Table of contents 目次

  1. About 922...223 922...223 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...223 922...223 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...223 922...223 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...223 922...223 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

92w3 = { 93, 923, 9223, 92223, 922223, 9222223, 92222223, 922222223, 9222222223, 92222222223, … }

1.3. General term 一般項

83×10n+79 (1≤n)

2. Prime numbers of the form 922...223 922...223 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. 83×105+79 = 922223 is prime. は素数です。
  2. 83×1029+79 = 9(2)283<30> is prime. は素数です。
  3. 83×1060+79 = 9(2)593<61> is prime. は素数です。
  4. 83×10147+79 = 9(2)1463<148> 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)
  5. 83×10186+79 = 9(2)1853<187> 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)
  6. 83×10456+79 = 9(2)4553<457> 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)
  7. 83×10678+79 = 9(2)6773<679> 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)
  8. 83×101373+79 = 9(2)13723<1374> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 6, 2006 2006 年 9 月 6 日)
  9. 83×103378+79 = 9(2)33773<3379> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / February 26, 2013 2013 年 2 月 26 日)
  10. 83×1015726+79 = 9(2)157253<15727> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / September 8, 2010 2010 年 9 月 8 日)
  11. 83×1068231+79 = 9(2)682303<68232> is PRP. はおそらく素数です。 (Bob Price / srsieve and LLR / November 15, 2015 2015 年 11 月 15 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+1+79 = 3×(83×101+79×3+83×10×103-19×3×k-1Σm=0103m)
  2. 83×106k+2+79 = 13×(83×102+79×13+83×102×106-19×13×k-1Σm=0106m)
  3. 83×1013k+6+79 = 79×(83×106+79×79+83×106×1013-19×79×k-1Σm=01013m)
  4. 83×1015k+1+79 = 31×(83×101+79×31+83×10×1015-19×31×k-1Σm=01015m)
  5. 83×1016k+15+79 = 17×(83×1015+79×17+83×1015×1016-19×17×k-1Σm=01016m)
  6. 83×1018k+9+79 = 19×(83×109+79×19+83×109×1018-19×19×k-1Σm=01018m)
  7. 83×1021k+16+79 = 43×(83×1016+79×43+83×1016×1021-19×43×k-1Σm=01021m)
  8. 83×1022k+3+79 = 23×(83×103+79×23+83×103×1022-19×23×k-1Σm=01022m)
  9. 83×1028k+26+79 = 29×(83×1026+79×29+83×1026×1028-19×29×k-1Σm=01028m)
  10. 83×1033k+28+79 = 67×(83×1028+79×67+83×1028×1033-19×67×k-1Σm=01033m)

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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 15.42%. 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 15.42% です。

3. Factor table of 922...223 922...223 の素因数分解表

3.1. Last updated 最終更新日

July 10, 2018 2018 年 7 月 10 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=191, 194, 196, 197, 206, 207, 208, 210, 211, 212, 213, 214, 216, 218, 220, 225, 228, 230, 231, 233, 234, 235, 236, 237, 240, 242, 243, 244, 248, 249 (30/250)

3.4. Factor table 素因数分解表

83×101+79 = 93 = 3 × 31
83×102+79 = 923 = 13 × 71
83×103+79 = 9223 = 23 × 401
83×104+79 = 92223 = 32 × 10247
83×105+79 = 922223 = definitely prime number 素数
83×106+79 = 9222223 = 79 × 107 × 1091
83×107+79 = 92222223 = 3 × 5087 × 6043
83×108+79 = 922222223 = 13 × 491 × 144481
83×109+79 = 9222222223<10> = 19 × 2713 × 178909
83×1010+79 = 92222222223<11> = 3 × 97 × 316914853
83×1011+79 = 922222222223<12> = 47 × 19621749409<11>
83×1012+79 = 9222222222223<13> = 89 × 63803 × 1624069
83×1013+79 = 92222222222223<14> = 32 × 10246913580247<14>
83×1014+79 = 922222222222223<15> = 132 × 5456936226167<13>
83×1015+79 = 9222222222222223<16> = 17 × 28493 × 98999 × 192317
83×1016+79 = 92222222222222223<17> = 3 × 31 × 43 × 167 × 373 × 2441 × 151667
83×1017+79 = 922222222222222223<18> = 523 × 1763331208837901<16>
83×1018+79 = 9222222222222222223<19> = 94789 × 189169 × 514313203
83×1019+79 = 92222222222222222223<20> = 3 × 79 × 139 × 157 × 6709 × 2657755297<10>
83×1020+79 = 922222222222222222223<21> = 13 × 1409203 × 50340632925257<14>
83×1021+79 = 9222222222222222222223<22> = 61 × 264101 × 572447551717343<15>
83×1022+79 = 92222222222222222222223<23> = 34 × 107687 × 10572733508787209<17>
83×1023+79 = 922222222222222222222223<24> = 1949 × 473177127871843110427<21>
83×1024+79 = 9222222222222222222222223<25> = 59 × 9483073777<10> × 16482931051661<14>
83×1025+79 = 92222222222222222222222223<26> = 3 × 23 × 389 × 12607477 × 272526479687339<15>
83×1026+79 = 922222222222222222222222223<27> = 13 × 29 × 953 × 2566854974858737929983<22>
83×1027+79 = 9222222222222222222222222223<28> = 192 × 857 × 2079163 × 14337024291901373<17>
83×1028+79 = 92222222222222222222222222223<29> = 3 × 67 × 2028319 × 226205555428512519817<21>
83×1029+79 = 922222222222222222222222222223<30> = definitely prime number 素数
83×1030+79 = 9222222222222222222222222222223<31> = 90619 × 51527041 × 1975063732643011837<19>
83×1031+79 = 92222222222222222222222222222223<32> = 32 × 17 × 31 × 541 × 2777 × 12942235957264002061973<23>
83×1032+79 = 922222222222222222222222222222223<33> = 13 × 79 × 181 × 4961198051623955533319824529<28>
83×1033+79 = 9222222222222222222222222222222223<34> = 3313 × 134005733 × 20772595698088229719187<23>
83×1034+79 = 92222222222222222222222222222222223<35> = 3 × 601 × 143134391383<12> × 357351706616116973627<21>
83×1035+79 = 922222222222222222222222222222222223<36> = 229 × 3843137 × 1047886472972359044916812451<28>
83×1036+79 = 9222222222222222222222222222222222223<37> = 192263 × 6214282914186449<16> × 7718783273905129<16>
83×1037+79 = 92222222222222222222222222222222222223<38> = 3 × 43 × 71 × 499 × 78427 × 30398089 × 8463989062086432401<19>
83×1038+79 = 922222222222222222222222222222222222223<39> = 13 × 17311803253<11> × 5827184902247<13> × 703219854525481<15>
83×1039+79 = 9222222222222222222222222222222222222223<40> = 3637 × 16250049731<11> × 156040591339497350621184209<27>
83×1040+79 = 92222222222222222222222222222222222222223<41> = 32 × 199 × 1867 × 19301089 × 1428939579840724474948442131<28>
83×1041+79 = 922222222222222222222222222222222222222223<42> = 769 × 5081 × 10139 × 19087 × 8051033929<10> × 151487080140044531<18>
83×1042+79 = 9222222222222222222222222222222222222222223<43> = 617 × 17053 × 45161 × 19408236555086524636956183739243<32>
83×1043+79 = 92222222222222222222222222222222222222222223<44> = 3 × 30269 × 84131 × 91121 × 132477378797685132011513529139<30>
83×1044+79 = 922222222222222222222222222222222222222222223<45> = 13 × 13063083487<11> × 23071972701761<14> × 235375794504325964053<21>
83×1045+79 = 9222222222222222222222222222222222222222222223<46> = 19 × 79 × 25976400094573<14> × 236524387175938801940069336551<30>
83×1046+79 = 92222222222222222222222222222222222222222222223<47> = 3 × 31 × 96329 × 42256777 × 243612300500136239452118384833067<33>
83×1047+79 = 922222222222222222222222222222222222222222222223<48> = 17 × 23 × 2358624609263995453253765274225632281898266553<46>
83×1048+79 = 9222222222222222222222222222222222222222222222223<49> = 4734407 × 1947914960040871480255546728919212526980089<43>
83×1049+79 = 92222222222222222222222222222222222222222222222223<50> = 33 × 5016607 × 15714590316769<14> × 43327005635129917441827744803<29>
