Table of contents 目次

  1. About 299...99 299...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 299...99 299...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 299...99 299...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 299...99 299...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

29w = { 2, 29, 299, 2999, 29999, 299999, 2999999, 29999999, 299999999, 2999999999, … }

1.3. General term 一般項

3×10n-1 (0≤n)

1.4. Related sequences 関連する数列

2. Prime numbers of the form 299...99 299...99 の形の素数

2.1. Last updated 最終更新日

September 9, 2015 2015 年 9 月 9 日

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

  1. 3×100-1 = 2 is prime. は素数です。
  2. 3×101-1 = 29 is prime. は素数です。
  3. 3×103-1 = 2999 is prime. は素数です。
  4. 3×106-1 = 2999999 is prime. は素数です。
  5. 3×107-1 = 29999999 is prime. は素数です。
  6. 3×1019-1 = 2(9)19<20> is prime. は素数です。
  7. 3×1027-1 = 2(9)27<28> is prime. は素数です。
  8. 3×1043-1 = 2(9)43<44> is prime. は素数です。
  9. 3×1055-1 = 2(9)55<56> is prime. は素数です。
  10. 3×10207-1 = 2(9)207<208> is prime. は素数です。
  11. 3×101311-1 = 2(9)1311<1312> is prime. は素数です。 (Harvey Dubner / Caldwell, Cruncher / December 31, 1989 1989 年 12 月 31 日)
  12. 3×103204-1 = 2(9)3204<3205> is prime. は素数です。 (Harvey Dubner / Caldwell, Cruncher / December 31, 1989 1989 年 12 月 31 日)
  13. 3×107050-1 = 2(9)7050<7051> is prime. は素数です。 (Harvey Dubner / Cruncher / July 31, 1993 1993 年 7 月 31 日)
  14. 3×109439-1 = 2(9)9439<9440> is prime. は素数です。 (Harvey Dubner / Cruncher / July 31, 1993 1993 年 7 月 31 日)
  15. 3×1026044-1 = 2(9)26044<26045> is prime. は素数です。 (Harvey Dubner / Cruncher / September 10, 2000 2000 年 9 月 10 日)
  16. 3×1033058-1 = 2(9)33058<33059> is prime. は素数です。 (Harvey Dubner / Cruncher / October 9, 2000 2000 年 10 月 9 日)
  17. 3×1034507-1 = 2(9)34507<34508> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / January 4, 2002 2002 年 1 月 4 日)
  18. 3×1049314-1 = 2(9)49314<49315> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / February 8, 2002 2002 年 2 月 8 日)
  19. 3×10119292-1 = 2(9)119292<119293> is prime. は素数です。 (Daniel Heuer / NewPGen, PRP, OpenPFGW / August 7, 2006 2006 年 8 月 7 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≤366000 / Completed 終了 / Predrag Kurtovic / September 23, 2013 2013 年 9 月 23 日
  24. n≤400000 / Completed 終了 / Predrag Kurtovic / October 25, 2013 2013 年 10 月 25 日
  25. n≤410000 / Completed 終了 / Predrag Kurtovic / October 31, 2013 2013 年 10 月 31 日
  26. 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. 3×106k+2-1 = 13×(3×102-113+27×102×106-19×13×k-1Σm=0106m)
  2. 3×106k+5-1 = 7×(3×105-17+27×105×106-19×7×k-1Σm=0106m)
  3. 3×1016k+5-1 = 17×(3×105-117+27×105×1016-19×17×k-1Σm=01016m)
  4. 3×1018k+13-1 = 19×(3×1013-119+27×1013×1018-19×19×k-1Σm=01018m)
  5. 3×1022k+2-1 = 23×(3×102-123+27×102×1022-19×23×k-1Σm=01022m)
  6. 3×1027k+21-1 = 757×(3×1021-1757+27×1021×1027-19×757×k-1Σm=01027m)
  7. 3×1028k+1-1 = 29×(3×101-129+27×10×1028-19×29×k-1Σm=01028m)
  8. 3×1034k+15-1 = 103×(3×1015-1103+27×1015×1034-19×103×k-1Σm=01034m)
  9. 3×1035k+26-1 = 71×(3×1026-171+27×1026×1035-19×71×k-1Σm=01035m)
  10. 3×1041k+15-1 = 83×(3×1015-183+27×1015×1041-19×83×k-1Σm=01041m)

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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 21.47%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 21.47% です。

3. Factor table of 299...99 299...99 の素因数分解表

3.1. Last updated 最終更新日

March 7, 2017 2017 年 3 月 7 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=204, 205, 206, 208, 211, 215, 216, 217, 224, 227, 229, 231, 234, 237, 238, 240, 245, 247, 249, 254, 255, 256, 257, 258, 261, 263, 264, 266, 267, 270, 272, 274, 277, 280, 281, 282, 283, 286, 289, 290, 291, 292, 293, 294, 295, 296, 299, 300 (48/300)

