Table of contents 目次

  1. About 922...221 922...221 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 922...221 922...221 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 922...221 922...221 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 922...221 922...221 について

1.1. Classification 分類

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

1.2. Sequence 数列

92w1 = { 91, 921, 9221, 92221, 922221, 9222221, 92222221, 922222221, 9222222221, 92222222221, … }

1.3. General term 一般項

83×10n-119 (1≤n)

2. Prime numbers of the form 922...221 922...221 の形の素数

2.1. Last updated 最終更新日

November 16, 2015 2015 年 11 月 16 日

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

  1. 83×103-119 = 9221 is prime. は素数です。
  2. 83×104-119 = 92221 is prime. は素数です。
  3. 83×1024-119 = 9(2)231<25> is prime. は素数です。
  4. 83×1039-119 = 9(2)381<40> is prime. は素数です。
  5. 83×1063-119 = 9(2)621<64> is prime. は素数です。
  6. 83×1076-119 = 9(2)751<77> is prime. は素数です。
  7. 83×10108-119 = 9(2)1071<109> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 7, 2004 2004 年 12 月 7 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 8, 2005 2005 年 1 月 8 日)
  8. 83×10166-119 = 9(2)1651<167> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / December 7, 2004 2004 年 12 月 7 日) (certified by: (証明: Makoto Kamada / PPSIQS / January 8, 2005 2005 年 1 月 8 日)
  9. 83×10520-119 = 9(2)5191<521> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 1, 2006 2006 年 6 月 1 日)
  10. 83×101810-119 = 9(2)18091<1811> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / June 25, 2006 2006 年 6 月 25 日)
  11. 83×102349-119 = 9(2)23481<2350> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Ray Chandler / Primo 3.0.9 / September 20, 2010 2010 年 9 月 20 日)
  12. 83×102562-119 = 9(2)25611<2563> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / December 20, 2012 2012 年 12 月 20 日)
  13. 83×105784-119 = 9(2)57831<5785> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 22, 2004 2004 年 12 月 22 日)
  14. 83×106448-119 = 9(2)64471<6449> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 25, 2004 2004 年 12 月 25 日)
  15. 83×1011692-119 = 9(2)116911<11693> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 8, 2010 2010 年 9 月 8 日)
  16. 83×1016036-119 = 9(2)160351<16037> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 8, 2010 2010 年 9 月 8 日)
  17. 83×1017554-119 = 9(2)175531<17555> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 8, 2010 2010 年 9 月 8 日)

2.3. Range of search 捜索範囲

  1. n≤20000 / Completed 終了 / Ray Chandler / September 8, 2010 2010 年 9 月 8 日
  2. n≤30000 / Completed 終了 / Ray Chandler / September 10, 2010 2010 年 9 月 10 日
  3. n≤50000 / Completed 終了 / Erik Branger / May 1, 2013 2013 年 5 月 1 日
  4. n≤100000 / Completed 終了 / Bob Price / November 15, 2015 2015 年 11 月 15 日

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

  1. 83×103k+2-119 = 3×(83×102-119×3+83×102×103-19×3×k-1Σm=0103m)
  2. 83×106k+1-119 = 7×(83×101-119×7+83×10×106-19×7×k-1Σm=0106m)
  3. 83×106k+1-119 = 13×(83×101-119×13+83×10×106-19×13×k-1Σm=0106m)
  4. 83×1013k+8-119 = 79×(83×108-119×79+83×108×1013-19×79×k-1Σm=01013m)
  5. 83×1015k+6-119 = 31×(83×106-119×31+83×106×1015-19×31×k-1Σm=01015m)
  6. 83×1016k+11-119 = 17×(83×1011-119×17+83×1011×1016-19×17×k-1Σm=01016m)
  7. 83×1018k+12-119 = 19×(83×1012-119×19+83×1012×1018-19×19×k-1Σm=01018m)
  8. 83×1021k+5-119 = 43×(83×105-119×43+83×105×1021-19×43×k-1Σm=01021m)
  9. 83×1022k+18-119 = 23×(83×1018-119×23+83×1018×1022-19×23×k-1Σm=01022m)
  10. 83×1028k+15-119 = 29×(83×1015-119×29+83×1015×1028-19×29×k-1Σm=01028m)

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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 14.73%. 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 14.73% です。

3. Factor table of 922...221 922...221 の素因数分解表

3.1. Last updated 最終更新日

May 27, 2018 2018 年 5 月 27 日

3.2. Range of factorization 分解範囲

3.3. Terms that have not been factored yet まだ分解されていない項

n=189, 194, 196, 203, 205, 207, 211, 214, 219, 220, 221, 224, 225, 227, 230, 231, 233, 234, 235, 236, 240, 242, 244, 245, 246, 247 (26/250)

