Table of contents 目次

  1. About 800...003 800...003 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 800...003 800...003 の形の素数
    1. Last updated 最終更新日
    2. Known (probable) prime numbers 既知の (おそらく) 素数
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 800...003 800...003 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 800...003 800...003 について

1.1. Classification 分類

Quasi-repdigit of the form ABB...BBC ABB...BBC の形のクワージレプディジット (Quasi-repdigit)

1.2. Sequence 数列

80w3 = { 83, 803, 8003, 80003, 800003, 8000003, 80000003, 800000003, 8000000003, 80000000003, … }

1.3. General term 一般項

8×10n+3 (1≤n)

2. Prime numbers of the form 800...003 800...003 の形の素数

2.1. Last updated 最終更新日

September 9, 2015 2015 年 9 月 9 日

2.2. Known (probable) prime numbers 既知の (おそらく) 素数

  1. 8×101+3 = 83 is prime. は素数です。
  2. 8×1031+3 = 8(0)303<32> is prime. は素数です。
  3. 8×10105+3 = 8(0)1043<106> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  4. 8×10113+3 = 8(0)1123<114> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  5. 8×10369+3 = 8(0)3683<370> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 6, 2004 2004 年 12 月 6 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 6, 2005 2005 年 1 月 6 日)
  6. 8×101359+3 = 8(0)13583<1360> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 6, 2006 2006 年 9 月 6 日)
  7. 8×106219+3 = 8(0)62183<6220> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 25, 2004 2004 年 12 月 25 日)
  8. 8×10105571+3 = 8(0)1055703<105572> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)
  9. 8×10150975+3 = 8(0)1509743<150976> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)

2.3. Range of search 捜索範囲

  1. n≤100000 / Completed 終了 / Dmitry Domanov / March 8, 2010 2010 年 3 月 8 日
  2. n≤200000 / Completed 終了 / Bob Price / September 8, 2015 2015 年 9 月 8 日

2.4. Prime factors that appear periodically 周期的に現れる素因数

  1. 8×102k+3 = 11×(8×100+311+72×102-19×11×k-1Σm=0102m)
  2. 8×106k+4+3 = 7×(8×104+37+72×104×106-19×7×k-1Σm=0106m)
  3. 8×108k+2+3 = 73×(8×102+373+72×102×108-19×73×k-1Σm=0108m)
  4. 8×1013k+3+3 = 53×(8×103+353+72×103×1013-19×53×k-1Σm=01013m)
  5. 8×1015k+11+3 = 31×(8×1011+331+72×1011×1015-19×31×k-1Σm=01015m)
  6. 8×1016k+5+3 = 17×(8×105+317+72×105×1016-19×17×k-1Σm=01016m)
  7. 8×1018k+17+3 = 19×(8×1017+319+72×1017×1018-19×19×k-1Σm=01018m)
  8. 8×1022k+7+3 = 23×(8×107+323+72×107×1022-19×23×k-1Σm=01022m)
  9. 8×1028k+8+3 = 29×(8×108+329+72×108×1028-19×29×k-1Σm=01028m)
  10. 8×1034k+24+3 = 103×(8×1024+3103+72×1024×1034-19×103×k-1Σm=01034m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 13.93%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 13.93% です。

3. Factor table of 800...003 800...003 の素因数分解表

3.1. Last updated 最終更新日

February 16, 2015 2015 年 2 月 16 日

3.2. Range of factorization 分解範囲

3.3. Terms that have not been factored yet まだ分解されていない項

n=197, 202, 206, 207, 209, 211, 212, 213, 214, 217, 218, 219, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 236, 239, 240, 241, 242, 244, 245, 247, 248, 250 (35/250)

