Table of contents 目次

  1. About 500...003 500...003 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 500...003 500...003 の形の素数
    1. Last updated 最終更新日
    2. Known (probable) prime numbers 既知の (おそらく) 素数
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 500...003 500...003 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 500...003 500...003 について

1.1. Classification 分類

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

1.2. Sequence 数列

50w3 = { 53, 503, 5003, 50003, 500003, 5000003, 50000003, 500000003, 5000000003, 50000000003, … }

1.3. General term 一般項

5×10n+3 (1≤n)

2. Prime numbers of the form 500...003 500...003 の形の素数

2.1. Last updated 最終更新日

August 11, 2015 2015 年 8 月 11 日

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

  1. 5×101+3 = 53 is prime. は素数です。
  2. 5×102+3 = 503 is prime. は素数です。
  3. 5×103+3 = 5003 is prime. は素数です。
  4. 5×108+3 = 500000003 is prime. は素数です。
  5. 5×1018+3 = 5(0)173<19> is prime. は素数です。
  6. 5×1020+3 = 5(0)193<21> is prime. は素数です。
  7. 5×1031+3 = 5(0)303<32> is prime. は素数です。
  8. 5×1042+3 = 5(0)413<43> is prime. は素数です。
  9. 5×10103+3 = 5(0)1023<104> 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 / PFGW / January 2, 2005 2005 年 1 月 2 日)
  10. 5×10175+3 = 5(0)1743<176> 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 / PFGW / January 2, 2005 2005 年 1 月 2 日)
  11. 5×10181+3 = 5(0)1803<182> 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)
  12. 5×10531+3 = 5(0)5303<532> 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)
  13. 5×10706+3 = 5(0)7053<707> 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 29, 2006 2006 年 5 月 29 日)
  14. 5×101077+3 = 5(0)10763<1078> 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 14, 2006 2006 年 9 月 14 日)
  15. 5×101177+3 = 5(0)11763<1178> 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)
  16. 5×101552+3 = 5(0)15513<1553> 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 4, 2006 2006 年 9 月 4 日)
  17. 5×1019737+3 = 5(0)197363<19738> 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. 5×1032197+3 = 5(0)321963<32198> 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. 5×1051508+3 = 5(0)515073<51509> 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. 5×1058275+3 = 5(0)582743<58276> 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)
  21. 5×1062233+3 = 5(0)622323<62234> 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)
  22. 5×1090033+3 = 5(0)900323<90034> 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)

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 / August 10, 2015 2015 年 8 月 10 日

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

  1. 5×106k+5+3 = 7×(5×105+37+45×105×106-19×7×k-1Σm=0106m)
  2. 5×1013k+1+3 = 53×(5×101+353+45×10×1013-19×53×k-1Σm=01013m)
  3. 5×1015k+4+3 = 31×(5×104+331+45×104×1015-19×31×k-1Σm=01015m)
  4. 5×1016k+12+3 = 17×(5×1012+317+45×1012×1016-19×17×k-1Σm=01016m)
  5. 5×1018k+12+3 = 19×(5×1012+319+45×1012×1018-19×19×k-1Σm=01018m)
  6. 5×1022k+16+3 = 23×(5×1016+323+45×1016×1022-19×23×k-1Σm=01022m)
  7. 5×1028k+23+3 = 29×(5×1023+329+45×1023×1028-19×29×k-1Σm=01028m)
  8. 5×1032k+28+3 = 353×(5×1028+3353+45×1028×1032-19×353×k-1Σm=01032m)
  9. 5×1041k+6+3 = 83×(5×106+383+45×106×1041-19×83×k-1Σm=01041m)
  10. 5×1046k+24+3 = 47×(5×1024+347+45×1024×1046-19×47×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 24.96%. 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 24.96% です。

3. Factor table of 500...003 500...003 の素因数分解表

3.1. Last updated 最終更新日

August 26, 2016 2016 年 8 月 26 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=190, 193, 197, 199, 200, 202, 203, 204, 207, 208, 209, 210, 213, 215, 217, 219, 221, 222, 226, 229, 230, 238, 239, 245, 247, 248, 250 (27/250)

