Table of contents 目次

  1. About 300...001 300...001 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
    4. Related sequences 関連する数列
  2. Prime numbers of the form 300...001 300...001 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 300...001 300...001 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 300...001 300...001 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

30w1 = { 31, 301, 3001, 30001, 300001, 3000001, 30000001, 300000001, 3000000001, 30000000001, … }

1.3. General term 一般項

3×10n+1 (1≤n)

1.4. Related sequences 関連する数列

2. Prime numbers of the form 300...001 300...001 の形の素数

2.1. Last updated 最終更新日

June 12, 2013 2013 年 6 月 12 日

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

  1. 3×101+1 = 31 is prime. は素数です。
  2. 3×103+1 = 3001 is prime. は素数です。
  3. 3×107+1 = 30000001 is prime. は素数です。
  4. 3×1010+1 = 30000000001<11> is prime. は素数です。
  5. 3×1028+1 = 3(0)271<29> is prime. は素数です。
  6. 3×1036+1 = 3(0)351<37> is prime. は素数です。
  7. 3×1067+1 = 3(0)661<68> is prime. は素数です。
  8. 3×1081+1 = 3(0)801<82> is prime. は素数です。
  9. 3×10147+1 = 3(0)1461<148> is prime. は素数です。
  10. 3×10483+1 = 3(0)4821<484> is prime. は素数です。
  11. 3×10643+1 = 3(0)6421<644> is prime. は素数です。
  12. 3×101020+1 = 3(0)10191<1021> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  13. 3×101900+1 = 3(0)18991<1901> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  14. 3×102620+1 = 3(0)26191<2621> is prime. は素数です。 (Harvey Dubner / Cruncher / December 31, 1984 1984 年 12 月 31 日)
  15. 3×1010453+1 = 3(0)104521<10454> is prime. は素数です。 (Chris Caldwell / Cruncher / May 1, 1994 1994 年 5 月 1 日)
  16. 3×1027720+1 = 3(0)277191<27721> is prime. は素数です。 (Jim Liddle / Proth.exe / March 13, 2000 2000 年 3 月 13 日)
  17. 3×1052824+1 = 3(0)528231<52825> is prime. は素数です。 (Peter Benson / NewPGen, OpenPFGW / June 9, 2004 2004 年 6 月 9 日)
  18. 3×10105589+1 = 3(0)1055881<105590> is prime. は素数です。 (Roman Makarchuk / LLR, OpenPFGW / December 5, 2008 2008 年 12 月 5 日)
  19. 3×10111988+1 = 3(0)1119871<111989> is prime. は素数です。 (Alexander Gramolin / NewPGen, OpenPFGW / February 24, 2012 2012 年 2 月 24 日)
  20. 3×10618853+1 = 3(0)6188521<618854> is prime. は素数です。 (Alexander Gramolin / NewPGen, OpenPFGW / August 5, 2012 2012 年 8 月 5 日)
  21. 3×10665829+1 = 3(0)6658281<665830> is prime. は素数です。 (Alexander Gramolin / NewPGen, OpenPFGW / September 13, 2012 2012 年 9 月 13 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了 / Erik Branger / September 7, 2010 2010 年 9 月 7 日
  2. n≤112000 / Completed 終了 / Ray Chandler / March 2, 2012 2012 年 3 月 2 日
  3. n≤500000 / Completed 終了 / Alexander Gramolin / March 13, 2012 2012 年 3 月 13 日
  4. n≤620000 / Completed 終了 / Alexander Gramolin / August 8, 2012 2012 年 8 月 8 日

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

  1. 3×106k+2+1 = 7×(3×102+17+27×102×106-19×7×k-1Σm=0106m)
  2. 3×106k+5+1 = 13×(3×105+113+27×105×106-19×13×k-1Σm=0106m)
  3. 3×1015k+1+1 = 31×(3×101+131+27×10×1015-19×31×k-1Σm=01015m)
  4. 3×1016k+13+1 = 17×(3×1013+117+27×1013×1016-19×17×k-1Σm=01016m)
  5. 3×1018k+4+1 = 19×(3×104+119+27×104×1018-19×19×k-1Σm=01018m)
  6. 3×1021k+2+1 = 43×(3×102+143+27×102×1021-19×43×k-1Σm=01021m)
  7. 3×1022k+13+1 = 23×(3×1013+123+27×1013×1022-19×23×k-1Σm=01022m)
  8. 3×1028k+15+1 = 29×(3×1015+129+27×1015×1028-19×29×k-1Σm=01028m)
  9. 3×1033k+12+1 = 67×(3×1012+167+27×1012×1033-19×67×k-1Σm=01033m)
  10. 3×1034k+32+1 = 103×(3×1032+1103+27×1032×1034-19×103×k-1Σm=01034m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 20.74%. 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 20.74% です。

3. Factor table of 300...001 300...001 の素因数分解表

3.1. Last updated 最終更新日

September 27, 2016 2016 年 9 月 27 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=201, 203, 214, 216, 221, 222, 226, 231, 233, 235, 236, 237, 241, 243, 245, 246, 249, 250, 251, 252, 253, 258, 259, 260, 262, 263, 266, 271, 273, 274, 277, 279, 281, 287, 288, 290, 291, 292, 293, 294, 295, 296, 297, 298, 300 (45/300)