3.4. Factor table 素因数分解表

3×100-1 = 2 = definitely prime number 素数
3×101-1 = 29 = definitely prime number 素数
3×102-1 = 299 = 13 × 23
3×103-1 = 2999 = definitely prime number 素数
3×104-1 = 29999 = 131 × 229
3×105-1 = 299999 = 7 × 17 × 2521
3×106-1 = 2999999 = definitely prime number 素数
3×107-1 = 29999999 = definitely prime number 素数
3×108-1 = 299999999 = 13 × 23076923
3×109-1 = 2999999999<10> = 16937 × 177127
3×1010-1 = 29999999999<11> = 2113 × 3767 × 3769
3×1011-1 = 299999999999<12> = 7 × 683 × 953 × 65843
3×1012-1 = 2999999999999<13> = 359 × 8356545961<10>
3×1013-1 = 29999999999999<14> = 19 × 1578947368421<13>
3×1014-1 = 299999999999999<15> = 13 × 107 × 33203 × 6495563
3×1015-1 = 2999999999999999<16> = 83 × 103 × 227 × 1545895313<10>
3×1016-1 = 29999999999999999<17> = 100126307 × 299621557
3×1017-1 = 299999999999999999<18> = 7 × 157 × 3257 × 6961 × 12040213
3×1018-1 = 2999999999999999999<19> = 61 × 3145189 × 15636684431<11>
3×1019-1 = 29999999999999999999<20> = definitely prime number 素数
3×1020-1 = 299999999999999999999<21> = 13 × 23076923076923076923<20>
3×1021-1 = 2999999999999999999999<22> = 17 × 191 × 757 × 11059 × 110363948159<12>
3×1022-1 = 29999999999999999999999<23> = 167 × 311 × 337 × 1559 × 1099432012969<13>
3×1023-1 = 299999999999999999999999<24> = 7 × 50367072601<11> × 850896044657<12>
3×1024-1 = 2999999999999999999999999<25> = 23 × 130434782608695652173913<24>
3×1025-1 = 29999999999999999999999999<26> = 23057 × 10833241 × 120104713180327<15>
3×1026-1 = 299999999999999999999999999<27> = 13 × 59 × 71 × 5508933654075692748407<22>
3×1027-1 = 2999999999999999999999999999<28> = definitely prime number 素数
3×1028-1 = 29999999999999999999999999999<29> = 47 × 638297872340425531914893617<27>
3×1029-1 = 299999999999999999999999999999<30> = 74 × 29 × 4308549598586795731663531<25>
3×1030-1 = 2999999999999999999999999999999<31> = 19441 × 45949 × 671304589 × 5002728961799<13>
3×1031-1 = 29999999999999999999999999999999<32> = 19 × 16187 × 546924986987<12> × 178350167647709<15>
3×1032-1 = 299999999999999999999999999999999<33> = 13 × 146437799 × 157588568214707166713677<24>
3×1033-1 = 2999999999999999999999999999999999<34> = 113 × 149 × 34303 × 5194269029314101397578509<25>
3×1034-1 = 29999999999999999999999999999999999<35> = 46811 × 51047 × 12554606696004419459257547<26>
3×1035-1 = 299999999999999999999999999999999999<36> = 7 × 478631 × 3887236453<10> × 23034640168453340899<20>
3×1036-1 = 2999999999999999999999999999999999999<37> = 193 × 2347451 × 6621668120347220058071014093<28>
3×1037-1 = 29999999999999999999999999999999999999<38> = 173 × 6106248727864848361489924689599023<34>
3×1038-1 = 299999999999999999999999999999999999999<39> = 13 × 2423 × 9524111876567510079685069367281501<34>
3×1039-1 = 2999999999999999999999999999999999999999<40> = 20474512935513701<17> × 146523632061420300823699<24>
3×1040-1 = 29999999999999999999999999999999999999999<41> = 1316507 × 13940701 × 24313333578409<14> × 67230905546473<14>
3×1041-1 = 299999999999999999999999999999999999999999<42> = 7 × 42857142857142857142857142857142857142857<41>
3×1042-1 = 2999999999999999999999999999999999999999999<43> = 9063097 × 331012677013166691253552731477992567<36>
3×1043-1 = 29999999999999999999999999999999999999999999<44> = definitely prime number 素数
3×1044-1 = 299999999999999999999999999999999999999999999<45> = 13 × 594332567 × 10550048513531<14> × 3680390637464286032999<22>
3×1045-1 = 2999999999999999999999999999999999999999999999<46> = 499 × 6012024048096192384769539078156312625250501<43>
3×1046-1 = 29999999999999999999999999999999999999999999999<47> = 23 × 1304347826086956521739130434782608695652173913<46>
3×1047-1 = 299999999999999999999999999999999999999999999999<48> = 7 × 1404819661871<13> × 30507220264887130087041437378722567<35>
3×1048-1 = 2999999999999999999999999999999999999999999999999<49> = 443 × 757 × 334127 × 26773803868940651228170563387195934487<38>
3×1049-1 = 29999999999999999999999999999999999999999999999999<50> = 19 × 103 × 1321 × 665293 × 17442737999925077569064711017059757319<38>
3×1050-1 = 2(9)50<51> = 132 × 431 × 4118672689081398701245212042998942874009802441<46>
3×1051-1 = 2(9)51<52> = 1066480229<10> × 1356476046074293<16> × 2073749608604567097036502567<28>
3×1052-1 = 2(9)52<53> = 390621169 × 72645380763102632869<20> × 1057200780089282053600259<25>
3×1053-1 = 2(9)53<54> = 7 × 17 × 6132679193<10> × 679927496140561<15> × 604590671733065589907762577<27>
3×1054-1 = 2(9)54<55> = 3217 × 1390016294869897<16> × 670888430310272971761577811789656151<36>
3×1055-1 = 2(9)55<56> = definitely prime number 素数
3×1056-1 = 2(9)56<57> = 13 × 83 × 4331167543529607187088879<25> × 64194057375964295426367330839<29>
3×1057-1 = 2(9)57<58> = 29 × 1136834253520662461<19> × 90996797063160225886700832599613151271<38>
3×1058-1 = 2(9)58<59> = 6686869667<10> × 52776674411<11> × 626931419603<12> × 135592709679897593746997509<27>
3×1059-1 = 2(9)59<60> = 7 × 19531 × 641317 × 3421574356367246644163949706650392458891569799391<49>
3×1060-1 = 2(9)60<61> = 743 × 808716498647<12> × 1057972676861663008729<22> × 4719127225971742808162711<25>
3×1061-1 = 2(9)61<62> = 71 × 422535211267605633802816901408450704225352112676056338028169<60>
3×1062-1 = 2(9)62<63> = 13 × 23076923076923076923076923076923076923076923076923076923076923<62>
3×1063-1 = 2(9)63<64> = 1728967 × 7703231 × 1605051241<10> × 140337174186780324552365181567296961903007<42>
3×1064-1 = 2(9)64<65> = 277 × 108303249097472924187725631768953068592057761732851985559566787<63>
3×1065-1 = 2(9)65<66> = 7 × 611704123343575338233723<24> × 70061883223682835822554541457490468968459<41>
3×1066-1 = 2(9)66<67> = 503 × 15763439 × 50162659539371570232061<23> × 7542611608385988025064828485248227<34>
3×1067-1 = 2(9)67<68> = 19 × 107 × 15920843 × 10644771958592162966987<23> × 87072588295411188803975078531858983<35>
3×1068-1 = 2(9)68<69> = 13 × 23 × 1003344481605351170568561872909698996655518394648829431438127090301<67>
3×1069-1 = 2(9)69<70> = 17 × 36493 × 329860332209700670780056854383<30> × 14659956248770104285450993620607013<35>
3×1070-1 = 2(9)70<71> = 661 × 434132891 × 637935136493979035228233<24> × 163877972349517148682713565578488753<36>
3×1071-1 = 2(9)71<72> = 72 × 2371 × 2582222260477366821886915879806161182313498997237022181289217500581<67>
3×1072-1 = 2(9)72<73> = 4188054211417<13> × 4267778689730745828517<22> × 167844482547367204773786131605885255691<39>
3×1073-1 = 2(9)73<74> = 373 × 275676723385625913658191645377<30> × 291750980771364417216161647598876663509219<42>
3×1074-1 = 2(9)74<75> = 13 × 47 × 1069 × 367823 × 90855262284385309<17> × 13744007092186107278415663200174774248999883123<47>
3×1075-1 = 2(9)75<76> = 757 × 51378297061009<14> × 1405847460733497973<19> × 54866526792220496038143451174747976388551<41>
3×1076-1 = 2(9)76<77> = 2402214527<10> × 135999956282039<15> × 91827063621559306927394843586328922240326571839259783<53>
3×1077-1 = 2(9)77<78> = 7 × 23677 × 4275127 × 4369427 × 3621327289<10> × 247502724582139745843<21> × 108112340743472502401674533227<30>
3×1078-1 = 2(9)78<79> = 61 × 1427 × 2713 × 5410076687<10> × 4849502882804430492203<22> × 484191331287271863114267578513481652669<39>
3×1079-1 = 2(9)79<80> = 293611531788139<15> × 102175823331241199704581398426177346644437517656619757456424151741<66>
3×1080-1 = 2(9)80<81> = 13 × 109 × 502441 × 394460147 × 121000994263045222745790261071<30> × 8828242660013348139969025855696091<34>
3×1081-1 = 2(9)81<82> = 198347 × 580610829637<12> × 546035880317951<15> × 47707790680126762810965842706145250687293836957191<50>
3×1082-1 = 2(9)82<83> = 3623 × 1179592811783<13> × 81901814233106783<17> × 85709168379882713447112804288382078260973732635217<50>
3×1083-1 = 2(9)83<84> = 7 × 103 × 2917 × 2092564310751650241184817<25> × 55817750862408931155328183<26> × 1221232670144955999083128837<28>
3×1084-1 = 2(9)84<85> = 59 × 3037200296737<13> × 16741555597023462687292691535071815284183972598585064174887691519199853<71>
3×1085-1 = 2(9)85<86> = 17 × 19 × 29 × 223 × 977 × 6563 × 14653 × 152859471551123480004843160977546975097365506330010478081244364258113<69>
3×1086-1 = 2(9)86<87> = 13 × 17309375399<11> × 1207510782643354586857133772644363<34> × 1104092571873395520541318241400785866473479<43>
3×1087-1 = 2(9)87<88> = 2741 × 964927 × 394211670918873961<18> × 2877320783415929720655717276789004987147764455948869723172437<61>
3×1088-1 = 2(9)88<89> = 1304488873<10> × 3300924483140581825965792499050421<34> × 6966991598609698357143166308824300493706869803<46> (Robert Backstrom / GMP-ECM 5.1-beta for P34 x P46 / May 2, 2003 2003 年 5 月 2 日)
3×1089-1 = 2(9)89<90> = 7 × 12594245972471028228269<23> × 186182086789309759054543090955981<33> × 18277346698490628671886518504139713<35>
3×1090-1 = 2(9)90<91> = 23 × 416998450980192814055629<24> × 312794405595744596969514780116162611260899355352176462266677835197<66>
3×1091-1 = 2(9)91<92> = 1597 × 184553 × 446028257 × 14076488831<11> × 16212071708719648632278491157629276678664053603353596806375780717<65>
3×1092-1 = 2(9)92<93> = 13 × 2473 × 8354651 × 1116928758657913030746751251796032617863380560312387775178668625667297149218675001<82>
3×1093-1 = 2(9)93<94> = 503699641 × 48503123144589502741752878729057<32> × 122794781146491779173462117695893007175726748617613527<54>
3×1094-1 = 2(9)94<95> = 97 × 380774519116859555009563691113510103<36> × 812234892273730400146403072480506371926158526721772968889<57>
3×1095-1 = 2(9)95<96> = 7 × 157 × 7544219843<10> × 14044244326009837<17> × 2576385525477167077559755888656850563188888467559516732456150855611<67>
3×1096-1 = 2(9)96<97> = 71 × 225175496540201364974370054300058530191<39> × 187647065404458407478575579255133377195945562460800825959<57>
3×1097-1 = 2(9)97<98> = 832 × 1129 × 6823 × 23264344193<11> × 18929164970412319489<20> × 1283729395505707376279023867054907059411215130486873257049<58>
3×1098-1 = 2(9)98<99> = 13 × 1019 × 187379 × 376657 × 2065995084482425229722350759373801066391<40> × 155312880582011749094355956606205409844262829<45> (Robert Backstrom / PPSIQS Ver 1.1 for P40 x P45 / June 8, 2003 2003 年 6 月 8 日)
3×1099-1 = 2(9)99<100> = 345221647 × 477752776081611404646500077456166023<36> × 18189468758616411279538180668857592713662364213329197479<56> (Robert Backstrom / PPSIQS Ver 1.1 for P36 x P56 / June 13, 2003 2003 年 6 月 13 日)
3×10100-1 = 2(9)100<101> = 30908839729<11> × 52687875503<11> × 18421621929042446518945642871526259144172571872058046358421612697832167819925377<80>
3×10101-1 = 2(9)101<102> = 7 × 17 × 461 × 42703 × 128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187<93>