3.4. Factor table 素因数分解表

5×101+3 = 53 = definitely prime number 素数
5×102+3 = 503 = definitely prime number 素数
5×103+3 = 5003 = definitely prime number 素数
5×104+3 = 50003 = 31 × 1613
5×105+3 = 500003 = 7 × 71429
5×106+3 = 5000003 = 83 × 107 × 563
5×107+3 = 50000003 = 491 × 101833
5×108+3 = 500000003 = definitely prime number 素数
5×109+3 = 5000000003<10> = 149 × 33557047
5×1010+3 = 50000000003<11> = 3947 × 12667849
5×1011+3 = 500000000003<12> = 7 × 607 × 117674747
5×1012+3 = 5000000000003<13> = 17 × 19 × 2447 × 6326063
5×1013+3 = 50000000000003<14> = 131 × 197 × 29363 × 65983
5×1014+3 = 500000000000003<15> = 53 × 349 × 27031410499<11>
5×1015+3 = 5000000000000003<16> = 35855291 × 139449433
5×1016+3 = 50000000000000003<17> = 23 × 2297 × 252829 × 3743297
5×1017+3 = 500000000000000003<18> = 7 × 919 × 77724234416291<14>
5×1018+3 = 5000000000000000003<19> = definitely prime number 素数
5×1019+3 = 50000000000000000003<20> = 31 × 6079 × 265323774602147<15>
5×1020+3 = 500000000000000000003<21> = definitely prime number 素数
5×1021+3 = 5000000000000000000003<22> = 57179 × 5077207 × 17222991151<11>
5×1022+3 = 50000000000000000000003<23> = 811 × 4943 × 12472644372729511<17>
5×1023+3 = 500000000000000000000003<24> = 7 × 29 × 2463054187192118226601<22>
5×1024+3 = 5000000000000000000000003<25> = 47 × 106382978723404255319149<24>
5×1025+3 = 50000000000000000000000003<26> = 199 × 991 × 253538124527785243067<21>
5×1026+3 = 500000000000000000000000003<27> = 46853 × 10671675239579109128551<23>
5×1027+3 = 5000000000000000000000000003<28> = 53 × 59 × 2104591 × 759756482347799579<18>
5×1028+3 = 50000000000000000000000000003<29> = 17 × 353 × 8331944675887352107982003<25>
5×1029+3 = 500000000000000000000000000003<30> = 7 × 3919 × 758405810021<12> × 24032284101871<14>
5×1030+3 = 5000000000000000000000000000003<31> = 19 × 953 × 11815707734539<14> × 23370271767211<14>
5×1031+3 = 50000000000000000000000000000003<32> = definitely prime number 素数
5×1032+3 = 500000000000000000000000000000003<33> = 139 × 1399 × 2571209651292547091704763423<28>
5×1033+3 = 5000000000000000000000000000000003<34> = 11056091 × 491616683 × 919902475321705451<18>
5×1034+3 = 50000000000000000000000000000000003<35> = 31 × 79283 × 15393925741<11> × 1321535543256512971<19>
5×1035+3 = 500000000000000000000000000000000003<36> = 72 × 179 × 69149 × 366893806043<12> × 2246956213564399<16>
5×1036+3 = 5000000000000000000000000000000000003<37> = 1381 × 188603 × 952741 × 5302163 × 11131999 × 341371013
5×1037+3 = 50000000000000000000000000000000000003<38> = 823 × 15972841 × 320859611 × 11854219044193544311<20>
5×1038+3 = 500000000000000000000000000000000000003<39> = 23 × 257 × 2011 × 4454299 × 17548455863<11> × 538119463428139<15>
5×1039+3 = 5000000000000000000000000000000000000003<40> = 97 × 1559965879<10> × 97759865719<11> × 338004571812645299<18>
5×1040+3 = 50000000000000000000000000000000000000003<41> = 53 × 347 × 653 × 40193 × 79861 × 1649506973<10> × 786343236668809<15>
5×1041+3 = 500000000000000000000000000000000000000003<42> = 7 × 389 × 409 × 5743 × 418493 × 186797921971643578708178771<27>
5×1042+3 = 5000000000000000000000000000000000000000003<43> = definitely prime number 素数
5×1043+3 = 50000000000000000000000000000000000000000003<44> = 223 × 3847 × 58283141834356979581084089751375773563<38>
5×1044+3 = 500000000000000000000000000000000000000000003<45> = 17 × 970699463 × 315264813713<12> × 96108276943703779480261<23>
5×1045+3 = 5000000000000000000000000000000000000000000003<46> = 95383 × 166277281610172003269<21> × 315257996121076539889<21>
5×1046+3 = 50000000000000000000000000000000000000000000003<47> = 317 × 101207 × 173779 × 8968150684572007656776936763178403<34>
5×1047+3 = 500000000000000000000000000000000000000000000003<48> = 7 × 83 × 64811 × 13278381724315247796777873202130351695733<41>
5×1048+3 = 5000000000000000000000000000000000000000000000003<49> = 19 × 863 × 304933829359029090687320851375251570409221199<45>
5×1049+3 = 50000000000000000000000000000000000000000000000003<50> = 31 × 193 × 8357011532675915092762828012702657529667390941<46>
5×1050+3 = 500000000000000000000000000000000000000000000000003<51> = 227 × 683 × 58534097027240535143<20> × 55095295959251801328567781<26>
5×1051+3 = 5(0)503<52> = 29 × 5861 × 29417129005877542375374332966599791726726638387<47>
5×1052+3 = 5(0)513<53> = 32749 × 3558972331<10> × 29085384481<11> × 14749338414541363898106228077<29>
5×1053+3 = 5(0)523<54> = 7 × 53 × 3809891 × 91510157 × 240221858056469<15> × 16091692378493428511531<23>
5×1054+3 = 5(0)533<55> = 46261 × 392684768327<12> × 35295194285332489<17> × 7798217700500651888041<22>
5×1055+3 = 5(0)543<56> = 10102595440132567406550851<26> × 4949223226476531491438676389953<31>
5×1056+3 = 5(0)553<57> = 379 × 977 × 1087621 × 6727485300773<13> × 184546532145417521101908247004177<33>
5×1057+3 = 5(0)563<58> = 433 × 21613517 × 534264928324922938927673513586476428661285292223<48>
5×1058+3 = 5(0)573<59> = 61 × 1009 × 3623 × 9137 × 89867 × 928148539 × 829575336381901<15> × 354652873447672069<18>
5×1059+3 = 5(0)583<60> = 7 × 107 × 1679641 × 8255453 × 152778774688461206737<21> × 315114064590027073770947<24>
5×1060+3 = 5(0)593<61> = 17 × 23 × 353 × 55547 × 1801549 × 20071516765709788013<20> × 18035644307512020473625799<26>
5×1061+3 = 5(0)603<62> = 487 × 68659499 × 1495341591663140431129087408437897497393539829257231<52>
5×1062+3 = 5(0)613<63> = 964061489687<12> × 9379273348781507513<19> × 55296300467873121298489939248413<32>
5×1063+3 = 5(0)623<64> = 269 × 18587360594795539033457249070631970260223048327137546468401487<62>
5×1064+3 = 5(0)633<65> = 31 × 97039 × 16621185562572281380715236208654385383462385758436332050067<59>
5×1065+3 = 5(0)643<66> = 7 × 77383 × 923052497687753493292177499303095364245746112564405988026163<60>
5×1066+3 = 5(0)653<67> = 19 × 53 × 109 × 161814173 × 281512366641983858237678980579702094481390934249786997<54>
5×1067+3 = 5(0)663<68> = 151 × 2952913 × 2940403168993<13> × 87780946932937<14> × 434445458499472845535660211291741<33>
5×1068+3 = 5(0)673<69> = 6240836117<10> × 102789413199797<15> × 779433089899991989110704703313079188033682747<45>
5×1069+3 = 5(0)683<70> = 1663 × 147227767 × 2384032997<10> × 8565954590598526685670743287535875319826645623119<49>
5×1070+3 = 5(0)693<71> = 47 × 751 × 11423 × 2176374330047<13> × 6532322710476609889<19> × 8722697390504230048895798797411<31>
5×1071+3 = 5(0)703<72> = 7 × 27107 × 19694704307<11> × 83887747003342561<17> × 1594933254404032348498814610541821137261<40>
5×1072+3 = 5(0)713<73> = 1951 × 28236083 × 3257582762131<13> × 27862034580050919463307956209849711034004812471861<50>
5×1073+3 = 5(0)723<74> = 2458369 × 186255721 × 109197655021346519032188868746864673772325722708428922430347<60>
5×1074+3 = 5(0)733<75> = 113 × 1367 × 3236853519430831677143282557891125195020424545707608547882774112940293<70>
5×1075+3 = 5(0)743<76> = 1391278548773<13> × 3593816640391396113855304555439641249068664080681220038212949511<64>
5×1076+3 = 5(0)753<77> = 17 × 914237 × 51585917 × 615543491473607<15> × 101314683185894239551114563306314916300880780653<48>
5×1077+3 = 5(0)763<78> = 73 × 75337 × 19349402651046177697715969421906797719912830167080930927624681649115533<71>
5×1078+3 = 5(0)773<79> = 139 × 35971223021582733812949640287769784172661870503597122302158273381294964028777<77>
5×1079+3 = 5(0)783<80> = 29 × 31 × 532 × 6217 × 59353297 × 8427422669<10> × 6367047377656506462904155066986354326719808015871093<52>
5×1080+3 = 5(0)793<81> = 631 × 1075771 × 59752210914727863661279<23> × 12327267863683037631960515363901872892062001409457<50>
5×1081+3 = 5(0)803<82> = 4259 × 1552251396894823280891<22> × 148457018476693417664950589<27> × 5094476587689179975610939251983<31>
