Table of contents 目次

  1. About 899...99 899...99 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
    4. Algebraic factorization 代数的因数分解
    5. Related sequences 関連する数列
  2. Prime numbers of the form 899...99 899...99 の形の素数
    1. Last updated 最終更新日
    2. Known (probable) prime numbers 既知の (おそらく) 素数
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 899...99 899...99 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 899...99 899...99 について

1.1. Classification 分類

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

1.2. Sequence 数列

89w = { 8, 89, 899, 8999, 89999, 899999, 8999999, 89999999, 899999999, 8999999999, … }

1.3. General term 一般項

9×10n-1 (0≤n)

1.4. Algebraic factorization 代数的因数分解

  1. 9×102k-1 = (3×10k-1)×(3×10k+1)

1.5. Related sequences 関連する数列

2. Prime numbers of the form 899...99 899...99 の形の素数

2.1. Last updated 最終更新日

November 8, 2017 2017 年 11 月 8 日

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

  1. 9×101-1 = 89 is prime. は素数です。
  2. 9×103-1 = 8999 is prime. は素数です。
  3. 9×107-1 = 89999999 is prime. は素数です。
  4. 9×1019-1 = 8(9)19<20> is prime. は素数です。
  5. 9×1029-1 = 8(9)29<30> is prime. は素数です。
  6. 9×1037-1 = 8(9)37<38> is prime. は素数です。
  7. 9×1093-1 = 8(9)93<94> is prime. は素数です。
  8. 9×10935-1 = 8(9)935<936> is prime. は素数です。
  9. 9×108415-1 = 8(9)8415<8416> is prime. は素数です。 (Harvey Dubner / Cruncher / October 1, 1994 1994 年 10 月 1 日)
  10. 9×109631-1 = 8(9)9631<9632> is prime. は素数です。 (Harvey Dubner / Cruncher / October 1, 1994 1994 年 10 月 1 日)
  11. 9×1011143-1 = 8(9)11143<11144> is prime. は素数です。 (Harvey Dubner / Cruncher / December 1, 1994 1994 年 12 月 1 日)
  12. 9×1041475-1 = 8(9)41475<41476> is prime. は素数です。 (Dr. Dirk Augustin / Proth.exe / October 27, 2000 2000 年 10 月 27 日)
  13. 9×1041917-1 = 8(9)41917<41918> is prime. は素数です。 (Eric J. Sorensen / Proth.exe / January 23, 2002 2002 年 1 月 23 日)
  14. 9×1048051-1 = 8(9)48051<48052> is prime. は素数です。 (Harvey Dubner / Proth.exe / December 10, 2000 2000 年 12 月 10 日)
  15. 9×10107663-1 = 8(9)107663<107664> is prime. は素数です。 (Jiong Sun / NewPGen, PRP, OpenPFGW / January 21, 2004 2004 年 1 月 21 日)
  16. 9×10212903-1 = 8(9)212903<212904> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 4, 2010 2010 年 11 月 4 日)
  17. 9×10223871-1 = 8(9)223871<223872> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 9, 2010 2010 年 11 月 9 日)
  18. 9×10260253-1 = 8(9)260253<260254> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / November 5, 2010 2010 年 11 月 5 日)
  19. 9×10364521-1 = 8(9)364521<364522> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / December 19, 2010 2010 年 12 月 19 日)
  20. 9×10383643-1 = 8(9)383643<383644> is prime. は素数です。 (David Broadhurst / Srsieve, NewPGen, LLR, OpenPFGW / January 7, 2011 2011 年 1 月 7 日)
  21. 9×101009567-1 = 8(9)1009567<1009568> is prime. は素数です。 (Predrag Kurtovic / Srsieve, LLR / September 19, 2016 2016 年 9 月 19 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了 / Ray Chandler / September 30, 2010 2010 年 9 月 30 日
  2. n≤100000 / Completed 終了 / Gary Barnes / December 1, 2010 2010 年 12 月 1 日
  3. n≤135000 / Completed 終了 / Gary Barnes / January 3, 2010 2010 年 1 月 3 日
  4. n≤140000 / Completed 終了 / Gary Barnes / January 14, 2011 2011 年 1 月 14 日
  5. n≤145000 / Completed 終了 / Gary Barnes / January 16, 2011 2011 年 1 月 16 日
  6. n≤150000 / Completed 終了 / Gary Barnes / January 18, 2011 2011 年 1 月 18 日
  7. n≤155000 / Completed 終了 / Gary Barnes / January 20, 2011 2011 年 1 月 20 日
  8. n≤160000 / Completed 終了 / Gary Barnes / January 24, 2011 2011 年 1 月 24 日
  9. n≤165000 / Completed 終了 / Gary Barnes / January 25, 2011 2011 年 1 月 25 日
  10. n≤170000 / Completed 終了 / Gary Barnes / January 28, 2011 2011 年 1 月 28 日
  11. n≤175000 / Completed 終了 / Gary Barnes / January 31, 2011 2011 年 1 月 31 日
  12. n≤180000 / Completed 終了 / Gary Barnes / February 3, 2011 2011 年 2 月 3 日
  13. n≤185000 / Completed 終了 / Gary Barnes / February 7, 2011 2011 年 2 月 7 日
  14. n≤190000 / Completed 終了 / Gary Barnes / February 11, 2011 2011 年 2 月 11 日
  15. n≤195000 / Completed 終了 / Gary Barnes / February 17, 2011 2011 年 2 月 17 日
  16. n≤200000 / Completed 終了 / Gary Barnes / February 20, 2011 2011 年 2 月 20 日
  17. n≤205000 / Completed 終了 / Gary Barnes / February 27, 2011 2011 年 2 月 27 日
  18. n≤210000 / Completed 終了 / Gary Barnes / February 28, 2011 2011 年 2 月 28 日
  19. n≤215000 / Completed 終了 / Gary Barnes / March 5, 2011 2011 年 3 月 5 日
  20. n≤220000 / Completed 終了 / Gary Barnes / March 9, 2011 2011 年 3 月 9 日
  21. n≤225000 / Completed 終了 / Gary Barnes / March 15, 2011 2011 年 3 月 15 日
  22. n≤230000 / Completed 終了 / Gary Barnes / April 17, 2011 2011 年 4 月 17 日
  23. 1000001≤n≤1010000 / Completed 終了 / Predrag Kurtovic / September 19, 2016 2016 年 9 月 19 日
  24. 1010001≤n≤1015000 / Completed 終了 / Predrag Kurtovic / June 12, 2017 2017 年 6 月 12 日
  25. 1015000≤n≤1020001 / Completed 終了 / Predrag Kurtovic / November 8, 2017 2017 年 11 月 8 日

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

  1. 9×102k-1 = (3×10k-1)×(3×10k+1)
  2. 9×106k+4-1 = 7×(9×104-17+81×104×106-19×7×k-1Σm=0106m)
  3. 9×106k+4-1 = 13×(9×104-113+81×104×106-19×13×k-1Σm=0106m)
  4. 9×1015k+2-1 = 31×(9×102-131+81×102×1015-19×31×k-1Σm=01015m)
  5. 9×1016k+10-1 = 17×(9×1010-117+81×1010×1016-19×17×k-1Σm=01016m)
  6. 9×1018k+8-1 = 19×(9×108-119+81×108×1018-19×19×k-1Σm=01018m)
  7. 9×1021k+4-1 = 43×(9×104-143+81×104×1021-19×43×k-1Σm=01021m)
  8. 9×1022k+4-1 = 23×(9×104-123+81×104×1022-19×23×k-1Σm=01022m)
  9. 9×1027k+15-1 = 757×(9×1015-1757+81×1015×1027-19×757×k-1Σm=01027m)
  10. 9×1028k+2-1 = 29×(9×102-129+81×102×1028-19×29×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 18.02%. 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 18.02% です。

3. Factor table of 899...99 899...99 の素因数分解表

3.1. Last updated 最終更新日

May 14, 2016 2016 年 5 月 14 日

3.2. Range of factorization 分解範囲

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

n=203, 207, 211, 215, 217, 219, 221, 231, 235, 241, 245, 247, 251, 253, 257, 259, 267, 269, 271, 279, 281, 283, 287, 289, 293, 297 (26/300)

