Table of contents 目次

  1. About 199...99 199...99 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 199...99 199...99 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 199...99 199...99 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 199...99 199...99 について

1.1. Classification 分類

Near-repdigit of the form ABB...BB ABB...BB の形のニアレプディジット (Near-repdigit)

1.2. Sequence 数列

19w = { 1, 19, 199, 1999, 19999, 199999, 1999999, 19999999, 199999999, 1999999999, … }

1.3. General term 一般項

2×10n-1 (0≤n)

1.4. Related sequences 関連する数列

2. Prime numbers of the form 199...99 199...99 の形の素数

2.1. Last updated 最終更新日

February 1, 2015 2015 年 2 月 1 日

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

  1. 2×101-1 = 19 is prime. は素数です。
  2. 2×102-1 = 199 is prime. は素数です。
  3. 2×103-1 = 1999 is prime. は素数です。
  4. 2×105-1 = 199999 is prime. は素数です。
  5. 2×107-1 = 19999999 is prime. は素数です。
  6. 2×1026-1 = 1(9)26<27> is prime. は素数です。
  7. 2×1027-1 = 1(9)27<28> is prime. は素数です。
  8. 2×1053-1 = 1(9)53<54> is prime. は素数です。
  9. 2×10147-1 = 1(9)147<148> is prime. は素数です。
  10. 2×10236-1 = 1(9)236<237> is prime. は素数です。
  11. 2×10248-1 = 1(9)248<249> is prime. は素数です。
  12. 2×10386-1 = 1(9)386<387> is prime. は素数です。
  13. 2×10401-1 = 1(9)401<402> is prime. は素数です。
  14. 2×10546-1 = 1(9)546<547> is prime. は素数です。
  15. 2×10785-1 = 1(9)785<786> is prime. は素数です。
  16. 2×101325-1 = 1(9)1325<1326> is prime. は素数です。 (Hugh C. Williams / December 31, 1985 1985 年 12 月 31 日)
  17. 2×101755-1 = 1(9)1755<1756> is prime. は素数です。 (Hugh C. Williams / December 31, 1985 1985 年 12 月 31 日)
  18. 2×102906-1 = 1(9)2906<2907> is prime. は素数です。 (Hugh C. Williams / December 31, 1985 1985 年 12 月 31 日)
  19. 2×103020-1 = 1(9)3020<3021> is prime. は素数です。 (Hugh C. Williams / December 31, 1985 1985 年 12 月 31 日)
  20. 2×105407-1 = 1(9)5407<5408> is prime. は素数です。 (Harvey Dubner / Cruncher / October 1, 1994 1994 年 10 月 1 日)
  21. 2×105697-1 = 1(9)5697<5698> is prime. は素数です。 (Harvey Dubner / Cruncher / October 1, 1994 1994 年 10 月 1 日)
  22. 2×105969-1 = 1(9)5969<5970> is prime. は素数です。 (Harvey Dubner / Cruncher / October 1, 1994 1994 年 10 月 1 日)
  23. 2×107517-1 = 1(9)7517<7518> is prime. は素数です。 (Harvey Dubner / Cruncher / July 31, 1993 1993 年 7 月 31 日)
  24. 2×1015749-1 = 1(9)15749<15750> is prime. は素数です。 (Harvey Dubner / Cruncher / June 16, 1999 1999 年 6 月 16 日)
  25. 2×1019233-1 = 1(9)19233<19234> is prime. は素数です。 (Roland Clarkson / Proth.exe / September 21, 2000 2000 年 9 月 21 日)
  26. 2×1038232-1 = 1(9)38232<38233> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / September 3, 2001 2001 年 9 月 3 日)
  27. 2×1055347-1 = 1(9)55347<55348> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / July 18, 2002 2002 年 7 月 18 日)
  28. 2×101059002-1 = 1(9)1059002<1059003> is prime. は素数です。 (Serge Batalov / Srsieve, LLR / September 17, 2013 2013 年 9 月 17 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了 / Ray Chandler / September 30, 2010 2010 年 9 月 30 日
  2. n≤100000 / Completed 終了 / Gary Barnes / December 1, 2010 2010 年 12 月 1 日
  3. n≤135000 / Completed 終了 / Gary Barnes / January 3, 2010 2010 年 1 月 3 日
  4. n≤140000 / Completed 終了 / Gary Barnes / January 14, 2011 2011 年 1 月 14 日
  5. n≤145000 / Completed 終了 / Gary Barnes / January 16, 2011 2011 年 1 月 16 日
  6. n≤150000 / Completed 終了 / Gary Barnes / January 18, 2011 2011 年 1 月 18 日
  7. n≤155000 / Completed 終了 / Gary Barnes / January 20, 2011 2011 年 1 月 20 日
  8. n≤160000 / Completed 終了 / Gary Barnes / January 24, 2011 2011 年 1 月 24 日
  9. n≤165000 / Completed 終了 / Gary Barnes / January 25, 2011 2011 年 1 月 25 日
  10. n≤170000 / Completed 終了 / Gary Barnes / January 28, 2011 2011 年 1 月 28 日
  11. n≤175000 / Completed 終了 / Gary Barnes / January 31, 2011 2011 年 1 月 31 日
  12. n≤180000 / Completed 終了 / Gary Barnes / February 3, 2011 2011 年 2 月 3 日
  13. n≤185000 / Completed 終了 / Gary Barnes / February 7, 2011 2011 年 2 月 7 日
  14. n≤190000 / Completed 終了 / Gary Barnes / February 11, 2011 2011 年 2 月 11 日
  15. n≤195000 / Completed 終了 / Gary Barnes / February 17, 2011 2011 年 2 月 17 日
  16. n≤200000 / Completed 終了 / Gary Barnes / February 20, 2011 2011 年 2 月 20 日
  17. n≤205000 / Completed 終了 / Gary Barnes / February 27, 2011 2011 年 2 月 27 日
  18. n≤210000 / Completed 終了 / Gary Barnes / February 28, 2011 2011 年 2 月 28 日
  19. n≤215000 / Completed 終了 / Gary Barnes / March 5, 2011 2011 年 3 月 5 日
  20. n≤220000 / Completed 終了 / Gary Barnes / March 9, 2011 2011 年 3 月 9 日
  21. n≤225000 / Completed 終了 / Gary Barnes / March 15, 2011 2011 年 3 月 15 日
  22. n≤230000 / Completed 終了 / Gary Barnes / April 17, 2011 2011 年 4 月 17 日
  23. n≤300000 / Completed 終了 / Predrag Kurtovic / August 21, 2013 2013 年 8 月 21 日
  24. n≤350000 / Completed 終了 / Predrag Kurtovic / August 31, 2013 2013 年 8 月 31 日
  25. n≤400000 / Completed 終了 / Predrag Kurtovic / September 2, 2013 2013 年 9 月 2 日
  26. n≤410000 / Completed 終了 / Predrag Kurtovic / October 31, 2013 2013 年 10 月 31 日
  27. 500000≤n≤600000 / Completed 終了 / Predrag Kurtovic / September 17, 2013 2013 年 9 月 17 日
  28. 1000000≤n≤1059700 / Completed 終了 / Serge Batalov / September 17, 2013 2013 年 9 月 17 日

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

  1. 2×106k+4-1 = 7×(2×104-17+18×104×106-19×7×k-1Σm=0106m)
  2. 2×1015k+9-1 = 31×(2×109-131+18×109×1015-19×31×k-1Σm=01015m)
  3. 2×1016k+6-1 = 17×(2×106-117+18×106×1016-19×17×k-1Σm=01016m)
  4. 2×1018k+1-1 = 19×(2×101-119+18×10×1018-19×19×k-1Σm=01018m)
  5. 2×1022k+14-1 = 23×(2×1014-123+18×1014×1022-19×23×k-1Σm=01022m)
  6. 2×1028k+17-1 = 29×(2×1017-129+18×1017×1028-19×29×k-1Σm=01028m)
  7. 2×1035k+6-1 = 71×(2×106-171+18×106×1035-19×71×k-1Σm=01035m)
  8. 2×1042k+36-1 = 127×(2×1036-1127+18×1036×1042-19×127×k-1Σm=01042m)
  9. 2×1044k+8-1 = 89×(2×108-189+18×108×1044-19×89×k-1Σm=01044m)
  10. 2×1046k+16-1 = 47×(2×1016-147+18×1016×1046-19×47×k-1Σm=01046m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 27.85%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 27.85% です。

3. Factor table of 199...99 199...99 の素因数分解表

3.1. Last updated 最終更新日

May 28, 2018 2018 年 5 月 28 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=203, 206, 208, 209, 226, 227, 228, 230, 233, 234, 237, 239, 246, 252, 254, 255, 256, 257, 259, 262, 263, 264, 265, 266, 267, 269, 272, 273, 274, 275, 277, 278, 281, 282, 283, 284, 285, 287, 288, 289, 290, 293, 294, 295, 296, 297, 300 (47/300)