5×1082+3 = 5(0)813<83> = 23 × 4398173539<10> × 874965724061328499<18> × 1405617153215469079<19> × 401894181192586916650815560145826219<36>
5×1083+3 = 5(0)823<84> = 7 × 36071941452443329<17> × 2300363559615287218357043<25> × 860807352173688904077437529359880857107207<42>
5×1084+3 = 5(0)833<85> = 192 × 421 × 24181 × 1010117135473163<16> × 1346898009406529223327940117955488165597586573906124580504921<61>
5×1085+3 = 5(0)843<86> = 59 × 114414247 × 41171227740870361<17> × 93013262654070633768573203<26> × 1934190248802853050684809734724717<34>
5×1086+3 = 5(0)853<87> = 8191 × 61042607740202661457697472836039555609815651324624587962397753632035160542058356733<83>
5×1087+3 = 5(0)863<88> = 1015349 × 1532507 × 3330409 × 78384201665678636303903501861<29> × 12309093795615004924776021889954551509929<41>
5×1088+3 = 5(0)873<89> = 83 × 999828754498801<15> × 137688575402049362965673005049117<33> × 4375910015802456779964680584557999666773<40> (Makoto Kamada / msieve 0.81 / 5.8 minutes)
5×1089+3 = 5(0)883<90> = 7 × 4729 × 147487 × 1799897942758773045413<22> × 56898527585042673029472232819497892488272923031472385106071<59>
5×1090+3 = 5(0)893<91> = 1172507923409530160430980839447069<34> × 4264363506781706010639612444247484405646223517613650045087<58> (Makoto Kamada / GGNFS-0.70.3 / 0.22 hours)
5×1091+3 = 5(0)903<92> = 4211 × 309172364789<12> × 63965188254948038831773448357514251<35> × 600399625571213025489918330607991148393607<42> (Makoto Kamada / msieve 0.83 / 14 minutes)
5×1092+3 = 5(0)913<93> = 17 × 53 × 353 × 1021 × 10651 × 4796118223711<13> × 30141475017152446658517232590409850398172859190985867927921020636471<68>
5×1093+3 = 5(0)923<94> = 90128760589243643561619256691730383092807<41> × 55476187260437282036868709902133261637660094894409829<53> (Makoto Kamada / GGNFS-0.70.7 / 0.39 hours)
5×1094+3 = 5(0)933<95> = 31 × 72620645868563173343<20> × 19286687324592734936063<23> × 17927430443998405953241699<26> × 64235116700341599654502943<26>
5×1095+3 = 5(0)943<96> = 7 × 176507 × 446041 × 31830437 × 10225181741<11> × 2787543241477667783403610272474345922702013146942423703332326626551<67>
5×1096+3 = 5(0)953<97> = 762667462116924669758247090489861920682702481277<48> × 6555937218196741695801550898218372577739396832639<49> (Makoto Kamada / GGNFS-0.70.7 / 0.46 hours)
5×1097+3 = 5(0)963<98> = 941 × 40927 × 390491 × 70228999 × 253795301693352795581<21> × 186534593164781287357321331812963179886263954927271847401<57>
5×1098+3 = 5(0)973<99> = 420785350832911<15> × 44186432061632719<17> × 44648887351839256399<20> × 1627023998074869019103<22> × 370182477871326723400149811<27>
5×1099+3 = 5(0)983<100> = 859493 × 2698836149<10> × 46606393157<11> × 201991350982876187<18> × 6930035321787863868408416051<28> × 33039801179985499802003182831<29>
5×10100+3 = 5(0)993<101> = 28903494311221<14> × 35433579205312085193587<23> × 881356810145768386810291<24> × 55392742297889665879812947278570656198079<41>
5×10101+3 = 5(0)1003<102> = 7 × 19999297 × 49766137 × 69229464001<11> × 12612692590259314008604763383<29> × 82191049054613077031122732232691363349783303067<47>
5×10102+3 = 5(0)1013<103> = 19 × 162623 × 676909 × 181097177 × 346247253640091932231<21> × 38124673116508318887370655005740219912736845196103157426773093<62>
5×10103+3 = 5(0)1023<104> = definitely prime number 素数
5×10104+3 = 5(0)1033<105> = 23 × 4937 × 103177537189<12> × 42677000098645109324308290726585519293533411209782702927345171483821485714344207412464777<89>
5×10105+3 = 5(0)1043<106> = 53 × 1901 × 710051 × 11430203 × 1112199245327374990611151<25> × 5497761996707844977724388584029597517146142849063721507614356717<64>
5×10106+3 = 5(0)1053<107> = 1621 × 11717 × 96703376493620307418141<23> × 27222557349131022163291502450760695089748925325604647937096952630760247896519<77>
5×10107+3 = 5(0)1063<108> = 7 × 29 × 2463054187192118226600985221674876847290640394088669950738916256157635467980295566502463054187192118226601<106>
5×10108+3 = 5(0)1073<109> = 17 × 587 × 1279 × 42083 × 31574329 × 33785145833<11> × 8726615021574227019550590292567300416626509252436250133495291885139609885644493<79>
5×10109+3 = 5(0)1083<110> = 31 × 30391 × 53071739192736389487125326789234079274318266974199704708843131614728893634681744701582917693162555552843<104>
5×10110+3 = 5(0)1093<111> = 181 × 140869 × 11063288894785937<17> × 6039261878537983804809377055481<31> × 293499849169094259922144875395852639709254512750131598291<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.51 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10111+3 = 5(0)1103<112> = 197 × 1283 × 1568123 × 187503779304601503581<21> × 514518939710253831299<21> × 130763219671540435495217673836027799045080694557054765098369<60>
5×10112+3 = 5(0)1113<113> = 107 × 1307 × 13028359 × 16956931 × 19979299 × 1885793599<10> × 257539314091<12> × 1285526516447<13> × 7683151853911<13> × 10915764011597<14> × 1546967309963728120162537277<28>
5×10113+3 = 5(0)1123<114> = 7 × 337 × 370704791593<12> × 571760124756203207111421010779436699943573302892601652250624532679408487285021037322799934126403469<99>
5×10114+3 = 5(0)1133<115> = 316469363851<12> × 1081354250785203149101117499513<31> × 33280544906954346861035663714839<32> × 439015556833735689338180321004768868727479<42> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.54 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10115+3 = 5(0)1143<116> = 1801 × 53693 × 95436841 × 10577844127<11> × 10231135104177199<17> × 13047158872579191461385245774333<32> × 3836945517031630316195569878396294937246859<43> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3062116458 for P32 / July 5, 2007 2007 年 7 月 5 日)
5×10116+3 = 5(0)1153<117> = 47 × 80071 × 306437 × 1987703 × 63855381214883<14> × 21154501478439364069<20> × 161474482564732608964784497483670363380086179206807934842681777127<66>
5×10117+3 = 5(0)1163<118> = 67639007175241<14> × 959920477452168131953<21> × 8882987148662865123217<22> × 8669189372599413963937258433861366490975991382760707781192683<61>
5×10118+3 = 5(0)1173<119> = 53 × 61 × 7417037 × 116452580393<12> × 100025451298640466942990019<27> × 69193464626049628817643522282497<32> × 2587075728644263778201293352077733123357<40> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=580784386 for P32 / July 5, 2007 2007 年 7 月 5 日)
5×10119+3 = 5(0)1183<120> = 72 × 71843 × 90543020753040293576959578835244863827338385803<47> × 1568680455115318344001740770037613906724896970510571219229245382643<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.79 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10120+3 = 5(0)1193<121> = 19 × 134597 × 558083 × 1698377 × 14830426043<11> × 178545183437<12> × 6615705888443<13> × 869534162635048412617189<24> × 135420222955486281342936174320416216393490783<45>
5×10121+3 = 5(0)1203<122> = 25471 × 548719 × 3577453604054472240686475872076060031580119080879340748916182043557349462446802287368512689896452336202696942547<112>
5×10122+3 = 5(0)1213<123> = 10429 × 13016717839<11> × 156557721619969<15> × 1754709718977289<16> × 2222035728477287<16> × 1377019286670908784926607287<28> × 4381824822381470268103344915542062697<37>
5×10123+3 = 5(0)1223<124> = 29103572282156559112182740936226932631374490509<47> × 171800215847231475291585450337672992777067604341481417436023086954002453065167<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.06 hours on Core 2 Quad Q6600 / July 13, 2007 2007 年 7 月 13 日)
5×10124+3 = 5(0)1233<125> = 17 × 31 × 139 × 199 × 353 × 17749 × 4211985913711273004737734377<28> × 128040753937687879477084697015491<33> × 1015097562328485295738336683852546474132803693053831<52> (Jo Yeong Uk / Msieve v. 1.21 for P33 x P52 / 00:21:25 on Core 2 Quad Q6600 / July 13, 2007 2007 年 7 月 13 日)
5×10125+3 = 5(0)1243<126> = 7 × 317 × 8380969 × 114941807971087<15> × 4767017037828203<16> × 49067478362324376456479774885211551370446703191142766443539812337024088376179137517293<86>