3.4. Factor table 素因数分解表

9×100-1 = 8 = 23
9×101-1 = 89 = definitely prime number 素数
9×102-1 = 899 = 29 × 31
9×103-1 = 8999 = definitely prime number 素数
9×104-1 = 89999 = 7 × 13 × 23 × 43
9×105-1 = 899999 = 397 × 2267
9×106-1 = 8999999 = 2999 × 3001
9×107-1 = 89999999 = definitely prime number 素数
9×108-1 = 899999999 = 19 × 131 × 229 × 1579
9×109-1 = 8999999999<10> = 151 × 523 × 113963
9×1010-1 = 89999999999<11> = 7 × 13 × 17 × 47 × 491 × 2521
9×1011-1 = 899999999999<12> = 677 × 1329394387<10>
9×1012-1 = 8999999999999<13> = 853 × 3517 × 2999999
9×1013-1 = 89999999999999<14> = 3547 × 69427 × 365471
9×1014-1 = 899999999999999<15> = 29999999 × 30000001
9×1015-1 = 8999999999999999<16> = 757 × 7639 × 1556360213<10>
9×1016-1 = 89999999999999999<17> = 72 × 13 × 6122449 × 23076923
9×1017-1 = 899999999999999999<18> = 31 × 71 × 408905043162199<15>
9×1018-1 = 8999999999999999999<19> = 7589 × 16937 × 177127 × 395309
9×1019-1 = 89999999999999999999<20> = definitely prime number 素数
9×1020-1 = 899999999999999999999<21> = 2113 × 3767 × 3769 × 30000000001<11>
9×1021-1 = 8999999999999999999999<22> = 20173 × 446140881376096763<18>
9×1022-1 = 89999999999999999999999<23> = 7 × 132 × 683 × 953 × 65843 × 1775147929<10>
9×1023-1 = 899999999999999999999999<24> = 613 × 1468189233278955954323<22>
9×1024-1 = 8999999999999999999999999<25> = 67 × 359 × 8356545961<10> × 44776119403<11>
9×1025-1 = 89999999999999999999999999<26> = 43 × 2093023255813953488372093<25>
9×1026-1 = 899999999999999999999999999<27> = 17 × 19 × 23 × 62191 × 1233721 × 1578947368421<13>
9×1027-1 = 8999999999999999999999999999<28> = 401 × 2221158668683<13> × 10104586669453<14>
9×1028-1 = 89999999999999999999999999999<29> = 7 × 13 × 107 × 33203 × 95773 × 6495563 × 447486691
9×1029-1 = 899999999999999999999999999999<30> = definitely prime number 素数
9×1030-1 = 8999999999999999999999999999999<31> = 29 × 83 × 103 × 227 × 1545895313<10> × 103448275862069<15>
9×1031-1 = 89999999999999999999999999999999<32> = 33168293 × 2713434785444038377253843<25>
9×1032-1 = 899999999999999999999999999999999<33> = 31 × 379 × 15901 × 100126307 × 160581649 × 299621557
9×1033-1 = 8999999999999999999999999999999999<34> = 197 × 5879 × 13729 × 566022790462260918263237<24>
9×1034-1 = 89999999999999999999999999999999999<35> = 7 × 13 × 157 × 2281 × 3257 × 6961 × 23911 × 12040213 × 423111547
9×1035-1 = 899999999999999999999999999999999999<36> = 347 × 2593659942363112391930835734870317<34>
9×1036-1 = 8999999999999999999999999999999999999<37> = 61 × 16921 × 3145189 × 5188801 × 34168681 × 15636684431<11>
9×1037-1 = 89999999999999999999999999999999999999<38> = definitely prime number 素数
9×1038-1 = 899999999999999999999999999999999999999<39> = 163 × 184049079754601227<18> × 29999999999999999999<20>
9×1039-1 = 8999999999999999999999999999999999999999<40> = 1399 × 1920599 × 479099653 × 6991369252979250035683<22>
9×1040-1 = 89999999999999999999999999999999999999999<41> = 7 × 13 × 23076923076923076923<20> × 42857142857142857143<20>
9×1041-1 = 899999999999999999999999999999999999999999<42> = 283 × 10756524547<11> × 295654232948432987792498206799<30>
9×1042-1 = 8999999999999999999999999999999999999999999<43> = 17 × 191 × 263 × 757 × 11059 × 13472579 × 110363948159<12> × 846671161213<12>
9×1043-1 = 89999999999999999999999999999999999999999999<44> = 199 × 1321 × 3098747 × 110484281593087312987107983402323<33>
9×1044-1 = 899999999999999999999999999999999999999999999<45> = 19 × 167 × 181 × 311 × 337 × 1381 × 1559 × 10452973 × 604304143 × 1099432012969<13>
9×1045-1 = 8999999999999999999999999999999999999999999999<46> = 89 × 2663569 × 37965449930382121705159463727220672039<38>
9×1046-1 = 89999999999999999999999999999999999999999999999<47> = 7 × 13 × 43 × 233 × 50367072601<11> × 850896044657<12> × 2303316007278478583<19>
9×1047-1 = 899999999999999999999999999999999999999999999999<48> = 31 × 8045533 × 496034351476796569<18> × 7274685820245550016477<22>
9×1048-1 = 8999999999999999999999999999999999999999999999999<49> = 23 × 6709 × 15056940637<11> × 29697967297<11> × 130434782608695652173913<24>
9×1049-1 = 89999999999999999999999999999999999999999999999999<50> = 563 × 1597 × 2250041 × 44487578424013102272197374535613136049<38>
9×1050-1 = 8(9)50<51> = 2309 × 23057 × 10833241 × 120104713180327<15> × 12992637505413598960589<23>
9×1051-1 = 8(9)51<52> = 498703999 × 18046777282810599639887788427379344114704001<44>
9×1052-1 = 8(9)52<53> = 7 × 13 × 59 × 71 × 109 × 877 × 17011 × 26355258412811941<17> × 5508933654075692748407<22>
9×1053-1 = 8(9)53<54> = 6803 × 132294575922387182125532853153020726150227840658533<51>
9×1054-1 = 8(9)54<55> = 2069 × 85577 × 4296989 × 3943115191193<13> × 2999999999999999999999999999<28>
9×1055-1 = 8(9)55<56> = 10111 × 266886276333463982401<21> × 33352021088284568499350580217409<32>
9×1056-1 = 8(9)56<57> = 47 × 638297872340425531914893617<27> × 30000000000000000000000000001<29>
9×1057-1 = 8(9)57<58> = 67 × 43963 × 1028901501145942434599<22> × 2969659015069271464332605919481<31>
9×1058-1 = 8(9)58<59> = 74 × 13 × 17 × 29 × 6389 × 212469253928379447424129<24> × 4308549598586795731663531<25>
9×1059-1 = 8(9)59<60> = 277 × 8360003 × 136729631331044067193877<24> × 2842455434324503230899065277<28>
9×1060-1 = 8(9)60<61> = 19441 × 45949 × 1637539 × 671304589 × 5002728961799<13> × 1832017435920610135086859<25>
9×1061-1 = 8(9)61<62> = 3271 × 487728452339437218839<21> × 56413607656198423151756876816941602271<38>
9×1062-1 = 8(9)62<63> = 19 × 31 × 383 × 16187 × 546924986987<12> × 178350167647709<15> × 2526741345910890255200875937<28>
9×1063-1 = 8(9)63<64> = 7507 × 3750042827<10> × 319697960707742776204872853555157517164263616445391<51>
9×1064-1 = 8(9)64<65> = 7 × 13 × 103 × 326707 × 146437799 × 157588568214707166713677<24> × 1273583870573108963459083<25>
9×1065-1 = 8(9)65<66> = 547 × 167443 × 167713163761626573605467<24> × 58589667726693100081417128713675957<35>
9×1066-1 = 8(9)66<67> = 113 × 149 × 6287 × 34303 × 42299 × 5194269029314101397578509<25> × 11281002465075774324342877<26>
9×1067-1 = 8(9)67<68> = 43 × 293 × 443563 × 644416991 × 24991029011406741167065731522199613715156685911797<50>
9×1068-1 = 8(9)68<69> = 20107 × 28711 × 46811 × 51047 × 12554606696004419459257547<26> × 51966762052062599154639013<26>
9×1069-1 = 8(9)69<70> = 757 × 2591 × 392256582083<12> × 21780210678601<14> × 537089795232790722426894637937014549319<39>
9×1070-1 = 8(9)70<71> = 7 × 13 × 23 × 478631 × 3887236453<10> × 2618448681461<13> × 23034640168453340899<20> × 383182793960858193559<21>
9×1071-1 = 8(9)71<72> = 83 × 1733 × 1498377899910864444260923<25> × 4175846206181211096667355922507161379269267<43>
9×1072-1 = 8(9)72<73> = 193 × 2347451 × 6621668120347220058071014093<28> × 3000000000000000000000000000000000001<37>
9×1073-1 = 8(9)73<74> = 140502570236729<15> × 235496966083627<15> × 1512112539516804163933<22> × 1798824562611511313552041<25>
9×1074-1 = 8(9)74<75> = 173 × 179 × 613 × 1569611 × 3874630228127<13> × 44955771308579<14> × 6106248727864848361489924689599023<34>
9×1075-1 = 8(9)75<76> = 3187 × 311603 × 84476058053251419255636408187321<32> × 107281583641067522945308063892662879<36>
9×1076-1 = 8(9)76<77> = 7 × 13 × 2423 × 3571 × 2173333 × 1283942706199<13> × 4300920803658799<16> × 9524111876567510079685069367281501<34>
9×1077-1 = 8(9)77<78> = 31 × 18011849 × 1611842185914179551042098149730715167446968722035825309468013474477721<70>
9×1078-1 = 8(9)78<79> = 2990993 × 20474512935513701<17> × 146523632061420300823699<24> × 1003011374483323765719277845183857<34>
9×1079-1 = 8(9)79<80> = 146677 × 613593133211069220123127688731021223504707622872024925516611329656319668387<75>
9×1080-1 = 8(9)80<81> = 19 × 1316507 × 13940701 × 979150369 × 5634413557<10> × 24313333578409<14> × 67230905546473<14> × 286199942061324334063<21>
9×1081-1 = 8(9)81<82> = 107 × 881 × 1289 × 74067878585596169433169141580363117445575313729107580902512656492774188773<74>
9×1082-1 = 8(9)82<83> = 7 × 13 × 257 × 17107 × 4735035242785279<16> × 1108530656089810937<19> × 42857142857142857142857142857142857142857<41>
9×1083-1 = 8(9)83<84> = 75151717 × 34075476493<11> × 1189363009648277267277306121<28> × 295493027153652320799403521100632052199<39>
9×1084-1 = 8(9)84<85> = 151 × 1669 × 119299 × 9063097 × 39546174097<11> × 2523171052478922495193<22> × 331012677013166691253552731477992567<36>
9×1085-1 = 8(9)85<86> = 4079 × 113969197 × 424929061889<12> × 997291710148063198144733<24> × 456838474047838579932292360842873376729<39>
9×1086-1 = 8(9)86<87> = 29 × 12654046331183595167<20> × 81751143590441508737707<23> × 29999999999999999999999999999999999999999999<44>
9×1087-1 = 8(9)87<88> = 71 × 1670665903849<13> × 75874274496320064714620165130539981500883716490481715486373775461808043681<74>
9×1088-1 = 8(9)88<89> = 7 × 13 × 43 × 37021 × 594332567 × 4191314061691<13> × 10550048513531<14> × 3680390637464286032999<22> × 6423273420722757827509291<25>
9×1089-1 = 8(9)89<90> = 89 × 11959 × 1099117 × 1914361 × 12296003050864343151685451606293<32> × 32683300833001233692001425701333824461689<41>
9×1090-1 = 8(9)90<91> = 17 × 67 × 269 × 499 × 1249 × 7839399777505813901392825897156132039<37> × 6012024048096192384769539078156312625250501<43>
9×1091-1 = 8(9)91<92> = 643 × 1161022741558831<16> × 177336476131893903178439219449597<33> × 679818119154979438389142378569498499291799<42>
9×1092-1 = 8(9)92<93> = 23 × 31 × 97 × 700963 × 77575909 × 968862613 × 189366722010724917133<21> × 1304347826086956521739130434782608695652173913<46>
9×1093-1 = 8(9)93<94> = definitely prime number 素数
9×1094-1 = 8(9)94<95> = 7 × 13 × 1404819661871<13> × 109311862154664874542821<24> × 211110876917197143984737<24> × 30507220264887130087041437378722567<35>
9×1095-1 = 8(9)95<96> = 494191 × 1559287059348753978721<22> × 5784258946596082121965138243<28> × 201917460656553827347624605886704346651163<42>
9×1096-1 = 8(9)96<97> = 61 × 443 × 757 × 8221 × 334127 × 864195651219961261<18> × 6922368189145372572420061<25> × 26773803868940651228170563387195934487<38>