3.4. Factor table 素因数分解表

8×101+3 = 83 = definitely prime number 素数
8×102+3 = 803 = 11 × 73
8×103+3 = 8003 = 53 × 151
8×104+3 = 80003 = 7 × 11 × 1039
8×105+3 = 800003 = 17 × 47059
8×106+3 = 8000003 = 11 × 727273
8×107+3 = 80000003 = 23 × 3478261
8×108+3 = 800000003 = 11 × 29 × 2507837
8×109+3 = 8000000003<10> = 677 × 11816839
8×1010+3 = 80000000003<11> = 7 × 11 × 73 × 389 × 36587
8×1011+3 = 800000000003<12> = 31 × 6983 × 3695611
8×1012+3 = 8000000000003<13> = 11 × 51679 × 14072887
8×1013+3 = 80000000000003<14> = 227 × 352422907489<12>
8×1014+3 = 800000000000003<15> = 11 × 313 × 232355503921<12>
8×1015+3 = 8000000000000003<16> = 443 × 112939 × 159897739
8×1016+3 = 80000000000000003<17> = 7 × 11 × 53 × 2267 × 56843 × 152123
8×1017+3 = 800000000000000003<18> = 19 × 42105263157894737<17>
8×1018+3 = 8000000000000000003<19> = 112 × 73 × 905694554511491<15>
8×1019+3 = 80000000000000000003<20> = 109 × 16253 × 1287743 × 35067173
8×1020+3 = 800000000000000000003<21> = 11 × 150413 × 675151 × 716161571
8×1021+3 = 8000000000000000000003<22> = 17 × 439 × 1071954977890928581<19>
8×1022+3 = 80000000000000000000003<23> = 7 × 11 × 1038961038961038961039<22>
8×1023+3 = 800000000000000000000003<24> = 661 × 229689653 × 5269229272891<13>
8×1024+3 = 8000000000000000000000003<25> = 11 × 103 × 2383 × 12583 × 235478813120119<15>
8×1025+3 = 80000000000000000000000003<26> = 18649609621<11> × 4289634025900343<16>
8×1026+3 = 800000000000000000000000003<27> = 11 × 31 × 73 × 23603 × 1987537 × 685062695861<12>
8×1027+3 = 8000000000000000000000000003<28> = 784495495981<12> × 10197636622497263<17>
8×1028+3 = 80000000000000000000000000003<29> = 72 × 11 × 66221 × 654967 × 3529441 × 969572171
8×1029+3 = 800000000000000000000000000003<30> = 23 × 53 × 107 × 229 × 262288283 × 102114668361413<15>
8×1030+3 = 8000000000000000000000000000003<31> = 11 × 981482123 × 740994369871703993051<21>
8×1031+3 = 80000000000000000000000000000003<32> = definitely prime number 素数
8×1032+3 = 800000000000000000000000000000003<33> = 11 × 8693 × 11399091131<11> × 733934658021984031<18>
8×1033+3 = 8000000000000000000000000000000003<34> = 43874627 × 98517337073<11> × 1850818727789393<16>
8×1034+3 = 80000000000000000000000000000000003<35> = 7 × 11 × 73 × 199 × 262436075963<12> × 272520884534145539<18>
8×1035+3 = 800000000000000000000000000000000003<36> = 19 × 263 × 13411 × 41894466829<11> × 284946159087225121<18>
8×1036+3 = 8000000000000000000000000000000000003<37> = 11 × 29 × 2871563 × 25551370127189<14> × 341795831706491<15>
8×1037+3 = 80000000000000000000000000000000000003<38> = 17 × 475053005483611<15> × 9906015325911933748969<22>
8×1038+3 = 800000000000000000000000000000000000003<39> = 11 × 227699 × 4429417 × 503895548843<12> × 143103115325617<15>
8×1039+3 = 8000000000000000000000000000000000000003<40> = 33493639 × 668392133 × 357352086579892684476769<24>
8×1040+3 = 80000000000000000000000000000000000000003<41> = 7 × 112 × 132040897 × 715316282211507793844536899917<30>
8×1041+3 = 800000000000000000000000000000000000000003<42> = 31 × 1163 × 22189554267328655035641971541896652151<38>
8×1042+3 = 8000000000000000000000000000000000000000003<43> = 11 × 53 × 73 × 83 × 293 × 7729525946888643630815885058146243<34>
8×1043+3 = 80000000000000000000000000000000000000000003<44> = 47 × 161569 × 252798042738519287<18> × 41673539165929557083<20>
8×1044+3 = 800000000000000000000000000000000000000000003<45> = 11 × 59 × 1335106159<10> × 923271629851945325532435651049733<33>
8×1045+3 = 8000000000000000000000000000000000000000000003<46> = 3319 × 2410364567640855679421512503766194636938837<43>
8×1046+3 = 80000000000000000000000000000000000000000000003<47> = 7 × 11 × 808187 × 3874279 × 252890311 × 2404909901<10> × 545588877436513<15>
8×1047+3 = 800000000000000000000000000000000000000000000003<48> = 892704843854221<15> × 896152861169688318559696303598543<33>
8×1048+3 = 8000000000000000000000000000000000000000000000003<49> = 11 × 367 × 1751623 × 1131333372878431437831391824390899576353<40>
8×1049+3 = 80000000000000000000000000000000000000000000000003<50> = 2089 × 4493 × 8523444319587823279593372041845423714800439<43>
8×1050+3 = 800000000000000000000000000000000000000000000000003<51> = 11 × 73 × 1511298750851<13> × 659210503152769736257238319497783051<36>
8×1051+3 = 8(0)503<52> = 23 × 61 × 1075355269<10> × 5302495987758294626525975386152930218629<40>
8×1052+3 = 8(0)513<53> = 7 × 11 × 3923 × 8243 × 32128884983556876429528803078113287760113751<44>
8×1053+3 = 8(0)523<54> = 17 × 19 × 57424087729<11> × 43131380640248358587703649188273670155409<41>
8×1054+3 = 8(0)533<55> = 11 × 11721890915948123<17> × 62043976734439859046741982481053751051<38>
8×1055+3 = 8(0)543<56> = 53 × 4129 × 17431 × 19392167 × 121477320301<12> × 8902774761774115679578460147<28>
8×1056+3 = 8(0)553<57> = 11 × 31 × 15050214077<11> × 793606044487<12> × 2756979091572917<16> × 71245016449508401<17>
8×1057+3 = 8(0)563<58> = 71865389213<11> × 1307075859827<13> × 85166619881691312524283341358054053<35>
8×1058+3 = 8(0)573<59> = 7 × 11 × 73 × 103 × 4447099404637863059<19> × 31071508594872805524194675855096459<35>
8×1059+3 = 8(0)583<60> = 567383 × 27898757 × 2340629520184369<16> × 21592162274488674956986804816577<32>
8×1060+3 = 8(0)593<61> = 11 × 727272727272727272727272727272727272727272727272727272727273<60>
8×1061+3 = 8(0)603<62> = 1669 × 47932893948472139005392450569203115638106650689035350509287<59>
8×1062+3 = 8(0)613<63> = 112 × 409 × 231559 × 111039989 × 110409209191<12> × 5694229067442353566241963036625847<34>
8×1063+3 = 8(0)623<64> = 1193 × 14042761 × 477526017744974382138745095755344510601420905299813811<54>
8×1064+3 = 8(0)633<65> = 7 × 11 × 29 × 5870523053<10> × 6844629419<10> × 891609170101262599464086175914257228297013<42>
8×1065+3 = 8(0)643<66> = 1394389 × 148466510419<12> × 5272065747354949486171<22> × 732987756330063899024306423<27>
8×1066+3 = 8(0)653<67> = 11 × 73 × 1202269643<10> × 1676262932271402143218087<25> × 4943453107172608935036406237061<31>
8×1067+3 = 8(0)663<68> = 1613 × 1027787 × 789075952717253<15> × 61155242278618976517684297186637893855471721<44>
8×1068+3 = 8(0)673<69> = 11 × 532 × 204583 × 7496894159791<13> × 16880862804494345582361142441843437935407200649<47>
8×1069+3 = 8(0)683<70> = 17 × 317 × 51962327 × 15712673005300727<17> × 1818206220473972652653184549099598068790463<43>
8×1070+3 = 8(0)693<71> = 72 × 11 × 5171 × 1150477396992224280429460523647<31> × 24948738636797438946308049673214621<35> (Makoto Kamada / msieve 0.81 / 47 seconds)
8×1071+3 = 8(0)703<72> = 19 × 31 × 1103 × 266821 × 3098783 × 6508081816133<13> × 228841614712619592877279682697858576632311<42>
8×1072+3 = 8(0)713<73> = 11 × 131 × 587 × 7705057 × 42702809047<11> × 12935088148959819721<20> × 2222215702120388264670955570951<31>
8×1073+3 = 8(0)723<74> = 23 × 233 × 1942757 × 1320873538247<13> × 37677163045049972333<20> × 154400361613164759255471946730731<33>
8×1074+3 = 8(0)733<75> = 11 × 73 × 9439 × 2389619 × 4315068851<10> × 10236042095082544689857584995848601999525929187167911<53>
8×1075+3 = 8(0)743<76> = 188779 × 3909267091<10> × 701492506592451927206719<24> × 15453182230628394947646365908854574733<38>
8×1076+3 = 8(0)753<77> = 7 × 11 × 3232238695369<13> × 415036967988709934528267<24> × 774477945246471710078538349910933433893<39>
8×1077+3 = 8(0)763<78> = 8169308075963<13> × 97927510207857573992866361114049392028488341159366269518918869081<65>
8×1078+3 = 8(0)773<79> = 11 × 151 × 28181 × 4112490633703<13> × 89516675599707971<17> × 464253394020511340773358308194601595000791<42>
8×1079+3 = 8(0)783<80> = 762917 × 463929885844279024771<21> × 403260075284126100029633029<27> × 560499355568344229708718601<27>
8×1080+3 = 8(0)793<81> = 11 × 97 × 1801 × 140421419311<12> × 1794707887841403001<19> × 1651903695809972440677960373793941442033690119<46>