3.4. Factor table 素因数分解表

83×101-119 = 91 = 7 × 13
83×102-119 = 921 = 3 × 307
83×103-119 = 9221 = definitely prime number 素数
83×104-119 = 92221 = definitely prime number 素数
83×105-119 = 922221 = 32 × 43 × 2383
83×106-119 = 9222221 = 31 × 521 × 571
83×107-119 = 92222221 = 7 × 13 × 1013431
83×108-119 = 922222221 = 3 × 79 × 1171 × 3323
83×109-119 = 9222222221<10> = 127 × 6067 × 11969
83×1010-119 = 92222222221<11> = 20771 × 4439951
83×1011-119 = 922222222221<12> = 3 × 17 × 18082788671<11>
83×1012-119 = 9222222222221<13> = 19 × 485380116959<12>
83×1013-119 = 92222222222221<14> = 7 × 13 × 61 × 16613623171<11>
83×1014-119 = 922222222222221<15> = 33 × 140627 × 242886349
83×1015-119 = 9222222222222221<16> = 29 × 347 × 12451 × 73604417
83×1016-119 = 92222222222222221<17> = 977 × 1901 × 49654533073<11>
83×1017-119 = 922222222222222221<18> = 3 × 307407407407407407<18>
83×1018-119 = 9222222222222222221<19> = 23 × 400966183574879227<18>
83×1019-119 = 92222222222222222221<20> = 7 × 13 × 152821 × 1489021 × 4453591
83×1020-119 = 922222222222222222221<21> = 3 × 9467 × 145518713 × 223142917
83×1021-119 = 9222222222222222222221<22> = 31 × 79 × 3765709359829408829<19>
83×1022-119 = 92222222222222222222221<23> = 212477910923<12> × 434032045127<12>
83×1023-119 = 922222222222222222222221<24> = 32 × 47 × 27337 × 79752510472105171<17>
83×1024-119 = 9222222222222222222222221<25> = definitely prime number 素数
83×1025-119 = 92222222222222222222222221<26> = 72 × 13 × 739 × 3797 × 51595415603577551<17>
83×1026-119 = 922222222222222222222222221<27> = 3 × 43 × 1493 × 997609 × 9789587 × 490299371
83×1027-119 = 9222222222222222222222222221<28> = 17 × 12304163 × 44089440308188289951<20>
83×1028-119 = 92222222222222222222222222221<29> = 569 × 99377 × 1630937935291562784517<22>
83×1029-119 = 922222222222222222222222222221<30> = 3 × 307407407407407407407407407407<30>
83×1030-119 = 9222222222222222222222222222221<31> = 19 × 29609791 × 16392554643802258769249<23>
83×1031-119 = 92222222222222222222222222222221<32> = 7 × 13 × 673 × 16699327 × 90173755526681885161<20>
83×1032-119 = 922222222222222222222222222222221<33> = 32 × 102469135802469135802469135802469<33>
83×1033-119 = 9222222222222222222222222222222221<34> = 811 × 154937 × 73393835833709669069201503<26>
83×1034-119 = 92222222222222222222222222222222221<35> = 79 × 1167369901547116736990154711673699<34>
83×1035-119 = 922222222222222222222222222222222221<36> = 3 × 1433 × 1288967 × 19800239 × 2490308731<10> × 3375224893<10>
83×1036-119 = 9222222222222222222222222222222222221<37> = 31 × 827 × 61357 × 5862788975995389117359197069<28>
83×1037-119 = 92222222222222222222222222222222222221<38> = 7 × 132 × 2441 × 5009 × 40241 × 47540063 × 3332755929414181<16>
83×1038-119 = 922222222222222222222222222222222222221<39> = 3 × 9547 × 32199372306212151189631026228910381<35>
83×1039-119 = 9222222222222222222222222222222222222221<40> = definitely prime number 素数
83×1040-119 = 92222222222222222222222222222222222222221<41> = 23 × 4009661835748792270531400966183574879227<40>
83×1041-119 = 922222222222222222222222222222222222222221<42> = 33 × 941 × 36297958130523958838990129579337278003<38>
83×1042-119 = 9222222222222222222222222222222222222222221<43> = 107 × 86188992731048805815160955347871235721703<41>
83×1043-119 = 92222222222222222222222222222222222222222221<44> = 7 × 13 × 17 × 29 × 2389 × 60467367625966123<17> × 14230169038844148661<20>
83×1044-119 = 922222222222222222222222222222222222222222221<45> = 3 × 2131 × 6857821 × 16355627 × 2074110357833<13> × 620077075206227<15>
83×1045-119 = 9222222222222222222222222222222222222222222221<46> = 28352999 × 3664772941<10> × 11946402241181<14> × 7429376618396099<16>
83×1046-119 = 92222222222222222222222222222222222222222222221<47> = 229 × 2056376938152453498353<22> × 195838185177167691927833<24>
83×1047-119 = 922222222222222222222222222222222222222222222221<48> = 3 × 43 × 79 × 1291 × 551557 × 25716337 × 4941889495333285668159801349<28>
83×1048-119 = 9222222222222222222222222222222222222222222222221<49> = 19 × 671941 × 46654425731<11> × 433128925331<12> × 35747099132667745259<20>
83×1049-119 = 92222222222222222222222222222222222222222222222221<50> = 7 × 13 × 98940797 × 23512272428102004629<20> × 435636420675403146487<21>
83×1050-119 = 922222222222222222222222222222222222222222222222221<51> = 32 × 333483107 × 307269344838115400557513504881880376034967<42>
83×1051-119 = 9(2)501<52> = 31 × 127 × 45863 × 1509727 × 16454791 × 34438309 × 59700105372476625115207<23>
83×1052-119 = 9(2)511<53> = 3217 × 4774156071539866006194989<25> × 6004652922817621040577617<25>
83×1053-119 = 9(2)521<54> = 3 × 2089 × 2098788173<10> × 70114409377399014824226819048576116169331<41>
83×1054-119 = 9(2)531<55> = 59 × 12148090183<11> × 2372988854777<13> × 5422254096333047741107534497209<31>
83×1055-119 = 9(2)541<56> = 7 × 13 × 179 × 2305840799<10> × 2455341138821447721740969789014159326756211<43>
83×1056-119 = 9(2)551<57> = 3 × 499 × 839 × 6367 × 27529 × 4189156026573557623240582606038597494489909<43>
83×1057-119 = 9(2)561<58> = 2297 × 167470530125945003<18> × 23973762172178364684148115586756649631<38>
83×1058-119 = 9(2)571<59> = 521 × 617 × 1237 × 87013 × 43777229 × 385068879889<12> × 158114669179691748489247673<27>
83×1059-119 = 9(2)581<60> = 32 × 17 × 2153 × 194867 × 2845863427609<13> × 5048330376211258979144601812555256023<37>
83×1060-119 = 9(2)591<61> = 79 × 683545871 × 9363066497<10> × 18239911197679330348509866500045552951277<41>
83×1061-119 = 9(2)601<62> = 7 × 13 × 109 × 243813192875406299<18> × 38133835678298530573349051739776724895241<41>
83×1062-119 = 9(2)611<63> = 3 × 23 × 12893 × 5165299 × 4382711265147427<16> × 45792481977284411178766563263887781<35>
83×1063-119 = 9(2)621<64> = definitely prime number 素数
83×1064-119 = 9(2)631<65> = 95651 × 252449 × 33503549591<11> × 36720286661<11> × 35907120002353<14> × 86455963647897286693<20>
83×1065-119 = 9(2)641<66> = 3 × 24767 × 1361782876339<13> × 9114504321836105572231266176434225161791599367339<49>
83×1066-119 = 9(2)651<67> = 19 × 312 × 191 × 457 × 3087511357620956771<19> × 1874133238610279399924234404179380168147<40>
83×1067-119 = 9(2)661<68> = 73 × 13 × 30939001 × 77655967 × 8608292036426576207271487070195996794148691464257<49>
83×1068-119 = 9(2)671<69> = 34 × 43 × 330247373 × 1013744279861533343<19> × 790886787218096181296158637119107219533<39>
83×1069-119 = 9(2)681<70> = 47 × 199 × 2675303 × 79492279207502186816246537<26> × 4636462192803667201231623896308987<34>
83×1070-119 = 9(2)691<71> = 991 × 890467 × 3956429 × 404397422199661249159<21> × 65317919608263014066223119423956163<35>
83×1071-119 = 9(2)701<72> = 3 × 29 × 283 × 1730693 × 3170646643<10> × 1298770859066489<16> × 5255686814910106278354733276870832791<37>
83×1072-119 = 9(2)711<73> = 205339 × 11112338550379493140607<23> × 4041649761684107593998303240852565908628979977<46>
83×1073-119 = 9(2)721<74> = 7 × 13 × 61 × 79 × 181 × 15073 × 77083067737385404044109836873507490957854676257967489776344473<62>
83×1074-119 = 9(2)731<75> = 3 × 41887 × 1465861 × 71386614410117<14> × 70133497210144556144622533663950124973402182489753<50>
83×1075-119 = 9(2)741<76> = 17 × 3181 × 755425637 × 225751826616342329947198078946139387638759531637229803545527229<63>
83×1076-119 = 9(2)751<77> = definitely prime number 素数
83×1077-119 = 9(2)761<78> = 32 × 1801 × 82084801 × 104771248888183452850380739717339<33> × 6615679999584885024119843802624071<34> (Makoto Kamada / msieve 0.81 / 51 seconds)
83×1078-119 = 9(2)771<79> = 21277 × 757237324637<12> × 10540177340639<14> × 54305680340091283683292002267844742309762374945211<50>
83×1079-119 = 9(2)781<80> = 7 × 13 × 5978937348811140257<19> × 169500189466364852058679764990969252644852536621959232935383<60>
