736218.
Pruned matrix : 120366 x 121067 with weight 9730311.
Total sieving time: 7.77 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.30 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 8.23 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (7th)

By Jo Yeong Uk / GMP-ECM

6·10159-7 = 5(9)1583<160> = 13 · 46099251251888935727327<23> · C137

C137 = P41 · C96

P41 = 24879066220185916328457524320554279793687<41>

C96 = [402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389<96>]

Oct 4, 2007 (6th)

By Sinkiti Sibata / GGNFS

6·10135-7 = 5(9)1343<136> = 13 · 414413481743<12> · 36564792200396563<17> · C107

C107 = P43 · P65

P43 = 1126059761985818701739729351936313997694323<43>

P65 = 27048891575232108774848633209666793723302095208678124558846257723<65>

Number: 59993_135
N=30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529
  ( 107 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=1126059761985818701739729351936313997694323 (pp43)
 r2=27048891575232108774848633209666793723302095208678124558846257723 (pp65)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.79 hours.
Scaled time: 15.48 units (timescale=1.986).
Factorization parameters were as follows:
name: 59993_135
n: 30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529
m: 1000000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63888, largePrimes:1589402 encountered
Relations: rels:1605693, finalFF:183280
Max relations in full relation-set: 28
Initial matrix: 142452 x 183280 with sparse part having weight 16657071.
Pruned matrix : 130634 x 131410 with weight 10249543.
Total sieving time: 7.56 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.79 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007 (5th)

By Robert Backstrom / GGNFS, Msieve

(73·10158-1)/9 = 8(1)158<159> = 26530558669965200379377507<26> · C134

C134 = P54 · P81

P54 = 212107814191998704725420221052699981457889085100997601<54>

P81 = 144137600146936537044461384043301075248536512091523845543692062426638973343118573<81>

Number: n
N=30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373
  ( 134 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Oct 04 16:13:30 2007  prp54 factor: 212107814191998704725420221052699981457889085100997601
Thu Oct 04 16:13:30 2007  prp81 factor: 144137600146936537044461384043301075248536512091523845543692062426638973343118573
Thu Oct 04 16:13:30 2007  elapsed time 01:50:08 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 50.48 hours.
Scaled time: 60.38 units (timescale=1.196).
Factorization parameters were as follows:
name: KA_8_1_158
n: 30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373
type: snfs
skew: 0.11
deg: 5
c5: 73000
c0: -1
m: 10000000000000000000000000000000
rlim: 3200000
alim: 3200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2100000)
Primes: RFBsize:230209, AFBsize:230497, largePrimes:7060727 encountered
Relations: rels:6539168, finalFF:541829
Max relations in full relation-set: 28
Initial matrix: 460773 x 541829 with sparse part having weight 34927383.
Pruned matrix : 393656 x 396023 with weight 22051476.
Total sieving time: 50.21 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000
total time: 50.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Oct 4, 2007 (4th)

By Jo Yeong Uk / PRIMO

(38·102043+61)/9 is prime.

Oct 4, 2007 (3rd)

By Jo Yeong Uk / GGNFS, GMP-ECM

6·10131-7 = 5(9)1303<132> = 53 · 169607 · C125

C125 = P59 · P67

P59 = 12872498163753083570298872692434111691304047437203023579603<59>

P67 = 5185238891853061753866196726218370889062130742679403097113868915761<67>

Number: 59993_131
N=66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883
  ( 125 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=12872498163753083570298872692434111691304047437203023579603 (pp59)
 r2=5185238891853061753866196726218370889062130742679403097113868915761 (pp67)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.84 hours.
Scaled time: 6.06 units (timescale=2.135).
Factorization parameters were as follows:
n: 66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883
m: 100000000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78436, largePrimes:1617139 encountered
Relations: rels:1662134, finalFF:216620
Max relations in full relation-set: 28
Initial matrix: 157001 x 216620 with sparse part having weight 13625699.
Pruned matrix : 135783 x 136632 with weight 6867620.
Total sieving time: 2.75 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.04 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.84 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(86·10158+31)/9 = 9(5)1579<159> = 72 · 1657 · 48530561 · 369122094120620012071<21> · C126

C126 = P49 · P78

P49 = 3016236812826278990601156748919149544847529142617<49>

P78 = 217814388128186210847141219564082430746842862444289701637257172552121621783169<78>

Number: 95559_158
N=656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273
  ( 126 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=3016236812826278990601156748919149544847529142617 (pp49)
 r2=217814388128186210847141219564082430746842862444289701637257172552121621783169 (pp78)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 36.34 hours.
Scaled time: 76.82 units (timescale=2.114).
Factorization parameters were as follows:
n: 656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273
m: 100000000000000000000000000000000
c5: 43
c0: 1550
skew: 2.05
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4100001)
Primes: RFBsize:283146, AFBsize:282493, largePrimes:5699146 encountered
Relations: rels:5718310, finalFF:642706
Max relations in full relation-set: 28
Initial matrix: 565705 x 642706 with sparse part having weight 43053754.
Pruned matrix : 513370 x 516262 with weight 31561464.
Total sieving time: 34.80 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.38 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 36.34 hours.
 --------- CPU info (if available) ----------
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10141-7 = 5(9)1403<142> = 13 · 1447583 · 84331879 · C127

C127 = P37 · P90

P37 = 6476031936152650611823116269070611627<37>

P90 = 583799427952449996104077409330623614593075799711097271574870756751412606331718775669681999<90>

Oct 4, 2007 (2nd)

By Sinkiti Sibata / Msieve, GGNFS

6·10127-7 = 5(9)1263<128> = 343127 · 582525896334758811474813322548179<33> · C90

C90 = P42 · P48

P42 = 538379064288744086953750328027856177081161<42>

P48 = 557561730154771569560097260837268094018249256461<48>

Wed Oct 03 15:19:24 2007  Msieve v. 1.26
Wed Oct 03 15:19:24 2007  random seeds: ee28c423 6aa74c56
Wed Oct 03 15:19:24 2007  factoring 300179562563939145447468893460840371948057004209201877467016267991673377504711137500631221 (90 digits)
Wed Oct 03 15:19:25 2007  commencing quadratic sieve (90-digit input)
Wed Oct 03 15:19:26 2007  using multiplier of 5
Wed Oct 03 15:19:26 2007  using 64kb Pentium 2 sieve core
Wed Oct 03 15:19:26 2007  sieve interval: 18 blocks of size 65536
Wed Oct 03 15:19:26 2007  processing polynomials in batches of 6
Wed Oct 03 15:19:26 2007  using a sieve bound of 1579619 (60000 primes)
Wed Oct 03 15:19:26 2007  using large prime bound of 126369520 (26 bits)
Wed Oct 03 15:19:26 2007  using double large prime bound of 382786039401520 (42-49 bits)
Wed Oct 03 15:19:26 2007  using trial factoring cutoff of 49 bits
Wed Oct 03 15:19:26 2007  polynomial 'A' values have 12 factors
Thu Oct 04 01:00:41 2007  60563 relations (16228 full + 44335 combined from 633835 partial), need 60096
Thu Oct 04 01:00:52 2007  begin with 650063 relations
Thu Oct 04 01:01:24 2007  reduce to 146669 relations in 10 passes
Thu Oct 04 01:01:24 2007  attempting to read 146669 relations
Thu Oct 04 01:01:38 2007  recovered 146669 relations
Thu Oct 04 01:01:38 2007  recovered 124245 polynomials
Thu Oct 04 01:02:13 2007  attempting to build 60563 cycles
Thu Oct 04 01:02:14 2007  found 60563 cycles in 6 passes
Thu Oct 04 01:02:17 2007  distribution of cycle lengths:
Thu Oct 04 01:02:17 2007     length 1 : 16228
Thu Oct 04 01:02:17 2007     length 2 : 11907
Thu Oct 04 01:02:17 2007     length 3 : 10599
Thu Oct 04 01:02:17 2007     length 4 : 8065
Thu Oct 04 01:02:17 2007     length 5 : 5670
Thu Oct 04 01:02:17 2007     length 6 : 3510
Thu Oct 04 01:02:18 2007     length 7 : 2163
Thu Oct 04 01:02:18 2007     length 9+: 2421
Thu Oct 04 01:02:18 2007  largest cycle: 19 relations
Thu Oct 04 01:02:20 2007  matrix is 60000 x 60563 with weight 3581602 (avg 59.14/col)
Thu Oct 04 01:02:25 2007  filtering completed in 3 passes
Thu Oct 04 01:02:25 2007  matrix is 55899 x 55963 with weight 3306276 (avg 59.08/col)
Thu Oct 04 01:02:28 2007  saving the first 48 matrix rows for later
Thu Oct 04 01:02:28 2007  matrix is 55851 x 55963 with weight 2583325 (avg 46.16/col)
Thu Oct 04 01:02:28 2007  matrix includes 64 packed rows
Thu Oct 04 01:02:28 2007  using block size 10922 for processor cache size 256 kB
Thu Oct 04 01:02:29 2007  commencing Lanczos iteration
Thu Oct 04 01:06:36 2007  lanczos halted after 885 iterations
Thu Oct 04 01:06:37 2007  recovered 17 nontrivial dependencies
Thu Oct 04 01:07:05 2007  prp42 factor: 538379064288744086953750328027856177081161
Thu Oct 04 01:07:05 2007  prp48 factor: 557561730154771569560097260837268094018249256461
Thu Oct 04 01:07:05 2007  elapsed time 09:47:41

6·10123-7 = 5(9)1223<124> = 132 · 1660493 · C116

C116 = P45 · P71

P45 = 419726743015322283340796841866026105998611897<45>

P71 = 50940224585810878707118381444742680923300871417714179798205170107648957<71>

Number: 59993_123
N=21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429
  ( 116 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=419726743015322283340796841866026105998611897 (pp45)
 r2=50940224585810878707118381444742680923300871417714179798205170107648957 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.06 hours.
Scaled time: 2.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_123
n: 21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429
m: 2000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64283, largePrimes:2107214 encountered
Relations: rels:2116210, finalFF:152007
Max relations in full relation-set: 28
Initial matrix: 113447 x 152007 with sparse part having weight 13697410.
Pruned matrix : 103414 x 104045 with weight 7180122.
Total sieving time: 2.74 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------

6·10128-7 = 5(9)1273<129> = 47 · 157 · 8893 · C121

C121 = P35 · P42 · P46

P35 = 45062760365254252417196977668457049<35>

P42 = 107331866482129355939909099089742932497167<42>

P46 = 1890422922086710862023492300837255153472513593<46>

Number: 59993_128
N=9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519
  ( 121 digits)
SNFS difficulty: 129 digits.
Divisors found:
 r1=45062760365254252417196977668457049 (pp35)
 r2=107331866482129355939909099089742932497167 (pp42)
 r3=1890422922086710862023492300837255153472513593 (pp46)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.27 hours.
Scaled time: 3.57 units (timescale=0.677).
Factorization parameters were as follows:
name: 59993_128
n: 9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519
m: 20000000000000000000000000
c5: 375
c0: -14
skew: 0.52
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 950001)
Primes: RFBsize:63951, AFBsize:64283, largePrimes:1484571 encountered
Relations: rels:1488026, finalFF:176006
Max relations in full relation-set: 28
Initial matrix: 128300 x 176006 with sparse part having weight 12189392.
Pruned matrix : 113811 x 114516 with weight 6184426.
Total sieving time: 4.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.20 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 5.27 hours.
 --------- CPU info (if available) ----------

