Table of contents 目次

  1. About 400...009 400...009 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 400...009 400...009 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 400...009 400...009 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 400...009 400...009 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

40w9 = { 49, 409, 4009, 40009, 400009, 4000009, 40000009, 400000009, 4000000009, 40000000009, … }

1.3. General term 一般項

4×10n+9 (1≤n)

2. Prime numbers of the form 400...009 400...009 の形の素数

2.1. Last updated 最終更新日

May 25, 2015 2015 年 5 月 25 日

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

  1. 4×102+9 = 409 is prime. は素数です。
  2. 4×104+9 = 40009 is prime. は素数です。
  3. 4×105+9 = 400009 is prime. は素数です。
  4. 4×108+9 = 400000009 is prime. は素数です。
  5. 4×109+9 = 4000000009<10> is prime. は素数です。
  6. 4×1028+9 = 4(0)279<29> is prime. は素数です。
  7. 4×10191+9 = 4(0)1909<192> 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: Makoto Kamada / PPSIQS / January 1, 2005 2005 年 1 月 1 日)
  8. 4×10196+9 = 4(0)1959<197> 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: Makoto Kamada / PPSIQS / January 1, 2005 2005 年 1 月 1 日)
  9. 4×102038+9 = 4(0)20379<2039> 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: Jo Yeong Uk / PRIMO 3.0.4 / October 1, 2007 2007 年 10 月 1 日)
  10. 4×1034414+9 = 4(0)344139<34415> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / August 31, 2010 2010 年 8 月 31 日)
  11. 4×1039266+9 = 4(0)392659<39267> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 2, 2010 2010 年 9 月 2 日)
  12. 4×1050579+9 = 4(0)505789<50580> is PRP. はおそらく素数です。 (Bob Price / PFGW / May 24, 2015 2015 年 5 月 24 日)
  13. 4×1094286+9 = 4(0)942859<94287> is PRP. はおそらく素数です。 (Bob Price / PFGW / May 24, 2015 2015 年 5 月 24 日)
  14. 4×10108412+9 = 4(0)1084119<108413> is PRP. はおそらく素数です。 (Bob Price / PFGW / May 24, 2015 2015 年 5 月 24 日)
  15. 4×10130480+9 = 4(0)1304799<130481> is PRP. はおそらく素数です。 (Bob Price / PFGW / May 24, 2015 2015 年 5 月 24 日)
  16. 4×10178091+9 = 4(0)1780909<178092> is PRP. はおそらく素数です。 (Bob Price / PFGW / May 24, 2015 2015 年 5 月 24 日)
  17. 4×10185355+9 = 4(0)1853549<185356> is PRP. はおそらく素数です。 (Bob Price / PFGW / May 24, 2015 2015 年 5 月 24 日)

2.3. Range of search 捜索範囲

  1. n≤35000 / Completed 終了 / Ray Chandler / August 31, 2010 2010 年 8 月 31 日
  2. n≤39300 / Completed 終了 / Ray Chandler / September 2, 2010 2010 年 9 月 2 日
  3. n≤50000 / Completed 終了 / Ray Chandler / September 7, 2010 2010 年 9 月 7 日
  4. n≤200000 / Completed 終了 / Bob Price / May 24, 2015 2015 年 5 月 24 日

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

  1. 4×106k+9 = 13×(4×100+913+36×106-19×13×k-1Σm=0106m)
  2. 4×106k+1+9 = 7×(4×101+97+36×10×106-19×7×k-1Σm=0106m)
  3. 4×1016k+10+9 = 17×(4×1010+917+36×1010×1016-19×17×k-1Σm=01016m)
  4. 4×1018k+3+9 = 19×(4×103+919+36×103×1018-19×19×k-1Σm=01018m)
  5. 4×1022k+13+9 = 23×(4×1013+923+36×1013×1022-19×23×k-1Σm=01022m)
  6. 4×1028k+18+9 = 29×(4×1018+929+36×1018×1028-19×29×k-1Σm=01028m)
  7. 4×1030k+3+9 = 211×(4×103+9211+36×103×1030-19×211×k-1Σm=01030m)
  8. 4×1030k+23+9 = 241×(4×1023+9241+36×1023×1030-19×241×k-1Σm=01030m)
  9. 4×1044k+37+9 = 89×(4×1037+989+36×1037×1044-19×89×k-1Σm=01044m)
  10. 4×1046k+45+9 = 47×(4×1045+947+36×1045×1046-19×47×k-1Σm=01046m)

Read more続きを読むHide more続きを隠す

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 21.55%. 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 21.55% です。

3. Factor table of 400...009 400...009 の素因数分解表

3.1. Last updated 最終更新日

June 4, 2012 2012 年 6 月 4 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, 201, 207, 208, 214, 218, 221, 223, 224, 225, 228, 230, 231, 232, 233, 234, 235, 238, 239, 240, 241, 244, 245, 246, 247, 248 (26/250)