9×1097-1 = 8(9)97<98> = 406919384203<12> × 67062260616887028659416429612783594799<38> × 3298040175592624102239396210899246476628237804467<49> (Robert Backstrom / PPSIQS Ver 1.1 for P38 x P49 / June 11, 2003 2003 年 6 月 11 日)
9×1098-1 = 8(9)98<99> = 19 × 103 × 1321 × 1879 × 665293 × 35278466088721848125359<23> × 452568977610245073188041<24> × 17442737999925077569064711017059757319<38>
9×1099-1 = 8(9)99<100> = 10042199 × 29021107 × 178865803 × 62059279373249<14> × 3322781922608843<16> × 237070102292577121<18> × 3531726310132797957392482014523<31>
9×10100-1 = 8(9)100<101> = 72 × 132 × 431 × 586335359385372763185511<24> × 10441889409517628903684359<26> × 4118672689081398701245212042998942874009802441<46>
9×10101-1 = 8(9)101<102> = 1319 × 19161787 × 1469369655409<13> × 659073760694235716803<21> × 36770252919761093913960286455819525700098586256563863022729<59>
9×10102-1 = 8(9)102<103> = 47 × 994953497 × 1066480229<10> × 1356476046074293<16> × 2073749608604567097036502567<28> × 64153538257318726918841475967120159360039<41>
9×10103-1 = 8(9)103<104> = 49356163 × 9091817694893<13> × 169626415128661787<18> × 1182379569593309002107675592099711153725997386470829858657218695403<67>
9×10104-1 = 8(9)104<105> = 397 × 409369 × 589291 × 390621169 × 72645380763102632869<20> × 1057200780089282053600259<25> × 313246327159464677685910911080355191527<39>
9×10105-1 = 8(9)105<106> = 569 × 15817223198594024604569420035149384885764499121265377855887521968365553602811950790861159929701230228471<104>
9×10106-1 = 8(9)106<107> = 7 × 13 × 17 × 6581 × 6132679193<10> × 679927496140561<15> × 604590671733065589907762577<27> × 3506598249038607646721915070190408284922796395217<49>
9×10107-1 = 8(9)107<108> = 31 × 90375751 × 321239466817997772790381177757837190841872131486157808686050410051453564309844930174516791888481879<99>
9×10108-1 = 8(9)108<109> = 3217 × 1011559 × 754590459935761<15> × 1390016294869897<16> × 3930236875017125218405813407578599<34> × 670888430310272971761577811789656151<36>
9×10109-1 = 8(9)109<110> = 43 × 257952658918547<15> × 8113982094965966882913022903825652784116805670330081715571245645005923072638770280742633395119<94>
9×10110-1 = 8(9)110<111> = 59 × 409 × 3299 × 321114319 × 1645263250196710211<19> × 713293966588391497181<21> × 29999999999999999999999999999999999999999999999999999999<56>
9×10111-1 = 8(9)111<112> = 57911347104281043346744436873757530216532584665017043759<56> × 155409957633927725277408352755179538794416195817608717361<57> (Robert Backstrom / NFSX v1.8 for P56 x P57 / September 19, 2003 2003 年 9 月 19 日)
9×10112-1 = 8(9)112<113> = 7 × 13 × 83 × 157 × 4331167543529607187088879<25> × 64194057375964295426367330839<29> × 272975432211101000909918107370336669699727024567788899<54>
9×10113-1 = 8(9)113<114> = 15566337715963<14> × 1844388924344907947<19> × 3111951006249079679<19> × 10073277648984868000793647415535559194360160011293741583417872921<65>
9×10114-1 = 8(9)114<115> = 23 × 29 × 1117 × 23447 × 1136834253520662461<19> × 3339120189577212023<19> × 1491491939550947497031924913731<31> × 90996797063160225886700832599613151271<38>
9×10115-1 = 8(9)115<116> = 18947 × 32191 × 189046327186963<15> × 341959240782299323<18> × 1701788651525214775643<22> × 1341279770756789373831679980291996574469540696232940241<55>
9×10116-1 = 8(9)116<117> = 19 × 21871 × 6686869667<10> × 52776674411<11> × 626931419603<12> × 135592709679897593746997509<27> × 72193652252802918548715073312653862721363786220156949<53>
9×10117-1 = 8(9)117<118> = 12853 × 348827 × 11387293 × 773615041 × 227867563523506276061507599487908080754267671542431861210571087958319647416988375015231858733<93>
9×10118-1 = 8(9)118<119> = 7 × 13 × 1039 × 19531 × 641317 × 338082920595701<15> × 17500711862350918541<20> × 3753906133691874100123<22> × 3421574356367246644163949706650392458891569799391<49>
9×10119-1 = 8(9)119<120> = 163 × 557 × 1907 × 6433003 × 28275072734748305314573<23> × 28577980272943488159095038515733572330735309004719529484965168826870990782736731133<83>
9×10120-1 = 8(9)120<121> = 577 × 743 × 808716498647<12> × 1057972676861663008729<22> × 4719127225971742808162711<25> × 5199306759098786828422876949740034662045060658578856152513<58>
9×10121-1 = 8(9)121<122> = 3115546111<10> × 532239416828107<15> × 16227736442292637<17> × 3344593534603521012190562638941239530793459663861323024832822206675524934481857151<82>
9×10122-1 = 8(9)122<123> = 17 × 31 × 71 × 10103893 × 392494829757049332889<21> × 14354496404471703713440320501419<32> × 422535211267605633802816901408450704225352112676056338028169<60>
9×10123-1 = 8(9)123<124> = 67 × 757 × 1009 × 2853732877<10> × 2928134549833431345521<22> × 21046326978627893893642405241813254831500226029451768720143892395483726603325958317957<86>
9×10124-1 = 8(9)124<125> = 7 × 13 × 14811936975361976113<20> × 2893419201582547140630722876441221402622311<43> × 23076923076923076923076923076923076923076923076923076923076923<62>
9×10125-1 = 8(9)125<126> = 613 × 5757253 × 421434479 × 13085937734441050241784803<26> × 46241488644874736742662004807641849153986050652868738868818218301387466307168035443<83>
9×10126-1 = 8(9)126<127> = 389 × 1867 × 1728967 × 7703231 × 1605051241<10> × 140337174186780324552365181567296961903007<42> × 4130735009218423628905782065174736975448288016875429424327<58>
9×10127-1 = 8(9)127<128> = 5114630123<10> × 60258797969<11> × 9550600474282622707<19> × 2054569117136440829401479323<28> × 22503817322752644844861904639<29> × 661302532344055465819400753846963<33>
9×10128-1 = 8(9)128<129> = 277 × 7927 × 1026139 × 3688129845545438409852942740111089271467757989074336517<55> × 108303249097472924187725631768953068592057761732851985559566787<63>
9×10129-1 = 8(9)129<130> = 2488670444801039122027<22> × 3616388830751562164695567680810031305706130669466325149662667495187284610366974843928941556852902980883055037<109>
9×10130-1 = 8(9)130<131> = 7 × 13 × 43 × 1525331 × 1434687874937293<16> × 1663870743431261569<19> × 147390107888415272711657<24> × 611704123343575338233723<24> × 70061883223682835822554541457490468968459<41>
9×10131-1 = 8(9)131<132> = 197 × 4568527918781725888324873096446700507614213197969543147208121827411167512690355329949238578680203045685279187817258883248730964467<130>
9×10132-1 = 8(9)132<133> = 103 × 503 × 15763439 × 50162659539371570232061<23> × 7542611608385988025064828485248227<34> × 29126213592233009708737864077669902912621359223300970873786407767<65>
9×10133-1 = 8(9)133<134> = 89 × 1011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191<133>
9×10134-1 = 8(9)134<135> = 19 × 107 × 15920843 × 10644771958592162966987<23> × 87072588295411188803975078531858983<35> × 30000000000000000000000000000000000000000000000000000000000000000001<68>
9×10135-1 = 8(9)135<136> = 307 × 23053 × 190837 × 6663679532492486082436027119610049449264833150151608508638140565200828143270809367528992570566338049019410075675926996337237<124>
9×10136-1 = 8(9)136<137> = 7 × 13 × 23 × 1003344481605351170568561872909698996655518394648829431438127090301<67> × 42857142857142857142857142857142857142857142857142857142857142857143<68>
9×10137-1 = 8(9)137<138> = 31 × 191 × 1373 × 2557 × 17118340529663775761<20> × 175528354159933984438280203<27> × 113999489871325457335482883679<30> × 126396291857824621117649973702535113094004864696623547<54>
9×10138-1 = 8(9)138<139> = 17 × 131 × 1193 × 36493 × 13010688596546599947627907<26> × 329860332209700670780056854383<30> × 14659956248770104285450993620607013<35> × 1475398144671508730120834597876984040721<40>
9×10139-1 = 8(9)139<140> = 361192209361<12> × 1576375569625015882582733569<28> × 158068175129660699440495594381607684640976655757346105877589668692644831393506386802023923223289218511<102> (Robert Backstrom / GMP-ECM 5.0c for P28 x P102 / October 16, 2003 2003 年 10 月 16 日)
9×10140-1 = 8(9)140<141> = 661 × 434132891 × 246245887325083<15> × 637935136493979035228233<24> × 163877972349517148682713565578488753<36> × 121829445867639276545602652290090242139072129211660761747<57>
9×10141-1 = 8(9)141<142> = 3088098192434236868514129081431<31> × 2914415099250980525087836816093806062043396989421160680186718286929717431403185618664074628448524836833717733529<112> (Robert Backstrom / GMP-ECM 5.0c for P31 x P112 / October 28, 2003 2003 年 10 月 28 日)
9×10142-1 = 8(9)142<143> = 72 × 13 × 29 × 199 × 2371 × 185621 × 736259 × 738845467 × 1270904911<10> × 31160357553605870175480621392732932109<38> × 2582222260477366821886915879806161182313498997237022181289217500581<67>
9×10143-1 = 8(9)143<144> = 227 × 3333067 × 1189522355611543758822100810964928256357991373554799891947489952464823084738919978913363635904288488333037192931627131280917098580141311<136>
9×10144-1 = 8(9)144<145> = 4188054211417<13> × 4267778689730745828517<22> × 294984638384826331048078719260608561<36> × 10170021111697037216236753300358009041<38> × 167844482547367204773786131605885255691<39>
9×10145-1 = 8(9)145<146> = 467 × 4363 × 44171323878379658418244523614725934113071718033826399826063142416691656184157120343790321670304256986799154462702470305827522759274628335119<140>
9×10146-1 = 8(9)146<147> = 373 × 22739 × 117485247043<12> × 275676723385625913658191645377<30> × 291750980771364417216161647598876663509219<42> × 11229658739992996031059261706955788780792567645986856808713<59>
9×10147-1 = 8(9)147<148> = 245811829401098369<18> × 44854455549564788096962189425408270743305049<44> × 816270574399695328594421683160134958538390249344775592075492092574375764259533960310679<87> (Tetsuya Kobayashi / NFSX for P44 x P87 / 128 hours / July 10, 2004 2004 年 7 月 10 日)
9×10148-1 = 8(9)148<149> = 7 × 13 × 47 × 1069 × 1873 × 22189 × 46861 × 367823 × 3179107 × 363937864783<12> × 90855262284385309<17> × 19019704578369356396789725755065110611923659<44> × 13744007092186107278415663200174774248999883123<47>