3.4. Factor table 素因数分解表

2×100-1 = 1
2×101-1 = 19 = definitely prime number 素数
2×102-1 = 199 = definitely prime number 素数
2×103-1 = 1999 = definitely prime number 素数
2×104-1 = 19999 = 7 × 2857
2×105-1 = 199999 = definitely prime number 素数
2×106-1 = 1999999 = 17 × 71 × 1657
2×107-1 = 19999999 = definitely prime number 素数
2×108-1 = 199999999 = 89 × 1447 × 1553
2×109-1 = 1999999999<10> = 31 × 64516129
2×1010-1 = 19999999999<11> = 7 × 97 × 193 × 152617
2×1011-1 = 199999999999<12> = 251 × 1831 × 435179
2×1012-1 = 1999999999999<13> = 3833 × 521784503
2×1013-1 = 19999999999999<14> = 61 × 21031 × 15589789
2×1014-1 = 199999999999999<15> = 23 × 8695652173913<13>
2×1015-1 = 1999999999999999<16> = 109 × 18348623853211<14>
2×1016-1 = 19999999999999999<17> = 7 × 47 × 281081 × 216273151
2×1017-1 = 199999999999999999<18> = 29 × 599 × 31139 × 369743471
2×1018-1 = 1999999999999999999<19> = 432809599 × 4620969601<10>
2×1019-1 = 19999999999999999999<20> = 19 × 110394419 × 9535188359<10>
2×1020-1 = 199999999999999999999<21> = 82647847 × 2419905747817<13>
2×1021-1 = 1999999999999999999999<22> = 1023039389<10> × 1954958940491<13>
2×1022-1 = 19999999999999999999999<23> = 7 × 17 × 168067226890756302521<21>
2×1023-1 = 199999999999999999999999<24> = 1042402171<10> × 191864527496269<15>
2×1024-1 = 1999999999999999999999999<25> = 31 × 601 × 75991441 × 1412632357369<13>
2×1025-1 = 19999999999999999999999999<26> = 2129 × 13421 × 127241 × 5501009364371<13>
2×1026-1 = 199999999999999999999999999<27> = definitely prime number 素数
2×1027-1 = 1999999999999999999999999999<28> = definitely prime number 素数
2×1028-1 = 19999999999999999999999999999<29> = 7 × 2441 × 3673 × 536441 × 594047653107889<15>
2×1029-1 = 199999999999999999999999999999<30> = 73571 × 783988798759<12> × 3467476119491<13>
2×1030-1 = 1999999999999999999999999999999<31> = 77513 × 25802123514765265181324423<26>
2×1031-1 = 19999999999999999999999999999999<32> = 149 × 3371 × 11251 × 3050246411<10> × 1160269631321<13>
2×1032-1 = 199999999999999999999999999999999<33> = 233 × 337 × 1609 × 71527 × 1752732671<10> × 12627065623<11>
2×1033-1 = 1999999999999999999999999999999999<34> = 59 × 479 × 70768904143519337603057216659<29>
2×1034-1 = 19999999999999999999999999999999999<35> = 7 × 2857142857142857142857142857142857<34>
2×1035-1 = 199999999999999999999999999999999999<36> = 15139 × 39359 × 37071341 × 9054207739320799639<19>
2×1036-1 = 1999999999999999999999999999999999999<37> = 23 × 127 × 6151 × 69447808883207<14> × 1602854731722967<16>
2×1037-1 = 19999999999999999999999999999999999999<38> = 19 × 55631 × 11222041 × 123838721 × 13615425524177731<17>
2×1038-1 = 199999999999999999999999999999999999999<39> = 17 × 313 × 37586919751926329637286224393910919<35>
2×1039-1 = 1999999999999999999999999999999999999999<40> = 31 × 64516129032258064516129032258064516129<38>
2×1040-1 = 19999999999999999999999999999999999999999<41> = 73 × 151 × 911 × 461656937321<12> × 918165954776278710553<21>
2×1041-1 = 199999999999999999999999999999999999999999<42> = 71 × 3209 × 218670799 × 4014312132842477314284979759<28>
2×1042-1 = 1999999999999999999999999999999999999999999<43> = 8722673 × 1613620812708167<16> × 142095039505177227289<21>
2×1043-1 = 19999999999999999999999999999999999999999999<44> = 14188750452331121<17> × 1409567394055769572492644719<28>
2×1044-1 = 199999999999999999999999999999999999999999999<45> = 191 × 367 × 487 × 1193 × 799792657 × 9702575167<10> × 632844093134623<15>
2×1045-1 = 1999999999999999999999999999999999999999999999<46> = 29 × 5639 × 496833131 × 4030140119<10> × 6108002533693456695361<22>
2×1046-1 = 19999999999999999999999999999999999999999999999<47> = 7 × 8862577 × 1372013570237203199<19> × 234970600783390805159<21>
2×1047-1 = 199999999999999999999999999999999999999999999999<48> = 131 × 181 × 39955089541<11> × 211109616525086721812252364759149<33>
2×1048-1 = 1999999999999999999999999999999999999999999999999<49> = 2671 × 5879 × 10159 × 35184223258595449<17> × 356331092452560202721<21>
2×1049-1 = 19999999999999999999999999999999999999999999999999<50> = 1259 × 2539 × 46320316841<11> × 1164438729401<13> × 115998774646597401239<21>
2×1050-1 = 1(9)50<51> = 5830990703831<13> × 34299488741869997945614291216474011929<38>
2×1051-1 = 1(9)51<52> = 242491 × 1442849 × 5716279930669628639686312159912662372461<40>
2×1052-1 = 1(9)52<53> = 7 × 89 × 265105242719<12> × 121094280907789168180922247062764590127<39>
2×1053-1 = 1(9)53<54> = definitely prime number 素数
2×1054-1 = 1(9)54<55> = 17 × 31 × 6271 × 62702211983<11> × 9651608955277596810279846533429791009<37>
2×1055-1 = 1(9)55<56> = 19 × 3769 × 289099 × 966059037781851620509711964214025433791507591<45>
2×1056-1 = 1(9)56<57> = 2063 × 82421359754551<14> × 1176226589206430376979832613058926559223<40>
2×1057-1 = 1(9)57<58> = 8069 × 11399 × 21744204634013996157429389690948641047550541984629<50>
2×1058-1 = 1(9)58<59> = 7 × 23 × 3160024442975017<16> × 39310962534049663193199913018639770440327<41>
2×1059-1 = 1(9)59<60> = 136541 × 3253850111311<13> × 8440450795922006821<19> × 53333947698860662675169<23>
2×1060-1 = 1(9)60<61> = 113 × 33865129 × 50444908681<11> × 177392212820479<15> × 58404582869837934023118113<26>
2×1061-1 = 1(9)61<62> = 251 × 34215721 × 747704799966603649<18> × 3114586591265797592737180752552581<34>
2×1062-1 = 1(9)62<63> = 47 × 504034073 × 1220285033049641423<19> × 6918484257964090228128626296689623<34>
2×1063-1 = 1(9)63<64> = 63131399 × 31679956910189809036229341282299161467972537722473091401<56>
2×1064-1 = 1(9)64<65> = 7 × 179057 × 673639 × 23687183764533030482444354714936509818804335751543359<53>
2×1065-1 = 1(9)65<66> = 57416791 × 5685045319<10> × 612713075321401087046458038954535213178204467231<48>
2×1066-1 = 1(9)66<67> = 114208550488870843707673320090031<33> × 17511823689548461809824420102206129<35>
2×1067-1 = 1(9)67<68> = 11351 × 2779351 × 2757356547351191<16> × 229910892853430932296715347004611670569289<42>
2×1068-1 = 1(9)68<69> = 743 × 720744137 × 68629286397718712091266647<26> × 5441900295212874899182199873287<31>
2×1069-1 = 1(9)69<70> = 31 × 439 × 212039 × 35458744861<11> × 2626410054718091<16> × 7442213814490672036679386751621599<34>
2×1070-1 = 1(9)70<71> = 7 × 17 × 431 × 3761 × 42743 × 114889 × 21113439137145151982518690557051200255934635601139753<53>
2×1071-1 = 1(9)71<72> = 311 × 49801 × 812126836567325311<18> × 15900386507052020800133836615165276113430575119<47>
2×1072-1 = 1(9)72<73> = 10337 × 1539265796448195743859457<25> × 125696116580006172197631576931601768549558111<45>
2×1073-1 = 1(9)73<74> = 19 × 29 × 61 × 100236345329109106048850820884161<33> × 5936402484004975288098822472966741469<37>
2×1074-1 = 1(9)74<75> = 128375657 × 1557927761958795661703994239343990270678809456842740832087815527207<67>
2×1075-1 = 1(9)75<76> = 1468399 × 9773656519171<13> × 7233357124959028127639<22> × 19265883761065596281172138321530429<35>
2×1076-1 = 1(9)76<77> = 7 × 71 × 3449 × 4847041 × 18395633 × 130854596492286412438405476816657478703173293235697757911<57>
2×1077-1 = 1(9)77<78> = 3296551 × 180273339366603915157042541456190941<36> × 336541551884960929475454162660123389<36>
2×1078-1 = 1(9)78<79> = 127 × 359 × 46271 × 948031877361413200744641307998671084939526110708897790110817166822633<69>
2×1079-1 = 1(9)79<80> = 569 × 35149384885764499121265377855887521968365553602811950790861159929701230228471<77>
2×1080-1 = 1(9)80<81> = 23 × 167 × 53831 × 967282300096325356931642416182002212551860417333658191869546350550040969<72>
2×1081-1 = 1(9)81<82> = 2108272811<10> × 948643832792851968340448327301413934517604515082844276171808962345907709<72>
2×1082-1 = 1(9)82<83> = 72 × 4519 × 91904895863405227344778390349737714039<38> × 982772344963126877180586765965485256911<39>
2×1083-1 = 1(9)83<84> = 6513641919379205078817101<25> × 30704788883921543079717165000137354872639579175495937407099<59>
2×1084-1 = 1(9)84<85> = 31 × 5279 × 2777773327500151246091548687369<31> × 4399667297165328486109956191774908451162855011079<49>
2×1085-1 = 1(9)85<86> = 3221 × 3559 × 8609 × 32017949 × 3150065531<10> × 2009303209580006097231729520903062138499743525512613270571<58>
2×1086-1 = 1(9)86<87> = 17 × 181080943 × 251205089 × 948078166247963353<18> × 272794586998137561888016756471696403803458600092137<51>
2×1087-1 = 1(9)87<88> = 921931 × 450550616424617211226759254709757392949<39> × 4814907952466029143993425793168884042462921<43>
2×1088-1 = 1(9)88<89> = 7 × 6436743191<10> × 443880200337614672260915257189551147164470252848224458992113121441892420973727<78>
2×1089-1 = 1(9)89<90> = 44631941 × 1933104657299<13> × 2318082317880034624227670197644714374137252517098838392013073847972961<70>
2×1090-1 = 1(9)90<91> = 80167993 × 4929387429353<13> × 5060996433095582084426587425815186568202349049458676369614394590046431<70>
2×1091-1 = 1(9)91<92> = 192 × 59 × 2392009 × 277008180319054489<18> × 1417148555239242589493953615337812898464524297144004015596172901<64>
2×1092-1 = 1(9)92<93> = 17959 × 93725918953<11> × 118819614217291384918987207691847487670858136634284548153181194724631410443137<78>
2×1093-1 = 1(9)93<94> = 3271 × 195271 × 3510809 × 188511887280438155140061<24> × 4731139534950256209818001722774195895013399032810281011<55>
2×1094-1 = 1(9)94<95> = 7 × 35105979704639<14> × 81386216285122117970986616615500698542756666511802516848971201948267512301305463<80>
2×1095-1 = 1(9)95<96> = 3489506136409<13> × 1300129261094015351<19> × 44083848023961543456909075367830478670129039588228131584939384161<65>
2×1096-1 = 1(9)96<97> = 89 × 6308297 × 20833138324174178606300119<26> × 1063589346407609366536943849663<31> × 160767841543596929071753957211399<33>
2×1097-1 = 1(9)97<98> = 9046841 × 70490471 × 1895717321<10> × 1798944871369504725121<22> × 9196258973996581459861670806010127798180137991647849<52>
2×1098-1 = 1(9)98<99> = 631 × 3617 × 327597071560393<15> × 2611076388342167<16> × 65900319199437532470998302369<29> × 1554551166870405208151291923028983<34>
2×1099-1 = 1(9)99<100> = 31 × 2478018041<10> × 31432234741<11> × 388140989339<12> × 2134022874173671561245124315872113656324653675736472637270988672831<67>
2×10100-1 = 1(9)100<101> = 7 × 177127 × 8330999 × 6901128649<10> × 3286723567201<13> × 85362436740497267761077074834813442709379486887811387639018981441<65>
2×10101-1 = 1(9)101<102> = 29 × 199 × 38699 × 429889 × 6743968248359<13> × 14788707227523176951956429<26> × 20887050552140849265065287732960465588673292637589<50>
2×10102-1 = 1(9)102<103> = 17 × 23 × 9815219231716313<16> × 4294644227406457937<19> × 121346161107148719947481128979092586902298579384881960317202311969<66>