3.4. Factor table 素因数分解表

4×101+9 = 49 = 72
4×102+9 = 409 = definitely prime number 素数
4×103+9 = 4009 = 19 × 211
4×104+9 = 40009 = definitely prime number 素数
4×105+9 = 400009 = definitely prime number 素数
4×106+9 = 4000009 = 13 × 307693
4×107+9 = 40000009 = 7 × 1051 × 5437
4×108+9 = 400000009 = definitely prime number 素数
4×109+9 = 4000000009<10> = definitely prime number 素数
4×1010+9 = 40000000009<11> = 17 × 2352941177<10>
4×1011+9 = 400000000009<12> = 379 × 383 × 2755637
4×1012+9 = 4000000000009<13> = 13 × 307692307693<12>
4×1013+9 = 40000000000009<14> = 7 × 23 × 248447204969<12>
4×1014+9 = 400000000000009<15> = 157 × 1009 × 2525045293<10>
4×1015+9 = 4000000000000009<16> = 16049939 × 249222131
4×1016+9 = 40000000000000009<17> = 15811657 × 2529779137<10>
4×1017+9 = 400000000000000009<18> = 589451 × 678597542459<12>
4×1018+9 = 4000000000000000009<19> = 13 × 29 × 2549 × 238949 × 17419817
4×1019+9 = 40000000000000000009<20> = 7 × 6299 × 907173474247613<15>
4×1020+9 = 400000000000000000009<21> = 61 × 11353 × 577589804384773<15>
4×1021+9 = 4000000000000000000009<22> = 192 × 131 × 3539 × 23900166756841<14>
4×1022+9 = 40000000000000000000009<23> = 277 × 80657 × 1790350894900181<16>
4×1023+9 = 400000000000000000000009<24> = 241 × 21048023413<11> × 78855434773<11>
4×1024+9 = 4000000000000000000000009<25> = 13 × 54409 × 2464093 × 2295032289289<13>
4×1025+9 = 40000000000000000000000009<26> = 7 × 5714285714285714285714287<25>
4×1026+9 = 400000000000000000000000009<27> = 17 × 1022981 × 3987718793<10> × 5767916669<10>
4×1027+9 = 4000000000000000000000000009<28> = 7019 × 76367 × 7462408494990913333<19>
4×1028+9 = 40000000000000000000000000009<29> = definitely prime number 素数
4×1029+9 = 400000000000000000000000000009<30> = 2287 × 125887 × 357103 × 3890625634969687<16>
4×1030+9 = 4000000000000000000000000000009<31> = 13 × 9277 × 127636573 × 259856717052784933<18>
4×1031+9 = 40000000000000000000000000000009<32> = 7 × 571 × 3169 × 343615357 × 9190328573803009<16>
4×1032+9 = 400000000000000000000000000000009<33> = 109 × 313 × 2017 × 33637 × 1333413721<10> × 129598830553<12>
4×1033+9 = 4000000000000000000000000000000009<34> = 167 × 211 × 463 × 1297134327053<13> × 189014499795463<15>
4×1034+9 = 40000000000000000000000000000000009<35> = 977 × 3853 × 1658413 × 6407280323676719495153<22>
4×1035+9 = 400000000000000000000000000000000009<36> = 23 × 17391304347826086956521739130434783<35>
4×1036+9 = 4000000000000000000000000000000000009<37> = 13 × 673 × 5007481 × 746382589 × 122326560499727449<18>
4×1037+9 = 40000000000000000000000000000000000009<38> = 7 × 89 × 4528956463<10> × 448619261063<12> × 31600640349007<14>
4×1038+9 = 400000000000000000000000000000000000009<39> = 904681 × 1286773 × 343607458511598560508359293<27>
4×1039+9 = 4000000000000000000000000000000000000009<40> = 19 × 263 × 519769 × 1283603623<10> × 1199801315721338023931<22>
4×1040+9 = 40000000000000000000000000000000000000009<41> = 4583989 × 53282040853<11> × 163770461681236137270577<24>
4×1041+9 = 400000000000000000000000000000000000000009<42> = 62819 × 6127387209188263<16> × 1039186860760131986597<22>
4×1042+9 = 4000000000000000000000000000000000000000009<43> = 13 × 17 × 45833 × 394902090443833421215502710854762613<36>
4×1043+9 = 40000000000000000000000000000000000000000009<44> = 72 × 59 × 1711627703<10> × 8083558631051769306511133155933<31>
4×1044+9 = 400000000000000000000000000000000000000000009<45> = 193 × 2355253 × 3497454495313<13> × 251601394578025584961717<24>
4×1045+9 = 4000000000000000000000000000000000000000000009<46> = 47 × 929 × 66624257486510533<17> × 1375035901286364383510971<25>
4×1046+9 = 40000000000000000000000000000000000000000000009<47> = 29 × 15749 × 15174253 × 5771672627053216076534421888239293<34>
4×1047+9 = 400000000000000000000000000000000000000000000009<48> = 179 × 125598986305571<15> × 17791838431495856399012139229201<32>
4×1048+9 = 4000000000000000000000000000000000000000000000009<49> = 132 × 19273 × 1228072383814374403041689680231442521453657<43>
4×1049+9 = 40000000000000000000000000000000000000000000000009<50> = 7 × 397 × 249317 × 1718251 × 33599510223775788866714735067436013<35>
4×1050+9 = 400000000000000000000000000000000000000000000000009<51> = 31922437 × 869065517089313<15> × 14418212915647076935693405589<29>
4×1051+9 = 4(0)509<52> = 4007 × 27798720260849<14> × 35910036425522125848807593285603263<35>
4×1052+9 = 4(0)519<53> = 229 × 174672489082969432314410480349344978165938864628821<51>
4×1053+9 = 4(0)529<54> = 197 × 241 × 8425132169260905280451587084272384523032205067717<49>
4×1054+9 = 4(0)539<55> = 13 × 997 × 475193993 × 25247442031965497<17> × 25723683351603508297888489<26>
4×1055+9 = 4(0)549<56> = 7 × 677 × 122431502244020573213<21> × 68941400929034921180003690681887<32>
4×1056+9 = 4(0)559<57> = 3793 × 172993 × 84752742673813<14> × 146959922063821<15> × 48943603822015947817<20>
4×1057+9 = 4(0)569<58> = 19 × 23 × 487 × 53462532493<11> × 5987021575531<13> × 58720432098028690323400449917<29>
4×1058+9 = 4(0)579<59> = 17 × 3037 × 45377 × 425501 × 147091452241<12> × 7711552449617<13> × 35375343067509032209<20>
4×1059+9 = 4(0)589<60> = 213215086383851<15> × 1876039856203609462964493535094492291509072859<46>
4×1060+9 = 4(0)599<61> = 13 × 1489 × 934393 × 4136898509025393647125969<25> × 53458589846946159335647861<26>
4×1061+9 = 4(0)609<62> = 7 × 24700762903<11> × 2567700548529169<16> × 90096352763492210148648083325153241<35>
4×1062+9 = 4(0)619<63> = 403527973 × 10826954736233<14> × 91554569382040361567203501448605749162701<41>
4×1063+9 = 4(0)629<64> = 211 × 37361 × 4240968143<10> × 419984477169421934009<21> × 284879235313752456517988117<27>
4×1064+9 = 4(0)639<65> = 1597 × 5700138373<10> × 144238295165635283803033<24> × 30464152178623676841281024833<29>
4×1065+9 = 4(0)649<66> = 1560967 × 19109364969489013<17> × 2326000573697615609<19> × 5765144496937827306805931<25>
4×1066+9 = 4(0)659<67> = 13 × 31489 × 233437 × 41858925579992246364265263179325757684603546066726770001<56>
4×1067+9 = 4(0)669<68> = 7 × 167877046243575356903<21> × 34038517129940267875217471598280286468835644729<47>
4×1068+9 = 4(0)679<69> = 15961331320453<14> × 25129811447748016546609<23> × 997244497429145435634148422533317<33>
4×1069+9 = 4(0)689<70> = 69070887333625876615877<23> × 57911518939654252993752435202349130212411571317<47>
4×1070+9 = 4(0)699<71> = 149 × 617 × 12049 × 155626061 × 53732793159025489<17> × 4318329850917723450333923623115539313<37>
4×1071+9 = 4(0)709<72> = 19037 × 229637 × 68581343 × 1222634490013<13> × 9859196657767<13> × 110681607761504959695884947637<30>
4×1072+9 = 4(0)719<73> = 13 × 97 × 12637 × 251015719420151177982256577349207483757557220445205245199371431537<66>
4×1073+9 = 4(0)729<74> = 7 × 1713527371<10> × 340600150189835637263<21> × 9790977897241649225111881493361677824490819<43>
4×1074+9 = 4(0)739<75> = 17 × 29 × 773533 × 891355313 × 13449275209940041<17> × 87495252332015317829606877480592687626617<41>
4×1075+9 = 4(0)749<76> = 19 × 523264691 × 594425449 × 676842413772890773564250466145830931111773051905671410329<57>
4×1076+9 = 4(0)759<77> = 26394552178453<14> × 1212653972086849<16> × 1249708718647360341792282910050980386773415815397<49>
4×1077+9 = 4(0)769<78> = 280375220670188124973<21> × 167275912846527789937393693<27> × 8528780833485390011481371994481<31>
4×1078+9 = 4(0)779<79> = 13 × 2297 × 25908900351533158191833<23> × 5170191902706730568983218736959359584557656302590493<52>
4×1079+9 = 4(0)789<80> = 7 × 23 × 1373 × 21165307905757<14> × 228952072338551443223<21> × 37341727758086475203174398794805115602823<41>
4×1080+9 = 4(0)799<81> = 61 × 6557377049180327868852459016393442622950819672131147540983606557377049180327869<79>
4×1081+9 = 4(0)809<82> = 892 × 34296992681708836771<20> × 14723936549902970214724395162795722124772868939644951294099<59>
4×1082+9 = 4(0)819<83> = 1731521829941<13> × 23101065957316266056825665141832323444266427229053022800477270532146949<71>