83×1080-119 = 9(2)791<81> = 3 × 10139 × 11377763 × 109080896272855009<18> × 24429446336538664480979027436240339512266695435171839<53>
83×1081-119 = 9(2)801<82> = 31 × 6917 × 133271 × 481384083542857014767333147<27> × 670391856739311307246755244220896767074043379<45>
83×1082-119 = 9(2)811<83> = 842558929 × 109454922436911498474217964429431881579670758224463872748563824456511364349<75>
83×1083-119 = 9(2)821<84> = 3 × 84967 × 1053288079745286350449506773989183453<37> × 3434921959582671251153584436084736255572557<43> (Makoto Kamada / GGNFS-0.70.1 / 0.13 hours)
83×1084-119 = 9(2)831<85> = 19 × 23 × 43696254109<11> × 150869425106344384349140411253<30> × 3201169734074104820586705941360204272979129<43> (Makoto Kamada / msieve 0.83 / 4.8 minutes)
83×1085-119 = 9(2)841<86> = 7 × 13 × 554478719779<12> × 1678340855535114380244420726957983<34> × 1089003162231665347795308084994968730883<40> (Makoto Kamada / msieve 0.83 / 4.7 minutes)
83×1086-119 = 9(2)851<87> = 32 × 792 × 881 × 1021 × 2338727387089652953358647<25> × 7804725606770681538254557703665696042279028383039247<52>
83×1087-119 = 9(2)861<88> = 97 × 577 × 17757680855255105057<20> × 9279013124960965669112222733901049132736837082051867480891084237<64>
83×1088-119 = 9(2)871<89> = 2463767 × 162510199 × 8406660372631<13> × 27398817810883021839980720838845975057393004126790504063163627<62>
83×1089-119 = 9(2)881<90> = 3 × 43 × 23833 × 98573 × 17790492419567783137<20> × 171049266608248804623996844298478147531172188503618043252553<60>
83×1090-119 = 9(2)891<91> = 3340943 × 98135011975319818721024981414144795729069<41> × 28128238574377447526281781448255954879746063<44> (Makoto Kamada / GGNFS-0.70.3 / 0.27 hours)
83×1091-119 = 9(2)901<92> = 7 × 13 × 17 × 5881 × 428552243113<12> × 86979450302117<14> × 271940354003280065824180255976161655784477481901878269486043<60>
83×1092-119 = 9(2)911<93> = 3 × 7777917509<10> × 7907771419<10> × 195832714920801748079<21> × 25521820124241489646216378626436254076601129717684023<53>
83×1093-119 = 9(2)921<94> = 127 × 21313 × 33986178757546388093712467070398225231<38> × 100250128897676298006953926977890144673387275928541<51> (Makoto Kamada / GGNFS-0.71.4 / 0.29 hours)
83×1094-119 = 9(2)931<95> = 863 × 2687 × 1125169 × 12988691 × 327818695014845779519678031<27> × 8301188205686590665219161736904423541204789522209<49>
83×1095-119 = 9(2)941<96> = 33 × 107 × 131 × 193 × 63799 × 34990271711<11> × 5655854779777445044713988488368656140047554875753486548367140908281575647<73>
83×1096-119 = 9(2)951<97> = 31 × 8723694194935723<16> × 34101497918074974368438362212761815368446235924473354161750355954160570406487417<80>
83×1097-119 = 9(2)961<98> = 7 × 13 × 2743720407366451<16> × 7590610171541767<16> × 17710212000769781<17> × 2747602412835167427055352585292180648640665364703<49>
83×1098-119 = 9(2)971<99> = 3 × 254623 × 49438573867920371<17> × 24420286966778357407799518563146273775612763533243971500177974853627556154379<77>
83×1099-119 = 9(2)981<100> = 29 × 79 × 140083681 × 478317938632207<15> × 41314485764834514901<20> × 6847102083423552215766329<25> × 212371935637254775720788399317<30>
83×10100-119 = 9(2)991<101> = 752201 × 67144828600960459<17> × 1119751098463043324459<22> × 1630675738672225808590582015534270681374211478311608604141<58>
83×10101-119 = 9(2)1001<102> = 3 × 421 × 10681870423130414777876826141539044783<38> × 68357304166006055253316970327770652012559473791352737524402349<62> (Erik Branger / GGNFS, Msieve snfs / May 20, 2010 2010 年 5 月 20 日)
83×10102-119 = 9(2)1011<103> = 19 × 929 × 17401 × 747113 × 62739372999617925837512361617579058757<38> × 640568522248032584831799213989847295257231881302931<51> (Erik Branger / GGNFS, Msieve snfs / May 20, 2010 2010 年 5 月 20 日)
83×10103-119 = 9(2)1021<104> = 7 × 13 × 30382537 × 2729332516604797<16> × 58176977379553111295093<23> × 210069282639700486362715668824944090832489695406810409503<57>
83×10104-119 = 9(2)1031<105> = 32 × 30790763 × 5499583372546825513333<22> × 605121846404724047481872083546496244671822497680193339578827674004481043411<75>
83×10105-119 = 9(2)1041<106> = 368653 × 81186117561427<14> × 163758238993529669<18> × 76928944650384824033<20> × 24459248150433249929832612205493692502565593193983<50>
83×10106-119 = 9(2)1051<107> = 23 × 245711 × 2777981 × 5874269624581264415341353447697170166854480055569049015409990189080403789562860668868557144697<94>
83×10107-119 = 9(2)1061<108> = 3 × 17 × 4932682755713573889156518493894421730960875081<46> × 3665913574125256092049643359161426520811143215775498510872391<61> (Dmitry Domanov / Msieve 1.40 snfs / May 20, 2010 2010 年 5 月 20 日)
83×10108-119 = 9(2)1071<109> = definitely prime number 素数
83×10109-119 = 9(2)1081<110> = 72 × 13 × 11677 × 142612597 × 67668312005341<14> × 1284758911503723761487970173759639723779681092471286220231776494796638878949623877<82>
83×10110-119 = 9(2)1091<111> = 3 × 43 × 113 × 521 × 319411 × 380171746012041675578242053862126876515377861310453994814769377972986780063374934255316976226350583<99>
83×10111-119 = 9(2)1101<112> = 31 × 30707 × 555097 × 755789 × 23092292673257210835558041214685352467314378677465299192267383657310116095948663330870302274861<95>
83×10112-119 = 9(2)1111<113> = 59 × 79 × 2966681 × 98731643 × 113607701 × 3101950343341<13> × 95181249374728906357721525781327373<35> × 2013887710898858899662910254538557560719<40> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1329102838 for P40 / May 17, 2010 2010 年 5 月 17 日)
83×10113-119 = 9(2)1121<114> = 32 × 167 × 176809 × 7478683 × 464031122258023396448115222355407129260006366457701009208677936531197913952055706286418628810850881<99>
83×10114-119 = 9(2)1131<115> = 10301 × 69481 × 1207897045214550793<19> × 47005450455943756240479145770404848736057<41> × 226940494892379107574645976350284040914548440041<48> (Erik Branger / GGNFS, Msieve snfs / May 20, 2010 2010 年 5 月 20 日)
83×10115-119 = 9(2)1141<116> = 7 × 132 × 47 × 123373 × 655477531 × 20510443241884138252844908264471401601174933751535158377259355850588723492303216299619752285392867<98>
83×10116-119 = 9(2)1151<117> = 3 × 1597 × 27073 × 15004273 × 2566942106641970484923<22> × 286443699416334655471275012511<30> × 644470026121315871218292386252029137667049740194863<51> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=2567312157 for P30 / May 17, 2010 2010 年 5 月 17 日)
83×10117-119 = 9(2)1161<118> = 11779 × 43313 × 23384491897102248990998949229057800863<38> × 773002605594782328186917069125931682131401476401190944555221740784275521<72> (Dmitry Domanov / Msieve 1.40 snfs / May 20, 2010 2010 年 5 月 20 日)
83×10118-119 = 9(2)1171<119> = 4663 × 41987578649124941032811295746008100537<38> × 471030833847474511810077581998564253659355090206827267591148928620024127853491<78> (Dmitry Domanov / Msieve 1.40 snfs / May 20, 2010 2010 年 5 月 20 日)
83×10119-119 = 9(2)1181<120> = 3 × 3083 × 16963 × 5878115852795245537408275109374154788465827647497378046948175626285960451088961789848260638925995203416388128783<112>
83×10120-119 = 9(2)1191<121> = 192 × 45562547381740483<17> × 25919300106282748540475909<26> × 10826676915904325942901359704175159<35> × 1998029686166008834377902916814443214306157<43> (Makoto Kamada / Msieve 1.45 for P35 x P43 / May 20, 2010 2010 年 5 月 20 日)
83×10121-119 = 9(2)1201<122> = 7 × 13 × 401 × 75421334439743187209<20> × 1380735493511010397695952496281937<34> × 24268621969862918689305627505158430638363466685488795113445317407<65> (Dmitry Domanov / Msieve 1.40 snfs / May 20, 2010 2010 年 5 月 20 日)
83×10122-119 = 9(2)1211<123> = 33 × 4751 × 13581103 × 92460526727<11> × 27672079789247617<17> × 1213165993819556593051<22> × 170542785794914894580425356111202963189697140654911041515722499<63>