2×10103-1 = 1(9)103<104> = 2371 × 52121 × 17860533770510789<17> × 9061315838249284839230431449032937631731673431289424282378423055101150833155001<79>
2×10104-1 = 1(9)104<105> = 1303 × 71011247 × 566415155891210886867230610377<30> × 3816133640761471827501849984755061159520992920755373571951487807<64>
2×10105-1 = 1(9)105<106> = 179 × 1946778557392743509<19> × 72730962098229789779<20> × 78911641588436255085236273256281696186149357416443127576789651371<65>
2×10106-1 = 1(9)106<107> = 7 × 97 × 263 × 17881 × 116783220530087<15> × 8021287689120119<16> × 11820859413554627801<20> × 565638649816888769162746135608453549230787088159<48>
2×10107-1 = 1(9)107<108> = 409 × 488997555012224938875305623471882640586797066014669926650366748166259168704156479217603911980440097799511<105>
2×10108-1 = 1(9)108<109> = 47 × 15289 × 73592101706551199<17> × 1107361514270525062886494609<28> × 34153280519193239456615876347476578405728210716399805244983<59>
2×10109-1 = 1(9)109<110> = 19 × 21114980841716492601531213816684580682795131715128639<53> × 49852357756711903215458867437681135752537509295755288539<56> (Naoki Yamamoto / GGNFS for P53 x P56 / 10h / May 17, 2004 2004 年 5 月 17 日)
2×10110-1 = 1(9)110<111> = 2953 × 72231431473962184466663<23> × 5794959279504231267574677581855623<34> × 161804255083499559497589699998069972906439305506967<51>
2×10111-1 = 1(9)111<112> = 71 × 251 × 20489561 × 61766756955040092454850909626450969<35> × 88676893883253092463061598605662088178855904485539747444406236091<65>
2×10112-1 = 1(9)112<113> = 7 × 176321 × 528554163011666951<18> × 4805884917611229567797426753<28> × 6379182849099375599312076766228046254582324644749798842977839<61>
2×10113-1 = 1(9)113<114> = 4650259 × 89387497645595816161332104338818611<35> × 481145107556798585845390975569987436831798400147931324271186928514607751<72> (Naoki Yamamoto / GGNFS for P35 x P72 / 17h / May 18, 2004 2004 年 5 月 18 日)
2×10114-1 = 1(9)114<115> = 31 × 3343 × 439334993723776937237137<24> × 43927463681771939706724007487311284435681736327581150722112162661577762516222809268319<86>
2×10115-1 = 1(9)115<116> = 151 × 739 × 4796780842151<13> × 10128647880475486409875491239<29> × 3688988149130245867088923249513885021476204048478897892443543945278019<70>
2×10116-1 = 1(9)116<117> = 1414973875906225217477423519<28> × 2166851807361589573177075751475697<34> × 65230748710190317012308794178134036269360841135247689393<56> (Naoki Yamamoto / for P34 x P56 / May 9, 2004 2004 年 5 月 9 日)
2×10117-1 = 1(9)117<118> = 1047589 × 85168019463062283512091014704502999<35> × 22416227110785555037014333292452400377314259442753749222567258532701137582309<77> (Sander Hoogendoorn / for P35 x P77)
2×10118-1 = 1(9)118<119> = 7 × 17 × 228023 × 935187333561872655816153034416501361<36> × 788144343693189519772431006559145070846257778116348967005552162769367495807<75> (Sander Hoogendoorn / for P36 x P75 / June 10, 2004 2004 年 6 月 10 日)
2×10119-1 = 1(9)119<120> = 117839 × 2883845398187423145137576280203368673508491<43> × 588530497766278656698413595437639465348609061819280096585286457602098451<72> (Naoki Yamamoto / GGNFS-0.41.4 for P43 x P72 / 3 hours / July 20, 2004 2004 年 7 月 20 日)
2×10120-1 = 1(9)120<121> = 127 × 6520884276873089204884529<25> × 232643528042555620464254561737409431506439<42> × 10380751776128730049253466514320685686318545305162727<53> (Naoki Yamamoto / for P42 x P53 / May 15, 2004 2004 年 5 月 15 日)
2×10121-1 = 1(9)121<122> = 883721 × 3737013818915101<16> × 54651912365194411802671<23> × 414156484133784682062584316119<30> × 267559446031256771375027432233435194554265777931<48>
2×10122-1 = 1(9)122<123> = 457 × 823 × 63311 × 675551 × 12433020390731958082612922116557055210986253471707899721351412214103965642265147545115773163707697033603169<107>
2×10123-1 = 1(9)123<124> = 109 × 217114861 × 2825376469<10> × 7802871694458922680414327278941<31> × 3833391338808287460914354109964295906385875484435011906494407451701606919<73> (Makoto Kamada / GGNFS-0.42.0 for P31 x P73 / Total time: 4.2 hours (actual time: 5.0 hours))
2×10124-1 = 1(9)124<125> = 72 × 23 × 5113 × 1705943 × 16967566179235566887<20> × 119907464293147010278459239593073153841105705184957642035719565130190948172143714050658360689<93>
2×10125-1 = 1(9)125<126> = 5593144113982773671594705011644916102525868355090939299<55> × 35758063072253600104111297707041995548298752568202917692898922932429301<71> (Chris Monico / GGNFS for P55 x P71 / July 22, 2004 2004 年 7 月 22 日)
2×10126-1 = 1(9)126<127> = 17453998045111<14> × 4238151318667093204129<22> × 11368527580482054806969<23> × 2378232963001131757769639706588850023529714425979822496939392861679009<70>
2×10127-1 = 1(9)127<128> = 19 × 1621 × 25802217629<11> × 39207910645081881480209<23> × 641893009635956926635449807862431482825313241818779071863244093976975917450117813399293941<90>
2×10128-1 = 1(9)128<129> = 881 × 394688828423<12> × 17386334653013755032137<23> × 33081958964030418702365503289996434209148788857519087576245799267917760536678826112565014929<92>
2×10129-1 = 1(9)129<130> = 29 × 31 × 484733313451<12> × 41463885135837930748140461<26> × 50291757440027988007781239460876655467039<41> × 2200901625430665915052040182443813421490599481669<49> (Naoki Yamamoto / for P41 x P49 / May 13, 2004 2004 年 5 月 13 日)
2×10130-1 = 1(9)130<131> = 7 × 311043047257<12> × 5855691034209378660658810843429609687<37> × 4953517607135850515490609742784611284137<40> × 316679239119493368730697918313185363275679<42> (Chris Monico / GGNFS for P42 / July 23, 2004 2004 年 7 月 23 日) (Makoto Kamada / PPSIQS 1.1 for P37 x P40 / 0:36:01:60)
2×10131-1 = 1(9)131<132> = 296654321 × 40446252302369793894595799<26> × 16668673139090432255450876222723095772151061212853891918012066247975638378220012821097748974099881<98>
2×10132-1 = 1(9)132<133> = 383 × 6784703 × 40846423 × 295764098205281929<18> × 157992194582767457565322208346460391<36> × 403241538412822815665069568615264515364295352454530261564930183<63> (Chris Monico / GGNFS for P36 x P63 / August 26, 2004 2004 年 8 月 26 日)
2×10133-1 = 1(9)133<134> = 61 × 3121 × 32569 × 5302472891<10> × 195683616035351<15> × 2006104662270156242546379421<28> × 18396048166882590003259808473789<32> × 84234678108171370226414993709593727370279<41>
2×10134-1 = 1(9)134<135> = 17 × 2663 × 321847 × 760897 × 2200797068497<13> × 70625917741087<14> × 15680639486676961734577<23> × 712632491139172966014554311<27> × 10386305153265760923350299594057384995789127<44>
2×10135-1 = 1(9)135<136> = 1009429609<10> × 66466428376467003161<20> × 29809288752202930186816586029758071927997326505795469392435769431182067143900175746749373167148751794271551<107>
2×10136-1 = 1(9)136<137> = 7 × 96589511 × 29580260087897713270927967086849183270605261239420263167676072582486282002785404484994826641757642371156192548248255000927141487<128>
2×10137-1 = 1(9)137<138> = 107933154040501<15> × 11254877967108971721971687364747575335643268954022536802019<59> × 164639613139898133672159836253458304835231081639583063417570849921<66> (Chris Monico / GGNFS for P59 x P66 / August 20, 2004 2004 年 8 月 20 日)
2×10138-1 = 1(9)138<139> = 2364127787039<13> × 10572381256746831649151<23> × 212908302086690775047301300781111<33> × 53426146938130791258323633576562641<35> × 7034606050525602062378853866875504841<37>
2×10139-1 = 1(9)139<140> = 191 × 619 × 6991 × 383697359 × 37017759367171503340151408851<29> × 1574876758726287513138659381798639<34> × 1081735706601386314068213756663600329276092976490261046845791<61>
2×10140-1 = 1(9)140<141> = 89 × 68567 × 411986842103<12> × 78243273145651897<17> × 45790969898680950598430026489151331148057<41> × 22203152531205841279242744607049040699497136455068620741800643479<65> (Chris Monico / GGNFS for P41 x P65 / August 19, 2004 2004 年 8 月 19 日)
2×10141-1 = 1(9)141<142> = 32015917066318421<17> × 83095559222912033513201<23> × 457218767870528707150601057398381<33> × 1644228552092592766221749652915894943375075120633042497702698329709599<70>
2×10142-1 = 1(9)142<143> = 7 × 9554829631<10> × 4356731702671<13> × 3357467657868616871<19> × 2187736421927986737235449390719177<34> × 9344183469892461100358281997257285354029613953632153751125132345671<67> (Chris Monico / GMP-ECM for P34 x P67 / August 18, 2004 2004 年 8 月 18 日)
2×10143-1 = 1(9)143<144> = 644351574301<12> × 107281422616573668503595416894220191851<39> × 2893227456310286462832991811810130099788185702416662782780831395802057171334344263213571023649<94> (Chris Monico / GGNFS for P39 x P94 / August 18, 2004 2004 年 8 月 18 日)
2×10144-1 = 1(9)144<145> = 31 × 9804138075439<13> × 13854961586932530041353553255527433<35> × 474956195168874037512374864466717106402173543729681853735275008639338252700754042774999705598967<96> (Chris Monico / GGNFS-0.52.2 for P35 x P96 / August 16, 2004 2004 年 8 月 16 日)
2×10145-1 = 1(9)145<146> = 19 × 1559 × 20089 × 172563109 × 181058459 × 1075734715959193269283226578855658554592998492316955174560854450407945424319248073957227218305717039530716235292611964941<121>
2×10146-1 = 1(9)146<147> = 23 × 71 × 474911 × 257888265970814323320086855272227027633371129996351925483990159123030217349661840078449713663628105479699749408553570696882551093342254273<138>
2×10147-1 = 1(9)147<148> = definitely prime number 素数
2×10148-1 = 1(9)148<149> = 7 × 117070574659995165200777586374365068986623688168229103<54> × 24405303086969361747536590638875719351910103103955718453805022842339158858638099335114643253319<95> (Chris Monico / GGNFS for P54 x P95 / August 15, 2004 2004 年 8 月 15 日)
2×10149-1 = 1(9)149<150> = 59 × 8885059 × 1493309014925537823429198505631<31> × 255486514302691494846148453167109949281503703507120073976338942411963652635881540252707023179121976597815727409<111> (Chris Monico / GGNFS for P31 x P111 / August 13, 2004 2004 年 8 月 13 日)
2×10150-1 = 1(9)150<151> = 17 × 336263 × 6516017 × 11385821807<11> × 55120529024967151191001971500609072753<38> × 85554335523575100570067317351631393271852473171138400561538366131132422284355387689070967<89> (Chris Monico / GGNFS for P38 x P89 / August 1, 2004 2004 年 8 月 1 日)
2×10151-1 = 1(9)151<152> = 401 × 15791 × 320609 × 13051070336175283765241555981<29> × 754838685673403250817815467686560425964416958861401194449084381071630229722100857179323372193549672196641809541<111> (Wataru Sakai / GMP-ECM B1=10000000, sigma=629645722 for P29 for P111 / October 10, 2004 2004 年 10 月 10 日)
2×10152-1 = 1(9)152<153> = 127873 × 386726542721257<15> × 120528515901893905389937<24> × 33555008398613958752729265693235379355563530553168817452380845249912167919983150062798194145182858583305123607<110>
2×10153-1 = 1(9)153<154> = 15691768246211<14> × 353513036560672278720383066571230366372013904846573971289155955705721<69> × 360539354070797054614614477395854393904128587102075385793873356333263229<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 for P69 x P72 / 18.09 hours on Core 2 Duo E6300@2.33GHz / March 1, 2007 2007 年 3 月 1 日)