5×10126+3 = 5(0)1253<127> = 23 × 32869 × 1771845148714035530042375961149100976639<40> × 3732758672015730547173100481173208742246650750942529540645311897013388939508906671<82> (Jo Yeong Uk / GMP-ECM B1=1000000, sigma=1186508037 for P40 / July 14, 2007 2007 年 7 月 14 日)
5×10127+3 = 5(0)1263<128> = 1063 × 19759 × 9528013351973<13> × 231486198826356536297596881484840829<36> × 1079305320539789652825036330387473369897040690627974500945419108513238427<73> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=1941662947 for P36 / July 14, 2007 2007 年 7 月 14 日)
5×10128+3 = 5(0)1273<129> = 824220383604228418854258476629<30> × 778977109190834486013530928931812523699<39> × 778756989881128479103802248680558442310201163296540906795693<60> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2699720113 for P30 / July 6, 2007 2007 年 7 月 6 日) (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 2.38 hours on Cygwin on AMD 64 3400+ / July 14, 2007 2007 年 7 月 14 日)
5×10129+3 = 5(0)1283<130> = 83 × 9112993 × 6610447726166549973975394451332171072956009338494889024590216395372856347981022975220555572196990459083946973373390231537<121>
5×10130+3 = 5(0)1293<131> = 349 × 223050252687486781077222133508703494233225969<45> × 642305820856559171936319435779114051384175861818268799381835937621892642342986131663<84> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.97 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10131+3 = 5(0)1303<132> = 7 × 53 × 4048842607<10> × 523541404697611061806834745219853229328170446317<48> × 635790693115827427508005325491084683125703813484245526914108384957137147<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.42 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10132+3 = 5(0)1313<133> = 16187 × 18572566704029876782615951371188489713635855833627934104693<59> × 16631511131550278291805996309948604657716454712748581690326108061640533<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.52 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10133+3 = 5(0)1323<134> = 11057031539<11> × 886544732452880113982144287654486535090287<42> × 5100711993689431955514377563639991758308507294250704290195426082082810455667928671<82> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.78 hours on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10134+3 = 5(0)1333<135> = 263 × 5903 × 11971 × 278147 × 16482571679993<14> × 5868291632963730471838954369553973220736366210274717393253287404971603430766504804331656302563208217332747<106>
5×10135+3 = 5(0)1343<136> = 29 × 97 × 293 × 12415969 × 8179360663<10> × 3544624710199<13> × 502246085292724499<18> × 103888204664039275506234925332227<33> × 322982960901345113517889401979443805784667940709243<51> (Jo Yeong Uk / Msieve v. 1.21 for P33 x P51 / 00:17:15 on Core 2 Quad Q6600 / July 13, 2007 2007 年 7 月 13 日)
5×10136+3 = 5(0)1353<137> = 229 × 82132721813<11> × 5824999790723064946307734440392437977214744000689735893063<58> × 456375574500296265791802787296814526424506695836333278231520021053<66> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 5.26 hours on Cygwin on AMD 64 3200+ / July 15, 2007 2007 年 7 月 15 日)
5×10137+3 = 5(0)1363<138> = 7 × 3343 × 1231884389<10> × 14133656423605033089328341238732583072598888641345800951<56> × 1227188017945406154897963678957290689881567366655657179710045847933577<70> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 6.48 hours on Cygwin on AMD XP 2700+ / July 15, 2007 2007 年 7 月 15 日)
5×10138+3 = 5(0)1373<139> = 19 × 1847 × 2243 × 1854888679869283637<19> × 34245411060208811631845963850057003813261211150174679440970851907502195211520682605734863208860691750207700435881<113>
5×10139+3 = 5(0)1383<140> = 312 × 13757 × 1676267 × 5477477407<10> × 914935539886441<15> × 17576529389171235892873769570959<32> × 25613885676592741147760266044980021990273525624421672846346548400112549<71> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3401522408 for P32 / July 7, 2007 2007 年 7 月 7 日)
5×10140+3 = 5(0)1393<141> = 172 × 1373153 × 15490764900917<14> × 319431831015906441432555931<27> × 254625665901514898141664498789886532707133045914495460376688572293867265692738371876322076917<93>
5×10141+3 = 5(0)1403<142> = 419 × 8814679 × 820452221 × 1264532627<10> × 1304866692393062556786750201496972923992670107959398922183378289671457073707297377923507000277567238580923722862209<115>
5×10142+3 = 5(0)1413<143> = 151 × 1207221004937<13> × 450592298232999465856873727<27> × 608726921836642240976758217841530281701416949077763948523572993771478344517382951480137814937359007347<102>
5×10143+3 = 5(0)1423<144> = 7 × 59 × 131 × 19163 × 23789 × 96365852833312759<17> × 81671235362417718269737<23> × 137584931502707732683063<24> × 45841742692394767309895959<26> × 408399015003123572141614553519801012571413<42>
5×10144+3 = 5(0)1433<145> = 53 × 8915485535218874463020966252542555006448848732763244901456195853393<67> × 10581546262269091742312886939766011985159784242637011168380827339866200032807<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 7.42 hours on Cygwin on AMD 64 3200+ / July 15, 2007 2007 年 7 月 15 日)
5×10145+3 = 5(0)1443<146> = 10903 × 323797439456498340561904697913457873787<39> × 2465188889777582684991267296272427043966702509<46> × 5745136880246153704523428561631148137811827694096870119147<58> (JMB / GMP-ECM B1=1000000, sigma=3545776710 for P39 / July 14, 2007 2007 年 7 月 14 日) (JMB / GGNFS / July 15, 2007 2007 年 7 月 15 日)
5×10146+3 = 5(0)1453<147> = 167 × 218145541 × 410197723711<12> × 93608508393331353137<20> × 357436272055582929707974317324577158309861213723960622293612294882451166203030222793037973760928293170607<105>
5×10147+3 = 5(0)1463<148> = 82106351993586265631239<23> × 138949891016035954229041<24> × 2969683976039291151435611<25> × 147579080976547109286694585045799451429111810694887599444933015273486191902127<78>
5×10148+3 = 5(0)1473<149> = 23 × 122117 × 553249 × 2522659 × 13292482722648700239840631<26> × 15947741321569901709147142457<29> × 7037119119859597676550832006219<31> × 8550404596993401489765767474006096463155418031<46> (Makoto Kamada / Msieve 1.25 for P31 x P46 / 10 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / July 13, 2007 2007 年 7 月 13 日)
5×10149+3 = 5(0)1483<150> = 7 × 1931 × 5243209539041849099760187057760329315540666673453359958582230909941313<70> × 7054926221581529213954354507669417037749392705948230321975121930804768049743<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 10.32 hours on Core 2 Quad Q6600 / July 15, 2007 2007 年 7 月 15 日)
5×10150+3 = 5(0)1493<151> = 1245381079<10> × 232068384169<12> × 3281330425711817<16> × 3983269107490187761662938933<28> × 1323616429220128741691304002012098418070492757816238358912574567043595352601660216811473<88>
5×10151+3 = 5(0)1503<152> = 443 × 947 × 16270985621257205906905273044911329<35> × 1985841848915255165882503532099473704607<40> × 3688567872296026104787199609577180339676172266118012744852132484083849981<73> (Robert Backstrom / GMP-ECM 5.0 B1=891500, sigma=1474273551 for P35, GGNFS-0.77.1-20060513-athlon-xp / 19.96 hours on Cygwin on AMD 64 3200+ / July 16, 2007 2007 年 7 月 16 日)
5×10152+3 = 5(0)1513<153> = 14869 × 135268966532217716081858222979343678676268459159986363363<57> × 248593672856895851344394797338957581879512075361661154360125070884478563005695290561420504349<93> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 24.70 hours on Cygwin on AMD XP 2700+ / July 16, 2007 2007 年 7 月 16 日)
5×10153+3 = 5(0)1523<154> = 1109 × 4508566275924256086564472497745716862037871956717763751127141568981064021641118124436429215509467989179440937781785392245266005410279531109107303877367<151>