83×10123-119 = 9(2)1221<124> = 17 × 542483660130718954248366013071895424836601307189542483660130718954248366013071895424836601307189542483660130718954248366013<123>
83×10124-119 = 9(2)1231<125> = 269281 × 21680993 × 268610701 × 355794847 × 165282829188775247317311567906045645350450674034699907130273486696719775557917912363486363559071<96>
83×10125-119 = 9(2)1241<126> = 3 × 79 × 3891233005157055789967182372245663384903891233005157055789967182372245663384903891233005157055789967182372245663384903891233<124>
83×10126-119 = 9(2)1251<127> = 31 × 877 × 15497 × 222338884604029<15> × 98448984344760761611844900622029062965328234235787596364942340759942751839589964438781873107867589438291<104>
83×10127-119 = 9(2)1261<128> = 7 × 13 × 29 × 127312657170808772910482933411709287<36> × 274488788400492175570086046511471101347891458939859671958743314262679604386972528811781797<90> (Dmitry Domanov / Msieve 1.40 snfs / May 20, 2010 2010 年 5 月 20 日)
83×10128-119 = 9(2)1271<129> = 3 × 23 × 123626313911224003211236213<27> × 53411038761459248618094666347<29> × 2024158643976199669353717620873270857306439510880438705420078393414971119<73> (Dmitry Domanov / Msieve 1.40 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10129-119 = 9(2)1281<130> = 4452893 × 214832161431978915792967151<27> × 718898085190443605295066447442680124547<39> × 13409935801145517595972039889076528814137715974092652458101<59> (Markus Tervooren / Msieve 1.43 for P39 x P59 / May 21, 2010 2010 年 5 月 21 日)
83×10130-119 = 9(2)1291<131> = 443 × 470201 × 227758021 × 8975702211684070309<19> × 216573937396899822722469028207920332066673455733510024668190415792666663368868969001037783546823<96>
83×10131-119 = 9(2)1301<132> = 32 × 43 × 257 × 16819502839104101<17> × 10032866375493522269790692844668065329563714107539901<53> × 54948179970618654281428819006984882236683427199067546771519<59> (Markus Tervooren / Msieve 1.39 snfs / May 20, 2010 2010 年 5 月 20 日)
83×10132-119 = 9(2)1311<133> = 4591 × 12058586809775981501752021<26> × 166583459100855412672365210111723408405110322485260857297487578782504531943872413305572773788648839702711<105>
83×10133-119 = 9(2)1321<134> = 7 × 13 × 61 × 829 × 833871827 × 46185396268696837<17> × 976198338095974315473677<24> × 533049801268043129587624818397760988282722985461035024240881024566296790626213<78>
83×10134-119 = 9(2)1331<135> = 3 × 677 × 10234811 × 193373165892701<15> × 12117890934867506983496849539<29> × 18933137346406100071193840729966930898652015896002623214726951789443446238404470479<83>
83×10135-119 = 9(2)1341<136> = 127 × 389 × 2411 × 1884494137<10> × 7274333964821081<16> × 12261358782229619<17> × 1356140257878777958635693260375983913621<40> × 339667359353866521840198690673534458934884914779<48> (Markus Tervooren / Msieve 1.43 for P40 x P48 / May 21, 2010 2010 年 5 月 21 日)
83×10136-119 = 9(2)1351<137> = 2897 × 1668197 × 10407437119<11> × 504481268953<12> × 138511452478999<15> × 1612588350563845418277148663403057<34> × 16272028975368762907635702674204518786036785139380365226569<59> (Erik Branger / GGNFS, Msieve gnfs for P34 x P59 / May 20, 2010 2010 年 5 月 20 日)
83×10137-119 = 9(2)1361<138> = 3 × 6317 × 1577591537<10> × 66783711259689520645881035774647<32> × 134871654059222582751477608663525767807<39> × 3424661489090666622761976418088424840704485703998433827<55> (JMB / May 20, 2010 2010 年 5 月 20 日)
83×10138-119 = 9(2)1371<139> = 19 × 79 × 149 × 1523 × 965392313 × 20590042799441296427<20> × 12421951957157599776053<23> × 109652310687891885890560986984749979228991673463194868935381259835548685834764241<81>
83×10139-119 = 9(2)1381<140> = 7 × 13 × 17 × 260270489 × 470379036522568150379<21> × 486936559636347328117640471664722403718133284105733085500096904500193612177414228655366733605388126893362653<108>
83×10140-119 = 9(2)1391<141> = 32 × 3912512652939174848118809<25> × 1949871239183678700160847431820540366336191<43> × 13431712427857216974662825001159679657120273969918540213344935242831340051<74> (Dmitry Domanov / Msieve 1.40 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10141-119 = 9(2)1401<142> = 31 × 299242533549944886179853098351567357<36> × 994146907852157799393549442678859982049875520527750086530562852085863998330317597454390409417697401122063<105> (Dmitry Domanov / Msieve 1.40 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10142-119 = 9(2)1411<143> = 601 × 37616441 × 36625027489598381<17> × 227790629935025275486757199802225415915269867243342301<54> × 488955789411613079715175773955463082249735714105585141290623301<63> (Dmitry Domanov / Msieve 1.40 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10143-119 = 9(2)1421<144> = 3 × 8234209 × 1774972984213526699050445740497243921526015815487351017621286321<64> × 21032974479657833353566342381526766342922980267996226877801875089019171263<74> (Dmitry Domanov / Msieve 1.40 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10144-119 = 9(2)1431<145> = 1655827 × 6795857 × 880546556543<12> × 15789942840733401740291<23> × 58944530152557672974430372072992171420566302684912512511159273057367787412348019301594345811986203<98>
83×10145-119 = 9(2)1441<146> = 7 × 13 × 132019 × 222367 × 120911207759741949595489489200200706659<39> × 285509692045144414658322710682161724928440013246135934412192901753143175625353358926996777734833<96> (Sinkiti Sibata / Msieve 1.42 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10146-119 = 9(2)1451<147> = 3 × 617 × 887 × 183274388076503849<18> × 3064811483361775185903744833506144188523624134136227513156964051948617205980391165788800079901958432494990731633308328018617<124>
83×10147-119 = 9(2)1461<148> = 1123 × 28317719 × 319140535316753179<18> × 12692149429094765221<20> × 71594624073817071419295456578487469182284478884973974260038495040891386468406160612292773028516422287<101>
83×10148-119 = 9(2)1471<149> = 107 × 8033198843597855838010803378326411<34> × 107290998777825660273684888828920752986541479278495133763365732874520696909622822965961103272446104319406179546773<114> (Sinkiti Sibata / Msieve 1.42 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10149-119 = 9(2)1481<150> = 34 × 275803402585406470034599888026190963935678863165917<51> × 41281069873973042441498527751929104786858041508297511301800399292832833979495831041838183129015073<98> (Sinkiti Sibata / Msieve 1.42 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10150-119 = 9(2)1491<151> = 23 × 1288062007<10> × 148635392458568202128119<24> × 18502257732617135082468430748023316954713<41> × 113194158723894542918179062955600523343802688477825589763214278870577241559363<78> (Sinkiti Sibata / Msieve 1.40 snfs / May 22, 2010 2010 年 5 月 22 日)
83×10151-119 = 9(2)1501<152> = 72 × 13 × 79 × 462405176021<12> × 439242013298443627<18> × 7836745149126559366003000994788324872651967<43> × 1151348435781149061902944939530595037363337693820247383099557127248860723543<76> (Sinkiti Sibata / Msieve 1.42 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10152-119 = 9(2)1511<153> = 3 × 43 × 4243683341119058480510238773883052394307773873<46> × 1684623686532105271743714621413433179791851851446827496089745447137730401792375495318792090151229571651613<106> (Sinkiti Sibata / Msieve 1.42 snfs / May 22, 2010 2010 年 5 月 22 日)
83×10153-119 = 9(2)1521<154> = 1103 × 3142273 × 957666979263098072427117922652786099<36> × 2778443972989503162227704273476376245415469553707919406980318212509902959519782270014586491033192986952916241<109> (Sinkiti Sibata / Msieve 1.40 snfs / May 22, 2010 2010 年 5 月 22 日)
83×10154-119 = 9(2)1531<155> = 461 × 23046193 × 1538227584293<13> × 4181200053698339391229<22> × 1349627505452212930409991721217269681900882260152152895281205399047356681401534577141751871933313883423449008641<112>