3×10102-1 = 2(9)102<103> = 757 × 341667013 × 11599047429948021078058597960005614850022606973185675972655317149495105361550724254328327239<92>
3×10103-1 = 2(9)103<104> = 19 × 60083 × 23917741750007011930592110720920008759435096557<47> × 1098742369919843494185783706649927078558709517031491<52> (Makoto Kamada / SNFS for P47 x P52 / 5:47:41:70)
3×10104-1 = 2(9)104<105> = 13 × 347 × 1321 × 133881109 × 2813505323<10> × 15058978723753<14> × 8380200882966911<16> × 32926128941294964210169<23> × 32165325017020156619259454561<29>
3×10105-1 = 2(9)105<106> = 69233 × 43331937082027356896277786604653850042609738130660234281339823494576285875232909161815897043317493103<101>
3×10106-1 = 2(9)106<107> = 218279 × 137438782475638975806192991538352292249827056198718154288777207152314240032252300954283279655853288681<102>
3×10107-1 = 2(9)107<108> = 7 × 35491 × 132967 × 3286888271596093<16> × 2762969980683717258321223144209234268699368337958266176306842668501370570391151817<82>
3×10108-1 = 2(9)108<109> = 479 × 1537022713<10> × 12042349012118749379843<23> × 5580815161537522052816552016371<31> × 60631261945090711190778038575214536541054929<44>
3×10109-1 = 2(9)109<110> = 941 × 60259 × 78121 × 524086391 × 14770997282202389<17> × 26506062415929309987997152493<29> × 33005323977166274796073777418225748488133943<44>
3×10110-1 = 2(9)110<111> = 13 × 23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923<110>
3×10111-1 = 2(9)111<112> = 966767341958861<15> × 3103125095145859264337050293405093023943285127966189415280642637135368146774978576169338417355259<97>
3×10112-1 = 2(9)112<113> = 23 × 181 × 3407 × 127103 × 3483791461<10> × 954027040968047<15> × 5006959449134196242766265868072792925075855906976643628238419170429812879439<76>
3×10113-1 = 2(9)113<114> = 72 × 29 × 8139497 × 183196997235114666313664862887412748867877758421<48> × 141583048280838478129901762617470802340141205501351431287<57> (Sander Hoogendoorn / SNFS for P48 x P57 / June 8, 2004 2004 年 6 月 8 日)
3×10114-1 = 2(9)114<115> = 171141301 × 5078181337<10> × 3451900116240059527310349962515641788338540306292431489892874508205404626512683628520178446569627<97>
3×10115-1 = 2(9)115<116> = 66935581832507131<17> × 448192115145409256752005959887688729242511151091393953380282171310853902822633424231824418287457229<99>
3×10116-1 = 2(9)116<117> = 13 × 191 × 419 × 342803 × 3080389672652381470662675187786673261869<40> × 273073929335371915922432805053316071687914686044309883829457031841<66> (Sander Hoogendoorn / for P40 x P66 / June 8, 2004 2004 年 6 月 8 日)
3×10117-1 = 2(9)117<118> = 17 × 103 × 7717 × 1343893 × 698810987349616407838127758561787<33> × 236408012483724037920438356017353423704940485863994051049626928720839267<72> (Sander Hoogendoorn / for P33 x P72)
3×10118-1 = 2(9)118<119> = 1801 × 2322347 × 269136729617782632743<21> × 525337354976588234359540934329<30> × 50730503927128935534261432720820845779278829698082773940411<59>
3×10119-1 = 2(9)119<120> = 7 × 7141775796359<13> × 6000908468590146007802970302085578213299657647019234436854511092567500093029441038440754743913961970037423<106>
3×10120-1 = 2(9)120<121> = 47 × 107 × 587 × 44209021499<11> × 11890818970927053203<20> × 2047296729179266187110579273833644931841<40> × 944274051192262206631103925845322418206838969<45>
3×10121-1 = 2(9)121<122> = 19 × 695084724889<12> × 2271589796011125260933021182971065840770325771072812443357936760347860632353214061224348430869129003298879789<109>
3×10122-1 = 2(9)122<123> = 13 × 2294796717664213509541276266917758467689777187014509<52> × 10056194912293669804719011098323636255061719884507348567986171070655047<71> (Makoto Kamada / GGNFS-0.70.0 for P52 x P71 / 3.39 hours)
3×10123-1 = 2(9)123<124> = 2990366970937067399<19> × 1003221353484891513387954898308810381727983558088177158306275171844453418150696067538783658365482703827401<106>
3×10124-1 = 2(9)124<125> = 2602864396977816164601828457<28> × 11525763706642949500110430345615582532053120160077139973457388941551304686760716557918497750074407<98>
3×10125-1 = 2(9)125<126> = 7 × 3599650081<10> × 31612646761<11> × 3876544332029444008036492867365402990466431683<46> × 97153246083586305759374376504412500632762391535023918322219<59> (Sander Hoogendoorn / GGNFS for P46 x P59)
3×10126-1 = 2(9)126<127> = 179 × 2927 × 292983186719575321<18> × 5647443464815144203568297<25> × 3460596075084905650466669068797064557997911238583417117155774526018030889091019<79>
3×10127-1 = 2(9)127<128> = 148738622029916094823<21> × 201696100115584238393124824460099143584753960141821190136295028657532443918821279751573958245772262039795113<108>
3×10128-1 = 2(9)128<129> = 132 × 227 × 541 × 601 × 148983787999561869461523139665361324139<39> × 161435091255666683067612614137458155297916999164385294636452087869504653287195627<81> (Makoto Kamada / GGNFS-0.77.1 for P39 x P81 / 3.83 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 5, 2005 2005 年 5 月 5 日)
3×10129-1 = 2(9)129<130> = 757 × 3862845783794364415817<22> × 4154462659947867699343214598881767<34> × 246946653468267095788453656414425393826920686199248335419564218437793213<72> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=2577217194 for P34 x P72)
3×10130-1 = 2(9)130<131> = 176410843726584853883407743387462128062837<42> × 170057573368314684049302929168844425493413216950195208787238174395441995530703625941928227<90> (Sander Hoogendoorn / GGNFS for P42 x P90)
3×10131-1 = 2(9)131<132> = 7 × 71 × 2281 × 151813 × 977057 × 18215699449<11> × 168678924343<12> × 85892292823905156190531<23> × 546893930756919181751220197647<30> × 12360804653411226627683395388566345189673<41>
3×10132-1 = 2(9)132<133> = 1823 × 751446263 × 2189962393226079924195568697698785877427193914407518505622793919738599146505349576421961755644686047247091066773551414951<121>
3×10133-1 = 2(9)133<134> = 17 × 277 × 947 × 63911747 × 284800447 × 1908595079<10> × 308272668350011<15> × 628163081468531196471678625762635108684284589253543477082381703073219111516811871677753<87>
3×10134-1 = 2(9)134<135> = 13 × 23 × 131 × 50237491883<11> × 74611295693503631<17> × 6270336254236758322137851221<28> × 325878274972959912313450677639337986912758521683301002776370480401214035687<75>
3×10135-1 = 2(9)135<136> = 9661029311<10> × 2737810280944238993239874575304072948881248252017519<52> × 113421269769628317461074177992926273808105712904085317777627767022874178511<75> (Makoto Kamada / GGNFS-0.77.1 for P52 x P75 / 5.63 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 6, 2005 2005 年 5 月 6 日)
3×10136-1 = 2(9)136<137> = 835817364193303896837129099287216945204282453961493<51> × 35893008790209509851297098644911189995904355230294598135551859369093208362424725320643<86> (Anton Korobeynikov / GGNFS-0.72.10 for P51 x P86 / 16.41 hours)
3×10137-1 = 2(9)137<138> = 7 × 487 × 1050233 × 6621524008283<13> × 42100336899241<14> × 300583449314555435059595288664414400507392811785133653676322034725504693698971499976681413695127808189<102>
3×10138-1 = 2(9)138<139> = 61 × 83 × 2617 × 58211 × 123215977 × 18301389014578223<17> × 1879512152331664267523<22> × 413385011612455959639469<24> × 1643961787701703715784696623<28> × 1350398306002428325645695676549<31>
3×10139-1 = 2(9)139<140> = 19 × 233 × 18257 × 3189010880100257960332198816490123216053698925938885318275266097<64> × 116392853688224551320628030044644926368910927741779050815872100922653<69> (Makoto Kamada / GGNFS-0.77.1 for P64 x P69 / 11.04 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 6, 2005 2005 年 5 月 6 日)
3×10140-1 = 2(9)140<141> = 13 × 1043951 × 26883947 × 182071650990950202615387530626934743348640561028796729<54> × 4516088321889703271038563016128691273952825632884219310105789502309547671<73> (Makoto Kamada / GGNFS-0.77.1 for P54 x P73 / 8.19 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 10, 2005 2005 年 5 月 10 日)
3×10141-1 = 2(9)141<142> = 29 × 12049787588762983115267162180707134919286653<44> × 8585070491909711967989582026822386992430936673986287924871109410890430123873686351241585281361127<97> (Makoto Kamada / GGNFS-0.77.1 for P44 x P97 / 7.74 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 10, 2005 2005 年 5 月 10 日)
3×10142-1 = 2(9)142<143> = 59 × 1667 × 93717112244395171896790558091<29> × 3254728338396397350299417788498932335144337966986383779784082085195537945799463747173648638531505035959656813<109> (Tetsuya Kobayashi / GMP-ECM 5.0.3 for P29 x P109 / February 24, 2004 2004 年 2 月 24 日)
3×10143-1 = 2(9)143<144> = 7 × 368161095989<12> × 2773039137463081<16> × 24566776282235900088908433900766498349491<41> × 1708760320079077756989239124726576953642075628982585485036155402183550090703<76> (Makoto Kamada / GGNFS-0.77.1 for P41 x P76 / 14.68 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 11, 2005 2005 年 5 月 11 日)
3×10144-1 = 2(9)144<145> = 114960971 × 2213287753<10> × 108090137887270909297090797793<30> × 109080439628348269202774046214310086366771298172396864071466868126105645656536199141927505676107861<99> (Tetsuya Kobayashi / GMP-ECM 5.0.3 B1=1000000 for P30 x P99 / August 14, 2004 2004 年 8 月 14 日)
3×10145-1 = 2(9)145<146> = 113 × 1051 × 115336553 × 2287852509381529362215874023304871802874572090778188945277943<61> × 957293486672798203907184531262070219175708798167529171237812739812913587<72> (Makoto Kamada / GGNFS-0.77.1 for P61 x P72 / 11.34 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 12, 2005 2005 年 5 月 12 日)
3×10146-1 = 2(9)146<147> = 13 × 493573 × 18325201302275702459091151740961<32> × 2551395316378933371196249242159398075810419408174368073290161677105829014102810175513071204192402345218026591<109> (Makoto Kamada / GMP-ECM 5.0.3 B1=450000, sigma=3350150933 for P32 x P109)
3×10147-1 = 2(9)147<148> = 2515313 × 4380884647177105247767<22> × 272249694675382115672371457148969342652091706433155665804841695191724637927901103092611354783625552190520929023861944169<120>
3×10148-1 = 2(9)148<149> = 5698826293<10> × 120232877212186884433<21> × 123074961607917110161534951484159374642729<42> × 355748343355447265512908734948080985968709118990801171190063642693710339565499<78> (Makoto Kamada / GGNFS-0.77.1 for P42 x P78 / 28.55 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 14, 2005 2005 年 5 月 14 日)
3×10149-1 = 2(9)149<150> = 7 × 17 × 1249 × 3803 × 29983 × 47363 × 59021 × 25970585924786847027298660631<29> × 243827637273805306729808414600327800876310711471007497576365833251559647434564618561961895558734917<99> (Tetsuya Kobayashi / GMP-ECM 5.0.3 for P29 x P99 / February 24, 2004 2004 年 2 月 24 日)
3×10150-1 = 2(9)150<151> = 383399 × 23802994718148901<17> × 328729499631075215103914984155771879133819146534222325019886723795831518647675685691088397349572871406691314755646056939225744501<129>