83×1050+79 = 922222222222222222222222222222222222222222222222223<51> = 13 × 16333 × 4343364411937239954138258185279553062569042487<46>
83×1051+79 = 9(2)503<52> = 543857 × 27698131 × 82876231 × 7387039189181871977511791819699<31>
83×1052+79 = 9(2)513<53> = 3 × 1979 × 511477 × 518340563567237<15> × 58590503239136726626126108871<29>
83×1053+79 = 9(2)523<54> = 7927 × 44623 × 2607161655889020043883625627896366363273683463<46>
83×1054+79 = 9(2)533<55> = 29 × 163 × 1701199 × 1146818953372280129317792812190417566386153351<46>
83×1055+79 = 9(2)543<56> = 3 × 2897 × 67777 × 535644173 × 6670554431999<13> × 43817255702965491513444407<26>
83×1056+79 = 9(2)553<57> = 13 × 89 × 10447586533<11> × 427031031556369<15> × 178659786852714167294230174807<30>
83×1057+79 = 9(2)563<58> = 47 × 351079 × 12049838497<11> × 1996683042751<13> × 15832540495501<14> × 1467208752508493<16>
83×1058+79 = 9(2)573<59> = 32 × 43 × 79 × 347 × 29888251 × 290848983355950103596181988952695993015462083<45>
83×1059+79 = 9(2)583<60> = 107 × 463 × 2304545989253<13> × 8077657503933905952968512090824709780670951<43>
83×1060+79 = 9(2)593<61> = definitely prime number 素数
83×1061+79 = 9(2)603<62> = 3 × 31 × 67 × 5625068341020967<16> × 2631176783625320254692759188641829294158799<43>
83×1062+79 = 9(2)613<63> = 13 × 2314498198619506874512330043<28> × 30650346145217798103377589939882097<35>
83×1063+79 = 9(2)623<64> = 17 × 19 × 13791797 × 3792329174492758015595663<25> × 545891305538581777520515432991<30>
83×1064+79 = 9(2)633<65> = 3 × 13291 × 21997 × 920231564180924088208279891<27> × 114260492007239025572212247113<30>
83×1065+79 = 9(2)643<66> = 139 × 8753 × 4659030982091<13> × 50254386167263<14> × 288529120206563<15> × 11220304202940769411<20>
83×1066+79 = 9(2)653<67> = 10799 × 379909 × 10149467 × 703093069222939<15> × 315004245434216270353447732220376181<36>
83×1067+79 = 9(2)663<68> = 32 × 169086217 × 60601708182086264194123602518393995296771667558491261178591<59>
83×1068+79 = 9(2)673<69> = 13 × 70940170940170940170940170940170940170940170940170940170940170940171<68>
83×1069+79 = 9(2)683<70> = 23 × 349 × 12821 × 89610813467714529742267866990773216113406643248856323369184169<62>
83×1070+79 = 9(2)693<71> = 3 × 680244497 × 823175440625913943<18> × 937617929427446353<18> × 58550550511025512331031907<26>
83×1071+79 = 9(2)703<72> = 79 × 5507 × 724117 × 5169136152949<13> × 566326260421844607458697825612801150833988661027<48>
83×1072+79 = 9(2)713<73> = 71 × 399728261 × 324946886440225465936700088075133700138616264465619205913285733<63>
83×1073+79 = 9(2)723<74> = 3 × 151002451 × 119945849980550081<18> × 492702962079642833<18> × 3444767634223708525014483479767<31>
83×1074+79 = 9(2)733<75> = 13 × 257 × 222195239511149<15> × 3952918293653024935163<22> × 314272600825389298101718946912477269<36>
83×1075+79 = 9(2)743<76> = 659 × 1277 × 18919 × 579243399747397953773474244079395766893783451412806281116122466719<66>
83×1076+79 = 9(2)753<77> = 33 × 31 × 4721 × 3058202825671042591869847600417<31> × 7631498782417098646863799841898501430547<40> (Makoto Kamada / msieve 0.83 / 3.5 minutes)
83×1077+79 = 9(2)763<78> = 149 × 32029 × 193243962889801885125125116735069208928364672498396948198208423578846063<72>
83×1078+79 = 9(2)773<79> = 5629399 × 606838292486773<15> × 2699607174359222364878436099747063240556686126375164778949<58>
83×1079+79 = 9(2)783<80> = 3 × 17 × 43 × 593 × 87957817733<11> × 55168468445591<14> × 14614261852233187758204872233879539643732307122709<50>
83×1080+79 = 9(2)793<81> = 13 × 4116181 × 6036421 × 438868109 × 10074262780404547<17> × 2501616870951278021<19> × 258136935664601834908337<24>
83×1081+79 = 9(2)803<82> = 19 × 61 × 57913799 × 315554011 × 1154575102727710799934583<25> × 377115340727847051755607255239329131131<39>
83×1082+79 = 9(2)813<83> = 3 × 29 × 59 × 723209 × 4635731231387<13> × 5358981378074302509586657380699505964288294283423416960558857<61>
83×1083+79 = 9(2)823<84> = 232741 × 84939523 × 184109801 × 1377453904121<13> × 2019442655261<13> × 113352040442963011<18> × 803596467060819447271<21>
83×1084+79 = 9(2)833<85> = 79 × 761 × 1559 × 1462937153939<13> × 67259254600047812638610967382701785824592037052397355892516000517<65>
83×1085+79 = 9(2)843<86> = 32 × 197 × 277787 × 633221162483039111<18> × 303124593753433605598747106171<30> × 975524846154370595247191303333<30>
83×1086+79 = 9(2)853<87> = 13 × 42487 × 154627003 × 515773429 × 129634471409218581938002781702861<33> × 161499565940406809104675845606919<33> (Makoto Kamada / msieve 0.81 / 57 seconds)
83×1087+79 = 9(2)863<88> = 513751452669439<15> × 1179533512163078878771993903<28> × 15218513565369138631195836680119151612879757919<47>
83×1088+79 = 9(2)873<89> = 3 × 71665676200178343086637937643<29> × 428946496714479352090647691608866335902033452141014033060687<60>
83×1089+79 = 9(2)883<90> = 1232870671<10> × 1379647507478561973277<22> × 542188024682740120422463290958736800453024044715067853561269<60>
83×1090+79 = 9(2)893<91> = 193 × 2729 × 17509540062355058453384435875317729590679692920639802813044733921442921114459019554359<86>
83×1091+79 = 9(2)903<92> = 3 × 23 × 31 × 4351759 × 6602971978649<13> × 834876063182279<15> × 35472446592582661679<20> × 50664919263234918970374648445972147<35>
83×1092+79 = 9(2)913<93> = 132 × 1033 × 5419 × 1061203754256888527<19> × 618617048800089891201395835232757<33> × 1484939443440588597225717170103239<34> (Makoto Kamada / msieve 0.81 / 1.4 minutes)
83×1093+79 = 9(2)923<94> = 11602898129<11> × 16354201479836729<17> × 94366547650344087523085237<26> × 515017152017148957595490903283498954377819<42>
83×1094+79 = 9(2)933<95> = 32 × 67 × 18797929 × 10045340399<11> × 7620109712591<13> × 2316281700667289<16> × 45887141816256565050536831858524512222046219229<47>
83×1095+79 = 9(2)943<96> = 17 × 313 × 1297 × 80673158470941646604776650807739<32> × 1656430762362857288177974586618724179858920980275892208261<58> (Makoto Kamada / GGNFS-0.71.4 / 0.35 hours)
83×1096+79 = 9(2)953<97> = 109 × 96604289 × 875815599896808447240709702660694687712027481305932362483790974552949621414445395519723<87>
83×1097+79 = 9(2)963<98> = 3 × 79 × 157 × 3593 × 20812596009883<14> × 81887713649535541404467<23> × 7196541593772455208592103<25> × 56242099924024163512634777113<29>
83×1098+79 = 9(2)973<99> = 13 × 1435657 × 75279267915437<14> × 656396340047594067059716483068597793032970426416740301466086451399497619893919<78>
83×1099+79 = 9(2)983<100> = 19 × 227 × 38447 × 356917640507<12> × 1111338677027384572919<22> × 140210076023107239849806387913378480967168502754242536267021<60>
83×10100+79 = 9(2)993<101> = 3 × 43 × 89 × 131 × 61317518437180460928957449262154480400889502950591599544300023219392825067251650567863015777293<95>
83×10101+79 = 9(2)1003<102> = 971 × 50512544611011983<17> × 18802565317157183787970237809703815831522199858153254837233439224926723001239152611<83>
83×10102+79 = 9(2)1013<103> = 39209 × 49879178520859<14> × 1051579162260052501<19> × 4484236949693050886453148790725073982680938814164328067475057831233<67>
83×10103+79 = 9(2)1023<104> = 35 × 472 × 233 × 438341 × 511343101 × 32577430957987561<17> × 1498903415635577157887<22> × 67369402439206347354554923929139261130408299<44>