3.4. Factor table 素因数分解表

3×101+1 = 31 = definitely prime number 素数
3×102+1 = 301 = 7 × 43
3×103+1 = 3001 = definitely prime number 素数
3×104+1 = 30001 = 19 × 1579
3×105+1 = 300001 = 13 × 47 × 491
3×106+1 = 3000001 = 853 × 3517
3×107+1 = 30000001 = definitely prime number 素数
3×108+1 = 300000001 = 72 × 6122449
3×109+1 = 3000000001<10> = 7589 × 395309
3×1010+1 = 30000000001<11> = definitely prime number 素数
3×1011+1 = 300000000001<12> = 132 × 1775147929<10>
3×1012+1 = 3000000000001<13> = 67 × 44776119403<11>
3×1013+1 = 30000000000001<14> = 17 × 23 × 62191 × 1233721
3×1014+1 = 300000000000001<15> = 7 × 95773 × 447486691
3×1015+1 = 3000000000000001<16> = 29 × 103448275862069<15>
3×1016+1 = 30000000000000001<17> = 31 × 379 × 15901 × 160581649
3×1017+1 = 300000000000000001<18> = 13 × 2281 × 23911 × 423111547
3×1018+1 = 3000000000000000001<19> = 16921 × 5188801 × 34168681
3×1019+1 = 30000000000000000001<20> = 163 × 184049079754601227<18>
3×1020+1 = 300000000000000000001<21> = 7 × 42857142857142857143<20>
3×1021+1 = 3000000000000000000001<22> = 263 × 13472579 × 846671161213<12>
3×1022+1 = 30000000000000000000001<23> = 19 × 181 × 1381 × 10452973 × 604304143
3×1023+1 = 300000000000000000000001<24> = 13 × 43 × 233 × 2303316007278478583<19>
3×1024+1 = 3000000000000000000000001<25> = 6709 × 15056940637<11> × 29697967297<11>
3×1025+1 = 30000000000000000000000001<26> = 2309 × 12992637505413598960589<23>
3×1026+1 = 300000000000000000000000001<27> = 7 × 109 × 877 × 17011 × 26355258412811941<17>
3×1027+1 = 3000000000000000000000000001<28> = 2069 × 85577 × 4296989 × 3943115191193<13>
3×1028+1 = 30000000000000000000000000001<29> = definitely prime number 素数
3×1029+1 = 300000000000000000000000000001<30> = 13 × 17 × 6389 × 212469253928379447424129<24>
3×1030+1 = 3000000000000000000000000000001<31> = 1637539 × 1832017435920610135086859<25>
3×1031+1 = 30000000000000000000000000000001<32> = 31 × 383 × 2526741345910890255200875937<28>
3×1032+1 = 300000000000000000000000000000001<33> = 7 × 103 × 326707 × 1273583870573108963459083<25>
3×1033+1 = 3000000000000000000000000000000001<34> = 6287 × 42299 × 11281002465075774324342877<26>
3×1034+1 = 30000000000000000000000000000000001<35> = 20107 × 28711 × 51966762052062599154639013<26>
3×1035+1 = 300000000000000000000000000000000001<36> = 13 × 23 × 2618448681461<13> × 383182793960858193559<21>
3×1036+1 = 3000000000000000000000000000000000001<37> = definitely prime number 素数
3×1037+1 = 30000000000000000000000000000000000001<38> = 179 × 613 × 1569611 × 3874630228127<13> × 44955771308579<14>
3×1038+1 = 300000000000000000000000000000000000001<39> = 7 × 3571 × 2173333 × 1283942706199<13> × 4300920803658799<16>
3×1039+1 = 3000000000000000000000000000000000000001<40> = 2990993 × 1003011374483323765719277845183857<34>
3×1040+1 = 30000000000000000000000000000000000000001<41> = 19 × 979150369 × 5634413557<10> × 286199942061324334063<21>
3×1041+1 = 300000000000000000000000000000000000000001<42> = 13 × 257 × 17107 × 4735035242785279<16> × 1108530656089810937<19>
3×1042+1 = 3000000000000000000000000000000000000000001<43> = 151 × 1669 × 119299 × 39546174097<11> × 2523171052478922495193<22>
3×1043+1 = 30000000000000000000000000000000000000000001<44> = 29 × 12654046331183595167<20> × 81751143590441508737707<23>
3×1044+1 = 300000000000000000000000000000000000000000001<45> = 7 × 43 × 37021 × 4191314061691<13> × 6423273420722757827509291<25>
3×1045+1 = 3000000000000000000000000000000000000000000001<46> = 17 × 67 × 269 × 1249 × 7839399777505813901392825897156132039<37>
3×1046+1 = 30000000000000000000000000000000000000000000001<47> = 31 × 97 × 700963 × 77575909 × 968862613 × 189366722010724917133<21>
3×1047+1 = 300000000000000000000000000000000000000000000001<48> = 13 × 109311862154664874542821<24> × 211110876917197143984737<24>
3×1048+1 = 3000000000000000000000000000000000000000000000001<49> = 61 × 8221 × 864195651219961261<18> × 6922368189145372572420061<25>
3×1049+1 = 30000000000000000000000000000000000000000000000001<50> = 1879 × 35278466088721848125359<23> × 452568977610245073188041<24>
3×1050+1 = 300000000000000000000000000000000000000000000000001<51> = 72 × 586335359385372763185511<24> × 10441889409517628903684359<26>
3×1051+1 = 3(0)501<52> = 47 × 994953497 × 64153538257318726918841475967120159360039<41>
3×1052+1 = 3(0)511<53> = 397 × 409369 × 589291 × 313246327159464677685910911080355191527<39>
3×1053+1 = 3(0)521<54> = 13 × 6581 × 3506598249038607646721915070190408284922796395217<49>
3×1054+1 = 3(0)531<55> = 1011559 × 754590459935761<15> × 3930236875017125218405813407578599<34>
3×1055+1 = 3(0)541<56> = 59 × 409 × 3299 × 321114319 × 1645263250196710211<19> × 713293966588391497181<21>
3×1056+1 = 3(0)551<57> = 7 × 157 × 272975432211101000909918107370336669699727024567788899<54>
3×1057+1 = 3(0)561<58> = 23 × 1117 × 23447 × 3339120189577212023<19> × 1491491939550947497031924913731<31>
3×1058+1 = 3(0)571<59> = 19 × 21871 × 72193652252802918548715073312653862721363786220156949<53>
3×1059+1 = 3(0)581<60> = 13 × 1039 × 338082920595701<15> × 17500711862350918541<20> × 3753906133691874100123<22>
3×1060+1 = 3(0)591<61> = 577 × 5199306759098786828422876949740034662045060658578856152513<58>
3×1061+1 = 3(0)601<62> = 17 × 31 × 10103893 × 392494829757049332889<21> × 14354496404471703713440320501419<32>
3×1062+1 = 3(0)611<63> = 7 × 14811936975361976113<20> × 2893419201582547140630722876441221402622311<43>
3×1063+1 = 3(0)621<64> = 389 × 1867 × 4130735009218423628905782065174736975448288016875429424327<58>
3×1064+1 = 3(0)631<65> = 7927 × 1026139 × 3688129845545438409852942740111089271467757989074336517<55>
3×1065+1 = 3(0)641<66> = 13 × 43 × 1525331 × 1434687874937293<16> × 1663870743431261569<19> × 147390107888415272711657<24>
3×1066+1 = 3(0)651<67> = 103 × 29126213592233009708737864077669902912621359223300970873786407767<65>
3×1067+1 = 3(0)661<68> = definitely prime number 素数
3×1068+1 = 3(0)671<69> = 7 × 42857142857142857142857142857142857142857142857142857142857142857143<68>
3×1069+1 = 3(0)681<70> = 131 × 1193 × 13010688596546599947627907<26> × 1475398144671508730120834597876984040721<40>
3×1070+1 = 3(0)691<71> = 246245887325083<15> × 121829445867639276545602652290090242139072129211660761747<57>
3×1071+1 = 3(0)701<72> = 13 × 29 × 199 × 185621 × 736259 × 738845467 × 1270904911<10> × 31160357553605870175480621392732932109<38>
3×1072+1 = 3(0)711<73> = 294984638384826331048078719260608561<36> × 10170021111697037216236753300358009041<38>
3×1073+1 = 3(0)721<74> = 22739 × 117485247043<12> × 11229658739992996031059261706955788780792567645986856808713<59>
3×1074+1 = 3(0)731<75> = 7 × 1873 × 22189 × 46861 × 3179107 × 363937864783<12> × 19019704578369356396789725755065110611923659<44>
3×1075+1 = 3(0)741<76> = 5815181 × 242995654571<12> × 30296635088429<14> × 558665640875791<15> × 125433387853024282821592391909<30>
3×1076+1 = 3(0)751<77> = 19 × 31 × 1291 × 415543 × 4516945831<10> × 21019329800602844759367800353109139799041028297946332303<56>
3×1077+1 = 3(0)761<78> = 13 × 17 × 40949 × 7243627 × 189330424333774697273<21> × 24171811200974383408786576437714478568683739<44>
3×1078+1 = 3(0)771<79> = 67 × 547 × 1783 × 5851837 × 29488903 × 774480196801059841<18> × 343515729084853263740131391420318235853<39>
3×1079+1 = 3(0)781<80> = 23 × 31588957 × 64560983 × 822776055137967966312899<24> × 777331654853277695714263410548853568823<39>
3×1080+1 = 3(0)791<81> = 7 × 997 × 156742903 × 274245916962662936878665224768927142918789143313534242324532556092973<69>
3×1081+1 = 3(0)801<82> = definitely prime number 素数
3×1082+1 = 3(0)811<83> = 396556147820323<15> × 7877327463333877<16> × 9603679718327062465169317706939506976097026342997631<52>
3×1083+1 = 3(0)821<84> = 13 × 9532847 × 2420779760434954733153372027991540924036326511578658182920267479056684422091<76>
3×1084+1 = 3(0)831<85> = 367 × 84631 × 440527 × 981319 × 223430768225151152811482584017892586519419195709078993848314952801<66>
3×1085+1 = 3(0)841<86> = 1661583485297<13> × 54023475012308291507621<23> × 334207792110584172091449693805941060369350577909373<51>
3×1086+1 = 3(0)851<87> = 7 × 43 × 147929130938493357761877823<27> × 6737535295047400422939574997854853936889567773370251541787<58>
3×1087+1 = 3(0)861<88> = 57704100757<11> × 78212992366947111793224659<26> × 664715300063407687268091985902707716360249006586927<51>
3×1088+1 = 3(0)871<89> = 613 × 3751676989<10> × 13044737394181493541891572756624031685359114648899761380720804186090822001393<77>
3×1089+1 = 3(0)881<90> = 132 × 113 × 250451 × 278917 × 4115541273187<13> × 81816795564710189<17> × 667865368081651529733187254777823845221359793<45>
3×1090+1 = 3(0)891<91> = 3967 × 180331 × 381318197437<12> × 564094907179255318210761991225027<33> × 19496154286820318385804086168513204587<38>
3×1091+1 = 3(0)901<92> = 31 × 283 × 883 × 16347505193<11> × 52155548314181870086767536446091569<35> × 4542139018383436278421775174894971465367<40>
3×1092+1 = 3(0)911<93> = 72 × 769 × 17929 × 1795678883533<13> × 1896995229026274291292255877683<31> × 130361051090105258563806462474876437765791<42>
3×1093+1 = 3(0)921<94> = 17 × 863 × 9439 × 1290996163<10> × 16780720353433491782468421724289387703811042473187542015809353308503757977083<77>
3×1094+1 = 3(0)931<95> = 19 × 140395141 × 770083117 × 4819894883232336708373<22> × 1001770522456725752538019<25> × 3024629329448324924475066105061<31>
3×1095+1 = 3(0)941<96> = 13 × 40093 × 6579763843<10> × 10684622854603<14> × 8187283801493673414908347666397742188102045797947618728529480372841<67>
3×1096+1 = 3(0)951<97> = 2833205979816856630365091<25> × 1058871123868630697170279213402229282716267254260527378849368062541824011<73>
3×1097+1 = 3(0)961<98> = 47 × 199771102072963<15> × 336014103925942214219<21> × 9508964463243707970091052874294858739920079951513408696616239<61>
3×1098+1 = 3(0)971<99> = 7 × 3756512436102370044614142122779<31> × 11408758412526373980350866244775600239574193508591183341548280948117<68>
3×1099+1 = 3(0)981<100> = 29 × 643 × 160883788276934627554030138896337212420228454979353247171126722797232798841636724406070681610983<96>
3×10100+1 = 3(0)991<101> = 103 × 163 × 313 × 271975894534095225991176221835439<33> × 20990446375297618944778008551499605099634313008134910244350187<62>
3×10101+1 = 3(0)1001<102> = 13 × 23 × 112455688781<12> × 608906393745935368545043<24> × 14652714986922379314736190545012031169061014220429491786130421653<65>
3×10102+1 = 3(0)1011<103> = 3184685509<10> × 4357048548962608484941710525445154377541575699<46> × 216203292699210532299880330172360087254034249311<48> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.57 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10103+1 = 3(0)1021<104> = 83301251819<11> × 1141870773049<13> × 5959534140575605571563<22> × 52922512935658165935800313758093233844200674356148904094417<59>
3×10104+1 = 3(0)1031<105> = 7 × 32089 × 1335571157005293313685597645833240585336319076853216277941261580514907200064107415536254079056908687<100>