8×1081+3 = 8(0)803<82> = 53 × 1009 × 34330441972126526344107580271537<32> × 4357561814692112077426598342166795767977005047<46> (Makoto Kamada / GGNFS-0.70.1 / 0.10 hours)
8×1082+3 = 8(0)813<83> = 7 × 11 × 73 × 107 × 461 × 216317 × 31845991 × 107411984579<12> × 11034870330762312227<20> × 35336725616889405113813031847859<32>
8×1083+3 = 8(0)823<84> = 83 × 33536059111<11> × 287408672109179772000016984618101405815598080263717980858338163868549831<72>
8×1084+3 = 8(0)833<85> = 112 × 55787 × 172352981 × 6876268239228814677307933716672056455100832624154722455550862026057869<70>
8×1085+3 = 8(0)843<86> = 17 × 4705882352941176470588235294117647058823529411764705882352941176470588235294117647059<85>
8×1086+3 = 8(0)853<87> = 11 × 31 × 51992894757193071098834645121805421870281<41> × 45122339632645802553442119914381794587095743<44> (Makoto Kamada / GGNFS-0.70.3 / 0.13 hours)
8×1087+3 = 8(0)863<88> = 2237 × 2783233637<10> × 452322196859180670722705119853<30> × 2840706977234826416475037502646911280607974079<46> (Makoto Kamada / msieve 0.83 / 11 minutes)
8×1088+3 = 8(0)873<89> = 7 × 11 × 197 × 2209987429321358015127649757841903166192063<43> × 2386399955666281289040005203830649017037949<43> (Makoto Kamada / GGNFS-0.70.3 / 0.15 hours)
8×1089+3 = 8(0)883<90> = 19 × 472 × 3109501 × 14296927638194957491<20> × 428753077450911004740266186056240330736025446540684248842023<60>
8×1090+3 = 8(0)893<91> = 11 × 73 × 193 × 170085607 × 938130909964865534091552476961419737<36> × 323508818017133291941816792568731577689423<42> (Makoto Kamada / GGNFS-0.70.3 / 0.21 hours)
8×1091+3 = 8(0)903<92> = 113 × 77573 × 12149329 × 1074573224735595634039887047<28> × 699057095784542323854892532766371206825997051691169<51>
8×1092+3 = 8(0)913<93> = 11 × 29 × 103 × 3491 × 66248925079<11> × 24290370549213544581361<23> × 4334103262048748903730959906132907155843386084534351<52>
8×1093+3 = 8(0)923<94> = 2053937786051542486210180283<28> × 3894957312888757681393174562958023891479027822449758422495835754841<67>
8×1094+3 = 8(0)933<95> = 7 × 11 × 53 × 601 × 21433 × 26261246527<11> × 369459993133008966638741<24> × 1970926442135483927984839<25> × 79581621853365472371143407<26>
8×1095+3 = 8(0)943<96> = 23 × 54751 × 79231 × 25642081 × 490826459119<12> × 267423707733290178422117579389<30> × 2382285558188963882135861228559133111<37> (Makoto Kamada / msieve 0.81 / 1.4 minutes)
8×1096+3 = 8(0)953<97> = 11 × 232701226253<12> × 267430733679223334492428286586361<33> × 11686576711987162822836634581578879259881985725704181<53> (Makoto Kamada / GGNFS-0.71.4 / 0.31 hours)
8×1097+3 = 8(0)963<98> = 3511 × 25981 × 5878069 × 5775687991<10> × 677628322879<12> × 38121794928848640593468164444529611540856155116816184893745613<62>
8×1098+3 = 8(0)973<99> = 11 × 73 × 8311 × 222796787 × 295089888774096271<18> × 1823299056393473406307522267792201685796264235812755890403426181683<67>
8×1099+3 = 8(0)983<100> = 2131 × 2752211938103<13> × 1364032326697768990154089754568863333576918442246231127582930452520001873599418846071<85>
8×10100+3 = 8(0)993<101> = 7 × 11 × 179 × 36408319 × 6115017566381<13> × 2455669220460404089924466119<28> × 10616418433959711373400277784445293578937077817201<50>
8×10101+3 = 8(0)1003<102> = 17 × 31 × 557 × 922283 × 309525393822366661<18> × 9546928899824104087628266915435753352884151337437783966611208571902614279<73>
8×10102+3 = 8(0)1013<103> = 11 × 59 × 2909 × 250321394839<12> × 73893077891192132187902179374341<32> × 229086681980295270219691452305688749689507823847518717<54> (Robert Backstrom / Msieve v. 1.25 for P32 x P54 / 41.33 minutes / August 9, 2007 2007 年 8 月 9 日)
8×10103+3 = 8(0)1023<104> = 8447 × 4354457 × 12301281430605925812079463<26> × 92650460140163238877679901473<29> × 1908339112582881881543260411801319113043<40>
8×10104+3 = 8(0)1033<105> = 11 × 21107 × 237845132143<12> × 77926895668201<14> × 1712194848032429<16> × 108576531164926624074615159282254415664503512696871914972137<60>
8×10105+3 = 8(0)1043<106> = definitely prime number 素数
8×10106+3 = 8(0)1053<107> = 7 × 112 × 73 × 10499 × 106273 × 47189860490284841929338677754779<32> × 24573337579454995751875650980653118980652254383713835857903861<62> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4256974982 for P32 / August 1, 2007 2007 年 8 月 1 日)
8×10107+3 = 8(0)1063<108> = 192 × 53 × 4311041529493168981918983158515670589329095421550917<52> × 9698949742404051679952742591797529833940595342191923<52> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.82 hours on Cygwin on AMD XP 2700+ / August 9, 2007 2007 年 8 月 9 日)
8×10108+3 = 8(0)1073<109> = 11 × 5527 × 9958256083822556593072164658877<31> × 13213703178894954610665804924839486965167161792188153823634168464500913387<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.96 hours on Cygwin on AMD 64 3200+ / August 9, 2007 2007 年 8 月 9 日)
8×10109+3 = 8(0)1083<110> = 41389 × 296676938035337991737<21> × 6515102690147474147803980219580376568939662956483643880211324239313109630254913501671<85>
8×10110+3 = 8(0)1093<111> = 11 × 14747 × 67853 × 229991531503<12> × 3428025182905969<16> × 203471506518364613<18> × 453069803603611603225742588679081501394410587616941028533<57>
8×10111+3 = 8(0)1103<112> = 61 × 1270823 × 157003159 × 9770136203<10> × 242125581741895343<18> × 277859595771752157056080803440560953539521517341413915037994444184691<69>
8×10112+3 = 8(0)1113<113> = 72 × 11 × 147858293717<12> × 3840117103591<13> × 454057872231532423<18> × 5215142530978054082743<22> × 110391000996324009180070685590142723852019595619<48>
8×10113+3 = 8(0)1123<114> = definitely prime number 素数
8×10114+3 = 8(0)1133<115> = 11 × 73 × 1229 × 652743731 × 20457301024193281<17> × 607059854616891932209263404593988019400899404926677156356776277950084265934947019079<84>
8×10115+3 = 8(0)1143<116> = 1583 × 1488167 × 33959196211481846962456934024507853554622045456700995229980508257619816127584031170371932845565540728475723<107>
8×10116+3 = 8(0)1153<117> = 11 × 31 × 501077 × 30244611063283188190841459<26> × 47772235073471907793622686848045341<35> × 3240466788618869376438883648133185467425146712141<49> (Robert Backstrom / Msieve v. 1.25 for P35 x P49 / 27.1 minutes / August 9, 2007 2007 年 8 月 9 日)
8×10117+3 = 8(0)1163<118> = 17 × 23 × 95569 × 3626149 × 743563094142647141671434594596447952314537<42> × 79402233062151798302517520827673963545042250342272076178284489<62> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.14 hours on Cygwin on AMD 64 3400+ / August 9, 2007 2007 年 8 月 9 日)
8×10118+3 = 8(0)1173<119> = 7 × 11 × 17483 × 22901138627205461270741<23> × 5535500757107990826350590321<28> × 34034286784005507880536617237<29> × 13773764714661578982854007624838469<35>
8×10119+3 = 8(0)1183<120> = 181 × 7879 × 5340576803<10> × 7656422875069<13> × 14906395578079<14> × 920351219985499557329425477239335493763008845217762342623031845746947655049449<78>
8×10120+3 = 8(0)1193<121> = 11 × 29 × 53 × 967 × 50671 × 2402101204589<13> × 4020186343903541310162314350309733821840427310675442992491335802827098230138099978328162594451973<97>
8×10121+3 = 8(0)1203<122> = 268643 × 14246316379<11> × 791708730619<12> × 26402584382264426724108231728453509277741367521807668516494911008472968065215131360301307538921<95>
8×10122+3 = 8(0)1213<123> = 11 × 73 × 81135620752009<14> × 5586942927233741<16> × 2197802401562353589182156357544860335050188368321982663784948515492198227650802517969668029<91>
8×10123+3 = 8(0)1223<124> = 3167 × 316094792597854896892960037<27> × 7991431521932828511913808110150837880640721341059920292042849101514929681722100481673801255257<94>
8×10124+3 = 8(0)1233<125> = 7 × 11 × 83 × 3559 × 101267 × 209717 × 176677715696117<15> × 937367355983571473432402332509988855496923996553784249014018921332426151398109873328705702649<93>
8×10125+3 = 8(0)1243<126> = 19 × 14029 × 949651 × 4975503961<10> × 418225494423564917<18> × 221118619773890855246685841<27> × 6868671502290063230111711508454885225930210859465739472430659<61>