83×10155-119 = 9(2)1541<156> = 3 × 17 × 29 × 307 × 5101 × 42237713742155839<17> × 9426995665930381653227222804017015740539794776196519289151400086698263542738382987733351767187844851353240243882294365680179602163<130>
83×10156-119 = 9(2)1551<157> = 19 × 31 × 983 × 1384387 × 11758610993941422220343<23> × 939329850481905728529895584754198783438925316607<48> × 1041681883418416028638273186277897544380847559166518964050647420831520900709<76> (Sinkiti Sibata / Msieve 1.40 snfs / May 21, 2010 2010 年 5 月 21 日)
83×10157-119 = 9(2)1561<158> = 7 × 13 × 379 × 761 × 5233 × 14401 × 894917 × 120092057 × 68040725520643961<17> × 6376185760459104241932180442298013584803959575228021093681180352907306349189906244003180111970051311244225068217<112>
83×10158-119 = 9(2)1571<159> = 32 × 3907 × 31643 × 118057 × 30241778729<11> × 232152271083195400123178425611204473660499719629681033129249828916160338176265986723258160187598770249237798933526557914994431347455173<135>
83×10159-119 = 9(2)1581<160> = 249832753 × 269093280601846735189979957658467114993416117<45> × 137177649143883094981099842439549833840551785796898257537368476626923047884701947066865292239344939982930121<108> (Dmitry Domanov / Msieve 1.40 snfs / May 22, 2010 2010 年 5 月 22 日)
83×10160-119 = 9(2)1591<161> = 12527 × 73112227 × 16261805383<11> × 240494485322074341433<21> × 25746880146652191018635587357579907738533486599016855948584641368318744048039150705209452065790306210211001276095507791<119>
83×10161-119 = 9(2)1601<162> = 3 × 47 × 191 × 3914634906821991435917<22> × 8747658870163797949806002627422191490082605865026720059104822903109198755239623537815470277349290646780002602016945605903948226479926523<136>
83×10162-119 = 9(2)1611<163> = 439 × 521 × 541 × 16087 × 72857884438063<14> × 63589360278502789732976166157476239408951587110943597356343310350613898477738065343020636661072982320329502710389013737938961399748041879<137>
83×10163-119 = 9(2)1621<164> = 7 × 13 × 4621 × 23777790646396485021890878109<29> × 38054702316457941330045812070347209195247083163862066691<56> × 242369738417860062797699812026161783008719053125639499024228564393145322469<75> (Dmitry Domanov / Msieve 1.40 snfs / May 22, 2010 2010 年 5 月 22 日)
83×10164-119 = 9(2)1631<165> = 3 × 79 × 3559 × 14251 × 43456099 × 1479638363267<13> × 76813589610776093<17> × 939033496648021343<18> × 2939998851422276452963775861015567339<37> × 5626538336120045299233832222109914657829674089664399952264030749<64> (Dmitry Domanov / Msieve 1.40 gnfs for P37 x P64 / May 23, 2010 2010 年 5 月 23 日)
83×10165-119 = 9(2)1641<166> = 4051 × 13009613 × 1667186252356501<16> × 104960246414634233580604052041558800924413589117630602567810431962430233586172488090006837121248362984706992056345265843784892646093877190767<141>
83×10166-119 = 9(2)1651<167> = definitely prime number 素数
83×10167-119 = 9(2)1661<168> = 32 × 1996321 × 6344963 × 980428269007054863016276043586213669622584541<45> × 8251212640821936660752747607587051302804242089816773170327323247505314454334952883486311682567922826749722883<109> (Sinkiti Sibata / Msieve 1.40 snfs / May 23, 2010 2010 年 5 月 23 日)
83×10168-119 = 9(2)1671<169> = 199 × 16195284717891361212371136325028293527707971687<47> × 120515013424696991875482475590345970531498315902855961<54> × 23743938876756372889300921504672054983986978155296643052928592214597<68> (Dmitry Domanov / Msieve 1.40 snfs / May 23, 2010 2010 年 5 月 23 日)
83×10169-119 = 9(2)1681<170> = 7 × 13 × 109 × 9533423 × 13436269697503<14> × 603634193164983337120622227<27> × 1754620243251305581589401930135035280786215463<46> × 68530381380900262030969239033209356295972696830777520370160801679437518311<74> (Sinkiti Sibata / Msieve 1.40 snfs / May 24, 2010 2010 年 5 月 24 日)
83×10170-119 = 9(2)1691<171> = 3 × 59 × 383 × 21341 × 2128553067154855238760220976689<31> × 180647355367793930696474732502061<33> × 270194209182705265590946316234119605793815941543<48> × 6135594504199211489774644405508560273769660543382653<52> (Sinkiti Sibata / Msieve 1.40 snfs / May 24, 2010 2010 年 5 月 24 日)
83×10171-119 = 9(2)1701<172> = 17 × 31 × 11491 × 2245811581327<13> × 32264939964497248366854518828635010796569<41> × 1921776779655273902683325736864136800280658210597210471<55> × 10936038312036140403431029989264865287729644829392843432161<59> (JMB / GMP-ECM 6.2.3 B1=3000000, sigma=1165691650 for P41, Msieve 1.45 for P55 x P59 / May 27, 2010 2010 年 5 月 27 日)
83×10172-119 = 9(2)1711<173> = 23 × 89897111964522584205461<23> × 265319637187868464017908009<27> × 168109637766246622119939478275561398365091995916557837198208400978741605079930781552224001313097139226979975626608504855223<123>
83×10173-119 = 9(2)1721<174> = 3 × 43 × 10243 × 697940981606059742234418530652600885476882470859072009261929093737089668514192125325309871080209984373690046764568445852771620340623789377220534970921508295869459136943<168>
83×10174-119 = 9(2)1731<175> = 19 × 1973 × 40961 × 19130261 × 392451115431541<15> × 27590669915397907<17> × 44654882581987395247416532571266074301941374249<47> × 649301917913703648018564240357893511618811805001137643116507043846458130949375121<81> (ruffenach timothee / Msieve 1.44 snfs / July 25, 2010 2010 年 7 月 25 日)
83×10175-119 = 9(2)1741<176> = 7 × 13 × 2568454838595976526563775644397085974987839609838831319647737<61> × 394568360012511129199465130984570642209047514144295684507864584261620178324277873988435785739446724789262901638063<114> (Sinkiti Sibata / Msieve 1.42 snfs / May 24, 2010 2010 年 5 月 24 日)
83×10176-119 = 9(2)1751<177> = 33 × 478927 × 55601362466267<14> × 4296630500327777<16> × 45572692958102747309<20> × 816255282427837913241950900580008250039467911909183259687<57> × 8025246098938835216680958051713999452711124875779028340843386017<64> (Justin Card / CADO-NFS / June 2, 2010 2010 年 6 月 2 日)
83×10177-119 = 9(2)1761<178> = 79 × 127 × 123743588513<12> × 30050170266617<14> × 82581572518279<14> × 472630864898360529514555169<27> × 868268211166086279650546364901798887516564805252123<51> × 7294171972154829677952047324485154841035200826689709421289<58> (Dmitry Domanov / Msieve 1.40 gnfs for P51 x P58 / May 24, 2010 2010 年 5 月 24 日)
83×10178-119 = 9(2)1771<179> = 5813807 × 113741982830742846121078887948761<33> × 139461450399087760429746681587800477197064052088860859827471775274050417653512198104466938412512924998983778302756566918527179074874033508923<141> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=799662603 for P33 / May 20, 2010 2010 年 5 月 20 日)
83×10179-119 = 9(2)1781<180> = 3 × 95087 × 464816213758895999881997089<27> × 6955236690749668701086379596364089093014298587684567416739327205566992407446128160458042944132149709752673197583096761657160898801972313279612854049<148>
83×10180-119 = 9(2)1791<181> = 603267381950258709041340704167<30> × 15287122258140957169113128501535738992138947978447817613318788482924514616173686978891959723164502372330143145754005494791623740911740956294482299829163<152> (Serge Batalov / GMP-ECM 6.2.3 B1=1000000, sigma=1703715866 for P30 / May 21, 2010 2010 年 5 月 21 日)
83×10181-119 = 9(2)1801<182> = 7 × 13 × 3989863 × 1160803400958395002349027<25> × 21304054718321599357473100141037<32> × 10271060002108553677099357608468152114324935103022614034749628014084297094424956607606137596355292050187182448731183463<119> (Serge Batalov / GMP-ECM 6.2.3 B1=1800000, sigma=1087619979 for P32 / May 21, 2010 2010 年 5 月 21 日)
83×10182-119 = 9(2)1811<183> = 3 × 3927723753673<13> × 105952731365069<15> × 702833360725773735456158711813<30> × 1051014889301704252338663615586869481061677668489792444384278404910680884193562888523746289080486316132967012925529006059016247<127> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3052064960 for P30 / May 20, 2010 2010 年 5 月 20 日)