2×10154-1 = 1(9)154<155> = 7 × 47 × 6473 × 60889 × 820757286744157311721<21> × 709409658839905576587856324121<30> × 264897466561486457459040040838987171311953866242931984277806029435709662518462889628767297703<93> (Alexander Mkrtychyan / GMP-ECM 6.1.1 B1=50000 for P30 x P93 / January 5, 2007 2007 年 1 月 5 日)
2×10155-1 = 1(9)155<156> = 5012795239<10> × 136754115856816167695867638454568058370179471864695591167031691027321981<72> × 291749166878241872177396255297205394204088421236507456460074010898849116061<75> (Anton Korobeynikov / GGNFS-0.77.1-20050930-athlon for P72 x P75 / 141.14 hours / January 26, 2006 2006 年 1 月 26 日)
2×10156-1 = 1(9)156<157> = 31543 × 99879751314103257507070930078903<32> × 634818460244410667590194554947948312452377489168571246831381943469948522781850559392697592627523228359592226813837713231<120> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P32 x P120 / 21.97 hours on Cygwin on AMD 64 3400+ / April 7, 2007 2007 年 4 月 7 日)
2×10157-1 = 1(9)157<158> = 29 × 121465463101<12> × 904379301033768345717044160825785309<36> × 6457091006561228200494377454089107772956770149<46> × 972280702625490682212362702573778085813248187465970804365743191<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P36 x P46 x P63 / 25.26 hours on Cygwin on AMD 64 3400+ / April 18, 2007 2007 年 4 月 18 日)
2×10158-1 = 1(9)158<159> = 1285907719<10> × 586074106312714207<18> × 19164974945145553260890513<26> × 2146234644932441031676835698745485661674751462177<49> × 6451819391586870357110797574746788420003224310291851364103<58> (Tyler Cadigan / GGNFS-0.77.1-20050930-pentium4 gnfs for P49 x P58 / 26.18 hours on P4 3.2 gig, 1024 mb RAM / October 8, 2005 2005 年 10 月 8 日)
2×10159-1 = 1(9)159<160> = 31 × 269 × 1069 × 624521 × 972779112004724071<18> × 198218330943890143039085853511<30> × 1863087356568022561958848459430622336906208220440978054782168211919375375101660488520582074357218689<100> (Wataru Sakai / GMP-ECM B1=10000000, sigma=3417462312 for P30 x P100 / October 23, 2004 2004 年 10 月 23 日)
2×10160-1 = 1(9)160<161> = 7 × 719 × 3521112583666989208128791647491651766924820281<46> × 1128556103542058996746525728749181096617698429611282103116231114503378579024061149030723533547291222035342709663<112> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P46 x P112 / 35.80 hours on Cygwin on AMD 64 3200+ / May 11, 2007 2007 年 5 月 11 日)
2×10161-1 = 1(9)161<162> = 251 × 161655888580414988449<21> × 4929067267522476772399515516679414108163602547357526247362820879771056978480295956320713767470483290988234487400884405613572415718545590701<139>
2×10162-1 = 1(9)162<163> = 127 × 5273 × 450446783 × 424040923727<12> × 6946941874684115687<19> × 44150768863179970138761108743<29> × 50978294951850258538993701135036765568108019089176244471733547982180755616368273282307049<89> (Wataru Sakai / GMP-ECM B1=2500000, sigma=2720998571 for P29 x P89 / October 10, 2004 2004 年 10 月 10 日)
2×10163-1 = 1(9)163<164> = 19 × 174487618126653641<18> × 4186331092881099761<19> × 3386583439103419048139<22> × 425516521298612683073279360167322442366672360115379403028822515179046853259828285118116601104061750216839<105>
2×10164-1 = 1(9)164<165> = 67809912161<11> × 3472891059585089<16> × 849269746741852513804011594433218560999910505467277257825655691807743756218811823354778193394745179939468558916819232666784782605675043231<138>
2×10165-1 = 1(9)165<166> = 7655941307665973375570133663486511<34> × 261235022530460006598408687183638970951651414830860078908511421097709137512874249975566177407311365807827101538554263013466888047409<132> (Makoto Kamada / GMP-ECM 6.0 B1=38000000, sigma=3142880293 for P34 x P132 / March 15, 2005 2005 年 3 月 15 日)
2×10166-1 = 1(9)166<167> = 72 × 17 × 857 × 8209 × 257263 × 851690129 × 6530536353569<13> × 32405593978005727<17> × 1054154281592478309289721<25> × 69820339848213929486700226609055408555720325559518563085005422922099263299504866066872511<89>
2×10167-1 = 1(9)167<168> = 4909 × 16729 × 76379 × 2075226395886463745978813668503914095832906194613111381<55> × 15364821936988404978129042011260705176086625946572656434503802043499982149928090393044705627002582341<101> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.32 for P55 x P101 / January 4, 2008 2008 年 1 月 4 日)
2×10168-1 = 1(9)168<169> = 23 × 1777 × 18839 × 135391 × 364756495659471337<18> × 636103204077055081116683110150349594823972754883063<51> × 82686854649109369630282597434781951218127495551479593262504037019953021599941887782351<86> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P51 x P86 / 24.35 hours on Core 2 Quad Q6700 / May 9, 2009 2009 年 5 月 9 日)
2×10169-1 = 1(9)169<170> = 9479 × 22528741 × 58898760265545578947543164298726379592443127301<47> × 1590099849864182210494369250009957128474833068460631622744916529265419584880420247201933949436069843089442684241<112> (matsui / GGNFS-0.77.1-20060513-prescott snfs for P47 x P112 / 177.49 hours / June 4, 2008 2008 年 6 月 4 日)
2×10170-1 = 1(9)170<171> = 372939703851234256631<21> × 1476778544474435499113<22> × 435805161629542059835776832137316524513544223593929263<54> × 833265940121934456634651862380154649875027665246097890955759336287836945791<75> (Dmitry Domanov / gnfs-lasieve4I12e for sieving, msieve for postprocessing and linear algebra for P54 x P75 / 1.27 hours / May 12, 2009 2009 年 5 月 12 日)
2×10171-1 = 1(9)171<172> = 6569 × 568471 × 1534359796328829895031<22> × 5602144536868763044479389<25> × 4966249304875500322389200136777001930696447359469<49> × 12546205073768228751789097590163050732197922850972414927607422229231<68> (Wataru Sakai / GMP-ECM B1=2500000, sigma=1049067351 for P25 / October 9, 2004 2004 年 10 月 9 日) (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P49 x P68 / 79.11 hours / July 23, 2005 2005 年 7 月 23 日)
2×10172-1 = 1(9)172<173> = 7 × 113 × 3109031 × 8132582165700864725384794456880466047998180331487391565237349262086355212969573987951557563542321517007668473186555972632366243814534380143640927376057118826501119<163>
2×10173-1 = 1(9)173<174> = 8039 × 201325174297090859039<21> × 123574790609783027246842790818912629400260138380434404128998437307189726999390879145839993022426984160482292441955959427540282984682342556834245432119<150>
2×10174-1 = 1(9)174<175> = 31 × 433 × 432861613054879<15> × 619180306815359879947719443746703720133427088087349543290858026082921<69> × 555922429864657334982749661703084805904449869206638420241546962493043429452142780416407<87> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P69 x P87 / 34.42 hours on Core 2 Quad Q6700 / May 10, 2009 2009 年 5 月 10 日)
2×10175-1 = 1(9)175<176> = 28907629 × 2056488191<10> × 132225919007591<15> × 252597480480496167240007038032606644816424127704209356727130090671<66> × 10072695254702194408495084787330701009705144691937916451329143381917222375956381<80> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P66 x P80 / 38.52 hours on Core 2 Quad Q6700 / May 12, 2009 2009 年 5 月 12 日)
2×10176-1 = 1(9)176<177> = 257 × 156577 × 16506330678736007<17> × 6963592316914968855505993<25> × 2638173759595778891884183100234637053647717064980325343311<58> × 16390100988022968074152500639629002445679211540543545306742330563674831<71> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P58 x P71 / 43.15 hours on Core 2 Quad Q6700 / May 13, 2009 2009 年 5 月 13 日)
2×10177-1 = 1(9)177<178> = 131 × 2341 × 6451 × 8219 × 1213759 × 9792964619<10> × 906338562589<12> × 1221030562037153341<19> × 9350775329684102171038671577136759905391113341535845981610226391224406406632918776058863102655323754585576897765428069<118>
2×10178-1 = 1(9)178<179> = 7 × 19697 × 49871 × 2168131776887<13> × 21546540858697<14> × 34452787495073<14> × 702699414074538345359<21> × 11232286032052640081577527<26> × 67824241037706050027234164121994583646719<41> × 3375775122619098833564433321864778716021439<43> (Wataru Sakai / GMP-ECM B1=2500000, sigma=2325465454 for P26, PPSIQS for P41 x P43 / October 18, 2004 2004 年 10 月 18 日)
2×10179-1 = 1(9)179<180> = 149 × 19645014971<11> × 838639710091<12> × 13513905648601<14> × 7736164186569272400196540924681661<34> × 779308440001156560248963164065011218680470960978737478778245389819252290693403741828408530381050760178412831<108> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3871587776 for P34 x P108 / August 8, 2008 2008 年 8 月 8 日)
2×10180-1 = 1(9)180<181> = 2089 × 25247 × 906097649 × 2812810690923703<16> × 3646742702319169110919751900918642423<37> × 4080009229030868132507753050857621102187848916600309751871730009887972204041194243916993303782420351451924397113<112> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=386652535 for P37 x P112 / April 24, 2009 2009 年 4 月 24 日)
2×10181-1 = 1(9)181<182> = 19 × 71 × 7349 × 808897818779368181<18> × 797129087967153857493783971<27> × 5050517525163785428349019657192204840675990331<46> × 619486140631122497714177220241924734371086778583423922913708782283498388270677109979<84> (Wataru Sakai / GMP-ECM B1=10000000, sigma=1614436620 for P27 / October 16, 2004 2004 年 10 月 16 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P46 x P84 / 68.24 hours on Core 2 Quad Q6700 / May 19, 2009 2009 年 5 月 19 日)
2×10182-1 = 1(9)182<183> = 17 × 503 × 12703 × 4906991 × 33194257 × 15819838750753<14> × 714539966219975752093651873450560138857789232148671578445867424286812032749141116170524740216510076628678028776224537205938204657599155251444716553<147>
2×10183-1 = 1(9)183<184> = 298385575419109<15> × 138315648629492573181397043870991531509<39> × 48459714744214666303053112592352799187563839995254738535415184574936072669072865614713121962535167281027204906904020713946527407079<131> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=3048775659 for P39 x P131 / April 22, 2009 2009 年 4 月 22 日)
2×10184-1 = 1(9)184<185> = 7 × 89 × 32102728731942215088282504012841091492776886035313001605136436597110754414125200642054574638844301765650080256821829855537720706260032102728731942215088282504012841091492776886035313<182>
2×10185-1 = 1(9)185<186> = 29 × 1019 × 3061 × 185641 × 1163879 × 1106128781<10> × 9251391506601896548962062072135342672345671944336259503519575724578399287203123684189569944151269941558109673013010611619075630257857646553294751235396292351<157>
2×10186-1 = 1(9)186<187> = 296901871784840474596451067124798270007983<42> × 6736232371917697306232661533335076985833929307159972549000421272481243378053186113524491727400346082186043249318474480674836559545201820196754353<145> (Makoto Kamada / GMP-ECM 6.0 B1=30000000, sigma=424246314 for P42 x P145 / March 15, 2005 2005 年 3 月 15 日)