83×10104+79 = 9(2)1033<105> = 13 × 113 × 228082487 × 16757273941<11> × 1252955488619<13> × 1046696944675481027602439<25> × 125245427233238328394624639233022296479516738861<48>
83×10105+79 = 9(2)1043<106> = 27211 × 338915226276954989607960832833127125876381692044475477645886671648312161339980971747536739635523215693<102>
83×10106+79 = 9(2)1053<107> = 3 × 31 × 97 × 390503 × 26179209312367202840153955505364245569455699127029603402294729830125731531689901000221691631911821<98>
83×10107+79 = 9(2)1063<108> = 71 × 20753 × 133010217521<12> × 27950642773391131<17> × 36719064611099008346378689<26> × 4584879599098922258589015505501161867269901510139<49>
83×10108+79 = 9(2)1073<109> = 1408343263<10> × 742841755447890911116511<24> × 858877764030478469167781028353598541<36> × 10263592376617725009630393607683991032971<41> (Lionel Debroux / msieve 1.44 SVN for P36*P41 / October 22, 2009 2009 年 10 月 22 日)
83×10109+79 = 9(2)1083<110> = 3 × 574486331 × 4265068463<10> × 122131823103151407395995642759<30> × 102725859000750192289212057276781301309924046275782905665184583<63> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=1162449980 for P30 / October 22, 2009 2009 年 10 月 22 日)
83×10110+79 = 9(2)1093<111> = 13 × 29 × 79 × 571 × 62260951271<11> × 393854541172230339186777355842066105426479<42> × 2211461708879282181705305020872043074904345739338579<52> (Erik Branger / GGNFS, Msieve snfs / 0.61 hours / October 24, 2009 2009 年 10 月 24 日)
83×10111+79 = 9(2)1103<112> = 17 × 139 × 157557018736267429<18> × 2063787493415599751<19> × 12002428581008194681619707130452545473579863130057755407970960374326657599<74>
83×10112+79 = 9(2)1113<113> = 32 × 107 × 937 × 355260536248363<15> × 287688656380346852292940762629236917226065691238914114882485579561746079554384079106161883191<93>
83×10113+79 = 9(2)1123<114> = 23 × 2207 × 300402573552794249941004323<27> × 60478604949075109527532347345501397705673180933801208728782651465553975731618070141<83>
83×10114+79 = 9(2)1133<115> = 14783 × 43197357823673<14> × 4807877726238647<16> × 16815226936861589<17> × 178632170432343876002417026278464989396208314355516164923131111059<66>
83×10115+79 = 9(2)1143<116> = 3 × 1331261 × 448998983579618286682910369713303867<36> × 51428725407187141859088119824597898798122680510169179933669682357162579243<74> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs / 2.08 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 24, 2009 2009 年 10 月 24 日)
83×10116+79 = 9(2)1153<117> = 13 × 28771 × 4193324461626729101<19> × 588002003760109972363982611060259373760608391312018827444282076395997996716164926056539934301<93>
83×10117+79 = 9(2)1163<118> = 19 × 16547 × 36779934795762142506535701356535567163<38> × 797538689045240465818445964027040354448230908021748469854654299849630902597<75> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs / 3.04 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / October 24, 2009 2009 年 10 月 24 日)
83×10118+79 = 9(2)1173<119> = 3 × 1092919 × 705070381600235455186991830596638083559201<42> × 39892741314093663141511170138983554044263787963680068665654734350406339<71> (Serge Batalov / Msieve 1.44 snfs / 1.05 hours / October 25, 2009 2009 年 10 月 25 日)
83×10119+79 = 9(2)1183<120> = 95625825247499506271903<23> × 57021249694926733050118769<26> × 64232491469851844845343551<26> × 2633109304439454422327978236848684879752900639<46>
83×10120+79 = 9(2)1193<121> = 454211 × 1986087784573<13> × 14576354568418510459<20> × 701343168472795245758518812506794635249684567700427099477696945640962052182896709099<84>
83×10121+79 = 9(2)1203<122> = 32 × 31 × 43 × 3898731713<10> × 1971694265674563127302738847424056515108769909710388218878657203135271243641430741888473363732137819102953243<109>
83×10122+79 = 9(2)1213<123> = 13 × 108887 × 128563 × 1114283 × 15088320696223135169809198089153969811751774911547<50> × 301414255803061414574888662754994760101373439276969078791<57> (Erik Branger / GGNFS, Msieve snfs / 3.72 hours / October 24, 2009 2009 年 10 月 24 日)
83×10123+79 = 9(2)1223<124> = 79 × 821 × 14629 × 7159526527<10> × 2516911254162300908118301<25> × 82029330638585517333524578140444853<35> × 6575508169682318613714237264732213652900628903<46> (Lionel Debroux / msieve 1.44 SVN for P35*P46 / October 22, 2009 2009 年 10 月 22 日)
83×10124+79 = 9(2)1233<125> = 3 × 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741<125>
83×10125+79 = 9(2)1243<126> = 5167 × 19671863550587<14> × 1372812720692545914763847<25> × 6609069566981902729738560544578957237958162237436492054538445426683221758996503636821<85>
83×10126+79 = 9(2)1253<127> = 16529 × 7754729 × 7892361753012923<16> × 23575104566973985873<20> × 121587270360139099086662315555319282367<39> × 3180340781656413018252773669024917053099371<43> (Lionel Debroux / msieve 1.44 SVN for P39*P43 / October 22, 2009 2009 年 10 月 22 日)
83×10127+79 = 9(2)1263<128> = 3 × 172 × 67 × 631 × 163789 × 15361286605512694309852552226709308276693969450751906766439043625783306722857088540488628615446678726515585657650373<116>
83×10128+79 = 9(2)1273<129> = 13 × 71941439 × 100409639027639587<18> × 9820592810583398635137607636154538595939304998948317168683740932909685190468412384777053857499793378247<103>
83×10129+79 = 9(2)1283<130> = 370756134989<12> × 13462314290065597650967239163411<32> × 1847683206138391614740683802658317179021351885853039473016213575460366458036348637474537<88> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=2972610773 for P32 / October 24, 2009 2009 年 10 月 24 日)
83×10130+79 = 9(2)1293<131> = 33 × 617 × 37019 × 79273 × 2814789675443<13> × 18725939174006909792965987<26> × 35788798637065090661667947378058207453359061300346652454633711105808937632886191<80>
83×10131+79 = 9(2)1303<132> = 76387 × 43367675339139224364346189125221<32> × 7843573642229967705735870502674301<34> × 35492452308175667954508706834786569657774757103698283837470549<62> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=2893670017 for P32 / October 22, 2009 2009 年 10 月 22 日) (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=1860510252 for P34 / October 22, 2009 2009 年 10 月 22 日)
83×10132+79 = 9(2)1313<133> = 189713 × 7870399 × 1148350510487<13> × 196629277734844846889<21> × 27353889576230756540705247991579378210734839218909059004474573716526215521708814458115503<89>
83×10133+79 = 9(2)1323<134> = 3 × 443060879 × 1102721758403<13> × 39506537573708128936553<23> × 1592634101142138075578116211332880711493202461823564059696840082085072727787886920481636881<91>
83×10134+79 = 9(2)1333<135> = 13 × 461 × 2346931 × 2846929 × 23031082308375208913430001877366782323102074287286853387793682413754333224293745756108397454447506253386342257131776989<119>
83×10135+79 = 9(2)1343<136> = 19 × 23 × 163 × 25247 × 2104339789333<13> × 2436917880406052619765524576367257559003946607712171728153991577001876363310153074667066326277489098832245690952883<115>
83×10136+79 = 9(2)1353<137> = 3 × 31 × 79 × 8573 × 147026213 × 15609740203<11> × 637972961958141914757818496241108177084093883645655861455644057627038059747253335531819856838622818964404678447<111>
