Table of contents 目次

  1. About 500...009 500...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 500...009 500...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 500...009 500...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 500...009 500...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

50w9 = { 59, 509, 5009, 50009, 500009, 5000009, 50000009, 500000009, 5000000009, 50000000009, … }

1.3. General term 一般項

5×10n+9 (1≤n)

2. Prime numbers of the form 500...009 500...009 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. 5×101+9 = 59 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  2. 5×102+9 = 509 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  3. 5×103+9 = 5009 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  4. 5×105+9 = 500009 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  5. 5×108+9 = 500000009 is prime. は素数です。 (Makoto Kamada / December 3, 2004 2004 年 12 月 3 日)
  6. 5×1020+9 = 5(0)199<21> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 3, 2004 2004 年 12 月 3 日)
  7. 5×1029+9 = 5(0)289<30> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 3, 2004 2004 年 12 月 3 日)
  8. 5×1086+9 = 5(0)859<87> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 3, 2004 2004 年 12 月 3 日)
  9. 5×10283+9 = 5(0)2829<284> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 3, 2004 2004 年 12 月 3 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 4, 2005 2005 年 1 月 4 日)
  10. 5×10757+9 = 5(0)7569<758> 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 / May 30, 2006 2006 年 5 月 30 日)
  11. 5×101199+9 = 5(0)11989<1200> 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 11, 2006 2006 年 9 月 11 日)
  12. 5×102473+9 = 5(0)24729<2474> 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: suberi / PRIMO 3.0.4 / September 21, 2007 2007 年 9 月 21 日)
  13. 5×102733+9 = 5(0)27329<2734> 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: suberi / PRIMO 3.0.4 / October 9, 2007 2007 年 10 月 9 日)
  14. 5×1024853+9 = 5(0)248529<24854> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  15. 5×1039629+9 = 5(0)396289<39630> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  16. 5×1053492+9 = 5(0)534919<53493> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  17. 5×1071237+9 = 5(0)712369<71238> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  18. 5×1072302+9 = 5(0)723019<72303> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  19. 5×1081653+9 = 5(0)816529<81654> is PRP. はおそらく素数です。 (Dmitry Domanov / Prime95 v25.11, pfgw / March 8, 2010 2010 年 3 月 8 日)
  20. 5×10167510+9 = 5(0)1675099<167511> is PRP. はおそらく素数です。 (Bob Price / PFGW / 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. 5×106k+9 = 7×(5×100+97+45×106-19×7×k-1Σm=0106m)
  2. 5×1016k+7+9 = 17×(5×107+917+45×107×1016-19×17×k-1Σm=01016m)
  3. 5×1018k+17+9 = 19×(5×1017+919+45×1017×1018-19×19×k-1Σm=01018m)
  4. 5×1021k+4+9 = 43×(5×104+943+45×104×1021-19×43×k-1Σm=01021m)
  5. 5×1022k+14+9 = 23×(5×1014+923+45×1014×1022-19×23×k-1Σm=01022m)
  6. 5×1028k+22+9 = 29×(5×1022+929+45×1022×1028-19×29×k-1Σm=01028m)
  7. 5×1033k+6+9 = 67×(5×106+967+45×106×1033-19×67×k-1Σm=01033m)
  8. 5×1041k+32+9 = 83×(5×1032+983+45×1032×1041-19×83×k-1Σm=01041m)
  9. 5×1044k+12+9 = 89×(5×1012+989+45×1012×1044-19×89×k-1Σm=01044m)
  10. 5×1046k+42+9 = 47×(5×1042+947+45×1042×1046-19×47×k-1Σm=01046m)

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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 27.25%. 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 27.25% です。

3. Factor table of 500...009 500...009 の素因数分解表

3.1. Last updated 最終更新日

March 29, 2017 2017 年 3 月 29 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=193, 197, 200, 201, 204, 207, 208, 212, 214, 215, 216, 221, 225, 227, 228, 229, 230, 232, 234, 236, 237, 239, 240, 243, 244, 245, 250 (27/250)

3.4. Factor table 素因数分解表

5×101+9 = 59 = definitely prime number 素数
5×102+9 = 509 = definitely prime number 素数
5×103+9 = 5009 = definitely prime number 素数
5×104+9 = 50009 = 43 × 1163
5×105+9 = 500009 = definitely prime number 素数
5×106+9 = 5000009 = 72 × 67 × 1523
5×107+9 = 50000009 = 17 × 1451 × 2027
5×108+9 = 500000009 = definitely prime number 素数
5×109+9 = 5000000009<10> = 131 × 521 × 73259
5×1010+9 = 50000000009<11> = 881 × 56753689
5×1011+9 = 500000000009<12> = 39041 × 12807049
5×1012+9 = 5000000000009<13> = 7 × 89 × 283 × 28359301
5×1013+9 = 50000000000009<14> = 193 × 259067357513<12>
5×1014+9 = 500000000000009<15> = 233 × 3221 × 12758387
5×1015+9 = 5000000000000009<16> = 7643 × 654193379563<12>
5×1016+9 = 50000000000000009<17> = 22237301 × 2248474309<10>
5×1017+9 = 500000000000000009<18> = 19 × 26315789473684211<17>
5×1018+9 = 5000000000000000009<19> = 7 × 947 × 14303 × 62627 × 842041
5×1019+9 = 50000000000000000009<20> = 953 × 33961 × 340267 × 4540219
5×1020+9 = 500000000000000000009<21> = definitely prime number 素数
5×1021+9 = 5000000000000000000009<22> = 2803 × 1783803068141277203<19>
5×1022+9 = 50000000000000000000009<23> = 29 × 4547 × 2196583 × 172623307721<12>
5×1023+9 = 500000000000000000000009<24> = 17 × 8443 × 3483568009698253339<19>
5×1024+9 = 5000000000000000000000009<25> = 7 × 714285714285714285714287<24>
5×1025+9 = 50000000000000000000000009<26> = 43 × 419 × 500990627 × 5539338755651<13>
5×1026+9 = 500000000000000000000000009<27> = 467 × 1070663811563169164882227<25>
5×1027+9 = 5000000000000000000000000009<28> = 38229259 × 130789874844291384251<21>
5×1028+9 = 50000000000000000000000000009<29> = 9917983 × 5041347620781362500823<22>
5×1029+9 = 500000000000000000000000000009<30> = definitely prime number 素数
5×1030+9 = 5000000000000000000000000000009<31> = 7 × 28033828861<11> × 25479420518237224667<20>
5×1031+9 = 50000000000000000000000000000009<32> = 5657 × 345518153 × 25580731312635837929<20>
5×1032+9 = 500000000000000000000000000000009<33> = 83 × 6024096385542168674698795180723<31>
5×1033+9 = 5000000000000000000000000000000009<34> = 50175249121<11> × 99650725957379148415529<23>
5×1034+9 = 50000000000000000000000000000000009<35> = 643 × 44251321 × 1757246923028242930520603<25>
5×1035+9 = 500000000000000000000000000000000009<36> = 19 × 227 × 883 × 23201 × 5658784281801726741329771<25>
5×1036+9 = 5000000000000000000000000000000000009<37> = 7 × 23 × 2087 × 5749742137487<13> × 2588053866024938401<19>
5×1037+9 = 50000000000000000000000000000000000009<38> = 163 × 233 × 523 × 3530347 × 9417739 × 206052251 × 367437419
5×1038+9 = 500000000000000000000000000000000000009<39> = 131221 × 3616841640941<13> × 1053506373010666479769<22>
5×1039+9 = 5000000000000000000000000000000000000009<40> = 17 × 67 × 683 × 22073 × 4234294121<10> × 68767492974126051929<20>
5×1040+9 = 50000000000000000000000000000000000000009<41> = 61 × 298583 × 2745206964721839433613291369733643<34>
5×1041+9 = 500000000000000000000000000000000000000009<42> = 97 × 113 × 1201 × 89387 × 133345804411<12> × 3186567348716898017<19>
5×1042+9 = 5000000000000000000000000000000000000000009<43> = 7 × 47 × 1609 × 11025983 × 2324785346489<13> × 368483362950980287<18>
5×1043+9 = 50000000000000000000000000000000000000000009<44> = 1361 × 36737692872887582659808963997060984570169<41>
5×1044+9 = 500000000000000000000000000000000000000000009<45> = 68460047252221<14> × 7303529869880112596022145893629<31>
5×1045+9 = 5000000000000000000000000000000000000000000009<46> = 107 × 13963 × 8574080104358951233<19> × 390319233268226939953<21>