9×10149-1 = 8(9)149<150> = 63311 × 120680249231<12> × 4845174713445464969<19> × 1769758061206129497344911<25> × 2370379070062373950322764021016099899973<40> × 5795434379521086306033002324642348356418074944582677<52> (Robert Backstrom / PPSIQS Ver 1.1 for P40 x P52 / September 29, 2003 2003 年 9 月 29 日)
9×10150-1 = 8(9)150<151> = 757 × 5815181 × 242995654571<12> × 30296635088429<14> × 51378297061009<14> × 558665640875791<15> × 1405847460733497973<19> × 125433387853024282821592391909<30> × 54866526792220496038143451174747976388551<41>
9×10151-1 = 8(9)151<152> = 43 × 14827 × 456116917 × 179731384178285533302271<24> × 1721950516998024380415578396384985182297058118806541188405885728003478172983414981063001642029372359426306786893637<115>
9×10152-1 = 8(9)152<153> = 19 × 31 × 1291 × 415543 × 2402214527<10> × 4516945831<10> × 135999956282039<15> × 91827063621559306927394843586328922240326571839259783<53> × 21019329800602844759367800353109139799041028297946332303<56>
9×10153-1 = 8(9)153<154> = 83 × 439 × 1321 × 255239 × 732571543742082600902906509573882920452058244205322963068764577538584500131043321313808298931759821413544052372970501976655713377851769823133<141>
9×10154-1 = 8(9)154<155> = 7 × 13 × 17 × 23677 × 40949 × 4275127 × 4369427 × 7243627 × 3621327289<10> × 189330424333774697273<21> × 247502724582139745843<21> × 108112340743472502401674533227<30> × 24171811200974383408786576437714478568683739<44>
9×10155-1 = 8(9)155<156> = 20201 × 1225603 × 884030473598129112046273401306743817009226878392237244963203638811597<69> × 41119951100362876196136581974904931337399314543041289673940222500296800769089<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P69 x P77 / 28.22 hours on Athlon XP 3000+ / April 4, 2007 2007 年 4 月 4 日)
9×10156-1 = 8(9)156<157> = 61 × 67 × 547 × 1427 × 1783 × 2713 × 5851837 × 29488903 × 5410076687<10> × 774480196801059841<18> × 4849502882804430492203<22> × 343515729084853263740131391420318235853<39> × 484191331287271863114267578513481652669<39>
9×10157-1 = 8(9)157<158> = 71 × 63884014085651210449<20> × 19842297825920895868076869512333486451963849498579143936408592898904669063601930034114973826323985369401002583755484203670540836150708281<137>
9×10158-1 = 8(9)158<159> = 23 × 31588957 × 64560983 × 293611531788139<15> × 822776055137967966312899<24> × 777331654853277695714263410548853568823<39> × 102175823331241199704581398426177346644437517656619757456424151741<66>
9×10159-1 = 8(9)159<160> = 151 × 2081 × 37756997 × 2749349496945658330354039617246556963<37> × 275909138843910536233458866490589939907450080666251250831272212920006003585355634397268342209549828865520254039<111> (Wataru Sakai / GMP-ECM B1=10000000, sigma=1818651899 for P37 x P111 / September 29, 2004 2004 年 9 月 29 日)
9×10160-1 = 8(9)160<161> = 7 × 13 × 109 × 997 × 502441 × 156742903 × 394460147 × 121000994263045222745790261071<30> × 8828242660013348139969025855696091<34> × 274245916962662936878665224768927142918789143313534242324532556092973<69>
9×10161-1 = 8(9)161<162> = 19719536661599<14> × 364476297372081551843<21> × 350687078928628930904081<24> × 357072782623657793890645461337532959671489824735156071156272420215234324125007941980132527605527295321147<105>
9×10162-1 = 8(9)162<163> = 198347 × 580610829637<12> × 546035880317951<15> × 47707790680126762810965842706145250687293836957191<50> × 3000000000000000000000000000000000000000000000000000000000000000000000000000000001<82>
9×10163-1 = 8(9)163<164> = 9311 × 9923 × 1563631 × 2134098490901084289819240413<28> × 60061438682395359593398744400877001<35> × 4860251353176521897528790975585779837716210646651067100277891814302127723420307300678561<88> (Sander Hoogendoorn / P-1 for P28 / September 7, 2004 2004 年 9 月 7 日) (Wataru Sakai / GMP-ECM B1=10000000, sigma=1023421099 for P35 x P88 / September 27, 2004 2004 年 9 月 27 日)
9×10164-1 = 8(9)164<165> = 3623 × 1179592811783<13> × 396556147820323<15> × 7877327463333877<16> × 81901814233106783<17> × 85709168379882713447112804288382078260973732635217<50> × 9603679718327062465169317706939506976097026342997631<52>
9×10165-1 = 8(9)165<166> = 1139239 × 3500008777892854273507<22> × 107006813752674037531328510242074918993021462449577391740200262799<66> × 21093424816570316132097077241926854067827836439105917046567434042812717837<74> (Sander Hoogendoorn / GMP-ECM for P22) (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.34 for P66 x P74 / April 14, 2008 2008 年 4 月 14 日)
9×10166-1 = 8(9)166<167> = 7 × 13 × 103 × 2917 × 9532847 × 2092564310751650241184817<25> × 55817750862408931155328183<26> × 1221232670144955999083128837<28> × 2420779760434954733153372027991540924036326511578658182920267479056684422091<76>
9×10167-1 = 8(9)167<168> = 31 × 319757 × 754329661637<12> × 120364819700553846638797060139385759413189559742346095183692229222962686316649830243684679949703382813179419866699952709431562628548833450954366190881<150>
9×10168-1 = 8(9)168<169> = 59 × 367 × 84631 × 440527 × 981319 × 3037200296737<13> × 223430768225151152811482584017892586519419195709078993848314952801<66> × 16741555597023462687292691535071815284183972598585064174887691519199853<71>
9×10169-1 = 8(9)169<170> = 90911 × 303273671083<12> × 561921476752175312039<21> × 5809192057492029790189790649473348809407304780607105559887659626527691939992391503927629486440677147928852285888430859909715432233957<133> (Sander Hoogendoorn / P-1 for P21 x P133 / September 7, 2004 2004 年 9 月 7 日)
9×10170-1 = 8(9)170<171> = 17 × 19 × 29 × 223 × 977 × 6563 × 14653 × 1661583485297<13> × 54023475012308291507621<23> × 334207792110584172091449693805941060369350577909373<51> × 152859471551123480004843160977546975097365506330010478081244364258113<69>
9×10171-1 = 8(9)171<172> = 136963579157<12> × 429373702687757<15> × 42679129855580064934964485511968838445123658843<47> × 3585802901069120875169780945172816193378262142753545298800676974244410697305766876766285241909080157<100> (matsui / Msieve 1.41 snfs for P47 x P100 / 78.73 hours / May 29, 2009 2009 年 5 月 29 日)
9×10172-1 = 8(9)172<173> = 7 × 13 × 43 × 17309375399<11> × 147929130938493357761877823<27> × 1207510782643354586857133772644363<34> × 1104092571873395520541318241400785866473479<43> × 6737535295047400422939574997854853936889567773370251541787<58>
9×10173-1 = 8(9)173<174> = 1289 × 1997 × 34668071675443361<17> × 3806940299291622726460350337947914704889277467532053374128676991<64> × 2649145276309295977725794028033536754856664922424512618104600287851523960480215455939453<88> (Serge Batalov / Msieve-1.38 snfs for P64 x P88 / 20.00 hours on Opteron-2.6GHz; Linux x86_64 / October 8, 2008 2008 年 10 月 8 日)
9×10174-1 = 8(9)174<175> = 2741 × 964927 × 57704100757<11> × 394211670918873961<18> × 78212992366947111793224659<26> × 664715300063407687268091985902707716360249006586927<51> × 2877320783415929720655717276789004987147764455948869723172437<61>
9×10175-1 = 8(9)175<176> = 13121 × 38329823123<11> × 4599492339001072307<19> × 38907099798570231897603470622116937108505920099498106776524393816994508400543016486790808673861173494962222191538268942891622488072438703124679<143>
9×10176-1 = 8(9)176<177> = 613 × 1304488873<10> × 3751676989<10> × 3300924483140581825965792499050421<34> × 6966991598609698357143166308824300493706869803<46> × 13044737394181493541891572756624031685359114648899761380720804186090822001393<77>
9×10177-1 = 8(9)177<178> = 89 × 757 × 2795376519729848150784923706882701877318922481507609115407740172075186231071<76> × 47787719999108578060151819968036562451065721814882830579492456551763376466710619837746260674550853<98> (Serge Batalov / Msieve 1.36 snfs for P76 x P98 / 76.00 hours on Opteron-2.6GHz; Linux x86_64 / August 21, 2008 2008 年 8 月 21 日)
9×10178-1 = 8(9)178<179> = 7 × 132 × 113 × 250451 × 278917 × 4115541273187<13> × 81816795564710189<17> × 12594245972471028228269<23> × 186182086789309759054543090955981<33> × 18277346698490628671886518504139713<35> × 667865368081651529733187254777823845221359793<45>
9×10179-1 = 8(9)179<180> = 2326512347<10> × 7735574032453<13> × 13523336658151<14> × 3697947499634836846572228151356031258255841276556757089615402605153955880412188967672797717739121202635047054593576835933232331288153309349852239<145>
9×10180-1 = 8(9)180<181> = 23 × 3967 × 180331 × 381318197437<12> × 416998450980192814055629<24> × 564094907179255318210761991225027<33> × 19496154286820318385804086168513204587<38> × 312794405595744596969514780116162611260899355352176462266677835197<66>
9×10181-1 = 8(9)181<182> = 2347 × 18121 × 14881545317<11> × 18520231788365026399039<23> × 17738923518084523699884246605505981299970476762186445669696079694627<68> × 432838167071524524325390063835161654015589966865342977397547062601404043877<75> (Sander Hoogendoorn / GMP-ECM for P23) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P68 x P75 / July 3, 2010 2010 年 7 月 3 日)
9×10182-1 = 8(9)182<183> = 31 × 283 × 883 × 1597 × 184553 × 446028257 × 14076488831<11> × 16347505193<11> × 52155548314181870086767536446091569<35> × 4542139018383436278421775174894971465367<40> × 16212071708719648632278491157629276678664053603353596806375780717<65>
9×10183-1 = 8(9)183<184> = 9587 × 44803933 × 328987231 × 2440572839378229347582719<25> × 26095932910686069765618451295488481733475751249529060617603572778843532932969652780988006968716186630596900105613502368966849560241018262121<140> (Sander Hoogendoorn / P-1 for P25 x P140 / September 7, 2004 2004 年 9 月 7 日)
9×10184-1 = 8(9)184<185> = 72 × 13 × 769 × 2473 × 17929 × 8354651 × 1795678883533<13> × 1896995229026274291292255877683<31> × 130361051090105258563806462474876437765791<42> × 1116928758657913030746751251796032617863380560312387775178668625667297149218675001<82>
9×10185-1 = 8(9)185<186> = 51506797 × 6651080365041166203291134547420211961<37> × 13635914747983825156232567934596474089<38> × 192664408261061364385641328101036179407234081077935012206807836686745494869074119500810375175750225723323<105> (Wataru Sakai / GMP-ECM B1=10000000, sigma=308127902 for P37 / September 21, 2004 2004 年 9 月 21 日) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=250000, sigma=7824051411 for P38 x P105 / February 18, 2010 2010 年 2 月 18 日)