5×10154+3 = 5(0)1533<155> = 31 × 4021 × 167160802616143494509108495516497129<36> × 2399605173928420299498820740137566306845129879546122780196166540333527775067120892884179276851300720910497809301857<115> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 18.03 hours on Cygwin on AMD 64 3400+ / July 15, 2007 2007 年 7 月 15 日)
5×10155+3 = 5(0)1543<156> = 7 × 55469 × 1287720554337944231398232732311226605336829065398176072606835735790647543157954378636200915311770023410759677863826126819871073418099685023552408938841<151>
5×10156+3 = 5(0)1553<157> = 17 × 19 × 353 × 9781 × 2903959 × 3738923 × 48999199953669556762469285191647229<35> × 16220542161012079506892689114089790259652611<44> × 519539008028015605717126723388083053475004321678810798119<57> (JMB / GMP-ECM B1=1000000, sigma=2562771777 for P35 / July 14, 2007 2007 年 7 月 14 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P44 x P57 / 3.73 hours on Core 2 Quad Q6600 / July 15, 2007 2007 年 7 月 15 日)
5×10157+3 = 5(0)1563<158> = 53 × 149 × 13437119575793745653860491268913351112372015271429983467581637225087533319599<77> × 471196096929417376262628665137399248660726397583286864726053838970722199918901<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 29.27 hours on Cygwin on AMD 64 3200+ / July 16, 2007 2007 年 7 月 16 日)
5×10158+3 = 5(0)1573<159> = 23535093831695777<17> × 3336615942677038549001641449007892174836007<43> × 6367190586858022590177464026314548769045456613292917746979423848926661873487443619330012203341779877<100> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 29.31 hours on Cygwin on AMD 64 3400+ / July 16, 2007 2007 年 7 月 16 日)
5×10159+3 = 5(0)1583<160> = 83066365779588590821426749068056416859826527<44> × 60192834405048939466899798943567903902651745875844194867985009267232595787118690954252254004124505688435636777703389<116> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 24.58 hours on Core 2 Quad Q6600 / July 15, 2007 2007 年 7 月 15 日)
5×10160+3 = 5(0)1593<161> = 2207 × 7760503636757<13> × 120355074834623<15> × 82551714075637674821552052888550681<35> × 1770092901260328461943147499208826822490849<43> × 165993545605717346668480035353143215370070055379374031<54> (JMB / GMP-ECM B1=1000000, sigma=2567545950 for P35 / July 14, 2007 2007 年 7 月 14 日) (Jo Yeong Uk / Msieve v. 1.21 for P43 x P54 / 03:16:10 on Core 2 Quad Q6600 / July 15, 2007 2007 年 7 月 15 日)
5×10161+3 = 5(0)1603<162> = 72 × 1447 × 180463 × 26314542158435393005535533221629<32> × 11706943567107084998551285511603272813010623152246453284257<59> × 126846321501220363453898438705886991913400990993746411945018359<63> (JMB / GMP-ECM B1=1000000, sigma=1129548668 for P32 / July 14, 2007 2007 年 7 月 14 日) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 80.52 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 19, 2007 2007 年 7 月 19 日)
5×10162+3 = 5(0)1613<163> = 47 × 11117 × 5487049 × 1743996874287927570615560828385603584978842879167210331182020108181733721422878319766121326268352912079842952192701661035149571920584229278614898636153<151>
5×10163+3 = 5(0)1623<164> = 29 × 227 × 1372379 × 3452401427<10> × 1652368488234263596749387089016071429414818510198454291329<58> × 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013<87> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.31 / December 18, 2007 2007 年 12 月 18 日)
5×10164+3 = 5(0)1633<165> = 557 × 217837300066202477<18> × 1196687247426772242533735797290481529635161715296376005028120547<64> × 3443514377361480174374528664126918435300112338137700545497427175846407441531435641<82> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.32 / January 9, 2008 2008 年 1 月 9 日)
5×10165+3 = 5(0)1643<166> = 107 × 3347 × 76127449 × 526115281 × 8629342554611<13> × 669110924591646330515236469<27> × 90824126989341694860705521906459719377905473<44> × 664708541046310574292268644887995665738412289611807142993429<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P44 x P60 / 6.17 hours on Core 2 Quad Q6600 / July 15, 2007 2007 年 7 月 15 日)
5×10166+3 = 5(0)1653<167> = 58411 × 205212516206615635610167665320053000460472202204809200220862876866413<69> × 4171300883176815364229387134807678863679793387097531618573030009987940624111825593896704727821<94> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 80.81 hours on Cygwin on AMD XP 2700+ / July 20, 2007 2007 年 7 月 20 日)
5×10167+3 = 5(0)1663<168> = 7 × 773 × 8329 × 66986389608208370945649030468786635518218514529828739674619854324867<68> × 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811<93> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.32 / December 28, 2007 2007 年 12 月 28 日)
5×10168+3 = 5(0)1673<169> = 30261601 × 890150258236321<15> × 498727304848409587637<21> × 142978063635046612431340573579<30> × 12718944880656352612135685179437522176294183<44> × 204659137232336784991399810699824456814839775637627027<54> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1087748790 for P30 / July 9, 2007 2007 年 7 月 9 日) (Jo Yeong Uk / Msieve v. 1.21 for P44 x P54 / 04:25:25 on Core 2 Quad Q6600 / July 14, 2007 2007 年 7 月 14 日)
5×10169+3 = 5(0)1683<170> = 31 × 16244243 × 29298332253113065055747<23> × 219470599991522042446043080605252718567618567796903842516245509<63> × 15441503431769976028446348762595181204879730780351588237227771804855548607617<77> (matsui / GGNFS-0.77.1-20060722-nocona / April 23, 2009 2009 年 4 月 23 日)
5×10170+3 = 5(0)1693<171> = 232 × 53 × 83 × 139 × 16067 × 187471 × 10244358647<11> × 21800705213641<14> × 2297848350912936021727670498427026103832182756085324531838897331823600222770129524405223296299394736813992554953763915717858142333<130>
5×10171+3 = 5(0)1703<172> = 2141 × 3463 × 22115239687<11> × 2126176738288566290549353<25> × 147260649364933694278877144916097788377722854278739967<54> × 97391963406433881857367240605552004713811188886749910103549282496731302376393<77> (Markus Tervooren / Msieve 1.42 snfs / 30.58 hours / September 30, 2009 2009 年 9 月 30 日)
5×10172+3 = 5(0)1713<173> = 17 × 9089719 × 870832992287<12> × 13385200156201<14> × 47347314846917<14> × 724273923844727<15> × 199380097814707075827853407010411667<36> × 4060045237533688631179618384328067264911276818684333348445532508588775649451<76> (JMB / GMP-ECM B1=1000000, sigma=3089909484 for P36 / July 14, 2007 2007 年 7 月 14 日)
5×10173+3 = 5(0)1723<174> = 7 × 313 × 169061906987<12> × 59249254073379949902901368057587<32> × 22782373957682117221393919745453826568924577598689253992144435924521117243880060681895434415464594199441242777852408944634407357<128> (suberi / GMP-ECM 6.1.2 B1=1000000, sigma=2699943498 for P32 / July 15, 2007 2007 年 7 月 15 日)
5×10174+3 = 5(0)1733<175> = 19 × 109 × 22313393 × 2476448641<10> × 247625824575833330688018021306592807497411725702106465009811<60> × 176440804984726174091559159344056990761822509286650165941609797204052222532610996092081714713351<96> (Wataru Sakai / Msieve / 86.59 hours / February 25, 2010 2010 年 2 月 25 日)
5×10175+3 = 5(0)1743<176> = definitely prime number 素数
5×10176+3 = 5(0)1753<177> = 233 × 167483 × 164607553791153072943705556256499<33> × 77838344545335028846811880278194243230332959322516120862226515570460253216262769544776639596904080563916319548577503073466720983267686923<137> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2250673457 for P33 / July 10, 2007 2007 年 7 月 10 日)
5×10177+3 = 5(0)1763<178> = 176218992155079534631185354899<30> × 5025246186222864782538544032838260174977753632718898331835688721<64> × 5646247985540647264030815556578582247146679308667203035114340476157533562848981624257<85> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=3025299345 for P30 / July 14, 2007 2007 年 7 月 14 日) (Serge Batalov / Msieve 1.46 snfs / October 18, 2010 2010 年 10 月 18 日)