5×1046+9 = 50000000000000000000000000000000000000000000009<47> = 43 × 3218003 × 56881969 × 57584503764527<14> × 110315072348952167<18>
5×1047+9 = 500000000000000000000000000000000000000000000009<48> = 96947818283<11> × 5157413636070199547885992936408986523<37>
5×1048+9 = 5000000000000000000000000000000000000000000000009<49> = 73 × 46181 × 816499501 × 386595351583335394960379488752223<33>
5×1049+9 = 50000000000000000000000000000000000000000000000009<50> = 673 × 74294205052005943536404160475482912332838038633<47>
5×1050+9 = 500000000000000000000000000000000000000000000000009<51> = 29 × 559483 × 36737339281<11> × 111380200900349<15> × 7531290773176140323<19>
5×1051+9 = 5(0)509<52> = 8685601 × 575665403004351685047471096127947853004069609<45>
5×1052+9 = 5(0)519<53> = 7687 × 6504488096786782880187329257187459346949395082607<49>
5×1053+9 = 5(0)529<54> = 19 × 9817 × 180791745249396947921<21> × 14827195545433457804439544123<29>
5×1054+9 = 5(0)539<55> = 7 × 661949 × 1079064571871419528867459146075776662120927313563<49>
5×1055+9 = 5(0)549<56> = 17 × 638800385912203<15> × 4604218368447372626058840598874681080459<40>
5×1056+9 = 5(0)559<57> = 89 × 282889 × 141958412421016283<18> × 139895196755438724831578856461963<33>
5×1057+9 = 5(0)569<58> = 929 × 685739 × 7848658635434627030195458395342903586868548001339<49>
5×1058+9 = 5(0)579<59> = 23 × 1049 × 2072367057653251543913457951672400215526173995938160567<55>
5×1059+9 = 5(0)589<60> = 59 × 8474576271186440677966101694915254237288135593220338983051<58>
5×1060+9 = 5(0)599<61> = 7 × 714285714285714285714285714285714285714285714285714285714287<60>
5×1061+9 = 5(0)609<62> = 521 × 1788410916885976820867<22> × 53661766946915792941405969398212844587<38>
5×1062+9 = 5(0)619<63> = 19087 × 378809 × 241921579651815579609688769<27> × 285849497117142539285475167<27>
5×1063+9 = 5(0)629<64> = 1171 × 461239187131<12> × 9257354847699093469647841246437162300255068266409<49>
5×1064+9 = 5(0)639<65> = 34019723 × 72622682281362131383<20> × 20237969911868334968581999677034335901<38>
5×1065+9 = 5(0)649<66> = 809 × 4217402874793<13> × 146546818010639901011494971603668463199190231099257<51>
5×1066+9 = 5(0)659<67> = 7 × 412123 × 64830657850998191927<20> × 26734045524059271201467690581226945450347<41>
5×1067+9 = 5(0)669<68> = 43 × 1881419 × 7310835987761<13> × 84537418591674234024959808389652980359300209857<47>
5×1068+9 = 5(0)679<69> = 6848103860303<13> × 73012911340085471172155105462263973760020341740365169703<56>
5×1069+9 = 5(0)689<70> = 3881 × 1454569 × 183339272189671009<18> × 4830994366338537465366958647013901853403609<43>
5×1070+9 = 5(0)699<71> = 661516035855949879828125047347<30> × 75583957591147311467549473414250961320147<41> (Makoto Kamada / msieve 0.81 / 4.8 minutes)
5×1071+9 = 5(0)709<72> = 17 × 19 × 1365967239980788525931<22> × 1133253837127779641432627363227591632625700009993<49>
5×1072+9 = 5(0)719<73> = 7 × 67 × 10660980810234541577825159914712153518123667377398720682302771855010661<71>
5×1073+9 = 5(0)729<74> = 83 × 433 × 6073 × 305611 × 749603753501605288424145281502663564017620417646448616688977<60>
5×1074+9 = 5(0)739<75> = 125183 × 122519240587<12> × 181834481946896153987<21> × 179285063493382499988918212377351014167<39>
5×1075+9 = 5(0)749<76> = 1033 × 1162449123692095313<19> × 4163856255322156263287430495312710177536572328117951921<55>
5×1076+9 = 5(0)759<77> = 5821 × 104934834477007<15> × 81856415559581999892797157293747572823024326906418532029747<59>
5×1077+9 = 5(0)769<78> = 554603842763590774854107<24> × 96645962301785609615798089<26> × 9328319559054896361192603283<28>
5×1078+9 = 5(0)779<79> = 7 × 29 × 139031467 × 18598155365672747<17> × 9525570370514334259949302184159203077791802771608147<52>
5×1079+9 = 5(0)789<80> = 21014041 × 25333753 × 23875370105413281285113<23> × 3933786491028175936276587457270285958264641<43>
5×1080+9 = 5(0)799<81> = 23 × 5701 × 3513891428605307<16> × 13669314742856167<17> × 49275427904951189<17> × 1611111660341383156829727763<28>
5×1081+9 = 5(0)809<82> = 2114448363162865003999867433<28> × 2364682953297959493065525144202878377750866292338907873<55>
5×1082+9 = 5(0)819<83> = 18521 × 2266087 × 1191321537290803217004374509835384744175234361056212434137932067292803367<73>
5×1083+9 = 5(0)829<84> = 331 × 1341831617963<13> × 1125755272051236731692928679628520785391938162105210030791535104016753<70>
5×1084+9 = 5(0)839<85> = 7 × 6067 × 1206703 × 18030361 × 132090443412074025530946664889<30> × 40965829838534850254316339044447864203<38>
5×1085+9 = 5(0)849<86> = 1552307 × 839148015940481082011376560756651<33> × 38384316916961200488450737386931246465595058937<47> (Makoto Kamada / GGNFS-0.70.3 / 0.13 hours)
5×1086+9 = 5(0)859<87> = definitely prime number 素数
5×1087+9 = 5(0)869<88> = 17 × 179 × 1737563 × 945643609294936732157826975017260307968257321482190468181018917821873678506201<78>
5×1088+9 = 5(0)879<89> = 433 × 47 × 409 × 651863 × 68945909 × 727911597434487648470920532262477861798924423072702919264326934807<66>
5×1089+9 = 5(0)889<90> = 193 × 3011 × 742465915145593<15> × 44745198224019587051<20> × 56884941266103164579<20> × 12810856738004556521779641553<29>
5×1090+9 = 5(0)899<91> = 72 × 15569 × 2396614603<10> × 2734733460602543658912730972232617458607407010498152972567272491614185971963<76>
5×1091+9 = 5(0)909<92> = 337 × 3617 × 30113 × 38119019 × 1866066787032935500021508462387<31> × 19149995307730563514569962471639149140267689<44> (Makoto Kamada / msieve 0.81 / 6.5 minutes)
5×1092+9 = 5(0)919<93> = 99661 × 343432729635769692729424579402880625583<39> × 14608414466712331918005565230921123831736128191843<50> (Makoto Kamada / GGNFS-0.70.7 / 0.46 hours)
5×1093+9 = 5(0)929<94> = 83890990181873177438748091<26> × 59601156085536103027283046013722293996618509805655506860541862329099<68>
5×1094+9 = 5(0)939<95> = 109 × 391397801 × 18100189307<11> × 19098648383<11> × 3390309720106776346732689640650568907539912025395595046149733121<64>
5×1095+9 = 5(0)949<96> = 5147 × 720352566823276968795938793404225033752577<42> × 134856141053300575228963888060633028811058261092011<51> (Makoto Kamada / GGNFS-0.70.7 / 0.37 hours)
5×1096+9 = 5(0)959<97> = 7 × 686135269 × 447843243467<12> × 63005839061456852693059027258607<32> × 36893970369927097221019327042044405178406567<44> (Makoto Kamada / msieve 0.83 / 9.9 minutes)
5×1097+9 = 5(0)969<98> = 2169017172332513641<19> × 55130213181442287264979<23> × 3157018438248129351915280289<28> × 132446419956734001747280889179<30>
5×1098+9 = 5(0)979<99> = 107 × 263203937924865017242635664386495697410529<42> × 17753903049868583054857060245466213431862981456495593403<56> (Makoto Kamada / GGNFS-0.70.7 / 0.49 hours)
5×1099+9 = 5(0)989<100> = 907 × 59246083817<11> × 529632079556254522325931446630827<33> × 175682614675517925123451219617166344582046244425465993<54> (Makoto Kamada / GGNFS-0.70.7 / 0.54 hours)
5×10100+9 = 5(0)999<101> = 61 × 89 × 3089 × 26011791101<11> × 61758258689<11> × 10010888244821<14> × 6867893807717461<16> × 26994219183140788012598001149243195020919521<44>
5×10101+9 = 5(0)1009<102> = 307 × 1259 × 7297 × 16187 × 17921 × 4567287396811955371<19> × 11795651178736649977<20> × 343253010253945407673<21> × 33047478581174415086987617<26>
5×10102+9 = 5(0)1019<103> = 7 × 23 × 7001 × 31854706908327006451053849450780933259103<41> × 139254884403520782870512217316445103008038584589836414223<57> (Robert Backstrom / GMP-ECM 6.0.1 B1=1368000, sigma=184601020 for P41 / December 16, 2007 2007 年 12 月 16 日)