4×1083+9 = 4(0)829<84> = 241 × 1510423 × 1881823 × 24014942053<11> × 296504111296141409<18> × 82007452975672193441598211869098496220253<41>
4×1084+9 = 4(0)839<85> = 13 × 2340397 × 161235647917<12> × 804751742812242961168447141<27> × 1013220838694846677506606443514254189377<40>
4×1085+9 = 4(0)849<86> = 72 × 11427939927179945352419<23> × 71432518530370723066022585835435015818776257106487682609128339<62>
4×1086+9 = 4(0)859<87> = 6581 × 129517 × 661217 × 5939487721517107421<19> × 935158874428412604506761<24> × 127780012112319901067893338821<30>
4×1087+9 = 4(0)869<88> = 7087203689<10> × 564397493782826142221802876138558235249276183178146553761339199460956821950881<78>
4×1088+9 = 4(0)879<89> = 39709 × 227066013979431575629775037253704301<36> × 4436279546316510561053538117916593800255543972401<49> (Makoto Kamada / GGNFS-0.70.3 / 0.14 hours)
4×1089+9 = 4(0)889<90> = 120597493 × 393261610875202721<18> × 8434127417487660929933523595618508935578844027530225186128214053<64>
4×1090+9 = 4(0)899<91> = 13 × 17 × 708427940710019381<18> × 6191433608351527831077953<25> × 4126490178135686653661208549277346519074674953<46>
4×1091+9 = 4(0)909<92> = 7 × 47 × 277 × 7717 × 73009 × 360985277 × 142832331115207891119797<24> × 15109267513556344459821913417914464701403941289<47>
4×1092+9 = 4(0)919<93> = 157 × 11689 × 2637190441<10> × 37888645549<11> × 12825589219153<14> × 170080718155863190539989016654763752295474602135072529<54>
4×1093+9 = 4(0)929<94> = 19 × 211 × 6619 × 28463 × 14882677 × 64542503754065251<17> × 2061698683044393167<19> × 7486363660015639579<19> × 357213532352044923703<21>
4×1094+9 = 4(0)939<95> = 269 × 79059613 × 17597633788453<14> × 424533421492688455002213933013<30> × 251760078702864752532178096774092670676873<42> (Makoto Kamada / msieve 0.81 / 2.9 minutes)
4×1095+9 = 4(0)949<96> = 331 × 4099 × 4889 × 34693 × 88169 × 272887 × 72242609324325654720653718868360903335894524888506429179407105334472531<71>
4×1096+9 = 4(0)959<97> = 13 × 2547471757<10> × 399733992462149249766148608632773681<36> × 302159449066235946897726987287804354073508327774129<51> (Makoto Kamada / GGNFS-0.70.5 / 0.35 hours)
4×1097+9 = 4(0)969<98> = 7 × 6601354341023269328787238886180533176329<40> × 865623237155293890321262656296684879904072617420643595703<57> (Makoto Kamada / GGNFS-0.70.5 / 0.36 hours)
4×1098+9 = 4(0)979<99> = 492812940973<12> × 534245715799090304732940984466061<33> × 1519276567383994276568017830452390519397881383785065153<55> (Makoto Kamada / GGNFS-0.70.5 / 0.44 hours)
4×1099+9 = 4(0)989<100> = 1316299 × 23733644234291195486041<23> × 129584034370431955586616801502452527<36> × 988074099247265431730733375219977213<36> (Makoto Kamada / msieve 0.81 / 4.3 minutes)
4×10100+9 = 4(0)999<101> = 252457 × 3825781 × 10271377715017<14> × 48957260176284394201<20> × 82358165261737491066942986862344637371473106120272751581<56>
4×10101+9 = 4(0)1009<102> = 23 × 59 × 1499 × 81649 × 6412969 × 375550634611270931868287759153559145368061864762321629151337933025837844916175163823<84>
4×10102+9 = 4(0)1019<103> = 13 × 29 × 762397 × 139157598651276497<18> × 94240010293401725751188992794810989<35> × 1061195040716664263009908396266920779032617<43> (Makoto Kamada / Msieve 1.30 for P35 x P43 / 11 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 25, 2007 2007 年 11 月 25 日)
4×10103+9 = 4(0)1029<104> = 7 × 367 × 3169 × 568241 × 666051610994839819<18> × 1496329584881976087324454469014561<34> × 8675728169628497526212806700903471333651<40> (Makoto Kamada / Msieve 1.30 for P34 x P40 / 4.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 25, 2007 2007 年 11 月 25 日)
4×10104+9 = 4(0)1039<105> = 6961 × 57463008188478666858210027294928889527366757649762965091222525499209883637408418330699612124694727769<101>
4×10105+9 = 4(0)1049<106> = 293 × 5643331 × 19768913443163251<17> × 8953380387844556721529<22> × 2095769500190024736613561<25> × 6521439887479099964996594817625517<34>
4×10106+9 = 4(0)1059<107> = 17 × 6037 × 54277 × 65033 × 393637 × 280507422006808725959915242330927724994392904816732535909164558725741506632948525385813<87>
4×10107+9 = 4(0)1069<108> = 203011 × 55710113896285389095562461197<29> × 35367663875448023865453351769377203005505502624744560709320766733028552527<74>
4×10108+9 = 4(0)1079<109> = 13 × 2521 × 2372437 × 358672215493<12> × 92423592503653<14> × 193356441377348233<18> × 934976288415640021<18> × 8584386883329884351795149483500680797<37>
4×10109+9 = 4(0)1089<110> = 7 × 40423 × 15317212331<11> × 4650625584472051961707336921<28> × 7801469023564348490753986729<28> × 254370012959068487857734251326987346411<39>
4×10110+9 = 4(0)1099<111> = 113 × 2393 × 251419167001<12> × 165181848872234857617062189249532241<36> × 35618706443028798016568330143685321380313564206887456692761<59> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.95 hours on Cygwin on AMD XP 2700+ / November 26, 2007 2007 年 11 月 26 日)
4×10111+9 = 4(0)1109<112> = 19 × 653 × 123493 × 2610663324445005887897525533088460379846644819648266753109036179251775289078407266234168559870215728659<103>
4×10112+9 = 4(0)1119<113> = 47869 × 402422281 × 20200221739295708137<20> × 102793932584885084256697806937410407330622008971214709546957362708559810928828813<81>
4×10113+9 = 4(0)1129<114> = 241 × 6299 × 263494370113414564256066463819917407689687950204833935966915646888559667312008294802771170290482780972281051<108>
4×10114+9 = 4(0)1139<115> = 13 × 307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693<114>
4×10115+9 = 4(0)1149<116> = 7 × 1065570921703<13> × 666712140118867142401<21> × 8043428905639068320907024160786814258414902143560784208015289845368078367045948729<82>
4×10116+9 = 4(0)1159<117> = 3486469281397<13> × 2874109277349469<16> × 39918192825796476484273263602828739918551745682615894520536911408198521623282926063109513<89>
4×10117+9 = 4(0)1169<118> = 163890451 × 119008224119929<15> × 1049848161996414833607686052033851<34> × 195345258444219449654150537877637812726731604913236518703820721<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.75 hours on Cygwin on AMD XP 2700+ / November 26, 2007 2007 年 11 月 26 日)
4×10118+9 = 4(0)1179<119> = 3728574790867178284745181738866780429302431068160529<52> × 10727959674558907354142285722781332734722136495462711094331511744121<68> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.90 hours on Core 2 Quad Q6600 / November 25, 2007 2007 年 11 月 25 日)
4×10119+9 = 4(0)1189<120> = 59011 × 10299709529696676595537272509874674618354731<44> × 658115379703367141596436109463234164314654145602057711013672694021719049<72> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.09 hours on Cygwin on AMD XP 2700+ / November 26, 2007 2007 年 11 月 26 日)
4×10120+9 = 4(0)1199<121> = 13 × 2557 × 8521 × 18757 × 2782921 × 20807569 × 42423481 × 5260604677<10> × 9084332713196797189069<22> × 6413199442442194033714618165934461275077708047821501061<55>
4×10121+9 = 4(0)1209<122> = 7 × 7681 × 21529 × 5126081 × 160536083470159087<18> × 25197118973989779612749487725434152433845493<44> × 1666523008134979471401647272922628239564300453<46> (Makoto Kamada / Msieve 1.30 for P44 x P46 / 1.3 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / November 25, 2007 2007 年 11 月 25 日)
4×10122+9 = 4(0)1219<123> = 17 × 2706797501<10> × 6953571473897<13> × 17434028941619909<17> × 1172523685438153707688897631706842320781<40> × 61154439922943106826214876293148089769296229<44> (Makoto Kamada / Msieve 1.30 for P40 x P44 / 31 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / November 25, 2007 2007 年 11 月 25 日)
4×10123+9 = 4(0)1229<124> = 23 × 211 × 10289 × 15773 × 28999255687<11> × 4155424942588126939<19> × 34052378043650525917<20> × 1237691732108335720395890820493788321462836023188447935046340529<64>
4×10124+9 = 4(0)1239<125> = 5131897 × 10621340399206741<17> × 733842284467151960541788077521714305018167316607261871506456893259617021807177370441055990594693293517<102>