3×10105+1 = 3(0)1041<106> = 167 × 3851 × 2172689417<10> × 522970842054278052596796307<27> × 4105406260953967323411421624379333441658282336124257972514962287<64>
3×10106+1 = 3(0)1051<107> = 31 × 4744051332993243749733574090207<31> × 203990612149063181178190673768547952947112612321147898789683681650672394753<75> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.93 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10107+1 = 3(0)1061<108> = 13 × 43 × 149 × 319469 × 406859 × 27710893469268378687085304936496533197645542536668954891993497757911796495887926681123282141<92>
3×10108+1 = 3(0)1071<109> = 61 × 2050264538747272760451120621063903142800302077<46> × 23987308437233184406133324376083302948918445967347350246327033<62> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.33 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10109+1 = 3(0)1081<110> = 17 × 470317 × 11861956980462821<17> × 4194875121286899383<19> × 2554805335672876431983<22> × 29515385542052210711260544097911301044937947161<47>
3×10110+1 = 3(0)1091<111> = 7 × 7482121 × 228966966455977967620471917769017793<36> × 25016448656495401004069927663455363536577225267399577915957403823231<68> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.92 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10111+1 = 3(0)1101<112> = 67 × 6883 × 50769977 × 822533722631126307625175578433<30> × 1934766413697553399092247719779<31> × 80515494338141194672046088158648781419<38> (Makoto Kamada / GMP-ECM 6.1.2 B1=50000, sigma=2173873469 for P31 / March 18, 2007 2007 年 3 月 18 日) (Makoto Kamada / Msieve 1.17 for P30 x P38 / March 18, 2007 2007 年 3 月 18 日)
3×10112+1 = 3(0)1111<113> = 19 × 7807361641<10> × 8118226003<10> × 10210034882989784864647209757<29> × 2439916668000842264184198385585361045416127281052552280029060389<64>
3×10113+1 = 3(0)1121<114> = 13 × 59 × 10243 × 47825881 × 319042484686421<15> × 8860269191229929657<19> × 831972291458432430035984753<27> × 339493482302125699689696823651386878401<39>
3×10114+1 = 3(0)1131<115> = 919 × 967 × 295357 × 11429625511698592200629533241927411979327821030913432739903978629728413991676984595399531610900916380341<104>
3×10115+1 = 3(0)1141<116> = 832033003 × 403233877351<12> × 1577831737746491<16> × 5185040008134360225023375060014351<34> × 10929766662867956939358630793031023525224309137<47>
3×10116+1 = 3(0)1151<117> = 7 × 176989 × 805614854347532273657889152825813219506231<42> × 300572659388749176537866923029182472055638130513953259347940318716277<69> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.37 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10117+1 = 3(0)1161<118> = 151 × 787 × 983 × 5364595726158023<16> × 4787172289684415190372122785770632962010454236261129833023534339757976679455179640719536246397<94>
3×10118+1 = 3(0)1171<119> = 229 × 131004366812227074235807860262008733624454148471615720524017467248908296943231441048034934497816593886462882096069869<117>
3×10119+1 = 3(0)1181<120> = 13 × 1553 × 438721 × 642459091110046921<18> × 2909223957003733935959638857517450326431467<43> × 18121551992896711422356563612737888923327762681447<50> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.78 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10120+1 = 3(0)1191<121> = 129457 × 97356367 × 23194910287<11> × 14024472877652688033418848086042342088954204619<47> × 731732109565129767405444811518543619679358772542643<51> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.54 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 20, 2007 2007 年 3 月 20 日)
3×10121+1 = 3(0)1201<122> = 31 × 2533733441819<13> × 5680551281721563208659<22> × 67236972872290888335676434473866511834711951165578089027465183928012262948453258565151<86>
3×10122+1 = 3(0)1211<123> = 7 × 43711 × 2655233370133<13> × 92771425356838998606541<23> × 3980297609513933332382807187105798139082232720008215213498031449569053628602395321<82>
3×10123+1 = 3(0)1221<124> = 23 × 19553 × 166235481615022500575018646587621550923191<42> × 40128811045536569808228286660052417775119260016039979721737391386749724030769<77> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 3.14 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 21, 2007 2007 年 3 月 21 日)
3×10124+1 = 3(0)1231<125> = 2767 × 5449 × 17167 × 57571 × 158941 × 64072783 × 197691309554911543479077660268414631217739335706830786585014015880624021918384268676142039645857<96>
3×10125+1 = 3(0)1241<126> = 13 × 17 × 1471 × 7673 × 600701 × 634218826805839667438296844687<30> × 19233942138039946177234105344928717<35> × 16412899871082734672605658515241235597824962933<47> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2146302078 for P30, sigma=1408671498 for P35 / March 18, 2007 2007 年 3 月 18 日)
3×10126+1 = 3(0)1251<127> = 3187 × 1775837843273505241987971241538076876967<40> × 530073245617957365009268096007895652834218165933718492937784526257953798248555640269<84> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 2.45 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / March 21, 2007 2007 年 3 月 21 日)
3×10127+1 = 3(0)1261<128> = 29 × 19573583 × 103934947 × 322172298116923693<18> × 1578349333128622133308952388255710631082915998992096274067434685677424530735030916200883893133<94>
3×10128+1 = 3(0)1271<129> = 7 × 43 × 1693 × 3709 × 481153 × 1688691118297<13> × 330470429522606563<18> × 591119036400766694459860015179609950216121761960385602854728605249929171033537198231<84>
3×10129+1 = 3(0)1281<130> = 428657 × 1109161 × 4750400686003697<16> × 30976605475761427<17> × 42631129647954533977037566338810486942407<41> × 1005832896845130922388650295627982989490898661<46>
3×10130+1 = 3(0)1291<131> = 19 × 31627 × 273253 × 48049664319064769869<20> × 15662296387277294671225933171<29> × 41041333591559226903556091015401<32> × 5915309275092388734119687813085634306291<40> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1810344172 for P32 / March 19, 2007 2007 年 3 月 19 日)
3×10131+1 = 3(0)1301<132> = 13 × 3559 × 10267451 × 885106597 × 3970843397400821<16> × 14248760853504781734593<23> × 5960458521395615500271408429<28> × 2115690668630032081669968821003525873818602277<46>
3×10132+1 = 3(0)1311<133> = 193 × 13426297 × 297991711 × 3885111721371994174857293714863962860157745941710769201332177744305621026491718623507381980843580642456489942771671<115>
3×10133+1 = 3(0)1321<134> = 602551 × 49788316673609370825042195598380883941774223260769627799140653654213502259559771703971945943164976906519116224186832317928274951<128>
3×10134+1 = 3(0)1331<135> = 72 × 103 × 109 × 157 × 567979 × 4821502235119<13> × 19159624248086059537256114689<29> × 921148200730835944300579540106197<33> × 71867188082562346821361859984554535876161847527<47> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3094951228 for P33 / March 19, 2007 2007 年 3 月 19 日)
3×10135+1 = 3(0)1341<136> = 523 × 13477 × 1075774213<10> × 5752978421<10> × 147095946235219350911667697013541493<36> × 467532449005166182402814318007788918674002841796260849988478421239468688979<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 4.34 hours on Core 2 Duo E6300@2.33GHz / March 21, 2007 2007 年 3 月 21 日)
3×10136+1 = 3(0)1351<137> = 31 × 631 × 5683 × 21061 × 5619844367191367822413<22> × 28731552996140783336205349164799<32> × 79357900169239460936673489505340712129651144134050386938660184759316861<71> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3689886608 for P32 / March 19, 2007 2007 年 3 月 19 日)
3×10137+1 = 3(0)1361<138> = 13 × 182924718029<12> × 126155302167881834100782103641129548809713983877462483723115599111940271236775421520981050242583796793870945402002290692420313<126>
3×10138+1 = 3(0)1371<139> = 2341 × 30427 × 40687364143<11> × 296243498740348121248054677331<30> × 3494236713686476798561678201951209134404038145161222453838652958294043118897029832719756771<91>
3×10139+1 = 3(0)1381<140> = 613 × 701 × 176531 × 13156471 × 5476593989<10> × 2191957616240599<16> × 6168537428391373109<19> × 405935904781531709647711583561114892568580809007984843638690234553821712672323<78>
3×10140+1 = 3(0)1391<141> = 7 × 25860237801109<14> × 12123679087138214273443<23> × 136696145417512502469827638712574449098511977307412418748966651137389231633470826169247101765890038190889<105>
3×10141+1 = 3(0)1401<142> = 17 × 32069 × 1247451965855923922740201<25> × 106149839857628546463274992773903<33> × 41556957164328385196956218832346458694372291760513828318831460900821120143747579<80> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=662962843 for P33 / March 19, 2007 2007 年 3 月 19 日)
3×10142+1 = 3(0)1411<143> = 97 × 203543020951<12> × 33690430121780543888212711166213824692220327981<47> × 45101059976427355505564135250839549784926008407968873075769527543445669278405405443<83> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.87 hours on Core 2 Duo E6300@2.33GHz / March 22, 2007 2007 年 3 月 22 日)
3×10143+1 = 3(0)1421<144> = 13 × 47 × 2099 × 4231 × 4259 × 17736799 × 74115735887240684807<20> × 120940167904876203213061027933433<33> × 81650848796699811506688800647364367461674661533783095495619303656848309<71> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 gnfs for P33 x P71 / 13.81 hours on Pentium 4 2.80GHz / March 23, 2007 2007 年 3 月 23 日)
3×10144+1 = 3(0)1431<145> = 67 × 307 × 26505761839<11> × 5502597989341811453280325654661188430257915760736811008735182048955323276663102194362600358957490858193629421824587327740094756711<130>
3×10145+1 = 3(0)1441<146> = 23 × 163365916333<12> × 1512111483928357227059586147307533255856999<43> × 5280173022660233758936952412889720282802454835751048118163212654450579862340614890525644261<91> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.90 hours on Core 2 Duo E6300@2.33Ghz / March 23, 2007 2007 年 3 月 23 日)
3×10146+1 = 3(0)1451<147> = 7 × 62162502049965253<17> × 6699066280481465227<19> × 102915420634079625638666204942525818485234829450766386797107818368315755086070464205897735709733756055701964353<111>
3×10147+1 = 3(0)1461<148> = definitely prime number 素数
3×10148+1 = 3(0)1471<149> = 19 × 61197589 × 97631503 × 108817550461206481<18> × 2428535299870600499821029291580376841317100236944884307563528984399789039459262784278489760915114603226966299572177<115>
3×10149+1 = 3(0)1481<150> = 13 × 43 × 280811 × 18451977947946169372964490164450899739<38> × 103574394682250651492366474771488310679253472549528420564006228321981430254572052540584974107852577311191<105> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 22.38 hours on Cygwin on AMD XP 2700+ / March 25, 2007 2007 年 3 月 25 日)
3×10150+1 = 3(0)1491<151> = 3757884014173930271262822327673582373969961097805606684684809<61> × 798321605638876885936868160206937968803884648888029502380986396890251623546215931267628089<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 16.21 hours on Core 2 Duo E6300@2.33GHz / March 22, 2007 2007 年 3 月 22 日)