5×10103+9 = 5(0)1029<104> = 172 × 443 × 10243 × 38127757484732153201407718594358514362635881713363295767200258201783730725897194384292844493369<95>
5×10104+9 = 5(0)1039<105> = 8144467 × 61391371590062308558681617839448548321209969909633128846860083047791832172688525842145348492418227<98>
5×10105+9 = 5(0)1049<106> = 67 × 74626865671641791044776119402985074626865671641791044776119402985074626865671641791044776119402985074627<104>
5×10106+9 = 5(0)1059<107> = 29 × 20483 × 47129 × 127727 × 3533097401<10> × 28173215461583<14> × 22059849968389477777367<23> × 6368144705357452087345960316687446098468852649<46>
5×10107+9 = 5(0)1069<108> = 19 × 22161612064368328651072431710802457<35> × 1187449243189082427047892522175799526276103441537325771419337450292326123<73> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.95 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 16, 2007 2007 年 12 月 16 日)
5×10108+9 = 5(0)1079<109> = 7 × 5303 × 7069 × 166067022630167<15> × 39679832069422478909<20> × 3696356500679645166847399161227<31> × 782285498959505352039418971804950261<36> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3105078903 for P31 / December 6, 2007 2007 年 12 月 6 日)
5×10109+9 = 5(0)1089<110> = 43 × 347 × 33560809 × 1718022845923<13> × 10396696314670459<17> × 1476704263696277768852508934603<31> × 3785487624900931809465373935855122668411<40> (Makoto Kamada / msieve 0.81 / 2.5 minutes)
5×10110+9 = 5(0)1099<111> = 102351290979660258935783<24> × 4885136232422924748754824062645835630207855495226994094323652961290586468144457276219023<88>
5×10111+9 = 5(0)1109<112> = 37648321 × 132808047402698250474436828139029095082354403002460587817448751565840080889663047656228812966187788294729<105>
5×10112+9 = 5(0)1119<113> = 2723543 × 105675047 × 46460846723<11> × 1444412879087<13> × 582643246090279161892289311534169<33> × 4443059500442994389593557673470074354185141<43> (Makoto Kamada / Msieve 1.31 for P33 x P43 / 6.8 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 15, 2007 2007 年 12 月 15 日)
5×10113+9 = 5(0)1129<114> = 521 × 1101697 × 22533180272459<14> × 17263640466344363904251273<26> × 2239315262988667230883645834735621781769533897240535687958663543051<67>
5×10114+9 = 5(0)1139<115> = 7 × 83 × 463 × 48623 × 70541614319082877066125526339209355501<38> × 5419082164403195929289385747756719945734828037540124137574223619561<67> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.67 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 16, 2007 2007 年 12 月 16 日)
5×10115+9 = 5(0)1149<116> = 135421895166312842522319888209<30> × 369216513611735769279047612969429696678364471964023447259439318187354371487074921830201<87> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=989697153 for P30 / December 6, 2007 2007 年 12 月 6 日)
5×10116+9 = 5(0)1159<117> = 5647 × 14738747 × 1770527491110016131038045568525078001<37> × 3393039989462346591698405537211579666741526697212892785900831616289301<70> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.65 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / December 17, 2007 2007 年 12 月 17 日)
5×10117+9 = 5(0)1169<118> = 59 × 332357898097<12> × 1265189197313<13> × 11831791067641<14> × 5117087672337662321081<22> × 3328765210525162276770289658681319020048706829969245092971<58>
5×10118+9 = 5(0)1179<119> = 163 × 602621 × 15219761 × 2752078124375388307<19> × 12152609620876343177249530162273567278753039101351904352948362704705439240405131422229<86>
5×10119+9 = 5(0)1189<120> = 17 × 2593 × 94580474563119451933897100137<29> × 15965640489715142434408651583449<32> × 7511570223506641566186351791523369253492069749689636953<55> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3078422050 for P32 / December 6, 2007 2007 年 12 月 6 日)
5×10120+9 = 5(0)1199<121> = 7 × 34721 × 2785008450118031203921<22> × 7386746963131167222296134640785615719982739289744534293985309779088292403445731952430581447007<94>
5×10121+9 = 5(0)1209<122> = 401 × 234394740470022334833839226247804877881<39> × 531958520279564508033197824266783726238632647326464705045488524626649705389905089<81> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.07 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 16, 2007 2007 年 12 月 16 日)
5×10122+9 = 5(0)1219<123> = 563 × 1103 × 7804123 × 3948244567<10> × 2410138726755667729<19> × 6681015153121540500967283<25> × 1622831567493453273039190563446439782323039898282167685563<58>
5×10123+9 = 5(0)1229<124> = 811 × 1127443 × 5468327989477248328562623641561651975454867361094814734212470372585282192294862726883703459865692855590000419891033<115>
5×10124+9 = 5(0)1239<125> = 23 × 149 × 167 × 6460450123<10> × 6953868486893733509549<22> × 1944689090613734229350292333670044866828013925222095993423081207217861923565333570256363<88>
5×10125+9 = 5(0)1249<126> = 19 × 257 × 3539 × 72161 × 14266174514220259441<20> × 8511237533168796478492331<25> × 3302173828418610957378900422288253209285083101378400928303335558839347<70>
5×10126+9 = 5(0)1259<127> = 7 × 541 × 18583998288422002372740046473239078846323774567438627504014367<62> × 71045331073170059497410700220270620432737612295639886159776421<62> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.52 hours on Core 2 Quad Q6600 / December 16, 2007 2007 年 12 月 16 日)
5×10127+9 = 5(0)1269<128> = 1019 × 839981899259<12> × 46454812444268681<17> × 575720638209858683<18> × 2184154640335527683633902539704197471893904969893340491524363981688082417012523<79>
5×10128+9 = 5(0)1279<129> = 1061 × 8263 × 32606581229675929243<20> × 50847077318647819597365017797483<32> × 34398983328133519473445264118353961811708231206373516604583058844886827<71> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=936022278 for P32 / December 6, 2007 2007 年 12 月 6 日)
5×10129+9 = 5(0)1289<130> = 1283 × 6673 × 421483 × 55851141761388119444538473036013289<35> × 188165401070611685235607528162110379<36> × 131847024827184141097638546699400890537611235187<48> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.96 hours on Core 2 Quad Q6600 / December 16, 2007 2007 年 12 月 16 日)
5×10130+9 = 5(0)1299<131> = 43 × 2729 × 4487041153498275432117890383<28> × 78135195210740856984970374463<29> × 7060100599535070668439701056024123<34> × 172139433524725729134981937062884041<36> (Makoto Kamada / Msieve 1.31 for P34 x P36 / 1.9 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / December 15, 2007 2007 年 12 月 15 日)
5×10131+9 = 5(0)1309<132> = 5885314119166091<16> × 13332471407775771697<20> × 6372204365476312950913816735019063814243023355650351480867857852028362091440340463534238494772267<97>
5×10132+9 = 5(0)1319<133> = 72 × 229 × 22300386396977126153628581<26> × 19981406441268275756000542641630447824819009373157008685181470252009773998008824239285747825708240073409<104>
5×10133+9 = 5(0)1329<134> = 1808856091842673778141469519200801928271629226769243833<55> × 27641778815618891492508230793764960546620767858028425576294203682615206075499473<80> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.70 hours on Core 2 Quad Q6600 / December 16, 2007 2007 年 12 月 16 日)
5×10134+9 = 5(0)1339<135> = 29 × 47 × 119827 × 520808921 × 955172286847<12> × 6154026101686828576608812562593033624216444548216648106543167686080887041458007345100969545743780170474807<106>
5×10135+9 = 5(0)1349<136> = 17 × 46451 × 114083191571<12> × 5521717201379083<16> × 14621385899793089<17> × 687450849368862654035411061536810182490746946568835388523943169013068756578917509321651<87>