3×10151-1 = 2(9)151<152> = 103 × 15607 × 35159 × 14094323 × 803919452098002873794823857201688324440053056001<48> × 46845872075351073831628759072931045137614880228706167557837224075618406020863534117667<86> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 for P48 x P86 / 32.36 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / June 15, 2006 2006 年 6 月 15 日)
3×10152-1 = 2(9)152<153> = 13 × 263 × 87744954665106756361509213220239836209417958467388125182801988885639075753144194208832992102954080140391927464170810178414741152383737935068733547821<149>
3×10153-1 = 2(9)153<154> = 72019 × 1472927109551<13> × 6437899768974245773<19> × 45425367911692522245626027985214885364243<41> × 96705293648696981037155654696825961344230797647139452351613239823428072265389<77> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=4238945311 for P41 x P77 / September 6, 2005 2005 年 9 月 6 日)
3×10154-1 = 2(9)154<155> = 169973521 × 3541566709633<13> × 62282513633822346544465252554897044469175211<44> × 800162926125406274759982565017119197917086497848155175255046781462749015168218472947165613<90> (Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 for P44 x P90 / 63.81 hours on Pentium 4 3.20 GHz, 1 Gig RAM, Windows XP and Cygwin / March 17, 2007 2007 年 3 月 17 日)
3×10155-1 = 2(9)155<156> = 72 × 844643 × 159010443754010418818537<24> × 5423853441107577188852485479594908047413233<43> × 8404625993321570476494919510450078586561494231252473102406403901939727050282602317<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P43 x P82 / 27.74 hours on Cygwin on AMD XP 2700+ / March 16, 2007 2007 年 3 月 16 日)
3×10156-1 = 2(9)156<157> = 232 × 757 × 37958325803<11> × 34508927160252119290871470429799344288040408510935452205656946628557<68> × 5719146168209700929932117892283471025039070385347664045593119483067546173<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P68 x P73 / 29.42 hours on Cygwin on AMD XP 2700+ / April 14, 2007 2007 年 4 月 14 日)
3×10157-1 = 2(9)157<158> = 19 × 409 × 8669 × 1478382377561711<16> × 301223302549621999298659687439059017007707324952067882550054765883129452999327273835105189723866856348822058327855755819455471102120191<135>
3×10158-1 = 2(9)158<159> = 13 × 8713 × 5289083 × 695325459814498871<18> × 8252373899553049676093269<25> × 998030902239641757418958240703001<33> × 87441739575224379973751656500118777910978931283986448286477478905281163<71> (Anton Korobeynikov / GGNFS-0.77.1 gnfs for P33 x P71 / 13.78 hours / May 27, 2005 2005 年 5 月 27 日)
3×10159-1 = 2(9)159<160> = 1321 × 6967 × 398760584767619777<18> × 1365996837467415111026906770750469<34> × 598426350404332450433128876484310209991358869759713755798077815328602741567697247226824883321819832989<102> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=2625841172 for P34 x P102 / July 11, 2007 2007 年 7 月 11 日)
3×10160-1 = 2(9)160<161> = 3119 × 62171 × 716003 × 80479894854409<14> × 22773127470380768369771978355584433053642892841637684786821<59> × 117894381311324651726376382743763178993218466198694259251340381195966953253<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 for P59 x P75 / November 2, 2007 2007 年 11 月 2 日)
3×10161-1 = 2(9)161<162> = 7 × 445307 × 12654241 × 4753427389819<13> × 1600002742222315874207495930489789942851093204466890859980649901635579490615534553038031986322050491140769704228139579001336217079639569<136>
3×10162-1 = 2(9)162<163> = 1586308304691323221318531843777<31> × 152512406662190891155427973892329217<36> × 12400194079641198397538641885769926694273799859212033454948583982801438301040530455353496340235711<98> (Makoto Kamada / GMP-ECM 6.0 B1=36000000, sigma=757237952 for P31 / March 19, 2005 2005 年 3 月 19 日) (Wataru Sakai / GMP-ECM 6.0.1 B1=110000000, sigma=1534915970 for P36 x P98 / January 4, 2006 2006 年 1 月 4 日)
3×10163-1 = 2(9)163<164> = 997 × 2287 × 45747879641691574163746483574403221719068934066339<50> × 287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719<108> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P50 x P108 / 63.42 hours on Cygwin on AMD 64 3200+ / July 24, 2007 2007 年 7 月 24 日)
3×10164-1 = 2(9)164<165> = 13 × 2591 × 20864331285956384714363476632186247632145067881<47> × 16745773198975668201316866017478902963614694091371<50> × 25491818321127692702503378138106307806982680946323585329451086103<65> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 for P47 x P50 x P65 / 125.82 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / July 7, 2007 2007 年 7 月 7 日)
3×10165-1 = 2(9)165<166> = 17 × 563 × 10366352216620195513339<23> × 32537822232223537739373298666992795881162109492993066147359<59> × 929286216648341931114487283109312466413415118752186358498797622230367374713700369<81> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.33 for P59 x P81 / February 6, 2008 2008 年 2 月 6 日)
3×10166-1 = 2(9)166<167> = 47 × 71 × 2667289 × 10991159 × 627960539 × 2137781721901653563<19> × 10345389693582740479529989859541374220406006881752101849<56> × 22080500640751102476087504432625828948573909939464280318314247588489<68> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=3068145495 for P56 x P68 / September 14, 2005 2005 年 9 月 14 日)
3×10167-1 = 2(9)167<168> = 7 × 7643 × 5308447 × 22854213927330216399615920416772214007<38> × 39688758719895871031552328771144713882109670630545445702193<59> × 1164549798963657623144995222566231913164712125722393092919267<61> (Wataru Sakai / GMP-ECM 6.0.1 B1=110000000, sigma=2117868705 for P38 / January 4, 2006 2006 年 1 月 4 日) (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P59 x P61 / 127.93 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / March 9, 2006 2006 年 3 月 9 日)
3×10168-1 = 2(9)168<169> = 1812361 × 130589868517<12> × 5316091494767<13> × 175320276174094299158123<24> × 14218271534104519162365193<26> × 7346438825607067443755539899769423966309<40> × 130202342717147930171665152085069493289786784935131<51> (Makoto Kamada / msieve 0.87 for P40 x P51 / 3.4 hours / December 11, 2004 2004 年 12 月 11 日)
3×10169-1 = 2(9)169<170> = 29 × 257 × 1187 × 893281 × 162352619114966156197<21> × 2228251805235709353313536175233325312147783871786905403<55> × 10493678433883386533453073734793889071910451026636427224419520005990497132630462879<83> (Sinkiti Sibata / Msieve 1.40 snfs for P55 x P83 / 59.94 hours / July 13, 2009 2009 年 7 月 13 日)
3×10170-1 = 2(9)170<171> = 13 × 5783 × 173013747441272949252140271307882198468644836377812061<54> × 23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321<113> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P54 x P113 / 83.81 hours on Cygwin on AMD 64 3200+ / May 26, 2007 2007 年 5 月 26 日)
3×10171-1 = 2(9)171<172> = 727 × 111443 × 75309234594877<14> × 1030775741943931673<19> × 203808353944020828211710001231914168129351013132544641<54> × 2340451493876462621104078626827590279589654809102234493298958220750325105388919<79> (Sander Hoogendoorn / GNFS & msieve with the factmsieve.py (python script) for P54 x P79 / 25.57 hours on Intel Core 2 Duo 2,2 GHz using 2 cores on Windows 2003 / January 27, 2010 2010 年 1 月 27 日)
3×10172-1 = 2(9)172<173> = 38122987748499595028686163894145203<35> × 144305979336767394731126911499701100363397016943877899<54> × 5453182077435764716694269821536175903777022858744153878594451246373586312292773813167<85> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=111443754 for P35 / September 1, 2005 2005 年 9 月 1 日) (Wataru Sakai / Msieve for P54 x P85 / 3.49 hours / January 13, 2010 2010 年 1 月 13 日)
3×10173-1 = 2(9)173<174> = 7 × 107 × 157 × 3013176114760906824959<22> × 3438554741560059188437<22> × 30644010457996651884427900089832310981<38> × 1965123061305630337817335362597030221689<40> × 4088876295547466384808084321913583821345407444169<49> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=1547437923 for P38, Msieve 1.01 for P40 x P49 / August 30, 2005 2005 年 8 月 30 日)
3×10174-1 = 2(9)174<175> = 166087909788096950834522423<27> × 8463645713858598762260867888847965297310229007204191808496082691<64> × 2134154023417552716331724005141659076217090584552967921447661573925237208250265541843<85> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P64 x P85 / 47.56 hours on Core 2 Quad Q6700 / February 27, 2010 2010 年 2 月 27 日)
3×10175-1 = 2(9)175<176> = 19 × 1358197 × 127908438358629022538945818383105074917390387700273693347951544125819<69> × 9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147<100> (matsui / GGNFS-0.77.1-20060513-prescott snfs for P69 x P100 / 170.28 hours / May 27, 2008 2008 年 5 月 27 日)
3×10176-1 = 2(9)176<177> = 13 × 58742557 × 57269690852172211230698590365937264946108274851869337123769319131139186850180629<80> × 6859622507929484284606361644307751405797667931674866097064318293703456089128520372145691<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P80 x P88 / March 2, 2010 2010 年 3 月 2 日)
3×10177-1 = 2(9)177<178> = 311 × 116471 × 1402627451282133493<19> × 6212798730210408050381624569671817339<37> × 9504153515554352849906622482432664871708559936002497935758971157239414990468164783447373021653755199704052528655977<115> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=6359294935 for P37 x P115 / February 21, 2010 2010 年 2 月 21 日)
3×10178-1 = 2(9)178<179> = 23 × 28871 × 950809 × 3670957 × 6486841 × 20123971618573<14> × 15822535005390769197619578154346714884187993498909473<53> × 6266658034440589293040361904117425689899050899063420689751835198468171995771249785353879<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P53 x P88 / March 4, 2010 2010 年 3 月 4 日)
3×10179-1 = 2(9)179<180> = 7 × 83 × 269 × 8731 × 81853 × 116981 × 341557 × 12603850771<11> × 40741126949<11> × 135924365039<12> × 65229101266939367735801851025243606155752420471073669310383<59> × 14765247618055126790247356701740302955486828755600519733418471207<65> (matsui / GGNFS-0.77.1-20060513-pentium4 gnfs for P59 x P65 / February 16, 2008 2008 年 2 月 16 日)
3×10180-1 = 2(9)180<181> = 572624573272440906246891681503<30> × 18430490162974811893591210694438204036249222668991102941368207733<65> × 284259107445064507092201327543954373371556380517472751352150669366327959473078731952701<87> (Makoto Kamada / GMP-ECM 6.0 B1=16000000, sigma=2663771591 for P30 / March 20, 2005 2005 年 3 月 20 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P65 x P87 / March 4, 2010 2010 年 3 月 4 日)
3×10181-1 = 2(9)181<182> = 17 × 149 × 67651 × 175070045379264539259437251461445348065890039216448801818566940450735222120090896600987641321136218833541784373309607529547899173169269046904608994971714020303094918024122353<174>