3×10151+1 = 3(0)1501<152> = 31 × 397 × 38197 × 60017 × 2703403 × 2730124326417233<16> × 373344263955479291<18> × 62705195924448530372188252023190597<35> × 6154025449218468087679049299048266043351577284513852625291792459<64> (Shaopu Lin / Msieve v. 1.17 for P35 x P64 / March 22, 2007 2007 年 3 月 22 日)
3×10152+1 = 3(0)1511<153> = 7 × 585049 × 88220869831<11> × 12289698182411593<17> × 87212223991413427425069271951<29> × 28233780160855150696140036523537581907<38> × 27439236958583695018558967396484435036752651468698597<53> (Makoto Kamada / GMP-ECM 5.0.3 B1=81740, sigma=2715751568 for P38)
3×10153+1 = 3(0)1521<154> = 21391504829<11> × 120702410173837<15> × 1161887222229059094198302587921696702480855120609398699198129858656050707831596728698528953452207727214370278996536041206825232937<130>
3×10154+1 = 3(0)1531<155> = 709 × 8035475151373083659527183835942623308307448782043954239<55> × 5265789050328925623147256769024288482438775097245447059422020562309429069222311849609536376272051<97> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 25.09 hours on Core 2 Duo E6300@2.33GHz / March 28, 2007 2007 年 3 月 28 日)
3×10155+1 = 3(0)1541<156> = 13 × 292 × 847002118930358570602520920381717175156063<42> × 213090300524279549137442960054809434214996463074123<51> × 152031551632891694465641580404499699339343734544590141354153<60> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 19.48 hours on Cygwin on AMD 64 3200+ / April 1, 2007 2007 年 4 月 1 日)
3×10156+1 = 3(0)1551<157> = 1297177961174555143<19> × 2667221954249769199<19> × 14120876924458604253497663539366736456941609<44> × 61404594566872242448503276730228599364013338843483356019440687469832045039377<77> (Robert Backstrom / GMP-ECM 5.0 B1=988000, sigma=501477544 for P44 / May 10, 2007 2007 年 5 月 10 日)
3×10157+1 = 3(0)1561<158> = 17 × 772006355756021<15> × 7401761985090177770309<22> × 248529780208636811981353203838303673<36> × 1242618760787690302557066234608127824342363929964979635799811131131051551936554388849<85> (Robert Backstrom / GMP-ECM 5.0 B1=618000, sigma=3187509690 for P36 / May 8, 2007 2007 年 5 月 8 日)
3×10158+1 = 3(0)1571<159> = 7 × 518209 × 1248630547<10> × 14187037984758391993529228654317591874792986868087928456850474187179<68> × 4668663539228271717902874354562882580267735906322278836949839530064145731879<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 35.69 hours on Cygwin on AMD 64 3400+ / May 18, 2007 2007 年 5 月 18 日)
3×10159+1 = 3(0)1581<160> = 509 × 55231796185538374229<20> × 106712256956479168420438191693967482450298743599582395615105036976264392819677967849715055994621546022928882386524388902088895096621815041<138>
3×10160+1 = 3(0)1591<161> = 12697 × 44454007667553277<17> × 29275289584766911761299359521184239465004060018132044373477<59> × 1815549170260446417865866950799703327121370197342878399772057644753731002595701977<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 31.82 hours on Cygwin on AMD 64 3200+ / August 20, 2007 2007 年 8 月 20 日)
3×10161+1 = 3(0)1601<162> = 13 × 16217 × 1423008144349946162858538760370171851950232661831601216197627371087320523097793863040209466798848312075172776905526489296607074247821611699024290749024053581<157>
3×10162+1 = 3(0)1611<163> = 7130941393003213<16> × 103809697153908617469853075665675511<36> × 3853176322382181446159610642291595255342267<43> × 1051762253929606176068974362696177686302006839768383025664246236931321<70> (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=447522327 for P36 / April 1, 2007 2007 年 4 月 1 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs for P43 x P70 / 22.19 hours on Core 2 Duo E6300@2.33GHz / April 11, 2007 2007 年 4 月 11 日)
3×10163+1 = 3(0)1621<164> = 2693727049321118094591486398079193352608837<43> × 11136985838101413491867306813366781640721780664180020279181015243224647866545476655493916704578164265918304339860447237773<122> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 69.52 hours on Core 2 Duo E6300@2.33GHz / April 3, 2007 2007 年 4 月 3 日)
3×10164+1 = 3(0)1631<165> = 7 × 153643579 × 3358957632992895950040793<25> × 9126754553793380350961701881130062943<37> × 9098879264948989983429360562774153133639098883364585761384303273204226621258077428446473075683<94> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=1587404188 for P37 / January 14, 2008 2008 年 1 月 14 日)
3×10165+1 = 3(0)1641<166> = 116891557 × 518126347 × 1922556849772274468793737<25> × 1996780824920828139624227695148118615121<40> × 12903063841818771390850986103947680780972868837668201185568690923523136035069365410047<86> (matsui / GGNFS-0.77.1-20060513-pentium4 snfs / January 3, 2008 2008 年 1 月 3 日)
3×10166+1 = 3(0)1651<167> = 192 × 31 × 373 × 193939 × 23755628747941<14> × 447212374355192497<18> × 625649191871122082626948379908529671729699051<45> × 5575285937796913330137969587393113913079322142661733106598322245299860531890319<79> (matsui / GGNFS-0.77.1-20060513-prescott snfs / December 23, 2007 2007 年 12 月 23 日)
3×10167+1 = 3(0)1661<168> = 132 × 23 × 11240783 × 107653808874199343653823320575009810381715666999<48> × 63779447095061318423367850224578695523579815789150289866244003646649681085810329261922617536898003393691354119<110> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.32 / January 2, 2008 2008 年 1 月 2 日)
3×10168+1 = 3(0)1671<169> = 61 × 103 × 3587283476490020290143529<25> × 133103200368004275753921527821276712486591327532406362051431716830496515837378906946751049169170845802264215168161428832251246693080356564843<141>
3×10169+1 = 3(0)1681<170> = 547 × 849763 × 14923933 × 55353326319623081657<20> × 78128429892476209929315813823129326676823648239826037322173456012994919551810835086092109845502537595408447887249501891256847905505461<134>
3×10170+1 = 3(0)1691<171> = 7 × 43 × 199 × 57529 × 1526651229058273<16> × 261968755177133227477927295381326837835413<42> × 217683509057887059702713392168572709659690627314116574373411276814837715368246493032016769217598949465919<105> (Dmitry Domanov / June 14, 2009 2009 年 6 月 14 日)
3×10171+1 = 3(0)1701<172> = 59 × 2421821 × 1600388452377973<16> × 19226964394318121967711782431<29> × 454231567465961238949597490091615349190531<42> × 1502151578223577638654775137097332901436078950967469661170957656557872845681903<79> (Sinkiti Sibata / GGNFS-0.77.1-20060722-nocona gnfs for P42 x P79 / 72.45 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / December 28, 2007 2007 年 12 月 28 日)
3×10172+1 = 3(0)1711<173> = 19055977 × 42387494983<11> × 170190139057<12> × 64419666286924261<17> × 220505600678738400241<21> × 161183636530960926117651862009<30> × 43118791680011201738092517077520575807<38> × 2210508874952327084358149851144464520021<40> (Makoto Kamada / GMP-ECM 5.0.3 B1=81890, sigma=3324633473 for P30) (Makoto Kamada / Msieve 1.17 for P38 x P40 / March 18, 2007 2007 年 3 月 18 日)
3×10173+1 = 3(0)1721<174> = 13 × 172 × 174049 × 774588953 × 12611006885941538144348959163533388476292214481<47> × 46966420872041728923042134741468255845053552181689376339650679605897258834983257116186121020998659761857245949<110> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 46.77 hours on Core 2 Quad Q6700 / February 25, 2010 2010 年 2 月 25 日)
3×10174+1 = 3(0)1731<175> = 695560069 × 1643541565177<13> × 71351928287190764577186860389973946644375041147413525042917228498224426603<74> × 36779024533280465224669710936399171144239527439795317971764523788345662032284959<80> (Sinkiti Sibata / Msieve 1.40 snfs / 107.61 hours on Core i7 2.93GHz,Windows 7 64bit,and Cygwin / February 22, 2010 2010 年 2 月 22 日)
3×10175+1 = 3(0)1741<176> = 15121 × 219026567 × 1760550942973475119<19> × 13665215516791006616079599568928505553737443408115338063335149<62> × 376512035673525912981714375103400745951238068357605716524865327747958279485266707053<84> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 38.42 hours on Core 2 Quad Q6700 / February 27, 2010 2010 年 2 月 27 日)
3×10176+1 = 3(0)1751<177> = 73 × 306883 × 27571321 × 2223696949<10> × 34295441066827<14> × 347643917547496021010376334823202287471882962223991221550177697<63> × 3898971861838388511992153855470451485586777241557337666486351147434474027779<76> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / February 28, 2010 2010 年 2 月 28 日)
3×10177+1 = 3(0)1761<178> = 67 × 971 × 1181 × 1487 × 230479 × 825733 × 3109400284219346651<19> × 126785306124523882133503879<27> × 559219839704943337643116206350631409<36> × 625845632053760575390249120386323002760427242323498242975273828154385498197<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 21.23 hours on Core 2 Duo E6300@2.33GHz / March 24, 2007 2007 年 3 月 24 日)
3×10178+1 = 3(0)1771<179> = 2050459 × 12264541 × 340688242377207018081711127<27> × 5069346827014420672241942756293<31> × 690732220068543526727568186205626712603241853899400661384995347253624067067728995244495344555464573552973589<108> (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=1794784119 for P31 / April 1, 2007 2007 年 4 月 1 日)
3×10179+1 = 3(0)1781<180> = 13 × 7127 × 5174677 × 1117157777<10> × 167717010985879<15> × 3339613976591229119259320197203139774767853553791481874729761460795419995848020835478379082095535623034053752302201130407369915797564759568306961<145>
3×10180+1 = 3(0)1791<181> = 661 × 430259544631759600727768857693217721153099730144795861<54> × 1538326517326993101925943385140082111132168130040478949<55> × 6857104304052897516728603587977821413916030196167551914714888140645269<70> (matsui / GGNFS-0.77.1-20060513-prescott snfs / March 2, 2008 2008 年 3 月 2 日)
3×10181+1 = 3(0)1801<182> = 31 × 163 × 45831510539<11> × 129541161070962276375524706597797231237380084278534888904236011409595074063067722554009382796484727145428087893614131520398789497295078620266068259167231776212559687903<168>
3×10182+1 = 3(0)1811<183> = 7 × 184711 × 7889052315362488613741228856217<31> × 11735682321665466429260422263096870074719<41> × 2506093524035973475056243745303107978159574127232539987471423928398343143614831973004552648105617964923431<106> (Makoto Kamada / GMP-ECM 5.0.3 B1=81970, sigma=4128059153 for P31) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=4493511091 for P41 / February 21, 2010 2010 年 2 月 21 日)
3×10183+1 = 3(0)1821<184> = 29 × 114790045871334151<18> × 1101389595565427900135637266257614239472879203677<49> × 818235010066326138538100859598190229483882089378270186381507788966713023837462117831003813129078116756632188914525247<117> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / March 9, 2010 2010 年 3 月 9 日)
3×10184+1 = 3(0)1831<185> = 19 × 196797409 × 10762263913<11> × 745494836636572130172819523037276149944686381269674094578751262163539451085510590830500109309643116762278895320239001816323158684183587595033024231399271515596849987<165>
3×10185+1 = 3(0)1841<186> = 13 × 2023746225668777<16> × 36720090322313647694051<23> × 310540401257397737348038834696050663179011279285556879255610037091646723630434622079930149152479120433809319536685872800872343331623558391188304351<147>