4×10125+9 = 4(0)1249<126> = 89 × 1704513258290743<16> × 218192536144132173623<21> × 767414207295499894139<21> × 8209262080507660256729<22> × 13019490676902258793481<23> × 147333586169105084996339<24>
4×10126+9 = 4(0)1259<127> = 132 × 1093 × 157478185310284045321<21> × 51219530045909995936125110786993<32> × 2684708475243401264102954877320619544959453611256556529626076156285909<70> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.80 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 26, 2007 2007 年 11 月 26 日)
4×10127+9 = 4(0)1269<128> = 72 × 223 × 557 × 1247945470942529<16> × 5266332114282325726310265118334367446631931663513799714242971304507693394428854385705650075423382761675139<106>
4×10128+9 = 4(0)1279<129> = 1993 × 51913 × 1430797079340329352472921<25> × 181803558476376236283955641729897094029004670893<48> × 14862646249026576411818998493115073085499220973317<50> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 3.78 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 26, 2007 2007 年 11 月 26 日)
4×10129+9 = 4(0)1289<130> = 19 × 13921 × 42456366769<11> × 1961107985919825167<19> × 90496029963707513725625363116699<32> × 2007068038467510110982557191892561779029831762757164209225700983<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 4.35 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 26, 2007 2007 年 11 月 26 日)
4×10130+9 = 4(0)1299<131> = 29 × 29327982001<11> × 329323186569671308148482561<27> × 142809633071539376801441849555115905105958179055428369664898581960137530212268159989282516461<93>
4×10131+9 = 4(0)1309<132> = 619 × 194167 × 14543527 × 80094272947449979071432758202536808045156517<44> × 2857082077051308573674020837361541499660528541802562865615658481450429087<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.68 hours on Cygwin on AMD XP 2700+ / November 26, 2007 2007 年 11 月 26 日)
4×10132+9 = 4(0)1319<133> = 13 × 37897 × 74413 × 4795671157<10> × 238753385743005127820360651581<30> × 95293671318403094554219044478411340076428386781973958525263323355023354847784827289<83> (Makoto Kamada / GMP-ECM 6.1.3 B1=50000, sigma=200747974 for P30 / November 18, 2007 2007 年 11 月 18 日)
4×10133+9 = 4(0)1329<134> = 7 × 14039910954930703<17> × 212045331507039776360742002829387808898620546351104409<54> × 1919414992157459171757261776221197366678153779688615271444343881<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.87 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 26, 2007 2007 年 11 月 26 日)
4×10134+9 = 4(0)1339<135> = 233 × 940913 × 20129983336618458257<20> × 90638182001720257986508099682792568767343035039944010471235455177949468770983476603141594355101924799589153<107>
4×10135+9 = 4(0)1349<136> = 4432543729<10> × 350104414826237<15> × 50076108520827966913691944342129<32> × 4390119913201648970056724078503841<34> × 11724718391352138352586053521568560187634367997<47> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / November 27, 2007 2007 年 11 月 27 日)
4×10136+9 = 4(0)1359<137> = 15397849 × 2597765441134018134610879740410494998359835844604009300260055803898323720410558643613143628048307266813695861025783536388751441841<130>
4×10137+9 = 4(0)1369<138> = 47 × 210996161 × 27663076039007<14> × 144128879329630272184991648078450696106391196441<48> × 10116635425360137333667412655105196323996222926944429943963917753921<68> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / November 27, 2007 2007 年 11 月 27 日)
4×10138+9 = 4(0)1379<139> = 13 × 17 × 151237 × 23622629 × 2358576581457354735036391367836589<34> × 9655958096615738258431632197488338493<37> × 222451879743848962799083986064899346768400423382735149<54> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=193689354 for P34 / November 20, 2007 2007 年 11 月 20 日) (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3022877036 for P37 / November 20, 2007 2007 年 11 月 20 日)
4×10139+9 = 4(0)1389<140> = 7 × 1609 × 16477 × 12613903 × 79168561468111998367<20> × 215836815580611127367881401108630068848301320097806396732865375805443310325317266878546524937161202815859<105>
4×10140+9 = 4(0)1399<141> = 61 × 109 × 181 × 332372499831736421960183436382657135331279825238539588472989333335549149998878242813067889575884380902208532168256930589819928888903661<135>
4×10141+9 = 4(0)1409<142> = 3264208176022063<16> × 1989887208412614157281179<25> × 12560245906602427344287633654384461339<38> × 49029282824428429410597115467691293631272803877265436025347251103<65> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 8.54 hours on Core2 Duo E6300 1.86GHz, Windows Vista / November 27, 2007 2007 年 11 月 27 日)
4×10142+9 = 4(0)1419<143> = 257 × 3989 × 6279116232481<13> × 6213900707545681120308304861181972524657170097039234485897815848245930015477488248356291397342887327051188390965392632031493<124>
4×10143+9 = 4(0)1429<144> = 241 × 56854471504091<14> × 343717243907717<15> × 84933104950680254110902658606958111217295042787312058537647957343210132528078258529488349178237267769702479147167<113>
4×10144+9 = 4(0)1439<145> = 13 × 6170977 × 33845281 × 260772951042433<15> × 4957419885753409<16> × 16811608672680433<17> × 67785541316170185933535335881094717003677525321680844690099265573069837995189233789<83>
4×10145+9 = 4(0)1449<146> = 7 × 23 × 16196138573250129419<20> × 270390616492056889150461299<27> × 1605173021880918410125104138533069730893<40> × 35343468163557001022907513872788192718182385124531802470493<59> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 11.67 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 27, 2007 2007 年 11 月 27 日)
4×10146+9 = 4(0)1459<147> = 220681 × 486209806553<12> × 764412203911204700836054966106935734613<39> × 4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501<91> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 10.26 hours on Cygwin on AMD XP 2700+ / November 27, 2007 2007 年 11 月 27 日)
4×10147+9 = 4(0)1469<148> = 19 × 4057594903<10> × 44338326960703<14> × 256008644002393841860575255628769<33> × 404664799012214157417672549706061106703<39> × 11295575051062064761509401409725052595688718501423797<53> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2766072150 for P33 / November 20, 2007 2007 年 11 月 20 日) (Sinkiti Sibata / Msieve v. 1.28 for P39 x P53 / 11.94 hours on Pentium3 750MHz, Windows Me / November 26, 2007 2007 年 11 月 26 日)
4×10148+9 = 4(0)1479<149> = 397 × 853 × 7321 × 29011093 × 4493636292960215751289<22> × 92434815990640075017640402187985349<35> × 1338913300569270255707383411990054108086821389860006097017974083996576133953<76> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1573321121 for P35 / November 20, 2007 2007 年 11 月 20 日)
4×10149+9 = 4(0)1489<150> = 18493 × 15208906085724863<17> × 35274210892827613264081<23> × 40317847369951035346198806666122621921229309916638852314732468437701852182835351772288656466406535552362771<107>
4×10150+9 = 4(0)1499<151> = 13 × 461 × 346705813 × 880078819597<12> × 70157489449933<14> × 1211697258811082095589<22> × 25731485325266264685316538802440540399877528238993196754275086696533047049847435968257497009<92>
4×10151+9 = 4(0)1509<152> = 7 × 131 × 197 × 1531 × 47933 × 2296496011<10> × 1404598779340570579<19> × 6104431168415592413869608635611<31> × 153232696611883288817148088275635599149717352290249536018399392505789557880036813<81> (Robert Backstrom / GMP-ECM 6.0.1 B1=1448000, sigma=536718007 for P31 / December 1, 2007 2007 年 12 月 1 日)
4×10152+9 = 4(0)1519<153> = 26713 × 1234873 × 1996467668952176494127953<25> × 35974049014171230767387935670841612478177<41> × 168835367899724431687288680957130059518243845115630566914418157002167566445961<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / December 6, 2007 2007 年 12 月 6 日)
4×10153+9 = 4(0)1529<154> = 211 × 499 × 823 × 7213 × 5983931 × 20484293 × 1674567153955540249123309372823653<34> × 31178204285060110569074580607563260199102302136786304734413870091585370032227633400052324234081<95> (Robert Backstrom / GMP-ECM 6.0.1 B1=1155000, sigma=3343519632 for P34 / November 29, 2007 2007 年 11 月 29 日)