3×10182-1 = 2(9)182<183> = 13 × 1307 × 3253 × 15313 × 30483181 × 712236001 × 217790685050910667548997<24> × 18282126687045549663745432739326772351099604880474511<53> × 4100225547077532938162524694413091222368841653737008072666860688562574061951363<79> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P53 x P79 / March 8, 2010 2010 年 3 月 8 日)
3×10183-1 = 2(9)183<184> = 757 × 705259 × 94685971491169408238495197<26> × 59345951695499727131645089060192058135909213873136735226382733194452511684809704681156559640467203767085254024562482893630526915384657525961066917309<149> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=517744189 for P26 x P149 / July 21, 2005 2005 年 7 月 21 日)
3×10184-1 = 2(9)184<185> = 10073641022189321360228001328707180659381468877455557544719139<62> × 2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741<124> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P62 x P124 / 343.63 hours on Core 2 Quad Q6600 / September 12, 2007 2007 年 9 月 12 日)
3×10185-1 = 2(9)185<186> = 7 × 103 × 5419 × 40859069 × 34405086211<11> × 54620506344778751196212174083932539853598979159171505198079512296438983419526842906298190446596589467895874271186208542033563390832223006082042424056219876319739<161>
3×10186-1 = 2(9)186<187> = 1000926126622857454738657<25> × 169578631674993232722608070359<30> × 5038740629385387262999058978219<31> × 3507729531114303162480919388024654186192017726789378826407554907313223454226891369837005953138455530667<103> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=2779326909 for P31) (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=1358866576 for P30 x P103 / July 30, 2005 2005 年 7 月 30 日)
3×10187-1 = 2(9)187<188> = 337638313967807182936900258849<30> × 99433004049017708218656527004744377<35> × 47527930809248160978423930812756482163<38> × 18801394593718690635972065355070083787495002798358052698294076860191499763907183853901<86> (Makoto Kamada / GMP-ECM 6.0 B1=11000000, sigma=588872100 for P35 / March 21, 2005 2005 年 3 月 21 日) (Makoto Kamada / GMP-ECM 6.0 B1=13000000, sigma=2468554643 for P30 / March 21, 2005 2005 年 3 月 21 日) (anonymous / GMP-ECM B1=1000000, sigma=2711386167 for P38 x P86 / January 27, 2007 2007 年 1 月 27 日)
3×10188-1 = 2(9)188<189> = 13 × 109 × 167 × 769 × 25375234751<11> × 5153248863097<13> × 3749089470469489319<19> × 3362726945702192537278270379287745910169270402907379473520095703855904159132288646009078852590438801004689733992343446479621750210601907473<139>
3×10189-1 = 2(9)189<190> = 467 × 53231 × 120681235922282410424252068989278960590214915983533769445820098792073350698826821501228716003542718361734522440414343737249273167086349073612617335851494820140105283114760171990070187<183>
3×10190-1 = 2(9)190<191> = 97 × 29924824213<11> × 247984694771318430568948981693<30> × 7668447060104434870881489582121<31> × 512358733922895524489343752888689<33> × 10607461577425281731753905244766737614406396259890391295260540539167282031764330723127<86> (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=2904675407 for P33 / March 28, 2005 2005 年 3 月 28 日) (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=3586049989 for P31 / March 28, 2005 2005 年 3 月 28 日) (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=2685518144 for P30 x P86 / September 12, 2005 2005 年 9 月 12 日)
3×10191-1 = 2(9)191<192> = 7 × 359 × 1301 × 281993 × 2790288133<10> × 23268995217971929<17> × 13515484787040813847<20> × 9986328167407533917958306774605218725739829<43> × 37132056081125955472819112147087747804782221939881071336471506401331809870109280710565214621<92> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=11000000, sigma=7007836905 for P43 x P92 / March 6, 2010 2010 年 3 月 6 日)
3×10192-1 = 2(9)192<193> = 179209 × 592154051319954517820401873<27> × 294029254151558642128613500432031<33> × 9740471141873076715269094836964843996395634689724625712596839367<64> × 9870888065300008002666195086781466583752845796759751444217049391<64> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=53705871 for P33) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P64(9740...) x P64(9870...) / March 1, 2010 2010 年 3 月 1 日)
3×10193-1 = 2(9)193<194> = 19 × 1882472591<10> × 838762474401972650861798055481516772627977863833371814325102897830745962547163252918274564975563762894145974622026976657878272172382120181983904157118943370077801881231942155301549131<183>
3×10194-1 = 2(9)194<195> = 13 × 1744151 × 2118866528953<13> × 6244392889110125089580580780440747420845559279279194303632447024695108721938978055392965370236240048699212656733908110604978637693204515295186661381098719191277421837118682341<175>
3×10195-1 = 2(9)195<196> = 12377 × 26641 × 4242465959<10> × 2549430086848235938069023022334565304647820249008607<52> × 841189548672696590223631459471770406069927514620180520789383724252020064883602521044531561533541571410124284972274340308388639<126> (Justin Card / ggnfs/msieve for P52 x P126 / April 7, 2010 2010 年 4 月 7 日)
3×10196-1 = 2(9)196<197> = 122344767534061284667205826233542620221024729103782351<54> × 349916959335497159053279727421119255555113601555011417<54> × 700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P54(1223...) x P54(3499...) x P90 / 516.20 hours on Core 2 Quad Q6700 / October 3, 2008 2008 年 10 月 3 日)
3×10197-1 = 2(9)197<198> = 72 × 17 × 29 × 310459974207253356569798917<27> × 68053976324751545794284630967427895603244001434280187721763258182322358947<74> × 587785857793798607044597286642006113609085738682247451587060917433885743162793893936656523493<93> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P74 x P93 / April 6, 2010 2010 年 4 月 6 日)
3×10198-1 = 2(9)198<199> = 61 × 7304109398819<13> × 245186388835201614679588776888220094897052023<45> × 27461723689325607345365923884323524383870179087245314211471108082418732281332903742131945838261002031868993262649351286813848647212990461807<140> (Robert Backstrom / Msieve 1.42 snfs for P45 x P140 / March 20, 2010 2010 年 3 月 20 日)
3×10199-1 = 2(9)199<200> = 112403 × 277334011 × 1601852971<10> × 252830208606500054458883<24> × 747259820832076009467740924242262873561358607<45> × 3179925708804289450372549233037593965881328406446880827201957011485530677908247685109118491928166361686144753<109> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=7401064585 for P45 x P109 / February 28, 2010 2010 年 2 月 28 日)
3×10200-1 = 2(9)200<201> = 13 × 23 × 59 × 17005838671277138484212913100164389773822345672014058159968255767813616008162802562213026472422198288078907091434725922566747916784762768550535683918145229862252706762655178277875403888668442832039<197>
3×10201-1 = 2(9)201<202> = 712 × 274818953 × 1154915948058749<16> × 45592979882964819734189<23> × 4198545201102514144301929<25> × 51680027931445099736270712486418113352984366948483125672373<59> × 189534357475685771189652977002654801785730673893347954721465838236699<69> (Erik Branger / GGNFS, Msieve gnfs for P59 x P69 / October 1, 2010 2010 年 10 月 1 日)
3×10202-1 = 2(9)202<203> = 277 × 360959 × 1489398605083370326967975894222389<34> × 201452503151630272092171137067216064475573143899301503387898381245497334238104480994753555248962880536691887832549083203575674684283685304601450640255059157512937<162> (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=908324205 for P34 x P162 / September 25, 2010 2010 年 9 月 25 日)
3×10203-1 = 2(9)203<204> = 7 × 296047 × 195439185049<12> × 5911299004317409433064334686882431<34> × 125304878537135736559526197866845333384642570946536343308979146223992751323209664439152035917197388371173912085442221646664802334553324599448976142255649<153> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=4160805105 for P34 x P153 / November 8, 2010 2010 年 11 月 8 日)
3×10204-1 = 2(9)204<205> = 1085374429<10> × 4865205201866784469055303560140189723401751827411<49> × [568120560373225254164514458290434909296187061758164146646542004177074857111598932545636638875579623614078218214806508414742019317598743155787823721<147>] ([GPU Force] Robert 7NBI / GMP-ECM B1=110000000, sigma=750827538 for P49 / December 17, 2011 2011 年 12 月 17 日) Free to factor
3×10205-1 = 2(9)205<206> = 379 × 529749497444143<15> × [149420949345148181719699535053705287463550759220795172490599713901320150351284050444645249857895456018220795783374213760898507208017731266900132583026126643223196734357678182348227739334467<189>] Free to factor
3×10206-1 = 2(9)206<207> = 132 × 26283540729538778269<20> × 189346637458613088402776207<27> × [356691765312898855044551272462171319600662901965207529994372265149522460288111238503858604269568126993217825659728460473792118819630651862147288307034367744637<159>] Free to factor
3×10207-1 = 2(9)207<208> = definitely prime number 素数
3×10208-1 = 2(9)208<209> = 13883 × 98193131 × [22006796264403422387844463869487013235192616976826946055177833450863429637244372917858265566233094615802865562868317232717097705372400590534460408595262895389268651053833693204802349545017606604263<197>] Free to factor
3×10209-1 = 2(9)209<210> = 7 × 1747661 × 4891355507<10> × 272169036755873<15> × 18420358354564417017849878330782298558113545462340294123133168425830643649462789809665306769555825852572778532343313379921358047457980863518068457902537737631893938810610967605567<179>
3×10210-1 = 2(9)210<211> = 757 × 36263 × 39261367232392369<17> × 54773739454063334542547<23> × 50818733134845399004857583515009494891738906885537809922619055051051744548567230947396508666826938743615478468388554605159866505649927500437383887193986349471755223<164>
3×10211-1 = 2(9)211<212> = 19 × 191 × 4399667 × [1878946781381709724491378145579778608088716843263249290841971430663918549250875025970168267719275484887812888079566745722014265650030351382069949278833115235222438638400864625470496643200102186044705593<202>] Free to factor
3×10212-1 = 2(9)212<213> = 13 × 47 × 27316646893<11> × 275304983921517806903<21> × 20975006445313415306232251<26> × 2932138393579874431181967347<28> × 1061578256042879534892931314264450816128500117873330246121049342968047659102482672078662722328086068788629637212004699432078943<127>
3×10213-1 = 2(9)213<214> = 17 × 1553287 × 113611063657452948262013925005109657587993946348084076277104806850020027737005081330562788688079650747471803532842061421246382292367544363889571712420556043599230307765933487766114508060875383091772858612281<207>
3×10214-1 = 2(9)214<215> = 1321 × 694381 × 51700214952073<14> × 95030588319999601<17> × 6656789768401722637374672011092358566245481684417596914862082726978087245450004988692807331971873956471416540034155654065083427486911332392774104470484098863847009857794583163<175>