8×10126+3 = 8(0)1253<127> = 11 × 103 × 227 × 60103 × 2949429481414692226044768697960391260971797<43> × 175468859339115509595120669476348065354330998690902949927637469395852909063<75> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 2.10 hours on Cygwin on AMD 64 3200+ / August 9, 2007 2007 年 8 月 9 日)
8×10127+3 = 8(0)1263<128> = 109 × 733944954128440366972477064220183486238532110091743119266055045871559633027522935779816513761467889908256880733944954128440367<126>
8×10128+3 = 8(0)1273<129> = 112 × 78881689 × 10518172897<11> × 31189870538527<14> × 15581864538979112551<20> × 16396649515932494065701296267925360926143309101983646833808095861719319963723<77>
8×10129+3 = 8(0)1283<130> = 4373 × 82883 × 9383621683393851037733688168129743757022677767<46> × 2352201687843988988161223366148433683159763965903221828415227547320810905051<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.89 hours on Cygwin on AMD XP 2700+ / August 9, 2007 2007 年 8 月 9 日)
8×10130+3 = 8(0)1293<131> = 7 × 11 × 73 × 1301 × 1879 × 3920377 × 125920165279<12> × 15660751854468820254646065544043536489389591847<47> × 753072171293408570603918263199513415256851689104201069517<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.27 hours on Cygwin on AMD 64 3200+ / August 9, 2007 2007 年 8 月 9 日)
8×10131+3 = 8(0)1303<132> = 31 × 18556133 × 140515311157889484872449865329<30> × 9897309858587474462533808559524778559507284816320764852168510088136599686173598612238548962409<94> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.46 hours on Cygwin on AMD 64 3400+ / August 9, 2007 2007 年 8 月 9 日)
8×10132+3 = 8(0)1313<133> = 11 × 10091 × 41507 × 72923 × 59137933926855043059088194258782854822196623669244767645811<59> × 402634584408763303069783264206996096355933083613814946383593<60> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 2.77 hours on Cygwin on AMD 64 3200+ / August 9, 2007 2007 年 8 月 9 日)
8×10133+3 = 8(0)1323<134> = 17 × 53 × 199 × 571 × 781404686078041874871538290553591912711548591811568479537585023300852847539770299645938699447036043629300874590125160421161107<126>
8×10134+3 = 8(0)1333<135> = 11 × 149 × 43405903 × 643534253 × 99025999314875960050767509377639719951680928982163689<53> × 176457993407320655445898143590093815879839497274040644855506527<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.16 hours on Cygwin on AMD 64 3200+ / August 9, 2007 2007 年 8 月 9 日)
8×10135+3 = 8(0)1343<136> = 47 × 107 × 167 × 445141 × 64394703446581<14> × 671518907669361327306106053768429944141723<42> × 494864033010832382214144161118931762517426636975925163439107088158187<69> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.65 hours on Cygwin on AMD XP 2700+ / August 9, 2007 2007 年 8 月 9 日)
8×10136+3 = 8(0)1353<137> = 7 × 11 × 525529 × 3285647117<10> × 143530513309195232999340064204983398299225538897530547<54> × 4192155846886791687644896239201840126733252957278980362790474381809<67> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.95 hours on Cygwin on AMD 64 3400+ / August 9, 2007 2007 年 8 月 9 日)
8×10137+3 = 8(0)1363<138> = 234197724741713<15> × 3415917045659973707995573522830132950656230966488448714185425810779379160872606705826467649195998166540203490196881882061331<124>
8×10138+3 = 8(0)1373<139> = 11 × 73 × 114702851 × 1670593388520748238821421178145481837<37> × 104636458414847985111598726280566932595983083<45> × 496874190989597803112505558533083407730421846981<48> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 5.54 hours on Cygwin on AMD 64 3200+ / August 10, 2007 2007 年 8 月 10 日)
8×10139+3 = 8(0)1383<140> = 23 × 8543458983547141<16> × 407125600563378075866452671220053277190892468365831516466241632483837061786795743263207884948689538425917458131593362006321<123>
8×10140+3 = 8(0)1393<141> = 11 × 25554223 × 15891364671711296496697<23> × 179090862327462564452009054626614549314357041631189636105018439331780893059507069609327444017287416114796903583<111>
8×10141+3 = 8(0)1403<142> = 56055709 × 364100444483<12> × 531838425845359<15> × 737002931992221038534166527565828073535776760460419692699121627832970580889326908528540386492382636610843611<108>
8×10142+3 = 8(0)1413<143> = 7 × 11 × 2052821 × 555623953052671<15> × 66874197333983887<17> × 7352063485952674581275466674908134761977993<43> × 1852675630827404483230700868124109595424698262269677635106219<61> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 10.17 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 12, 2007 2007 年 8 月 12 日)
8×10143+3 = 8(0)1423<144> = 19 × 379 × 11813 × 221087 × 4516212432004069217<19> × 8406016943441479893959693<25> × 1120492986465098726033974583382789488826987710649084441975785272765641292908005564346173<88>
8×10144+3 = 8(0)1433<145> = 11 × 683 × 393806677683834962330167370796793978219439105832001<51> × 2703918032157216794192284740946405968077357310935054868472060871084932805552853385839924731<91> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 6.79 hours on Cygwin on AMD 64 3200+ / August 10, 2007 2007 年 8 月 10 日)
8×10145+3 = 8(0)1443<146> = 11766775508491<14> × 605396612359960159<18> × 51046027337556414770008979411652470215926317473591<50> × 220004003518038430086171786263037474229055943495226606880307715457<66> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 7.75 hours on Cygwin on AMD 64 3200+ / August 11, 2007 2007 年 8 月 11 日)
8×10146+3 = 8(0)1453<147> = 11 × 31 × 53 × 73 × 1663 × 273919 × 1623467 × 423225567534437<15> × 1030135101140839<16> × 1880671419246688595464604866691528974862487144051760955949638153504473954417737826119959617250051<97>
8×10147+3 = 8(0)1463<148> = 31466053047841<14> × 446393418652404001<18> × 2323850000470988610164769082031528440943605820371041061<55> × 245087883633789932212635585467307279310123198991773916587660103<63> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 18.83 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 17, 2007 2007 年 8 月 17 日)
8×10148+3 = 8(0)1473<149> = 7 × 11 × 29 × 317 × 509 × 13229 × 1633127480251888041774589540737718105895353<43> × 10277254618113551226936717541671467485926625997768564715394439356053800695383219974495822267431<95> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 17.86 hours on Cygwin on AMD XP 2700+ / August 16, 2007 2007 年 8 月 16 日)
8×10149+3 = 8(0)1483<150> = 17 × 65286080108845637650879<23> × 7385100750797983107672043705537569949<37> × 97603197957078940502415021668837796258378802054006942074636790201088264247159331747210129<89> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3224045903 for P37 / August 3, 2007 2007 年 8 月 3 日)
8×10150+3 = 8(0)1493<151> = 112 × 333847094812043<15> × 123915190735934296426572399348483454050629019309155367871597523<63> × 1598204928807240823149342852972588765245266509250337333568977262671359787<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 16.97 hours on Cygwin on AMD XP 2700+ / August 13, 2007 2007 年 8 月 13 日)
8×10151+3 = 8(0)1503<152> = 1131077 × 70729048508633806540138292972096506250237605397333691693845777077953136700684391955631667870534013157371248818603861629225950134252575200450544039<146>
8×10152+3 = 8(0)1513<153> = 11 × 2579 × 28371454403<11> × 336678847633<12> × 3422844640710287449<19> × 20918851613784488258393673803<29> × 41230965182166976497662730773979766302299982947056022070519379750159227452766779<80>
8×10153+3 = 8(0)1523<154> = 151 × 347 × 2843 × 1902048496423825078608398414836733249964757502655492013897910231644363411<73> × 28234826233775491249880369404044758618051858710202572340818371819411450863<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 26.88 hours on Cygwin on AMD XP 2700+ / August 11, 2007 2007 年 8 月 11 日)
8×10154+3 = 8(0)1533<155> = 72 × 11 × 73 × 6763250917489964555182738767583283902011275699423252245547421266789261<70> × 300623454884502196692218573721100636698457518684754797248879483662802680386190709<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 17.23 hours on Cygwin on AMD 64 3400+ / August 10, 2007 2007 年 8 月 10 日)