4×10154+9 = 4(0)1539<155> = 17 × 13913 × 1396989572897<13> × 61059519554988608394921409<26> × 42618868918024524866536599051397923694814520254443166653<56> × 46520226216352324323002797548303105981922548494168073941<56> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / December 10, 2007 2007 年 12 月 10 日)
4×10155+9 = 4(0)1549<156> = 1975423 × 3095912878954409<16> × 34448312105302906122201979845692525321041884536529688865372252369<65> × 1898642540091341888277141518857734481586769553402869501770427156234223<70> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 26.75 hours on Cygwin on AMD XP 2700+ / December 1, 2007 2007 年 12 月 1 日)
4×10156+9 = 4(0)1559<157> = 13 × 1213 × 1237 × 205062448436406520514216646323617354906654804487566115337476654281065666481409833041743075925448111433805354621412938712524645302201299244913925806253<150>
4×10157+9 = 4(0)1569<158> = 7 × 87972114341735599736283329579<29> × 22156740177008454467142813185853133375535106690625343<53> × 2931642819433829612544003364072511581602586787125479620745479951967818422771<76> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / December 1, 2007 2007 年 12 月 1 日)
4×10158+9 = 4(0)1579<159> = 29 × 617 × 16694516335098246170350962150521377733606416852014894432101<59> × 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513<97> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / November 29, 2007 2007 年 11 月 29 日)
4×10159+9 = 4(0)1589<160> = 59 × 5613936607<10> × 78918344807<11> × 2118843795331<13> × 3878257691504423440325364853<28> × 392955123090102563686734374525767<33> × 47389698841229495008237336545522944129176490198562383160258074779<65> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=4262207878 for P33 / November 21, 2007 2007 年 11 月 21 日)
4×10160+9 = 4(0)1599<161> = 277 × 138637 × 247609 × 15173733529<11> × 60797126856307127135595444344471160234256633836042739865882569<62> × 4559940072470123498850798447077277366305328269178339465898539108054593612449<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve / December 1, 2007 2007 年 12 月 1 日)
4×10161+9 = 4(0)1609<162> = 4051 × 127235411 × 1969369859<10> × 3315928709727846416041854024938819789689<40> × 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619<102> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / December 4, 2007 2007 年 12 月 4 日)
4×10162+9 = 4(0)1619<163> = 13 × 14484959608208348655122569360348676482871487639034491862149522347733039174529<77> × 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317<86> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / December 1, 2007 2007 年 12 月 1 日)
4×10163+9 = 4(0)1629<164> = 7 × 1303 × 257837 × 959561 × 5915543 × 878200471969328827561876462072079282958405245015115821377184281733<66> × 3412018883530127490227807989559980166714774210829016758904628027464337410663<76> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.32 / January 9, 2008 2008 年 1 月 9 日)
4×10164+9 = 4(0)1639<165> = 433 × 325501909 × 155697059191893120469<21> × 2480292169582768150613622571493155466576298122188305452881<58> × 7349119396569529045017568501654084454037447639806748910113839336437017179473<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 46.42 hours on Cygwin on AMD 64 X2 6000+ / April 9, 2008 2008 年 4 月 9 日)
4×10165+9 = 4(0)1649<166> = 19 × 1877 × 8893 × 11427643437022285783<20> × 128867463506675408316022657357<30> × 467807742471873906594101709631462254293<39> × 18307391061578173853638901084078048550027933080852242492899530687116597<71> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=366089251 for P30 / November 22, 2007 2007 年 11 月 22 日) (JMB / GMP-ECM 6.1.3 B1=44000000, sigma=3065949829 for P39 / November 28, 2007 2007 年 11 月 28 日)
4×10166+9 = 4(0)1659<167> = 95273 × 8165188054910845523309<22> × 14974400622659504557368769453<29> × 16787178947577077116058498947766265186683375867777<50> × 204548731765952768246248790510940164302339098214505480636361977<63> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P50 x P63 / 17.28 hours on Core 2 Quad Q6600 / December 9, 2007 2007 年 12 月 9 日)
4×10167+9 = 4(0)1669<168> = 23 × 23041 × 82571 × 9141201602713997050786878892618917530515110570413840519864945246628360383497926678911136034798895190617262127600989109943630852760886838694749338794680669053<157>
4×10168+9 = 4(0)1679<169> = 13 × 97 × 373 × 8504251062499867121077148439576233169555631621356725693255916301161042876307794358705057690713145233473582607105726975271763973016011378687921624822208001224612153<163>
4×10169+9 = 4(0)1689<170> = 73 × 89 × 7481 × 207246019 × 845142638547421004330094762180574773307401004688254872802529628697418322901667891284028031254706560428688361394220866920309297472989125841285693158433253<153>
4×10170+9 = 4(0)1699<171> = 17 × 157 × 460710007049003831439916489<27> × 325299781750580975452236640340504586671040660826393559465921119070610988900472254166029502281750728082670126640485912086213508796918658218149<141>
4×10171+9 = 4(0)1709<172> = 4727579 × 42758299609<11> × 70786206663533<14> × 52842317195285609<17> × 1749706642519018677552131<25> × 13309174465738976322573197980572388901369971<44> × 227171538029579664285228640378502521594404174584065064527<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P44 x P57, Msieve 1.30 / November 28, 2007 2007 年 11 月 28 日)
4×10172+9 = 4(0)1719<173> = 379417 × 2183353693<10> × 369214042069<12> × 10392906827609765461<20> × 1432364659536702101368956541<28> × 521485688834094616003641826229481656646415453<45> × 16846429736694498814138730507079319979241737624177166277<56> (Sinkiti Sibata / Msieve v. 1.30 for P45 x P56 / 41.96 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 1, 2007 2007 年 12 月 1 日)
4×10173+9 = 4(0)1729<174> = 241 × 2609 × 49277 × 37490161253921<14> × 817315416761140501205161<24> × 192750975747012200555324918025716343881<39> × 2185853367735352411488999932909611191071596551799121040574783002059359617054726183998413<88> (Robert Backstrom / GMP-ECM 6.0 B1=2442000, sigma=3323678714 for P39 / February 11, 2008 2008 年 2 月 11 日)
4×10174+9 = 4(0)1739<175> = 13 × 358073 × 217328021421685514569<21> × 3953933292618172077127265772121748539513833728170513039266006786871318220832367759947355161281839742703467990288076776537526836881557524261264927789<148>
4×10175+9 = 4(0)1749<176> = 7 × 401 × 3169 × 1891223 × 193971539 × 12257858029676611496353462983004900423146023624367849810522129522038355641907452161755324282656343366460821500502010627996593854818607457321748280042339459<155>
4×10176+9 = 4(0)1759<177> = 5949217 × 260808949 × 37078796641<11> × 25253318745384671209<20> × 30659586774476168038113800824694868364850678869<47> × 8979813218286857062544785990149537754786720685038107462329302196640845737147656966793<85> (Sinkiti Sibata / Msieve / 80.41 hours / March 6, 2009 2009 年 3 月 6 日)
4×10177+9 = 4(0)1769<178> = 769 × 1583 × 4447 × 133051 × 27471971 × 202151814940210900000057206424771165643787269558489323119112883608470657437185553048798123972788401866993683733316406001935656948253709753290720354776020041<156>
4×10178+9 = 4(0)1779<179> = 1599137 × 25013491652059829770682561906828495619824943078673059281349878090495060773404655135863906594619472878183670317177327521031656449697555619062031583285234473344059952336791657<173>
4×10179+9 = 4(0)1789<180> = 921163045658547580756150590548571589420901651<45> × 434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659<135> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 514.08 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 10, 2007 2007 年 12 月 10 日)
4×10180+9 = 4(0)1799<181> = 13 × 2293 × 3697 × 15493021 × 356679403981<12> × 7613777314732978779697<22> × 425332272985269084222506529751921<33> × 2028245328547010720335723720294520432822986427659668208529742591478467559455377267252935084340950609<100> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1221583337 for P33 / November 23, 2007 2007 年 11 月 23 日)