83×10137+79 = 9(2)1363<138> = 479 × 3603461352528397<16> × 8448076247396329<16> × 63244443582876802473668374307040444323048884333784252006895078477921773847089538112579452637277562481549<104>
83×10138+79 = 9(2)1373<139> = 29 × 296315088385031<15> × 93988310201234862601570372294932527271313227418747<50> × 11418524212125215153704901048888926793883689926626226465167573286606626391<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.42 snfs / 5.21 hours, 0.33 hours / October 25, 2009 2009 年 10 月 25 日)
83×10139+79 = 9(2)1383<140> = 32 × 199 × 2879 × 70379 × 12219268597<11> × 20797447139796186176102121613814835040216521623928827467936461038863151321741090837322691676968618632677697254346316889<119>
83×10140+79 = 9(2)1393<141> = 13 × 59 × 179 × 196835519 × 780759681572696281<18> × 950945206033983716590046745708439382556184867498061651<54> × 45963262403462441886100482311242817697783998352022258799<56> (Sinkiti Sibata / Msieve 1.40 snfs / 6.58 hours / October 26, 2009 2009 年 10 月 26 日)
83×10141+79 = 9(2)1403<142> = 61 × 91303 × 45529459 × 61880267 × 90583254195064513964951551233389<32> × 32008672599379556241790724929001261<35> × 202703127076465420436501533853575825089948645698619413<54> (Jo Yeong Uk / GMP-ECM v6.2.3/YAFU v1.10 B1=1000000, sigma=8461231021 for P32, Msieve 1.38 for P35 x P54 / October 25, 2009 2009 年 10 月 25 日)
83×10142+79 = 9(2)1413<143> = 3 × 43 × 71 × 557 × 3493359870103<13> × 391944702424322680440077<24> × 1535181644225391274770405393769327<34> × 8600118470782546419223756731522576547964652510173823240589849178233<67> (Serge Batalov / GMP-ECM B1=1000000, sigma=4109546562 for P34 / October 24, 2009 2009 年 10 月 24 日)
83×10143+79 = 9(2)1423<144> = 17 × 155801 × 8102399 × 40274967908951<14> × 1067007793632934103644968655055324141913085358617302379962538504598383082599467848202541517872354102173614515609686431<118>
83×10144+79 = 9(2)1433<145> = 89 × 607 × 530743 × 26578672453<11> × 7620243200305720178433627196673681023<37> × 1588073113575697728528935879433186144051276413419026749657921230265554117895252647777853<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 7.02 hours on Core 2 Quad Q6700 / October 25, 2009 2009 年 10 月 25 日)
83×10145+79 = 9(2)1443<146> = 3 × 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741<146>
83×10146+79 = 9(2)1453<147> = 13 × 6112473163<10> × 70315458832223316419214342764791<32> × 5791378332563386734299789562740645717003706558548593<52> × 28499846000487846733642226699203988710334388566768759<53> (Serge Batalov / GMP-ECM B1=2000000, sigma=4092763463 for P32 / October 24, 2009 2009 年 10 月 24 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P52 x P53 / 4.39 hours on Core 2 Quad Q6700 / October 26, 2009 2009 年 10 月 26 日)
83×10147+79 = 9(2)1463<148> = definitely prime number 素数
83×10148+79 = 9(2)1473<149> = 32 × 83190091 × 15957527611<11> × 96848151779<11> × 2187959079676380646987853455829<31> × 36427161991085465012267963305165008643465020724740675750954972178493289679477335914567617<89> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=1502291535 for P31 / October 22, 2009 2009 年 10 月 22 日)
83×10149+79 = 9(2)1483<150> = 47 × 79 × 839 × 2179 × 9787 × 192553 × 72092745486001826977871939294006268929722900663919069297319803340432987263905136571716109339724963580110831657634231701927067982881<131>
83×10150+79 = 9(2)1493<151> = 683 × 457774760749<12> × 217375335251647<15> × 11308769787978757239763271<26> × 2575066817748426191576488926119<31> × 4659602872122867229740242181336706128925444176490831026516282315023<67> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=358144910 for C56 / October 22, 2009 2009 年 10 月 22 日) (Lionel Debroux / msieve 1.44 SVN for P26*P31 / October 22, 2009 2009 年 10 月 22 日)
83×10151+79 = 9(2)1503<152> = 3 × 31 × 80916331 × 11518173626755972249580540857<29> × 1063978448701314905986945548465336047220961605943500665205947892884749261108712689995929125674636100826315975334233<115>
83×10152+79 = 9(2)1513<153> = 13 × 7307478318443130895321<22> × 9707886612694712573566887864559174607603461672196349764934176935908575412169806657396159125704674398763073171472323888288678782851<130>
83×10153+79 = 9(2)1523<154> = 19 × 11845787618552744408592793547872783337647<41> × 99267096564836654377879865186188878175450767609761<50> × 412774367410497933703892824746397001142527586353054293958148251<63> (Dmitry Domanov / GGNFS/msieve snfs / 19.76 hours / October 24, 2009 2009 年 10 月 24 日)
83×10154+79 = 9(2)1533<155> = 3 × 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741<155>
83×10155+79 = 9(2)1543<156> = 635729 × 1450653064784243321009773381774659048465969339486199657750743197529485397429128169742488107703474628689618095481285614188155994491713013284311746392287<151>
83×10156+79 = 9(2)1553<157> = 528078673 × 2354032321<10> × 54455392027<11> × 29549430643279790678513909646388049663<38> × 4610356690548903466239224249245927737326743875914578310194061475922915915676673744740852531<91> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 13.30 hours on Core 2 Quad Q6700 / November 14, 2009 2009 年 11 月 14 日)
83×10157+79 = 9(2)1563<158> = 33 × 23 × 139 × 677 × 626045116755851438475264246925740973<36> × 1012848459600439964833165666804565900201<40> × 2488802357902899188563060987762312568445426174233937076223149292666541768377<76> (Dmitry Domanov / Msieve 1.40 snfs / 25.44 hours / October 25, 2009 2009 年 10 月 25 日)
83×10158+79 = 9(2)1573<159> = 13 × 4591 × 1627060507<10> × 118433541662640753023<21> × 80187471138526969412012906520706183033050175182821873233725033935186356353430136504738089642455083494853274500661833105555521<125>
83×10159+79 = 9(2)1583<160> = 17 × 1511 × 3463 × 24181 × 4287414265258464094126107959330801127680383702273544074954767144025371532649794655536865053158413362526262633900346721008092691170002079926404549843<148>
83×10160+79 = 9(2)1593<161> = 3 × 67 × 919 × 15901 × 51803 × 9822552244867<13> × 16616425657922248321<20> × 3713493850267220792846798400357608497932245449846682217378268047075265318822700790153094842940494074053903077416677<115>
83×10161+79 = 9(2)1603<162> = 1697 × 2711 × 20543 × 1498481 × 53973738457<11> × 810578820825230269<18> × 65656961003311514015883035936551<32> × 2266995127807532404937686268783558513717904515654110062784739793001401834333714626621<85> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=6209770295 for P32 / November 12, 2009 2009 年 11 月 12 日)
83×10162+79 = 9(2)1613<163> = 79 × 7163407 × 123782203 × 1379440969<10> × 77479813795087138515341741319858289<35> × 1231796507361522933848450105124016132668124640732119124805549061730851641307686899069575749709590710917<103> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=33045363 for P35 / November 3, 2009 2009 年 11 月 3 日)
83×10163+79 = 9(2)1623<164> = 3 × 43 × 45523 × 246196289784241699303<21> × 63787193451595271752738519883600292632302926214294675067602830088149136854502579401609347771831807378753576513474903723602563936565690723<137>