5×10178+3 = 5(0)1773<179> = 61 × 5813 × 1266095772152669053113048638910331<34> × 2483588918013363077203791605530130852970240187791846376794145978507891<70> × 44842887995736482930697673402991298662157313456185424557641058335316451<71> (JMB / GMP-ECM B1=1000000, sigma=1453825301 for P34 / July 14, 2007 2007 年 7 月 14 日) (Andreas Tete / factmsieve.py via Msieve v1.48 snfs / July 21, 2013 2013 年 7 月 21 日)
5×10179+3 = 5(0)1783<180> = 7 × 6581 × 274649101458389267214457<24> × 17442996660668102907927206569<29> × 58420054131152676580667221137068677907<38> × 38780985245897447564182837100518071852832635692767107596372080155550102208945138108939<86> (JMB / GMP-ECM B1=1000000, sigma=557507828 for P38 / July 14, 2007 2007 年 7 月 14 日)
5×10180+3 = 5(0)1793<181> = 3636511 × 10065320359<11> × 170781899320909<15> × 28365504652386968928074018263317721<35> × 28198443896462682489337688478809235310463625892214771261649188513799597672988910349570886709139480460830651399289823<116> (JMB / GMP-ECM B1=1000000, sigma=1565609571 for P35 / July 16, 2007 2007 年 7 月 16 日)
5×10181+3 = 5(0)1803<182> = definitely prime number 素数
5×10182+3 = 5(0)1813<183> = 439 × 571 × 7643 × 63450664231189<14> × 11951894979697246105009<23> × 4279158799171957694024328911384178290437170971073603364995092311<64> × 80421870806926087339456474828653480091728973461916285528358822058404466319<74> (Dmitry Domanov / Msieve 1.50 snfs / February 20, 2014 2014 年 2 月 20 日)
5×10183+3 = 5(0)1823<184> = 53 × 2253971 × 22933567 × 872683629733718312183363<24> × 2091304986012211451175800619436595563347769212985491802204880825094576779945718852668828426711262227533259301616642053664190545178039143082872561<145>
5×10184+3 = 5(0)1833<185> = 31 × 2687 × 2535154133<10> × 1417051339821693683443908146967478536085563199783794038033753580109<67> × 167090088944912187410664550884662405683335874733212344807291369541357525365465340034574317720721862994867<105> (Cyp / yafu 1.34.3 / December 29, 2013 2013 年 12 月 29 日)
5×10185+3 = 5(0)1843<186> = 7 × 505752502245677956259<21> × 18507977608619856746602644452748137837<38> × 7630885880694883788242610766381704283225279287936847958869670360168616422552526506424965632629458726936822609309848264083247763<127> (suberi / GMP-ECM 6.1.2 B1=3000000, sigma=3614596123 for P38 / July 20, 2007 2007 年 7 月 20 日)
5×10186+3 = 5(0)1853<187> = 113 × 1999 × 3079 × 3797 × 92099093 × 298400119 × 7063295315177<13> × 6969354988860332281<19> × 2731892341376794135045007<25> × 7364382395306340008013769<25> × 1147035865427337017136577429<28> × 60645317696677687093610484674525646184452370191271<50>
5×10187+3 = 5(0)1863<188> = 43951 × 881623824379321<15> × 7538781648531214385240912695837561<34> × 171165708092478089670945899225361876860032835861904429144861641040302889862809476562441735553451758084446668158294751605231000217623613<135> (JMB / GMP-ECM B1=1000000, sigma=2383272046 for P34 / July 14, 2007 2007 年 7 月 14 日)
5×10188+3 = 5(0)1873<189> = 17 × 353 × 694042304507<12> × 534714061843976765275098162965857648543309727<45> × 224511622860875644540507133498734394246496745568262356156954776102962010083439706705021118582845752441312785525001232938868447927<129> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=2524047625 for P45 / July 4, 2008 2008 年 7 月 4 日)
5×10189+3 = 5(0)1883<190> = 91095965487358089320603<23> × 494396890325323305718414399<27> × 111018442640083081970947618984445439303130371746063567619735073193700750979768533007349526842130828718519132702632964174582139162807213505799<141>
5×10190+3 = 5(0)1893<191> = 11187623 × 1206015527<10> × 134932983931021<15> × [27463833498036978931279122698566196103643363675090766798128022755411351207988997570033945512205280674454048735810379350567552531540854521806185942636303194251583<161>] Free to factor
5×10191+3 = 5(0)1903<192> = 7 × 29 × 1862219 × 1322644751875111480766217733615045731619449911148296709860073523123561443621988373280727483817527432716882915071575833372600451608585601344814394148141349362228768778807682154562482779<184>
5×10192+3 = 5(0)1913<193> = 19 × 23 × 119565829 × 95693290407027618038419981193806055270319420783109072461031121968017956783476298754817280453990453982954882558845432530233709987476182148868297139208013635532470628324933123639220011<182>
5×10193+3 = 5(0)1923<194> = 68430913250627<14> × 13104913306486423<17> × [55754960965977667099262303619967816906897335637724058560887675987960359641171796316619144498801780827605775396781796574777058291468658191359929597537624685917709543<164>] Free to factor
5×10194+3 = 5(0)1933<195> = 10609553 × 438880348296833<15> × 251377856237628403616495573717000177946692552651717<51> × 427169035867717439785759694705331232401758225061288821171787707174800802175716471765814171496267634978316738059810277207991<123> (matsui / Msieve 1.50 snfs / November 13, 2011 2011 年 11 月 13 日)
5×10195+3 = 5(0)1943<196> = 751 × 3001 × 614843 × 258585653 × 362881860749<12> × 323707528193436770166251195214425203715555477<45> × 86471033758042007120079000192217930113174491067153908843741<59> × 1373746829732862042556123461993071957430124563209378760756799<61> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3769407467 for P45 / November 8, 2013 2013 年 11 月 8 日) (Dmitry Domanov / Msieve 1.50 gnfs for P59 x P61 / November 9, 2013 2013 年 11 月 9 日)
5×10196+3 = 5(0)1953<197> = 53 × 4831 × 81435758513<11> × 620177514568967<15> × 8335212300603379<16> × 35165888307807931<17> × 1724266535012524133<19> × 18149768500139575450781954504934682959012295193<47> × 421514178392323250396382121254673947852157285795193589239114535798571<69> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P47 x P69 / 23.37 hours on Core 2 Quad Q6600 / July 18, 2007 2007 年 7 月 18 日)
5×10197+3 = 5(0)1963<198> = 7 × 17493029 × 7120436377<10> × 24200822641<11> × [23695736351380415244004256931680513817197336811220426535223782896597104693816923457593254159300559653260891100543204615906939847399894235465448190699889311959028229521593<170>] Free to factor
5×10198+3 = 5(0)1973<199> = 8689333129<10> × 153432197600721917<18> × 3750308994519522383522483020395659550858969331709345535904461838009283679890347744226122442593080577079421507856574382850972150298227915214840092134048508484762597128198471<172>
5×10199+3 = 5(0)1983<200> = 31 × 577 × 9391 × 147844831 × 6158110597551295216831<22> × [326939223792247766844779917877606712606767451167966562253639127137004867273204642400811592400034256527386422238848074153248332576298397531106070913260400033724819<162>] Free to factor
5×10200+3 = 5(0)1993<201> = 15241 × 44657 × 932333 × 115950677407269228980611<24> × [6795519300541856100090453542286624239470214656784601069980675786414162837826425989504861017459421939671772935664803067817722265435063030431314634930760154024385613<163>] Free to factor
5×10201+3 = 5(0)2003<202> = 59 × 553452522997741091750436683206666962991<39> × 153122009911246344342781589006996827782851480542622578268342331532612877939854524721905250320423349869009972247327226527846207705436063614108811455277005511168887<162> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3463482801 for P39 / October 8, 2013 2013 年 10 月 8 日)
5×10202+3 = 5(0)2013<203> = 33985666879<11> × [1471208441429624477076897202762110319453649347352563980270278103198729349259093583784903313446027142176414669258842999324391747799194333414215891161415864827114313927716410134121705665765700157<193>] Free to factor
5×10203+3 = 5(0)2023<204> = 72 × 4380326507<10> × 5782008099199159888639992867169<31> × [402892093630509158361209333308262115645761616088359557821597138327145384608891562714921970769161835710929792684072138059603826092657721486712385680144328842132409<162>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1412419126 for P31 / September 19, 2013 2013 年 9 月 19 日) Free to factor