(37·10161-1)/9 = 4(1)161<162> = 3 · 41 · 1307 · 2075820356295079<16> · 1262790142328673659357<22> · C120

C120 = P38 · P83

P38 = 37343365815058483964552266720070550859<38>

P83 = 26124266598228484286956693574306899716358742145356317706463821362063741663610307863<83>

Number: 41111_161
N=975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317
  ( 120 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=37343365815058483964552266720070550859 (pp38)
 r2=26124266598228484286956693574306899716358742145356317706463821362063741663610307863 (pp83)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.17 hours.
Scaled time: 146.20 units (timescale=1.998).
Factorization parameters were as follows:
name: 41111_161
n: 975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317
m: 100000000000000000000000000000000
c5: 370
c0: -1
skew: 0.31
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:315496, largePrimes:5801398 encountered
Relations: rels:5906549, finalFF:737188
Max relations in full relation-set: 28
Initial matrix: 631511 x 737188 with sparse part having weight 47432370.
Pruned matrix : 551065 x 554286 with weight 33711664.
Total sieving time: 69.23 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.52 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.17 hours.
 --------- CPU info (if available) ----------

Oct 4, 2007

By Robert Backstrom / Msieve, GGNFS

6·10155-7 = 5(9)1543<156> = 9151759 · 44509450084691841113<20> · 1276610766484719268151<22> · 1340426558177838497399939<25> · C84

C84 = P36 · P49

P36 = 217264834889735630458321389261532721<36>

P49 = 3961899731258636703690742682913482426977474823891<49>

Wed Oct 03 15:36:33 2007  Msieve v. 1.26
Wed Oct 03 15:36:33 2007  random seeds: 965c87cc d2ef83b1
Wed Oct 03 15:36:33 2007  factoring 860781490961595669697733605784670171336258336753794416470408536041356301000209037411 (84 digits)
Wed Oct 03 15:36:34 2007  commencing quadratic sieve (84-digit input)
Wed Oct 03 15:36:34 2007  using multiplier of 1
Wed Oct 03 15:36:34 2007  using 64kb Opteron sieve core
Wed Oct 03 15:36:34 2007  sieve interval: 6 blocks of size 65536
Wed Oct 03 15:36:34 2007  processing polynomials in batches of 17
Wed Oct 03 15:36:34 2007  using a sieve bound of 1409117 (53799 primes)
Wed Oct 03 15:36:34 2007  using large prime bound of 119774945 (26 bits)
Wed Oct 03 15:36:34 2007  using trial factoring cutoff of 27 bits
Wed Oct 03 15:36:34 2007  polynomial 'A' values have 11 factors
Wed Oct 03 16:07:49 2007  54021 relations (27210 full + 26811 combined from 284568 partial), need 53895
Wed Oct 03 16:07:50 2007  begin with 311778 relations
Wed Oct 03 16:07:50 2007  reduce to 77387 relations in 2 passes
Wed Oct 03 16:07:50 2007  attempting to read 77387 relations
Wed Oct 03 16:07:51 2007  recovered 77387 relations
Wed Oct 03 16:07:51 2007  recovered 71517 polynomials
Wed Oct 03 16:07:51 2007  attempting to build 54021 cycles
Wed Oct 03 16:07:51 2007  found 54021 cycles in 1 passes
Wed Oct 03 16:07:51 2007  distribution of cycle lengths:
Wed Oct 03 16:07:51 2007     length 1 : 27210
Wed Oct 03 16:07:51 2007     length 2 : 26811
Wed Oct 03 16:07:51 2007  largest cycle: 2 relations
Wed Oct 03 16:07:51 2007  matrix is 53799 x 54021 with weight 1755888 (avg 32.50/col)
Wed Oct 03 16:07:51 2007  filtering completed in 4 passes
Wed Oct 03 16:07:51 2007  matrix is 46702 x 46766 with weight 1491481 (avg 31.89/col)
Wed Oct 03 16:07:52 2007  saving the first 48 matrix rows for later
Wed Oct 03 16:07:52 2007  matrix is 46654 x 46766 with weight 1088600 (avg 23.28/col)
Wed Oct 03 16:07:52 2007  matrix includes 64 packed rows
Wed Oct 03 16:07:52 2007  commencing Lanczos iteration
Wed Oct 03 16:08:46 2007  lanczos halted after 739 iterations
Wed Oct 03 16:08:47 2007  recovered 6 nontrivial dependencies
Wed Oct 03 16:08:47 2007  prp36 factor: 217264834889735630458321389261532721
Wed Oct 03 16:08:47 2007  prp49 factor: 3961899731258636703690742682913482426977474823891
Wed Oct 03 16:08:47 2007  elapsed time 00:32:14

(31·10158-13)/9 = 3(4)1573<159> = 7 · 127 · 78148787 · 4740691519332947<16> · C133

C133 = P41 · P92

P41 = 58339351804238222158586791687727596860143<41>

P92 = 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581<92>

Number: n
N=1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083
  ( 133 digits)
SNFS difficulty: 159 digits.
Divisors found:

Thu Oct 04 02:14:25 2007  prp41 factor: 58339351804238222158586791687727596860143
Thu Oct 04 02:14:25 2007  prp92 factor: 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581
Thu Oct 04 02:14:25 2007  elapsed time 01:06:27 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 42.50 hours.
Scaled time: 61.62 units (timescale=1.450).
Factorization parameters were as follows:
name: KA_3_4_157_3
n: 1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083
skew: 0.21
deg: 5
c5: 31000
c0: -13
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1800000)
Primes: RFBsize:183072, AFBsize:182522, largePrimes:7262660 encountered
Relations: rels:6751741, finalFF:444988
Max relations in full relation-set: 28
Initial matrix: 365661 x 444988 with sparse part having weight 40908464.
Pruned matrix : 320686 x 322578 with weight 26986987.
Total sieving time: 42.25 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 42.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(82·10160-1)/9 = 9(1)160<161> = 1183282325293<13> · 1398206145473<13> · C137

C137 = P59 · P79

P59 = 22056688036771319510990392077888123590637483193298813665679<59>

P79 = 2496729301249539633152615904948407043950273202114296465618776682890249002888781<79>

Number: n
N=55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299
  ( 137 digits)
SNFS difficulty: 161 digits.
Divisors found:

Thu Oct 04 02:36:45 2007  prp59 factor: 22056688036771319510990392077888123590637483193298813665679
Thu Oct 04 02:36:45 2007  prp79 factor: 2496729301249539633152615904948407043950273202114296465618776682890249002888781
Thu Oct 04 02:36:45 2007  elapsed time 01:27:51 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 36.40 hours.
Scaled time: 48.16 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_9_1_160
n: 55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299
skew: 0.41
deg: 5
c5: 82
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:250150, AFBsize:250142, largePrimes:7161867 encountered
Relations: rels:6671064, finalFF:562452
Max relations in full relation-set: 28
Initial matrix: 500360 x 562452 with sparse part having weight 39726103.
Pruned matrix : 448099 x 450664 with weight 25765807.
Total sieving time: 36.16 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 36.40 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

6·10133-7 = 5(9)1323<134> = 419 · C132

C132 = P39 · P40 · P53

P39 = 803784771613572434432727851402219930947<39>

P40 = 8211994164161688590117664996602372379877<40>

P53 = 21694458850171435203820744840123411555745339465862013<53>

Number: n
N=143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747
  ( 132 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=803784771613572434432727851402219930947 (pp39)
 r2=8211994164161688590117664996602372379877 (pp40)
 r3=21694458850171435203820744840123411555745339465862013 (pp53)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 4.50 hours.
Scaled time: 6.52 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_5_9_132_3
n: 143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747
skew: 0.52
deg: 5
c5: 375
c0: -14
m: 200000000000000000000000000
type: snfs
rlim: 1200000
alim: 1200000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 550001)
Primes: RFBsize:92938, AFBsize:93099, largePrimes:5807271 encountered
Relations: rels:5166926, finalFF:262402
Max relations in full relation-set: 28
Initial matrix: 186103 x 262402 with sparse part having weight 21646923.
Pruned matrix : 153360 x 154354 with weight 9710538.
Total sieving time: 3.84 hours.
Total relation processing time: 0.13 hours.
Matrix solve time: 0.40 hours.
Total square root time: 0.12 hours, sqrts: 4.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000
total time: 4.50 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

6·10140-7 = 5(9)1393<141> = 118447393 · C133

C133 = P39 · P95

P39 = 488302592269751645844131141513207371459<39>

P95 = 10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739<95>

Number: n
N=5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201
  ( 133 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=488302592269751645844131141513207371459 (pp39)
 r2=10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739 (pp95)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 7.15 hours.
Scaled time: 9.46 units (timescale=1.322).
Factorization parameters were as follows:
name: KA_5_9_139_3
n: 5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201
skew: 1.03
deg: 5
c5: 6
c0: -7
m: 10000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 850001)
Primes: RFBsize:114155, AFBsize:114412, largePrimes:6395094 encountered
Relations: rels:5722594, finalFF:311875
Max relations in full relation-set: 48
Initial matrix: 228633 x 311875 with sparse part having weight 33205990.
Pruned matrix : 195644 x 196851 with weight 15042093.
Total sieving time: 5.86 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.01 hours.
Total square root time: 0.04 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000
total time: 7.15 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 3, 2007 (5th)

By suberi / PRIMO

(13·102563+41)/9 is prime.

(13·102641+41)/9 is prime.

Oct 3, 2007 (4th)

By Robert Backstrom / GMP-ECM, Msieve

6·10125-7 = 5(9)1243<126> = 23 · 3623 · 10966621 · C114

C114 = P38 · P77

P38 = 50636596327829583320839536142290785563<38>

P77 = 12966349985343467300064590701602747532440337222241547532187032604088384653879<77>

6·10157-7 = 5(9)1563<158> = 53 · 97 · 739 · 1091 · 519487 · 709369890512947561<18> · 1398747574182377711176049107<28> · C98

C98 = P35 · P64

P35 = 22320341571287862440791180961911537<35>

P64 = 1258191770139023959637271001787399781177095229292345787867966729<64>

Wed Oct 03 16:19:38 2007  Msieve v. 1.26
Wed Oct 03 16:19:38 2007  random seeds: b8709f30 80cbbce4
Wed Oct 03 16:19:38 2007  factoring 28083270071686319089592401973395533416884243987372294079591744321397845903861895820202049357252473 (98 digits)
Wed Oct 03 16:19:38 2007  commencing quadratic sieve (98-digit input)
Wed Oct 03 16:19:38 2007  using multiplier of 1
Wed Oct 03 16:19:38 2007  using 64kb Opteron sieve core
Wed Oct 03 16:19:38 2007  sieve interval: 18 blocks of size 65536
Wed Oct 03 16:19:38 2007  processing polynomials in batches of 6
Wed Oct 03 16:19:38 2007  using a sieve bound of 2473301 (90543 primes)
Wed Oct 03 16:19:38 2007  using large prime bound of 370995150 (28 bits)
Wed Oct 03 16:19:38 2007  using double large prime bound of 2659884601469100 (43-52 bits)
Wed Oct 03 16:19:38 2007  using trial factoring cutoff of 52 bits
Wed Oct 03 16:19:38 2007  polynomial 'A' values have 13 factors
Wed Oct 03 23:18:45 2007  90718 relations (21893 full + 68825 combined from 1364772 partial), need 90639
Wed Oct 03 23:18:47 2007  begin with 1386665 relations
Wed Oct 03 23:18:48 2007  reduce to 237587 relations in 12 passes
Wed Oct 03 23:18:48 2007  attempting to read 237587 relations
Wed Oct 03 23:18:52 2007  recovered 237587 relations
Wed Oct 03 23:18:52 2007  recovered 225257 polynomials
Wed Oct 03 23:18:52 2007  attempting to build 90718 cycles
Wed Oct 03 23:18:53 2007  found 90718 cycles in 6 passes
Wed Oct 03 23:18:53 2007  distribution of cycle lengths:
Wed Oct 03 23:18:53 2007     length 1 : 21893
Wed Oct 03 23:18:53 2007     length 2 : 15660
Wed Oct 03 23:18:53 2007     length 3 : 15243
Wed Oct 03 23:18:53 2007     length 4 : 12310
Wed Oct 03 23:18:53 2007     length 5 : 9641
Wed Oct 03 23:18:53 2007     length 6 : 6118
Wed Oct 03 23:18:53 2007     length 7 : 4176
Wed Oct 03 23:18:53 2007     length 9+: 5677
Wed Oct 03 23:18:53 2007  largest cycle: 19 relations
Wed Oct 03 23:18:53 2007  matrix is 90543 x 90718 with weight 6047781 (avg 66.67/col)
Wed Oct 03 23:18:54 2007  filtering completed in 3 passes
Wed Oct 03 23:18:54 2007  matrix is 86539 x 86603 with weight 5807038 (avg 67.05/col)
Wed Oct 03 23:18:55 2007  saving the first 48 matrix rows for later
Wed Oct 03 23:18:55 2007  matrix is 86491 x 86603 with weight 4591383 (avg 53.02/col)
Wed Oct 03 23:18:55 2007  matrix includes 64 packed rows
Wed Oct 03 23:18:55 2007  using block size 21845 for processor cache size 512 kB
Wed Oct 03 23:18:55 2007  commencing Lanczos iteration
Wed Oct 03 23:20:21 2007  lanczos halted after 1370 iterations
Wed Oct 03 23:20:21 2007  recovered 17 nontrivial dependencies
Wed Oct 03 23:20:22 2007  prp35 factor: 22320341571287862440791180961911537
Wed Oct 03 23:20:22 2007  prp64 factor: 1258191770139023959637271001787399781177095229292345787867966729
Wed Oct 03 23:20:22 2007  elapsed time 07:00:44