5×10136+9 = 5(0)1359<137> = 16371023 × 5793834883<10> × 527142548039171574676075379341839881734065310318398610115706959043814690833903635286156984193675638715021992857781468301<120>
5×10137+9 = 5(0)1369<138> = 97 × 1506773568889<13> × 226074463554510734010057673<27> × 54141127725421474038977984368371957931<38> × 279493344149482372551112704180571406141518303948937390507771<60> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 12.19 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 17, 2007 2007 年 12 月 17 日)
5×10138+9 = 5(0)1379<139> = 7 × 67 × 24062444319260058179401<23> × 946212734975879332729540202137182929419049849<45> × 468240129107916666081642626977725725851067323112806555638980157404389<69> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 4.63 hours on Core 2 Quad Q6600 / December 17, 2007 2007 年 12 月 17 日)
5×10139+9 = 5(0)1389<140> = 131 × 282610139790019<15> × 78455385167226642559753<23> × 361425133128620455870659489761<30> × 47628824194260490142906266767584168352619460281990995952461920214677657<71> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1355475609 for P30 / December 7, 2007 2007 年 12 月 7 日)
5×10140+9 = 5(0)1399<141> = 61810747 × 783850709 × 7742590769<10> × 1166695489891936003<19> × 1142427982678355371560248151940857567642859886447565182142636179350905922564310186527257700664069<97>
5×10141+9 = 5(0)1409<142> = 643 × 241596601 × 32186089268360638063963449745124098829151333924059388070355309352494789212752383381530891699910594619974186134185297032324846260763<131>
5×10142+9 = 5(0)1419<143> = 124119796809023<15> × 1025700469575172569139010849<28> × 392742946512046794339065527722381007621302805949386146314016466541900456948672100290433074304738366167<102>
5×10143+9 = 5(0)1429<144> = 19 × 5273 × 637541457073<12> × 185800816873178987<18> × 3824573125525072931<19> × 11015890577017142235464148426939922449389984445577698968496531626423501964262247597778039547<92>
5×10144+9 = 5(0)1439<145> = 7 × 89 × 7121 × 1127044261056811370884795113496738221204075482211522314462029089914013285146931633269715441610879854151456265160154116540433952614100270423<139>
5×10145+9 = 5(0)1449<146> = 480587 × 664114531 × 173304257326374916002763<24> × 8011859098238196250376857716817447795633<40> × 112826851275727796887800559483225541997057785219800577879840211604843<69> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.31 / December 18, 2007 2007 年 12 月 18 日)
5×10146+9 = 5(0)1459<147> = 23 × 21739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434783<146>
5×10147+9 = 5(0)1469<148> = 5849697884884838262743075248501338289883<40> × 854744996817632047461743936663945403195159505305631899758967978986218123868623742456524092166116733189586923<108> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.31 / December 19, 2007 2007 年 12 月 19 日)
5×10148+9 = 5(0)1479<149> = 227 × 17783 × 32401 × 382279231706657177446345966604814284801783331417083885100710295462470507365902722102668169000019749852504938346554425099138010494417714149<138>
5×10149+9 = 5(0)1489<150> = 614655261608425773017<21> × 1292831320258423031896200514838978324604313<43> × 629211332393361618328576188689966621539549657057208953485058442782747222654866355168729<87> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 11.28 hours on Core 2 Quad Q6600 / December 17, 2007 2007 年 12 月 17 日)
5×10150+9 = 5(0)1499<151> = 7 × 255023 × 13056647802008927<17> × 214516609726937337795375277612524086859360726388205615391699600713352616520603057430188906655360677041562403995953612161398305247<129>
5×10151+9 = 5(0)1509<152> = 17 × 43 × 107 × 334673882571236023305008947620488003064113918729<48> × 1910060078664050756982889449663405594416053618701081486519366050468241477476722382784210606901891513<100> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 20.92 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 17, 2007 2007 年 12 月 17 日)
5×10152+9 = 5(0)1519<153> = 269 × 3947 × 10627 × 971784257430682151351647<24> × 45600547602041959825609953455638149769097156378999785299436499895993016950190180365657082964082002700405353066157872627<119>
5×10153+9 = 5(0)1529<154> = 113 × 283 × 9652395741655011049538026702985684108326820233080272800634433481<64> × 16198321181881033533347435589236482009169983223746311965676775774243157661743075509891<86> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.31 / December 22, 2007 2007 年 12 月 22 日)
5×10154+9 = 5(0)1539<155> = 829 × 15683 × 56596823 × 44630287349<11> × 6547416756766895807011708792092633881889587619560266369321<58> × 232538362293215384924110022839616818354212477256510811617282792627275661<72> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 32.09 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 18, 2007 2007 年 12 月 18 日)
5×10155+9 = 5(0)1549<156> = 83 × 45261347 × 2295961188217<13> × 57969545452466481902355264284165883894096544901441043472932304096269927626621529404060719584461696898291667870500090111982514941728377<134>
5×10156+9 = 5(0)1559<157> = 7 × 37447 × 28194483512088014904108943<26> × 74881270812473695723895111402915691073452855235176557355117707<62> × 9034780048660293802053456177468412100175147936351538480358818021<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 32.37 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 19, 2007 2007 年 12 月 19 日)
5×10157+9 = 5(0)1569<158> = 1097 × 14897 × 26348627 × 158905115827<12> × 230706227803<12> × 25360542995799645970199393340105446955335067305527210019419<59> × 124896659843040259553684977555818906011332891068066978344194417<63> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 49.75 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 20, 2007 2007 年 12 月 20 日)
5×10158+9 = 5(0)1579<159> = 1063 × 1663 × 293270942177563703<18> × 143124654506989800314807<24> × 1050308365652912360528088042107<31> × 6415701952940763212346399775006251107413632385311194081863553789375950404407329363<82> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2328324782 for P31 / December 8, 2007 2007 年 12 月 8 日)
5×10159+9 = 5(0)1589<160> = 158855819 × 595062504831659452988979151082530531460782679178587<51> × 52893741733194472069753410091559437984333289639309186156142766882448531546650531764689412803138414753<101> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 20.39 hours on Cygwin on AMD 64 X2 6000+ / December 20, 2007 2007 年 12 月 20 日)
5×10160+9 = 5(0)1599<161> = 61 × 355343390117122269067<21> × 47131759870825469359992643<26> × 48941612214808062630092426209218571595016131698596749580240130900967580342254483059775953820109515542721372425949<113>
5×10161+9 = 5(0)1609<162> = 19 × 499 × 81412523 × 290804753657827<15> × 2886044097090709483188406135551437413159237776161<49> × 771827378327791401197721327141510578461690263003677335551724101499521451664262614805569<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 26.60 hours on Cygwin on AMD 64 X2 6000+ / January 5, 2008 2008 年 1 月 5 日)
5×10162+9 = 5(0)1619<163> = 7 × 292 × 271229879065601402201623<24> × 64374435181365818315554180691915647<35> × 48643521375868913517679138570941692047144478517809618044912143356711058007954967110653981808106775647<101> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=3598900258 for P35 / December 19, 2007 2007 年 12 月 19 日)