3×10186+1 = 3(0)1851<187> = 439 × 169819005840667<15> × 40241155283092480818038774787149275870934631476611728723408637074158659177368013036434976879754984472537487184954630114161470383022045784968026778476870122069983476991877<170>
3×10187+1 = 3(0)1861<188> = 1990243 × 16565261 × 909948611529811412934384541301540732469732845232998558343616864089988451756330466262286003545679220186522513929107253571677653491327174671386973154651393239832076783199266487<174>
3×10188+1 = 3(0)1871<189> = 7 × 37135242979<11> × 9561060331429<13> × 13649588948170686463<20> × 8843237995130879985234228749128009724370323877568816254715812236482263635980946446461438878364758061388356047345722471760315601906705188372132071<145>
3×10189+1 = 3(0)1881<190> = 17 × 23 × 47 × 163247537682973281819665886706208848016542417151874625891059476519562496599009631604723295423627360287315666322032976002611960602927572509114654187299341568264678674429994014256951624313<186>
3×10190+1 = 3(0)1891<191> = 337 × 613 × 71359 × 799217773 × 2546343508839486516207701265886984349789271759336639159658352387359208880453389197974991386928337275420727244285163037733738941426151492090978763689643407394343548617013903<172>
3×10191+1 = 3(0)1901<192> = 13 × 43 × 41981 × 90059 × 222941 × 1235130679<10> × 8247897299<10> × 94927819198801891456854631<26> × 3509579947593832172401267969183483650808143002961993244596581<61> × 187600851274178017217228137473536104234402691756912413319983272561371<69> (matsui / GGNFS-0.77.1-20060513-prescott gnfs for P61 x P69 / 321.19 hours / July 3, 2008 2008 年 7 月 3 日)
3×10192+1 = 3(0)1911<193> = 151 × 791442937966190685229637395742267041720820331589<48> × 95011290548333356448178869786693410025075222062601524884381341878748749<71> × 264210140483694895177251228728197166603387493603667452462313902636578791<72> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, Msieve 1.36 snfs / 179.21 hours, 14.43 hours / September 1, 2008 2008 年 9 月 1 日)
3×10193+1 = 3(0)1921<194> = 228341 × 2462075533<10> × 5473356377065602643<19> × 1357719580098568998126229180312398158519931326779674308289602420380859<70> × 7180789172182775973577426596013909673703770702149408919816860214616948145656893782613577841<91> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / March 18, 2010 2010 年 3 月 18 日)
3×10194+1 = 3(0)1931<195> = 7 × 866651964229863762194029183<27> × 1540084418980857995257740189234537478220352847657<49> × 32109530978789813076257271286037083314295510350785006014514115403529785261917835776309897020262345060817683184264865953<119> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / March 19, 2010 2010 年 3 月 19 日)
3×10195+1 = 3(0)1941<196> = 2365233400223<13> × 4915625836818566124998293249332798002360191887638124020580909572598083179927780627999<85> × 258028948925019110925715656428927027410556073088642267531522278297928175897925446469202468246731713<99> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / March 26, 2010 2010 年 3 月 26 日)
3×10196+1 = 3(0)1951<197> = 31 × 223 × 11497565766727360956446718343<29> × 407860889630656506903738929464770934061766319<45> × 925415423037303753227949702423743909751718736584773967255509688489627341939861040910900541585089644524606114420502450681<120> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / March 27, 2010 2010 年 3 月 27 日)
3×10197+1 = 3(0)1961<198> = 13 × 10902448059185532910215851<26> × 1519936277907075536773984208930536626555103828499<49> × 29528257939777274468836163988499378044170730966997<50> × 47161832259808362402554552344067823944554851805496831500366081091347694209<74> (Jo Yeong Uk / GMP-ECM v6.2.3 B1=11000000, sigma=8431913116 for P50, GGNFS/Msieve v1.39 gnfs for P49 x P74 / March 28, 2010 2010 年 3 月 28 日)
3×10198+1 = 3(0)1971<199> = 1833911383348466522566074446250134380140228731863510782284501695384966021186952971<82> × 1635847853521917851052479217771526282232255683407487990801439756907074080101789715314755512178980013517705612191904931<118> (Serge Batalov / Msieve-1.37 snfs / 20 CPU-days on Opteron-2.6GHz; Linux x86_64 / September 8, 2008 2008 年 9 月 8 日)
3×10199+1 = 3(0)1981<200> = 131 × 229007633587786259541984732824427480916030534351145038167938931297709923664122137404580152671755725190839694656488549618320610687022900763358778625954198473282442748091603053435114503816793893129771<198>
3×10200+1 = 3(0)1991<201> = 7 × 433 × 610447 × 185263117033<12> × 2828858023360747867<19> × 71946058619987082202263149427813166064374899283502749388197<59> × 4300116574491911801115912993309512435558547293389634753775725666616660740182152959048556470675322021079<103> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / April 9, 2010 2010 年 4 月 9 日)
3×10201+1 = 3(0)2001<202> = 113 × 13451 × 702444933864903884262888346194011636329<39> × [2809803530740859090300663124592054881562783203942055737290014283958710621074071662219239930982958785755471809745984251020479345721645446240439635474365132763<157>] (Lionel Debroux / GMP-ECM 6.2.3 B1=11000000, sigma=2501388372 for P39 / May 29, 2010 2010 年 5 月 29 日) Free to factor
3×10202+1 = 3(0)2011<203> = 19 × 103 × 181 × 5197 × 16296679981305904562190862947062197744220184304162421569396041818582393538791404826121299082304779195497976533866185806252403688999267702709590692699666280770157346221557626470891550060557946749<194>
3×10203+1 = 3(0)2021<204> = 13 × 12839429 × 4286844554107369<16> × [419270644997684661946064945726094215262053317076179039826079568393349006546063667096061987406020969177815218413921978320430841332051838589415197230637645372628779740301029608125977<180>] Free to factor
3×10204+1 = 3(0)2031<205> = 2130343 × 77146733557<11> × 4508646387888076516159812297104455310980425763<46> × 136352371861637667035598724582234184278157697550214899<54> × 29692400293299388694525158836852711772581252961928331541053853915952443958144954689372723<89> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=4214310264 for P46 / December 21, 2011 2011 年 12 月 21 日) (Erik Branger / GGNFS, Msieve gnfs for P54 x P89 / March 15, 2015 2015 年 3 月 15 日)
3×10205+1 = 3(0)2041<206> = 17 × 1764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353<205>
3×10206+1 = 3(0)2051<207> = 7 × 643 × 115123 × 581863 × 526658621893051<15> × 238598149130221133501999455213<30> × 100651789626655200833466878334448081557013<42> × 78670449498183592681888274570136186746596501478832668972272557256898635392279893433309981142981445435545771<107> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=4252951790 for P30 / March 31, 2010 2010 年 3 月 31 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=502802239 for P42 / December 25, 2011 2011 年 12 月 25 日)
3×10207+1 = 3(0)2061<208> = 70390259 × 4472835397<10> × 26842753488248560481152841749693<32> × 354975771965862035298670738788755565144949832032893007546359835559295613218559618642700904670824505996960902329355925213755171413420832648609888076974295662059<159> (Serge Batalov / GMP-ECM B1=2000000, sigma=3860964342 for P32 / May 29, 2010 2010 年 5 月 29 日)
3×10208+1 = 3(0)2071<209> = 2707 × 19483 × 130045789 × 66548032112661598492136396571008011<35> × 65727279517384151538281843257462452720273361898184675641627389815155544746740419120885977894330600530517415712079384731477173544924846956670868332339523638399<158> (Serge Batalov / GMP-ECM B1=2000000, sigma=792812118 for P35 / May 29, 2010 2010 年 5 月 29 日)
3×10209+1 = 3(0)2081<210> = 13 × 11083 × 16127 × 35298027013683753031211625713<29> × 3657771334602970156065024492045797111272570407882412293127535397434057728384835779976596185051791197131245194540853336974497011665038466298904885432769697762216316205337569<172>
3×10210+1 = 3(0)2091<211> = 67 × 4096744513<10> × 20058899789060722980163<23> × 181524284630299701878178130303474629755299<42> × 3001689241690451329713541597313797470230443615174546667029017955346365264676506259574766350364335443237322238630987275822531966751885363<136> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1607468624 for P42 x P136 / September 26, 2016 2016 年 9 月 26 日)
3×10211+1 = 3(0)2101<212> = 23 × 29 × 31 × 647 × 6354092320620653651496654609613<31> × 3228069563074556482026347898069185253244041491317<49> × 109328412202765316382100118216919230803635718488549665063810411956077343868504526039670282237312740949463687045947483385475899<126> (Serge Batalov / GMP-ECM B1=2000000, sigma=1839554095 for P31 / May 29, 2010 2010 年 5 月 29 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=209364710 for P49 / December 25, 2011 2011 年 12 月 25 日)
3×10212+1 = 3(0)2111<213> = 7 × 43 × 157 × 397057 × 3797041 × 4210725817858195841984354613142505480034196400366581412596997183783085151029111166965230959862806245072285808011170431019149616597387393965640268993080842111849428098912232483767613522866982135289<196>
3×10213+1 = 3(0)2121<214> = 3907 × 457960152641863827659879437<27> × 58645297242391037198011550024209<32> × 28590184646172370467664812486509967655698788190054294292691094195932969692558101849300428943530634662469929096108401979987535278174571202772869059312871<152> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=102929466 for P32 / March 31, 2010 2010 年 3 月 31 日)
3×10214+1 = 3(0)2131<215> = 1401042277<10> × 37393657014313<14> × 83408005966249<14> × [6865376124268277641725610599680575904604174872585155128438746233312953819729456214086825668154896965229462826635076284490070997248760896589445990905661481152287816443449023841949<178>] Free to factor
3×10215+1 = 3(0)2141<216> = 13 × 179 × 1357351 × 5280129244847<13> × 17988218368554241499373069710797363782102691003211423884995854866539459028619620393299561990270857378154894825863267181995765955008092419643438214449973174265432834452352613693252841707772726479<194>
3×10216+1 = 3(0)2151<217> = 38803939 × 1567851421<10> × 1092224389639<13> × 2355584701403960042576444920681<31> × [19165931969960866642653491954843234962725497066351311448326047128820122256685013043388850155351895759375915684117918232035083722593135881177462736702792110681<158>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=652620030 for P31 / March 31, 2010 2010 年 3 月 31 日) Free to factor
3×10217+1 = 3(0)2161<218> = 228983 × 850061 × 29696573280804581<17> × 5189930996508257696989086012241344563360046239190708004723754109142965078261418368068821650599691452443857517166708715017873956056358345575771215116808574474230228850925964707087317714840167<190>
3×10218+1 = 3(0)2171<219> = 72 × 6122448979591836734693877551020408163265306122448979591836734693877551020408163265306122448979591836734693877551020408163265306122448979591836734693877551020408163265306122448979591836734693877551020408163265306122449<217>
3×10219+1 = 3(0)2181<220> = 853 × 18199 × 1218866044969<13> × 158550903017141020943362316384739584015996693990746807863308542029991380818515930134971417578743780393338596589867294092742426923402137478964602129674663856340802029884572819811278200411715709522706707<201>