4×10181+9 = 4(0)1809<182> = 7 × 4463 × 9013 × 44939 × 54440369 × 646495019927<12> × 17375472304230114852745301318776299103<38> × 96680330851377897032675335617773667304146317489<47> × 53466443788604542141782787390935555045766340238599979694824022367<65> (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=2640071409 for P38 / February 13, 2009 2009 年 2 月 13 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P47 x P65 / 11.56 hours on Core 2 Quad Q6700 / February 16, 2009 2009 年 2 月 16 日)
4×10182+9 = 4(0)1819<183> = 593 × 1328642261<10> × 23666791403837444777<20> × 30538114624651788954583755347034152657<38> × 702450347822345188677038220687379849426066288977031773444331177142414305322712815983768134833633739828814217175997<114> (matsui / GMP-ECM 6.2.1 for P38 / September 22, 2008 2008 年 9 月 22 日)
4×10183+9 = 4(0)1829<184> = 19 × 47 × 211 × 507371 × 12800256361540851179<20> × 3268750472332670260412090654062890935923767473781061060416941374621087285908953975000009434301764465129758225750004661863496951777328826637592647516829287<154>
4×10184+9 = 4(0)1839<185> = 86629 × 17315047017625261<17> × 288744426922067304879725083649398238432589757<45> × 92354785582575909641556220757639434258139568193136633677444230328449938740199812268290197677719701254300588804590341373<119> (Lionel Debroux / GMP-ECM 6.2.3 B1=43000000, sigma=1323134362 for P45 / December 19, 2009 2009 年 12 月 19 日)
4×10185+9 = 4(0)1849<186> = 160201 × 2496863315459953433499166671868465240541569653123263899725969251128270110673466457762435939850562730569721787005074874688672355353587056260572655601400740319973033876193032502918209<181>
4×10186+9 = 4(0)1859<187> = 13 × 17 × 29 × 9257 × 23480381 × 317354462816028263246502219337801494068219906395661<51> × 19679807803280643058874511949213903649314864995117749<53> × 459757532916870696178399472755844033607702272329244716693140391000477<69> (Dmitry Domanov / Msieve 1.40 snfs / October 29, 2011 2011 年 10 月 29 日)
4×10187+9 = 4(0)1869<188> = 7 × 463 × 659 × 31187419 × 1422552580681<13> × 313608486641729<15> × 1346046230331284293142797595459864282652758756687789596472452823720928516243501240585875399693070043664898447095535892488549047787841115893960827481<148>
4×10188+9 = 4(0)1879<189> = 337 × 1201 × 58693 × 876529 × 2430640727175969638994585027337101361<37> × 7903395490385727731463723829241886338897947794113256415232279926080628572269461573229661036837524536596561491729907318379745124431713621<136> (matsui / GMP-ECM B1=88000000, sigma=101061817 for P37 / September 17, 2008 2008 年 9 月 17 日)
4×10189+9 = 4(0)1889<190> = 23 × 1567 × 66173 × 246030458809<12> × 427784512582518755165413<24> × 15935599295478703223668355222203651040533146833365702079354227555185016378027753764240941825049498083902107324559043430408906071605031955805229689<146>
4×10190+9 = 4(0)1899<191> = 2789 × 17155258129<11> × 1411411376393248424585966404607993<34> × 8108541009938988911690412739095707962709473834181558677<55> × 73049607829538551249787368141925002919877809833548888619882773472702091313103567462825849<89> (matsui / GMP-ECM B1=88000000, sigma=2898798771 for P34 / September 17, 2008 2008 年 9 月 17 日) (Dmitry Domanov / Msieve 1.40 snfs / November 12, 2011 2011 年 11 月 12 日)
4×10191+9 = 4(0)1909<192> = definitely prime number 素数
4×10192+9 = 4(0)1919<193> = 13 × 3084049 × 20054833 × 362793721871669762743297557966121<33> × 34347828192180472650311406770836321<35> × 399224581811496883777327450848889939055934413354952004388681194427258371965399996716709123759572132028042808069<111> (matsui / GMP-ECM B1=88000000, sigma=2110858031 for P33 / September 17, 2008 2008 年 9 月 17 日) (matsui / GMP-ECM 6.2.1 for P35 / October 15, 2008 2008 年 10 月 15 日)
4×10193+9 = 4(0)1929<194> = 7 × 11437 × 13853895929<11> × 284374155722383<15> × 1455040861595700679822195920931<31> × 40774884715492908428204364418823<32> × 9456466122140544011470454984220083014832730601<46> × 226042958165565708353120714503974059356275405880402226161<57> (matsui / GMP-ECM 6.2.1 for P32 / October 1, 2008 2008 年 10 月 1 日) (matsui / GMP-ECM 6.2.1 for P31 / October 15, 2008 2008 年 10 月 15 日) (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.38 gnfs for P46 x P57 / 5.56 hours, 0.61 hours / October 15, 2008 2008 年 10 月 15 日)
4×10194+9 = 4(0)1939<195> = 2665781 × 777716085741029<15> × 192936520219429395619375328945303785182939062000314233861188124429897927487161084950952612036074378745402564000772073633249122495281275480660949529437417156696207244582964641<174>
4×10195+9 = 4(0)1949<196> = 569 × 325889 × 79087703 × 143864647583978940811727209<27> × 1895898028384615696251793941239978553891758796871307004276552920334711509119160356272879507632138997239520574377327997632182591163183607158544056351410687<154>
4×10196+9 = 4(0)1959<197> = definitely prime number 素数
4×10197+9 = 4(0)1969<198> = 1597 × 94202005886838037<17> × [2658856658086202185064250938079472746663859126592014100054321408287948245172160493783340251826354249244908998126266481100787212802533174219203369159238971497004207867105641270281<178>] Free to factor
4×10198+9 = 4(0)1979<199> = 13 × 119161480369370553888738724548996511607859620678122425499095327719568445123612055947061<87> × 2582145729799085189864734222137758538649682303628164199071706577153193715726836851292948073706300167943278781913<112> (matsui / GGNFS-0.77.1-20060722-nocona / February 18, 2009 2009 年 2 月 18 日)
4×10199+9 = 4(0)1989<200> = 7 × 167 × 807609247 × 69410343209<11> × 3583758997367<13> × 4408808231743453<16> × 902378687429809728877943<24> × 34354547702604499771852060945580290335045785027459957891<56> × 1246197671815972306658825990912399156490027586001311061642622929565689<70> (Erik Branger / GGNFS, Msieve gnfs for P56 x P70 / 97.56 hours / February 20, 2009 2009 年 2 月 20 日)
4×10200+9 = 4(0)1999<201> = 61 × 7428301 × 66571867650574241377<20> × 13260195340912706189613478602151803601200846612924840571496471519038131433542401429752928656391236967769486953577322329150096781747532322298039868635523760934059181669090897<173>
4×10201+9 = 4(0)2009<202> = 19 × 41969 × 1976453 × 8788979 × 21280979 × 869485926612010929713294429061619<33> × [15606254712063376725539740805651828004258104146302801666353687446609629914140730575528706598887037816965221011197626429846238635396925544675637<143>] (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3803940840 for P33 / February 27, 2009 2009 年 2 月 27 日) Free to factor
4×10202+9 = 4(0)2019<203> = 17 × 1117 × 2574721 × 818140179270228523740581736159729356875726252823169381283765288333363879380977392449236189870510353981946255578886811984387553107314994126577073197717093330333497463305005196150532668891965261<192>
4×10203+9 = 4(0)2029<204> = 241 × 10093 × 21504565484876647<17> × 26854677970110810209789011<26> × 284755456550999885678873494082877296058232996663262430689758616921765324930935277345456531034111703235800146701627398316294535586341742417321380828545176729<156>
4×10204+9 = 4(0)2039<205> = 133 × 3163073222102835073<19> × 4508275881317837026346541925669<31> × 104371341092297168434106963028253<33> × 277712800883526887911977386254011636208417750693<48> × 4404869454053780353240521351049554133150927234625419390350461907683070289<73> (Serge Batalov / GMP-ECM 6.2.3 B1=3000000, sigma=3928819928 for P33 / August 27, 2009 2009 年 8 月 27 日) (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2627431087 for P31 / September 1, 2010 2010 年 9 月 1 日) (Markus Tervooren / Msieve 1.46 for P48 x P73 / September 11, 2010 2010 年 9 月 11 日)
4×10205+9 = 4(0)2049<206> = 7 × 331 × 60009389597450539<17> × 425671499713583193200939<24> × 675834215075137281305080765018530502788335171916363536343854997460864501058814335086316421493681275023788311584199763573974729615452377074097473531714553921380437<162>