2×10187-1 = 1(9)187<188> = 112121 × 2328514751<10> × 9133133914964840069<19> × 8387725594967797877847445149097455195284251960530280357373107440551290859414624091276013600436646558649912416870390629400114457530426651435186232182834101<154>
2×10188-1 = 1(9)188<189> = 69761 × 2866931379997419761758002322214417797910007023981880993678416307105689425323604879517208755608434512119952408939092042831954817161451240664554693883401900775504938289302045555539628159<184>
2×10189-1 = 1(9)189<190> = 31 × 5439829 × 2720009561<10> × 13767101225803399878919<23> × 317174697888724493139312350540581<33> × 513218192797005307893534212745911015541469979463052889<54> × 1945671599615643697213895686057854815110769046170890008443525071<64> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=1000000, sigma=3783356541 for P33 / April 18, 2009 2009 年 4 月 18 日) (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m, Msieve 1.39 gnfs for P54 x P64 / 21.19 hours, 0.93 hours / April 21, 2009 2009 年 4 月 21 日)
2×10190-1 = 1(9)190<191> = 7 × 23 × 151 × 1043761 × 27676127635110233402503730692785558639486036666823955434117813714327581673274833<80> × 28478740748702695477340652489819896975660217520497038645376481346236576555545798008200801855853755193<101> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P80 x P101 / 128.90 hours on Core 2 Quad Q6700 / May 24, 2009 2009 年 5 月 24 日)
2×10191-1 = 1(9)191<192> = 2749 × 218227091623637911<18> × 1634251873308525786539681<25> × 374917624436804778786980691929301633251<39> × 544116308602057079193319001051462073305059198331631713353356980808064530293851666207891990993563912562753711<108> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=2535079878 for P39 x P108 / April 24, 2009 2009 年 4 月 24 日)
2×10192-1 = 1(9)192<193> = 13126437311707103<17> × 151419514294581983<18> × 34800207118492911860248366555234613008736732153524878679537<59> × 28914750508730044277748248804535726260023740804371880053958065619493865157416478604450813537747698223<101> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P59 x P101 / 185.08 hours on Core 2 Quad Q6700 / November 3, 2009 2009 年 11 月 3 日)
2×10193-1 = 1(9)193<194> = 61 × 3011 × 3019 × 2630399 × 1921011481<10> × 5467489597378404813936108409<28> × 394666621455911984281003929471901<33> × 27527725817981321521808835728186950658541825851539<50> × 120167217091555354429467632255431770850693114035283138229779<60> (Wataru Sakai / GMP-ECM B1=10000000, sigma=1047059932 for P28 / October 16, 2004 2004 年 10 月 16 日) (Jo Yeong Uk / GMP-ECM 6.2.1 B1=1000000, sigma=1344099513 for P33 / April 16, 2009 2009 年 4 月 16 日) (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m gnfs for P50 x P60 / 11.32 hours / April 19, 2009 2009 年 4 月 19 日)
2×10194-1 = 1(9)194<195> = 1039 × 1759 × 16487 × 63521 × 104493588576799778029745932897776423435623522437820868568575839405719277133251214352782274114545948413633042007458508830338272808110910294096478994736256530726368019295225237414137<180>
2×10195-1 = 1(9)195<196> = 5899211 × 14379834023187049<17> × 8005520506168541677107500091857021276142810375469214148691261<61> × 2945049630407235486850246768492493463787273516148281573264435077057996480481973645153052764487171176571079917881<112> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P61 x P112 / 209.06 hours on Core 2 Quad Q6700 / November 25, 2009 2009 年 11 月 25 日)
2×10196-1 = 1(9)196<197> = 7 × 21786481 × 1184519727783750416654949243024504531875874583481<49> × 110714007151192388668548159387672871512485358734847066883913445369139729551089568055349728260200404587217820110723312598003341429367614469537<141> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P49 x P141 / 216.90 hours on Core 2 Quad Q6700 / December 4, 2009 2009 年 12 月 4 日)
2×10197-1 = 1(9)197<198> = 3489781 × 1544884849<10> × 99635152957880897351925251119<29> × 3106715592670622545052652201311870702958135715650492536479382258704707479<73> × 119845468875413674461665854674334297323102627345704299514768319724130736097956971<81> (suberi / GMP-ECM 6.1.2 B1=1000000, sigma=1950883594 for P29 / March 6, 2007 2007 年 3 月 6 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P73 x P81 / 263.39 hours on Core 2 Quad Q6700 / December 13, 2009 2009 年 12 月 13 日)
2×10198-1 = 1(9)198<199> = 17 × 16054153 × 7328138633257663095941958591832354934613382300151097791258344766725762852911202551543553137639470462693287121993403495399748148729893790612017595549703483175313687661123097116439370584560599<190>
2×10199-1 = 1(9)199<200> = 19 × 17339562682791539<17> × 7572092218037286911<19> × 15088679290694653491630959079652649<35> × 531338312951247025629014580036481987176765320031147478358915519016343794161299690194525950929141452320767635858987664888979395601<129> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=1000000, sigma=1624952013 for P35 x P129 / April 19, 2009 2009 年 4 月 19 日)
2×10200-1 = 1(9)200<201> = 47 × 199 × 8832847 × 26986789362889673<17> × 22887618087703883422612434497873<32> × 446230848885739862951514158743047799808097303689909318714879633<63> × 8783486649009658366262878191277303628728254895476682026895585605704238396823777<79> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2533383244 for P32 / October 21, 2008 2008 年 10 月 21 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P63 x P79 / 292.58 hours on Core 2 Quad Q6700 / December 26, 2009 2009 年 12 月 26 日)
2×10201-1 = 1(9)201<202> = 229 × 289189 × 11850109 × 2140346269<10> × 58220374391<11> × 11232633946279<14> × 1820747652687313076970308237133116930047760557180215846455038964786067841935440364907863228689030237665702281690107267501915506813149396724639068863512991<154>
2×10202-1 = 1(9)202<203> = 7 × 97 × 193 × 10887269430851606110740157451334950006410956238169962350116393113059379144762607906298681010433<95> × 14017931766725193798009993413128300665116551857940075373015027011867140655651019500253515393441382615849<104> (Robert Backstrom / Msieve 1.42 snfs for P95 x P104 / April 28, 2010 2010 年 4 月 28 日)
2×10203-1 = 1(9)203<204> = 8641 × 14401 × 79899380269<11> × 97532565451<11> × [206243505403495911597908087256138164868498356076098099558980803593541802611700028125565284467739707634286604953739495769406508417342502338966508299184706373918392466485058481<174>] Free to factor
2×10204-1 = 1(9)204<205> = 31 × 127 × 223 × 2278031461892520197596449004557201939515986655291696233616682480001731303911038315350173301243463473474032149858021689137548678684801315790972389119666131708945032239840264433892096483744536995800449<199>
2×10205-1 = 1(9)205<206> = 4871 × 2292880818603421<16> × 1129082288029883803778855245661<31> × 18267480823362442131123116525295271<35> × 86821269170952872115709575612725419805572670772984827452764621752224307611971320114733839906029817493536229360718458620119<122> (Serge Batalov / GMP-ECM 6.2.3 B1=3000000, sigma=3975420477 for P31 / May 17, 2009 2009 年 5 月 17 日) (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=398694169 for P35 x P122 / September 16, 2010 2010 年 9 月 16 日)
2×10206-1 = 1(9)206<207> = 11887 × 25251681423007905250365508795903<32> × [666296345653486704742396440597318758413330523030411841134328740685319859888372657484412271028953068923412326473632165793283237236740121087632239829994708821140851105993359<171>] (Dmitry Domanov / GMP-ECM 6.2.3 B1=11000000, sigma=1034025118 for P32 / May 17, 2009 2009 年 5 月 17 日) Free to factor
2×10207-1 = 1(9)207<208> = 59 × 3094811768747411<16> × 617154916981980493532291<24> × 1381098786990645604063367397059<31> × 10018631606052288287701622273517610992315312691<47> × 1282674318787362762030604322874622092382640612854027342323747789696130963429438316715523069<91> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=4230776172 for P31 / May 14, 2009 2009 年 5 月 14 日) (Andreas Tete / Msieve 1.42/GGNFS gnfs for P47 x P91 / 358 hours on Intel Core 2 Duo/Windows Vista 32bit / June 17, 2009 2009 年 6 月 17 日)
2×10208-1 = 1(9)208<209> = 72 × 316769 × 1261104223<10> × 10800589647845288422796999<26> × [94600361508194417808845189664460761795365750560873194715127655656396575836163788368086818879930145147365854243279065054512833388878881284857599529159076473575765237927<167>] Free to factor
2×10209-1 = 1(9)209<210> = 10517839 × 16438921 × 24894579583324819<17> × [46464939100042697600614425001664512760626535616435264062210365888932453527175575025017747970911072980754755948405481423013229367366413363421783102983893777684592394221438848150259<179>] Free to factor
2×10210-1 = 1(9)210<211> = 29981284013647<14> × 66708283710918853648732669496601455073768019495372107410298266417531002281288366831362447914251993787664432276474332877903253883831469467663624285564104571869125582069868761507762676598626087944017<197>
2×10211-1 = 1(9)211<212> = 251 × 2801 × 4566241 × 25133017109<11> × 2484626288622811<16> × 35483368469100191<17> × 15854417124067871024502366511<29> × 177338696547218351291916369975797216832676052273918978821507669208855210386731730351736313471339489806102171229801686832536171611<129>
2×10212-1 = 1(9)212<213> = 23 × 2659264777745734405392508581327747941839503713<46> × 2624192453344997234656310661787467697906712795425020425430953<61> × 1246077046444953259325719448796658447093073224853980853958734916369485280891634235590281319558742952446417<106> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs for P46 x P61 x P106 / 95.16 hours, 39.93 hours / July 24, 2009 2009 年 7 月 24 日)
2×10213-1 = 1(9)213<214> = 29 × 821 × 7321 × 44902829 × 355233079 × 448280798882078069<18> × 6854966628808903721<19> × 234086219568768493384575699787100131203631236989253043340192309882596800453568219637513520191401486652706213975883087807418507263360931285631349876089449<153>
2×10214-1 = 1(9)214<215> = 7 × 17 × 79396251305573567<17> × 90288233488896424057<20> × 38115909555433345954531231<26> × 4527679177526271288878246116902813487115348661250329601<55> × 135853223202787949610434952210566450405247369397335279146560176050361418950930870598873587043489<96> (Maksym Voznyy / Msieve 1.53 gnfs for P55 x P96 / March 18, 2015 2015 年 3 月 18 日)
2×10215-1 = 1(9)215<216> = 12796511725008761<17> × 27429835724790464950651<23> × 5647867226197265737178521409151356032975171<43> × 100885955497876350459801214147186643323219778125710043383860749253138995567501898917844183928490667984665423619911084339929735901691879<135> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4157263564 for P43 x P135 / September 12, 2016 2016 年 9 月 12 日)