9×10186-1 = 8(9)186<187> = 17 × 863 × 9439 × 503699641 × 1290996163<10> × 48503123144589502741752878729057<32> × 122794781146491779173462117695893007175726748617613527<54> × 16780720353433491782468421724289387703811042473187542015809353308503757977083<77>
9×10187-1 = 8(9)187<188> = 107 × 3091427 × 119847129180121192841<21> × 386912236682092373627959407825258014879733519773<48> × 5867588321910159709473080934766101502074837748466527042095982698923896594410077844851777703274075380367412867987<112> (Sander Hoogendoorn / P-1 for P21) (Jo Yeong Uk / GMP-ECM 6.3 B1=3000000, sigma=5073000498 for P48 x P112 / July 7, 2010 2010 年 7 月 7 日)
9×10188-1 = 8(9)188<189> = 19 × 97 × 140395141 × 770083117 × 4819894883232336708373<22> × 1001770522456725752538019<25> × 3024629329448324924475066105061<31> × 380774519116859555009563691113510103<36> × 812234892273730400146403072480506371926158526721772968889<57>
9×10189-1 = 8(9)189<190> = 67 × 133187 × 2078087862871<13> × 234621664993637<15> × 5363095884001110231789672199<28> × 691358354460421844467019209205871535890349373591<48> × 557898347387098440001580823256703267645769945387362854355970765008372293831647517<81> (Sander Hoogendoorn / GMP-ECM) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P48 x P81 / June 26, 2010 2010 年 6 月 26 日)
9×10190-1 = 8(9)190<191> = 7 × 13 × 157 × 40093 × 6579763843<10> × 7544219843<10> × 10684622854603<14> × 14044244326009837<17> × 2576385525477167077559755888656850563188888467559516732456150855611<67> × 8187283801493673414908347666397742188102045797947618728529480372841<67>
9×10191-1 = 8(9)191<192> = 8267003 × 541664839 × 55178925990231014652186549222321181933859304676047173<53> × 3642424226862508398848580350600822774316487142753533424410444987210108318647092527767721916368395320150392755767831321109839<124> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P53 x P124 / August 6, 2010 2010 年 8 月 6 日)
9×10192-1 = 8(9)192<193> = 71 × 2833205979816856630365091<25> × 225175496540201364974370054300058530191<39> × 187647065404458407478575579255133377195945562460800825959<57> × 1058871123868630697170279213402229282716267254260527378849368062541824011<73>
9×10193-1 = 8(9)193<194> = 43 × 1821585162697457488304296102273254935173081<43> × 577907847913674910737796883693373565504125011795363899114213268519<66> × 1988227065562338941228938824773608620242017418041162968604820660552549013425070142387<85> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.36 snfs for P43 x P66 x P85 / 161.42 hours, 9.99 hours / September 17, 2008 2008 年 9 月 17 日)
9×10194-1 = 8(9)194<195> = 47 × 832 × 1129 × 6823 × 23264344193<11> × 199771102072963<15> × 18929164970412319489<20> × 336014103925942214219<21> × 1283729395505707376279023867054907059411215130486873257049<58> × 9508964463243707970091052874294858739920079951513408696616239<61>
9×10195-1 = 8(9)195<196> = 1093 × 1523 × 6053 × 5800422267260147<16> × 153989872412992395581191134339026335265738004835304876698908351736754429755549700376348268128472842956417110081496940644806387980047471097189853728379962366481054768297951<171>
9×10196-1 = 8(9)196<197> = 7 × 13 × 1019 × 187379 × 376657 × 3756512436102370044614142122779<31> × 2065995084482425229722350759373801066391<40> × 155312880582011749094355956606205409844262829<45> × 11408758412526373980350866244775600239574193508591183341548280948117<68>
9×10197-1 = 8(9)197<198> = 31 × 277 × 27450632285963828291729<23> × 1489832074586813735513236513490350941226266664547<49> × 249395759998680294566400124387703608743349127663629119243637<60> × 10275957717434739278151927137269035074845167225336546287885244467<65> (Wataru Sakai / GMP-ECM B1=2500000, sigma=2672822829) (Jo Yeong Uk / GMP-ECM 6.3 B1=11000000, sigma=4383276631 for P49 / July 26, 2010 2010 年 7 月 26 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P60 x P65 / July 29, 2010 2010 年 7 月 29 日)
9×10198-1 = 8(9)198<199> = 29 × 643 × 345221647 × 477752776081611404646500077456166023<36> × 18189468758616411279538180668857592713662364213329197479<56> × 160883788276934627554030138896337212420228454979353247171126722797232798841636724406070681610983<96>
9×10199-1 = 8(9)199<200> = 311 × 18816601 × 7199849885356048147<19> × 8780607192536057363<19> × 6189868364159015753089<22> × 653013029588688183402047290771742842951<39> × 60185198005340312093913851920027593244762401225251579516624254991791230274129125334702673471<92> (Sander Hoogendoorn / GMP-ECM) (Robert Backstrom / GMP-ECM 6.0.1 B1=1174000, sigma=378789720 for P39 / February 5, 2008 2008 年 2 月 5 日)
9×10200-1 = 8(9)200<201> = 103 × 163 × 313 × 30908839729<11> × 52687875503<11> × 271975894534095225991176221835439<33> × 20990446375297618944778008551499605099634313008134910244350187<62> × 18421621929042446518945642871526259144172571872058046358421612697832167819925377<80>
9×10201-1 = 8(9)201<202> = 2294564964667<13> × 12476080853161<14> × 21526411452773693247649336460817717544721<41> × 14604689683713612675759350975639688928844629281874513442158803123780191746093165741470914570714379415687044636713755667697834509576658037<137> (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=1051494959 for P41 x P137 / December 24, 2013 2013 年 12 月 24 日)
9×10202-1 = 8(9)202<203> = 7 × 13 × 17 × 23 × 461 × 42703 × 112455688781<12> × 608906393745935368545043<24> × 14652714986922379314736190545012031169061014220429491786130421653<65> × 128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187<93>
9×10203-1 = 8(9)203<204> = 359 × 397 × 1090121453<10> × [5792721746949381263246555450843623097856424498764256327126681154950325860138087923320433963121060453434022738399576909614780205538350127610792728900999389072499561154212711073600190303340321<190>] Free to factor
9×10204-1 = 8(9)204<205> = 757 × 341667013 × 3184685509<10> × 4357048548962608484941710525445154377541575699<46> × 216203292699210532299880330172360087254034249311<48> × 11599047429948021078058597960005614850022606973185675972655317149495105361550724254328327239<92>
9×10205-1 = 8(9)205<206> = 2162664653<10> × 1845200848424553733<19> × 82971532256549192147<20> × 23520974358253398538035066583893467<35> × 387368136607675618892389066306887433505264677<45> × 29833305015885463901134120844847304459919707565722390106565865986739908090859987<80> (Ignacio Santos / GMP-ECM 6.3 B1=3000000, sigma=280799415 for P35 / September 14, 2010 2010 年 9 月 14 日) (Dmitry Domanov / Msieve 1.40 gnfs for P45 x P80 / September 16, 2010 2010 年 9 月 16 日)
9×10206-1 = 8(9)206<207> = 19 × 60083 × 83301251819<11> × 1141870773049<13> × 5959534140575605571563<22> × 23917741750007011930592110720920008759435096557<47> × 1098742369919843494185783706649927078558709517031491<52> × 52922512935658165935800313758093233844200674356148904094417<59>
9×10207-1 = 8(9)207<208> = 31178093 × 437355437 × 8818647100342200893<19> × 1128079654607137676707<22> × [66346298944020392603484497612666103081441614843048626911193836751881822551731135061069119296731745472582789384820074691840937730214159201572718886363889<152>] Free to factor
9×10208-1 = 8(9)208<209> = 7 × 13 × 347 × 1321 × 32089 × 133881109 × 2813505323<10> × 15058978723753<14> × 8380200882966911<16> × 32926128941294964210169<23> × 32165325017020156619259454561<29> × 1335571157005293313685597645833240585336319076853216277941261580514907200064107415536254079056908687<100>
9×10209-1 = 8(9)209<210> = 11071883 × 3100246223387<13> × 791281198830680471<18> × 99298829407375475835861241993546194794503260649<47> × 335752786330490779746640797038024828325554318519<48> × 993871491604682044116953573701678592826498177135926957901481761489225768438719<78> (Serge Batalov / GMP-ECM B1=11000000, sigma=3051180308 for P47, Msieve 1.51 gnfs for P48 x P78 / May 27, 2014 2014 年 5 月 27 日)
9×10210-1 = 8(9)210<211> = 167 × 3851 × 69233 × 2172689417<10> × 522970842054278052596796307<27> × 4105406260953967323411421624379333441658282336124257972514962287<64> × 43331937082027356896277786604653850042609738130660234281339823494576285875232909161815897043317493103<101>
9×10211-1 = 8(9)211<212> = 922059280500261049<18> × [97607607128221426357377013488961714417672649880576719570712379297973765260634609757666743202155071041935920974507857219886770282749305052414640900808516085867306486791876528928802932236198738551<194>] Free to factor
9×10212-1 = 8(9)212<213> = 31 × 218279 × 4744051332993243749733574090207<31> × 203990612149063181178190673768547952947112612321147898789683681650672394753<75> × 137438782475638975806192991538352292249827056198718154288777207152314240032252300954283279655853288681<102>
9×10213-1 = 8(9)213<214> = 293 × 31517 × 297630677 × 653240602737601<15> × 2763180643414756163<19> × 1880839632718006855987957867<28> × 240517498236320119968635920027<30> × 179481389251375241524195452694409<33> × 22343541377353884509643293353805591669647127166940550303134256458298751571009<77> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3144849970 for P33 / November 23, 2008 2008 年 11 月 23 日) (Sinkiti Sibata / Msieve 1.38 for P30 x P77 / 46.3 hours / November 25, 2008 2008 年 11 月 25 日)
9×10214-1 = 8(9)214<215> = 7 × 13 × 43 × 149 × 35491 × 132967 × 319469 × 406859 × 3286888271596093<16> × 2762969980683717258321223144209234268699368337958266176306842668501370570391151817<82> × 27710893469268378687085304936496533197645542536668954891993497757911796495887926681123282141<92>
9×10215-1 = 8(9)215<216> = 1594837 × 3084860091146129<16> × [182932443168146329536107439965379476609018081738136475800750573255026519004566909056500589766164538310841930793505582466992062465914156687385003217573278263261011693459436670795419625561766346963<195>] Free to factor
9×10216-1 = 8(9)216<217> = 61 × 479 × 1537022713<10> × 12042349012118749379843<23> × 5580815161537522052816552016371<31> × 60631261945090711190778038575214536541054929<44> × 2050264538747272760451120621063903142800302077<46> × 23987308437233184406133324376083302948918445967347350246327033<62>