8×10155+3 = 8(0)1543<156> = 773 × 266449 × 3103527589<10> × 1251528627155639164199916747969826060711425922321229282587770871616682700815026262721404787403918692705714299304471900518721084606042891051<139>
8×10156+3 = 8(0)1553<157> = 11 × 217489 × 350411 × 747131311 × 101603729565571469689<21> × 21328690499264043747847<23> × 5894018504747416231693659414080884214710672916599792947454431000326270305908773811988954517099<94>
8×10157+3 = 8(0)1563<158> = 1243523 × 2355211711<10> × 1447349903160164528341<22> × 18872640887254146082294006254212089368658493319806297325592949968676605353833020130022985287385535952949960034686075647811<122>
8×10158+3 = 8(0)1573<159> = 11 × 631 × 1250671907<10> × 40979175159967469<17> × 2248854384424882488961561751344764306410287459803078696649448310882043257096537712187210405199786375583248400385713503467823016201<130>
8×10159+3 = 8(0)1583<160> = 53 × 1249 × 15803 × 153231313845746405825884701365885833226325571486615400562069271<63> × 49907361884479263130985185256128895476821348429200465525031812515377456758530477125109523<89> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 29.43 hours on Cygwin on AMD 64 3400+ / August 13, 2007 2007 年 8 月 13 日)
8×10160+3 = 8(0)1593<161> = 7 × 11 × 59 × 103 × 17191 × 15416167801<11> × 110265275957<12> × 5850509482617685466678711858680214178216504239137200505416320587381515785453594912361067953600933779570707101802765601106684653761<130>
8×10161+3 = 8(0)1603<162> = 19 × 23 × 31 × 129126249073062336423461145334519<33> × 2631015527810085421291051911982281677569752486170207<52> × 173823667706511661436246647779256732900511330139840852735400152888111969953<75> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1730702291 for P33 / August 3, 2007 2007 年 8 月 3 日) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 65.82 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 16, 2007 2007 年 8 月 16 日)
8×10162+3 = 8(0)1613<163> = 11 × 73 × 563 × 1519506206599<13> × 11645645572705370842511370232719758223630265958429311476732548901555870142467162509939957997664258756251989201839808616696129890956171898763439373<146>
8×10163+3 = 8(0)1623<164> = 263814841588028840292075635769021187187588777<45> × 2946574066938041203271903376456481181720414869700453<52> × 102913749296606783576701454837580698830029182185894558528664578737263<69> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 62.05 hours on Cygwin on AMD 64 3200+ / August 13, 2007 2007 年 8 月 13 日)
8×10164+3 = 8(0)1633<165> = 11 × 269 × 270361608651571476850287259209192294694153430212909766813112538019601216627238932071645826292666441365326123690435958093950659006421088205474822575194322406218317<162>
8×10165+3 = 8(0)1643<166> = 17 × 83 × 2221 × 12653 × 1033040033209816345546009288939<31> × 19558081525904346337653953996359<32> × 31235192130845769254279459512560137999028121<44> × 319693142674609372256180538787347658839023974155301<51> (JMB / GMP-ECM B1=1000000, sigma=2461535803 for P32 / August 10, 2007 2007 年 8 月 10 日) (JMB / GMP-ECM B1=1000000, sigma=3313357411 for P31 / August 14, 2007 2007 年 8 月 14 日) (JMB / MSieve, version 1.25 / August 15, 2007 2007 年 8 月 15 日)
8×10166+3 = 8(0)1653<167> = 7 × 11 × 7207 × 213557 × 675042207726840501923943437063716431944375391927644166365098739719847433933733106431880955429652535398774532475286500174046221017501050758866213895714122261<156>
8×10167+3 = 8(0)1663<168> = 251467910385709<15> × 126974570731714215575127079<27> × 837436146854618446845679601742976105039316057<45> × 29918440904777602878053870979485087624956432150490430623595618437356372457311766689<83> (Jo Yeong Uk / GMP-ECM 6.2 B1=1000000, sigma=127447873 for P45 / July 18, 2008 2008 年 7 月 18 日)
8×10168+3 = 8(0)1673<169> = 11 × 7508952959070127<16> × 67190157772167649<17> × 13469805809745432155725685004278020183984235651737<50> × 107016544227351834704803055140285312688017262106116130497648324056315093035478326557023<87> (Erik Branger / GGNFS, Msieve snfs / 78.19 hours / November 26, 2008 2008 年 11 月 26 日)
8×10169+3 = 8(0)1683<170> = 1224246060187948513536044665977519421<37> × 65346340577741579518249257770472291479731205704109850662463019782005485937532123816920926149530479698626097812995924318713137169466943<134> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=605871003 for P37 / August 12, 2007 2007 年 8 月 12 日)
8×10170+3 = 8(0)1693<171> = 11 × 73 × 25087 × 32666806785659<14> × 518810619846876503372769619770433<33> × 2343204381484500438488187466170885890773141731069741607646382933532921328434754372068190854059489563670232771599467309<118> (JMB / GMP-ECM B1=1000000, sigma=650741743 for P33 / August 14, 2007 2007 年 8 月 14 日)
8×10171+3 = 8(0)1703<172> = 612 × 4127 × 852049508559867811<18> × 41830988536643648556938375963<29> × 14616146588079515322204221559487489982957819195442464500318341681782225823320505611257273099132714329208444985035252613<119>
8×10172+3 = 8(0)1713<173> = 7 × 112 × 53 × 261587 × 13420331 × 14742878852145643127878371424312249<35> × 14102707670245966200868549502313038790457<41> × 2441555056445183184204788723617272663411410204503080174188931011979879367292787673<82> (JMB / GMP-ECM B1=3000000, sigma=3195193927 for p35 / August 15, 2007 2007 年 8 月 15 日) (Robert Backstrom / GMP-ECM 6.0.1 B1=2302000, sigma=733154304 for P41 / April 24, 2008 2008 年 4 月 24 日)
8×10173+3 = 8(0)1723<174> = 10399 × 18679 × 27631 × 28669 × 1023782077690866407<19> × 605286136297580386697019909685997659989184662614889822728933<60> × 8390104882831017059551806967313117034601771718718344939080921989027231408917027<79> (Markus Tervooren / GMP-ECM 6.3 B1=70000000, sigma=2225376710 for P60 / April 21, 2011 2011 年 4 月 21 日)
8×10174+3 = 8(0)1733<175> = 11 × 28860413 × 78072669179616838037<20> × 58319517970184659869796570451093775131605719061637600472721<59> × 5534543522203279785194526066815580052792755359139105399639480903579771606109043650904473<88> (Erik Branger / GGNFS, Msieve snfs / May 22, 2011 2011 年 5 月 22 日)
8×10175+3 = 8(0)1743<176> = 2311 × 8719 × 10144789 × 189170845637<12> × 64291971599470835512165635997396471<35> × 32178766751417498825847425179242872864738948414927779187900762406084025362150026649375978793241187540045915304472389<116> (JMB / GMP-ECM B1=1000000, sigma=3854916441 for P35 / August 11, 2007 2007 年 8 月 11 日)
8×10176+3 = 8(0)1753<177> = 11 × 29 × 31 × 97 × 62483 × 122288966750943559327954013<27> × 13203393905721557635469906716094551<35> × 4919037198222532817308550055704182012037503<43> × 1680548460217191645379213872474567141004274448100352481467434493<64> (JMB / GMP-ECM B1=1000000, sigma=265324565 for P35 / August 11, 2007 2007 年 8 月 11 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P43 x P64 / 10.56 hours on Core 2 Quad Q6600 / August 12, 2007 2007 年 8 月 12 日)
8×10177+3 = 8(0)1763<178> = 385193 × 2734184657326888957539301452070127<34> × 7595979059565388610562921211099574234745355573365762780772087213624892584821367744840306376847974198287155385422756473803526652906088908773<139> (JMB / GMP-ECM B1=1000000, sigma=2128350113 for P34 / August 10, 2007 2007 年 8 月 10 日)
8×10178+3 = 8(0)1773<179> = 7 × 11 × 73 × 120504276263123<15> × 1521121596498992083430684328800554217699357191<46> × 77644377170813478936009808463885244242858683928639274087657213019286395263296774458233906745544656020639399572401451<116> (matsui / GGNFS-0.77.1-20060722-nocona snfs / 118.65 hours / May 16, 2009 2009 年 5 月 16 日)
8×10179+3 = 8(0)1783<180> = 19 × 7459 × 51407 × 2954417 × 836674876807247<15> × 62090197398500355626187081108200291143581512383270387942014919066205633<71> × 715454395426326700595103002865314154588423636021155502764544719423503258590347<78> (Wataru Sakai / June 2, 2012 2012 年 6 月 2 日)
8×10180+3 = 8(0)1793<181> = 11 × 5171 × 58979 × 2987999523284992099934311763<28> × 47168122930429269185104632077539243740140053368886472724554691478585831<71> × 16919839605828614941138139135134771677002119316946618577025570077600336349<74> (Kenji Ibusuki / Msieve v. 1.49 (SVN unknown) + GGNFS-0.77.1-VC8 with factMsieve.pl (decomposed + modified) snfs / October 8, 2013 2013 年 10 月 8 日)