2×10216-1 = 1(9)216<217> = 71 × 1801 × 361107090626796555790432520736349127614104388447835771607771886723658185918374320268583<87> × 43313364268944003504537958096108351815974418622703052728674628970748248006983423154634967569396860724808442556827278605720343<125> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs for P87 x P125 / 137.94 hours, 48.48 hours / July 5, 2009 2009 年 7 月 5 日)
2×10217-1 = 1(9)217<218> = 19 × 709 × 904769 × 1017679331050547517629<22> × 1612432315273005029221547519325069893802446516438907896918769378970555182890470089771998244901998358319022222884085640839907182440601073478933029595896151707580359174848823467490814129269<187>
2×10218-1 = 1(9)218<219> = 280537 × 19393769 × 58898316075177396200124529<26> × 3030956834611636150588809938178190058201<40> × 205918326045304987023880462558062692443480025742698637164013327598552889889315972468367083189157957819465775123958129922233219809209026155527<141> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4126081929 for P40 x P141 / September 12, 2016 2016 年 9 月 12 日)
2×10219-1 = 1(9)219<220> = 31 × 1640071 × 236968351 × 123613914166095532351<21> × 1342913215371673709132384314428352010398059853915821653698975872597752690513694392930386600551103801376643091790715611067426270736623741054661220523808133279651838890148612649228345399<184>
2×10220-1 = 1(9)220<221> = 7 × 8524543 × 1083123216870509849562557573497140850225905243919<49> × 309444654420209152261395329908853882478560572701303797798488365664928863916804072609327933421236573012248026757692102667702446776183075707594247676208587347163650521<165> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs for P49 x P165 / 235.94 hours, 66.67 hours / July 18, 2009 2009 年 7 月 18 日)
2×10221-1 = 1(9)221<222> = 691 × 1982518332226609<16> × 37097990401449202253720579534566313541888993439274719<53> × 3580489073607615161649133570085492381353320404163647894963492515009441<70> × 1099112125634785520400440345168932001505476086416380946558560136852829946082886699<82> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P53 x P70 x P82 / May 12, 2018 2018 年 5 月 12 日)
2×10222-1 = 1(9)222<223> = 36871 × 11256575312887447441<20> × 4818798847159559414262808277270282791144542592689731754992479836058813152832171773431819211303910060300022756302770538507319834219489823272350428361324379186768464326384931447073139690789365926366009<199>
2×10223-1 = 1(9)223<224> = 991 × 193339181171<12> × 455014687811<12> × 18998952161651808949<20> × 799074967864522952685457304028905075280677907771442694579<57> × 75629236044055651197575543380317363904643978252608853610461<59> × 199803992325535795136733258502243246459023366997115850762238099<63> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P57 x P59 x P63 / May 18, 2018 2018 年 5 月 18 日)
2×10224-1 = 1(9)224<225> = 31327 × 16650167 × 298792177947158051676771293532839291402503<42> × 1283285747300574986840429251058206317425003659786792461103756796752804245034948493284193579262410083183856143565321174524437218836574564979076123321836485207392190657040737<172> (matsui / Msieve 1.50 snfs for P42 x P172 / January 2, 2012 2012 年 1 月 2 日)
2×10225-1 = 1(9)225<226> = 465989 × 1171249831<10> × 3664416157863497914695709514283907492583772450826105945310867548150665250560231881142370664182117663975949546153717737724708784247203715419468375490274182457967467037864404549763044312920788954980587932491493461<211>
2×10226-1 = 1(9)226<227> = 7 × 311 × 12569 × 6389177 × 3071556314807<13> × 19809992120726537<17> × 8808853316943552116581927<25> × [213434075618454817889307827911183051733506523621295255502038075545271146595314558414496284419727857644528369210795511529925032355177091381997205863095640994743<159>] Free to factor
2×10227-1 = 1(9)227<228> = 181 × 4861 × 462130701166480949<18> × 7738480982680100571956372754821<31> × [63563127649166232179850983810523035979538568532736072983841803065409398698919788148679008482535663116387673169125836528802130741623584444603820241686574015731518580408023591<173>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3852450360 for P31 / May 16, 2009 2009 年 5 月 16 日) Free to factor
2×10228-1 = 1(9)228<229> = 89 × 4457 × 48807636799<11> × 48162227057479<14> × 34737774326489662688405116708081<32> × [61744890455627167650213481924706733811913431676549506889611587102056636349376989460925182092585372167014570509513719102469122094560721050071607131701885496911760705063<167>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2228537699 for P32 / May 16, 2009 2009 年 5 月 16 日) Free to factor
2×10229-1 = 1(9)229<230> = 1056971 × 20359951 × 390310981301<12> × 108643587038686091238436979<27> × 1777618623438564041863144034323274186021259869341<49> × 12329252234488412163887223828461528074669331418533011815823499009355818179112922682304020152807889531609920127189559662624479524321<131> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2963965273 for P49 x P131 / October 25, 2016 2016 年 10 月 25 日)
2×10230-1 = 1(9)230<231> = 172 × 25153 × 11579637493057433<17> × 3138535457534232274156466055047<31> × [757042670140688023103262622021862593490644920682966776042577257267669929768884077607148297565333700408364576107072658343098036813677912475966387405833028216803233156249615548497<177>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1024525549 for P31 / May 16, 2009 2009 年 5 月 16 日) Free to factor
2×10231-1 = 1(9)231<232> = 109 × 745090121 × 3658606079<10> × 74179326541530901081<20> × 2663495355611645172619<22> × 16582409076525192548049071<26> × 2054454778228289133057901200440524855271655987429693148672852126767779762117802090904015020543843225676653356878188447330870794689978140306240641<145>
2×10232-1 = 1(9)232<233> = 7 × 173137 × 42049591 × 34613759961280378907193267864768175303<38> × 11337871068816284810015281720676567521820709766247790016536458359116649482490012289408508986811315047442941807203647099955100565546682002698657209705791404051679009408588287240060857<182> (Dmitry Domanov / GMP-ECM 6.2.3 B1=11000000, sigma=1689352593 for P38 x P182 / May 18, 2009 2009 年 5 月 18 日)
2×10233-1 = 1(9)233<234> = 1609 × 2381 × 13213674099181<14> × 699290917369818644406271<24> × [5649800040997989056384388666276247754857572198499623320374047344432258313975849273379481728725273412701866328473256643125763907979494222199150363306306029072375768573455960964597887867800881<190>] Free to factor
2×10234-1 = 1(9)234<235> = 23 × 31 × 191 × 541948937 × [27098717017062763064867378498742260949704289212960255697168605099948265071065644392435612897499759962854142243349748884751678132791707148264568135254763719255700170594345462167291546083222452237623025198919167166800699569<221>] Free to factor
2×10235-1 = 1(9)235<236> = 19 × 11742127529639617091<20> × 24734627499503903886129707945872081<35> × 3624300738197514433948116321239673665803105676015203953781909187510447394307807926421163333674526214961507164548119458454691392188999339202173399362786312285254118551376900585868551<181> (Ignacio Santos / GMP-ECM 6.3 for P35 x P181 / September 16, 2010 2010 年 9 月 16 日)
2×10236-1 = 1(9)236<237> = definitely prime number 素数
2×10237-1 = 1(9)237<238> = 1485139 × 82194942679035757862701<23> × [16383919137519665857365075857641648950126706196890408994238884156004817456673000176378488006652676248990990841296517567710303513779716763530757715660719586730070510285390992589610883686320391188064986690638041<209>] Free to factor
2×10238-1 = 1(9)238<239> = 7 × 5387087655569<13> × 13243072968935599629199<23> × 62965201671173612112077966434588577521<38> × 1241039626524645947231586749425822995875293485319<49> × 512510649384347540133797702038580058069144351063337492791094921435216754112692687058523185808550102482667836579363553<117> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=1922370290 for P38 / September 16, 2010 2010 年 9 月 16 日) (G.L.I.S. / GMP-ECM B1=110000000, sigma=1773303259 for P49 x P117 / January 22, 2011 2011 年 1 月 22 日)
2×10239-1 = 1(9)239<240> = 489989 × [408172428360636667353756921073738390045490817140792956576576208853668143570569951570341375010459418476741314600940021102514546244915702189232819512274765351875246178995855008989997734643022598466496186649088040751935247525964868599091<234>] Free to factor
2×10240-1 = 1(9)240<241> = 30977 × 12900409695855239366375680297<29> × 768939656364509785489313673103933999419281121209133111029372213981826682578132857<81> × 6508709340010733253384349660312181787852385389201935124287970592367702780481744684378246016036935733744823282720286097865105503<127> (Serge Batalov / GMP-ECM 6.2.3 B1=3000000, sigma=3362628703 for P29 / May 17, 2009 2009 年 5 月 17 日) (anonymous / Msieve 1.53 snfs for P81 x P127 / May 28, 2018 2018 年 5 月 28 日)
2×10241-1 = 1(9)241<242> = 29 × 701 × 133669 × 918389 × 184446439 × 351163758889561<15> × 3512634231671191069<19> × 14014547991207664249<20> × 6201568195346907610677619779217490862219680179451<49> × 1515640017221444140682592875943600041208754026883898419<55> × 267403465773318613650419497924556166158445720532258183938516061<63> (Markus Tervooren / Msieve 1.50 for P49 x P55 x P63 / October 27, 2011 2011 年 10 月 27 日)
2×10242-1 = 1(9)242<243> = 1481 × 27617 × 489791 × 2020958713<10> × 4940036927563734650289041073484385269463137652008107595132660457838595618772789751665642437488554396724081911017367445416108766859545418263719958746998767093055262294343333514391309710931883469086980384555738120196894689<220>
2×10243-1 = 1(9)243<244> = 2711 × 276599 × 2493259 × 2195287234559<13> × 155048588595419<15> × 113500420175207955079<21> × 1880865483204037445555499001<28> × 14722043681207988906567695591206047432455624041911631493232955914158275326256087253391941171571167467123648523248542231034633511941530066472057561401050311<155>
2×10244-1 = 1(9)244<245> = 7 × 46859370631284521074087<23> × 480341489765250824405167922015763435793<39> × 4921867679204973173415073673456768771903359<43> × 1730415597322884720968936035747421071554002453936505811409561<61> × 14904075737138928891311681306233787054300958970242645264699371714965654984552073<80> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2662639535 for P43 / January 13, 2011 2011 年 1 月 13 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1471543566 for P39 / October 30, 2016 2016 年 10 月 30 日) (Erik Branger / Msieve 1.51 gnfs for P61 x P80 / December 4, 2016 2016 年 12 月 4 日)
2×10245-1 = 1(9)245<246> = 240139 × 11646344158366741257794536820925991<35> × 71511794816116647592466076649315262164366978239860741017711346458660357589133354997489778453665412237637499789509689866120922247059753039227205632490112635124358150084519402014002012700683540453240769740251<206> (Serge Batalov / GMP-ECM 6.2.3 B1=1000000, sigma=4173179287 for P35 x P206 / May 18, 2009 2009 年 5 月 18 日)