3×10215-1 = 2(9)215<216> = 7 × 474819775515343<15> × 21653669935445881<17> × 135069937014825408795388841396935613723<39> × [30860588696865394908965590164247781143263880486360243555136283430839748294667419494363297502693077662043790594864423048152966858683535973337477773<146>] (Youcef Lemsafer / GMP-ECM 7.0 B1=3000000, sigma=3:3642554675-3:3642556274 for P39 / December 19, 2013 2013 年 12 月 19 日) Free to factor
3×10216-1 = 2(9)216<217> = 137469623 × 7100763731<10> × 30684681107<11> × 687751284877<12> × [145631870002781454717561682762880626089322799700979310229236886473776340441637327653247393670147665933591499388303122901639997221078477495535277351822564540046749106190357910357<177>] Free to factor
3×10217-1 = 2(9)217<218> = 4423 × 6619 × 1542213691<10> × [664457763405396538992691338359903803840677726330880068445312668031190518379701347612103585091181030075496852241141317187161117581399202379529553668839616058326490942902296102459875918674328395686129297<201>] Free to factor
3×10218-1 = 2(9)218<219> = 13 × 11114641 × 1347678337<10> × 166672864679<12> × 9243390811052682914271373889884578065723515716762589375390038238632098241288138699398805222911352206004217198555203792735963983033031506922365884079289647046633215863750058117512362752097661<190>
3×10219-1 = 2(9)219<220> = 103 × 21734061113<11> × 8524390652898344180739943187<28> × 51537980707374859288465624373661565777383269<44> × 78968497606560052814333700965974749136904008185517<50> × 38627671356147142887904952437828881669989202768143263641330016660368569254577218482091<86> (KTakahashi / GMP-ECM 6.4.4 B1=11000000, sigma=1583749019 for P44 / March 14, 2015 2015 年 3 月 14 日) (Erik Branger / GGNFS, Msieve gnfs for P50 x P86 / April 21, 2015 2015 年 4 月 21 日)
3×10220-1 = 2(9)220<221> = 83 × 63647 × 253439 × 22407416051217670255681525212768052854628254507021109065627944404868096201952445779664049591134394209771679259800355858603594584010379212530418393662879196712128973750947991222167705176569823030302270844630341<209>
3×10221-1 = 2(9)221<222> = 7 × 19470966117578317283<20> × 2201079422476709293304102934147095472613875263572223075854430954205168767071205736987199625637800238788499729721152926076158382902561089699675242864606921379659475025620454582645811204442672322265892579<202>
3×10222-1 = 2(9)222<223> = 23 × 383 × 340560790101033034396639800204336474060619820637983880122601884436371892382790328073561130661823135429674196844136678397093881257804518106482007038256328754682710863889204222953797252809626518333522533772278351685775911<219>
3×10223-1 = 2(9)223<224> = 8011 × 339735653858118751669853297<27> × 11022837278281468177184019681753494721420578660597187554220606694881660653433616079669970432650594458607139878955994963621056524432298086584868774567736696863915794172175888499022700746086140397<194>
3×10224-1 = 2(9)224<225> = 13 × 1597 × 14759 × 34154509247514536194799<23> × 43092828909137488757879<23> × [665216478586907855339972747484555374250749668841598036191771671137679236270989472674109002982763554683333874059637778491788808949793207676841176175320873503227364076562681<171>] Free to factor
3×10225-1 = 2(9)225<226> = 29 × 506449 × 332202603809371025659<21> × 614871702854921063581311595907749137038892782594239054812685270254519780265744700639026451609314841883703454384490985711907084212877323225678717366919402117773934880419297963490175523476599113521441<198>
3×10226-1 = 2(9)226<227> = 107 × 5903 × 18301 × 67189 × 17992383975144400018112539343077<32> × 2146856343293436332976432901719291039559467373504861438399416545721553677474102024253775003565260475976479068611061707728189411944382135346998937655661055842674313223981050711561623<181> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3230293330 for P32 x P181 / June 2, 2010 2010 年 6 月 2 日)
3×10227-1 = 2(9)227<228> = 7 × 1327 × 67915519953890986840301<23> × [475535848369823271621976282566183163495438065096859555918916346400668229763045871783484447687733321522397602287571986452276584696378999490671768883679253603813200090511825498243523391117806297158145091<201>] Free to factor
3×10228-1 = 2(9)228<229> = 193 × 304682332763<12> × 51017206379564777667944771877960688781577730637545661430297880536631723098875906132218302504946101189368190917319084295394703279581161326848527759552581494971662628894914130993316338286988242241010590075456432586861<215>
3×10229-1 = 2(9)229<230> = 17 × 19 × 3083 × 4806377 × 56289821727331<14> × 25558887279658179925339<23> × [4356678967073131699922919238013195777268404683816329412282933395427914670466940368270959639305823432531294732744114567989001133102965833856075412728110445335868062963377998453577527<181>] Free to factor
3×10230-1 = 2(9)230<231> = 13 × 10333 × 42731687 × 5205770389515937<16> × 10039600362922126506165694235549489901072609873947685746719477823037447110911886829953173365984406297217145461904123277565988103852836822351737903034548608586270178347348299167115051110532408257075660049<203>
3×10231-1 = 2(9)231<232> = 3049 × 3833 × 32421121 × [7917662474182316214227603643169139421570856799921026888010388859387406485741797396717628609075723138663392672268035950746935123514655318934038254620922525714676970209930134476969171144513307411981009875618829118031007<217>] Free to factor
3×10232-1 = 2(9)232<233> = 229 × 150551 × 12314386787<11> × 28101802461565621<17> × 298363907844779350307048893453665107<36> × 8427696243327701015938935430022630937488867323174880941163956638487776713388125224527233959937892819820286832747140750154647858167538283583428483700883633002034329<163> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2457181535 for P36 x P163 / November 12, 2010 2010 年 11 月 12 日)
3×10233-1 = 2(9)233<234> = 7 × 189463425949411434003748743265533094404392834958315942679047997<63> × 6937859318682358619779711655390966130774663036538025305503447222060484081<73> × 32604109221823010620391224287664218577256270072051779328401086054283813766714696419408318931140301<98> (matsui / Msieve 1.51 snfs for P63 x P73 x P98 / September 14, 2012 2012 年 9 月 14 日)
3×10234-1 = 2(9)234<235> = 1093 × 9949 × 352043 × 7270063305596659597<19> × [107792304307139560210666335830848687978750752449830788691580353046844516595060078066677756466921413394857447882633792760092630660543544064791722379156530851262917123495944561541496798422416709220741501217<204>] Free to factor
3×10235-1 = 2(9)235<236> = 2143011373<10> × 28210233977<11> × 852999186877<12> × 264076233311743<15> × 2136402331008922147165389780849956832607<40> × 1594264654009345926779168497144420365135920494761720601213<58> × 646798041172415267289633787963704266787787379285930212171336658990155749445764798817046701819<93> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3576123916 for P40 / November 10, 2010 2010 年 11 月 10 日) (NFS@Home + Lionel Debroux / ggnfs-lasieve4I14e on the NFS@Home grid + msieve for P58 x P93 / August 2, 2013 2013 年 8 月 2 日)
3×10236-1 = 2(9)236<237> = 13 × 71 × 3381553657046207<16> × 30764637576691042201<20> × 3124290925678702176243531096564451212258787328924578058773843423403842515900528302292941663485427408464992830488479676992630513214967568597682900875679076836617267488933612077777757703700315115811659<199>
3×10237-1 = 2(9)237<238> = 757 × 87629 × 5758947332450579298247<22> × 979344090486010814933143639196331587<36> × [8018610266659686546645654000385995234265376666722739667470794883946905113756811628514863257406251781280851390981204234613914060239590544033769436639667734592286755819943347<172>] (Serge Batalov / GMP-ECM B1=3000000, sigma=790511631 for P36 / September 23, 2010 2010 年 9 月 23 日) Free to factor
3×10238-1 = 2(9)238<239> = 3637 × 13043 × 253304171 × [2496652612664644627957996948295649875870728454253216521124577905928616719491614747261518459416393449262358038444327254901877738493874177411868975201646849395275164208146238013942678828358126885955935196778436587706174974259<223>] Free to factor
3×10239-1 = 2(9)239<240> = 72 × 19391 × 374639 × 77203796737224443766710102182926132323<38> × 10916246254259329875940527696399155789884824127541558495304859754181264740404524607872548942516259298620753621206702100588140627958595463239342669014541036268439465523024466804909854179973813<191> (Serge Batalov / GMP-ECM B1=3000000, sigma=3856446914 for P38 x P191 / September 24, 2010 2010 年 9 月 24 日)
3×10240-1 = 2(9)240<241> = 60527 × 417133 × [118822191232006729688401381615152200851216425256516527895826365031508309577783316897783810163554123651544367580943857351507569667245627542597771300614750834183579022215128012827701240637521739093698060789095658486338164144984899989<231>] Free to factor
3×10241-1 = 2(9)241<242> = 227 × 4880774711228399<16> × 23322340571998966245463<23> × 22880312729166736787542428497<29> × 695741014426238161421383101413887<33> × 7259452327746521153190995373860628441589099<43> × 229285497603320667207077634519116727893380825579<48> × 43817187363491904946764333609605587734192812331979<50> (Serge Batalov / GMP-ECM B1=2000000, sigma=4080826854 for P33 / September 23, 2010 2010 年 9 月 23 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=458411955 for P43 / September 26, 2010 2010 年 9 月 26 日) (Dmitry Domanov / Msieve 1.40 gnfs for P48 x P50 / September 27, 2010 2010 年 9 月 27 日)
3×10242-1 = 2(9)242<243> = 13 × 4130334436471098719<19> × 325604793963376923442516447201<30> × 17159391921704221233397448886585956653327687159531128913980146763772696050869104925233975758559439909831461606154328293077690950760879505172935739075402946024822168031615996367553533451071374917<194> (Serge Batalov / GMP-ECM B1=3000000, sigma=561220683 for P30 x P194 / September 23, 2010 2010 年 9 月 23 日)
3×10243-1 = 2(9)243<244> = 40706647 × 73280611 × 926940776073990033225313348679<30> × 1084962817215187500354747332697493900314682405003802303136902959791211670985589587208290809529514856971511927982385959707922331227570374226472022335751556553231608324376982822961551342678226949391893<199> (Serge Batalov / GMP-ECM B1=2000000, sigma=2462459920 for P30 x P199 / September 23, 2010 2010 年 9 月 23 日)
3×10244-1 = 2(9)244<245> = 23 × 12491 × 104423010654627853793862015433720974753996790732805881103960068640725670308709227165298145099254071627223775031065845669751786503673949591531989989314045243009749628428120420615886916840995081676198167028086309099073071742089086751156484843<240>
3×10245-1 = 2(9)245<246> = 7 × 17 × 877 × 3065243 × 7561187 × [124028020298159826909478862678703486017987474148853830173622993600839418469848645573751360701236893222794428896737010022306531909832922641384840829331594853253330125535001203914851531537824260502880310212948224997567767453170253<228>] Free to factor