5×10163+9 = 5(0)1629<164> = 470209 × 29802628633<11> × 994274499440732115855225384785607465089<39> × 20388243227799757288129029804812187656347787<44> × 176010423833552850724204320884474640196768850687932515195507552179<66> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.31 / December 21, 2007 2007 年 12 月 21 日)
5×10164+9 = 5(0)1639<165> = 6673964901781837641922867159706054031558290898862034367879686441388466755506249<79> × 74917984640061309718805919117074967560324362619058281263115508699855177428830489506241<86> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 39.42 hours on Core 2 Quad Q6600 / December 18, 2007 2007 年 12 月 18 日)
5×10165+9 = 5(0)1649<166> = 521 × 291041 × 51554521 × 247260059 × 2818939442454687157524932103668483<34> × 54054662364681162784830736490034092875986992681<47> × 16976121589164324923231167526328949052941343024340689600524177<62> (Robert Backstrom / GMP-ECM 6.1.3 B1=3218000, sigma=2627230434 for P34, GGNFS-0.77.1-20050930-k8 gnfs for P47 x P62, Msieve 1.33 / January 29, 2008 2008 年 1 月 29 日)
5×10166+9 = 5(0)1659<167> = 65147 × 767495049656929712803352418376901468985525043363470305616528773389411638294932997682164950036072267333875696501757563663714369042319677038083104363976852349302347<162>
5×10167+9 = 5(0)1669<168> = 17 × 1989241 × 4503242489106295715733929<25> × 13375753468061863141381463203<29> × 247594231851496673861477854899257<33> × 991401494836260862208699840210242066186026283682422229091025681417922365483<75> (Sinkiti Sibata / GGNFS-0.77.1-20060722-nocona snfs / 148.51 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 23, 2007 2007 年 12 月 23 日)
5×10168+9 = 5(0)1679<169> = 7 × 23 × 65990746049957014371607<23> × 657641273061186958218573106478356106521035023165800368518412163301<66> × 715602795845022032566832013234571359667906810279528894626944306683762500542867<78> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 32.75 hours, 1.24 hours / May 9, 2009 2009 年 5 月 9 日)
5×10169+9 = 5(0)1689<170> = 601 × 240050495558407698763546267<27> × 41281411513583644762377184791184555905650687227<47> × 8395341891024184763633786646465985958174272838380095043933734588514621669155826987694109067001<94> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 34.53 hours, 1.89 hours / June 23, 2009 2009 年 6 月 23 日)
5×10170+9 = 5(0)1699<171> = 1229 × 269779327 × 9721121141<10> × 1135807781724200936615878543627<31> × 136580362016148493813904780703942816587501804692389996888430943473407244830943299318103800800459480323996890131300495189<120> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2801141481 for P31 / December 9, 2007 2007 年 12 月 9 日)
5×10171+9 = 5(0)1709<172> = 67 × 40378193 × 44404164907<11> × 30861275933615391341234232012900752504190775857799782307643<59> × 1348685652951649280820481874144969335193186551718062790432538324525777278141762353767694766939<94> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 snfs / 45.61 hours, 1.31 hours / May 23, 2009 2009 年 5 月 23 日)
5×10172+9 = 5(0)1719<173> = 43 × 389 × 1087 × 9767 × 18244909 × 272145144727<12> × 3513617694467679263991193319689490714753909<43> × 16138546500973209789112130835645839209009465632063747758714892962102167170312235103575340218524576529<101> (Sinkiti Sibata / Msieve 1.40 snfs / 99.49 hours on Core i7 2.93GHz,Windows 7 64bit,and Cygwin / February 27, 2010 2010 年 2 月 27 日)
5×10173+9 = 5(0)1729<174> = 2083 × 4217 × 10278689 × 226341838289515047722055879603441350450576514056429807821686474775748639597657<78> × 24466653341794257255957958567501020770819886635243086406040717196519997052907339603<83> (Ignacio Santos / GGNFS, Msieve snfs / 57.65 hours / September 28, 2009 2009 年 9 月 28 日)
5×10174+9 = 5(0)1739<175> = 72 × 282683 × 6932341858585301203147155694949322507634968456323255381<55> × 52070801363035000937721717804698385278518754334939026472475690096827289091076030500703551512192216650466491354767<113> (matsui / GGNFS-0.77.1-20060513-prescott snfs / March 27, 2008 2008 年 3 月 27 日)
5×10175+9 = 5(0)1749<176> = 59 × 26881 × 558656639927101575566593<24> × 56432281261217521910024939360934445196959164552606902205685737711855756375516612702449074419597038116080351207873114891080287134201173098529207947<146>
5×10176+9 = 5(0)1759<177> = 380948814527<12> × 2267096085676004511924687932790476999892895181611193461<55> × 578939858728402285761082136856519791869569532806007328519852545263777434502583051890642867081693808902454599547<111> (Dmitry Domanov / Msieve 1.40 snfs / July 5, 2011 2011 年 7 月 5 日)
5×10177+9 = 5(0)1769<178> = 361873 × 59065588279102023578540722642848366939231685729<47> × 233926428229777021792526147696670859387164608180601153770469223624167359153947326848196873305595620698830254470527744319418777<126> (Ignacio Santos / GGNFS, Msieve snfs / 100.42 hours / March 11, 2009 2009 年 3 月 11 日)
5×10178+9 = 5(0)1779<179> = 181 × 6229 × 2197877777063<13> × 20177602434415427155945947753771940368781113387694354378331345522924194269734831121680214274744946677438905336337857083790303346513389206152115986380578240532007<161>
5×10179+9 = 5(0)1789<180> = 19 × 24379 × 343338641215057<15> × 14527279412530452112203563<26> × 12944269695080218973540346309891121<35> × 1416113441407550287859867356704288481<37> × 11806412269556885461858705275762974929092425790557887195787409499<65> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3581677858 for P35, pol51+Msieve 1.36 gnfs for P37 x P65 / 3.10 hours on Opteron-2.6GHz; Linux x86_64 / August 6, 2008 2008 年 8 月 6 日)
5×10180+9 = 5(0)1799<181> = 7 × 47 × 223 × 2861 × 26029 × 1895790587<10> × 114868130521<12> × 1302241640295817547<19> × 412549853389705450604184785579092801528490819701<48> × 7822327077399985893101213355973240293508438090353192378150797386362549707399870507<82> (Robert Backstrom / Msieve 1.44 gnfs for P48 x P82 / February 25, 2012 2012 年 2 月 25 日)
5×10181+9 = 5(0)1809<182> = 4406830028223101489<19> × 4659737595042735914021139189449725139<37> × 501637343728199539635857944531453487762460239323<48> × 4853917426095812702358607385787709745327615926086552205306331546905792229683673<79> (Rich Dickerson / GMP-ECM 6.4.4 [configured with GMP 5.1.1, --enable-asm-redc] [ECM] B1=3000000, sigma=1343730387 for P37 / June 12, 2013 2013 年 6 月 12 日) (Erik Branger / GGNFS, Msieve gnfs for P48 x P79 / June 23, 2013 2013 年 6 月 23 日)
5×10182+9 = 5(0)1819<183> = 743 × 240701 × 6936683303467<13> × 107082422725698159126343178713029289<36> × 3763858087528155671731302239613408517034992170585967034589679866741991612081596737189594926028919606343151862364864628885081801<127> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2705000972 for P36 / April 1, 2011 2011 年 4 月 1 日)
5×10183+9 = 5(0)1829<184> = 17 × 25793036896426201<17> × 14444222831811269753<20> × 25744339498794244614792434529796544380625347255625775543547<59> × 30664978879630357682946763894807689607891730850105143946828167404348392355269974240979947<89> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 (SVN 845) snfs / December 20, 2013 2013 年 12 月 20 日)
5×10184+9 = 5(0)1839<185> = 39523142107<11> × 303655768547<12> × 3886236073153540472820642619673481647228076494734007<52> × 339099975673693507374821943000971427996379494011666747<54> × 3161404501141495907846407447233946778908471163893150637149<58> (Dmitry Domanov / Msieve 1.50 snfs / January 5, 2014 2014 年 1 月 5 日)