83×10164+79 = 9(2)1633<165> = 13 × 1545982851058311934093379<25> × 45886777393169928139023123390096819551104547605265235410440846429279562691384815118005697838505970481352890054253081729067528013272949847449<140>
83×10165+79 = 9(2)1643<166> = 107 × 15031 × 42197 × 43567788308512159678025627034514610908398268888666684424948010635688847<71> × 3119010528746029397719209328603357416174022932664142751039778863736466253498609584641<85> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 24.53 hours on Core 2 Quad Q6700 / December 2, 2009 2009 年 12 月 2 日)
83×10166+79 = 9(2)1653<167> = 32 × 29 × 31 × 11398124115958747030308024004724041802276878287260193081475988409618368832310248698828602425191227564234609099273541246103352147104464494156744805613919444101127453<164>
83×10167+79 = 9(2)1663<168> = 72977 × 554283749 × 1263339556356659027<19> × 2338748470101799073342573023708987614335694102823853247817837<61> × 7716383793317477781726834228876669577245986975255470721134548118891243631749<76> (matsui / Msieve 1.43 snfs / December 28, 2009 2009 年 12 月 28 日)
83×10168+79 = 9(2)1673<169> = 727 × 829 × 29803 × 361007106779052829<18> × 41801453629419328737465449135987989297971016530858946596003527<62> × 34023541935465003733065506794691605795027595830657654320677086614969830086496069<80> (Sander Hoogendoorn / GGNFS and msieve using factmsieve.py (the python script) snfs / 35.36 hours on Intel core 2 duo 2.2 GHz on Windows 2003 (32 Bit) / January 24, 2010 2010 年 1 月 24 日)
83×10169+79 = 9(2)1683<170> = 3 × 58909 × 521834367256968217772169630120028191630153978861307113356885038631461079643870049410798702078472571945555700160259735197350841819428962310355645839188252062346003849<165>
83×10170+79 = 9(2)1693<171> = 132 × 1303 × 75175740784686081593779300770475028296195771<44> × 7924410550370980851226220768780461448204670107<46> × 7030072093617251150883355788994421962121941534602600580932819909233991111337<76> (Ignacio Santos / GGNFS, Msieve snfs / 54.19 hours / October 30, 2009 2009 年 10 月 30 日)
83×10171+79 = 9(2)1703<172> = 19 × 9085943052679721<16> × 1045747920219889599964943<25> × 414480050876205897564526516608493974620731<42> × 123248411170903455968666289818045506324912821743655323290796263214764333989033065943910969<90> (Sinkiti Sibata / Msieve 1.40 snfs / March 14, 2010 2010 年 3 月 14 日)
83×10172+79 = 9(2)1713<173> = 3 × 207643 × 2781397 × 596270881 × 29143070837<11> × 11375060320287883162114907<26> × 143429262780526985377533249569<30> × 1877429613954632937284559937876965605040449346263632688499677823745914083490553558241621<88> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=3851510662 for P30 / October 22, 2009 2009 年 10 月 22 日)
83×10173+79 = 9(2)1723<174> = 192462481768301161<18> × 26467128626144142057989900927132990654575890427714084716555879583<65> × 181043390088457156917263132510169158763482057682597992915781668852715848391334152136988335721<93> (Sinkiti Sibata / Msieve 1.40 snfs / March 23, 2010 2010 年 3 月 23 日)
83×10174+79 = 9(2)1733<175> = 269 × 142757 × 4190800321<10> × 9494097247<10> × 328749967218276899896391463438834065125811<42> × 18359866864047957026554208865672912611276659554631910658406148683586377668388348340420774014408955281366283<107> (Markus Tervooren / GMP-ECM 6.4 B1=3000000, sigma=4206441917 for P42 / July 13, 2012 2012 年 7 月 13 日)
83×10175+79 = 9(2)1743<176> = 32 × 17 × 79 × 157 × 8431 × 34301 × 113027 × 64751131 × 228197676384363546163284943988518915508316576964141582975929866068549<69> × 100621493819989480045692099987072299644492130045149482860654567065240879719095699<81> (Warut Roonguthai / Msieve 1.48 snfs / January 19, 2012 2012 年 1 月 19 日)
83×10176+79 = 9(2)1753<177> = 13 × 2258873 × 2888117 × 23981759 × 448964403094445779949056949<27> × 1009933295956839153812196002372139329374282053011695399487962065136443276902130483037433133824912891906816429081236910071535175941<130>
83×10177+79 = 9(2)1763<178> = 71 × 439646334341<12> × 295443049761378713050207581475475799181273943752124280532370464816981698035618384984496937484921170296043025391184457044539001978063770561342956957581256291163022693<165>
83×10178+79 = 9(2)1773<179> = 3 × 9780539 × 3143051803253454716630723597210822505870150994821526783006615559811247697160733241873555306179009228503740002543902819746513023539984937511188365052349440121934050949619519<172>
83×10179+79 = 9(2)1783<180> = 23 × 186011422453771<15> × 794553250696256268886654838337455612960366907519171633271<57> × 271297083013579997899168020534040018910362404448149127448152419241808759733975829226842925917002439175820061<108> (Dmitry Domanov / Msieve 1.50 snfs / January 9, 2014 2014 年 1 月 9 日)
83×10180+79 = 9(2)1793<181> = 52791723791<11> × 5936359082576308960136708250460423700727308473725617191341894012883404241153447<79> × 29427243090545521443803963805695334423408212151540871636346022089024714846752688125925237399<92> (matsui / Msieve 1.50 snfs / October 28, 2011 2011 年 10 月 28 日)
83×10181+79 = 9(2)1803<182> = 3 × 31 × 11239 × 88231764221764480081572923606280953536621444166886448802243170356508416087818456873217226709817314537628880828970378895897467461347843312717928471252868728249674206868194394349<176>
83×10182+79 = 9(2)1813<183> = 13 × 167 × 107542995173<12> × 2413099196181829597324709<25> × 19203045192868095067526379085343<32> × 85240964025562147008917896109917196062760689924279019476697191393386262467770447148683404330891559637685017455963<113> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=2482567879 for P32 / October 22, 2009 2009 年 10 月 22 日)
83×10183+79 = 9(2)1823<184> = 197 × 187504159 × 103695324197<12> × 10933903999027<14> × 231095300840004022549<21> × 224437963133592964448686504282443534327677<42> × 4245575694068388034155339395025821288916179217836087032692125228590049200357040943403523<88> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=4111386264 for P42 / October 29, 2009 2009 年 10 月 29 日)
83×10184+79 = 9(2)1833<185> = 34 × 43 × 777045488009125890335723<24> × 1595228996677190627105381551170307721<37> × 21360559803049456956223530961267356758266923829001386830212743091199974880058586188458362519500479102539819071366246888607<122> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=3000000, sigma=2881344130 for P37 / March 7, 2011 2011 年 3 月 7 日)
83×10185+79 = 9(2)1843<186> = 349 × 38333 × 132907943489<12> × 428870269888716571343<21> × 270123578257344590362034461927415689477395845637559<51> × 4477112150406724689840014558582311683358066679736718985377893666760786247044057064462462972519983<97> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P51 x P97 / January 16, 2015 2015 年 1 月 16 日)
83×10186+79 = 9(2)1853<187> = definitely prime number 素数
83×10187+79 = 9(2)1863<188> = 3 × 122936509 × 250053795986192683743286876160935566673206416986680016598980704265327240915395936131070231876689623102448278735007358479170258045482166251692902234117781404877380573257865494950249<180>
83×10188+79 = 9(2)1873<189> = 13 × 79 × 89 × 7811989061183<13> × 851978462964751<15> × 14353187954208977087056985847697973153<38> × 105617654288292534751048708124900443287651507157113193134225576244743532921411440021823187219527697584019818690984717309<120> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.1] [ECM] B1=11000000, sigma=4047888831 for P38 / March 8, 2011 2011 年 3 月 8 日)
