Table of contents 目次

  1. About 311...11 311...11 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 311...11 311...11 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 311...11 311...11 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 311...11 311...11 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

31w = { 3, 31, 311, 3111, 31111, 311111, 3111111, 31111111, 311111111, 3111111111, … }

1.3. General term 一般項

28×10n-19 (0≤n)

2. Prime numbers of the form 311...11 311...11 の形の素数

2.1. Last updated 最終更新日

October 28, 2014 2014 年 10 月 28 日

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

  1. 28×100-19 = 3 is prime. は素数です。
  2. 28×101-19 = 31 is prime. は素数です。
  3. 28×102-19 = 311 is prime. は素数です。
  4. 28×105-19 = 311111 is prime. は素数です。
  5. 28×1010-19 = 3(1)10<11> is prime. は素数です。
  6. 28×1011-19 = 3(1)11<12> is prime. は素数です。
  7. 28×1013-19 = 3(1)13<14> is prime. は素数です。
  8. 28×1034-19 = 3(1)34<35> is prime. は素数です。
  9. 28×1047-19 = 3(1)47<48> is prime. は素数です。
  10. 28×1052-19 = 3(1)52<53> is prime. は素数です。
  11. 28×1077-19 = 3(1)77<78> is prime. は素数です。
  12. 28×1088-19 = 3(1)88<89> is prime. は素数です。
  13. 28×10554-19 = 3(1)554<555> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / May 13, 2003 2003 年 5 月 13 日) (certified by: (証明: Philippe Strohl / primo 2.2.0 beta 5 / October 29, 2004 2004 年 10 月 29 日)
  14. 28×10580-19 = 3(1)580<581> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / May 13, 2003 2003 年 5 月 13 日) (certified by: (証明: Philippe Strohl / primo 2.2.0 beta 5 / October 29, 2004 2004 年 10 月 29 日)
  15. 28×101310-19 = 3(1)1310<1311> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / May 13, 2003 2003 年 5 月 13 日) (certified by: (証明: Philippe Strohl / primo 2.2.0 beta 5 / October 29, 2004 2004 年 10 月 29 日)
  16. 28×101505-19 = 3(1)1505<1506> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / May 13, 2003 2003 年 5 月 13 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / August 25, 2006 2006 年 8 月 25 日)
  17. 28×108537-19 = 3(1)8537<8538> is PRP. はおそらく素数です。 (Philippe Strohl / PFGW / October 29, 2004 2004 年 10 月 29 日)
  18. 28×1015892-19 = 3(1)15892<15893> is PRP. はおそらく素数です。 (Erik Branger / PFGW / February 25, 2010 2010 年 2 月 25 日)
  19. 28×1024022-19 = 3(1)24022<24023> is PRP. はおそらく素数です。 (Erik Branger / PFGW / February 25, 2010 2010 年 2 月 25 日)
  20. 28×1027041-19 = 3(1)27041<27042> is PRP. はおそらく素数です。 (Erik Branger / PFGW / February 25, 2010 2010 年 2 月 25 日)
  21. 28×1037922-19 = 3(1)37922<37923> is PRP. はおそらく素数です。 (Serge Batalov / October 13, 2010 2010 年 10 月 13 日)
  22. 28×1040033-19 = 3(1)40033<40034> is PRP. はおそらく素数です。 (Serge Batalov / sr*sieve + LLR / October 27, 2014 2014 年 10 月 27 日)
  23. 28×10134122-19 = 3(1)134122<134123> is PRP. はおそらく素数です。 (Serge Batalov / sr*sieve + LLR / October 28, 2014 2014 年 10 月 28 日)
  24. 28×10165358-19 = 3(1)165358<165359> is PRP. はおそらく素数です。 (Serge Batalov / sr*sieve + LLR / October 28, 2014 2014 年 10 月 28 日)
  25. 28×10183760-19 = 3(1)183760<183761> is PRP. はおそらく素数です。 (Serge Batalov / sr*sieve + LLR / October 28, 2014 2014 年 10 月 28 日)

2.3. Range of search 捜索範囲

  1. n≤38000 / Completed 終了 / Serge Batalov / October 13, 2010 2010 年 10 月 13 日
  2. n≤120000 / Completed 終了 / Serge Batalov / October 27, 2014 2014 年 10 月 27 日
  3. n≤200000 / Completed 終了 / Serge Batalov / October 28, 2014 2014 年 10 月 28 日