9×10217-1 = 8(9)217<218> = 4283 × 9437 × 1577290686429983687836459293964961<34> × [1411720564399112483471084781044967565528016798392234290981345680970916119805289999619210137081639694786400613276406019352676005253348050274461896592584529492199240348443770814929<178>] (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=421968920 for P34 / December 18, 2009 2009 年 12 月 18 日) Free to factor
9×10218-1 = 8(9)218<219> = 17 × 941 × 60259 × 78121 × 470317 × 524086391 × 11861956980462821<17> × 14770997282202389<17> × 4194875121286899383<19> × 2554805335672876431983<22> × 26506062415929309987997152493<29> × 33005323977166274796073777418225748488133943<44> × 29515385542052210711260544097911301044937947161<47>
9×10219-1 = 8(9)219<220> = 136523 × 3275933 × [20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561<209>] Free to factor
9×10220-1 = 8(9)220<221> = 7 × 13 × 7482121 × 228966966455977967620471917769017793<36> × 25016448656495401004069927663455363536577225267399577915957403823231<68> × 23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923<110>
9×10221-1 = 8(9)221<222> = 89 × 106488463511<12> × 551029570561<12> × [172335614263112567179081867466993970765225540021715938315260756668337285450737775572869450031393778581870591318194452990592879792164909246568202384476242199160419692269526807699774717892321366997121<198>] Free to factor
9×10222-1 = 8(9)222<223> = 67 × 6883 × 50769977 × 966767341958861<15> × 822533722631126307625175578433<30> × 1934766413697553399092247719779<31> × 80515494338141194672046088158648781419<38> × 3103125095145859264337050293405093023943285127966189415280642637135368146774978576169338417355259<97>
9×10223-1 = 8(9)223<224> = 6997 × 633790652387<12> × 20294801406914642962244218873248543299149735371441537563178842213852148072109436983033892161885256828504303661989445893971612432873129501966448138296925307809568065372164387244393430943718879147664031493401441<209>
9×10224-1 = 8(9)224<225> = 19 × 23 × 181 × 3407 × 127103 × 3483791461<10> × 7807361641<10> × 8118226003<10> × 954027040968047<15> × 10210034882989784864647209757<29> × 2439916668000842264184198385585361045416127281052552280029060389<64> × 5006959449134196242766265868072792925075855906976643628238419170429812879439<76>
9×10225-1 = 8(9)225<226> = 853 × 1049 × 55157579569<11> × 133538941942257663803<21> × 49761553125602982208933121512742791<35> × 11463956154931965286797745710924129499153087417812847999013<59> × 2393736906702047287437000757732253469057651184336837941798408040580556794719317538005566849654107<97> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=894971310 for P35 / October 28, 2008 2008 年 10 月 28 日) (NFS@Home + Dmitry Domanov / ggfns-lasieve4I14e on the NFS@Home grid + msieve for P59 x P97 / May 14, 2016 2016 年 5 月 14 日)
9×10226-1 = 8(9)226<227> = 72 × 13 × 29 × 59 × 10243 × 8139497 × 47825881 × 319042484686421<15> × 8860269191229929657<19> × 831972291458432430035984753<27> × 339493482302125699689696823651386878401<39> × 183196997235114666313664862887412748867877758421<48> × 141583048280838478129901762617470802340141205501351431287<57>
9×10227-1 = 8(9)227<228> = 31 × 71 × 401 × 613 × 5279 × 9710839 × 1506283955768878297951559<25> × 21542810126742033377137661884795289035742458338164984788784814332187585460966303502744555308850123798452119220786033876609974398994353793852854006302730531280828689067948109292411408837<185>
9×10228-1 = 8(9)228<229> = 919 × 967 × 295357 × 171141301 × 5078181337<10> × 3451900116240059527310349962515641788338540306292431489892874508205404626512683628520178446569627<97> × 11429625511698592200629533241927411979327821030913432739903978629728413991676984595399531610900916380341<104>
9×10229-1 = 8(9)229<230> = 197 × 208440677 × 1189638653569<13> × 1894742524089853<16> × 81036479966432843<17> × 49931612314311537707693<23> × 67387210716432592896081650429078156564311<41> × 6243050577365052581815882169888181821426803805681795893<55> × 571212953652346708852367194795436478812329554530967996239<57> (matsui / Msieve 1.43 gnfs for P41 x P55 x P57 / 251.99 hours / November 11, 2009 2009 年 11 月 11 日)
9×10230-1 = 8(9)230<231> = 832033003 × 403233877351<12> × 1577831737746491<16> × 66935581832507131<17> × 5185040008134360225023375060014351<34> × 10929766662867956939358630793031023525224309137<47> × 448192115145409256752005959887688729242511151091393953380282171310853902822633424231824418287457229<99>
9×10231-1 = 8(9)231<232> = 757 × 72043 × 267413919813067483<18> × 8396785017878813402797147<25> × [73495000374915762859216129340875350621606641556304628851630109938131596023912677555409049768864357258781866352609555924461782303651497588176040351979174743012122623433649443058580049<182>] Free to factor
9×10232-1 = 8(9)232<233> = 7 × 13 × 191 × 419 × 176989 × 342803 × 3080389672652381470662675187786673261869<40> × 805614854347532273657889152825813219506231<42> × 273073929335371915922432805053316071687914686044309883829457031841<66> × 300572659388749176537866923029182472055638130513953259347940318716277<69>
9×10233-1 = 8(9)233<234> = 1163 × 20690127509876948541763<23> × 37402413528078313225157455296433627979815209705817642004489823300246185036042952351622004569082719963544966038837562863463991077653816853769655709533603986694498817862617509179644966975536274976215393981970271<209>
9×10234-1 = 8(9)234<235> = 17 × 103 × 151 × 787 × 983 × 7717 × 1343893 × 5364595726158023<16> × 698810987349616407838127758561787<33> × 236408012483724037920438356017353423704940485863994051049626928720839267<72> × 4787172289684415190372122785770632962010454236261129833023534339757976679455179640719536246397<94>
9×10235-1 = 8(9)235<236> = 43 × 83 × 2689483 × 5892443 × 58191560460894047981383313738887921<35> × [27344611942873895787917311852899786249261776955362309600956203248188072656297980109517084855872487166215533244863997401609896656699572113589466043017774649115656658703302995084579323079<185>] (Ignacio Santos / GMP-ECM 6.3 B1=11000000, sigma=623682320 for P35 / September 14, 2010 2010 年 9 月 14 日) Free to factor
9×10236-1 = 8(9)236<237> = 229 × 1801 × 2322347 × 269136729617782632743<21> × 525337354976588234359540934329<30> × 50730503927128935534261432720820845779278829698082773940411<59> × 131004366812227074235807860262008733624454148471615720524017467248908296943231441048034934497816593886462882096069869<117>
9×10237-1 = 8(9)237<238> = 2038378317634843<16> × 16458968745184537055041<23> × 2159354328505218434763566894890844831<37> × 124231344744201153919364569063533864182777383411266889775463564074435226169459698293233029236580598968351185296036589989745373926734676124646349848201139449407154483<165> (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=2019345652 for P37 x P165 / January 8, 2014 2014 年 1 月 8 日)
9×10238-1 = 8(9)238<239> = 7 × 13 × 1553 × 438721 × 7141775796359<13> × 642459091110046921<18> × 2909223957003733935959638857517450326431467<43> × 18121551992896711422356563612737888923327762681447<50> × 6000908468590146007802970302085578213299657647019234436854511092567500093029441038440754743913961970037423<106>
9×10239-1 = 8(9)239<240> = 719 × 3714202444243<13> × 337014081628848980650804962314582987701723478832378345683527803207293332544866460706041453711708004510945624606887985056689566478244464427440359623860252710513541727202497061662621374053508032473519582460497645264664094703947<225>
9×10240-1 = 8(9)240<241> = 47 × 107 × 587 × 129457 × 97356367 × 23194910287<11> × 44209021499<11> × 11890818970927053203<20> × 2047296729179266187110579273833644931841<40> × 944274051192262206631103925845322418206838969<45> × 14024472877652688033418848086042342088954204619<47> × 731732109565129767405444811518543619679358772542643<51>
9×10241-1 = 8(9)241<242> = 199 × 17921668997152761272351<23> × [25235445794948821739748678732191479860646613915310649971905671891079318635081668702935911295793325871652144818294111071512155813738294274363970467769114647418288047846110437398740880356716473955611500403122023243195351<218>] Free to factor
9×10242-1 = 8(9)242<243> = 19 × 31 × 695084724889<12> × 2533733441819<13> × 5680551281721563208659<22> × 67236972872290888335676434473866511834711951165578089027465183928012262948453258565151<86> × 2271589796011125260933021182971065840770325771072812443357936760347860632353214061224348430869129003298879789<109>
9×10243-1 = 8(9)243<244> = 21874481 × 66131837310307559141778487480493107856542594017224928411277770245846665669403<77> × 6221486500765650681748200556437692560926457434114322812952883282505160895367768897268883784861247071526097233574950034555916608119515375191331045259329450567293<160> (RSALS + Tom Womack / ggnfs-lasieve4I14e on the RSALS grid + msieve for P77 x P160 / May 28, 2010 2010 年 5 月 28 日)
9×10244-1 = 8(9)244<245> = 7 × 13 × 43711 × 2655233370133<13> × 92771425356838998606541<23> × 2294796717664213509541276266917758467689777187014509<52> × 10056194912293669804719011098323636255061719884507348567986171070655047<71> × 3980297609513933332382807187105798139082232720008215213498031449569053628602395321<82>
9×10245-1 = 8(9)245<246> = 32111117 × 172807608592522667<18> × 477686215192476748920251227<27> × [339532637756691064099979297959976382666189473964798133778656689443265687015691551665577564600322675698680258500385768470772877278355959799098195918708103977987748420059618510280852951228327296483<195>] Free to factor
9×10246-1 = 8(9)246<247> = 23 × 19553 × 2990366970937067399<19> × 166235481615022500575018646587621550923191<42> × 40128811045536569808228286660052417775119260016039979721737391386749724030769<77> × 1003221353484891513387954898308810381727983558088177158306275171844453418150696067538783658365482703827401<106>