8×10181+3 = 8(0)1803<182> = 17 × 47 × 120077 × 766223541469<12> × 752719880879203667<18> × 148057738580234774662331071<27> × 147863869707137044125193702898663252618158313<45> × 66039126656639520936203017529360818061007971819918535640380875386612837009<74> (JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs for P45 x P74 / September 26, 2007 2007 年 9 月 26 日)
8×10182+3 = 8(0)1813<183> = 11 × 1973 × 84420643883<11> × 5926566082402689905841656871955090682501014991892889595891754317886568374399827<79> × 73674708315620104145812324277068641041277959520607179164803392413353949269314280582257461<89> (Dmitry Domanov / Msieve 1.50 snfs / January 14, 2014 2014 年 1 月 14 日)
8×10183+3 = 8(0)1823<184> = 23 × 2515879 × 1355535318203479635623337331431820531223886353<46> × 4423320781363593409790516375182404169528903650817164287<55> × 23057548329400141315608146805042346367263772462070880324331474711226599828269<77> (Ignacio Santos / GGNFS, Msieve snfs / July 7, 2010 2010 年 7 月 7 日)
8×10184+3 = 8(0)1833<185> = 7 × 11 × 2376827 × 2051700983727498703133<22> × 1110318608754654894718951253<28> × 6251933143278921306128502804250766527457272908701<49> × 30692034602608111743915901969538358525586340612777844002381534482914535307126593<80> (Sinkiti Sibata / Msieve 1.40 gnfs for P49 x P80 / May 16, 2010 2010 年 5 月 16 日)
8×10185+3 = 8(0)1843<186> = 53 × 73691670258525152691437<23> × 204831015088781947568739792176466994498276644848090684973300137421436242140325974678514325315436546927563999424400488904909084698669115778137936077456388472890323<162>
8×10186+3 = 8(0)1853<187> = 11 × 73 × 197 × 17401 × 3020497 × 220323797 × 848218051796218733728748337082343630038543764250141632268901738791143221<72> × 5148570707138498534773173047226007648015628439588975397717170630573590539325512276143021197<91> (Dmitry Domanov / Msieve 1.50 snfs / July 30, 2014 2014 年 7 月 30 日)
8×10187+3 = 8(0)1863<188> = 29837 × 17836048919020313496807619<26> × 150326718700801571261482640187071400500823957169070799823400912320987712536122844384584486226701092179304845411964672665222944185167552771742197754990530647301<159>
8×10188+3 = 8(0)1873<189> = 11 × 107 × 293 × 5441115131<10> × 106511956593119726957069<24> × 120170653503433884636230865776563068489370913771441083787209<60> × 33308969956148285965169143440241727201325798701721128078286392610462000876022167337166245273<92> (Youcef Lemsafer / GGNFS (SVN 430) , msieve v. 1.50 (SVN 708) snfs / June 29, 2013 2013 年 6 月 29 日)
8×10189+3 = 8(0)1883<190> = 619 × 1847 × 2087 × 17854618292333<14> × 66686803592942902296799<23> × 921080685636059212526826174467963<33> × 17588503812768618802899470677477549249528890421<47> × 173817279856071866628575928062476489118502849448260284689789701413<66> (JMB / GMP-ECM B1=1000000, sigma=1799117052 for P33 / August 11, 2007 2007 年 8 月 11 日) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs / 44.29 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 14, 2007 2007 年 8 月 14 日)
8×10190+3 = 8(0)1893<191> = 7 × 11 × 4733 × 1676294884572518313001<22> × 811922358971434495608319<24> × 3745732691597311546432103964452232875009218920280333835988821<61> × 43058713998396002559188487313145382092368907049402773817908183467795385440455817<80> (Dmitry Domanov / Msieve 1.50 snfs for P61 x P80 / December 5, 2014 2014 年 12 月 5 日)
8×10191+3 = 8(0)1903<192> = 31 × 2842729 × 66328803526681337<17> × 394363058467665716712642056888165131361172716779<48> × 347051913881296443978785985768838738343869801998600703563356838557407323661557275370273423291621772579034043419565715639<120> (Dmitry Domanov / Msieve 1.50 snfs for P48 x P120 / December 4, 2014 2014 年 12 月 4 日)
8×10192+3 = 8(0)1913<193> = 11 × 8191 × 54851 × 31110721 × 31559061199575423197<20> × 111240746516419665348698681303251591<36> × 14821009300798348228287447502125253135891921408999589668984959479548928948529970115095204543668718285000639456934545893559<122> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2806070677 for P36 / February 28, 2014 2014 年 2 月 28 日)
8×10193+3 = 8(0)1923<194> = 8129428296305567387872785743237<31> × 107771738852482404944838800699966613546803039431<48> × 91311419048092904997258430910908091567416312677267748236581730703715618225414401457053087359905471024091778214996449<116> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2872125755 for P31 / August 7, 2007 2007 年 8 月 7 日) (Dmitry Domanov / Msieve 1.50 snfs for P48 x P116 / February 16, 2015 2015 年 2 月 16 日)
8×10194+3 = 8(0)1933<195> = 112 × 73 × 103 × 223 × 1447 × 2027 × 6271 × 214378184259679859014420218347192295318775051793914037272297999880788819147087705064389099351363290877973395753601856563888270455996778458050773433660857868551510312782551402361<177>
8×10195+3 = 8(0)1943<196> = 499 × 237362465057<12> × 271511218869471860596611149917557039541<39> × 248765195426270128855273695905185781164444459135681071781539762368278807533856828891130215723482309481203848855092404756570858093995412384147181<144> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4058878550 for P39 / April 9, 2011 2011 年 4 月 9 日)
8×10196+3 = 8(0)1953<197> = 72 × 11 × 3621665081282620076674432630274353389234788872072180469<55> × 40981979900057019772289486633568158426513623345700595433142245023700808306621864377405722307822200045704430796237062488553288170254983146933<140> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 38.35 hours, 3.85 hours / May 6, 2009 2009 年 5 月 6 日)
8×10197+3 = 8(0)1963<198> = 17 × 19 × 49701979 × 780808607 × 26076920319273076996675767301<29> × [2447444719548378339619829614249789627085695960053062447396841606685367979050190055438702256834046939845645421862753151405036735916578790278144353058537<151>] (JMB / GMP-ECM B1=1000000, sigma=2545770276 for P29 / August 10, 2007 2007 年 8 月 10 日) Free to factor
8×10198+3 = 8(0)1973<199> = 11 × 53 × 1350678383321052486001773788083398163612589<43> × 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969<155> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=184675988 for P43 / August 25, 2009 2009 年 8 月 25 日)
8×10199+3 = 8(0)1983<200> = 1999 × 30221347231<11> × 178809515026945537373<21> × 81574210081044711372117470236664073805672402597803347<53> × 90786206570422045223799455798057329465676700394569252596618992729503954989288637948660786377031809671263318661877<113> (Youcef Lemsafer / GGNFS (SVN430), msieve 1.50 (SVN708) snfs / November 12, 2013 2013 年 11 月 12 日)
8×10200+3 = 8(0)1993<201> = 11 × 607472219 × 147010366511382569644373<24> × 7546527715304377195290179372975899421<37> × 34692193249030294673295482902597730861333432038265611757<56> × 3110598739765833446665105644263182259303399315680570519519952707333428543607<76> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4043050459 for P37 / October 21, 2008 2008 年 10 月 21 日) (Erik Branger / GGNFS, Msieve gnfs for P56 x P76 / November 10, 2010 2010 年 11 月 10 日)
8×10201+3 = 8(0)2003<202> = 20641 × 26387 × 174019 × 579129233 × 5163392545748224474211911523<28> × 653992126219270839674689511423657<33> × 19937262158346323791259586787139940454884250602677<50> × 2164830496156661544761592867569268811883498399071975164919220296201261<70> (Serge Batalov / GMP-ECM B1=3000000, sigma=2923002106 for P33 / January 9, 2014 2014 年 1 月 9 日) (Dmitry Domanov / Msieve 1.50 gnfs for P50 x P70 / January 10, 2014 2014 年 1 月 10 日)
8×10202+3 = 8(0)2013<203> = 7 × 11 × 73 × 131 × 507471413 × 125498349403910576121001916671<30> × [1705907622186509766016214725830792115159326048370022000969793502503494745563525347472742523705129945144812048123809811657133148488336975925959577068371322270711<160>] (Serge Batalov / GMP-ECM B1=1000000, sigma=4119984309 for P30 / November 26, 2013 2013 年 11 月 26 日) Free to factor