5×10185+9 = 5(0)1849<186> = 862676558302067280404855791214660371447819<42> × 94925236934868034108855999202179955670331840852817073137<56> × 6105768267782436484302791549973847288934435254969344035362231643572525042596866178941803<88> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=3000000, sigma=793546000 for P42 / December 18, 2007 2007 年 12 月 18 日) (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 for P56 x P88 / January 11, 2014 2014 年 1 月 11 日)
5×10186+9 = 5(0)1859<187> = 7 × 442327 × 956400619061<12> × 2378900410285943658343196924503<31> × 709761445603658522897886836144474609066572113623616004819382047836649901619841649255857391910948225303615884683894900000570255660696983907<138> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3159330637 for P31 / December 12, 2007 2007 年 12 月 12 日)
5×10187+9 = 5(0)1869<188> = 6361 × 9929 × 345707 × 8148129817<10> × 77973695918843<14> × 3604332642158090599424831828189860175978173363804614518721923814698978621243659661731211136981502030362947683158548698236639722861323990103353257593833<151>
5×10188+9 = 5(0)1879<189> = 89 × 20644698707<11> × 2095779451075181845289<22> × 17069365974029360492115172688628301<35> × 112851366896191612350337923343819108022586261622918801<54> × 67406481306382958257320834957187828313474877802170323638967682116047<68> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3476476497 for P35 / December 10, 2008 2008 年 12 月 10 日) (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P54 x P68 / 140.12 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / April 22, 2009 2009 年 4 月 22 日)
5×10189+9 = 5(0)1889<190> = 252731 × 19783880885209966327834733372637310025283799771298336966972789250230482212312696107719274643791224661794556267335625625665232994765185117773442909654929549600167767309906580514460038539<185>
5×10190+9 = 5(0)1899<191> = 23 × 29 × 1108901915063<13> × 863023775489507<15> × 570491116596192682901<21> × 20003741217730647692519940126886007237575003<44> × 6863855987367989449493849870476582843763507637047722564990549147458679178178484364190845574595849<97> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3851361271 for P44 / October 1, 2013 2013 年 10 月 1 日)
5×10191+9 = 5(0)1909<192> = 439217 × 1138389452138692263732961155875114123542576903899439229355876480190885143334615918782742926617139136235619295245857969978393368198407620834348397261490333935161890363988643426825464405977<187>
5×10192+9 = 5(0)1919<193> = 7 × 185946012230334004175737692114361<33> × 3841360756911088155477151257427655759049773811262830812715564417935995018641284052166995975037217217287976245074877594743197862509898796882391887621294514456167<160> (Robert Backstrom / GMP-ECM 6.2.1 B1=714000, sigma=3139830089 for P33 / August 11, 2008 2008 年 8 月 11 日)
5×10193+9 = 5(0)1929<194> = 43 × 331 × 13377953 × 100583509485916979<18> × [2610700813586231994597685342467236251884810695775351952392428887284025260539427325474746413174543122207566073197519258877763329650210891806918425495935009620481718379<166>] Free to factor
5×10194+9 = 5(0)1939<195> = 3403248951366474932718274863522798490198007146565255920384348350563174584990964183684189<88> × 146918432105661751654501039168244531252281316834293602197361365522821831096719447512829008767795879133716381<108> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 482.37 hours on Core 2 Quad Q6700 / September 6, 2008 2008 年 9 月 6 日)
5×10195+9 = 5(0)1949<196> = 15329 × 14697709207787<14> × 22192515375766661311304959483710130491428675557740477530902022723000013649298010707012997556333109901829620176695770473647097126034730857850001099061754660308392947590076080109883<179>
5×10196+9 = 5(0)1959<197> = 83 × 461 × 261574558839689<15> × 95803177273255182527<20> × 107921662328688797263<21> × 483177771373411742965790106119824369620152987973670431186653694886239191949710385689249176585926812654809240790190776776732161040426872887<138>
5×10197+9 = 5(0)1969<198> = 19 × 2699 × 5569 × 48131 × 413272931 × [88018599829249203203091362217039570610309712835983148905422965435791351798202024325109417643392328808090840441954837515327898778791654765420802270488669737048221026083896659921<176>] Free to factor
5×10198+9 = 5(0)1979<199> = 7 × 126906315203803<15> × 19830372094019801185891000999795485858256410322908528341<56> × 283829718646496285471987722779291877731636827042472861184391207320774345369455359203441141434328311313622049776976909693527762569<129> (matsui / Msieve 1.50 snfs / November 2, 2011 2011 年 11 月 2 日)
5×10199+9 = 5(0)1989<200> = 17 × 163 × 142242657902914511616833205346375249<36> × 1593430546178302621526623328857130497<37> × 20936594747368515028837001436919629905448834930134580307<56> × 3802458076980807630036456909859549691699291795614775513212139001856849<70> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1420271003 for P37 / October 22, 2008 2008 年 10 月 22 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1408040392 for P36 / April 1, 2011 2011 年 4 月 1 日) (Warut Roonguthai / Msieve 1.48 gnfs for P56 x P70 / September 8, 2011 2011 年 9 月 8 日)
5×10200+9 = 5(0)1999<201> = 141802671301<12> × 16940887815453769<17> × 195050622049838316248613163<27> × [1067092545200264470989589147188761198366121719458604459961620743379316751380986328374927045113259696266455091298668018562718304833351180930092355047<148>] Free to factor
5×10201+9 = 5(0)2009<202> = 3259 × 208529 × 2649593 × [2776770683817571927872503280709179491757048345114853331622028427224394004178918745266702937210998035478578437167415524223059574249989922292490586827651924823225813412312034395544454791283<187>] Free to factor
5×10202+9 = 5(0)2019<203> = 109 × 235152340577789<15> × 7060576556715814025437682580523<31> × 8992792339968420931044077508242381<34> × 30722706311375101753543942602125363376457093956001285665845710765153571516590789635740419517846075416124240811237850762943<122> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2490582752 for P31 / September 19, 2013 2013 年 9 月 19 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2560869766 for P34 / September 25, 2013 2013 年 9 月 25 日)
5×10203+9 = 5(0)2029<204> = 54163 × 9231394125140778760408396876096228052360467477798497129036427081217805512988571534073075715894614404667392869671177741262485460554252903273452356774920148440817532263722467367021767627347081956317043<199>
5×10204+9 = 5(0)2039<205> = 7 × 67 × 107 × 27107 × 85722539272603<14> × 1772640932772688401226894806914507<34> × [24188900461327027663283101456539589837084172711980800724798650376013125117887542121078452106329972620525224120848779283387258724121943480877728350909<149>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3161072209 for P34 / September 24, 2013 2013 年 9 月 24 日) Free to factor
5×10205+9 = 5(0)2049<206> = 193 × 501233 × 21558137 × 102365839152491<15> × 234210715424951383081091621029258813807356775930446324468325827243413053412666148688427243959215872961331627019590217587545371930029891742716491235143051578662961918139121322083<177>
5×10206+9 = 5(0)2059<207> = 16361 × 38707 × 362334283 × 66263861419142758823429921<26> × 32883987881901718679731399731441078555120610218350088577474873392074084658409055761929274570017673092485853639058743541421667836459181646351775771993922756137578769<164>
5×10207+9 = 5(0)2069<208> = 3299 × 1828606123<10> × 49724674009<11> × [16668463736254269915963720662071685715331091030973413111992293100426413027170085932006199421377196689451021321934160547013582137240939442816029503914972239598691872933835230473888349713<185>] Free to factor