5×10204+3 = 5(0)2033<205> = 17 × 317 × 1223 × 135347 × 423522414257<12> × 276261864155481933944840029<27> × [47905942854768216749771765368532183861998453234002042934177577347478324424933760373465848978354032212635775523958581649050276256554951931416559243698185839<155>] Free to factor
5×10205+3 = 5(0)2043<206> = 1181133564732949612469669<25> × 51734921678467808836956770527802117<35> × 42504775489855204236946455927370624979<38> × 19250830520755506723945635484449894530253448208748508766983841117800703971735518761103726190412665935775302809<110> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1010481965 for P35 / October 8, 2013 2013 年 10 月 8 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1475963172 for P38 / November 13, 2013 2013 年 11 月 13 日)
5×10206+3 = 5(0)2053<207> = 499 × 76781779 × 13050023339730537685617527994839141513098007714399723264274423163722461258358584025551239327529059853895272708339734429594078135833093123228471908591573174483115088593191565819578700975172319608043<197>
5×10207+3 = 5(0)2063<208> = 118787 × 60135169 × 2720227856525739639452312832553<31> × [257316283770537648973547713329205449513917429115126061372722099352434886633613802380179331173277284886713386933738286323172992202489751259828314389640963671059432217<165>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1969703585 for P31 / October 8, 2013 2013 年 10 月 8 日) Free to factor
5×10208+3 = 5(0)2073<209> = 47 × 141245821 × 826683554363<12> × 1959168180918167<16> × [4650348733865691287789535487711511791379351816158420837568471227349901573543083417911237450833105613300497760466116447266775955596904233496912535500767819397481919974038389<172>] Free to factor
5×10209+3 = 5(0)2083<210> = 7 × 53 × 197 × 39267580847723<14> × 5479260481091192501<19> × [31796094197477402111107783023599572471228470135206746563765977704605653123363198295255613769222194120850036798370926709134390007250704194718436531816995677004746701689759803<173>] Free to factor
5×10210+3 = 5(0)2093<211> = 19 × 6863 × 3099203 × [12372355227966888648259809326907556030190641158430082719037823096785143086275999922457213805599033254079831396963199081083275180780423988783265845712948805754196482793457187428329085808570050584436533<200>] Free to factor
5×10211+3 = 5(0)2103<212> = 83 × 179381 × 3358268927892122730221592688591819404655487616282580329960668625970313037008190750749750329496555860135621675691566641186360887773167471565369074091002237077263626058635509811753578554578217206520710478061<205>
5×10212+3 = 5(0)2113<213> = 1272645713<10> × 1888668101209<13> × 198515756906185747685672599<27> × 1047880735219916845857088790683289268136318729357980054687277627730072239638457090239345159644303180086597550724805399586455137904187707261242090673651843596174738541<166>
5×10213+3 = 5(0)2123<214> = 179 × 347 × 607 × 1277 × 1471 × 3704635157<10> × 378291634290349484957737<24> × [50375927633231622735958285114657406454731993385528596839089939523558494394916363084240799062403346010693325647743821559567455160600360402566420257161505010019249660811<167>] Free to factor
5×10214+3 = 5(0)2133<215> = 23 × 31 × 677 × 827 × 1579 × 19449664515733930645689539691285533<35> × 4078420974220094017435316513410209136996353526940932332216858355612189143114731504696134056848482797695524900424565302675763442528193389806403979828970180525244038177827<169> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1435513866 for P35 / October 8, 2013 2013 年 10 月 8 日)
5×10215+3 = 5(0)2143<216> = 7 × 467 × 192193 × [795824889982739942871582940606615962572559155283576068174829428503646573898961502157170109211224733807198563054758687692841999344058842579306222366840936029690138400744712558928664480396689803296391688406759<207>] Free to factor
5×10216+3 = 5(0)2153<217> = 139 × 2221 × 336774539215301428582971711769<30> × 48091397213176088017268712487943552622016474739861472372167341961796367061569267149468975590481884737465594798518509074103104132668838321556573661897622448082321715477482227833739573<182> (Ignacio Santos / GMP-ECM 7.0 B1=1000000, sigma=1:2330132853 for P30 / September 25, 2013 2013 年 9 月 25 日)
5×10217+3 = 5(0)2163<218> = 151 × 2392183 × [138419940202973408148056005582620145123728642955572683392876377790904848186920116825432907740095068420602708491207619382083808274064660267234145603597354853632775824231015704509062496057627078094063619183179891<210>] Free to factor
5×10218+3 = 5(0)2173<219> = 107 × 383 × 21851413739456660643278567<26> × 558351789720632751482546534042472580615534016919140598810651239270593775939728517221486854786308070754522946056417364285806861705912435447732699228120246716049132356347525902228479724429489<189>
5×10219+3 = 5(0)2183<220> = 29 × 26344308353147<14> × 620594414447620328872259<24> × [10545746874759397378411965885005881324158729530362742059737965559160866990788359584934310614462264829581026486976747614305755706573282299053453798856706976962638031312848854627953359<182>] Free to factor
5×10220+3 = 5(0)2193<221> = 17 × 353 × 1637 × 3605267585913289<16> × 5792066804397570504061<22> × 14738296734954993940111<23> × 3078831187946566879058244293<28> × 7642519006603519591700132941973808240570736277<46> × 702840746031828550753681332932037827527335768460302324464841336269339833168848541<81> (Serge Batalov / GMP-ECM B1=11000000, sigma=4007888246 for P46 / November 8, 2013 2013 年 11 月 8 日)
5×10221+3 = 5(0)2203<222> = 7 × 5790419 × 163760122841761<15> × 5937173194897403<16> × 161713304464409747180647<24> × [78456394929980347990883308357850634963476074602182537603227693305221656591740764235626803156695290331447738541871995795208803135358845970781893901099418548335891<161>] Free to factor
5×10222+3 = 5(0)2213<223> = 53 × 15497 × 19141 × 1590383 × 35413253745238537586631563869<29> × [5646954941103415085575277027368515189098055090350789161449170102513537116986390541085309561651494256565479610140292677303919377911017186400903786460389921116833669595538606752769<178>] Free to factor
5×10223+3 = 5(0)2223<224> = 199 × 2159845253<10> × 3470848853<10> × 8272620371<10> × 733868024951599<15> × 45426140962346181123557<23> × 64833579032933908050697703710951<32> × 21053416522920471553741154634622233579271530021834884489819387<62> × 89036710333296645464038392480989576522988658039948266967295953<62> (Ignacio Santos / GMP-ECM 7.0 B1=1000000, sigma=1 for P32 / September 23, 2013 2013 年 9 月 23 日) (Erik Branger / GGNFS, Msieve gnfs for P62(2105...) x P62(8903...) / October 14, 2013 2013 年 10 月 14 日)
5×10224+3 = 5(0)2233<225> = 421 × 4561 × 166247 × 596611 × 14091891469<11> × 633121556516883028777166087<27> × 2709264145707257438429463366391<31> × 880630513952722914538084947579497786743332125341609917142189<60> × 123333567282978452323767492110010335266741271427792041111191952387384006294821187<81> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=962939845 for P31 / October 8, 2013 2013 年 10 月 8 日) (Erik Branger / GGNFS, Msieve gnfs for P60 x P81 / August 25, 2016 2016 年 8 月 25 日)
5×10225+3 = 5(0)2243<226> = 1019 × 14995599491<11> × 617060399392940839356585869<27> × 208639959613444360749612904768283<33> × 2541597776255376567850174153735232526668685901368306182415653226024556014249430449933421627814798597337282302793184957982029082928204041583865113640032941<154> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3948059299 for P33 / October 8, 2013 2013 年 10 月 8 日)
5×10226+3 = 5(0)2253<227> = 422307665657<12> × 2159181714912529<16> × 15625978671491638853267938831703665322962427<44> × [3509171703104154675241107276135386094600310248416462373518235089791764263272904169219347567482893717580418058729978839014789328474337285873547055462012647313<157>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2182137660 for P44 / December 2, 2013 2013 年 12 月 2 日) Free to factor