3×10246-1 = 2(9)246<247> = 3853 × 43787 × 138637 × 9225404519<10> × 2940488297028181<16> × 144006707690744099<18> × 32832980392171410858940949160132475920882282111599718233331910455910220813852141246171785548588173194211897149622631194584602611789103747750774223496616306611669223931006970221775539164394237<191>
3×10247-1 = 2(9)247<248> = 19 × 3137 × [503330369276714259349361609314967367414391893025518849722329412949012633592268845527909668976393805680922101236514940523128030468265020217103165948022750532691307484522591144741036525007130513564753452007449289465295371038370551817861517037733<243>] Free to factor
3×10248-1 = 2(9)248<249> = 13 × 5231 × 46051493207244966325278220810248409<35> × 95796461103603119871604838434486717700243417657696515920803485868215910956344736478763290580783516682187399019799924476121631939704185675070918276440320191932973270470220436196777055717660460074352138830963837<209> (Serge Batalov / GMP-ECM B1=3000000, sigma=3783953849 for P35 x P209 / September 24, 2010 2010 年 9 月 24 日)
3×10249-1 = 2(9)249<250> = 360461 × 14274265427<11> × 1726063437369789654448846178369596291661<40> × [337794403708670653416593235656564566384717438342157284566726726000475319090394272283672990642619382693244597730757769829442822175463072436346392471826660197601711855162362683994360044079523320797<195>] (KTakahashi / GMP-ECM 6.4.4 B1=11000000, sigma=4190689324 for P40 / October 13, 2014 2014 年 10 月 13 日) Free to factor
3×10250-1 = 2(9)250<251> = 491 × 203589548174855797<18> × 278984038634718404823349055784265724393081891<45> × 1075734078846116826565575685145514189316212622504364684610726258420057585321791181765414619843667387655848719019083328558662837515216264295032917669234263799379404741177389335548295053507<187> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1225193389 for P45 x P187 / July 22, 2011 2011 年 7 月 22 日)
3×10251-1 = 2(9)251<252> = 7 × 157 × 823 × 9810373128146159410841244364459<31> × 33809457437605620451313519682836038864936868779214640560935095050861588240131319458653089032139770531125376321938627058190130151956558179379351873615333457736245639284910430377028606031721217678473477772435283844193<215> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=968664949 for P31 x P215 / September 14, 2015 2015 年 9 月 14 日)
3×10252-1 = 2(9)252<253> = 1103 × 167087 × 4447019 × 6368470185841<13> × 574776463405835502002879432403362519141068734377527378424436389333517326800244431479099567490399280128306676254243144238086357880126381580781082979381599880792503555878291270559119311459873346970719540777933706195366314742221<225>
3×10253-1 = 2(9)253<254> = 29 × 103 × 821 × 943219 × 12969712061432565787650413608082285516021982044487878427871739388972578299712341946993086990640060424132256857610713308260732448422058143166131332393462177930082411421928883851549676188657487247618356779334619052998090538685910373092503134323<242>
3×10254-1 = 2(9)254<255> = 13 × 15527 × 52200134711<11> × 307719686123<12> × 21802069806605651<17> × [4243905638787949384663828328592955185506026898991670618849869185658285372328512845058139212076375355053406042013500764639216677462822614069220243077742717156140096252756144860191755652275886802290799890162655883<211>] Free to factor
3×10255-1 = 2(9)255<256> = 5297 × 1377791 × 3165311 × [129864829971838041085624128957898621981599168578722458624082152515250670680189240672666982644243242746416468066110961347320093868040631097671098394462804886622205439254963578422474041344708873450926808441503597125283917181575416210247512367<240>] Free to factor
3×10256-1 = 2(9)256<257> = 313 × 6073 × [15782421433790900802746562194051184497032641730090080800736933864815143128149579477380896641448110817850339506189076565261101749797064364397172000511350454454825186008988615087258377703857592054918617943876657220010637352046375067141051182918790498351<251>] Free to factor
3×10257-1 = 2(9)257<258> = 7 × 113 × 389 × 571 × 2731 × 62549 × 73598297 × 358165651 × 1918260791<10> × 585689203642621693<18> × 84466016020313605155542793133<29> × [3995842971221230540766836244831620718081423427113993467184784222097410463605819765874460461575560183469989158085955159854647479710255131477946312229998564537327711868373<169>] Free to factor
3×10258-1 = 2(9)258<259> = 47 × 59 × 61 × [17735422960278564376629441984475593102102829982323695116255697504625989488805992208237512784284050534131821487056097142823361099123278924996896300981951251234089847652716771207132004753093353354655252936690451839458951363558435262750291156526931239765183<254>] Free to factor
3×10259-1 = 2(9)259<260> = 373 × 80428954423592493297587131367292225201072386058981233243967828418230563002680965147453083109919571045576407506702412868632707774798927613941018766756032171581769436997319034852546916890080428954423592493297587131367292225201072386058981233243967828418230563<257>
3×10260-1 = 2(9)260<261> = 13 × 18539 × 1841296467185422441<19> × 676032971789130536380734020793785435567612218211955330375719922563276137625614539981611247756094072753015917122859646976560458006888677571458560715134867709490576745522151837618998632779464198440215925416318804898419715186038217951947977<237>
3×10261-1 = 2(9)261<262> = 17 × 83 × 30859 × 319288564304741<15> × [215788863873980684377158450076063244942465670654353641602064431411491698198961364930376600711676130246587494393128106353986144289475087414180964857087166539396058186085330943280891404683319439601897146121931999596813187158092402864528431411<240>] Free to factor
3×10262-1 = 2(9)262<263> = 3301 × 1285429 × 83177506077359<14> × 53923144256085589110407627<26> × 880482910602817002739617065763601<33> × 1240234201995186467774823670217437<34> × 484926123512155816956321712789885135319<39> × 2976777117384252284440069138530511544288948482411776180555732631854282326207461563193028477806681944513366289<109> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3630484822 for P34 / September 13, 2015 2015 年 9 月 13 日) (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2935291095 for P33, B1=3000000, sigma=2402713257 for P39 x P109 / September 14, 2015 2015 年 9 月 14 日)
3×10263-1 = 2(9)263<264> = 7 × 1480495293649441684718533<25> × [28947841334570809944188515128289539305447627701679894424839554229884124348397124283186151627434187834443903570835879470316633372484665834773981258387383682856236196068746928648611377297972877193220221161762503462706761221862290673406363829<239>] Free to factor
3×10264-1 = 2(9)264<265> = 131 × 757 × 1098373 × 71605021 × 12154370646323<14> × 14512421906794002132541<23> × 7090403138520872214148127<25> × [307551220072541239625523592119776195188858031186020193003594546903027285502946302435324164339751910921544674699044970853550409463156142058187547471695391605232725529511388775552821454169<186>] Free to factor
3×10265-1 = 2(9)265<266> = 19 × 431 × 5039 × 31858282185262543<17> × 31914047027428913<17> × 715058856190927926297794100031945235861392108589449597349073685708531516156329989219377167650182482730668151946271171562954805990772321296728952420814103967673578439619508882651391308065818204591884230215445717696746582609691<225>
3×10266-1 = 2(9)266<267> = 13 × 23 × 4341866659986390329819<22> × 29599200727643563736033891<26> × [7807169358757201919417747766736534120388733280054744111302176922943511471319120042245971291792670097356914178811355582411201475093627362705197630522470175093863638503150989249817489893500721113377783177698057719165069<217>] Free to factor
3×10267-1 = 2(9)267<268> = 367 × 5357557 × 435992756237728927873183<24> × [3499525129136309762140291496255745929166445041477767199032025837214534907445599469180360681403064365117283597616833080774078796294569930713461789312161720972268723572760602829105042152448150637086219677766609754836060366453371802162387<235>] Free to factor
3×10268-1 = 2(9)268<269> = 76991 × 194963 × 4124168051<10> × 89604004706350021<17> × 36476621181142294259<20> × 10897768869036654459750187235772507313<38> × 13605456742999242476906542548944027844315547594008150218413222010976630012995570716449707863987622574087536615689070173534782027693607986524004601993049789434088019321083578679<176> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1874728461 for P38 x P176 / September 14, 2015 2015 年 9 月 14 日)
3×10269-1 = 2(9)269<270> = 7 × 443 × 1321 × 229903 × 485131 × 3505612159427059113418466173<28> × 187304899961664496957660715781706631021471192041867499583804491819398341297793162861232884929112387449078085444426859427535195398281402943922961636586023586123796179091836304583347245818636943254233478201608678231998029735971<225>
3×10270-1 = 2(9)270<271> = 73883 × 325751 × 163467210537049<15> × [762535950699948496833876051747241978604966231162321833008250353956975867186933381535991294227158619409729067237171812690781115366757058044973690312438562298273022833990928197350034184950583388560412479780780657948845218090435902774490048580916147<246>] Free to factor
3×10271-1 = 2(9)271<272> = 71 × 277 × 30649 × 14750570742387069931488097277147745589193<41> × 3374100413134691358447123278700866688221787483792841709503202068999786297462934676975457030379898605444234389425397579727678687403166228771716170472644362943938840093213228406849317274507878471659122590036142466394471710821<223> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2712479544 for P41 x P223 / February 21, 2017 2017 年 2 月 21 日)
3×10272-1 = 2(9)272<273> = 13 × [23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923<272>] Free to factor
3×10273-1 = 2(9)273<274> = 8281454161<10> × 404959776157<12> × 543265398769<12> × 3183054245603646499<19> × 517305004103715454478286719795124465811674988156271434140082408879387878823854395107749429286442433830374734727293671542679805497854549737544905531404387884401514837796965474711461144458870356772607090807979006817513203577<222>
3×10274-1 = 2(9)274<275> = 1607 × 102957611 × [181320505517836357160162547611969315640216780653983680226396255184258407610706906554966241453727528013298758730201544957169951182245681146018961017429078222843255424544226686623485767254114779495777519147464315566303803526125168129972881402933469696189918703388187<264>] Free to factor
3×10275-1 = 2(9)275<276> = 7 × 967 × 116082657840355438543<21> × 381794262307023854609443671952237899200757208075923823263709341393668752504010477499661628292298086502190195421951252202154849631782605417020246061771115799547354436894464646385819502627459569494664661947900450057233421482568896927143586423423060608097<252>