5×10208+9 = 5(0)2079<209> = 1489 × 15478283 × 1642776307<10> × [1320608514704595494380152311462748676366689290790715066078085725515824313125552175877716652615643890718481866032380754197331149070774127004946408829174744867331543148304607762519367877209801<190>] Free to factor
5×10209+9 = 5(0)2089<210> = 2353987 × 19128582419<11> × 1024929026882491<16> × 13013073513265461801175088129982803315617<41> × 411352267397785793917155957421550125795361893928356136291488553<63> × 2023930457894564477594282391088512288326592937602387952029130523096890380683<76> (Dmitry Domanov / October 4, 2013 2013 年 10 月 4 日) (Ignacio Santos / GGNFS, Msieve gnfs for P63 x P76 / January 11, 2014 2014 年 1 月 11 日)
5×10210+9 = 5(0)2099<211> = 7 × 25583 × 190909 × 465441187 × 314216711600017621478161293248638072227817455317949865138055133561690716749423049143773456180541680420930953794827016935082478401097793763294128494448035323964153160115004638229219581056958183<192>
5×10211+9 = 5(0)2109<212> = 1987 × 280932721 × 912756475573905289<18> × 6913542327961394693089<22> × 22390550583505799884201614971<29> × 5599153481417626512808417989631171381699<40> × 38896497396410348527263520484697701139089<41> × 2910828525209184299591130075961162507874728952260667<52> (Serge Batalov / GMP-ECM B1=11000000, sigma=1614689010 for P41, SIQS for P40 x P52 / November 8, 2013 2013 年 11 月 8 日)
5×10212+9 = 5(0)2119<213> = 23 × 31667 × 6110861 × 2152102993622083<16> × [52199914233573587976430216507838072842894985485296191677123911135288717185238295323210007961169185767948097054917311237496836521558558294491280768500566520713436999622670145273033691923<185>] Free to factor
5×10213+9 = 5(0)2129<214> = 225779 × 6789109960081<13> × 16137229959366227<17> × 78903878753061553<17> × 2561806219931020175086119942310682990984707305507701218135203473828885429929731499061485355352355665546348858694804880753598138845144298226633489130589188139093761<163>
5×10214+9 = 5(0)2139<215> = 43 × 168420251186338440781798058218540513422591721<45> × [6904102621174213113030183810927527185340406543599263506005583028589847787467354707028847081092256538899519495518069320912656723089623421166976663545571486518228540556003<169>] (Serge Batalov / GMP-ECM B1=11000000, sigma=2442028436 for P45 / January 5, 2014 2014 年 1 月 5 日) Free to factor
5×10215+9 = 5(0)2149<216> = 17 × 19 × 399560977 × 2668655689060879819098243659<28> × [1451750121488546090284847154279361260836766356989168281101524329493309195810209379936467801442271166632130626941660869565163168077029949781018952935304408641933034500559904363481<178>] Free to factor
5×10216+9 = 5(0)2159<217> = 72 × 133321 × 4600549687<10> × 6744257142990036307027048317689<31> × [24667862312100375656519178658733845619191174768915065172797324952797323238008395077048083675891954731248830534000804146375612888719245122397699815795519759385841844654447<170>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3090680696 for P31 / September 24, 2013 2013 年 9 月 24 日) Free to factor
5×10217+9 = 5(0)2169<218> = 521 × 284943910616899<15> × 3474626215985513<16> × 114973051143587339<18> × 30783110037091554662225285059769224051<38> × 27387743831963705808103849900416533559697719328037564313530626978521599116064472655605250298592505674210744870547781935608712837603<131> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3074912414 for P38 / September 25, 2013 2013 年 9 月 25 日)
5×10218+9 = 5(0)2179<219> = 29 × 1129 × 11149 × 1369752649162577473312568084069083869349277553688831685339632456846785186012231688433629740775215182730660476728876384861363321002993487574038178386881699167422425407921036849937753919438310243107014974785223401<211>
5×10219+9 = 5(0)2189<220> = 4520764483<10> × 51755770042103141116969<23> × 696949108152927589271330033<27> × 1668427169295803435606847113539<31> × 1573481297824070299100953004571139848547526735987929<52> × 11679639602856110907466980361487727017344865883274321946960285180846904596203729<80> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2365772274 for P31 / September 24, 2013 2013 年 9 月 24 日) (Erik Branger / GGNFS, Msieve gnfs for P52 x P80 / November 4, 2013 2013 年 11 月 4 日)
5×10220+9 = 5(0)2199<221> = 61 × 313163 × 2617397748608682965760825439305346825355653314779822145729063841105530179302738850238939623072738059261339993528745806339892235452935183861460508990682744538367726899462559250687184691908466669245675914962422282263<214>
5×10221+9 = 5(0)2209<222> = 2792390834719009901983587323<28> × [179058029335751466615051578590198060407594619444122680696799048335542391215720163006872994779295810800928579000753541842415920930121481657771106275961519929305048100977744338147849875157580001483<195>] Free to factor
5×10222+9 = 5(0)2219<223> = 7 × 168636167551518717943732951228139080229795696542790482074327259820341<69> × 4235661451850169911334556401514099957703760854950143276372591559084297994727960527097117500911216625526792568895480346597454230973851567349932722496565907<154> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 for P69 x P154 / January 9, 2014 2014 年 1 月 9 日)
5×10223+9 = 5(0)2229<224> = 168345237355529371<18> × 37693995748476865700906426093395217<35> × 324908947446970527690957463616073353<36> × 2112678050258351803554812196626138517923484919733873265819083<61> × 11478945695455227454438396151689557814700068352871997646765345040356816663113<77> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2594465528 for P35 / September 24, 2013 2013 年 9 月 24 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1300151452 for P36 / September 26, 2013 2013 年 9 月 26 日) (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 (SVN 845) for P61 x P77 / November 30, 2013 2013 年 11 月 30 日)
5×10224+9 = 5(0)2239<225> = 1392763 × 1985183 × 1091772421<10> × 46610211497329<14> × 3553685931054756556737188081302420490892450251324576581075748058716723287154844956644885118468909612534665482667022427433865358786761224415959266832399808967893653381780989846768510055111969<190>
5×10225+9 = 5(0)2249<226> = 19979 × 3971903347<10> × 23585978227554100489177<23> × [2671429345696722181995789034113743477679539321658103059423255918016749499926252956511425172567055533821911207633656050607387566481572645661168641648751941680345963327049078217647496698294209<190>] Free to factor
5×10226+9 = 5(0)2259<227> = 47 × 1069 × 1747663523667330646931755706629<31> × 246356983626500158449846545049463<33> × 9740042102177178830936135702579749<34> × 237307195624887520767770052163021632887874297205275691488000504437760569526395723423417903946759122992969650598357440085854781<126> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3077663554 for P31 / September 19, 2013 2013 年 9 月 19 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=926796749 for P33 / September 24, 2013 2013 年 9 月 24 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2223589952 for P34 / September 25, 2013 2013 年 9 月 25 日)
5×10227+9 = 5(0)2269<228> = 5213079822733178371<19> × [95912592364230052599414575272528199194727560391237403823422298940289287444155247765731123303720605372341445861323864890478915984681152071664098906194350749915208972945309851634068198023590936388726981915019779<209>] Free to factor
5×10228+9 = 5(0)2279<229> = 7 × 15984841673412807281025760481<29> × 48676633297005541529517792072297028635209<41> × [918000869447612249837425612733857768973851786094055475591772983566600815867860032572590793366390854567356187671327366526941317582568125433381811372853452601303<159>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1875199711 for P41 / September 26, 2013 2013 年 9 月 26 日) Free to factor