Oct 3, 2007 (3rd)

By Sinkiti Sibata / Msieve v. 1.26, GGNFS

6·10153-7 = 5(9)1523<154> = 13 · 139747 · 41191413729044567<17> · 28576336929599376517741<23> · 1025244729230700913218569<25> · C85

C85 = P42 · P43

P42 = 356746994819799697074718391780142365509993<42>

P43 = 7671217220429161293573234558957602035904237<43>

Wed Oct 03 14:47:30 2007  Msieve v. 1.26
Wed Oct 03 14:47:30 2007  random seeds: 460178a0 145787d5
Wed Oct 03 14:47:30 2007  factoring 2736683689998000234925592599907106848522357423838373040075488018168277701797414540341 (85 digits)
Wed Oct 03 14:47:30 2007  commencing quadratic sieve (85-digit input)
Wed Oct 03 14:47:31 2007  using multiplier of 21
Wed Oct 03 14:47:31 2007  using 64kb Pentium 2 sieve core
Wed Oct 03 14:47:31 2007  sieve interval: 6 blocks of size 65536
Wed Oct 03 14:47:31 2007  processing polynomials in batches of 17
Wed Oct 03 14:47:31 2007  using a sieve bound of 1425547 (54412 primes)
Wed Oct 03 14:47:31 2007  using large prime bound of 116894854 (26 bits)
Wed Oct 03 14:47:31 2007  using double large prime bound of 332683806537686 (41-49 bits)
Wed Oct 03 14:47:31 2007  using trial factoring cutoff of 49 bits
Wed Oct 03 14:47:31 2007  polynomial 'A' values have 11 factors
Wed Oct 03 19:20:05 2007  54584 relations (15772 full + 38812 combined from 574026 partial), need 54508
Wed Oct 03 19:20:07 2007  begin with 589798 relations
Wed Oct 03 19:20:09 2007  reduce to 128585 relations in 11 passes
Wed Oct 03 19:20:09 2007  attempting to read 128585 relations
Wed Oct 03 19:20:14 2007  recovered 128585 relations
Wed Oct 03 19:20:14 2007  recovered 109292 polynomials
Wed Oct 03 19:20:15 2007  attempting to build 54584 cycles
Wed Oct 03 19:20:15 2007  found 54584 cycles in 5 passes
Wed Oct 03 19:20:19 2007  distribution of cycle lengths:
Wed Oct 03 19:20:19 2007     length 1 : 15772
Wed Oct 03 19:20:19 2007     length 2 : 11077
Wed Oct 03 19:20:19 2007     length 3 : 9717
Wed Oct 03 19:20:19 2007     length 4 : 6987
Wed Oct 03 19:20:19 2007     length 5 : 4720
Wed Oct 03 19:20:19 2007     length 6 : 2838
Wed Oct 03 19:20:19 2007     length 7 : 1656
Wed Oct 03 19:20:19 2007     length 9+: 1817
Wed Oct 03 19:20:19 2007  largest cycle: 17 relations
Wed Oct 03 19:20:20 2007  matrix is 54412 x 54584 with weight 2905977 (avg 53.24/col)
Wed Oct 03 19:20:22 2007  filtering completed in 3 passes
Wed Oct 03 19:20:22 2007  matrix is 49748 x 49812 with weight 2673600 (avg 53.67/col)
Wed Oct 03 19:20:24 2007  saving the first 48 matrix rows for later
Wed Oct 03 19:20:24 2007  matrix is 49700 x 49812 with weight 1993341 (avg 40.02/col)
Wed Oct 03 19:20:24 2007  matrix includes 64 packed rows
Wed Oct 03 19:20:24 2007  commencing Lanczos iteration
Wed Oct 03 19:25:55 2007  lanczos halted after 787 iterations
Wed Oct 03 19:25:56 2007  recovered 19 nontrivial dependencies
Wed Oct 03 19:25:59 2007  prp42 factor: 356746994819799697074718391780142365509993
Wed Oct 03 19:25:59 2007  prp43 factor: 7671217220429161293573234558957602035904237
Wed Oct 03 19:25:59 2007  elapsed time 04:38:29

8·10160-3 = 7(9)1597<161> = 432 · 431 · 48859 · 4647456722639<13> · 626627965062020591<18> · C120

C120 = P47 · P74

P47 = 14692417462058974457446490078935236626410262041<47>

P74 = 48018970537507694295810504240418883922125431142142818767721221650978656473<74>

Number: 79997_160
N=705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393
  ( 120 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=14692417462058974457446490078935236626410262041 (pp47)
 r2=48018970537507694295810504240418883922125431142142818767721221650978656473 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 60.89 hours.
Scaled time: 41.22 units (timescale=0.677).
Factorization parameters were as follows:
name: 79997_160
n: 705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393
m: 100000000000000000000000000000000
c5: 8
c0: -3
skew: 0.82
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283367, largePrimes:5694153 encountered
Relations: rels:5794190, finalFF:713570
Max relations in full relation-set: 28
Initial matrix: 566578 x 713570 with sparse part having weight 44691099.
Pruned matrix : 447630 x 450526 with weight 27726964.
Total sieving time: 52.59 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 7.83 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 60.89 hours.
 --------- CPU info (if available) ----------

Oct 3, 2007 (2nd)

By Jo Yeong Uk / GGNFS

6·10111-7 = 5(9)1103<112> = 13 · 2423 · C108

C108 = P51 · P57

P51 = 360964079692659801539218828060656161476910423250161<51>

P57 = 527704135252280213728502010679882140961843051369612566587<57>

Number: 59993_111
N=190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507
  ( 108 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=360964079692659801539218828060656161476910423250161 (pp51)
 r2=527704135252280213728502010679882140961843051369612566587 (pp57)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.71 hours.
Scaled time: 1.53 units (timescale=2.145).
Factorization parameters were as follows:
n: 190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507
m: 10000000000000000000000
c5: 60
c0: -7
skew: 0.65
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 320001)
Primes: RFBsize:30757, AFBsize:30694, largePrimes:1074870 encountered
Relations: rels:1007128, finalFF:101389
Max relations in full relation-set: 28
Initial matrix: 61518 x 101389 with sparse part having weight 4955758.
Pruned matrix : 50735 x 51106 with weight 1760939.
Total sieving time: 0.68 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.00 hours.
Time per square root: 0.00 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000
total time: 0.71 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10122-7 = 5(9)1213<123> = 29 · C122

C122 = P38 · P84

P38 = 68004493287578401111324018574258290351<38>

P84 = 304239531422152873078652750157120871113171209374964566110469309352350285844274312067<84>

Number: 59993_122
N=20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517
  ( 122 digits)
SNFS difficulty: 123 digits.
Divisors found:
 r1=68004493287578401111324018574258290351 (pp38)
 r2=304239531422152873078652750157120871113171209374964566110469309352350285844274312067 (pp84)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 1.52 hours.
Scaled time: 3.26 units (timescale=2.144).
Factorization parameters were as follows:
n: 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517
m: 2000000000000000000000000
c5: 75
c0: -28
skew: 0.82
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [400000, 720001)
Primes: RFBsize:63951, AFBsize:63523, largePrimes:1389910 encountered
Relations: rels:1372098, finalFF:158574
Max relations in full relation-set: 28
Initial matrix: 127540 x 158574 with sparse part having weight 7799698.
Pruned matrix : 114540 x 115241 with weight 4337757.
Total sieving time: 1.46 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.03 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000
total time: 1.52 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10137-7 = 5(9)1363<138> = C138

C138 = P44 · P95

P44 = 11930304707794017951010060929038611787637529<44>

P95 = 50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017<95>

Number: 59993_137
N=599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
  ( 138 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=11930304707794017951010060929038611787637529 (pp44)
 r2=50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017 (pp95)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 4.81 hours.
Scaled time: 10.24 units (timescale=2.129).
Factorization parameters were as follows:
n: 599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993
m: 2000000000000000000000000000
c5: 75
c0: -28
skew: 0.82
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1600001)
Primes: RFBsize:107126, AFBsize:106878, largePrimes:2399412 encountered
Relations: rels:2552130, finalFF:267534
Max relations in full relation-set: 28
Initial matrix: 214070 x 267534 with sparse part having weight 24798377.
Pruned matrix : 197717 x 198851 with weight 15730218.
Total sieving time: 4.58 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 4.81 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

6·10130-7 = 5(9)1293<131> = 3581 · 11927683 · 77492399487775327777<20> · C101

C101 = P41 · P60

P41 = 41741913374238084153759348799228096820219<41>

P60 = 434269551129510598310111242531747787622152307167204480286557<60>

Number: 59993_130
N=18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983
  ( 101 digits)
SNFS difficulty: 130 digits.
Divisors found:
 r1=41741913374238084153759348799228096820219 (pp41)
 r2=434269551129510598310111242531747787622152307167204480286557 (pp60)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.61 hours.
Scaled time: 5.60 units (timescale=2.145).
Factorization parameters were as follows:
n: 18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983
m: 100000000000000000000000000
c5: 6
c0: -7
skew: 1.03
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1050001)
Primes: RFBsize:78498, AFBsize:78516, largePrimes:1562106 encountered
Relations: rels:1575211, finalFF:190100
Max relations in full relation-set: 28
Initial matrix: 157080 x 190100 with sparse part having weight 11252053.
Pruned matrix : 145006 x 145855 with weight 6877487.
Total sieving time: 2.51 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.61 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 3, 2007

The factor table of 599...993 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 1030.