3×10220+1 = 3(0)2191<221> = 19 × 21642949 × 4926428083<10> × 9850669309731121<16> × 200479287844425914803906947933089393470609<42> × 7498662712740437292546816503977186364696999749983462768757854303271779365656586356910927642878046520830449531708674198093542604799135158948444133<145> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=228017553 for P42 / May 28, 2011 2011 年 5 月 28 日)
3×10221+1 = 3(0)2201<222> = 13 × 17 × 593 × 31564114277992745624998768949<29> × [72523821545662415419969757826748890016156505491919261824962604444912023975376541267924071006797863676960563568491516552443718433546024880792492253867935571094221623238722232855375564699633<188>] Free to factor
3×10222+1 = 3(0)2211<223> = 48892312325764339<17> × [61359339685374569030760614312622356889456128629880055322156745802779292768290019266229866843673958507270766319365550067430206264579867435712190744786075728692198966550047156807409261885692202474073758336059<206>] Free to factor
3×10223+1 = 3(0)2221<224> = 360953 × 10585064621<11> × 7851942042646234145655277745479334676995008397978476915318273720122737763299398587054708767635236390815808939125499343020823317053320765524830566867992347300204715193721075011019714108916277721770015071252877<208>
3×10224+1 = 3(0)2231<225> = 7 × 423420739381<12> × 101216447072941769175048199047825792268610432902773527602058313068974734049523656384422738585773616194938220474329862374604139496655513864466393934699185265987804051600291391213943639176895231427150429878680419003<213>
3×10225+1 = 3(0)2241<226> = 3420023 × 17709622882130900231686107278159413<35> × 49531663609271321240731339281949464597288511551906465831875979553492634979397909534653881559914860856742042902698120119288261704497859065964974235553379418986054947130675219844282623499<185> (Ignacio Santos / GMP-ECM 6.2.3 B1=3000000, sigma=1705652662 for P35 / May 29, 2010 2010 年 5 月 29 日)
3×10226+1 = 3(0)2251<227> = 31 × 5725037010657586005784923241<28> × [169036799881353908256619389179847443093187167657478943750698415850411287771572363864945503376709142857534554461238682494958900816774621899245113926846138828944586842398837961305009062707068487687431<198>] (Serge Batalov / GMP-ECM B1=2000000, sigma=3753751540 for P28 / May 29, 2010 2010 年 5 月 29 日) Free to factor
3×10227+1 = 3(0)2261<228> = 13 × 196477 × 169489433 × 414912078193217092793<21> × 1670196156214918175868922203327155764167445597680333096186951423945293867015486247244213279773288478881675847618811134681353114644649619221498112923194247290277102620738452851533722933077251929<193>
3×10228+1 = 3(0)2271<229> = 61 × 619 × 8191 × 5445202831<10> × 83917541711533<14> × 55343003957923963<17> × 228822563610033969085327093<27> × 1676237123171481182917902856170098984196930458501396706472766143949602671721074163084770363214205366192013833964535989177794169605699761628965771797441997<154>
3×10229+1 = 3(0)2281<230> = 59 × 810224431 × 169438278481<12> × 55114163146995985285657076449211<32> × 37861965412109558108754843302777207<35> × 1774949521185831307048020576588298519169517077148634277149576533232187739150660110778384833934723350126669327337055798316483342855926094782337<142> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1756314111 for P32 / April 1, 2010 2010 年 4 月 1 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1763971781 for P35 / May 23, 2011 2011 年 5 月 23 日)
3×10230+1 = 3(0)2291<231> = 7 × 9802519 × 1483588383538821672841<22> × 41293479384736954180562583661<29> × 2825447634704980727833836014391810801063991009<46> × 9510140573584241263382623159573589012647961495675617<52> × 2655928752548787092486729682033752870280277264518405968052615927000842616349<76> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3449506571 for P46 / December 22, 2011 2011 年 12 月 22 日) (Warut Roonguthai / Msieve 1.48 gnfs for P52 x P76 / December 25, 2011 2011 年 12 月 25 日)
3×10231+1 = 3(0)2301<232> = 3596842811<10> × 34444004789909479<17> × 296884667473161175833778413493640397233142013<45> × [81563975569354948054017619896132578313813596405288388606947608743573301361487411642603760416319469991417709573137957547720476997629430605508649166449044809373433<161>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2551558429 for P45 / November 17, 2011 2011 年 11 月 17 日) Free to factor
3×10232+1 = 3(0)2311<233> = 283 × 1636011547<10> × 188379773774699791609038100624118443<36> × 52213801379936356632670975526388402493461661<44> × 6587625026680440949779084779344205291581932919180897405552876854199114576538377048263941820793750032274820071795086856470338416131923453135287<142> (Dmitry Domanov / May 31, 2011 2011 年 5 月 31 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2366215269 for P44 / November 17, 2011 2011 年 11 月 17 日)
3×10233+1 = 3(0)2321<234> = 13 × 23 × 43 × 9906271 × 31051173148619645635150291901<29> × [75856603527707462533597216608203050887982264928059751909406233807250262372918346402268499717026111465843867204537852493713612015549600176802184209964589035039966380906766892883608549057263686883<194>] (Serge Batalov / GMP-ECM B1=2000000, sigma=3128375383 for P29 / May 29, 2010 2010 年 5 月 29 日) Free to factor
3×10234+1 = 3(0)2331<235> = 770239 × 3894894961174388728693301689475604325410684216197829504867969552307790179411844894896259472709120156211253909500817278792686425901570811137841630974282008571365511224438128944392584639313252120445731779356797046111661445343588159<229>
3×10235+1 = 3(0)2341<236> = 47 × 57601 × 6361879 × 208766209 × 88595079564318036149591187074095414249<38> × [94175549172779417357018598509228787610601452340729790228375896061607583717356272715758574055019478531906785624345499242650209133877264896007123950409420960025311160302154571297<176>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=947518513 for P38 / May 30, 2011 2011 年 5 月 30 日) Free to factor
3×10236+1 = 3(0)2351<237> = 7 × 103 × 30091 × 486360307 × 73138918988341<14> × 148320878148563284112654936869<30> × [2620839467600335581619534769497130842506747729508160701527575059944051429500879686436064878786590137750833813882180130655491766660070330053368837276759260368486158747898386017497<178>] (Serge Batalov / GMP-ECM B1=2000000, sigma=1069467428 for P30 / May 29, 2010 2010 年 5 月 29 日) Free to factor
3×10237+1 = 3(0)2361<238> = 17 × 2667134504288670839385615754878397519979079571003<49> × [66164862683728473559694505736308364670744706279515302935257066704999251211418310410157365822911722064474139927143839635522136212415560416164300604994170561187178134927330013719469433120451<188>] (Dmitry Domanov / GMP-ECM B1=110000000, sigma=264913779 for P49 / April 20, 2011 2011 年 4 月 20 日) Free to factor
3×10238+1 = 3(0)2371<239> = 19 × 97 × 41876475285637<14> × 112704069315477840223357<24> × 16148085928627688816266155319833319<35> × 213582246612729634050398264948490534941455006982589151030227365428330659487400296784840486683195867288290975896875903690907973969079798705939833650466235855835074717<165> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2672111448 for P35 / March 15, 2011 2011 年 3 月 15 日)
3×10239+1 = 3(0)2381<240> = 13 × 29 × 1259 × 24517 × 799238177 × 205029801637<12> × 157323512904309133040178948468579460755074286526751693673571928587061099197798748936246532222545495382946169374225886635575365877484252884661681497293367191894095815403816969173179025849821190832476854393853779<210>
3×10240+1 = 3(0)2391<241> = 1021 × 21517 × 58771 × 48326347 × 203489833 × 24202428447700806869862211<26> × 317008955546132999609695735876891746340489381<45> × 30795946249333219676327887613371784972635456114149816941349495621056119910546387848010198620990679661736104974435876379297406992953662319096863<143> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=494451458 for P45 / November 15, 2011 2011 年 11 月 15 日)
3×10241+1 = 3(0)2401<242> = 31 × 613 × 3316823 × [475966941950159124878533163036082507348133251352662442728703178084257627746841694944490832075955055145404635711879658217155068716446972308201384652156305548038775789056243616710065762654912482844700307901994591745691376198780178629<231>] Free to factor
3×10242+1 = 3(0)2411<243> = 7 × 109 × 17509909 × 45137623 × 103181587 × 785705389233977380843<21> × 6136379458894908694050113270559941361253200574052967147373551598308712113300798585525353622301487685749018417101851164311286655957748352967339103228525587616407228534143053090353264148966126038721<196>
3×10243+1 = 3(0)2421<244> = 67 × 70849 × 623727802744831<15> × 65775715912534631119<20> × 1422516421325769746021<22> × 10335043661306300080219068335412751<35> × [1047809751987914244999083320306559154270761118439100309019537500298746532134308160853219164412564080798299416369349071620842711671328092995877088913<148>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1941766168 for P35 / March 15, 2011 2011 年 3 月 15 日) Free to factor
3×10244+1 = 3(0)2431<245> = 3319 × 70900382372572643536543<23> × 127486860101192294193224925234476870619945535375061090686099582237642817581891477013776789890690940380738887345721712168354414858986019385139767472715937575987173836031450279407128834215462875890941926113344187946766553<219>
3×10245+1 = 3(0)2441<246> = 132 × 2281 × 5497433 × 1446434809<10> × 4702201735367<13> × [20813695545456884431341364826343817956218338814073250475963784574551016611746660584682829696896576668646252008369278651603546762270830279377114030526084559487015217498237239572119195788987340252000783421712213591<212>] Free to factor
3×10246+1 = 3(0)2451<247> = 991 × 997 × 13295257 × 636706789 × 668599510824467436163<21> × [536475841964916331754190105958057471518855027124270932416616259883834417254764400198353111625806958475783538545614520505233103487370783522642693041118544449889534702159361370160528689793749445774080676037<204>] Free to factor
3×10247+1 = 3(0)2461<248> = 413704583 × 7466749431529<13> × 401922978396271<15> × 24959054610976291683350605218137<32> × 72956298068347930372910547505391587<35> × 13269837017974873953241877266863948728915789327924537640284631876889654984503605449785766525841407995703223267663489194716347118620716851916944307<146> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=4100507988 for P32 / May 20, 2010 2010 年 5 月 20 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=835559662 for P35 / May 26, 2011 2011 年 5 月 26 日)
3×10248+1 = 3(0)2471<249> = 7 × 1741 × 4441 × 2883313 × 6785978918485807<16> × 148308294897417575430637827379<30> × 49519853466820491274637255083159<32> × 38573991591189199743616066646959896782134957943494859969290630955917249474940668923604109337677322883874076383475936537677869571836050686327341619488477443553<158> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1608926838 for P30 / May 20, 2010 2010 年 5 月 20 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1884966465 for P32 / March 15, 2011 2011 年 3 月 15 日)