83×10189+79 = 9(2)1883<190> = 19 × 5990378735789383269628097762672663<34> × 510947666832600556692378497152716551054345642797<48> × 158581046878548152573618496134274475263915825966223145019584368532756472035230223947251229428999316247146847<108> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=3355232220 for P34 / November 10, 2009 2009 年 11 月 10 日) (funecm / for P48 x P108 / July 10, 2018 2018 年 7 月 10 日)
83×10190+79 = 9(2)1893<191> = 3 × 31409756452905266401572874729021762403039657905422482493898473135389505774302363727127<86> × 978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683<105> (Sinkiti Sibata / Msieve 1.42 snfs / 9 days 1 hours / November 7, 2009 2009 年 11 月 7 日)
83×10191+79 = 9(2)1903<192> = 17 × 709 × 1214773276402079<16> × [62986169418232690403456193749759328163205938137311235070186452724230962313703085138499613654395700107786810033756040467693321520584131727028146846986948633598824742091580429<173>] Free to factor
83×10192+79 = 9(2)1913<193> = 661 × 67189 × 1445718886316283565034229197590848301411089091968886986648304671591691072357<76> × 143632292272880529647040203913866451025244233853061390470672288273990302004970193140529440669279769961733945691<111> (Ignacio Santos / GGNFS, Msieve snfs / August 6, 2010 2010 年 8 月 6 日)
83×10193+79 = 9(2)1923<194> = 32 × 67 × 298128462431<12> × 17384808491550678926416760474409041<35> × 49345996008808778421521799549012365003<38> × 39613333896843399926140180479055079367199174258417151<53> × 15095642624117015742097063332468408068733345609167029607<56> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=2978660525 for P35 / March 22, 2011 2011 年 3 月 22 日) (Ignacio Santos / GMP-ECM 6.3 B1=11000000, sigma=2051369989 for P38 / March 24, 2011 2011 年 3 月 24 日) (Andreas Tete / factmsieve76.py via GGNFS, Msieve 1.48 gnfs for P53 x P56 / March 26, 2011 2011 年 3 月 26 日)
83×10194+79 = 9(2)1933<195> = 13 × 29 × 32573 × 2571073 × 185135653853<12> × 1961116926539291<16> × [80450456621052175560874943960542376268127340909983640363468050993627348120702231452378565297877889556549214244757721946851548466374237895598516382038003197<155>] Free to factor
83×10195+79 = 9(2)1943<196> = 47 × 550637 × 356346366280933746490755724819220873056239515179004951372652857575213845064403831176813137860263975978545475791972393065618208073141989330895340295130611483366410648117146729836659283556357<189>
83×10196+79 = 9(2)1953<197> = 3 × 31 × 383 × 265561 × 2148529 × 155111160951942343<18> × [29255349895259082424243974080752942403965160938758604874734763386822516510175200182615616323039774263050080905812755094760244976529092961207513194712453708970706651<164>] Free to factor
83×10197+79 = 9(2)1963<198> = 188833 × 1637304607<10> × 195883585566059947561313035547047<33> × [15227554455351745490858509417228865742861381502347939094707015461638464748811427986884533582268110168261516606740420898694964619411910498674723514524839<152>] (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=2276277847 for P33 / October 22, 2009 2009 年 10 月 22 日) Free to factor
83×10198+79 = 9(2)1973<199> = 59 × 154444451501<12> × 1768712691413262263737700905289<31> × 572208056879596242469452538427478382628866065177156497397386484500969860912702942329460577729499269562775948686560610675056699158916037497151328847217808073<156> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=3632594581 for P31 / October 22, 2009 2009 年 10 月 22 日)
83×10199+79 = 9(2)1983<200> = 3 × 563 × 4382069 × 12460249015408278163356362916967160715379495479034556305073296603490780114681012071612512518703158601812248290208454501382908085519537200577167339471706181906236894009369493464718056524794603<191>
83×10200+79 = 9(2)1993<201> = 13 × 1817177 × 754276925913022859240200609780057473043<39> × 51756413853064557977845778798045242171145092763877698881960484134403852783528030697315008971775938141452595045991910552572516580627863618160062103616314961<155> (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=1281041185 for P39 / June 22, 2010 2010 年 6 月 22 日)
83×10201+79 = 9(2)2003<202> = 232 × 61 × 792 × 15413 × 483494829597929657<18> × 13266546316066124487961252991807<32> × 167558463934031750374352058103581098448777872502617739676289963<63> × 2764347477342162989856658708335138898228999670829011948885790299879580023432827<79> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=979996634 for P31 / October 22, 2009 2009 年 10 月 22 日) (Erik Branger / GGNFS, Msieve gnfs for P63 x P79 / November 11, 2016 2016 年 11 月 11 日)
83×10202+79 = 9(2)2013<203> = 32 × 97 × 373 × 1871 × 311897 × 15178717 × 489522314254650189083341<24> × 142301471422513713840684191<27> × 23739020332057732538823647160802742454459284677<47> × 19335160525460825610228700800708024896815174338879192206734343487546470521001180913119<86> (Cyp / yafu 1.34.3 / December 28, 2013 2013 年 12 月 28 日)
83×10203+79 = 9(2)2023<204> = 139 × 223 × 401 × 739 × 1540079 × 5313601521061919<16> × 13454491405420908548181301399069<32> × 1205299253711062854387567544322640744361<40> × 756541844201920624470033800492636027457326708709348033031871917359771102502106519246596623874954304509<102> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2998647142 for P32 / November 16, 2013 2013 年 11 月 16 日) (Serge Batalov / GMP-ECM B1=3000000, sigma=2468484802 for P40 / December 4, 2013 2013 年 12 月 4 日)
83×10204+79 = 9(2)2033<205> = 109 × 47502179725970898803981932677942050189197308913<47> × 1781129704178229827859955868208821031604205138920247003746074136254009677358270509363697659238657585236964892545865506546891788439946950150483576769849480219<157> (Serge Batalov / GMP-ECM B1=43000000, sigma=3162721580 for P47 / January 5, 2014 2014 年 1 月 5 日)
83×10205+79 = 9(2)2043<206> = 3 × 43 × 378759599468313821<18> × 3453389293365237515078850846910319824222513<43> × 14484158243700009470879322204090426168500406613729967242716847909589<68> × 37734919237926101352551353121630937102676213494165248181178876325662429930271<77> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3105926848 for P43 / January 31, 2014 2014 年 1 月 31 日) (Alfred Reich / Msieve 1.54 for P68 x P77 / April 10, 2018 2018 年 4 月 10 日)
83×10206+79 = 9(2)2053<207> = 13 × 25097 × 360360983 × [7843910994210650072019040543289445541555625686135025383787578520006533994225641270846536716351992182318866877821674591600392188555174888667354211158489535252733840376397992534481656825650562821<193>] Free to factor
83×10207+79 = 9(2)2063<208> = 17 × 19 × 3019 × 135851 × 2355134640554900665721663946691<31> × [29559110950486066790611731539296596347170106930431923461851156924793143577419280294575164591028249646005240543798050549630155066465030012877823245018525207335490625519<167>] (Serge Batalov / GMP-ECM B1=1000000, sigma=1567213724 for P31 / January 6, 2014 2014 年 1 月 6 日) Free to factor