Oct 2, 2007 (3rd)

By Jo Yeong Uk / GGNFS

4·10158+7 = 4(0)1577<159> = 11 · 37 · 12007 · 64184521 · 801992267819<12> · C133

C133 = P47 · P86

P47 = 40168232933255472863199410867005086259141899511<47>

P86 = 39586568659768781756154959633375249919813838935426658359620291935490219828230564916987<86>

Number: 40007_158
N=1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357
  ( 133 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=40168232933255472863199410867005086259141899511 (pp47)
 r2=39586568659768781756154959633375249919813838935426658359620291935490219828230564916987 (pp86)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.50 hours.
Scaled time: 52.33 units (timescale=2.136).
Factorization parameters were as follows:
n: 1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357
m: 100000000000000000000000000000000
c5: 1
c0: 175
skew: 2.81
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3400001)
Primes: RFBsize:283146, AFBsize:283052, largePrimes:5731305 encountered
Relations: rels:5871089, finalFF:749665
Max relations in full relation-set: 28
Initial matrix: 566262 x 749665 with sparse part having weight 45967150.
Pruned matrix : 415205 x 418100 with weight 27576167.
Total sieving time: 23.50 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 24.50 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 2, 2007 (2nd)

By Sinkiti Sibata / GGNFS

(5·10161+7)/3 = 1(6)1609<162> = 570049 · 111524293 · 148946655411315836615893811933<30> · C119

C119 = P59 · P60

P59 = 19431998449239836919883891499392364284154878753810288198627<59>

P60 = 905771934729220258028194158863173230204066471520265077490687<60>

Number: 16669_161
N=17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749
  ( 119 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=19431998449239836919883891499392364284154878753810288198627 (pp59)
 r2=905771934729220258028194158863173230204066471520265077490687 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 73.18 hours.
Scaled time: 146.44 units (timescale=2.001).
Factorization parameters were as follows:
name: 16669_161
n: 17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749
m: 100000000000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316881, largePrimes:5795306 encountered
Relations: rels:5901400, finalFF:737692
Max relations in full relation-set: 28
Initial matrix: 632894 x 737692 with sparse part having weight 45414630.
Pruned matrix : 553191 x 556419 with weight 32190862.
Total sieving time: 69.32 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.47 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 73.18 hours.
 --------- CPU info (if available) ----------

Oct 2, 2007

By Robert Backstrom / GGNFS, Msieve

(4·10161-7)/3 = 1(3)1601<162> = 11 · 11124606089<11> · 100299923063<12> · C140

C140 = P45 · P95

P45 = 866216913035861859660556067350054626872174933<45>

P95 = 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091<95>

Number: n
N=10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:

prp45 factor: 866216913035861859660556067350054626872174933
prp95 factor: 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091
elapsed time 02:26:08 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.30 hours.
Scaled time: 48.24 units (timescale=1.197).
Factorization parameters were as follows:
name: KA_1_3_160_1
n: 10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903
type: snfs
skew: 0.71
deg: 5
c5: 40
c0: -7
m: 100000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:250150, AFBsize:249831, largePrimes:6771115 encountered
Relations: rels:6304352, finalFF:590349
Max relations in full relation-set: 28
Initial matrix: 500047 x 590349 with sparse part having weight 31375036.
Pruned matrix : 415114 x 417678 with weight 17906321.
Total sieving time: 40.07 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000
total time: 40.30 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

5·10161-1 = 4(9)161<162> = 23 · 5039 · 5503 · 121219311137<12> · C142

C142 = P69 · P74

P69 = 205172085665013628136788854347422145538579372307983152097920947502671<69>

P74 = 31521596990625887572504276079879084677165618298704568194646451128941172807<74>

Number: n
N=6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497
  ( 142 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 05:21:23 2007  prp69 factor: 205172085665013628136788854347422145538579372307983152097920947502671
Tue Oct 02 05:21:23 2007  prp74 factor: 31521596990625887572504276079879084677165618298704568194646451128941172807
Tue Oct 02 05:21:23 2007  elapsed time 01:18:32 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.84 hours.
Scaled time: 43.39 units (timescale=1.454).
Factorization parameters were as follows:
name: KA_4_9_161
n: 6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497
skew: 0.46
deg: 5
c5: 50
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 2800000
alim: 2800000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2800000/2800000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:203362, AFBsize:203587, largePrimes:7032000 encountered
Relations: rels:6494307, finalFF:456833
Max relations in full relation-set: 28
Initial matrix: 407014 x 456833 with sparse part having weight 35481673.
Pruned matrix : 369264 x 371363 with weight 25332214.
Total sieving time: 29.63 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000
total time: 29.84 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

(28·10160-1)/9 = 3(1)160<161> = 53 · 113 · 367 · 10608547 · 331545143 · C139

C139 = P51 · P88

P51 = 633091035242735539801967600647466189684568802167457<51>

P88 = 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001<88>

Number: n
N=4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457
  ( 139 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 06:04:18 2007  prp51 factor: 633091035242735539801967600647466189684568802167457
Tue Oct 02 06:04:18 2007  prp88 factor: 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001
Tue Oct 02 06:04:18 2007  elapsed time 01:22:53 (Msieve 1.26)

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 34.41 hours.
Scaled time: 44.59 units (timescale=1.296).
Factorization parameters were as follows:
name: KA_3_1_160
n: 4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457
skew: 0.51
deg: 5
c5: 28
c0: -1
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1700000)
Primes: RFBsize:216816, AFBsize:216531, largePrimes:7070916 encountered
Relations: rels:6546532, finalFF:488128
Max relations in full relation-set: 28
Initial matrix: 433413 x 488128 with sparse part having weight 35567073.
Pruned matrix : 391277 x 393508 with weight 24641110.
Total sieving time: 33.14 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.06 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 34.41 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

7·10161-3 = 6(9)1607<162> = 11759927 · 890858477521139<15> · C140

C140 = P52 · P89

P52 = 5434034586523956104106766412088428719802308238404951<52>

P89 = 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399<89>

Number: n
N=66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449
  ( 140 digits)
SNFS difficulty: 161 digits.
Divisors found:

Tue Oct 02 11:41:36 2007  prp52 factor: 5434034586523956104106766412088428719802308238404951
Tue Oct 02 11:41:36 2007  prp89 factor: 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399
Tue Oct 02 11:41:36 2007  elapsed time 02:02:16 (Msieve 1.26)

Version: GGNFS-0.77.1-20051202-athlon
Total time: 53.37 hours.
Scaled time: 70.61 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_6_9_160_7
n: 66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449
skew: 0.53
deg: 5
c5: 70
c0: -3
m: 100000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 2500000)
Primes: RFBsize:250150, AFBsize:249361, largePrimes:7482224 encountered
Relations: rels:6975734, finalFF:559949
Max relations in full relation-set: 28
Initial matrix: 499578 x 559949 with sparse part having weight 47483613.
Pruned matrix : 454399 x 456960 with weight 33007219.
Total sieving time: 53.09 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 53.37 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Oct 1, 2007 (3rd)

By Jo Yeong Uk / GGNFS

2·10158-7 = 1(9)1573<159> = 953 · 25057 · 2414090848213589432916932990633<31> · C121

C121 = P53 · P69

P53 = 31571248495465350553236417278124057355578453451578557<53>

P69 = 109891134207565565423460471928953710097707635400211726467910976480493<69>

Number: 19993_158
N=3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601
  ( 121 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=31571248495465350553236417278124057355578453451578557 (pp53)
 r2=109891134207565565423460471928953710097707635400211726467910976480493 (pp69)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 34.21 hours.
Scaled time: 72.22 units (timescale=2.111).
Factorization parameters were as follows:
n: 3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601
m: 100000000000000000000000000000000
c5: 1
c0: -350
skew: 3.23
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 4000001)
Primes: RFBsize:283146, AFBsize:283727, largePrimes:5808005 encountered
Relations: rels:5905005, finalFF:708062
Max relations in full relation-set: 28
Initial matrix: 566937 x 708062 with sparse part having weight 48034519.
Pruned matrix : 464821 x 467719 with weight 33043298.
Total sieving time: 32.81 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 1.26 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 34.21 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Oct 2, 2007 (2nd)

By Jo Yeong Uk / PRIMO

4·102038+9 is prime!

Oct 1, 2007

By Sinkiti Sibata / GGNFS

(5·10159+7)/3 = 1(6)1589<160> = 61 · 139 · 22354882834663<14> · C142

C142 = P50 · P93

P50 = 20633650419206281386733031458970921470010125270621<50>

P93 = 426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857<93>

Number: 16669_159
N=8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197
  ( 142 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=20633650419206281386733031458970921470010125270621 (pp50)
 r2=426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857 (pp93)
Version: GGNFS-0.77.1-20060513-k8
Total time: 40.03 hours.
Scaled time: 77.81 units (timescale=1.944).
Factorization parameters were as follows:
name: 16669_159
n: 8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197
m: 100000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3300001)
Primes: RFBsize:283146, AFBsize:283092, largePrimes:5781861 encountered
Relations: rels:5963802, finalFF:786585
Max relations in full relation-set: 28
Initial matrix: 566302 x 786585 with sparse part having weight 46911389.
Pruned matrix : 388163 x 391058 with weight 28940900.
Total sieving time: 37.70 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.02 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 40.03 hours.
 --------- CPU info (if available) ----------

(5·10154+7)/3 = 1(6)1539<155> = 172 · 211 · 89227 · 3642209 · 34988803 · C131

C131 = P64 · P67

P64 = 3039500772684756067905656547847651710767202885317667360748022141<64>

P67 = 7908169219491322981400916567456394408788268380654149703529298881099<67>

Number: 16669_154
N=24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959
  ( 131 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=3039500772684756067905656547847651710767202885317667360748022141 (pp64)
 r2=7908169219491322981400916567456394408788268380654149703529298881099 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 35.56 hours.
Scaled time: 24.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_154
n: 24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959
m: 10000000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216671, largePrimes:5670953 encountered
Relations: rels:5752856, finalFF:662121
Max relations in full relation-set: 28
Initial matrix: 433551 x 662121 with sparse part having weight 48626390.
Pruned matrix : 281115 x 283346 with weight 30459459.
Total sieving time: 31.66 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 3.54 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 35.56 hours.
 --------- CPU info (if available) ----------

September 2007

Sep 30, 2007 (4th)

By Jo Yeong Uk / GGNFS

(5·10162+7)/3 = 1(6)1619<163> = 26605422918850732566241<23> · 63779260936918673666795069<26> · C114

C114 = P56 · P59

P56 = 12345841030073355518195566173708094971913700674342341749<56>

P59 = 79557003995848246810709883183266502089230667106521497802989<59>

Number: 16669_162
N=982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761
  ( 114 digits)
Divisors found:
 r1=12345841030073355518195566173708094971913700674342341749 (pp56)
 r2=79557003995848246810709883183266502089230667106521497802989 (pp59)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 24.98 hours.
Scaled time: 53.55 units (timescale=2.144).
Factorization parameters were as follows:
name: 16669_162
n: 982198124161653180383430896087817726373941018203689950840839374285322703169061071123818762648082907378560911687761
skew: 79581.38
# norm 1.52e+16
c5: 14400
c4: -5104766820
c3: -426663243207224
c2: 28085394149617420745
c1: 790358088000437855793756
c0: -30202005118332397627600032105
# alpha -6.65
Y1: 1156683005687
Y0: -9263415975208444237468
# Murphy_E 5.69e-10
# M 282687440591493322167609652050488048787882302796981977330370789227978501143302103505532468545998949397979264317724
type: gnfs
rlim: 3600000
alim: 3600000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 75000
Factor base limits: 3600000/3600000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1800000, 3075001)
Primes: RFBsize:256726, AFBsize:255796, largePrimes:7643428 encountered
Relations: rels:7673917, finalFF:699431
Max relations in full relation-set: 28
Initial matrix: 512600 x 699431 with sparse part having weight 61343989.
Pruned matrix : 366077 x 368704 with weight 35631843.
Polynomial selection time: 1.18 hours.
Total sieving time: 22.62 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 0.87 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000
total time: 24.98 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 30, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(5·10160+7)/3 = 1(6)1599<161> = 79 · 22979881 · 8218427297<10> · 120437201921<12> · 576732416278247<15> · C116

C116 = P55 · P61

P55 = 4977320437750921565229473834967340708864912661751976709<55>

P61 = 3231130839822657913824785584822600613852060607675347893277881<61>

Number: 16669_160
N=16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629
  ( 116 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=4977320437750921565229473834967340708864912661751976709 (pp55)
 r2=3231130839822657913824785584822600613852060607675347893277881 (pp61)
Version: GGNFS-0.77.1-20060513-k8
Total time: 48.41 hours.
Scaled time: 96.57 units (timescale=1.995).
Factorization parameters were as follows:
name: 16669_160
n: 16082373566096614517840744716684819770544179685787058568186342091536319780818203204639102366383712317368525176873629
m: 100000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:282597, largePrimes:5621726 encountered
Relations: rels:5644743, finalFF:651649
Max relations in full relation-set: 28
Initial matrix: 565808 x 651649 with sparse part having weight 40725051.
Pruned matrix : 498172 x 501065 with weight 27770530.
Total sieving time: 45.45 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 2.62 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 48.41 hours.
 --------- CPU info (if available) ----------