8×10203+3 = 8(0)2023<204> = 113 × 1383595193780910666197<22> × 1661453706461449645536849227<28> × 17124019752506658660227886082367<32> × 24865824389973326287053640456925117<35> × 7232786931560991427546416170378991425421187610607342509794976715383313958351687308494791<88> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2580879625 for P32 / November 10, 2013 2013 年 11 月 10 日) (Serge Batalov / GMP-ECM B1=1000000, sigma=4199673 for P35 / November 26, 2013 2013 年 11 月 26 日)
8×10204+3 = 8(0)2033<205> = 11 × 29 × 23183737373<11> × 5900425474467971<16> × 8321680089186306173<19> × 22030355734515596605464611953703595673475391575041233272552682077648822043987859652798916879332641665071010722422536093931609113655788469671634077097758037543<158>
8×10205+3 = 8(0)2043<206> = 23 × 3478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261<205>
8×10206+3 = 8(0)2053<207> = 11 × 31 × 83 × 18987341 × 2061181004321671<16> × [722232843627579875490718259615168609558634027448844119880005973643000318426006789359100671279086288979887647178589542571679545987033888301230284610397428070310321156941768406043191<180>] Free to factor
8×10207+3 = 8(0)2063<208> = 27091 × 22600217 × 2215460285395495547<19> × [5897777337961960368713033892380132730225095594282233867114426720281788319466116433589392818201139161119498447438522207908622124433940229627555448419815472827083706596273280651867<178>] Free to factor
8×10208+3 = 8(0)2073<209> = 7 × 11 × 3107040573735918078561504595039<31> × 753828162708691538643142150295990516239<39> × 1333903091079681407379039279799914822235828140058201<52> × 332549041030046253552112785643483813233258855668027370980074963993846321082209098914359<87> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2243604407 for P31 / November 10, 2013 2013 年 11 月 10 日) (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=801811920 for P39 / January 2, 2014 2014 年 1 月 2 日) (Erik Branger / GGNFS, Msieve gnfs for P52 x P87 / May 16, 2014 2014 年 5 月 16 日)
8×10209+3 = 8(0)2083<210> = 64305413 × 8008131305371<13> × 10603613093653082576755085273<29> × [146506669915017384430523650120650873106908588609988975057198020136438976357883582045056068107853718039069668223192834451636313266927185829201520232957841346426157<162>] Free to factor
8×10210+3 = 8(0)2093<211> = 11 × 73 × 941 × 2321603 × 1015517071<10> × 4490654405302798784705688700315997939706772007375117457768443733540647829457171053598830817476517727260318616201646111756402368431694357203941885607854578678821621074833146058300991611789497<190>
8×10211+3 = 8(0)2103<212> = 53 × 204650701 × [7375659867708691324718337588759784520071150081045967934130830201334586875530133216763143480026210104339760333093716798504560032091709978536679505897903680483896480580656065983356814473332000082626198451<202>] Free to factor
8×10212+3 = 8(0)2113<213> = 11 × 1345042236112594424863<22> × 21754809308856704540737<23> × [2485456113172380726312479108498278110687407449041358090047090800057960363625114309844659142901570695431760389312108683505914215286708372360172355121561810690792029321783<169>] Free to factor
8×10213+3 = 8(0)2123<214> = 17 × 1861 × 217970239 × 47268371071<11> × 2894580980813358021917<22> × [8478931988097360101534734452188083231590876883775934480828099651875389677353420847988390950002071120149162912185286256120795780763246959948847999286998661977051873924003<169>] Free to factor
8×10214+3 = 8(0)2133<215> = 7 × 11 × 235489 × 6648399455706779<16> × [663607874912019158070786202046087489934380637891997500216263074395169253562222507465600176198119079460863278751791910761696025869600423814819852331678034042804043037074298791155166818516071869<192>] Free to factor
8×10215+3 = 8(0)2143<216> = 19 × 12379 × 73000936938913330110120940456946246327<38> × 46593183941713731878819796868308808791438101534279429907102030657837877182660906661349741320035489506050568544190984465227152812412522855372074314192829670012229996507611989<173> (Serge Batalov / GMP-ECM B1=1000000, sigma=2752252946 for P38 / November 27, 2013 2013 年 11 月 27 日)
8×10216+3 = 8(0)2153<217> = 113 × 1543 × 142547 × 74629940353<11> × 2963659171963037<16> × 123551087369938481007996117114231952752821559589794641085711935842859111898965353089369169683959895122965507138955846034973442024729929399135065513217189368492082978202939785786273<180>
8×10217+3 = 8(0)2163<218> = 372803 × 789209387 × 3356281849<10> × [81013971346499457862878782936061674204552998676188850031086034642191000108678901216691340500964188582125312356659106025031927378451778445585966330087183197083452219909463580607568080315724710427<194>] Free to factor
8×10218+3 = 8(0)2173<219> = 11 × 59 × 73 × 97369 × 201557 × 11320528895572879<17> × 583672316025277316487847159645291192951<39> × [130217100910930684272138076283597021480192393554611153190256905506268747657559947639142161664815498625681676532608397650215291984467105880528363823127<150>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=764220761 for P39 / February 28, 2014 2014 年 2 月 28 日) Free to factor
8×10219+3 = 8(0)2183<220> = 2687 × 386153 × 439171 × 588355351 × 602223487043<12> × 105221269189193<15> × 26008286985168151<17> × [18105752166589910044726998374942186646150383016862580216206988142002837710117808421337935922538404767282991418841378139100534067811458724384301296464818837<155>] Free to factor
8×10220+3 = 8(0)2193<221> = 7 × 11 × 37386491 × 2536408159548180748263956348854209271<37> × [10956337829311212070331776733820690992802737318256373552345282629217371917938605039638420100640494629562820046801643166940909592435888668704208115411380855823728060824839533099<176>] (Serge Batalov / GMP-ECM B1=1000000, sigma=2505410671 for P37 / November 27, 2013 2013 年 11 月 27 日) Free to factor
8×10221+3 = 8(0)2203<222> = 31 × 25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613<221>
8×10222+3 = 8(0)2213<223> = 11 × 4990303 × [145737188157257640012494777826662483766471239776968908045718411742278429331299668030724241138718977038614142814028071496405583534160696709744332704301267332409930364403269154744165379792114280981991018836476917879991<216>] Free to factor
8×10223+3 = 8(0)2223<224> = 140813 × 10153879103<11> × 1740166854405229<16> × [32153211363068807383477364137198721051621286563362419852691247486891814302560710791411686559411510483186302577427921244863934954431986856615483835039482448828634030441194914307086931483530805013<194>] Free to factor
8×10224+3 = 8(0)2233<225> = 11 × 53 × 1945621885589<13> × 296795750808933705882321447583<30> × [2376322119052367963078608135843207280722001489616315587037021419616201358192645162787290747057568366900022699052070408739535076688838712161397716474524512908693787063366471473563343<181>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1750346721 for P30 / November 10, 2013 2013 年 11 月 10 日) Free to factor
8×10225+3 = 8(0)2243<226> = 289446169 × 151199799067997<15> × [182797801076194446104611677334713489257101343932540577344436942153971448316479737537986434230800071350748066212436230589090651529168793389850506091997114978210712369275430939738683744049631798313957414071<204>] Free to factor
8×10226+3 = 8(0)2253<227> = 7 × 11 × 73 × [14232342999466287137520014232342999466287137520014232342999466287137520014232342999466287137520014232342999466287137520014232342999466287137520014232342999466287137520014232342999466287137520014232342999466287137520014232343<224>] Free to factor
8×10227+3 = 8(0)2263<228> = 23 × 47 × 3172 × 467 × 109159 × 2062141448841021613602689144931232949920224413<46> × [70056895479197943741774908391844290905627953860234497252628442840815645914473697647322582402056871488091048160530540375991648048237095632170287348624793686230993271603<167>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3494234900 for P46 / April 28, 2014 2014 年 4 月 28 日) Free to factor