3×10249+1 = 3(0)2481<250> = 2861 × 9277 × 71671 × 1000847 × 127689613 × 95805397904451481<17> × [128806901978980359409738747388806547013898035251822831114062354854548937963049409767595401352140833214846337696977400063172044390444414858743945998394647971068384994921191809082292693741847522943989103759453<207>] Free to factor
3×10250+1 = 3(0)2491<251> = 397 × 1153 × 27962809848703099<17> × 293227611564297957512888497<27> × [7993109606128662973266651333876029762859054831259374862240374941861670854158938665127501128334136125132561237821940015288266159519736262144626461199658916400914008194805022793627386971595885452076421487<202>] Free to factor
3×10251+1 = 3(0)2501<252> = 13 × 659 × [35018092681218629625306408310960663009221431072720905801330687521886307925761643515816505194350414380763394420450566125831679701178942453601027197385315746469008987977121512781603828644799813236839033500641998365822341543130617485700945488502392903<248>] Free to factor
3×10252+1 = 3(0)2511<253> = 12938080798470947705749052103360944725831<41> × [231873648551842939046611413051851698482017757979169036049236109359505393630745844670462927956546698253549359385145483775614051114255389273927428379215080571212836637409007942644958126151974837809969547239713086071<213>] (Serge Batalov / GMP-ECM 6.2.3 B1=11000000, sigma=990941280 for P41 / May 30, 2010 2010 年 5 月 30 日) Free to factor
3×10253+1 = 3(0)2521<254> = 17 × 1249 × 53925306199<11> × 3077327770739<13> × 1508282125501437885266222651<28> × [5644960857073993641072851777527068718794146356864889512851514025946918142282636970399881527019550577723926166207818641929417483422712969233280359100584921332150916092367931366448422914731253966608727<199>] (Serge Batalov / GMP-ECM B1=1500000, sigma=3820304387 for P28 / May 30, 2010 2010 年 5 月 30 日) Free to factor
3×10254+1 = 3(0)2531<255> = 7 × 43 × 10861 × 3273366076862041<16> × 28034342061398860440157467846211482230090049902713473325394592092619533260392247661843991893208723338266433484665206749998537974900418362140832610160965010004662091955202305669635873212044576015554450021974164046616177248397106942401<233>
3×10255+1 = 3(0)2541<256> = 23 × 149 × 233 × 6043 × 1041614209<10> × 596886476624441888490161864666258366204448569211039704103725967854196506914204692544563011008192525869003393669702176468677222214040664904378298726396960610677796804420469518237288465300215428311445542877649780298144352944092113559630953<237>
3×10256+1 = 3(0)2551<257> = 19 × 31 × 1279 × 280321443907<12> × 121170363995690892398461170637091496989198314304767<51> × 1172418550583598280746508399055638757195321311347641842030083500449969545610957092537652644960131593336022151349167272644256170151146080641826935392165692199616789294122084012139602109399959<190> (vanos0512 / GMP-ECM B1=110000000, sigma=2021938529 for P51 / February 23, 2013 2013 年 2 月 23 日)
3×10257+1 = 3(0)2561<258> = 13 × 27631 × 17787271 × 3696755072545627<16> × 605779845717838470216592120293159678987915522774228269<54> × 20967008920303438602237113913846126438807567401067291765131557207858733453800061717125038711577338452207750068457171887294998735442441880760423901550198457691792987459724626979<176> (MarcinGorecki / GMP-ECM B1=110000000, sigma=390679050 for P54 / December 17, 2011 2011 年 12 月 17 日)
3×10258+1 = 3(0)2571<259> = 7369 × 13200283763129851<17> × 7529192032761485431<19> × [4096199092030108689027396413261396247268527980024021048198182524032481442629859115030285500847730683654624793159820718062972108147404555458005220930156188761387794045743384915318584822821948243287406616286943541409539709<220>] Free to factor
3×10259+1 = 3(0)2581<260> = 409 × 1123 × 15241 × 5025857 × [852696734598692919636690222383258195692453084808166984639682171296665832258040671506746325952590075623875048891910281837727427556939084473950469883060956742895334893372592147501199503507370695053511302048271210464931213185143332529621238914539<243>] Free to factor
3×10260+1 = 3(0)2591<261> = 72 × 547 × 11113 × 463033 × [2175176938007639028199773101096420168885973882450078144189966802807305134415090808275143263619558107633191232974185729442563392913385690734700522734706997163480165924458936818596825552597458188772315336433021901578154760175831781236072976769199323<247>] Free to factor
3×10261+1 = 3(0)2601<262> = 995863431769667443336990081330167014392385069<45> × 3012461251508096244574336726991311286454428373180167054554775172659618286079599901521371639106392399618853565916455447037504613089904933947635790029291756053245784457959207979705517161548329550867558313109271785157029<217> (Wataru Sakai / GMP-ECM 6.2.3 B1=43000000, sigma=2062534725 for P45 / July 5, 2010 2010 年 7 月 5 日)
3×10262+1 = 3(0)2611<263> = 163 × [184049079754601226993865030674846625766871165644171779141104294478527607361963190184049079754601226993865030674846625766871165644171779141104294478527607361963190184049079754601226993865030674846625766871165644171779141104294478527607361963190184049079754601227<261>] Free to factor
3×10263+1 = 3(0)2621<264> = 13 × 9409198081<10> × 4194071823049<13> × 97457104250633<14> × 576802340910031<15> × 1257535432763607762277<22> × [8272345783747049643823846570564397295878452540592213642883044871173872589470625525805440774811265099636434589014732389710183570328895868566237951265712128308703683816457894747109105550313823<190>] Free to factor
3×10264+1 = 3(0)2631<265> = 456193 × 365309294121229<15> × 81124487796131374933953256217822203<35> × 3336432524667045190403367271440308587<37> × 66508568773973659966913682194011151884691539379982370563533521940785287925984075375919796364361550889477036062046085713393857626272320141337067981806434268229771085609917053<173> (Serge Batalov / GMP-ECM B1=2000000, sigma=122502563 for P35 / May 29, 2010 2010 年 5 月 29 日) (Serge Batalov / GMP-ECM B1=6000000, sigma=2544205403 for P37 / May 30, 2010 2010 年 5 月 30 日)
3×10265+1 = 3(0)2641<266> = 857 × 887 × 39465427627641059304698096056219817169828943681519261101953670218993657905780238081769735015963765475380808488750379854740916045195807719174541115740259603582934622888106304075857813957343134791537033699528651242700540281704222406101881316935009649297054958239<260>
3×10266+1 = 3(0)2651<267> = 7 × 24781 × 90901828797363532862887<23> × [19025311071937463686416066516162133952856804184621001113981066024382212544394654099181492243223818548893988699916389805184919492810219408157000155932646210153055004391504693446587329695677673463732554473187471052151366988785040529028610869<239>] Free to factor
3×10267+1 = 3(0)2661<268> = 29 × 151 × 1889183021021281<16> × 60551292405574961408598307111<29> × 1095859333660423976064955560344327<34> × 27862282737290655054973624447312377192764612797301<50> × 196145050069417527721491788279730723443696233903980326594082215831159349951043138463750634388076980064826730571420098330684294341016071767<138> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=2701436481 for P34 / May 24, 2010 2010 年 5 月 24 日) ([AF>France] intello222222 / GMP-ECM B1=110000000, sigma=2974508238 for P50 / December 21, 2011 2011 年 12 月 21 日)
3×10268+1 = 3(0)2671<269> = 2437 × 1239822140193241537989469519<28> × 2111358305276849849527821549308423484012312811<46> × 4702668841008920492170175909917886453687111593022828176799287978610229362708443854575376214581288395226233196000246355095218547951953873911534852816727314764266762161487137630700784785737561897<193> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3883293123 for P46 / October 24, 2011 2011 年 10 月 24 日)
3×10269+1 = 3(0)2681<270> = 13 × 17 × 199 × 6101 × 35381 × 5489740642917722529459594079502078563<37> × 5756426302938983720160829130986979084026383460075716045927443671593639203682554501398569708265773159494460460605107609046969295596935695085593920532025825692329299885309955247924804077786358932253582231682677335418780073<220> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=272020628 for P37 / June 18, 2010 2010 年 6 月 18 日)
3×10270+1 = 3(0)2691<271> = 103 × 2497721256180943286569<22> × 160373663103015337247527779487969063694544048771427<51> × 72712154154959470713399170878250703414599069707954289650093268017944827787689846273362564231827636405220015694788961174887668091960682698867638388416091446164778746160733358645706529976201806566709<197> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=796250227 for P51 / May 20, 2011 2011 年 5 月 20 日)
3×10271+1 = 3(0)2701<272> = 31 × 167 × 261407 × 20436038468831475601<20> × 113309604551471709859266017<27> × [9573317031800315424877126540248655962241191133253887071723976705238847276510200341547929087806126099307553924951449221754828761460154270087058270566413115436554468072063735455431403201765205885625451859746394121027527<217>] Free to factor
3×10272+1 = 3(0)2711<273> = 7 × 449011 × 1425738908541502279741<22> × 203562626166203345686482619687<30> × 233573179265757988538055341875342618729310094135577<51> × 1408008300830900148789511765862776008469769697407661776957286619121283939599358477651528003975444272474502791269815721706085832174250339872071035674318014289537140607<166> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3724094261 for P30 / May 25, 2010 2010 年 5 月 25 日) (Mr. Hankey / GMP-ECM B1=110000000, sigma=3238627378 for P51 / December 22, 2011 2011 年 12 月 22 日)
3×10273+1 = 3(0)2721<274> = 18133 × 118007505179<12> × [1401980471272873883769402744804350434108910384144617046522644822910461561611258796556087689657217407769871149253916414239473539404266931442993393579069083650886638060942294169326399550655505657058200368835215095159586571307252319315562702991698247256814287943<259>] Free to factor
3×10274+1 = 3(0)2731<275> = 19 × 6037 × 10981823581<11> × 12306640869577<14> × 92913806868936457<17> × 168797818590160201531282269164086483207<39> × [123391545471527948399894858190375947877065306336434077097491713391762409500088288001266308749433759893489400825111047552459669920134326897542050404183622566874090098006564696542585776181426909<192>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2313278193 for P39 / May 14, 2011 2011 年 5 月 14 日) Free to factor
3×10275+1 = 3(0)2741<276> = 13 × 43 × 44580128531831665779997688108049277<35> × 12038382287585459703839432541116837354433232334250492231456338768652490571833935651521884124821554321358326418869145481047809407759985133341905470662958583084863869395699060355892411768241000421659559205945593692022074858120613188556923707<239> (Serge Batalov / Prime95-ECM, GMP-ECM B1=3000000, sigma=8194046207800848 for P35 / May 29, 2010 2010 年 5 月 29 日)
3×10276+1 = 3(0)2751<277> = 67 × 36062360775416078848118422441405728135745511279089<50> × 1241630288206456404038894605201664381057098003244799990825828710652382391581704177985876415989050916401184457833671478786896751273678685232199635154782865113751989177703431054191433682016359606334550323003418240637090963456027<226> (Grubix / GMP-ECM B1=110000000, sigma=2532303676 for P50 / April 26, 2011 2011 年 4 月 26 日)