Sep 30, 2007 (2nd)

By Robert Backstrom / GGNFS, Msieve

(5·10164+7)/3 = 1(6)1639<165> = 13 · 191 · 111667 · C156

C156 = P59 · P98

P59 = 26302708085062711351718348313317723934590092763062351780943<59>

P98 = 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403<98>

Number: n
N=601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029
  ( 156 digits)
SNFS difficulty: 165 digits.
Divisors found:

Linear algebra by Msieve 1.26:

Sun Sep 30 03:05:26 2007  commencing square root phase
Sun Sep 30 03:05:26 2007  reading relations for dependency 1
Sun Sep 30 03:05:27 2007  read 217366 cycles
Sun Sep 30 03:05:27 2007  cycles contain 795544 unique relations
Sun Sep 30 03:06:01 2007  read 795544 relations
Sun Sep 30 03:06:08 2007  multiplying 1142918 relations
Sun Sep 30 03:08:47 2007  multiply complete, coefficients have about 24.09 million bits
Sun Sep 30 03:08:48 2007  initial square root is modulo 8296751
Sun Sep 30 03:15:04 2007  prp59 factor: 26302708085062711351718348313317723934590092763062351780943
Sun Sep 30 03:15:04 2007  prp98 factor: 22853183997916580633609069137995891297392038889869322628145873448439676832765537008398620936667403
Sun Sep 30 03:15:04 2007  elapsed time 01:26:28

Version: GGNFS-0.77.1-20051202-athlon
Total time: 40.61 hours.
Scaled time: 53.77 units (timescale=1.324).
Factorization parameters were as follows:
name: KA_1_6_163_9
n: 601100627511426222646761161680965546206801796708529971231335989315691212650463737172222577853390145565689747467684178070804876373058548212170868388304701029
skew: 1.70
deg: 5
c5: 1
c0: 14
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1900000)
Primes: RFBsize:250150, AFBsize:250091, largePrimes:7227599 encountered
Relations: rels:6752702, finalFF:576673
Max relations in full relation-set: 28
Initial matrix: 500305 x 576673 with sparse part having weight 39570403.
Pruned matrix : 436717 x 439282 with weight 24359944.
Total sieving time: 40.39 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 40.61 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10163+7)/3 = 1(6)1629<164> = 19 · 932483 · 3338407 · C150

C150 = P36 · P115

P36 = 179096204859467232396164279888334937<36>

P115 = 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283<115>

Number: n
N=281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171
  ( 150 digits)
SNFS difficulty: 164 digits.
Divisors found:

Linear algebra using Msieve 1.26:

Sun Sep 30 18:13:20 2007  commencing square root phase
Sun Sep 30 18:13:20 2007  reading relations for dependency 1
Sun Sep 30 18:13:21 2007  read 238377 cycles
Sun Sep 30 18:13:21 2007  cycles contain 836180 unique relations
Sun Sep 30 18:13:57 2007  read 836180 relations
Sun Sep 30 18:14:04 2007  multiplying 1175696 relations
Sun Sep 30 18:16:39 2007  multiply complete, coefficients have about 28.40 million bits
Sun Sep 30 18:16:40 2007  initial square root is modulo 143457841
Sun Sep 30 18:22:25 2007  prp36 factor: 179096204859467232396164279888334937
Sun Sep 30 18:22:25 2007  prp115 factor: 1573361650372442894213033131277538811100419125034880034126626043409760465523866973561143332026778461515089011520283
Sun Sep 30 18:22:25 2007  elapsed time 01:32:22

Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 65.07 hours.
Scaled time: 79.39 units (timescale=1.220).
Factorization parameters were as follows:
name: KA_1_6_162_9
n: 281783100453132491764192749729106318410556661674307444387519334626303961635821594561083163050656636337622215383852258673518554659375130169219873027171
skew: 0.45
deg: 5
c5: 8
c0: 35
m: 500000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3100000)
Primes: RFBsize:216816, AFBsize:217636, largePrimes:7586330 encountered
Relations: rels:7073916, finalFF:488697
Max relations in full relation-set: 28
Initial matrix: 434517 x 488697 with sparse part having weight 43843717.
Pruned matrix : 412969 x 415205 with weight 33648580.
Total sieving time: 64.61 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.20 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 65.07 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(55·10158-1)/9 = 6(1)158<159> = 13 · 23 · 5763827 · 1559789123863<13> · C138

C138 = P59 · P80

P59 = 15010258650299280272276491101329623983515589707475827317847<59>

P80 = 15145513101806035552114587951495643112100912817276775268355705388408504954678887<80>

Number: n
N=227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289
  ( 138 digits)
SNFS difficulty: 160 digits.
Divisors found:

Linear algebra using Msieve 1.26:

Sun Sep 30 21:00:47 2007  commencing square root phase
Sun Sep 30 21:00:47 2007  reading relations for dependency 1
Sun Sep 30 21:00:47 2007  read 187803 cycles
Sun Sep 30 21:00:48 2007  cycles contain 698085 unique relations
Sun Sep 30 21:01:15 2007  read 698085 relations
Sun Sep 30 21:01:20 2007  multiplying 993110 relations
Sun Sep 30 21:03:51 2007  multiply complete, coefficients have about 26.43 million bits
Sun Sep 30 21:03:52 2007  initial square root is modulo 38909441
Sun Sep 30 21:09:48 2007  prp59 factor: 15010258650299280272276491101329623983515589707475827317847
Sun Sep 30 21:09:48 2007  prp80 factor: 15145513101806035552114587951495643112100912817276775268355705388408504954678887
Sun Sep 30 21:09:48 2007  elapsed time 01:03:31

Version: GGNFS-0.77.1-20051202-athlon
Total time: 29.89 hours.
Scaled time: 43.28 units (timescale=1.448).
Factorization parameters were as follows:
name: KA_6_1_158
n: 227338069049605129053211193199122381737271351068558536526884137163254204545481577681925791011163714893896017433744000903964174094369196289
skew: 0.56
deg: 5
c5: 88
c0: -5
m: 50000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 1600000)
Primes: RFBsize:183072, AFBsize:183537, largePrimes:7075458 encountered
Relations: rels:6528000, finalFF:420262
Max relations in full relation-set: 28
Initial matrix: 366675 x 420262 with sparse part having weight 36710081.
Pruned matrix : 330856 x 332753 with weight 26194028.
Total sieving time: 29.67 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000
total time: 29.89 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

Sep 30, 2007

By Bruce Dodson

(10339-1)/9 is divisible by 777734075184513369134763199249605543798943174359980119<54>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (5th)

By Yousuke Koide

101075+1 is divisible by 17749774754658825560922224895404476651<38>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 29, 2007 (4th)

By suberi / PRIMO

6·102593+7 is prime!

(55·102969+71)/9 is prime!

Sep 29, 2007 (3rd)

By Robert Backstrom / GGNFS, Msieve

(2·10165-17)/3 = (6)1641<165> = 24310071773347<14> · C152

C152 = P50 · P102

P50 = 51734164323600805573653584774564809428106146895381<50>

P102 = 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723<102>

Number: n
N=27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463
  ( 152 digits)
SNFS difficulty: 165 digits.
Divisors found:

Linear algebra using Msieve 1.26:

...
Sat Sep 29 12:41:06 2007  commencing square root phase
Sat Sep 29 12:41:06 2007  reading relations for dependency 1
Sat Sep 29 12:41:06 2007  read 242194 cycles
Sat Sep 29 12:41:07 2007  cycles contain 838445 unique relations
Sat Sep 29 12:41:38 2007  read 838445 relations
Sat Sep 29 12:41:44 2007  multiplying 1189934 relations
Sat Sep 29 12:44:18 2007  multiply complete, coefficients have about 26.63 million bits
Sat Sep 29 12:44:18 2007  initial square root is modulo 44576321
Sat Sep 29 12:50:18 2007  prp50 factor: 51734164323600805573653584774564809428106146895381
Sat Sep 29 12:50:18 2007  prp102 factor: 530084446675280350994104791959744914314598013435184675057749458635575389733945696768078005752479641723
Sat Sep 29 12:50:18 2007  elapsed time 01:33:37

Version: GGNFS-0.77.1-20051202-athlon
Total time: 63.87 hours.
Scaled time: 92.54 units (timescale=1.449).
Factorization parameters were as follows:
name: KA_6_164_1
n: 27423475869683962390491718591322401700236139951798106363550172466967761626634044630890142340664811630560708218722793851241742987522268137155303643581463
skew: 1.53
deg: 5
c5: 2
c0: -17
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:216816, AFBsize:216686, largePrimes:7771552 encountered
Relations: rels:7297268, finalFF:503771
Max relations in full relation-set: 28
Initial matrix: 433567 x 503771 with sparse part having weight 49944999.
Pruned matrix : 407928 x 410159 with weight 37183923.
Total sieving time: 63.60 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 63.87 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3400+

5·10167-7 = 4(9)1663<168> = 13 · C167

C167 = P47 · P121

P47 = 27166347444900583109731812696436491851217550133<47>

P121 = 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417<121>

Number: n
N=38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461
  ( 167 digits)
SNFS difficulty: 167 digits.
Divisors found:

Linear algebra by Msieve 1.26:

Sat Sep 29 23:21:09 2007  commencing square root phase
Sat Sep 29 23:21:09 2007  reading relations for dependency 1
Sat Sep 29 23:21:09 2007  read 257497 cycles
Sat Sep 29 23:21:10 2007  cycles contain 895173 unique relations
Sat Sep 29 23:22:06 2007  read 895173 relations
Sat Sep 29 23:22:16 2007  multiplying 1259610 relations
Sat Sep 29 23:29:41 2007  multiply complete, coefficients have about 37.13 milli on bits
Sat Sep 29 23:29:43 2007  initial square root is modulo 214451
Sat Sep 29 23:41:15 2007  prp47 factor: 27166347444900583109731812696436491851217550133
Sat Sep 29 23:41:15 2007  prp121 factor: 1415778788059272495359858060016860902525618476647398886043545011620987173109239480930954828521246215935467936088821001417
Sat Sep 29 23:41:15 2007  elapsed time 02:44:57

Version: GGNFS-0.77.1-20051202-athlon
Total time: 199.44 hours.
Scaled time: 238.33 units (timescale=1.195).
Factorization parameters were as follows:
name: KA_4_9_166_3
n: 38461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461
type: snfs
skew: 1.00
deg: 5
c5: 500
c0: -7
m: 1000000000000000000000000000000000
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved  special-q in [100000, 3300000)
Primes: RFBsize:250150, AFBsize:249951, largePrimes:7696642 encountered
Relations: rels:7217894, finalFF:566646
Max relations in full relation-set: 28
Initial matrix: 500167 x 566646 with sparse part having weight 45760093.
Pruned matrix : 461435 x 463999 with weight 34043459.
Total sieving time: 198.86 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 0.00 hours.
Total square root time: 0.00 hours, sqrts: 0.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000
total time: 199.44 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD XP 2700+

Sep 29, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(5·10155+7)/3 = 1(6)1549<156> = 59 · 3975371759544157964120556169<28> · C126