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

  1. 28×103k-19 = 3×(28×100-19×3+28×103-19×3×k-1Σm=0103m)
  2. 28×1013k+4-19 = 53×(28×104-19×53+28×104×1013-19×53×k-1Σm=01013m)
  3. 28×1015k+1-19 = 31×(28×101-19×31+28×10×1015-19×31×k-1Σm=01015m)
  4. 28×1016k+3-19 = 17×(28×103-19×17+28×103×1016-19×17×k-1Σm=01016m)
  5. 28×1018k+8-19 = 19×(28×108-19×19+28×108×1018-19×19×k-1Σm=01018m)
  6. 28×1022k+7-19 = 23×(28×107-19×23+28×107×1022-19×23×k-1Σm=01022m)
  7. 28×1028k+14-19 = 29×(28×1014-19×29+28×1014×1028-19×29×k-1Σm=01028m)
  8. 28×1028k+15-19 = 281×(28×1015-19×281+28×1015×1028-19×281×k-1Σm=01028m)
  9. 28×1041k+26-19 = 83×(28×1026-19×83+28×1026×1041-19×83×k-1Σm=01041m)
  10. 28×1046k+40-19 = 47×(28×1040-19×47+28×1040×1046-19×47×k-1Σm=01046m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 19.45%. 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 19.45% です。

3. Factor table of 311...11 311...11 の素因数分解表

3.1. Last updated 最終更新日

September 30, 2015 2015 年 9 月 30 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=201, 203, 205, 208, 210, 215, 216, 217, 221, 222, 226, 231, 233, 234, 235, 236, 237, 238, 242, 243, 244, 245, 247, 249, 252, 253, 258, 259, 260, 261, 262, 263, 264, 265, 267, 268, 269, 272, 273, 275, 276, 278, 279, 280, 281, 283, 284, 285, 286, 288, 289, 291, 293, 294, 295, 296, 297, 298, 299, 300 (60/300)