4×10206+9 = 4(0)2059<207> = 409 × 977995110024449877750611246943765281173594132029339853300733496332518337408312958435207823960880195599022004889975550122249388753056234718826405867970660146699266503667481662591687041564792176039119804401<204>
4×10207+9 = 4(0)2069<208> = 4729 × 6299 × 672779 × [199593614015031885965678522461525277704984589327844858584170433570576450073980110630377240908325431940773119217247230833603250518299608272469290865559770772723407518884882554127225865675089455401<195>] Free to factor
4×10208+9 = 4(0)2079<209> = 56041 × 1840599613<10> × [387788377581688289371431249461030381022462384738758093566030054271723711277607755787221028097718270404721169014157843013308491791342913847779739566394836804064339457446263608159998580483142197173<195>] Free to factor
4×10209+9 = 4(0)2089<210> = 491 × 9108877 × 70880585949727<14> × 27616798594990984777138087<26> × 911983644963041595636328360421623<33> × 50098644988651417198307882444383609441864405318360740293378449718885700417103205673274994073777150060629427224793941922480588281<128> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2381347766 for P33 / September 1, 2010 2010 年 9 月 1 日)
4×10210+9 = 4(0)2099<211> = 13 × 26309 × 5253679217<10> × 4887281314249<13> × 455492686613620588551112306594985520246460381216022000109454281426119716020385406579545280511243688843395042669031581045292878825971759840975571999135334756871574845542745235488860369<183>
4×10211+9 = 4(0)2109<212> = 72 × 23 × 3943 × 346447 × 12214014041401<14> × 2249372628029918199931699321<28> × 3734617996063738353225188848986926253190037<43> × 1096330544073739628514840995852150566913308146738023<52> × 230974998413493216913461101667053490775006862404097197673740401437<66> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4173048104 for P43, Msieve 1.48 gnfs for P52 x P66 / July 8, 2011 2011 年 7 月 8 日)
4×10212+9 = 4(0)2119<213> = 1057477 × 1719841 × 2162154127181111154546903829<28> × 77175797637606010161708971689<29> × 1746066645189561080367807342423137376428492594383633<52> × 754870008751017698161582119509494539523940082054318759700337322475860229316028590649214989769<93> (Markus Tervooren / msieve 1.41, lattice siever (64bit/asm) gnfs for P52 x P93 / 669.60 hours on Q6700 / May 12, 2009 2009 年 5 月 12 日)
4×10213+9 = 4(0)2129<214> = 89 × 211 × 4912330291777329830182920462792184153201<40> × 209197765948292508715840081366263723462559353816430654219<57> × 207273092529491319737806399512561945738725389466995842008096844701461670330893312911176031446241487096666609893809<114> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 120.93 hours, 44.52 hours / August 4, 2009 2009 年 8 月 4 日)
4×10214+9 = 4(0)2139<215> = 29 × 1217 × 7786148386377735821<19> × [145562242988025635613919280477381116593397869108726341544922296125944767249979828847843443562035046129275107091067705011606526702249585186860819550088210631870598859509081945793235530181311953<192>] Free to factor
4×10215+9 = 4(0)2149<216> = 843511914000515635859<21> × 2916930098944506436921160385976815917<37> × 28362630078557841829410121067223024623<38> × 717624987931695445963400508727609072579019398622733700849<57> × 7987276063084717846585308264789381814811555069481543864388139489<64> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2573766023 for P38 / September 2, 2010 2010 年 9 月 2 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1375640089 for P37 / March 18, 2011 2011 年 3 月 18 日) (Andreas Tete / factmsieve76.py via GGNFS, Msieve 1.48 gnfs for P57 x P64 / March 25, 2011 2011 年 3 月 25 日)
4×10216+9 = 4(0)2159<217> = 13 × 3078594054131367145950769<25> × 99945722716964004103276231613096872237723482435939148019947815682703620556233148110226160098164250446605754074221702698752812874667061106151582439391765728778357025656680126191009903902639997<191>
4×10217+9 = 4(0)2169<218> = 7 × 59 × 10331 × 103801 × 2709378956041357<16> × 1746852043119607943<19> × 23516613293858822582041<23> × 1014018537142620832647766463<28> × 10240471134688208781527994263<29> × 9302958779121468396279950822681<31> × 8399983999392945602288689704976938270469713713532739350711371797<64> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1580648321 for P31 / February 28, 2009 2009 年 2 月 28 日)
4×10218+9 = 4(0)2179<219> = 17 × 149 × 423599432549<12> × 337295897470084021832970068474861587614613<42> × [1105244526892677725087648046720395027983786591544863821414990576149865798239702971273663414228304906039651872267015417500311959128042598898886574160406174745155629<163>] (Ignacio Santos / GMP-ECM 6.3 B1=11000000, sigma=2410163761 for P42 / September 2, 2010 2010 年 9 月 2 日) Free to factor
4×10219+9 = 4(0)2189<220> = 19 × 187290361394179498232863<24> × 9457269799406383426633156512971<31> × 118857114821080154967545816861734128831254596556026751501924605858763770033655810048872088003725641017149749577328038719567805266379972250629286861103129887452328807<165> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=734110824 for P31 / February 28, 2009 2009 年 2 月 28 日)
4×10220+9 = 4(0)2199<221> = 997 × 111121 × 709782838241307772064197157557<30> × 3149890093077505629623797990708333<34> × 161490804127142935646012681051558556806532046789676636263532663494011806060459900765337459585171509537960886365977455828683623598039688809043895612597<150> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1818859441 for P30 / February 28, 2009 2009 年 2 月 28 日) (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3816302787 for P34 / September 2, 2010 2010 年 9 月 2 日)
4×10221+9 = 4(0)2209<222> = 1380329 × 6586109027452037<16> × [43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133<200>] Free to factor
4×10222+9 = 4(0)2219<223> = 13 × 113 × 5862761853228757<16> × 17589576864839190157<20> × 5274182050091317198581965547001<31> × 5006398706548685269808541408685382119276014206454662384624282431054279618619937841652442041715222856369255023664857400346225756316048000059634993308331989<154> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3200907737 for P31 / February 28, 2009 2009 年 2 月 28 日)
4×10223+9 = 4(0)2229<224> = 7 × 849533 × 992539 × 1487466529<10> × 9123362680493<13> × [499380954823368629696796705151353215723452870181324733048397352617367205331038227787111897713991334784635822310237511116333018400381959894246044656091926067973774040951914432014443544920133<189>] Free to factor
4×10224+9 = 4(0)2239<225> = 577 × 102217 × 24814560283453144513<20> × 1701597111164796274950798372824306233415252657532469<52> × [160619298265426567764113785189916670566896327847917517736028824397501662669444653271349652523436394443167496032436394951696733944666847510380141533<147>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=9880405 for P52 / November 11, 2011 2011 年 11 月 11 日) Free to factor
4×10225+9 = 4(0)2249<226> = 179 × 606401909035756925044903<24> × [36850755880067866288379311590761764982953232025155359751431764103391286411481397176164432861437842634276290368953298183122387998136182422936489729834091611069263439255415555787541474497332341413143157<200>] Free to factor
4×10226+9 = 4(0)2259<227> = 31337 × 531224620086912350245859189067223101258904314192717467046517<60> × 12828873808972211083534637623968253935593516010624496794198042074986030103108677<80> × 187299167008031268767091402582120895508874986452679895321798595676055958571259869273<84> (matsui / Msieve 1.51 snfs / June 4, 2012 2012 年 6 月 4 日)
4×10227+9 = 4(0)2269<228> = 12659 × 42767 × 682259 × 1261349631343<13> × 5901066229103536592988364115598667117207<40> × 504069402763847616149058109148958768514693<42> × 288633158349352014090524660587578985749174921225052500539495360909719336795945620097341092667335238678340336883809215419<120> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3760815385 for P40 / July 1, 2011 2011 年 7 月 1 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=198537948 for P42 / July 1, 2011 2011 年 7 月 1 日)