C126 = P50 · P77

P50 = 12183673828219514815541105378476410328653530357743<50>

P77 = 58323116951920764556691672750208036680903493856562686440783028131664900724273<77>

Number: 16669_155
N=710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839
  ( 126 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=12183673828219514815541105378476410328653530357743 (pp50)
 r2=58323116951920764556691672750208036680903493856562686440783028131664900724273 (pp77)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 18.11 hours.
Scaled time: 38.82 units (timescale=2.143).
Factorization parameters were as follows:
n: 710589833587302941718597558350764196066850853049176811985093853269458721857536326881047933687224985740262132968074713493595839
m: 10000000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216351, largePrimes:5702060 encountered
Relations: rels:5761249, finalFF:638372
Max relations in full relation-set: 28
Initial matrix: 433232 x 638372 with sparse part having weight 49932713.
Pruned matrix : 308816 x 311046 with weight 30557046.
Total sieving time: 17.42 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.57 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 18.11 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 29, 2007

By Sinkiti Sibata / GGNFS

(5·10152+7)/3 = 1(6)1519<153> = 13 · 4987 · 377579803 · 3436321013<10> · 6969202531<10> · 1361822893003<13> · C108

C108 = P46 · P62

P46 = 2737389693912651920291775161351885326232522611<46>

P62 = 76264635966685860724726069046227515943445121318873286926559367<62>

Number: 16669_152
N=208766028505206032982047684947445945022194314191543387718652600248442907703745958949603148169464391261347237
  ( 108 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=2737389693912651920291775161351885326232522611 (pp46)
 r2=76264635966685860724726069046227515943445121318873286926559367 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 26.20 hours.
Scaled time: 51.28 units (timescale=1.957).
Factorization parameters were as follows:
name: 16669_152
n: 208766028505206032982047684947445945022194314191543387718652600248442907703745958949603148169464391261347237
m: 1000000000000000000000000000000
c5: 500
c0: 7
skew: 0.43
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176133, largePrimes:5921246 encountered
Relations: rels:6179778, finalFF:785801
Max relations in full relation-set: 28
Initial matrix: 352501 x 785801 with sparse part having weight 71297699.
Pruned matrix : 226386 x 228212 with weight 33405143.
Total sieving time: 24.91 hours.
Total relation processing time: 0.15 hours.
Matrix solve time: 1.02 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.20 hours.
 --------- CPU info (if available) ----------

5·10161-7 = 4(9)1603<162> = 13 · 103 · 58693 · 85201 · 56518060850527<14> · C136

C136 = P49 · P87

P49 = 4798551110626920975723815067816871876805464439071<49>

P87 = 275334764005974011025338002993961748286200016743548777673724333243675964471822107503727<87>

Number: 49993_161
N=1321207937615067776138099496089850613691726498550114845141787036218852281776516361293885682470727693894523974030933270087638528096917617
  ( 136 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=4798551110626920975723815067816871876805464439071 (pp49)
 r2=275334764005974011025338002993961748286200016743548777673724333243675964471822107503727 (pp87)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 94.90 hours.
Scaled time: 64.25 units (timescale=0.677).
Factorization parameters were as follows:
name: 49993_161
n: 1321207937615067776138099496089850613691726498550114845141787036218852281776516361293885682470727693894523974030933270087638528096917617
m: 100000000000000000000000000000000
c5: 50
c0: -7
skew: 0.67
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316881, largePrimes:5844440 encountered
Relations: rels:5989509, finalFF:769982
Max relations in full relation-set: 28
Initial matrix: 632894 x 769982 with sparse part having weight 47420540.
Pruned matrix : 526978 x 530206 with weight 32469606.
Total sieving time: 82.02 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 12.29 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 94.90 hours.
 --------- CPU info (if available) ----------

Sep 28, 2007 (5th)

By Bruce Dodson

10352+1 is divisible by 196492106862714324563103086902334481596741493532094589569<57>, cofactor is prime.

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 28, 2007 (4th)

By Robert Backstrom / GGNFS

(14·10164-41)/9 = 1(5)1631<165> = 7394276783<10> · C155

C155 = P33 · P122

P33 = 241913548612846605274086927369517<33>

P122 = 86962022362460490445785055865229214136443842893085986014021798676035510354833177041605490276301765124099002836589234876341<122>

Number: n
N=21037291424252539446163109033236138674247346680037789377346270695525241546202958190719320217737047557792989848315711277798343615987894452010473997907897297
  ( 155 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=241913548612846605274086927369517 (pp33)
 r2=86962022362460490445785055865229214136443842893085986014021798676035510354833177041605490276301765124099002836589234876341 (pp122)
Version: GGNFS-0.77.1-20051202-athlon
Total time: 74.48 hours.
Scaled time: 98.54 units (timescale=1.323).
Factorization parameters were as follows:
name: KA_1_5_163_1
n: 21037291424252539446163109033236138674247346680037789377346270695525241546202958190719320217737047557792989848315711277798343615987894452010473997907897297
skew: 1.96
deg: 5
c5: 7
c0: -205
m: 1000000000000000000000000000000000
type: snfs
rlim: 3500000
alim: 3500000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 2800001)
Primes: RFBsize:250150, AFBsize:250442, largePrimes:7581353 encountered
Relations: rels:7099178, finalFF:586042
Max relations in full relation-set: 48
Initial matrix: 500657 x 586042 with sparse part having weight 50177668.
Pruned matrix : 439767 x 442334 with weight 33392103.
Total sieving time: 60.70 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 13.32 hours.
Total square root time: 0.10 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000
total time: 74.48 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 28, 2007 (3rd)

By Sinkiti Sibata / GGNFS

(5·10138+7)/3 = 1(6)1379<139> = 17 · 3307 · 111476834769978619<18> · C117

C117 = P58 · P60

P58 = 2207115310302675107711411136506882374916425885644292317671<58>

P60 = 120491380689937645366860425953951437824016468528431170048099<60>

Number: 16669_138
N=265938371080269481663171733466742068358255746135570115355624735763817783285646181622002721514196167950503021257657429
  ( 117 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=2207115310302675107711411136506882374916425885644292317671 (pp58)
 r2=120491380689937645366860425953951437824016468528431170048099 (pp60)
Version: GGNFS-0.77.1-20060513-k8
Total time: 9.91 hours.
Scaled time: 19.51 units (timescale=1.969).
Factorization parameters were as follows:
name: 16669_138
n: 265938371080269481663171733466742068358255746135570115355624735763817783285646181622002721514196167950503021257657429
m: 5000000000000000000000000000
c5: 8
c0: 35
skew: 1.34
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1675001)
Primes: RFBsize:78498, AFBsize:63913, largePrimes:1600904 encountered
Relations: rels:1609087, finalFF:168926
Max relations in full relation-set: 28
Initial matrix: 142476 x 168926 with sparse part having weight 16797660.
Pruned matrix : 135545 x 136321 with weight 12105787.
Total sieving time: 9.60 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.18 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 9.91 hours.
 --------- CPU info (if available) ----------

(5·10139+7)/3 = 1(6)1389<140> = 6871 · 89220757 · C128

C128 = P41 · P87

P41 = 68519056331623047707327877417940217357011<41>

P87 = 396781599919562194526485294892308063321566863525043969970677953144473101558904885402357<87>

Number: 16669_139
N=27187100796240000941757996128380631790386988553157290361212166281105529340875250396473903242091659504609700154156408933849874927
  ( 128 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=68519056331623047707327877417940217357011 (pp41)
 r2=396781599919562194526485294892308063321566863525043969970677953144473101558904885402357 (pp87)
Version: GGNFS-0.77.1-20060513-k8
Total time: 7.76 hours.
Scaled time: 15.49 units (timescale=1.996).
Factorization parameters were as follows:
name: 16669_139
n: 27187100796240000941757996128380631790386988553157290361212166281105529340875250396473903242091659504609700154156408933849874927
m: 10000000000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1375001)
Primes: RFBsize:78498, AFBsize:63623, largePrimes:1550075 encountered
Relations: rels:1551224, finalFF:171077
Max relations in full relation-set: 28
Initial matrix: 142185 x 171077 with sparse part having weight 14886101.
Pruned matrix : 133835 x 134609 with weight 10106155.
Total sieving time: 7.52 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 7.76 hours.
 --------- CPU info (if available) ----------

Sep 28, 2007 (2nd)

By Jo Yeong Uk / GGNFS, GMP-ECM

(5·10142+7)/3 = 1(6)1419<143> = 813978461 · C134

C134 = P40 · P94

P40 = 5800307603283903977690274884081525862077<40>

P94 = 3530082139245880010115509104883085123122514153709233376692762673105064986713732631002976914277<94>

Number: 16669_142
N=20475562272484586870004004524471890991064770529188077209658090285348062381550740648734029175578721691342968676743237148957761754173329
  ( 134 digits)
SNFS difficulty: 144 digits.
Divisors found:
 r1=5800307603283903977690274884081525862077 (pp40)
 r2=3530082139245880010115509104883085123122514153709233376692762673105064986713732631002976914277 (pp94)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 6.83 hours.
Scaled time: 14.63 units (timescale=2.141).
Factorization parameters were as follows:
n: 20475562272484586870004004524471890991064770529188077209658090285348062381550740648734029175578721691342968676743237148957761754173329
m: 50000000000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1200001)
Primes: RFBsize:114155, AFBsize:114067, largePrimes:3312011 encountered
Relations: rels:3363019, finalFF:351333
Max relations in full relation-set: 28
Initial matrix: 228286 x 351333 with sparse part having weight 30146662.
Pruned matrix : 184826 x 186031 with weight 13060822.
Total sieving time: 6.64 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,144,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 6.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10143+7)/3 = 1(6)1429<144> = 2597673844567493<16> · C128

C128 = P33 · P96

P33 = 434046091093577317652060703761719<33>

P96 = 147818325628859156953088758822031349145171816910978388451598502100954879491436158318814376510207<96>

Number: 16669_143
N=64159966431203876277211145259729258839851155070514316316238539204930112595630101081864207165422843650012653726820231156499365833
  ( 128 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=434046091093577317652060703761719 (pp33)
 r2=147818325628859156953088758822031349145171816910978388451598502100954879491436158318814376510207 (pp96)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 8.24 hours.
Scaled time: 17.65 units (timescale=2.141).
Factorization parameters were as follows:
n: 64159966431203876277211145259729258839851155070514316316238539204930112595630101081864207165422843650012653726820231156499365833
m: 100000000000000000000000000000
c5: 1
c0: 140
skew: 2.69
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [750000, 1300001)
Primes: RFBsize:114155, AFBsize:114557, largePrimes:3356219 encountered
Relations: rels:3388872, finalFF:326333
Max relations in full relation-set: 28
Initial matrix: 228776 x 326333 with sparse part having weight 29776228.
Pruned matrix : 196932 x 198139 with weight 14882362.
Total sieving time: 8.02 hours.
Total relation processing time: 0.05 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000
total time: 8.24 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10158+7)/3 = 1(6)1579<159> = 132 · 98960718128861<14> · C142

C142 = P31 · P112

P31 = 2810189725402685724689364943993<31>

P112 = 3546202774378704117363718958207959078238914256676956218627386149550232256336887900588798661867954338838309183537<112>

Sep 28, 2007

By Sinkiti Sibata / GGNFS

5·10179-7 = 4(9)1783<180> = 13 · 157 · 319001 · 740321 · 1275172341197<13> · 3168934862695211<16> · 185503352859609293<18> · C121

C121 = P59 · P62

P59 = 20824276942434306550878491316554921169577070969181605095403<59>

P62 = 66452449689374424275673726430638274402626958940230091126916841<62>

Number: 49993_179
N=1383824215834715620070456110706078885338595809203545862722727074810567580733069553796012130255235581892164045691052381923
  ( 121 digits)
Divisors found:
 r1=20824276942434306550878491316554921169577070969181605095403 (pp59)
 r2=66452449689374424275673726430638274402626958940230091126916841 (pp62)
Version: GGNFS-0.77.1-20060513-k8
Total time: 84.55 hours.
Scaled time: 168.59 units (timescale=1.994).
Factorization parameters were as follows:
name: 49993_179
n: 1383824215834715620070456110706078885338595809203545862722727074810567580733069553796012130255235581892164045691052381923
skew: 50602.07
# norm 4.41e+16
c5: 37800
c4: 20128544688
c3: 731574065956501
c2: -49160751458878107328
c1: 392457585328640355756184
c0: -30872663122950055012866120
# alpha -5.82
Y1: 2624022091559
Y0: -129633393211373317821743
# Murphy_E 2.81e-10
# M 506787805364640852991178403337491309782409889508448185433954099888929241273787199158859515253510600449456791072798496402
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2500000, 4960001)
Primes: RFBsize:348513, AFBsize:348699, largePrimes:7743207 encountered
Relations: rels:7931207, finalFF:836390
Max relations in full relation-set: 28
Initial matrix: 697293 x 836390 with sparse part having weight 72523171.
Pruned matrix : 582401 x 585951 with weight 47666914.
Total sieving time: 78.91 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.74 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 84.55 hours.
 --------- CPU info (if available) ----------

Sep 27, 2007 (5th)

By suberi / PRIMO

(17·102465-11)/3 is prime!