3.4. Factor table 素因数分解表

28×100-19 = 3 = definitely prime number 素数
28×101-19 = 31 = definitely prime number 素数
28×102-19 = 311 = definitely prime number 素数
28×103-19 = 3111 = 3 × 17 × 61
28×104-19 = 31111 = 53 × 587
28×105-19 = 311111 = definitely prime number 素数
28×106-19 = 3111111 = 32 × 345679
28×107-19 = 31111111 = 23 × 1352657
28×108-19 = 311111111 = 19 × 16374269
28×109-19 = 3111111111<10> = 3 × 179 × 5793503
28×1010-19 = 31111111111<11> = definitely prime number 素数
28×1011-19 = 311111111111<12> = definitely prime number 素数
28×1012-19 = 3111111111111<13> = 3 × 89273 × 11616469
28×1013-19 = 31111111111111<14> = definitely prime number 素数
28×1014-19 = 311111111111111<15> = 29 × 1655939 × 6478481
28×1015-19 = 3111111111111111<16> = 32 × 281 × 809 × 839 × 1812409
28×1016-19 = 31111111111111111<17> = 31 × 7583791 × 132332791
28×1017-19 = 311111111111111111<18> = 53 × 5239369 × 1120367923<10>
28×1018-19 = 3111111111111111111<19> = 3 × 4958579 × 209139964703<12>
28×1019-19 = 31111111111111111111<20> = 17 × 1830065359477124183<19>
28×1020-19 = 311111111111111111111<21> = 2203 × 290837 × 485569465201<12>
28×1021-19 = 3111111111111111111111<22> = 3 × 1037037037037037037037<22>
28×1022-19 = 31111111111111111111111<23> = 59 × 25819 × 20423214221500991<17>
28×1023-19 = 311111111111111111111111<24> = 16979 × 1439293 × 12730756173313<14>
28×1024-19 = 3111111111111111111111111<25> = 34 × 149 × 265032319 × 972624932101<12>
28×1025-19 = 31111111111111111111111111<26> = 1951 × 2557 × 67987 × 91727941318879<14>
28×1026-19 = 311111111111111111111111111<27> = 19 × 83 × 727 × 271362241359075143209<21>
28×1027-19 = 3111111111111111111111111111<28> = 3 × 14506277 × 71488848381775491881<20>
28×1028-19 = 31111111111111111111111111111<29> = 193 × 12703 × 18089 × 701515637022519281<18>
28×1029-19 = 311111111111111111111111111111<30> = 23 × 13526570048309178743961352657<29>
28×1030-19 = 3111111111111111111111111111111<31> = 3 × 53 × 2399 × 69361991 × 117588973387831681<18>
28×1031-19 = 31111111111111111111111111111111<32> = 31 × 1003584229390681003584229390681<31>
28×1032-19 = 311111111111111111111111111111111<33> = 9433 × 236026804549<12> × 139734730202644883<18>
28×1033-19 = 3111111111111111111111111111111111<34> = 32 × 345679012345679012345679012345679<33>
28×1034-19 = 31111111111111111111111111111111111<35> = definitely prime number 素数
28×1035-19 = 311111111111111111111111111111111111<36> = 17 × 4614583 × 3965830410845626101007471201<28>
28×1036-19 = 3111111111111111111111111111111111111<37> = 3 × 7873983081212257<16> × 131704250103287958541<21>
28×1037-19 = 31111111111111111111111111111111111111<38> = 61487983 × 505970591214727455137227563817<30>
28×1038-19 = 311111111111111111111111111111111111111<39> = 30389 × 10237622531544674425322028073023499<35>
28×1039-19 = 3111111111111111111111111111111111111111<40> = 3 × 984649089601<12> × 1053204687831748981235441837<28>
28×1040-19 = 31111111111111111111111111111111111111111<41> = 47 × 59051 × 1334561 × 1987523 × 437230217 × 9665618432513<13>
28×1041-19 = 311111111111111111111111111111111111111111<42> = 1141233897997<13> × 272609420082200309275564220963<30>
28×1042-19 = 3111111111111111111111111111111111111111111<43> = 32 × 29 × 99233 × 120120987402924921161056688367252347<36>
28×1043-19 = 31111111111111111111111111111111111111111111<44> = 53 × 281 × 1423 × 1468008033841737545633488484480987149<37>
28×1044-19 = 311111111111111111111111111111111111111111111<45> = 19 × 4517 × 553055893937<12> × 6554548863145601889930661961<28>
28×1045-19 = 3111111111111111111111111111111111111111111111<46> = 3 × 3929 × 263944270052694588199805812429889803267253<42>
28×1046-19 = 31111111111111111111111111111111111111111111111<47> = 31 × 1003584229390681003584229390681003584229390681<46>
28×1047-19 = 311111111111111111111111111111111111111111111111<48> = definitely prime number 素数
28×1048-19 = 3111111111111111111111111111111111111111111111111<49> = 3 × 113 × 2381 × 11003 × 357703 × 397058527 × 2466426657688720386945403<25>
28×1049-19 = 31111111111111111111111111111111111111111111111111<50> = 317 × 941 × 29732458381<11> × 160654358299<12> × 21834502695894002244577<23>
28×1050-19 = 3(1)50<51> = 109 × 20872603 × 1993086344818092103<19> × 68609822763124648712831<23>
28×1051-19 = 3(1)51<52> = 33 × 17 × 23 × 461 × 4127 × 12703049 × 175926617 × 618387571 × 112082892252411163<18>
28×1052-19 = 3(1)52<53> = definitely prime number 素数
28×1053-19 = 3(1)53<54> = 1153 × 406352448017<12> × 3668471265463943<16> × 181008184517128175235377<24>
28×1054-19 = 3(1)54<55> = 3 × 223 × 2297 × 3407618304588272647<19> × 594124506381346926572780766941<30>
28×1055-19 = 3(1)55<56> = 10305728977658557<17> × 3018817123811022180979046309018038259923<40>
28×1056-19 = 3(1)56<57> = 53 × 131 × 4871 × 16187 × 568308118768362063731543171789304252565413101<45>
28×1057-19 = 3(1)57<58> = 3 × 563 × 743 × 168247 × 14669939 × 1004434037886341555641644222937119108421<40>