8×10228+3 = 8(0)2273<229> = 11 × 103 × 151 × [46760928905852714764178790411671527854900837605139026086753213352583249066242700911253602052804778966934178147448899072380072830146770865603245208466066178404634008054570004033130118129796648410420673006669277485197243443241<224>] Free to factor
8×10229+3 = 8(0)2283<230> = 17 × 503 × 36980543 × 342666925391911<15> × 47405986377238167467<20> × [15573793846133348043464016879947202399926197463032929846009005231341244092630510031316781727781809819487055101284173627529007665857635270628409946029749741237397786833461098985122327783<185>] Free to factor
8×10230+3 = 8(0)2293<231> = 11 × 3217 × 161338729 × [140122413666446879193546185167032794341379918396887228718894608031874930922532095867154609916518595791029633743938909328060968202522567118202157774799786311444951324513669609414343275286982254911317648458638557993176561<219>] Free to factor
8×10231+3 = 8(0)2303<232> = 61 × 257 × 2333 × 50024478473<11> × 7195591788428238292287740569<28> × [607663572744257612163127193195047930193102424317009152424099203884572089682850029079009297428636717691764297179966293483462940307190878250679529654137529832070181864681836903883544033259<186>] Free to factor
8×10232+3 = 8(0)2313<233> = 7 × 11 × 29 × 199 × 6589111 × 16009739 × 265221378454693013257<21> × 945597411900907997263<21> × 22803990296551063181040241<26> × 2385797862706813877432760732325986987961<40> × 30412751933888075489259309952584241972118724317<47> × 4112653273153585562141551353968989768290775883964495940306043<61> (Cyp / yafu 1.34.3 / December 26, 2013 2013 年 12 月 26 日)
8×10233+3 = 8(0)2323<234> = 19 × 653 × 857 × 41751001 × [1802085907618889740843058258599070717785104556798884827518285080901438671018046413895255015784862500187043074466540095071852171847485164866243095112106027715079392460088736602651820941132093332338401472679496185545234597<220>] Free to factor
8×10234+3 = 8(0)2333<235> = 11 × 73 × 19541239 × 20058318271<11> × 194755865356356318464441685677<30> × 2766756686174471968164941854125710651<37> × [47170047447151505280838189430839285014538543924066219672517946684124393458684188898716036805878109106714753383047187279013592772702896487906269089927<149>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=4174266189 for P30 / November 11, 2013 2013 年 11 月 11 日) (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=1862573454 for P37 / January 5, 2014 2014 年 1 月 5 日) Free to factor
8×10235+3 = 8(0)2343<236> = 109 × 7669 × 11941 × 1956091 × 576664591 × 448634446283<12> × 64743304222597406915710457<26> × 244615648902035728235754663265996267541734702082010072986359504992700185520475494503087116634019527335858357839127661314295874504172638305328800590970275250997438782886454393<174>
8×10236+3 = 8(0)2353<237> = 11 × 31 × 443 × 13752797 × 180527633401910197279<21> × 52370484776044097918741<23> × [40729639513541624531293463733651568888277665343578731513041017691054278272406815106541129054468277860767996487669950454335900635396904758362283165757127687232558968344359130879370507<182>] Free to factor
8×10237+3 = 8(0)2363<238> = 53 × 647 × 498301 × 468185628076150500791558778582587968582315174959028290013048954385671550451662417963926821841682456221608907853933304164904420107981618105936465182675157586253804170703162466120534892896615907233462282878105164856642291345278533<228>
8×10238+3 = 8(0)2373<239> = 73 × 112 × 487 × 3958052363152689637586377689923308282655008091495921647582834738301741231343163585166229046256323174183840944478371000221106700136617124879669023703340808939815389511190923038096105568381019535907475776348470096493853317844814760923<232>
8×10239+3 = 8(0)2383<240> = 227 × 1307 × 3391 × 365501365159932561182544300384859962859<39> × [2175563425394819286389105537079472476841419299767642447358439062678858267851747634540103154060046676257957798202282701742444471583545909217982250006527321693920305072390845046748293019294084583<193>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4049817206 for P39 / February 27, 2014 2014 年 2 月 27 日) Free to factor
8×10240+3 = 8(0)2393<241> = 11 × 439 × 44699 × 411871081 × [89985736331026131893243336906657283544227952841166263002244503205524128610878056139774848625890524524011056318822743537375244950846377374549320836721957540256520944466213207374392885868003380005016263214458874819759596562053<224>] Free to factor
8×10241+3 = 8(0)2403<242> = 107 × 138445831 × [5400404952619116128375903734488012583652612772819469063511457517407595962821348726434114269735069931734210723660975679267047686329155622747687998090018798908872508147619135379806983893020925969678944272367827425641127723911156931759<232>] Free to factor
8×10242+3 = 8(0)2413<243> = 11 × 73 × 337 × 13399 × 693212116739<12> × [318277551603414986643047974935433807095614709076102247808837467540231457106907459572333464680065125216990369740489559208988025639855859946058983621700863451189474969665369745227132275084337729789198583118450768120086742493<222>] Free to factor
8×10243+3 = 8(0)2423<244> = 661 × 169506203 × 1493564753<10> × 756049989031<12> × 3633835770974853023<19> × 17400553722182382026847080536451375190598120957293372734150844635165992124487695705660514386214268998626378610568779110183346669452285438449639781833294308906251295820626379509530162032551677869<194>
8×10244+3 = 8(0)2433<245> = 7 × 11 × 13037 × 1731498269<10> × [46025608033569116857981470473559361588905009524306978953865197717559838630922737279146464841336340829532900734131697203330769274042587221588224165111639965391302809601121030773296101069212867888150131871538324871288087413052145063<230>] Free to factor
8×10245+3 = 8(0)2443<246> = 172 × 6018541 × 7759849607<10> × 2718470318925079<16> × 5807557940898531657837345363031988857273519<43> × [3754304288594506373870527664857658809989741093132630317678714454841015453762329094055023463719942688915987794103441839852713021414572839447580497912405322642905852797121<169>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1930247653 for P43 / February 27, 2014 2014 年 2 月 27 日) Free to factor
8×10246+3 = 8(0)2453<247> = 11 × 167862468306041381610069444246667455181163<42> × 8923187030932899710971747357802149728693053<43> × 485538532155728022523628539078520280815616092056408037952930747712971743899452393746042324779562765067471059546724543733277366573714365752698603749122708549325207<162> (Serge Batalov / GMP-ECM B1=3000000, sigma=478419060 for P42 / December 4, 2013 2013 年 12 月 4 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2749438567 for P43 / April 28, 2014 2014 年 4 月 28 日)
8×10247+3 = 8(0)2463<248> = 83 × 1223573061663854904422097148849402675740979<43> × [787738347537714400969095124876974852129767630886571778534792137272346159230343404198741429100795158995081986742901745140296548627899197886466405281088042617560337718468039798307815306352991131932346075179<204>] (Serge Batalov / GMP-ECM B1=43000000, sigma=4277104190 for P43 / January 28, 2014 2014 年 1 月 28 日) Free to factor
8×10248+3 = 8(0)2473<249> = 11 × 20549 × 55680199 × [63563211400003582162350825927426003824344400676211623892600048818543145816473663216377941696561579437138630419469830522705603724733906070238507952954323714234217319301294373484671561401565107449584051941097917381707895618783484816939523<236>] Free to factor
8×10249+3 = 8(0)2483<250> = 23 × 166745163921479491<18> × 121855704930489941149<21> × 17118394772768468920565773624241676135950638673457066822687492154268060607434539915641616160925840289140199322181518452146425501426470700588119731397503803341487435079965636991063428268953732982061600668849927379<212>
8×10250+3 = 8(0)2493<251> = 7 × 11 × 53 × 73 × 11551 × 42103919923067<14> × [552151704545425503037456210152370902708243497621998947813648844657241470219002626465945185746094616240680436472055833275768595339246860657517510697704999287710077069780775654190539644417803921644778002696939753816804811688508543<228>] Free to factor
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