Sep 27, 2007 (4th)

By Sinkiti Sibata / GGNFS

(5·10141+7)/3 = 1(6)1409<142> = 3643 · 25537 · 51757591 · 63071636252236439379138851123<29> · C97 = P33 · P65

P33 = 391280500666926357614593359860867<33>

P65 = 14025661202251856928100285392792838965856556326678840999770191689<65>

Number: 16669_141
N=5487967737401790843509693098739988690283003641505514417737061993133022559891161126165558959734363
  ( 97 digits)
Divisors found:
 r1=391280500666926357614593359860867 (pp33)
 r2=14025661202251856928100285392792838965856556326678840999770191689 (pp65)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 13.08 hours.
Scaled time: 8.86 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_141
n:  5487967737401790843509693098739988690283003641505514417737061993133022559891161126165558959734363
m:  14369675926318849190988
deg: 4
c4: 128713368
c3: 321000566584
c2: 421345394109067688
c1: -1579948430526136245
c0: -274075801134666159754345
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.486
# E(F1,F2) = 1.904845e-05
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1190818402.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1680001)
Primes: RFBsize:92938, AFBsize:92333, largePrimes:1922598 encountered
Relations: rels:2011676, finalFF:220756
Max relations in full relation-set: 28
Initial matrix: 185350 x 220756 with sparse part having weight 21582414.
Pruned matrix : 170926 x 171916 with weight 14807077.
Polynomial selection time: 0.17 hours.
Total sieving time: 11.89 hours.
Total relation processing time: 0.14 hours.
Matrix solve time: 0.81 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 13.08 hours.
 --------- CPU info (if available) ----------

Sep 27, 2007 (3rd)

By Jo Yeong Uk / GMP-ECM, GGNFS

(5·10187+7)/3 = 1(6)1869<188> = C188

C188 = P30 · P158

P30 = 809800994185580459461342700011<30>

P158 = 20581188200970768756638678837132189543155931483203808645215586178063428078238759791181233823231551560665801684249575705334754779112834205568013634241048487879<158>

(5·10132+7)/3 = 1(6)1319<133> = 71 · C131

C131 = P34 · P97

P34 = 2485169554431976453434061661307773<34>

P97 = 9445704966847322970558865702100853962207830112965205476236509054211032779897889569875889195527943<97>

Number: 16669_132
N=23474178403755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
  ( 131 digits)
SNFS difficulty: 134 digits.
Divisors found:
 r1=2485169554431976453434061661307773 (pp34)
 r2=9445704966847322970558865702100853962207830112965205476236509054211032779897889569875889195527943 (pp97)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.33 hours.
Scaled time: 4.95 units (timescale=2.128).
Factorization parameters were as follows:
n: 23474178403755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939
m: 500000000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1100001)
Primes: RFBsize:107126, AFBsize:106873, largePrimes:2226874 encountered
Relations: rels:2343305, finalFF:290382
Max relations in full relation-set: 28
Initial matrix: 214063 x 290382 with sparse part having weight 19190038.
Pruned matrix : 176356 x 177490 with weight 8874710.
Total sieving time: 2.19 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.33 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10135+7)/3 = 1(6)1349<136> = 283 · 92553614341<11> · C122

C122 = P49 · P74

P49 = 2576769183774005584057447380213481615877532498847<49>

P74 = 24694111962373273863858692871467284566884745178594644170287579543940440309<74>

Number: 16669_135
N=63631026725308488187427141159783305023986096327229654593888951415465371751129423611565979517723069748777754256294214823723
  ( 122 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=2576769183774005584057447380213481615877532498847 (pp49)
 r2=24694111962373273863858692871467284566884745178594644170287579543940440309 (pp74)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.02 units (timescale=2.129).
Factorization parameters were as follows:
n: 63631026725308488187427141159783305023986096327229654593888951415465371751129423611565979517723069748777754256294214823723
m: 1000000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1200001)
Primes: RFBsize:107126, AFBsize:107203, largePrimes:2285972 encountered
Relations: rels:2456639, finalFF:329462
Max relations in full relation-set: 28
Initial matrix: 214394 x 329462 with sparse part having weight 24010778.
Pruned matrix : 168264 x 169399 with weight 9837861.
Total sieving time: 2.69 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

(5·10151+7)/3 = 1(6)1509<152> = 17701418095831<14> · 1812077986113440186399161321739<31> · C108

C108 = P39 · P70

P39 = 194105463026917266409863270055667221771<39>

P70 = 2676862394581312139459903416519678229802305636596524777765101615813171<70>

(5·10137+7)/3 = 1(6)1369<138> = 293 · 132893 · 1015853 · 512709215972310397<18> · C106

C106 = P44 · P63

P44 = 33067855423525789757242415631561806102865053<44>

P63 = 248525526252847290942368984924627161881822914913147146704360297<63>

Number: 16669_137
N=8218206171184817335096503188675348229821826657900353296819064455753352874913254325905363890559179282000741
  ( 106 digits)
SNFS difficulty: 139 digits.
Divisors found:
 r1=33067855423525789757242415631561806102865053 (pp44)
 r2=248525526252847290942368984924627161881822914913147146704360297 (pp63)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 3.56 hours.
Scaled time: 7.54 units (timescale=2.118).
Factorization parameters were as follows:
n: 8218206171184817335096503188675348229821826657900353296819064455753352874913254325905363890559179282000741
m: 5000000000000000000000000000
c5: 4
c0: 175
skew: 2.13
type: snfs
Factor base limits: 1400000/1400000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 47/47
Sieved algebraic special-q in [700000, 1350001)
Primes: RFBsize:107126, AFBsize:106873, largePrimes:2329174 encountered
Relations: rels:2479966, finalFF:306952
Max relations in full relation-set: 28
Initial matrix: 214063 x 306952 with sparse part having weight 23622463.
Pruned matrix : 181583 x 182717 with weight 11078387.
Total sieving time: 3.40 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000
total time: 3.56 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 27, 2007 (2nd)

By Robert Backstrom / GGNFS

2·10167-7 = 1(9)1663<168> = 23 · C166

C166 = P33 · P134

P33 = 817671420061668453239381786225641<33>

P134 = 10634653432374120218546314263462036182748850386624188463030773029103326239415114946154180410545538376172609896000131661254182519321751<134>

Number: n
N=8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391
  ( 166 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=817671420061668453239381786225641 (pp33)
 r2=10634653432374120218546314263462036182748850386624188463030773029103326239415114946154180410545538376172609896000131661254182519321751 (pp134)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 93.38 hours.
Scaled time: 121.68 units (timescale=1.303).
Factorization parameters were as follows:
name: KA_1_9_166_3
n: 8695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391
skew: 0.51
deg: 5
c5: 200
c0: -7
m: 1000000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 4100001)
Primes: RFBsize:216816, AFBsize:216921, largePrimes:7989364 encountered
Relations: rels:7543447, finalFF:491774
Max relations in full relation-set: 28
Initial matrix: 433802 x 491774 with sparse part having weight 54393195.
Pruned matrix : 412924 x 415157 with weight 43131647.
Total sieving time: 87.10 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 5.82 hours.
Total square root time: 0.15 hours, sqrts: 1.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000
total time: 93.38 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

(5·10148+7)/3 = 1(6)1479<149> = C149

C149 = P47 · P50 · P53

P47 = 18650313335606201329724729364112809673312876463<47>

P50 = 84145670486626078050750612549722130221630831476553<50>

P53 = 10620154668476690275768442467100096825061277196932171<53>

Number: n
N=16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
  ( 149 digits)
SNFS difficulty: 149 digits.
Divisors found:
 r1=18650313335606201329724729364112809673312876463 (pp47)
 r2=84145670486626078050750612549722130221630831476553 (pp50)
 r3=10620154668476690275768442467100096825061277196932171 (pp53)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 14.42 hours.
Scaled time: 18.77 units (timescale=1.302).
Factorization parameters were as follows:
name: KA_1_6_147_9
n: 16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669
skew: 0.84
deg: 5
c5: 8
c0: 35
m: 500000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 28
lpba: 28
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 28/28
Max factor residue bits: 48/48
Sieved algebraic special-q in [100000, 1700001)
Primes: RFBsize:148933, AFBsize:149505, largePrimes:6860845 encountered
Relations: rels:6228580, finalFF:338172
Max relations in full relation-set: 28
Initial matrix: 298503 x 338172 with sparse part having weight 28470354.
Pruned matrix : 279282 x 280838 with weight 20632016.
Total sieving time: 12.23 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 1.80 hours.
Total square root time: 0.19 hours, sqrts: 2.
Prototype def-par.txt line would be:
snfs,149,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000
total time: 14.42 hours.
 --------- CPU info (if available) ----------

Cygwin on AMD 64 3200+

Sep 27, 2007

By Jo Yeong Uk / GGNFS

(5·10131+7)/3 = 1(6)1309<132> = 502809239 · 2578087651229<13> · C111

C111 = P40 · P71

P40 = 1302814026384104145222921505524360161093<40>

P71 = 98688238257748130465524894016056404057253771100584036810592603966756843<71>

Number: 16669_131
N=128572421041330628945312107304054615470294816718767333011548094860238837956131360269939220155411684012240109399
  ( 111 digits)
SNFS difficulty: 131 digits.
Divisors found:
 r1=1302814026384104145222921505524360161093 (pp40)
 r2=98688238257748130465524894016056404057253771100584036810592603966756843 (pp71)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 2.83 hours.
Scaled time: 6.05 units (timescale=2.139).
Factorization parameters were as follows:
n: 128572421041330628945312107304054615470294816718767333011548094860238837956131360269939220155411684012240109399
m: 100000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 1000000/1000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [500000, 1100001)
Primes: RFBsize:78498, AFBsize:78386, largePrimes:1577484 encountered
Relations: rels:1592551, finalFF:190981
Max relations in full relation-set: 28
Initial matrix: 156949 x 190981 with sparse part having weight 11746680.
Pruned matrix : 144889 x 145737 with weight 7156255.
Total sieving time: 2.73 hours.
Total relation processing time: 0.03 hours.
Matrix solve time: 0.05 hours.
Time per square root: 0.01 hours.
Prototype def-par.txt line would be:
snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000
total time: 2.83 hours.
 --------- CPU info (if available) ----------
CPU0: Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Intel(R) Core(TM)2 Quad CPU           @ 2.40GHz stepping 07
Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init)
Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674)
Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066)
Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119)
Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124)
Total of 4 processors activated (19119.96 BogoMIPS).