83×10183-119 = 9(2)1821<184> = 29 × 97 × 752490188852439781<18> × 251024835058566650424322286487330883481777741<45> × 17355947130564768411084921780364136129666123583699351486619318568352701316237248965022960624945190410601240524448219377<119> (Dmitry Domanov / Msieve 1.40 snfs / June 17, 2012 2012 年 6 月 17 日)
83×10184-119 = 9(2)1831<185> = 4690133923<10> × 401954726683<12> × 13495048735981062990170100487<29> × 3948071941904208018865907780204638687019<40> × 918150096094768900182408398873226399747163427235486412475848690023425856410362737712130566052273<96> (Robert Backstrom / Msieve 1.44 gnfs for P40 x P96 / May 25, 2012 2012 年 5 月 25 日)
83×10185-119 = 9(2)1841<186> = 32 × 3533 × 2159018261065045254130808998573732326307850041182854445291442747791271661540790298957<85> × 13433621895733274778827100032877744759682640109893791705312577449131400289623750842893741432083549<98> (Wataru Sakai / May 30, 2010 2010 年 5 月 30 日)
83×10186-119 = 9(2)1851<187> = 31 × 269431 × 13304295469<11> × 876494091607009753417<21> × 100759558736962471335350657797691<33> × 30302750182857625835086476571426400321942611<44> × 31011098429293772642390266251724102240018365584267571060524652894351611857<74> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=718665100 for P33 / May 20, 2010 2010 年 5 月 20 日) (ruffenach timothee / Msieve 1.44 gnfs for P44 x P74 / June 15, 2010 2010 年 6 月 15 日)
83×10187-119 = 9(2)1861<188> = 7 × 13 × 17 × 87059851003659841<17> × 312384014320319101<18> × 2191989896989579227574808917006524244233249863019572616336400366700864615835296754362115576810869159212730024506843726001634547718770578267054274285523<151>
83×10188-119 = 9(2)1871<189> = 3 × 347 × 1259061094162474473555441930320235397<37> × 703619795448236759584255795313521994402420633439045482456589407973195892051757680600247308071578323729727540577741373075192724628629679708644455674073<150> (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=890106221 for P37 / May 22, 2010 2010 年 5 月 22 日)
83×10189-119 = 9(2)1881<190> = 223 × 22543 × 120791034556491736763<21> × [15187430652406402082449794189137647152188230254512371151003424843795568462786032404260793948805985921787124121299135626020308714787604819396412072613961319677750503<164>] Free to factor
83×10190-119 = 9(2)1891<191> = 79 × 53101 × 21983953250355299090227203097374795492950554036676279481309017809677288544763209117905529973385378621018656403815662062246848487733126249791053119031638113616831507910342869945766646799<185>
83×10191-119 = 9(2)1901<192> = 3 × 7109 × 4482035891<10> × 6654806673837446078603310968237074952891902714759<49> × 1449756419854078142051906344993914665825796676665878443332087199878346003207946769399696489236872865550447950239217767583713788967<130> (matsui / Msieve 1.49 snfs / April 2, 2011 2011 年 4 月 2 日)
83×10192-119 = 9(2)1911<193> = 19 × 485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959064327485380116959<192>
83×10193-119 = 9(2)1921<194> = 72 × 132 × 61 × 114547 × 1593819895705771543323312595857376544208450047458275678348646235776453295213450992672751969695524171279259940469033022292841992223260361400723370175753799884807543830834493339183101923<184>
83×10194-119 = 9(2)1931<195> = 32 × 23 × 43 × 478169 × 510089 × 409857172648277588558772500457011<33> × [1036422581670990010657055789211300784426005779405342157716364491527711599399302726887259615697165306940736808577577722632803363289842398858423964371<148>] (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3671820640 for P33 / May 20, 2010 2010 年 5 月 20 日) Free to factor
83×10195-119 = 9(2)1941<196> = 1913 × 24043 × 200508116072099829290047312692269316094911371921922303873233879520098850211332293063406505194968402952686382494437451905078462558168884125782355189638389917798702273303766503167758876650719<189>
83×10196-119 = 9(2)1951<197> = 1051 × 1097 × 2826293 × 5632642789<10> × 1805034379970199432776413<25> × [2783629101815003676414954896217767131638776903810111387520097450428583025970740953266006564758587580712227343128772953956406805225831243263156115268243<151>] Free to factor
83×10197-119 = 9(2)1961<198> = 3 × 216995084743<12> × 3154150469311<13> × 8317279692250253<16> × 54000865179111266001982447116599003979545980482197130953810485725030214019620561754935971523393129490483727484270195862380760809896344496759640835698351816003<158>
83×10198-119 = 9(2)1971<199> = 3881 × 285119 × 1556945355806680407969229<25> × 24573395670680021832351053<26> × 217834787882574212214387246016249505974725509201135437189029813168591525688182107448967484028692779873343188410967868912797122038783367113347<141>
83×10199-119 = 9(2)1981<200> = 7 × 13 × 1213 × 8893 × 23339 × 27457 × 30003791 × 52989319 × 79876830071149769174683494652365779<35> × 1154421691407758468645597535260051149676437175443896582380191349702538416317441405509477989037455547523137082500602431085689861170263<133> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2705369211 for P35 / June 15, 2012 2012 年 6 月 15 日)
83×10200-119 = 9(2)1991<201> = 3 × 3889 × 28073533 × 1324175601421<13> × 16874175618327401179640052404394861619<38> × 148291190057468209484077055454608039827<39> × 849759086391869962392883501775391798603549533741310408749163752308387193059071492658666805144924379007<102> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=4190306390 for P39 / November 7, 2010 2010 年 11 月 7 日) (Ignacio Santos / GMP-ECM 6.3 B1=43000000, sigma=1860985252 for P38 / November 19, 2010 2010 年 11 月 19 日)
83×10201-119 = 9(2)2001<202> = 31 × 107 × 946697 × 665823721 × 202952538504906889<18> × 2646199390622195591<19> × 12655011931494183287<20> × 15015372460755792563393<23> × 207161284863308353704389377<27> × 208639017905223281127480911064000733478516445228225319874333375671719515351851393<81>
83×10202-119 = 9(2)2011<203> = 63464399 × 1453133153001609961235467182510027743620832558773970619689035772988604559577129568692870190454686606615816565476689099698591996785823532689913635237012521338494393088355287540377121072590984785379<196>
83×10203-119 = 9(2)2021<204> = 33 × 17 × 79 × 130022783717<12> × 27193622967916175011<20> × 63898770748854659701<20> × [112568471967508718059305496477144977528597978173194314834091192515393940932238915535946949177040929697802052453393378301640634344330595222951797649003<150>] Free to factor
83×10204-119 = 9(2)2031<205> = 30629952526271009365025396406151916595983427344154699239801<59> × 301085096828420247265261532114866230266228458541618253779671518652871911085251711020575001218498190782254131436594239953854752259778508867095466421<147> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 snfs / July 23, 2012 2012 年 7 月 23 日)
83×10205-119 = 9(2)2041<206> = 7 × 13 × 31063 × 859278163 × 4025273352019<13> × [9432387642407859789125921781640763433228227583719741669270627020093836800856845455639640739446886507511374457290511199103674595596057658063643818709560521304938077076052936384121<178>] Free to factor
83×10206-119 = 9(2)2051<207> = 3 × 2003 × 22471159 × 9695769931<10> × 704410148996775810572565950912518785662003476801452246722509281244702458987101324521365005594819510323696087536608291886986255071549050759044106178423605957332404913790758116200433794361<186>
83×10207-119 = 9(2)2061<208> = 47 × 55385543 × 101660094708848707<18> × [34849038252481208101292953110320795941309975210948910157633502936794623388349990108482028404878937967142100416461771777508674678663633303571327044373986610624734080391688880540181943<182>] Free to factor
83×10208-119 = 9(2)2071<209> = 235889 × 206408516342338129<18> × 7064524001125246727048884351<28> × 268112694038801218052610392896546925199359627752646631001452108296053692526335155187581674679610631161881853678067996481472069711647641634378553358030996653491<159>