2×10246-1 = 1(9)246<247> = 17 × 472 × 127 × 167 × 2897 × 114206641463<12> × [7589712253318449977794714077767074684444795875302732461909050440959250085897090678216003417806198854786421223952603836981819020714301022097526214806505248296945201299456124540149851441228020294554464020975221227123422253217<223>] Free to factor
2×10247-1 = 1(9)247<248> = 5711 × 5137651 × 109424217918630909136935706451429<33> × 6229307717727602487152483306982713621811871446270813768407187294030930000936284989180582851699942671495245102701667423676129508232560794431964653471639690945651238874214201094168491986383412060065017416271<205> (Serge Batalov / GMP-ECM 6.2.3 B1=3000000, sigma=1912754877 for P33 x P205 / May 17, 2009 2009 年 5 月 17 日)
2×10248-1 = 1(9)248<249> = definitely prime number 素数
2×10249-1 = 1(9)249<250> = 31 × 41189 × 14688599 × 106636695609849807619380502086752177021121912178406288783928532675655707365659919290810756822029223802389954201096505087029547190893014999066365279027558324605884432982760052445287949857616056442896279752664753458991337176548938330442939<237>
2×10250-1 = 1(9)250<251> = 72 × 1567 × 2351 × 29569 × 820247 × 952297 × 125263889417<12> × 304562977541311<15> × 982182388506161<15> × 702888484216906112706328919441<30> × 182128123613230148821197951079533160449193425749123851243811061451992063535981022431453364971606385342015615469615412435780149477577202069344045728105606839<156> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3078787352 for P30 x P156 / May 17, 2009 2009 年 5 月 17 日)
2×10251-1 = 1(9)251<252> = 71 × 11161 × 785641 × 4677691 × 8457809 × 10792351 × 591124498256399<15> × 1149971024749331<16> × 1679457284483651<16> × 274652308943460228101<21> × 646558160282980885673664924252382663721<39> × 3711190639698634471777726491367182951334266196915917825578139811417732680942135477068744274563307871725360261517199<115> (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=841398543 for P39 x P115 / September 14, 2015 2015 年 9 月 14 日)
2×10252-1 = 1(9)252<253> = 772663 × [2588450592302206783552467246393317655950912622967580950556711011139397123972546893018042794853642532384752472940984620720805836438395523015855554103147167652650638117782267301527315271987917112635133298734377082893835993182021139875987332122801273<247>] Free to factor
2×10253-1 = 1(9)253<254> = 19 × 61 × 24564843700091<14> × 85612396275674017298609<23> × 8205327154445210057350266844187818519444484840555569504246761104176137828436109949433007921820005551105788689282318123337450055982211185949442747388652803924826643715600537498057776128490661459752869837355923796219<214>
2×10254-1 = 1(9)254<255> = 98953 × [2021161561549422453083787252534031307792588400553798267864541752144957707194324578335169221751740725394884440087718411771244934463836366759976958758198336584034844825321112043091164492233686699746344224025547482137984699806979070872030155730498317383<250>] Free to factor
2×10255-1 = 1(9)255<256> = 28279 × 645149 × 2136061 × 51172461041185067044021093247891401<35> × [1002896150901074685233242501626959881732830716239526443681892664728085009152154523933016880039124576931052072411899604614413125193226012365264916583004679630503369677335752428772889078440866535945091976329<205>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3508196250 for P35 / August 16, 2016 2016 年 8 月 16 日) Free to factor
2×10256-1 = 1(9)256<257> = 7 × 23 × 37777789535831<14> × 1093247873475356186061209<25> × [3007799865704962195020693948946480472572045005737835101646760914306572389752953592796637103505336216813892976809303873321222019779631837715133882240236328287177083898284580835601808922462409610112079536160573594778721<217>] Free to factor
2×10257-1 = 1(9)257<258> = 359 × 1014229 × 480114191 × 382271830773080329<18> × 2794970608942248209416807273438646754001<40> × [1070792789801865368549051477459376090946815715771871509367607652112457117865544841924856065325480891665271940611841653086631474640333731458209955143450768581293994658366185961134800931<184>] (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=3456226829 for P40 / September 14, 2015 2015 年 9 月 14 日) Free to factor
2×10258-1 = 1(9)258<259> = 217362508436713<15> × 30031443988031374566928967<26> × 7559804529108929175808240247593<31> × 40528317746227254140479246956901488970907744291407929180218085912184735496136799120409367124424447510944682406402074118061912199784886410334324124563330741683575702087460103871951826959033<188> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=3067278285 for P31 x P188 / September 14, 2015 2015 年 9 月 14 日)
2×10259-1 = 1(9)259<260> = 2939 × 136774879 × 204325739 × [243501136195883020955793057742361994950471703639984530234069999570095149547713599904552354270496780251686028152815034855466290753506115658594834268053140569580982834936244980500605199939367083553121511209585658474998749926199262827846527161<240>] Free to factor
2×10260-1 = 1(9)260<261> = 386017 × 39231295111<11> × 13206596803913358962108465614293535777777793010412434958136349704971177830167411229171396649594181648675471630552652005275839026124063638470130191325401139898361795028796806424724572289616568598061940474949287689760226550967274868500951606387177<245>
2×10261-1 = 1(9)261<262> = 251 × 78125639 × 115586920384842478460472349<27> × 882376633329532433591487559577582229860938630385559661712262077695729953647339411100790474302783328462277471574468178399152275709428434230314544140073705602789677534729040463019225230951066446306959904674392427279373439937159<225>
2×10262-1 = 1(9)262<263> = 7 × 17 × 2423 × 2713 × 31808191 × 7422381333423506137<19> × [108292303775780533373215275196355184386103563360010664528121204994406911517759230613632791196990127207549079948045609378909680880529569890829275524475652690275275256107814875503834699522660213700984638821856773619049814116659137<228>] Free to factor
2×10263-1 = 1(9)263<264> = 941 × 315701 × 4566209 × 775215785051<12> × 4881746622899<13> × 9489689589517871032476457142142210789721531051<46> × [4105431218283832152847258053278775112607772392837619100327350612401611970033958710514225304221864762287295341269035156175169543346068075543667686026510017693409513168997063794829<178>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3264853539 for P46 / September 15, 2016 2016 年 9 月 15 日) Free to factor
2×10264-1 = 1(9)264<265> = 31 × 233 × 1404112601<10> × 6631850207<10> × 881215824666769<15> × 3026675466451289<16> × [11148786317504377688886403828987938800746497957201982736570278616748541853810146169838479689183995264930141300685009006655175006064602586951396560488832657405432100871273285581527296277918787068596359469656831399<212>] Free to factor
2×10265-1 = 1(9)265<266> = 59 × 151 × 788651 × 53046614229989<14> × 1268889370978693309<19> × [42289714110879645367515569621211387901855360179797910825260079790891940741839813735395517654299967587656092910163402737608241817243983663268608225629107746182852925859192113044145941367032683662598859844329974991738648545761<224>] Free to factor
2×10266-1 = 1(9)266<267> = 31799 × 52433 × 266687 × 7278721 × 15558220966405270337<20> × [3971869510000064896818823955014221616689356304357798877113245752106581217328249938768766452612229277159677170474114359563558365367321257474516880069040659566699085363008215191844212838945909653143187473618607789706057415794903<226>] Free to factor
2×10267-1 = 1(9)267<268> = 126478930432031<15> × 387129313286407786309<21> × [40846585111218239496508271085728717933236769086081680959481527323763269733492730972328322207801130772599400985622354915339499252158856013665786084294956897477006218290221375521427895534438361910273976153464133960820121348027751751981<233>] Free to factor
2×10268-1 = 1(9)268<269> = 7 × 22679 × 87544374579480367<17> × 3662985299705113436018757467952969556751<40> × 392866171294596362136126067039462910020231728779488787271529878233527792630061999658470928675361967186152807544304648414212188681017077747994584960660749432993991314566581523518034594237955286078606809061599<207> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1434702423 for P40 x P207 / September 15, 2016 2016 年 9 月 15 日)
2×10269-1 = 1(9)269<270> = 29 × 10523212570221316729411<23> × 446616363458357804241109<24> × 753405342844286764094977271795554497743551<42> × [1947692212127630492307540540861666766968010151087395029149440647470601207529312442664462683377545489001798764276196371114530081917175314248448044306584288860761387241672302925823819<181>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3374645265 for P42 / September 14, 2016 2016 年 9 月 14 日) Free to factor
2×10270-1 = 1(9)270<271> = 6214591 × 504444529 × 11963274839<11> × 98864210549353<14> × 372186362097113<15> × 19166743996947554671<20> × 75614667576295154904964389723026073556496645815774706952599017315401846107654098200409107948614346806374705092228342394700688560677292273991805855511116185535967700976444352304508307491486154611801<197>
2×10271-1 = 1(9)271<272> = 19 × 33829 × 1245799 × 33540971 × 8247403279<10> × 2575357765991<13> × 35059750829045039266581329236184959550178492903791885875665390995920982770028135378770702019016588055519448951819156697442647596177131572369782589334721294162039881745296990832321258232465286567263978354403343281566522382126179229<230>
2×10272-1 = 1(9)272<273> = 89 × 479 × 1073539636841504993<19> × [4370049855969622657751509267718017056840768383209019041069977932155578409079992858851248068976479606787334534054713163162568856872412408968824497401314532691540645045717609568516317708642687488207778304745081739213219939286834923876278104413873771753<250>] Free to factor
2×10273-1 = 1(9)273<274> = 10009 × 12791 × 1774404026190979<16> × [8804045801773432780708162161915487816762951542776214509819236685837257208877680966324463008594347182085779821313133378680079233973331162087509063759816490930619055486570915334724249865063144119051158122750867133223978780197105794684933144620475951499<250>] Free to factor
2×10274-1 = 1(9)274<275> = 7 × 457 × 1279 × 115275593 × 25480342127<11> × 543906039760777<15> × [3059699035924711911349332437130162483890499762211859866765894598821201352373046421244777696078521712495231793918412001190960177537917172112457002142751537993050996792309644080363327669154190063154057913675660322510540325467164211818977<235>] Free to factor
2×10275-1 = 1(9)275<276> = 8831 × 6405274203091768482648930871<28> × [3535756795447177671096843954051273697838636528954804667471626988454569259733801599147259470286167575823039891444071754670523397237611987368703138114846314834392794694996673515466581011866074022898433000788362298691867313399523588421534265281799<244>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2354043752 for P28 / September 14, 2015 2015 年 9 月 14 日) Free to factor