Sep 26, 2007 (5th)

By JMB / GGNFS

8·10181+3 = 8(0)1803<182> = 17 · 47 · 120077 · 766223541469<12> · 752719880879203667<18> · 148057738580234774662331071<27> · C118

C118 = P45 · P74

P45 = 147863869707137044125193702898663252618158313<45>

P74 = 66039126656639520936203017529360818061007971819918535640380875386612837009<74>

Number: N
N=9764800819530466924518836952107346921926064836602594080779488507011172569982077589063765484307783295905707377627405817
  ( 118 digits)
Divisors found:
 r1=147863869707137044125193702898663252618158313 (pp45)
 r2=66039126656639520936203017529360818061007971819918535640380875386612837009 (pp74)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 72.97 hours.
Scaled time: 134.20 units (timescale=1.839).
Factorization parameters were as follows:
name: 8*10^181+3
n: 9764800819530466924518836952107346921926064836602594080779488507011172569982077589063765484307783295905707377627405817
skew: 67407.88
# norm 1.60e+16
c5: 12060
c4: 3987625233
c3: -501223287428036
c2: -13966524767850640108
c1: 532227260136176141487706
c0: 11552261902925874836942455365
# alpha -5.61
Y1: 2159113508321
Y0: -60487020326792030157938
# Murphy_E 3.57e-10
# M 5213949619208846846643369347895106390731876475313017475218358403523304199793861470938855378906618354132884471051345753
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 25000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1500000, 1900001)
Primes: RFBsize:216816, AFBsize:216818, largePrimes:8168351 encountered
Relations: rels:8459764, finalFF:541290
Max relations in full relation-set: 28
Initial matrix: 433714 x 541290 with sparse part having weight 68304122.
Pruned matrix : 370334 x 372566 with weight 51046323.
Total sieving time: 68.03 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.39 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,50,50,2.4,2.4,60000
total time: 72.97 hours.
 --------- CPU info (if available) ----------

Sep 26, 2007 (4th)

By suberi / PRIMO

(52·102482-43)/9 is prime!

Sep 26, 2007 (3rd)

By Sinkiti Sibata / GGNFS, Msieve

(5·10109+7)/3 = 1(6)1089<110> = 192 · C107

C107 = P42 · P66

P42 = 153946522305899923004676383646159813796121<42>

P66 = 299896685009093874497686190587633018428192207232800575636015338349<66>

Number: 16669_109
N=46168051708217913204062788550323176361957525392428439519852262234533702677746999076638965835641735918744229
  ( 107 digits)
SNFS difficulty: 110 digits.
Divisors found:
 r1=153946522305899923004676383646159813796121 (pp42)
 r2=299896685009093874497686190587633018428192207232800575636015338349 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.17 hours.
Scaled time: 0.79 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_109
n: 46168051708217913204062788550323176361957525392428439519852262234533702677746999076638965835641735918744229
m: 10000000000000000000000
c5: 1
c0: 14
skew: 1.7
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 450001)
Primes: RFBsize:49098, AFBsize:63623, largePrimes:1899503 encountered
Relations: rels:1884233, finalFF:172922
Max relations in full relation-set: 28
Initial matrix: 112785 x 172922 with sparse part having weight 11280001.
Pruned matrix : 87896 x 88523 with weight 3680813.
Total sieving time: 1.01 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.17 hours.
 --------- CPU info (if available) ----------

(5·10115+7)/3 = 1(6)1149<116> = 83 · 1069 · 1180428929<10> · C102

C102 = P39 · P63

P39 = 296398376609473226797596655124462993281<39>

P63 = 536880075739627642112309347769656425847569291133442846496928603<63>

Number: 16669_115
N=159130382883196664131166647978403378748111484644347405870264581612954267174235629404567704102325716443
  ( 102 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=296398376609473226797596655124462993281 (pp39)
 r2=536880075739627642112309347769656425847569291133442846496928603 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.63 hours.
Scaled time: 1.10 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_115
n: 159130382883196664131166647978403378748111484644347405870264581612954267174235629404567704102325716443
m: 100000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:2093547 encountered
Relations: rels:2213778, finalFF:271300
Max relations in full relation-set: 28
Initial matrix: 113391 x 271300 with sparse part having weight 21663794.
Pruned matrix : 76323 x 76953 with weight 4050572.
Total sieving time: 1.45 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.08 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.63 hours.
 --------- CPU info (if available) ----------

(5·10120+7)/3 = 1(6)1199<121> = 210451967185245864060738227648101<33> · C88

C88 = P34 · P55

P34 = 2003771457999863638436035664075387<34>

P55 = 3952278809073709433995319843828553332517951348922169387<55>

Wed Sep 26 14:24:28 2007  Msieve v. 1.26
Wed Sep 26 14:24:28 2007  random seeds: 5143490f 0701fb59
Wed Sep 26 14:24:28 2007  factoring 7919463471679591443105528414604368703900563230510077999800695379563554517322213551577769 (88 digits)
Wed Sep 26 14:24:29 2007  commencing quadratic sieve (88-digit input)
Wed Sep 26 14:24:30 2007  using multiplier of 1
Wed Sep 26 14:24:30 2007  using 64kb Pentium 2 sieve core
Wed Sep 26 14:24:30 2007  sieve interval: 14 blocks of size 65536
Wed Sep 26 14:24:30 2007  processing polynomials in batches of 8
Wed Sep 26 14:24:30 2007  using a sieve bound of 1527497 (57880 primes)
Wed Sep 26 14:24:30 2007  using large prime bound of 122199760 (26 bits)
Wed Sep 26 14:24:30 2007  using double large prime bound of 360351695070240 (42-49 bits)
Wed Sep 26 14:24:30 2007  using trial factoring cutoff of 49 bits
Wed Sep 26 14:24:30 2007  polynomial 'A' values have 11 factors
Wed Sep 26 19:19:22 2007  58229 relations (16203 full + 42026 combined from 608880 partial), need 57976
Wed Sep 26 19:19:29 2007  begin with 625083 relations
Wed Sep 26 19:19:47 2007  reduce to 139473 relations in 10 passes
Wed Sep 26 19:19:48 2007  attempting to read 139473 relations
Wed Sep 26 19:19:56 2007  recovered 139473 relations
Wed Sep 26 19:19:56 2007  recovered 112269 polynomials
Wed Sep 26 19:20:15 2007  attempting to build 58229 cycles
Wed Sep 26 19:20:15 2007  found 58229 cycles in 5 passes
Wed Sep 26 19:20:17 2007  distribution of cycle lengths:
Wed Sep 26 19:20:17 2007     length 1 : 16203
Wed Sep 26 19:20:17 2007     length 2 : 11462
Wed Sep 26 19:20:17 2007     length 3 : 10350
Wed Sep 26 19:20:17 2007     length 4 : 7641
Wed Sep 26 19:20:17 2007     length 5 : 5205
Wed Sep 26 19:20:17 2007     length 6 : 3172
Wed Sep 26 19:20:17 2007     length 7 : 1903
Wed Sep 26 19:20:17 2007     length 9+: 2293
Wed Sep 26 19:20:17 2007  largest cycle: 18 relations
Wed Sep 26 19:20:18 2007  matrix is 57880 x 58229 with weight 3346646 (avg 57.47/col)
Wed Sep 26 19:20:22 2007  filtering completed in 3 passes
Wed Sep 26 19:20:22 2007  matrix is 53415 x 53479 with weight 3096508 (avg 57.90/col)
Wed Sep 26 19:20:24 2007  saving the first 48 matrix rows for later
Wed Sep 26 19:20:24 2007  matrix is 53367 x 53479 with weight 2483927 (avg 46.45/col)
Wed Sep 26 19:20:24 2007  matrix includes 64 packed rows
Wed Sep 26 19:20:24 2007  using block size 10922 for processor cache size 256 kB
Wed Sep 26 19:20:24 2007  commencing Lanczos iteration
Wed Sep 26 19:23:14 2007  lanczos halted after 845 iterations
Wed Sep 26 19:23:15 2007  recovered 16 nontrivial dependencies
Wed Sep 26 19:23:35 2007  prp34 factor: 2003771457999863638436035664075387
Wed Sep 26 19:23:35 2007  prp55 factor: 3952278809073709433995319843828553332517951348922169387
Wed Sep 26 19:23:35 2007  elapsed time 04:59:07

(5·10121+7)/3 = 1(6)1209<122> = 79 · 2382356651<10> · C110

C110 = P39 · P72

P39 = 275708725429269016809228525155998997753<39>

P72 = 321191741127943587251282728962673310095889920760636481110578718074425937<72>

Number: 16669_121
N=88555365564793051234214008584940727814733466817154162992301027014493685329128418132245529605674917232827919561
  ( 110 digits)
SNFS difficulty: 121 digits.
Divisors found:
 r1=275708725429269016809228525155998997753 (pp39)
 r2=321191741127943587251282728962673310095889920760636481110578718074425937 (pp72)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.59 hours.
Scaled time: 1.75 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_121
n: 88555365564793051234214008584940727814733466817154162992301027014493685329128418132245529605674917232827919561
m: 1000000000000000000000000
c5: 50
c0: 7
skew: 0.67
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 600001)
Primes: RFBsize:49098, AFBsize:63963, largePrimes:2104728 encountered
Relations: rels:2144770, finalFF:180084
Max relations in full relation-set: 28
Initial matrix: 113126 x 180084 with sparse part having weight 15976568.
Pruned matrix : 96531 x 97160 with weight 6113251.
Total sieving time: 2.32 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.15 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.59 hours.
 --------- CPU info (if available) ----------

(5·10125+7)/3 = 1(6)1249<126> = 4105166921<10> · 20017012591<11> · C106

C106 = P33 · P74

P33 = 168513932435459060567620404345611<33>

P74 = 12036018680677828464748171772279011079478949036231241898241956856646325889<74>

Number: 16669_125
N=2028236838747666687478534951496303214000516428894914134664497036559678113327291556491062877412232492823179
  ( 106 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=168513932435459060567620404345611 (pp33)
 r2=12036018680677828464748171772279011079478949036231241898241956856646325889 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.06 hours.
Scaled time: 2.07 units (timescale=0.677).
Factorization parameters were as follows:
name: 16669_125
n: 2028236838747666687478534951496303214000516428894914134664497036559678113327291556491062877412232492823179
m: 10000000000000000000000000
c5: 5
c0: 7
skew: 1.07
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 650001)
Primes: RFBsize:49098, AFBsize:64228, largePrimes:2213124 encountered
Relations: rels:2360223, finalFF:266542
Max relations in full relation-set: 28
Initial matrix: 113391 x 266542 with sparse part having weight 25504051.
Pruned matrix : 85873 x 86503 with weight 6283883.
Total sieving time: 2.80 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.13 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 3.06 hours.
 --------- CPU info (if available) ----------

Sep 26, 2007 (2nd)

By Jo Yeong Uk / GGNFS

(5·10113+7)/3 = 1(6)1129<114> = 139 · C112

C112 = P56 · P56

P56 = 33323707073076001771345428051913373104674894761352370801<56>

P56 = 35981614073029109077263780581405124329331786404763064471<56>

Number: 16669_113
N=1199040767386091127098321342925659472422062350119904076738609112709832134292565947242206235011990407673860911271
  ( 112 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=33323707073076001771345428051913373104674894761352370801 (pp56)
 r2=35981614073029109077263780581405124329331786404763064471 (pp56)
Version: GGNFS-0.77.1-20050930-nocona
Total time: 0.70 hours.
Scaled time: 1.50 units (timescale=2.143).
Factorization parameters were as follows:
n: 1199040767386091127098321342925659472422062350119904076738609112709832134292565947242206235011990407673860911271
m: 100000000000000000000000
c5: 1
c0: 140
skew: 2.69
type: snfs
Factor base limits: 360000/360000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [180000, 340001)
Primes: RFBsize:30757, AFBsize:30764, largePrimes:1046995 encountered
Relations: rels:964799, finalFF:87555
Max relations in full relation-set: 28
Initial matrix: 61585 x 87555 with sparse part having weight 4230236.
Pruned matrix : 54927 x 55298 with weight 1881639.
Total sieving time: 0.67 hours.
Total relation processing time: 0.02 hours.
Matrix solve time: 0.01 hours.
Time p