9×10247-1 = 8(9)247<248> = 547 × 27920471 × 466553086942912739773<21> × [12630815039449560205963291928005946973269477358319164351123083186295835583586818232098279066553124847974445214981296311324549796426364058808409578975294269836041018310628409790287918526397585938651600317651381893456399<218>] Free to factor
9×10248-1 = 8(9)248<249> = 2767 × 5449 × 17167 × 57571 × 158941 × 64072783 × 2602864396977816164601828457<28> × 197691309554911543479077660268414631217739335706830786585014015880624021918384268676142039645857<96> × 11525763706642949500110430345615582532053120160077139973457388941551304686760716557918497750074407<98>
9×10249-1 = 8(9)249<250> = 1239961 × 17567289930891241<17> × 2211131180516999698877<22> × 132852679081112049264025722783994751<36> × 173971508153106043979381596158458837<36> × 12401770836281816440614430558156356059434053950562553627081<59> × 651903118776272291480393446015384353260696868728533727242356292283467348358521<78> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1540395319 for P36(1328...) / October 31, 2008 2008 年 10 月 31 日) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2491863350 for P36(1739...) / November 2, 2008 2008 年 11 月 2 日) (matsui / Msieve 1.41 gnfs for P59 x P78 / 226.30 hours / May 29, 2009 2009 年 5 月 29 日)
9×10250-1 = 8(9)250<251> = 7 × 13 × 17 × 1471 × 7673 × 600701 × 3599650081<10> × 31612646761<11> × 634218826805839667438296844687<30> × 19233942138039946177234105344928717<35> × 3876544332029444008036492867365402990466431683<46> × 16412899871082734672605658515241235597824962933<47> × 97153246083586305759374376504412500632762391535023918322219<59>
9×10251-1 = 8(9)251<252> = 25027337267<11> × [35960677334488249856212720050527299269163598793324240696580212829398636161352849682680547863493975425635918090494800539022120335099729968409028033417599126806860559817779675426627557741778203687640423565639720597289060379209377280175524315397<242>] Free to factor
9×10252-1 = 8(9)252<253> = 179 × 2927 × 3187 × 292983186719575321<18> × 5647443464815144203568297<25> × 1775837843273505241987971241538076876967<40> × 3460596075084905650466669068797064557997911238583417117155774526018030889091019<79> × 530073245617957365009268096007895652834218165933718492937784526257953798248555640269<84>
9×10253-1 = 8(9)253<254> = 6809213 × 1504443089<10> × 13787458908664269579677<23> × [637214419813345381623582058351385514761429359247194690390141831026842106136135052779775418117358598715878326743941135487780505604548660909451539379907416495127711658001188361926870695446194999576762451263045305207991<216>] Free to factor
9×10254-1 = 8(9)254<255> = 29 × 19573583 × 103934947 × 322172298116923693<18> × 148738622029916094823<21> × 1578349333128622133308952388255710631082915998992096274067434685677424530735030916200883893133<94> × 201696100115584238393124824460099143584753960141821190136295028657532443918821279751573958245772262039795113<108>
9×10255-1 = 8(9)255<256> = 67 × 79079995212176436924678907<26> × 321530786398558852998907635460027951<36> × 288710858605506615195314701757164872079<39> × 18298495829842078682637807148872885797179034186728330933469644452681342811521827144916564211949441219056503273481157035605485468948084125785526056633673199<155> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1110199049 for P36, B1=3000000, sigma=2093494911 for P39 x P155 / February 27, 2014 2014 年 2 月 27 日)
9×10256-1 = 8(9)256<257> = 7 × 132 × 43 × 227 × 541 × 601 × 1693 × 3709 × 481153 × 1688691118297<13> × 330470429522606563<18> × 148983787999561869461523139665361324139<39> × 161435091255666683067612614137458155297916999164385294636452087869504653287195627<81> × 591119036400766694459860015179609950216121761960385602854728605249929171033537198231<84>
9×10257-1 = 8(9)257<258> = 31 × 56093 × 113169594233921775105667581270054668671<39> × [4573433715062110605840328531636055663845343444149353909827869756842782418455462763272712593308922128566103142333063470783314468832603127823372633720269171838440887314100358711405038713473681724962205564602371497643<214>] (Serge Batalov / GMP-ECM B1=11000000, sigma=323121621 for P39 / March 2, 2014 2014 年 3 月 2 日) Free to factor
9×10258-1 = 8(9)258<259> = 757 × 428657 × 1109161 × 4750400686003697<16> × 30976605475761427<17> × 3862845783794364415817<22> × 4154462659947867699343214598881767<34> × 42631129647954533977037566338810486942407<41> × 1005832896845130922388650295627982989490898661<46> × 246946653468267095788453656414425393826920686199248335419564218437793213<72>
9×10259-1 = 8(9)259<260> = 9875644271<10> × 149638051159<12> × 29266833064460507783125316811706559201<38> × [2080938751271747344012902297788097975110446888671819766716719703735632773822053903590186078565752693364322848743836819442044507596733781993537734315840506038439836443149250824112860940096462233181339991<202>] (Serge Batalov / GMP-ECM B1=3000000, sigma=1850900544 for P38 / May 26, 2014 2014 年 5 月 26 日) Free to factor
9×10260-1 = 8(9)260<261> = 19 × 31627 × 273253 × 48049664319064769869<20> × 15662296387277294671225933171<29> × 41041333591559226903556091015401<32> × 5915309275092388734119687813085634306291<40> × 176410843726584853883407743387462128062837<42> × 170057573368314684049302929168844425493413216950195208787238174395441995530703625941928227<90>
9×10261-1 = 8(9)261<262> = 156738787 × 118123752347<12> × 486103550958252943839489254197563332642222421275093640896943697704097326523127945004639779680913499989864388900846112765561367571542160265233976720536865532126087178950428768893394875217538328512669161751911424352693947194008747484172696270191<243>
9×10262-1 = 8(9)262<263> = 7 × 13 × 71 × 2281 × 3559 × 151813 × 977057 × 10267451 × 885106597 × 18215699449<11> × 168678924343<12> × 3970843397400821<16> × 14248760853504781734593<23> × 85892292823905156190531<23> × 5960458521395615500271408429<28> × 546893930756919181751220197647<30> × 12360804653411226627683395388566345189673<41> × 2115690668630032081669968821003525873818602277<46>
9×10263-1 = 8(9)263<264> = 1321 × 1481 × 1030859653<10> × 26925974600010539623523869081<29> × 16573478128311777023144881398755941404840565198233369792725410145332307476430599690485167343154132962175643585155756781811649756897370352923840332726007284173002698877331639387326198268951835761356793664910816333105718043<221> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=3422898588 for P29 / February 27, 2014 2014 年 2 月 27 日)
9×10264-1 = 8(9)264<265> = 193 × 1823 × 13426297 × 297991711 × 751446263 × 3885111721371994174857293714863962860157745941710769201332177744305621026491718623507381980843580642456489942771671<115> × 2189962393226079924195568697698785877427193914407518505622793919738599146505349576421961755644686047247091066773551414951<121>
9×10265-1 = 8(9)265<266> = 89 × 761 × 1289 × 7043 × 1357919 × 107791216995669419693798010360922147530318623162307721563542807835209033137650913618426118705833957031855387352328333141469000407671242894832408180521982962111936585085806867516145648171841953089762712001631174241278434685194484872174020344824393987<249>
9×10266-1 = 8(9)266<267> = 17 × 277 × 947 × 602551 × 63911747 × 284800447 × 1908595079<10> × 308272668350011<15> × 628163081468531196471678625762635108684284589253543477082381703073219111516811871677753<87> × 49788316673609370825042195598380883941774223260769627799140653654213502259559771703971945943164976906519116224186832317928274951<128>
9×10267-1 = 8(9)267<268> = 6173 × 332053 × [4390751154139798089034743506019158060108552960344464068180356693685913330995167276322545729184189473549858676380578482332950924439212616177122850820430562629550301964665655478952554054794805418810801161390172290679889760474079432539555012367382429047831135071<259>] Free to factor
9×10268-1 = 8(9)268<269> = 72 × 13 × 23 × 103 × 109 × 131 × 157 × 567979 × 50237491883<11> × 4821502235119<13> × 74611295693503631<17> × 6270336254236758322137851221<28> × 19159624248086059537256114689<29> × 921148200730835944300579540106197<33> × 71867188082562346821361859984554535876161847527<47> × 325878274972959912313450677639337986912758521683301002776370480401214035687<75>
9×10269-1 = 8(9)269<270> = 599 × [1502504173622704507512520868113522537562604340567612687813021702838063439065108514190317195325542570951585976627712854757929883138564273789649415692821368948247078464106844741235392320534223706176961602671118530884808013355592654424040066777963272120200333889816360601<268>] Free to factor
9×10270-1 = 8(9)270<271> = 523 × 13477 × 1075774213<10> × 5752978421<10> × 9661029311<10> × 147095946235219350911667697013541493<36> × 2737810280944238993239874575304072948881248252017519<52> × 113421269769628317461074177992926273808105712904085317777627767022874178511<75> × 467532449005166182402814318007788918674002841796260849988478421239468688979<75>
9×10271-1 = 8(9)271<272> = 4957 × 866093 × [20963271644411838927441728760084969087306909264366908202912611759763559507679065469536740702838697010884667064607483220739411108917610124394281376859696927725464778390159379470817290536546251956503016042608777591425188584095168458732479431249557865675843564222999<263>] Free to factor
9×10272-1 = 8(9)272<273> = 31 × 631 × 5683 × 21061 × 5619844367191367822413<22> × 28731552996140783336205349164799<32> × 835817364193303896837129099287216945204282453961493<51> × 79357900169239460936673489505340712129651144134050386938660184759316861<71> × 35893008790209509851297098644911189995904355230294598135551859369093208362424725320643<86>
9×10273-1 = 8(9)273<274> = 364287532977087361<18> × 24705759009782182519576195918577207554549040662133927532699274809409684572625212254289335700875900549865870631095624653701767559994342748380744661486715871168235461002307447575880804884194546370438063953054928265182384153978226417315861083174157579455013759<257>
9×10274-1 = 8(9)274<275> = 7 × 13 × 487 × 1050233 × 182924718029<12> × 6621524008283<13> × 42100336899241<14> × 300583449314555435059595288664414400507392811785133653676322034725504693698971499976681413695127808189<102> × 126155302167881834100782103641129548809713983877462483723115599111940271236775421520981050242583796793870945402002290692420313<126>