83×10208+79 = 9(2)2073<209> = 3 × 883 × 620340785622336899161876283<27> × [56120727075687437178004937772394626824282858602463505810456097781786509578331652066521541772318482314735988423892738875297361644843738282505241363854576993889690000124345090417669<179>] Free to factor
83×10209+79 = 9(2)2083<210> = 44818303409121073177773172034528071479837474471193475378600256743855665586277016438589<86> × 20576910593954761681636186506519850931791980031135779130294644173655351719337396884038815041725174612362575450532893986398907<125> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / January 12, 2014 2014 年 1 月 12 日)
83×10210+79 = 9(2)2093<211> = 5153 × 454747069272903434921<21> × 3363057172325920492698633734609<31> × [1170230144785396306910561152508807666410413974795805988494392905283358157438181586432474213250336132692740230109515468619672196407238187743853735088562783719<157>] (Serge Batalov / GMP-ECM B1=1000000, sigma=2416093582 for P31 / January 6, 2014 2014 年 1 月 6 日) Free to factor
83×10211+79 = 9(2)2103<212> = 33 × 31 × 1281968173<10> × [85947427381465801772010319670912561276207146090759618092017344718414912925454562556712674938497504431363566017571404022939346473679179327162489902366622918995222236040439844843030626092774135977883823<200>] Free to factor
83×10212+79 = 9(2)2113<213> = 13 × 71 × 181 × 227 × [24318089351510360931455366246261690727350507336432084913236382619282594155562096828602083511195985344794278911063734199251858961914265380596014630219616752830198569007012923854445640747946024588477206196323<206>] Free to factor
83×10213+79 = 9(2)2123<214> = 463 × 2309 × 15361 × 89071 × 3149803 × [2001665248747377461191108477229613926313124579778820514060008703813115092732364113966438373087902023984558438735441633698120298254048893482264390376369333606554357273089002057048536313036817033<193>] Free to factor
83×10214+79 = 9(2)2133<215> = 3 × 79 × 4817 × 250347267598509788381<21> × [322676795215018113867562965668382187201444980430614188489595322567182333099863879389058146410737014946635835767462150944880674353401507520324108389507562424440794228235741306985550858214327<189>] Free to factor
83×10215+79 = 9(2)2143<216> = 127103 × 100425146477062779779004848743<30> × 3389730404545266705936608578555367<34> × 21314352747275220932083100090844224524196192843095117466450555167437233667168961089503005472296630326690865974929001171984998221983271408740195362561<149> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=2652562094 for P30, B1=3000000, sigma=342702127 for P34 / January 3, 2014 2014 年 1 月 3 日)
83×10216+79 = 9(2)2153<217> = 113 × 163 × 263 × 7517 × 19631021 × 7909410394646439931014552291055651<34> × [1631106199413470940851610892879033271300213530514899652241651926705003162659328326272541572370672720143676526101552427374317500998010412075741196974817926619871160937<166>] (Serge Batalov / GMP-ECM B1=3000000, sigma=3461371121 for P34 / January 9, 2014 2014 年 1 月 9 日) Free to factor
83×10217+79 = 9(2)2163<218> = 3 × 2707875623189860737553<22> × 13866911541026101436683697066477<32> × 818664334223669352607401635428368341492559948688558809213158893442643634918757212759119210158285923944437704879972768722717259038888201886995800955693702326081805161<165> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=2078554457 for P32 / January 3, 2014 2014 年 1 月 3 日)
83×10218+79 = 9(2)2173<219> = 13 × 107 × 617 × 23210796331431873780606240688124842357<38> × [46294910425935873969843294303450228535478545161921526992005943147059578529800627939784461710393812225861532017919524464627928064567021982351722797858962465763252556193818432437<176>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1121747650 for P38 / January 13, 2014 2014 年 1 月 13 日) Free to factor
83×10219+79 = 9(2)2183<220> = 88032802129<11> × 56266440585788203723203555501391<32> × 1861836818933853145493177525809393429062709504846738618318935034506937605196195868051768687377909900157921937234023308597635087457664289644828644025061888296545083636268443071857<178> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=1076366604 for P32 / January 3, 2014 2014 年 1 月 3 日)
83×10220+79 = 9(2)2193<221> = 32 × 8887 × 209874169 × 3812195331448267<16> × 114766046821562928599<21> × [12557128433723241339462196989659101510586219071278580993899221833866326979152428631314964597276783150045647033616419656456451904370430979299802281019531409829120776930516253<173>] Free to factor
83×10221+79 = 9(2)2203<222> = 337 × 28025627724974471959<20> × 119170132202991478325676878618033<33> × 819375383154619074050721345870307897449431711345419963279759183642361636163982616140151492609195976697616253205825470658636147920029536232021212222107035769378402730057<168> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2758567618 for P33 / November 16, 2013 2013 年 11 月 16 日)
83×10222+79 = 9(2)2213<223> = 29 × 28069 × 11329497411209841538551208441048871220332926153926373827823580342311891781732727874071680774620942999114524702331105517342389287264047860165063952282886903360342582161719976046985473263819359217276418852338292240700223<218>
83×10223+79 = 9(2)2223<224> = 3 × 17 × 23 × 456138880969<12> × 1228967875269150860246633<25> × 140249056171981915669024224910917673870618220000972829796546422625874525205994069030136418214747298874629228894981727374928161076158785702431195723763006984698812760506334087275198263363<186>
83×10224+79 = 9(2)2233<225> = 13 × 1913 × 378927228923<12> × 97863658380719189103022827514207923797729336824399328209724150992206543721821865549950296018805231523342665594636859959768898883978695771096133697382506515405831676217843301041908946884906321750573688123691129<209>
83×10225+79 = 9(2)2243<226> = 19 × 149 × 6491008829<10> × 63183418427244867010060643<26> × 5869529009085025308114998228609077<34> × [1353247213170593951627970553293230987952846278272449972374000853625737270336280703540422834564277341328034202778723342421397874810584994635702171835894507<154>] (Serge Batalov / GMP-ECM B1=3000000, sigma=997491191 for P34 / January 9, 2014 2014 年 1 月 9 日) Free to factor
83×10226+79 = 9(2)2253<227> = 3 × 31 × 43 × 67 × 70253717 × 8538287221<10> × 573811580941981039226224863924607354978289264022190993733609468611523901018080457564941334151520155519716402837687699214670402572606263512418275467049389925972977179438199510296608512267511010280143417683<204>
83×10227+79 = 9(2)2263<228> = 79 × 27035611400044737154624961<26> × 431789717744347010644388460107143264265764299226646326607908732823802925523379252957450365734632169915726375489011476109945973420992480119601967789264817650543525489862239763612570730469129903113628417<201>
83×10228+79 = 9(2)2273<229> = 5564475198097609<16> × [1657339083005550851889902413959883506250109438094157408818643747274159963772119726557974207693220257890615668814735386912022806690767927488557934549714129355484850481664902094430611710255832942576062969906387799447<214>] Free to factor
83×10229+79 = 9(2)2283<230> = 32 × 462373 × 5158350728726903177246795327<28> × 4296251929369576390280558660580484833903345988304998978071850162191283239432587290521673888844977126559481495309662592527646039042340327788624884276474609197856760897103338387116658619224293171957<196>