3×10277+1 = 3(0)2761<278> = 23 × 12757 × 14923 × 1118850578960063<16> × 1739160682129458449683<22> × 19719469844614430686573<23> × [178558977305554370892270499947060154776506565654981139645949472833031735496936490234865719069453058890184242606518631072932319369658953103380653895017970567893768869425114486103720717767924943556672198299178201<210>] Free to factor
3×10278+1 = 3(0)2771<279> = 7 × 601 × 1047480289<10> × 24521561397666811964281<23> × 94334098721000996950744300639<29> × 626115805699450185469519554311884183<36> × 47003629177431291093023220945166238521421617154032067261832992440160505648986037394897154046043643065681786137904834565616161585076229547587351810036482389503561740830634773239471<179> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3903547347 for P36 / May 9, 2011 2011 年 5 月 9 日)
3×10279+1 = 3(0)2781<280> = 1518060001<10> × [1976206472750611653853858441791590291693615343468890990165809658270549478762005797687834606215937047141788172310851894977239440485066834983421712591451120119460943494024647580448304032483364272503481896299565302886865273515628319357845988065131820833740549890162081940001<271>] Free to factor
3×10280+1 = 3(0)2791<281> = 11091219297373<14> × 3655852816142757196069<22> × 40049069614558054280307962562823<32> × 179806994415353386413053301196877491806559<42> × 1685830117608555878024162213368547954955073252471586323<55> × 60945330750594823707608076202355403412583227422527742597800756810342955043031815781887020703344858474019501282956807043<119> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=2048388426 for P32 / May 26, 2010 2010 年 5 月 26 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3683190088 for P42 / October 30, 2011 2011 年 10 月 30 日) (Lionel Debroux / GMP-ECM 6.3 + ECMNet 2.7.3 B1=43000000, sigma=2745925504 for P55 / November 1, 2011 2011 年 11 月 1 日)
3×10281+1 = 3(0)2801<282> = 13 × 47 × 1619 × [303272614786157424770700630503766140421286098286610817329805935853798337863889228666540640046744419025706397737990657181647154443600897282576280644434088246265450476087459778469463985871539785828879438015626626931214738240351634487757389995440801691048100047613800521426715689<276>] Free to factor
3×10282+1 = 3(0)2811<283> = 80987827 × 25248366440491<14> × 15074985786601825640976385847887<32> × 3446483892133820284482754061777078017<37> × 10176715588975981464587005586971581625287961<44> × 111792808381176064199306739195975917326906699<45> × 24820673140548908191619076499350337902784096889404228421270215684937658959560883931632207868893267127806053<107> (Serge Batalov / GMP-ECM B1=2000000, sigma=4036774683 for P32 / May 29, 2010 2010 年 5 月 29 日) (Serge Batalov / GMP-ECM B1=2000000, sigma=570903822 for P44 / May 29, 2010 2010 年 5 月 29 日) (Ignacio Santos / GMP-ECM 6.2.3 B1=11000000, sigma=946848283 for P37 / May 29, 2010 2010 年 5 月 29 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=11000000, sigma=232213904 for P45 / July 19, 2010 2010 年 7 月 19 日)
3×10283+1 = 3(0)2821<284> = 263 × 49367 × 1754317418317<13> × 21437157501257<14> × 3123960118524643<16> × 253901065132752025451<21> × 30679747053280703459636449<26> × 247214911349201948573383056821<30> × 20847759846550308773998563980449<32> × 9288960575905414053187770562617622461157<40> × 52738823769926066112592116216231434219581962873358438237235460121624242028433108165762069<89> (Serge Batalov / GMP-ECM B1=2000000, sigma=3300553058 for P30 / May 29, 2010 2010 年 5 月 29 日) (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=3039296181 for P32 / May 29, 2010 2010 年 5 月 29 日) (Erik Branger / GGNFS, Msieve gnfs for P40 x P89 / October 29, 2010 2010 年 10 月 29 日)
3×10284+1 = 3(0)2831<285> = 7 × 769 × 9540571 × 1155101141584929738692179<25> × 1463735960835112950721857721485040651220234929<46> × 3454933967548500437503482599692093090773890478165487838892470126206276436786854033692433869103022190992789276177400800578463982928770815450746781036939774434173305688668369074186257543786151303715492490727<205> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=586748838 for P46 / October 24, 2011 2011 年 10 月 24 日)
3×10285+1 = 3(0)2841<286> = 17 × 2755237 × 4433057 × 3695964384983780574217033267<28> × 81781675729707054708819370524269<32> × 47799821319647034112480467544549072521616563349535754108301950869062354531814701594105726123834744325266830361747877433944602725765460013949191250233063117616362601780236100846431607482766320869926238873775787179<212> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1947032832 for P32 / May 27, 2010 2010 年 5 月 27 日)
3×10286+1 = 3(0)2851<287> = 31 × 187887865009106329<18> × 5150635648752342706993174953903155427577411151625392925556428324988131295646511802463296215496025513521638351808476276104271087313614107763034293031853459143330085698831694210331862808890070372295468024463468430640784296917431602707134204019611842555814677425455263799<268>
3×10287+1 = 3(0)2861<288> = 13 × 59 × 356338115053<12> × 12535184880998365929862861503445027<35> × 76685281895886958149967438434707339200038671689<47> × [1141881009476402943384664970640345762740311709101434279378516652956613440999316653196852867022726591486426721016674887641744244854049225652005215371158434470969799706025387831009853725497797217<193>] (Serge Batalov / GMP-ECM B1=2000000, sigma=619037551 for P35 / May 29, 2010 2010 年 5 月 29 日) (Makso / GMP-ECM B1=110000000, sigma=1130791073 for P47 / December 21, 2011 2011 年 12 月 21 日) Free to factor
3×10288+1 = 3(0)2871<289> = 61 × 29179 × 35249999016000540600754850359<29> × [47814751881663037669911697805465074290217828629898987858417013706249202194353307717138662534238566687653459572453471019967112289372582560259170648717032748145426107033100016342757792429405208619850451218034379326141337566556504811107344690050947149377481<254>] Free to factor
3×10289+1 = 3(0)2881<290> = 96263 × 616156733162904270381047<24> × 5124305024667687158500295402029823<34> × 98704213118703015315968955442582137514456930117898499138463321330095300533252025313207406762471000972570368239776194000632524213542796394700297097996251779836226502895497902347815903570427686207150283169237399414972679770264767<227> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=508110751 for P34 / May 8, 2011 2011 年 5 月 8 日)
3×10290+1 = 3(0)2891<291> = 7 × 157 × 5653 × 1378843 × 1608474085717<13> × 22753177123514018788963<23> × 5974977314559185228171779<25> × [160153849334008325060127089845049336708076607181708266147881131828776752909266991290020555600697088354755790773728502564521427956265380623481958777170567906203549965746322622222393918951789197088787774616562987618233209<219>] Free to factor
3×10291+1 = 3(0)2901<292> = 27407 × 14936801007013<14> × [7328281774144694546043563500738474702321623928745070535827902335389971130011794997923474060908623041297142082837890294473523981914059415796780827702586418987073438465674982695971589914161551320590655964811115397705463670502331797527378804161465998463633431698285819187799811<274>] Free to factor
3×10292+1 = 3(0)2911<293> = 19 × 613 × 1029171564312851501005530601<28> × [2502761127509086669132792978670314284246265039873761428436897992771163392853488943104486977719705456495226858564931723926515081168184534703179672381773247733925216072538548420074818166685483244465982870657169578175494574401783087060927066531366853949874816134183<262>] Free to factor
3×10293+1 = 3(0)2921<294> = 13 × 16811 × 69389 × 24629504974103<14> × 121479408873068145993360410900009780225327<42> × [6612038482485724152368814538072191217832677221074962349095446629996561479778741030092233342130465736190656430270540423301598712541748167603296481194643296399404821904165492251046375297882985467061843591203095423974236656533855523<229>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3230870182 for P42 / October 14, 2011 2011 年 10 月 14 日) Free to factor
3×10294+1 = 3(0)2931<295> = 499 × 84163 × 415213 × 555049039063849963<18> × [309953970443144435498213987719435781091129786806315781099272465063167094933370228912609686917066227046638901371459415904026843233711464532679840923911853090576545252653997696164073750953817786028749537710184108087891286191628770508463811184229183661033050914029767<264>] Free to factor
3×10295+1 = 3(0)2941<296> = 29 × 10402673 × 254240706351833<15> × [391140893383953653853755792040765335356706252950271149442135423321804247839651144185729158709779521553859513324931823783240946958437991434855623070705282873195063074715418885014445177346803212506600693008944725918701948973425047546987925597260490500050725100238652314620941<273>] Free to factor
3×10296+1 = 3(0)2951<297> = 7 × 43 × 4007116618048254572444635886065060772611<40> × [248726911608886238967982250133017013314878464176228415474782933610001552135995589627028573822748792306060308844738357025795559798355100251007582682885698844744976887728022759966325736797094443600638476728600692159952365528634251529711784873493159098811191<255>] (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 B1=11000000, sigma=2222750386 for P40 / June 5, 2010 2010 年 6 月 5 日) Free to factor
3×10297+1 = 3(0)2961<298> = 257 × 307 × 386297 × 3503939689721772138561271952468298459303188533<46> × [28091297430382950889427302845165580753513899671715896039639017203474521637671901009675168954884009770287727633281130194801599419050549088808998669378251757821722485982120926831177733450616970273119353622348668916182887611413182137196910623399<242>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2328726034 for P46 / December 24, 2010 2010 年 12 月 24 日) Free to factor
3×10298+1 = 3(0)2971<299> = 280005331 × 118693332957739<15> × 10056791215154855325270948342691987<35> × [89757179211382084550314110864172149901723629213163094868472385284949212017096802229421037625343512910887675293137263889954981829832362846921768921788385488232432728510507265445363590322373453469250696515597864830202792227464507524126338508747<242>] (Serge Batalov / GMP-ECM B1=3000000, sigma=3528964167 for P35 / May 30, 2010 2010 年 5 月 30 日) Free to factor
3×10299+1 = 3(0)2981<300> = 13 × 23 × 4139 × 24115835683<11> × 41195338338523<14> × 649246457151365359213753339534758908964845356301<48> × 375832784322408936300885472372711200454922479672254517005359195806723598907646694626646362197279079270603265356642180457974471760652997209781691846924046629612518387128025129425821538893950717848170163819208972030445327549<222> ([SG]marodeur6 / GMP-ECM B1=110000000, sigma=2911128451 for P48 / December 29, 2011 2011 年 12 月 29 日)
3×10300+1 = 3(0)2991<301> = 1549 × 114319033399<12> × 171075172359981103969606910676242501541629863365403<51> × [99029436318040208068993088380803051255111531076439116970281800232416389795182251096910432391708894368210759137712164695871647868352889176511845117608519628044190420472117996566711036095111573214605783976699985346765174684826769047200217<236>] (Dmitry Domanov / ECMNET/GMP-ECM 6.2.3 B1=11000000, sigma=968510242 for P51 / August 14, 2010 2010 年 8 月 14 日) Free to factor
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