9×10275-1 = 8(9)275<276> = 93601658933<11> × 235113077989262426556488191951<30> × 40896126582964269485422161068681865989327902646026689675612095866675454214888748756530240776421270525375601263737570346689096374819301683282537494803670691046721525962840391531123442708536479519133540643930160685107705013242100108827053<236> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3714314234 for P30 x P236 / December 3, 2013 2013 年 12 月 3 日)
9×10276-1 = 8(9)276<277> = 61 × 83 × 2341 × 2617 × 30427 × 58211 × 123215977 × 40687364143<11> × 18301389014578223<17> × 1879512152331664267523<22> × 413385011612455959639469<24> × 1643961787701703715784696623<28> × 296243498740348121248054677331<30> × 1350398306002428325645695676549<31> × 3494236713686476798561678201951209134404038145161222453838652958294043118897029832719756771<91>
9×10277-1 = 8(9)277<278> = 43 × 560415042841<12> × 3734773508582963709339230305137886122027770026197657310421119235462744732661521187726709349064280453281109881083174787379347993851656096312830074559281602137042792101071235818568382805956807549811592431457146964369958254580216275262167455812742305282119487222816773<265>
9×10278-1 = 8(9)278<279> = 19 × 233 × 613 × 701 × 18257 × 176531 × 13156471 × 5476593989<10> × 2191957616240599<16> × 6168537428391373109<19> × 3189010880100257960332198816490123216053698925938885318275266097<64> × 116392853688224551320628030044644926368910927741779050815872100922653<69> × 405935904781531709647711583561114892568580809007984843638690234553821712672323<78>
9×10279-1 = 8(9)279<280> = 1895489 × 1512725443<10> × 4963934279<10> × [632317361770969431562065367045606333435582829491949146963959401360423465107007112921429708756171266859039368494651488506267368646315403931326683298670119974603371117573424996843672164935060690299048176029766066088373737878922423795924993624086981241542403<255>] Free to factor
9×10280-1 = 8(9)280<281> = 7 × 13 × 1043951 × 26883947 × 25860237801109<14> × 12123679087138214273443<23> × 182071650990950202615387530626934743348640561028796729<54> × 4516088321889703271038563016128691273952825632884219310105789502309547671<73> × 136696145417512502469827638712574449098511977307412418748966651137389231633470826169247101765890038190889<105>
9×10281-1 = 8(9)281<282> = 163 × 136686439 × 639434438563013<15> × 481494437034795133<18> × 2658894104223988246372524653<28> × [49344771035846861855860960739394285052969137490941733916898179138172560555444499782875144143795614440409301727944141950743221032111825475182283488057991843331816120723558798322106281297308100180084168354493335711<212>] Free to factor
9×10282-1 = 8(9)282<283> = 17 × 29 × 32069 × 1247451965855923922740201<25> × 106149839857628546463274992773903<33> × 12049787588762983115267162180707134919286653<44> × 41556957164328385196956218832346458694372291760513828318831460900821120143747579<80> × 8585070491909711967989582026822386992430936673986287924871109410890430123873686351241585281361127<97>
9×10283-1 = 8(9)283<284> = 70639 × 11329274053<11> × 17521271906969<14> × [6418451370813267448524277647696297398474009627636426333345782343860915871597598615147601129811338663102416694894416807207133716630586784518397412403890770756123503732260888347558733249474644576611122443913114640909775700194790825272340807209964739146367813<256>] Free to factor
9×10284-1 = 8(9)284<285> = 59 × 97 × 1667 × 203543020951<12> × 93717112244395171896790558091<29> × 33690430121780543888212711166213824692220327981<47> × 45101059976427355505564135250839549784926008407968873075769527543445669278405405443<83> × 3254728338396397350299417788498932335144337966986383779784082085195537945799463747173648638531505035959656813<109>
9×10285-1 = 8(9)285<286> = 757 × 967329041046312853<18> × 37387188723449217376834547<26> × 328737761387188128586190714008106305942655081357650573545137550008505156081308860669660023535749983567156732926611380463675173362263704773740514947815336713038283988114794104917230194707562917719911415943540699791925840187833343011435633677<240>
9×10286-1 = 8(9)286<287> = 7 × 13 × 47 × 2099 × 4231 × 4259 × 17736799 × 368161095989<12> × 2773039137463081<16> × 74115735887240684807<20> × 120940167904876203213061027933433<33> × 24566776282235900088908433900766498349491<41> × 81650848796699811506688800647364367461674661533783095495619303656848309<71> × 1708760320079077756989239124726576953642075628982585485036155402183550090703<76>
9×10287-1 = 8(9)287<288> = 31 × 1910677 × 35339640032625827<17> × 287037722320380133<18> × [1497933188329108508773131324355856824860834967482782098046300804961612760551924707848502945910421775684390461843887295591372802033093576101212834286745930385104334107311126715527272469034728820749193902559133227578312129578883080672006389406582547<247>] Free to factor
9×10288-1 = 8(9)288<289> = 67 × 307 × 114960971 × 2213287753<10> × 26505761839<11> × 108090137887270909297090797793<30> × 109080439628348269202774046214310086366771298172396864071466868126105645656536199141927505676107861<99> × 5502597989341811453280325654661188430257915760736811008735182048955323276663102194362600358957490858193629421824587327740094756711<130>
9×10289-1 = 8(9)289<290> = 2039 × 180361 × 556781301065161787<18> × 2899401437637363389453<22> × 49479379330461245853559<23> × [3063835292205742080634463277548004024647898602763269955423905521655591988702405161307010938063902328858820151492253313476664663225199088095769520300806078493049402447838138088358949303303135124340125725016755366580459369<220>] Free to factor
9×10290-1 = 8(9)290<291> = 23 × 113 × 1051 × 115336553 × 163365916333<12> × 1512111483928357227059586147307533255856999<43> × 2287852509381529362215874023304871802874572090778188945277943<61> × 957293486672798203907184531262070219175708798167529171237812739812913587<72> × 5280173022660233758936952412889720282802454835751048118163212654450579862340614890525644261<91>
9×10291-1 = 8(9)291<292> = 419137113410927696279896831<27> × 3801150868583505451430911707427<31> × 15435654256774777392802798353839<32> × 365970636963182381920245893844044874346052564692282193625222042499960645560808671628406226445962642741667496404721477120689558268778923581587518194687754810687012055553357846166862445709026648899786161893<204> (Serge Batalov / GMP-ECM B1=3000000, sigma=3418511468 for P32, B1=3000000, sigma=1240117216 for P31 x P204 / February 28, 2014 2014 年 2 月 28 日)
9×10292-1 = 8(9)292<293> = 7 × 13 × 493573 × 62162502049965253<17> × 6699066280481465227<19> × 18325201302275702459091151740961<32> × 2551395316378933371196249242159398075810419408174368073290161677105829014102810175513071204192402345218026591<109> × 102915420634079625638666204942525818485234829450766386797107818368315755086070464205897735709733756055701964353<111>
9×10293-1 = 8(9)293<294> = 107 × 3719 × 211528969 × [10692092339193328223798093001974330417546533254540513658880065598074859517779319447464284099169756226446111168107563700050410125306398012967743210525864002104269878851516834196229296368729206291299062263564154246619638230441965109737418955687189027574553511004550155906115982361987<281>] Free to factor
9×10294-1 = 8(9)294<295> = 2515313 × 4380884647177105247767<22> × 272249694675382115672371457148969342652091706433155665804841695191724637927901103092611354783625552190520929023861944169<120> × 3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<148>
9×10295-1 = 8(9)295<296> = 8677 × 618292559 × 170817465494572286559534373061975039<36> × 101600533495874780237942975753175937120369<42> × 966608544760943657203822452479774279633858548406331200434477660193332321843364655771133424343997568643698689199630918778933149756392441549750199250480543723364793255164542262416453461219451954746840988428723<207> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=2445747929 for P42 / December 3, 2013 2013 年 12 月 3 日) (Serge Batalov / GMP-ECM B1=3000000, sigma=2225292069 for P36 x P207 / May 27, 2014 2014 年 5 月 27 日)
9×10296-1 = 8(9)296<297> = 19 × 61197589 × 97631503 × 5698826293<10> × 108817550461206481<18> × 120232877212186884433<21> × 123074961607917110161534951484159374642729<42> × 355748343355447265512908734948080985968709118990801171190063642693710339565499<78> × 2428535299870600499821029291580376841317100236944884307563528984399789039459262784278489760915114603226966299572177<115>
9×10297-1 = 8(9)297<298> = 71 × 19751 × 599479 × 1169449 × 12454333 × 249518837746271<15> × [2945886419244823256861693699607909778863624774158900448614345842561979447852102951601439857288447477492536291909679107892245085904124014097104672963132357471927026989830186237671597540047571052408944691621536868845801675322591529050747936876450870810300435723<259>] Free to factor
9×10298-1 = 8(9)298<299> = 7 × 13 × 17 × 43 × 1249 × 3803 × 29983 × 47363 × 59021 × 280811 × 25970585924786847027298660631<29> × 18451977947946169372964490164450899739<38> × 243827637273805306729808414600327800876310711471007497576365833251559647434564618561961895558734917<99> × 103574394682250651492366474771488310679253472549528420564006228321981430254572052540584974107852577311191<105>
9×10299-1 = 8(9)299<300> = 161561 × 5570651332933071719041105217224453921429057755275097331658011525058646579310600949486571635481335223228378135812479496908288510222145195932186604440428073606872945822320980929803603592451148482616473034952742307858951108250134624073879215899876826709416257636434535562419148185515068611855583959<295>
9×10300-1 = 8(9)300<301> = 383399 × 23802994718148901<17> × 3757884014173930271262822327673582373969961097805606684684809<61> × 798321605638876885936868160206937968803884648888029502380986396890251623546215931267628089<90> × 328729499631075215103914984155771879133819146534222325019886723795831518647675685691088397349572871406691314755646056939225744501<129>
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