83×10230+79 = 9(2)2293<231> = 13 × 131 × 2707 × 40459 × [4944444823358399185052697268655451894889707311561822308892001793147658246561151525142705199159168679453727156781220000404481667007869659447710830200886053638599536566010098190339637262430734264850923336645664524186165257<220>] Free to factor
83×10231+79 = 9(2)2303<232> = 347 × 4969 × 2438603 × 98501201 × [22266629450829713747995945155251058469061980030971656037331239010296461628578898757644186169234323099855046195540518128408401711280675277454504703788786039591495544615536002561927763755023937738569902421431117487<212>] Free to factor
83×10232+79 = 9(2)2313<233> = 3 × 89 × 15593101 × 494243676161299804620319<24> × 719915338392562742750843<24> × 62254289616446636323225763102848800048528883572480844361695089391305776886414466717532047649390460046937326214283733408974227174319629637145400542733503372008576973056240782957<176>
83×10233+79 = 9(2)2323<234> = 367 × 769 × [3267707529939878118446130266570131499637599423938595444815703263809902886094408401236689505186403029597949926909650248995376784394688676054829770154176740457801887947552900444762553803985579567300405077623801824168201111256780001<229>] Free to factor
83×10234+79 = 9(2)2333<235> = 44866514622416121907480321<26> × 8568239642486668342634607626207569<34> × [23989524777775340269278117254853183295796669953734511283034688336995461031003716896045420993011872799863385129878986257892241934168612892593552922406665285131949581759926863327<176>] (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=224872059 for P34 / January 2, 2014 2014 年 1 月 2 日) Free to factor
83×10235+79 = 9(2)2343<236> = 3 × 7848227 × 274422327079<12> × 89728736018955773<17> × [159071281355965595156758230268907218710162303275585259048967155169003564670003779653030319417079750254697696910637857738213266632127710277402881826155523576765542888754571062677618284836536603539004549<201>] Free to factor
83×10236+79 = 9(2)2353<237> = 13 × 40597 × 6632377 × 30385279 × [8670933509294755758956914187906673973309830860530516599946513294766512920431283878910643612615918429225785712097324058174038142193341557936071468781602621034339731647707233336934662230939487936743012919955738619314921<217>] Free to factor
83×10237+79 = 9(2)2363<238> = 1265549 × [7287131689268627466990390907204874897947232562486495759723426135394380006007054821442885437246777661095873982139152432835253492533455616670885301337381817868942429113548524966020456120009752464916192278783533646047859247032096127627<232>] Free to factor
83×10238+79 = 9(2)2373<239> = 33 × 199 × 1301 × 30431551903<11> × 2321421075948304036464075589<28> × 186751209122848084187080543909211429239307076662091976348202101865778801373340799703063553970449242260250040054115476243071893303648663488457160982741204515860313841610697760316801873421186698653<195>
83×10239+79 = 9(2)2383<240> = 17 × 16361 × 103553 × 1112239 × 635911070395380527772362723443<30> × 45270951949428902288397709546726578792488607441109748358735943626521219526632915356699636888677279100097707609218138511266966362484521441010843216013838910146499141137414959256846808191261185459<194> (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=1574996317 for P30 / January 4, 2014 2014 年 1 月 4 日)
83×10240+79 = 9(2)2393<241> = 79 × 2069 × 875129 × 1676243 × 441679719946711<15> × 66687104258536503269509<23> × [1305838983984473884500096003114723456907761065933188164092101337082658423317832612719349280611107944032975450224990102274619390522230550404123050771146325845716595947640299302653058254141<187>] Free to factor
83×10241+79 = 9(2)2403<242> = 3 × 31 × 47 × 180722887673<12> × 8843911200161678230027033<25> × 13200708647300364298109289330034391367272979533555422428358856890195204627393095498939627160478310041193588707641560100308844805055844330241340914822365831397950065419946173736487309808667848282273607557<203>
83×10242+79 = 9(2)2413<243> = 13 × 1861 × [38119382557856496599108098302080032332584723772257356351929162246196098963428356227926351515819543761510446088629860795363213418022660365486802886050602332171381069822767834589435879065110661026835126781392230075733568479404051677023197711<239>] Free to factor
83×10243+79 = 9(2)2423<244> = 19 × 1574022717569<13> × [308369194129999494807424945451813027119924664040174201403550007569836346382377679411530010275080128409953396130124997783639487171702140534205396427844088346547695484241526501761981181036251630575863097649594377805735496515488639893<231>] Free to factor
83×10244+79 = 9(2)2433<245> = 3 × 591007133 × 32434500496137622661618678656230067819<38> × [1603667735696103066527952731672791941438623417602075432579764636770816342140567632458088634278237345046971648109378408165523738851633101575341627415009984591327178985704579273961499717043315883451483<199>] (Cyp / GMP-ECM 6.4.4 B1=3000000, sigma=4236212669 for P38 / January 5, 2014 2014 年 1 月 5 日) Free to factor
83×10245+79 = 9(2)2443<246> = 23 × 1317853 × 52805521 × 156089815043<12> × 703799598352225176251<21> × 5244907880390582730817555138207563685313464898631029457157576541783785409739253357425611034184376998247488208146015091390343641320417787223217085053636972661158316277708306881731123712150218871288989<199>
83×10246+79 = 9(2)2453<247> = 726715497139<12> × 12690278738418417789131118734809362016513762196441517851540809017394670708122195161875345414192466587305306035859566488971876817228697882890246410281901517221997415762229963057017700225672718646942125592647526498040561310604037111992757<236>
83×10247+79 = 9(2)2463<248> = 32 × 43 × 71 × 503 × 44220031199759<14> × 102974223558359380745886713911<30> × 1465381530660765679818112888905095934157358037579806437585230489677933340747933258087671867147983912173298366759367087969141486698895208768931851776034891621667137263632220584504752548510812651315117<199> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1541354796 for P30 / November 16, 2013 2013 年 11 月 16 日)
83×10248+79 = 9(2)2473<249> = 132 × 7151 × 2605013 × 25006901 × [11714191799596134980930804215122590595794307635099902289514971987659731782290253859203991963724729897814668249790704811209861262623707829443697237371682152831827556550660029829121747504488938791511768087804696044713649900624829409<230>] Free to factor
83×10249+79 = 9(2)2483<250> = 139 × 21329952801274597<17> × [3110504888602741563494789311173755754194635683563513192014191158732537502654090869693111342019717858326249903090518856126554525034448418897627099816197041334053732521556522408084078738086000346839719016436978680280770493115464486281<232>] Free to factor
83×10250+79 = 9(2)2493<251> = 3 × 29 × 577 × 2429951011<10> × 220033317936058769474157493650613<33> × 3436011046817773908025074810533516555592849830381050752333726294975850607366633494797435790315228572758445985262358165339858054821454146503812928034348048976757186704571899469432477777520569204447106472439<205> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=678710742 for P33 / November 16, 2013 2013 年 11 月 16 日)
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