3×10276-1 = 2(9)276<277> = 41149 × 90998377 × 801176722398766270909449182853399333710822500740071029196135666675185898247405713888818650273848779654259252110586414821767375536080329127418977171236158371710259945538202976186957003760163095531897583200872462784983801585550312681234882980293862153058091442051763<264>
3×10277-1 = 2(9)277<278> = 17 × 347 × 159617 × 89417047 × 402255983069<12> × 24059267190781606387105992962851<32> × [36817855059728842956489648835118295829539523290243462670764438238669390779341348213689122321454988584037627461796343942496334663616788081950745311008721494625588577912522119090493505470375734224370585853127366634391021<218>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=355649155 for P32 / September 14, 2015 2015 年 9 月 14 日) Free to factor
3×10278-1 = 2(9)278<279> = 13 × 128833 × 2401381 × 24484211 × 129537719 × 5802867349292744413<19> × 7759093814952037969<19> × 36510718907360225494603099513007<32> × 414793047030090727937655318594575732628523814389<48> × 34490687826095882852042991459260753867331943552198052585877345799304804663749015120653535671545538734359355772561294058718507528224669<134> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2168117003 for P32 / September 14, 2015 2015 年 9 月 14 日) (Erik Branger / GMP-ECM B1=43000000, sigma=2701930693 for P48 x P134 / November 4, 2015 2015 年 11 月 4 日)
3×10279-1 = 2(9)279<280> = 107 × 1531 × 6869 × 129504149743<12> × 2183333953749593339023317375031307053<37> × 9428984382447595657235939635641010558397379499756881557614001834224003278685757524914560895963691625574036787087723415835630838196513489549760529705048313894231609462626355973156389646539073179048298902982348334372701095897<223> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2967735357 for P37 x P223 / September 15, 2015 2015 年 9 月 15 日)
3×10280-1 = 2(9)280<281> = 4969 × 19211 × 50691920390500885952031670235569<32> × 70826888213408535989715027789680943239<38> × [87531703457487725949994801266005358068384775586795162032877987797431212359478145238175325395582320588906475001706530078862969974036012214416606752891186978621861815056396990703732477319186187685742286771<203>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3215036991 for P32 / September 13, 2015 2015 年 9 月 13 日) (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1621429921 for P38 / September 14, 2015 2015 年 9 月 14 日) Free to factor
3×10281-1 = 2(9)281<282> = 72 × 29 × 1097 × [192451167120102999864642679125527556761867982348378951744152852414973470606612493801468659006682546026300376498633275961502068529294595907076878467729467545355928811030274493099663402908706939853236739954209452303223492898872685213399476661126211399909034748341231315397312227<276>] Free to factor
3×10282-1 = 2(9)282<283> = 48167109226154771<17> × 10279164266996145047<20> × [6059166206839113917233142979165815607944292614686531067171650026285366327903878933517135239879749942462929047405152337130478267592320689291081474856740091041405072316423591924548697842313221759898719087341343200556649344607527121485319737263193827<247>] Free to factor
3×10283-1 = 2(9)283<284> = 19 × 834825739651<12> × 15630988526598864961<20> × 201781068202100853698922810943<30> × 4620474432330019491083597480544397<34> × [129783173762855209175766742279074614187771261068739847879120474748522082755908758964202337299572311619125746393456135106371531211569451669931835273761734854760004277618293437282864184450541<189>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=324818788 for P30, B1=1000000, sigma=987654321 for P34 / September 14, 2015 2015 年 9 月 14 日) Free to factor
3×10284-1 = 2(9)284<285> = 132 × 599 × 4513 × 950459 × 79046252450516653<17> × 1959412175405071686345785025143<31> × 4460688734829337637742714594377010471959773612476103017073703030834258244937859059981088523201881272674826741794638035041216479101421332178900028391237373447287744669876656519134068851507022074900989881641650876550164366953<223> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1120367998 for P31 x P223 / September 13, 2015 2015 年 9 月 13 日)
3×10285-1 = 2(9)285<286> = 118357885034727703<18> × 1281873610485759385561<22> × 112422233103862820222980319<27> × 136880389899229905837160580703119<33> × 1284947578966578175628548427486419443193730997866398993993054678496950345137138914635480377389508471425354669443290047980292800713842199452031657584396449108022851607095641153476662816709873<190> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1732866669 for P33 x P190 / September 14, 2015 2015 年 9 月 14 日)
3×10286-1 = 2(9)286<287> = 97 × 48023 × 14638633 × 425664623 × [1033551575065161692772599228849739033103225329661798481298286776509428529340621621170340489447237925603380443466031809094838343034684493706344648408342064775584316537687270869109071248659442713962839467824889942759906617103331059588981061465572807492137299813456831<265>] Free to factor
3×10287-1 = 2(9)287<288> = 7 × 103 × 286879051 × 2258752400414238765259735743461689<34> × 663819354791150401866569369061347881<36> × 9079649562854343798202500970257660006847<40> × 30149367146749551891331686966988768800629<41> × 3533632081128482559549190867044706541977488971402868795544572483032266550633803060407988441139591224388590997887097515849946407<127> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3610460432 for P36 / September 13, 2015 2015 年 9 月 13 日) (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=597366400 for P40 / September 14, 2015 2015 年 9 月 14 日) (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=3425338188 for P34 / September 15, 2015 2015 年 9 月 15 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=680710756 for P41 x P127 / September 16, 2015 2015 年 9 月 16 日)
3×10288-1 = 2(9)288<289> = 23 × 12853 × 10148197510985423805641721269607163274349754244483608969653506709649921013196039496784712755269451557579181311079463769243519530206109891448113957492583358985721486102043508705462098173662721272989895778011562179697516059522561134433172428023909153335881658486091895311194476674368021<284>
3×10289-1 = 2(9)289<290> = 15473407 × 162190031767<12> × 648620617440233<15> × 40188214538900266543<20> × [458586943310135900390553142868687839532102607905618973831931898942883436414762225811787466336187010491661453038297910104306479011010798440707312488652559560568044172399596296718270750892622593589621689281228976608353072943801399370760609<237>] Free to factor
3×10290-1 = 2(9)290<291> = 13 × 661 × 39901 × 1180541572869387539<19> × 3119967510830314574341<22> × 46908491174594925173187254540327<32> × [5064188256914463733706728788645342241850973708120361793592359294750005243191378757608171214923629299905775985699444763587246204393916921524805853476595263334415464739699771100576399378173059365290982729918655091<211>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3752690032 for P32 / September 14, 2015 2015 年 9 月 14 日) Free to factor
3×10291-1 = 2(9)291<292> = 757 × 9257 × 10402288791571<14> × [41155341038021548872479711663101089076061285056638618117490880049710234771719225723081957284034129117418889523586955286495465037229189378976716640857466226435394113309271486477877812072971589999189413630654553611096979199630919931148457425895944887859615932037083532391881<272>] Free to factor
3×10292-1 = 2(9)292<293> = 181 × 28749899 × [5765093517496919214255134431537361121210407273111767428531416955624956191174466655858743358863770048249868278807015108535805744523625392533423185877350184739606480854398558589488267967336384506643317981551000861656834388390959245760455776486581782599388460133642027981727318560098121<283>] Free to factor
3×10293-1 = 2(9)293<294> = 7 × 17 × 7411 × 45389 × 4725656043701<13> × 157861526033361859<18> × [10046353610324682659248076016528504470375606586540177428779339568685289494359477675482884666145661544321251706850323096862340478594817322104496971780288014924503214893571307188841485716992785852800424262476182926794879170977597646938580083897653327098161<254>] Free to factor
3×10294-1 = 2(9)294<295> = 101666627 × 13514324659863619539289646433527<32> × [2183476346545598047103995156221159188402352323062946599237158999863708884447053677862846728730182256425306007707202721586646748069509523667817264000220990526233941668424401734496357432326352506978016680282381907620962034464582905394625123085135492408485331<256>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2886526743 for P32 / September 14, 2015 2015 年 9 月 14 日) Free to factor
3×10295-1 = 2(9)295<296> = 11057 × 162187279428737<15> × 81324312152902969<17> × [205705904436717939619041352302221263739916844744412586643504933754812568104231429336222214862819674961036611619766472847352072865015835748362026804171507927766941746098200277992560630134709289172322602933884361204145669009596408204108058522663890653833460161319<261>] Free to factor
3×10296-1 = 2(9)296<297> = 13 × 109 × 584336663 × [362316630154649705388282696311859636273057120898396664559544058859194988506560644656514222600777107040901351438417086990095609969491560147945854946623390006518671957871553500755756019106746868142863810989857288954843847809170608165626568809409214691817453514729802529383680062430303569<285>] Free to factor
3×10297-1 = 2(9)297<298> = 86957712657619<14> × 34499527509560684148292821355325254108943916534170201634508577816722035703343616064816362084958362083535119748639638609849227599612565647660833019053337682610176386650771294294247670839259673142698292332851302416543104953535804432857408031489423131785678186866670277972897429382010021<284>
3×10298-1 = 2(9)298<299> = 525348937 × 310834547361024848872269443<27> × 537852406398139185353428805100536591<36> × 416019575231946770566704102313780673081132711<45> × 821045514121100849016920430250756282665600182262029718447961121045217677841035522832585942062645696504044032765730706341310048416542214722894067438018027733865708890047100821382053189<183> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=759521296 for P45, B1=11000000, sigma=4014515366 for P36 x P183 / March 6, 2017 2017 年 3 月 6 日)
3×10299-1 = 2(9)299<300> = 7 × 719 × 3739 × 155501 × 18590255248396054135119519862636579<35> × [5514680043451945451722659577266014534499613782731427020199543126528843055153003041820782385421251376314589830261452074675316729827943389772405084621134231830243391229918560179885010369147268754986907047166766418542405996783654594184325600079994508505363<253>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1248788013 for P35 / September 15, 2015 2015 年 9 月 15 日) Free to factor
3×10300-1 = 2(9)300<301> = [2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<301>] Free to factor
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