5×10229+9 = 5(0)2289<230> = 313 × 379 × 2017 × 5150713 × 41082227 × 78107161728067<14> × [12643530849811651471445833021280493463426724370081912430027885567314848372114700568409999954310243142945185091082176379325398979593265665274732252428235594208023091781546854715769642850778582803<194>] Free to factor
5×10230+9 = 5(0)2299<231> = 60167 × 520485745714764502351551810043<30> × [15966245638792315418449762238580744313395700722432013260321673974834515216956233402951981374753174275086982928112687127530518122983584155726089060251970763585298054665122705563832541187813524808989<197>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2334190644 for P30 / September 19, 2013 2013 年 9 月 19 日) Free to factor
5×10231+9 = 5(0)2309<232> = 17 × 10836814391645220835432511876314630171<38> × 27140600219708224461354507470930724794074214941199294626435415054122545641807444358816269857939242459402177135741955316769260938506960641138202694081159763176968269060241147146042825307743515387<194> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1404452063 for P38 / September 27, 2013 2013 年 9 月 27 日)
5×10232+9 = 5(0)2319<233> = 89 × 236881 × 75070529 × [31592230812888858503292085356717497637628707419700014869457581896352686472865913728015273480122964005340090170644962158702038431771526555857600644526769512372912363231641604465493623450996203468685309959149688165003169<218>] Free to factor
5×10233+9 = 5(0)2329<234> = 19 × 59 × 97 × 764604697 × 78873090848674121<17> × 76247715445714965528903843108390836482232624967377129642836018497049197800967394908729191927282118800784980665983837071026406463757789604953157258251973765039757058511933680584011810633114672672709323561<203>
5×10234+9 = 5(0)2339<235> = 7 × 23 × 44741 × 82787 × [8384483153875399665485818690112818774666727730640597710288853395203620248208217652140016231507220572946472260143667390028841305802858980565779330337255210533885383562484133778521508273561354218307983508105316983796719378407<223>] Free to factor
5×10235+9 = 5(0)2349<236> = 43 × 5152835147<10> × 224572150262151427<18> × 3461858547198214226322930549401<31> × 290261933918571622641069649879196231784514338173941486645496153523602094843269118919612936035954145787877181635017899390205738696002153668338700761458437543535129115081150715827<177> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1643937751 for P31 / September 24, 2013 2013 年 9 月 24 日)
5×10236+9 = 5(0)2359<237> = 493490149 × [1013191450757814417892260702452238818651676874709002549917161568305186168974570554193575199410920763891479422419027861891524809343256008946188711053683059436309031570962523914535120740576323034160505603121978428793317209661261141<229>] Free to factor
5×10237+9 = 5(0)2369<238> = 67 × 83 × 34483 × 18786737 × 2629291496797683107219<22> × 16471659183685057753020716902344251<35> × [32046796820259611838390201146914264810731324105193365848941723640646467080266742053688228008287865040869616845585099455446210245651235185930651233429969912746194185531<167>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=701972193 for P35 / September 26, 2013 2013 年 9 月 26 日) Free to factor
5×10238+9 = 5(0)2379<239> = 2663984116560283462723906287447909666071595033259154603<55> × 202257618857795192716689629824310560603735718078120890663551311812708712347<75> × 92796903175073991321555147968618241117717774771484946314878796558802615590903089266791593290401437884164453249<110> (Dmitry Domanov / Msieve 1.52 for P55 x P75 x P110 / March 29, 2017 2017 年 3 月 29 日)
5×10239+9 = 5(0)2389<240> = [500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<240>] Reserved
5×10240+9 = 5(0)2399<241> = 7 × 16369 × 710430784741<12> × 3862300709224781<16> × [15903106213566883619852416152846339431131175970218841397512915007186322369422468889989022354082448973641068671212734691671477466100362357565877558603234987817470569895308978583414823376381772572448760077356863<209>] Free to factor
5×10241+9 = 5(0)2409<242> = 569 × 1201 × 733409 × 10468456259<11> × 11207043889<11> × 5148948426137<13> × 5791299866096891<16> × 28516760321548209326102355242511020380939682371005973110025099762820679241209471442375199178423306050920056128485715357403114622664041068781961493225661030336146970356934220237715337<182>
5×10242+9 = 5(0)2419<243> = 933055941707<12> × 114204698887190450242132133239424858871143<42> × 4692219807087976986560531243344361323551484635285317735784611606943840207658183185650153064765429624021169979421818484626560701130679378334163537538276145092357334526146358124965350347740109<190> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=156663253 for P42 / September 26, 2013 2013 年 9 月 26 日)
5×10243+9 = 5(0)2429<244> = 1609 × 553043 × 1064507 × 1120219 × 159332863601<12> × [29573194724261944721522264046503229297135499791490014183417262010671814332584933360571289415052163173537123669036502911465638298511273698999506370497249978569470201976797834009679543029871842202837797811383550179<212>] Free to factor
5×10244+9 = 5(0)2439<245> = 263 × 351054133721<12> × 1346728726196183654647<22> × [402124043307100124551281325014974417740509221977241485441965571447939705600056832921839680802569255721748880398101296555593675053562384783074594304908904551307607319720208934861518387849115595024156276075259889<210>] Free to factor
5×10245+9 = 5(0)2449<246> = [500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<246>] Reserved
5×10246+9 = 5(0)2459<247> = 7 × 29 × 9878303887<10> × 1023528883938418221716010582442023355423<40> × 2436079635088585377470471419324967601518163472626414577210621383772052802910952544694285476997346527179091590062224686906465389384083214697652027614819766950278190679129382189296982077651020152203<196> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3733100399 for P40 / September 24, 2013 2013 年 9 月 24 日)
5×10247+9 = 5(0)2469<248> = 17 × 491 × 2707 × 3361 × 21803 × 185161 × 608737 × 267909029121216417591376783852853492773569307745802532320244062344342630990986321779202577350817154750741518427725402738286075031590532223678779117013879301028048795164953575003467174447482636361629219453141467444520241091<222>
5×10248+9 = 5(0)2479<249> = 643 × 88003546838443<14> × 1584098697096743<16> × 5577975708358239416233710799252937403879348736189362925769018677807006984541911329169685531725872363980504191182612443620592654407109952083972645304942287521761495835455481790783800459454795494574751270090124976673487<217>
5×10249+9 = 5(0)2489<250> = 135829727011459164560211559546453460624103398911541319763<57> × 464728731865608913260038214522626984403208827108850140785926329054103982893555379011<84> × 79209204723174522376608656845550577077880783270025527539186192941746268459342094908968542335913305270808335313<110> (Youcef Lemsafer / GGNFS (svn-440), msieve 1.53 snfs for P57 x P84 x P110 / November 17, 2015 2015 年 11 月 17 日)
5×10250+9 = 5(0)2499<251> = 907 × 300688447 × 188910221267<12> × 13000157627426089562946769067269<32> × [74652077862770848059448513822813717324279507259426055532150642878625233605109189079514569966624237637131708688329670377222309299683096319546813665670841360384741051605368087157982139503249374817627<197>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1784506820 for P32 / September 25, 2013 2013 年 9 月 25 日) Free to factor
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