5×10227+3 = 5(0)2263<228> = 7 × 14551 × 132241 × 809843 × 2478173 × 18496116205458962464597447808835154837398802255053139516318710639078245101411266296116160065594182770680798173223070269252343127537380093486662929037337598279871697512807875622472672557924408924153344183221<206>
5×10228+3 = 5(0)2273<229> = 19 × 6691 × 9609917 × 498621649 × 16779837304131721<17> × 489155409299330263018675772141460373512143128753820230787318441328465883595269060875531071873972769485076818031383371545248339567664712559757910005324359345832618622420304592697894386374111599<192>
5×10229+3 = 5(0)2283<230> = 31 × 14458781 × [111551812411188163988598057225682642487344296287003947691472165800369049538243431671439414679073099302524300831669406048242441961449340135444559662840983130128729832176924405024631856095145628559669926754254487402008732673<222>] Free to factor
5×10230+3 = 5(0)2293<231> = 61907054117<11> × 1950097109813500843371813437<28> × [4141652215518294290587144580603463888408825900853970675181459447883621199283460099918951336167694472369368848129135130055524235644974131666206199679597635667475713738694708297365793195273717907<193>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=30852199 for P28 / October 8, 2013 2013 年 10 月 8 日) Free to factor
5×10231+3 = 5(0)2303<232> = 97 × 80713 × 1371032137<10> × 998420703695313876269<21> × 55870774695700353122051<23> × 318752799549009070625147<24> × 87218596601040005194333434669588409753021969<44> × 300362542562738897673349973863000909011000305788562796707628020034182891810425391347747783182512487497887<105> (Serge Batalov / GMP-ECM B1=11000000, sigma=549904282 for P44 / May 24, 2014 2014 年 5 月 24 日)
5×10232+3 = 5(0)2313<233> = 308582584527562187329336103907078627863<39> × 162031179032833806245808529347473408708038493981295918565129973145374348214644858503647402419100494894794786890513964944750573572855960402496447283785699813528365305363530650010982070243212353781<195> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2189953707 for P39 / October 22, 2013 2013 年 10 月 22 日)
5×10233+3 = 5(0)2323<234> = 7 × 6866551 × 10402394364881499980329072256009083537197724363886823031159103227890017648078135796059976627484245209650584197427292308550745282664990244530540670480503447592747592121367980602114303298493148681401852462549455843469096993318979<227>
5×10234+3 = 5(0)2333<235> = 59610201179056425571<20> × 83878260785952700286233431067806217497495050593919983500624115144167188676996640992320039188286570623554220394672527214232818740977728279100878532929483464882131019468589190374516731814579776282729335460379402048993<215>
5×10235+3 = 5(0)2343<236> = 53 × 943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264151<234>
5×10236+3 = 5(0)2353<237> = 17 × 23 × 11901744954641140663996287394295984815223<41> × 107444108690798387422090977647144507728467654070746079326120052348060658113724997347056764071693386164737381495044475781839987755651496911941312844647793076182616937602087075970391320375229375171<195> (Serge Batalov / GMP-ECM B1=11000000, sigma=3752609157 for P41 / May 25, 2014 2014 年 5 月 25 日)
5×10237+3 = 5(0)2363<238> = 367 × 132169 × 508229 × 202821921730333264930436860273890770904901266680084481859499578939459994308297010398658578119269542450097901444554766606520646961580892579999777672334656415278830657570139452748322728335018247236410370491520678257315964151809<225>
5×10238+3 = 5(0)2373<239> = 61 × 698359 × 27911467792147613084249700601<29> × 509515108921569866993364071358122233675309<42> × [82531871341217103648222115367913602173735317222927928461698933210872884272037610394152625557604667110095124837988617394172828227937744856618684678467418299444133<161>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2900030416 for P42 / December 2, 2013 2013 年 12 月 2 日) Free to factor
5×10239+3 = 5(0)2383<240> = 7 × 4349 × 7968893 × [2061031176049834668597043723281727722184097885608001731467377501142402282526496576743155767970946809922965129616020481769434063468230954086204989041572279088149041549802141673018388853516265226269781130996553640663658673724491197<229>] Free to factor
5×10240+3 = 5(0)2393<241> = 4178609921944444452712054358442787954933849801748717<52> × 1196570173669940400545161416178559766814638265431589628435757933023922053336192587542154752891917952849469012020247593094400875256157180191089301644659383670646424813528747540416355379562159<190> (Serge Batalov / GMP-ECM B1=300000000, sigma=3274779239 for P52 / November 25, 2013 2013 年 11 月 25 日)
5×10241+3 = 5(0)2403<242> = 193 × 331653173 × 169733384641<12> × 12293896486580428876810441464314315311<38> × 374344722689059836623745727979425738549364706792610988604533796564713984291198831533349919966184303548280545604935863176392378175061218143152607303013284041306493085142951616840111577<183> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2977172208 for P38 / October 8, 2013 2013 年 10 月 8 日)
5×10242+3 = 5(0)2413<243> = 743 × 1877 × 2510491 × 8393311 × 348681481 × 2134160057<10> × 1321539718240798507521617<25> × 17301702662468420115739076563408634282425350157617822289478003641607803027331897190537211431733974373526180935674084174941604383103622152796553542468647847789137441272075140882786157<182>
5×10243+3 = 5(0)2423<244> = 463730143 × 1145258636211421356751360046522358193<37> × 9414583301119425570254285626606207360420683884226907034872831491589081543212668927152422893568149785957215602156838287041022685270897452107102705947557595336687417032942644820987635215668807336985197<199> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3554824416 for P37 / October 8, 2013 2013 年 10 月 8 日)
5×10244+3 = 5(0)2433<245> = 31 × 471345847761379<15> × 3421910330740817892883890456736259885125092948015823044133265227186958668676322290854292521483811525110623660010786675746949256205645477708653870104247333990245331567446488867261858712497066048805791752424417845658354534938629247<229>
5×10245+3 = 5(0)2443<246> = 72 × 409 × 7907 × 35837 × 54422313559907021<17> × 110359543933553818921<21> × [14659539684968096175683150416601368434591303464865851447845048988902316582554710983990903546242968508363927792893586595470339014456936824852030759954460318760413704548271826950185833074068831856857<197>] Free to factor
5×10246+3 = 5(0)2453<247> = 19 × 349 × 754034082340521791584979641079776805911627205549690846026240386065450158347157291509576232845724626753129241441713165435077665510481073744533252903031217011008897602171618157140702759764741366309757201025486351983109636555572311868496456039813<243>
5×10247+3 = 5(0)2463<248> = 29 × 10046622157721152709<20> × 44897936337370553551<20> × [3822306926258840557417646125685068419720484865015480241051370957377959218210046722725758451215296425902018024539751211407825579196541023752915257779108496216510936259744060797842247205308356087176027054062973<208>] Free to factor
5×10248+3 = 5(0)2473<249> = 53 × 3096017 × 53210722751723<14> × 3313056630641064407<19> × [17284737194885886520366096018451225318262721676769235384346522559162908084600674676567144012855095001967582406421854381318188362240910596177626076366929229174553554790294259586832650894162093943634400984250323<209>] Free to factor
5×10249+3 = 5(0)2483<250> = 2689349093<10> × 1646402723317339009409641<25> × 1129241288106765440954656267967445738292591470782941753128762909333230854347013141335420418510953551740067679092706201330507532912170549690167454852820994691454200703580291708200431354802438689278837675846026636602031<217>
5×10250+3 = 5(0)2493<251> = 619 × 5172278147<10> × 1193876579191<13> × [13080912816094396829349624401591815806037749803502601828778991199392989341349268336865995797060619125764491006645434141994332266676292444425551992744026007881270902542343728628812036538926160516173134141778458163397387611804181<227>] Free to factor
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