4×10228+9 = 4(0)2279<229> = 13 × 3709 × 150632969593<12> × 4403428148909407333<19> × [125068762717615453072552784419259101041847217761882153020627138105379041537855404135343604356436230123327708618669324962368940498132532367904187316334787007263739067493710719624375982749809158533<195>] Free to factor
4×10229+9 = 4(0)2289<230> = 7 × 47 × 277 × 1457422598837<13> × 551420791056445453796063<24> × 1638406192738208329601682412911049<34> × 333345124197251305675550256925290253496716079465791821716379169270916804717942808852818711966723328607977587292438599629740745367231278762393317263765016767<156> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1467685157 for P34 / March 1, 2009 2009 年 3 月 1 日)
4×10230+9 = 4(0)2299<231> = 857 × 191476712521<12> × 8028511193274445924646050673<28> × [303618471635148302875013276431116991069591797728221416774456900877195412292456052212417141607687467184408454701436005671448750185847346472867664341696586874423661292335225895959134470575289<189>] Free to factor
4×10231+9 = 4(0)2309<232> = 541531 × 563327077 × 344974725091<12> × [38009203123631100628260875115373462909570627247507581597846937241698038932991128761302797949815480281608468227351024708950725931512554168319349399262249588296729091658547310572038707875049320136138761605477<206>] Free to factor
4×10232+9 = 4(0)2319<233> = 6781 × 86869 × 101923364225918527839065891102757815508373<42> × [666235353567257533671029519064380742774418132917318448895197569176610167844598276515950058676003746683731464996043877358855070285429649231163084825310162994068656389331159825129096997<183>] (Erik Branger / GMP-ECM B1=3000000, sigma=1485941456 for P42 / December 19, 2009 2009 年 12 月 19 日) Free to factor
4×10233+9 = 4(0)2329<234> = 23 × 241 × 27435761 × [2630256495534832519671588725579347129934832765132385401880987530726835813648218261659450838411306287985736604149222639690330902569007746369148047095242274982762927550208536640183181644396978572408122581585106484958034907583<223>] Free to factor
4×10234+9 = 4(0)2339<235> = 13 × 17 × 450941691481658427023872957905116856101<39> × [40137223621622923305784563330723918564343099541748933606691232297924670660195689952463507168033570551778022926601144629887894992572061188383263948386610882029148373847181106478208835204848344729<194>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3367706013 for P39 / April 13, 2011 2011 年 4 月 13 日) Free to factor
4×10235+9 = 4(0)2349<236> = 7 × 5573 × 8768013343<10> × 46382191979<11> × 10820413408068465014936896931386007<35> × [233011085568350111742887411902261194543558824623920618901107914979275770821459276196474055441316863432392745125871371556152366932432291042713657364456524053682882334776676446561<177>] (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3588486229 for P35 / September 2, 2010 2010 年 9 月 2 日) Free to factor
4×10236+9 = 4(0)2359<237> = 193 × 355609 × 1104193 × 18648457 × 530224333 × 533804697044331114759261601310823323308616585540765221910067593417055899599861135187191821602666626954933164454857594632226846906361814501701071096132360386705581599307667050223485405435238108503423601188429<207>
4×10237+9 = 4(0)2369<238> = 19 × 210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211<237>
4×10238+9 = 4(0)2379<239> = 13729 × 264609763147329391577993<24> × [11010707411765256858548653740610118023871093778797409212334316791131530420978652697027293273646597863356436417140752877085791009381027209760498750978639429609881935669897916419922021608892184845951587489960464097<212>] Free to factor
4×10239+9 = 4(0)2389<240> = 983 × 15389903 × 4267139508637<13> × 4298785922742343<16> × 4683933785766256278623<22> × [307735206107618533007178043551976557773308392564547725453111499852890428470219213622437527093012915272048008076083287455361528811183959201431237451388873164800706110104091958584237<180>] Free to factor
4×10240+9 = 4(0)2399<241> = 13 × 1490226374629<13> × [206473535115703058091169633368038883546960933024843422503449663774127952585655839101348618000599167338270994828011178351007134386489404705171227058245317212907807375024552379461007218096204591883823161619459382651519463716391017<228>] Free to factor
4×10241+9 = 4(0)2409<242> = 7 × 14106394181773<14> × 361359963110065133152257674112686956001291<42> × [1121000748864440204384814511452758084832827077359933485692492437596330603285932433535326273791220914043463454890538420740974580768765019732234486389530677759019140071542765980948670696609<187>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2724147305 for P42 / November 9, 2011 2011 年 11 月 9 日) Free to factor
4×10242+9 = 4(0)2419<243> = 29 × 601 × 625969 × 517852967663401<15> × 70799179713688698262849292594179995807285084551686552728241575523541225198203701982092213878982229208841071044222232816034911143025108079862389175062848934863876184987776645670063173630755076343585771533822100108376109<218>
4×10243+9 = 4(0)2429<244> = 211 × 761 × 127566948277192337869764297638109721127023<42> × 195278627055004260165165796713698923970426519764143364350420080659555185314378363696270057757429282480559027603944657848259735353558435498871600913917817557530384015450970490735110900823076695659173<198> (Serge Batalov / GMP-ECM 6.2.3 B1=11000000, sigma=3161935447 for P42 / August 27, 2009 2009 年 8 月 27 日)
4×10244+9 = 4(0)2439<245> = 829 × 6316202857<10> × 1689891773761<13> × [4520541901810601412828688084585610269711053287930096735843239402848347423859601728154320827801543215029968038993623272398634917346080013126137602777923239382485019101358635086637511611394830186880467634412467118783619573<220>] Free to factor
4×10245+9 = 4(0)2449<246> = 284957 × 82069760818893961<17> × [17103992351646896947820678886143627407011692156056123625751845024762478944067537148965053674138922458858308356979643268213517888423902840640814811396361041225592982387853888071093551960355253612128950692336805235956024526517<224>] Free to factor
4×10246+9 = 4(0)2459<247> = 13 × 389 × 617 × 50777 × [25247293880461782697257293776006595553265668303841196016434660636737328692147797578872494846335590484101524509724047825017096872684282247614713977077985155453305008960962275583155890044223894846623484113855736194731737883080211281448393<236>] Free to factor
4×10247+9 = 4(0)2469<248> = 7 × 397 × 3169 × 927184488768257538302423<24> × 2038397694076319403460923851542990961<37> × [2403223313824451720795323864725094961991660457228605519711132564663483598544589846208332995874772829662288525781188920635720881737165963500384485216250378600848387944659873754749053<181>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2707386711 for P37 / June 28, 2011 2011 年 6 月 28 日) Free to factor
4×10248+9 = 4(0)2479<249> = 109 × 157 × 222437485156209239721584649092089<33> × 6560309672844283720660829781088994533627296541<46> × [16017750489352840895477293468622238661957966467022028228917991107131060497661368854872813269731952418051134476100822003976644240550551033029977808957008815664991186957<167>] (Serge Batalov / GMP-ECM 6.2.2 B1=1000000, sigma=566428965 for P33 / March 2, 2009 2009 年 3 月 2 日) (jdommer / GMP-ECM B1=110000000, sigma=3033104531 for P46 / January 5, 2012 2012 年 1 月 5 日) Free to factor
4×10249+9 = 4(0)2489<250> = 197 × 1259 × 2179 × 62971 × 1088579 × 1306928213<10> × 184515969747407<15> × 45612632227388977327638067728993389575890276691087<50> × 9816110396361358500270022591395885816614186034354967937216550816188529309383183030824865870104961377461601943985848001078435104879840148882081058752705845009<157> (steinrar / GMP-ECM B1=110000000, sigma=3264100850 for P50 / October 1, 2011 2011 年 10 月 1 日)
4×10250+9 = 4(0)2499<251> = 172 × 6390680809561<13> × 25515781715614181<17> × 848801510394874251260023659751607386622798929408796565018046486638110030688061988932479753368130172131465836796733021998704961471009396587265763132158986835121915788572798426422377356074179066275604034230905886064881341<219>
plain text versionプレーンテキスト版

4. Related links 関連リンク