2×10276-1 = 1(9)276<277> = 1779289 × 3266437831<10> × 16984971893241167<17> × 46779489058185361<17> × 805076905571526933740972859409<30> × 438252239243562129190754046796081<33> × 1227516351620276694225716631380968574251313090662689912864889903032256031277061039239522531226668451516880322872759629601867912327181077307436390643182383339924656207<166> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=4105922315 for P33, B1=1e6, sigma=1762603124 for P30 x P166 / September 9, 2015 2015 年 9 月 9 日)
2×10277-1 = 1(9)277<278> = 154991 × 84694022182309689901276527161<29> × [1523599273835817429045711768552023103471233104106477755008217801206735510354187748915969775234646307717017137130851471651107684573618931181780752567828225703490348174320106373979888180842437453819427207072566690514699688065590648509216087533049<244>] Free to factor
2×10278-1 = 1(9)278<279> = 17 × 23 × 1588160625767<13> × 2215488502224760200112879<25> × [145374861213860603157185167952310246020101213745400136729423418658756473753286261475234720606946818161365252394481595777689640875722729583672371549410467963278478244082275542618375197927574541260134702778600488065891027284507326230796429473<240>] Free to factor
2×10279-1 = 1(9)279<280> = 31 × 3791549 × 8194344228471868770848514206025218519<37> × 2076526247509635870571938874207255908037922857407715522200564034754677678799116780558307064278406287979109781903832485098417880019273957622512312253010046652752657133488924289192852070381115895176580385114714570072404801119795143970259<235> (Serge Batalov / GMP-ECM B1=3000000, sigma=3216141061 for P37 x P235 / September 17, 2015 2015 年 9 月 17 日)
2×10280-1 = 1(9)280<281> = 7 × 414553 × 754417 × 111344873 × 82048416322485613899042386968263929264007554924334615770540296600756394186255099850328330241224845511334257693297038106934221312831582424700501809936097608189959422519537794826734651337850627490776554688691683793113061443227031691498239654935819467171768507609<260>
2×10281-1 = 1(9)281<282> = 2609 × 4139 × 82822441864994939<17> × 9643293030540064101084121<25> × [23189270980210829399539378318357869004445333199294378074063601481665297531795987827857087019967837796703207497946861305832128490405376090892553441787961835663955069836728674365084067481772537906105081440793141113511273515891648981871<233>] Free to factor
2×10282-1 = 1(9)282<283> = 60426833 × 1127563655613537436926871<25> × [29353446006877275996414691398446541279628495425912119227643437540624576290097460180789918330670910591087064652118571948819904807066718401254036908886838229841279022230322720096152937969136882932404697284051575135902725529556862610481590941264309667593<251>] Free to factor
2×10283-1 = 1(9)283<284> = 179 × 389 × 138773951538073970441<21> × 5124966083290521492848576111<28> × [403857742128385142583506513911328492817948123452119520644068750960897874146763733684257265695783665414441283802270822816671467468300416926481399870886424455278242266074755208011001254167097825157077569220374171254174071256008638679<231>] Free to factor
2×10284-1 = 1(9)284<285> = 113 × 4919 × 54720742511<11> × 29853514414241986159<20> × 14508228312863817006419096349489344523161<41> × [15181437712130025685195916562580479869536740062048525648673023604787775388198635826914341855875493161713513923161703297067827492884711613407923215197006493542128961815773305914471222914272373005525812112431953<209>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1815942234 for P41 / August 17, 2016 2016 年 8 月 17 日) Free to factor
2×10285-1 = 1(9)285<286> = 431 × 971 × 68773969284491<14> × [69487934917314733702517849002695798831024031331447053662139621514698368762419550303080376959420862594618132081847247157866546800163808668989477150450505893133006285973353417693439219058519543359964030327328158903797827919256205375785498441569345943398073532951416889<266>] Free to factor
2×10286-1 = 1(9)286<287> = 7 × 71 × 706049 × 56995263348794371927486875679335449364178368124329741046324117135605122543905610053175640282579893901208451475371265221863908516925596955493136939586841848941959737046994985582378441578115287072046826122865891801052687125331127875020262172340892329185046131096976748095523935983<278>
2×10287-1 = 1(9)287<288> = 80241211 × [2492484815564411160245325808953705845740538487137239242314027389242667337111848922619076623856038264427489759594979193422192992575847341087611451925868865563357462289545954135712134254803307990952429668590121352979082033046585002312589724001049784754619418692472126324215121828109<280>] Free to factor
2×10288-1 = 1(9)288<289> = 127 × 439 × 3719 × 80929 × 94841 × 648871 × 83219404740653479<17> × 185245277253272070755759886423577<33> × [125633414472075551386683570675809589383190687529563725372359576335205681238468055135306564785012267201358134525325444003972268720359672375938969767365339092042686331390961199902922319544647905728152345183583906923041<216>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2560321964 for P33 / August 18, 2016 2016 年 8 月 18 日) Free to factor
2×10289-1 = 1(9)289<290> = 19 × 3121 × 11336701058190554755769<23> × [29750613870482226866005841193762091858631893244516678102573014990558967510573836516249763984353777612120450390963553632138823715303151958566268379286361172131963307250250056240696705071853052947969412720436872199672446804772852152395406322651393974318684528928029<263>] Free to factor
2×10290-1 = 1(9)290<291> = 41969 × 787876271398481<15> × 16763397698323796831<20> × 206414341181145490844588973655889960374711<42> × [1748000035701010303413225740883228247309831922542558944623667709586782325049581715671273543344678826824626417700922538008039980422031687695053277408227823094374228617052613131510160547614318636389688458265541351<211>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=171572746 for P42 / August 18, 2016 2016 年 8 月 18 日) Free to factor
2×10291-1 = 1(9)291<292> = 461 × 50741 × 2334301741980627466631<22> × 36627987232422897456590027583327312878718230865012976385057805440008035460796812972274818623497095335845037034336277194058558047274861893726834536096448686986875815980196014279038337373277429316710653509629737672912816461204245057380842103707730760452365486010329<263>
2×10292-1 = 1(9)292<293> = 72 × 47 × 205441 × 182320172029734674147687<24> × 284369231088868727447681872721<30> × 3473291648929580613575847254067555870289<40> × 234741761699046838290560869887731369635833214557051361651835461924287571558033034875489384315340446516523406511250941828398158072326800269484904072652350923201985630008137652615404257304977271<192> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=160173365 for P30 / September 10, 2015 2015 年 9 月 10 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=804687410 for P40 x P192 / September 14, 2016 2016 年 9 月 14 日)
2×10293-1 = 1(9)293<294> = 2239 × 234461 × 959930351 × 17994963291161<14> × 169809405442025201420652239<27> × [129883163899643078569960347789075514997501969037199373583669145521773604844739741234114951644202887962820071869418943975814855426085143358440052103085365202588604140749390486585268252972784566372448652152585548951120728497014122447388989<237>] Free to factor
2×10294-1 = 1(9)294<295> = 17 × 31 × 112129 × 6012847 × 5753194801<10> × 623331893287<12> × [1569613952298245836419802228638515846656652560426801936051182630789378085771892517676432930045172053341398807957449386936794199102568804249127160742749485362742060346488635059709905156068819200916897929275614534278672000007987710401744943057543077210973017977<259>] Free to factor
2×10295-1 = 1(9)295<296> = 77554517134769978005361<23> × 80599757774651616620196245733333986359<38> × [3199551911512591536773441610985245325109493316353894623184815520019023691743777639404834506137313448066389285861009949310269182845445313676719456606796185200855400080714347431242541433677399820984677315271963318782693136161783363230601<235>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=765687372 for P38 / August 18, 2016 2016 年 8 月 18 日) Free to factor
2×10296-1 = 1(9)296<297> = 10831 × 44732641 × 87252708801845102729<20> × 169710850657848324876535355632759<33> × [27877149957833052759357433012617164889258625835376414761589420368515845232756921277629078662927073433741056918906236335270575379083570292058632599316773996186341582601909520685555453479482995471145550568156148883807876390154557261279<233>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=245227043 for P33 / September 10, 2015 2015 年 9 月 10 日) Free to factor
2×10297-1 = 1(9)297<298> = 29 × 1399 × 108350219 × [454971811209739570017930168614958085656573137236257812464667157503730893237232045868860249047093866656543634982938019504278942672465617216413868519540214187225732002884730372645139289088912129114703964890266538768261649083832915800559222715732632590965747587788691342410526923981612551<285>] Free to factor
2×10298-1 = 1(9)298<299> = 7 × 97 × 11927 × 66283561471999<14> × 6064873804149756050641<22> × 41465797689962363425304293515259329673<38> × 148153315061957048507460250829948073738540749533994134352112796204154362712279669985568060348849453794395888759436777483089722027255345849774590516208966742813211718177152705110735130705745477492790285679038514629181929<219> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=715752665 for P38 x P219 / August 18, 2016 2016 年 8 月 18 日)
2×10299-1 = 1(9)299<300> = 199 × 362741 × 1372148771519<13> × 436104415345231166071<21> × 17791487776890066588709<23> × 3150567955572954240630224669<28> × 4340164002992204927990637569<28> × 42479852665756075785721235189397258725909<41> × 1488454526970607486375903736260852824900429960437579<52> × 300997408672128086563922024310896708228743907667520819618218767439331412800972615425338251<90> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=786417369 for P28, B1=11000000, sigma=1515296608 for P41 / September 14, 2015 2015 年 9 月 14 日) (Erik Branger / GGNFS; Msieve gnfs for P52 x P90 / November 1, 2016 2016 年 11 月 1 日)
2×10300-1 = 1(9)300<301> = 23 × 727 × 11959 × 12873599 × 268672194037246941588714048096066318243887<42> × [2891679684489757608277345277115956468986475509083037564984900075816173985690487060385305933254319903597363191065152404925906220705425124831906472178497066585342406002438488701500789214469670693647399317009747041990818440722830709966453103386457<244>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1463677292 for P42 / September 15, 2015 2015 年 9 月 15 日) Free to factor
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