83×10209-119 = 9(2)2081<210> = 3 × 207187 × 2669753 × 793287878099<12> × 10777337835103365612726464496748873<35> × 65003752507773248564707470883498159472909071124804003808886485001256279487282000115770187222851874111989635845980761911212211708372652556052129578612631<152> (Serge Batalov / GMP-ECM B1=2000000, sigma=2986922167 for P35 / June 14, 2012 2012 年 6 月 14 日)
83×10210-119 = 9(2)2091<211> = 19 × 39240796058837<14> × 11292795959786776489<20> × 1095324221496388787327762276219863048435310579116122186087127122911803348264163111443826480685007663447783489344302560328058207851798034071653830112074505734625375702836298811563<178>
83×10211-119 = 9(2)2101<212> = 7 × 13 × 29 × 790688911429879878677872409<27> × [44196771334084422748229908474427047099543965645266021763557339165703895104076061272451792130431706530160339703962445698811610240848576574344072906963834168218483979357128523102865371<182>] Free to factor
83×10212-119 = 9(2)2111<213> = 32 × 283 × 2333 × 1267663 × 434982002121398281558271865060150977<36> × 281460073519021525569115815996918295223972041654425660653032659755779729988118116013793685552272347787725223797154860962732717589982124383957815570226555213152162821<165> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=789096099 for P36 / June 15, 2012 2012 年 6 月 15 日)
83×10213-119 = 9(2)2121<214> = 953 × 6283573 × 57906286411<11> × 382873524883<12> × 1535511637027<13> × 2603920604357<13> × 17372971871245828071480233035949785613649557349534499137531128865316770201185620658365496645535930912383712399440811759543700280812587510382751130058080581087<158>
83×10214-119 = 9(2)2131<215> = 233 × 521 × 3923 × 490033 × 6344701404757<13> × [62285522922734625452504985160612238766940360019529440997753676322312434903781702064544455337581884988128229222584078467039794369805069936590130458889794946669866472427646938046949511254019<188>] Free to factor
83×10215-119 = 9(2)2141<216> = 3 × 43 × 10627 × 845717 × 49139276330113<14> × 798608213737227403<18> × 83479057154686389829<20> × 32918772878912308358484391829780561486797<41> × 7376093778460540079450427378549599328617679976760228902562235066123570399874861887701733926772275820971698450873<112> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=878810205 for P41 / June 22, 2012 2012 年 6 月 22 日)
83×10216-119 = 9(2)2151<217> = 23 × 31 × 79 × 19840039931<11> × 134128933676250403770723173762628365973031<42> × 61525329454173778728392436896727350989161783281120055811208344575297304267382168554762424084146423651717217495716272906424672537093408868524600152193988316159143<161> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1266995732 for P42 / June 15, 2012 2012 年 6 月 15 日)
83×10217-119 = 9(2)2161<218> = 7 × 13 × 918353 × 5515789 × 13939411 × 16263281 × 147282191557<12> × 5992031256127587274510996346666802007113887229571482913739408759656722595831384744093783941871692197489653113210399365805640689887881607723530523110545374861643575902550076470989<178>
83×10218-119 = 9(2)2171<219> = 3 × 457 × 1619 × 75767 × 1151222327<10> × 2157975391244407422539<22> × 560513425147407340397091360929<30> × 3938034141626044509920162382305684688489840886731003163339947758678957610801112338258736516111683508130661835116194659563818759943217916174688829751<148> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3059709574 for P30 / June 15, 2012 2012 年 6 月 15 日)
83×10219-119 = 9(2)2181<220> = 17 × 127 × 647 × 3617798303293660747<19> × [1824879990262696323773984358909455018760248664759644539847115127109348246680791068580836940534332343699882320764312426939767699639738700732394601469632230860204999578239636293399637391750979957391<196>] Free to factor
83×10220-119 = 9(2)2191<221> = 17747 × 70393 × 791388907 × 1230012247<10> × [75837108378384579596642229175421812534107707197141864340696333148582677746158793303445693197844105656056344195290141583967757877486471478808314119905582183399159056312800362323102744996885396419<194>] Free to factor
83×10221-119 = 9(2)2201<222> = 32 × 144813653 × 5414538347<10> × 8332682713<10> × 82138556602653082379<20> × [190937054449474851571394944193279358109883286411948836545612971087131275141077428115567674143425409728337505470433556633089637282810182590698233366629442487540462781210256417<174>] Free to factor
83×10222-119 = 9(2)2211<223> = 113 × 21147353 × 154712606228578879415375455107200750987508734961257<51> × 48493402999376744061931856556827883102472528321696954996705579<62> × 514390288852328223009141377215076362476038426539509971461111745680983666772934732925969912122909123863<102> (Bob Backstrom / Msieve 1.53 snfs for P51 x P62 x P102 / May 26, 2018 2018 年 5 月 26 日)
83×10223-119 = 9(2)2221<224> = 7 × 13 × 1669 × 19133113 × 31798325172435705577191983045713531<35> × 4303488047164297647468735204428976595974647<43> × 231914215569040908497714033727398799930695952527512913793315233148600573909534685305315876786682345829602035600131739861231233902140239<135> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1005354088 for P35, B1=11000000, sigma=273100570 for P43 / June 17, 2012 2012 年 6 月 17 日)
83×10224-119 = 9(2)2231<225> = 3 × 263 × 12953 × 28087 × 42683 × 414760517807<12> × 4944374729719189<16> × 147138126024953919769<21> × [249455978551840166462439142616473470640181300419219251140398581940655238068513503819530754418167380917562699941216308577416039286797687668936231899606515396783319<162>] Free to factor
83×10225-119 = 9(2)2241<226> = 131 × 2920289 × 129323283572419<15> × 102084947446600406884259<24> × 1086274510853316523199440883<28> × [1680971820674878509605232779943528925894082169784307705328411487111475846019905705371790662552166690293106002908144425059141289678746150239394059133325933<154>] Free to factor
83×10226-119 = 9(2)2251<227> = 4469781354115755916092263<25> × 146746691454729170293096946813<30> × 1696485806913304504046881680328723696417<40> × 82876376437584981344606793642000001911233995058492223093812489491332844907562821811988991737842471212111173988146482023009061207138727<134> (Serge Batalov / GMP-ECM B1=3000000, sigma=362468945 for P30 / June 15, 2012 2012 年 6 月 15 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2471136528 for P40 / June 18, 2012 2012 年 6 月 18 日)
83×10227-119 = 9(2)2261<228> = 3 × 406262579803<12> × 151838719710409<15> × 4467876698449514237<19> × 9353565815663777897069867971379<31> × [119246759861055617758131582048985940540957974177624603399327901712233893145273604084653637453723316413935249358009249020069734489934557983324712251031267<153>] (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=1961837189 for P31 / June 11, 2012 2012 年 6 月 11 日) Free to factor
83×10228-119 = 9(2)2271<229> = 19 × 59 × 145368589 × 638712749 × 2412708599577973<16> × 139131571217488357<18> × 708757509519818933502289280465599<33> × 372413636616617153524712394166206890446860841600706759199765101830095555279504006849110404969241703253991408948235123210729086140023167457382019<144> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=1733387289 for P33 / June 11, 2012 2012 年 6 月 11 日)
83×10229-119 = 9(2)2281<230> = 7 × 13 × 79 × 4817 × 2663118263720560964236449004267621349002428144601302431035207620245316379524603036794825896188948458994156852217570717188368807239736411998153772407930282336065650960419751331685068476968472501171828186120920450549428089417<223>
83×10230-119 = 9(2)2291<231> = 35 × 4261 × 990497 × 413389237 × 4477988297<10> × 35564851464893804504333916294070087<35> × [13658452354703849454428555352759208607220232683523160198684916508548751643889091910103386717285790748524378411153549733113138729245420897324796594397601476476293399737<167>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=68114172 for P35 / June 15, 2012 2012 年 6 月 15 日) Free to factor
83×10231-119 = 9(2)2301<232> = 31 × 164555728446881<15> × [1807843714918463915911583176957615777054143185047672596053504257804100203011732221301592227224166899449166359607345388643094674997954078145066594284568403298347742042310151171504164423970017771579194005682650723917811<217>] Free to factor
83×10232-119 = 9(2)2311<233> = 20063 × 20369 × 3782186926633<13> × 838887603221237<15> × 4657059727236210976276755434363<31> × 15272545513537118664252808087261689902052609103963799439494812640791170669755666528671386427258677859299194017949733899356486637490896875715031521646060692932009924141<167> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=1311639433 for P31 / June 11, 2012 2012 年 6 月 11 日)
83×10233-119 = 9(2)2321<234> = 3 × 179 × 80577013262519790707<20> × 323612115749468541206177323697<30> × [65860550880257464594641930412438148346653456075557139574133774684466148071109227554376208324842776532115860195191142214526104973748766968018429979982020570683014729976836150940363527<182>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2934534417 for P30 / June 15, 2012 2012 年 6 月 15 日) Free to factor
83×10234-119 = 9(2)2331<235> = 617 × 63611 × 355491544621<12> × [660980915746859634051900742587232165093386351279839355590286661736887356050353958805950828729242619089147246577220099694727686071761491678683905031861377919541002317997679709591327327106521816590054497812631339653723<216>] Free to factor
83×10235-119 = 9(2)2341<236> = 72 × 13 × 17 × 2378479183<10> × 219997752421582657317843731968966701167598347<45> × [16275323533352642361447713178824618501286051568795985234489780198886197094675476693265021024540509121710991331020007805829233955218681611218149899193935364162152448597543232075949<179>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=578848312 for P45 / June 18, 2012 2012 年 6 月 18 日) Free to factor
83×10236-119 = 9(2)2351<237> = 3 × 43 × 24523171 × [291520597992440290030483782438844914058614489496871126122716336608712204249233100389307280427746920246965906203951951844642754688984123406833069822297818233807971650147003787131549621781771498841217336488414965060962527015403919<228>] Free to factor
83×10237-119 = 9(2)2361<238> = 1179063628337327539915078591222953890301260027519284628960080842009873310091438297668594171890357435736483<106> × 7821649316099304269560579640018398710349328715787996309040848207725532575674945993974591479951354962570980590119047288584704872585487<133> (NFS@Home + Tom Womack / ggnfs-lasieve4I14e on the NFS@Home grid + msieve for P106 x P133 / January 4, 2014 2014 年 1 月 4 日)
83×10238-119 = 9(2)2371<239> = 23 × 7451 × 1197199 × 43121719 × 10423912877632819097569357731695962614431363202339027121101922045554602817594580989998829392886270977466679644137503455106085009488862039073278023767770231272725275870100723266483904795089883258109540239661734854822418217<221>
83×10239-119 = 9(2)2381<240> = 32 × 29 × 583377139 × 286835761368260771<18> × 354124179272479650863<21> × 13311471894483883790431<23> × 4559475489842582565730949257203803368501<40> × 982462148298228449332359598426490174279238677828855433468711226387169211614793907161715939585603135161414847849716632439202382173<129> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=689699694 for P40 / June 20, 2012 2012 年 6 月 20 日)
83×10240-119 = 9(2)2391<241> = 144870900863839<15> × 20694927206857291<17> × 330293079421325032979<21> × 3954818703949660779765187066864937927078677<43> × [2354856598974778289718437963588187018494080100111834309129242002329541379550888218726421251022318726827883609021371647731751593104245007341018448663<148>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3931028894 for P43 / June 18, 2012 2012 年 6 月 18 日) Free to factor
83×10241-119 = 9(2)2401<242> = 7 × 13 × 421 × 551849 × 36151395029756564573<20> × 1551139927994791943521750637952888357807301<43> × 77788571626269689889403452329173392705298382987040493653445443954039725871079568238192944007481276945226812127673807175884010942923618760177257608779921886676130212711043<170> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2204897881 for P43 / June 17, 2012 2012 年 6 月 17 日)
83×10242-119 = 9(2)2411<243> = 3 × 79 × 337 × 63799 × 2199959 × 1699655476919<13> × [48402520700908177296291244208028024721826977953688025488870659617257621939021979678333655312321089245361007081225834979656897687975821482798442307938736518689405376061705015352050114964731666111661695485030234690471<215>] Free to factor
83×10243-119 = 9(2)2421<244> = 6485447 × 136313698142165914830797431<27> × 10431725923392777254298194956804088888706940446182355903009650073552012570473328494641314319323675425687643614836559050282787668453736319188341796981609052746587950279759589535546849463410402834679676336344714253<212>
83×10244-119 = 9(2)2431<245> = 3809718615374558075459843390788832293753<40> × [24207095466328885061733456883197511017607353917281694917971769210518751423816099717555742514038278637962615088044019950341480229815246045129608037403079515846354099622801273887338141571791177137273481951157<206>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1690068205 for P40 / June 15, 2012 2012 年 6 月 15 日) Free to factor
83×10245-119 = 9(2)2441<246> = 3 × 34431992542684391107<20> × 74585163868556676761401<23> × [119701536307353705212280401753768147524190695825794810487168393612511428742622347340902757581682001090450543739849173938345260649710642357064087588247653200804459100369760360489565123285725213346001799501<204>] Free to factor
83×10246-119 = 9(2)2451<247> = 19 × 31 × 6047 × [2589287767109600214904645422465228438977366099740550246111802263767500426686547405319963124798647780339300892926805171100915556556330875662495012111471521250549872692831513142023650679249731720150901195368094864765399453635324149347997062687<241>] Free to factor
83×10247-119 = 9(2)2461<248> = 7 × 13 × 1981876229<10> × 5738388122669<13> × 3031902252557733805718101<25> × 185150265471221929614807583<27> × [158740669716852120049341579660827065613306054222436888692394648927273465345436369603752335642809851383393479200514015275926700703503501960836091704451712336439091639166288357<174>] Free to factor
83×10248-119 = 9(2)2471<249> = 32 × 28789 × 189723026611904657967805620363814689179069240019181<51> × 18760588151165204402482637895410705678233676284225076444917168694732227961123966508150179174840409672739945316579936654756776843893658989873710181901166691315332349649444742737357708257691318741<194> (axels / GMP-ECM B1=110000000, sigma=1579273215 for P51 / March 31, 2013 2013 年 3 月 31 日)
83×10249-119 = 9(2)2481<250> = 1597 × 4079 × 329209693283<12> × 521033339696208659<18> × 81783408240541403987792811893<29> × 456044503322327244285304313803<30> × 221292350993919732358544741070818795913297475507836724570676622204736281741263868135390246682902374108632214585044592309590224741260103755775036209795378609<156> (Makoto Kamada / GMP-ECM 6.4 B1=1e6, sigma=3378469723 for P30 / June 13, 2012 2012 年 6 月 13 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2951692731 for P29 / June 15, 2012 2012 年 6 月 15 日)
83×10250-119 = 9(2)2491<251> = 5269541929<10> × 95918699637948670033259<23> × 1234753890041553487341445477<28> × 218188824438431508152528677007117429333<39> × 34145228422983915228555502728931857657282071<44> × 463594707000853987827262023411430576605438610069<48> × 42783670348708567588829617796669262735875264279721322639567229<62> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2523775286 for P44, B1=43000000, sigma=717151756 for P39, Msieve 1.48 gnfs for P48 x P62 / June 16, 2012 2012 年 6 月 16 日)
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