28×1058-19 = 3(1)58<59> = 62613390969440647597195433<26> × 496876317181021701706806628758767<33>
28×1059-19 = 3(1)59<60> = 1220661151<10> × 254870985986766372571409140480715692991781886495961<51>
28×1060-19 = 3(1)60<61> = 32 × 11197 × 371281 × 12928739 × 6431502472561515498871659114782660780681273<43>
28×1061-19 = 3(1)61<62> = 31 × 752201 × 2465710309<10> × 541100419569080158880937327196873292052533309<45>
28×1062-19 = 3(1)62<63> = 19 × 11173 × 131059 × 5955043 × 713240779 × 4273371527<10> × 616074953335710586854596293<27>
28×1063-19 = 3(1)63<64> = 3 × 61 × 97 × 467 × 1303 × 288025806674149605309443583668674530537358089976034861<54>
28×1064-19 = 3(1)64<65> = 167 × 1098885738288171992459999<25> × 169529981160601412291752231218245903167<39>
28×1065-19 = 3(1)65<66> = 277 × 2731265421713<13> × 882387070434382440120383<24> × 466028750818884132089939717<27>
28×1066-19 = 3(1)66<67> = 3 × 233 × 1279 × 295073 × 11793381008626718937668153135582690713731904244031911867<56>
28×1067-19 = 3(1)67<68> = 17 × 83 × 26923671769<11> × 30046035446412187639163<23> × 27256309088967007530068628752783<32>
28×1068-19 = 3(1)68<69> = 6299 × 1452540317<10> × 34002881188287057286394077989200233428969452678733372617<56>
28×1069-19 = 3(1)69<70> = 32 × 53 × 509 × 12813841878106498585672202703995218606430626546527746315219594927<65>
28×1070-19 = 3(1)70<71> = 29 × 53087 × 20208279519767558595169485036021619106119954759435949388941322157<65>
28×1071-19 = 3(1)71<72> = 281 × 7069 × 956309477 × 551314697847853<15> × 297066165154666421634772855894739164447979<42>
28×1072-19 = 3(1)72<73> = 3 × 1037037037037037037037037037037037037037037037037037037037037037037037037<73>
28×1073-19 = 3(1)73<74> = 23 × 211086469419401<15> × 6408070628834890618176730719516389519460607077923464526857<58>
28×1074-19 = 3(1)74<75> = 977 × 2659 × 1225138571<10> × 1280159150118539761289893<25> × 76357806333374019845264954114336459<35>
28×1075-19 = 3(1)75<76> = 3 × 18457 × 1703414339663<13> × 32984724121350876722047384465928677306354817463532069898107<59>
28×1076-19 = 3(1)76<77> = 312 × 1823 × 17758466713688549600697704787942660701597697538682855792307628396726937<71>
28×1077-19 = 3(1)77<78> = definitely prime number 素数
28×1078-19 = 3(1)78<79> = 33 × 115752673 × 995452929614503768581594691253707268155783070183554241682404495735141<69>
28×1079-19 = 3(1)79<80> = 181 × 100547 × 136673949648076323302899<24> × 803606188557366787692859<24> × 15564630399106440370064153<26>
28×1080-19 = 3(1)80<81> = 19 × 59 × 395012791 × 6855049875977<13> × 188951197797943373669<21> × 542423481856191544227716844567811477<36>
28×1081-19 = 3(1)81<82> = 3 × 29437 × 548521 × 833882964887968166420099052781<30> × 77019795002109397955703837511285695837901<41>
28×1082-19 = 3(1)82<83> = 53 × 337 × 2293 × 213973 × 764510173423<12> × 31800013132706449<17> × 146028005208300155573058700761488311827917<42>
28×1083-19 = 3(1)83<84> = 17 × 91150910060779<14> × 993019086102188075666331040482241<33> × 202184563904484935250160062652222597<36>
28×1084-19 = 3(1)84<85> = 3 × 1037037037037037037037037037037037037037037037037037037037037037037037037037037037037<85>
28×1085-19 = 3(1)85<86> = 226141 × 7004189 × 5269335553<10> × 7376164687231297<16> × 378554537173912327<18> × 1334945209514487383698041864377<31>
28×1086-19 = 3(1)86<87> = 47 × 1991351 × 54834422329<11> × 4687421105760497995436331363568733<34> × 12932503472534699423088556688846659<35>
28×1087-19 = 3(1)87<88> = 32 × 199 × 8867 × 275391138935557<15> × 711366264282390326538044301720153947771653265865388243378638356759<66>
28×1088-19 = 3(1)88<89> = definitely prime number 素数
28×1089-19 = 3(1)89<90> = 1117769 × 2485175319103<13> × 45208270789599497<17> × 6825088147729655743980727<25> × 362977971120456250454538406367<30>
28×1090-19 = 3(1)90<91> = 3 × 155381 × 1805146194077<13> × 3697293906208041139004158773189991620139421878108638056267018828529725101<73>
28×1091-19 = 3(1)91<92> = 31 × 23293 × 1008001 × 2706893791001<13> × 206509226796023<15> × 34783931531314994351888051<26> × 2198255124989930542257903329<28>
28×1092-19 = 3(1)92<93> = 197 × 283 × 2887 × 5234641131965670413091625395670792675699<40> × 369257362188426890230154686886098333714658797<45>
28×1093-19 = 3(1)93<94> = 3 × 1558034289153729226854041891236579541<37> × 665606042342187460521540478345491947724951031946561795257<57>
28×1094-19 = 3(1)94<95> = 216376462114727<15> × 12746810535942537179<20> × 11279866915809189925645141080640620189083468112706527271988467<62>
28×1095-19 = 3(1)95<96> = 23 × 53 × 2309 × 892103 × 14353993 × 733540282757233444966511657331751<33> × 11767282643290228608913205662738482079583729<44>
28×1096-19 = 3(1)96<97> = 32 × 439 × 84227929 × 13722618602567238968771<23> × 681263900693166601483667775674056429499135533440274159892748379<63> (Tetsuya Kobayashi / GMP-ECM 5.0.1 for P23 x P63 / May 1, 2003 2003 年 5 月 1 日)
28×1097-19 = 3(1)97<98> = 349 × 491 × 19148262958813<14> × 15100290487635613957<20> × 29653125935065103669679403343<29> × 21175000823758822976744202823783<32>
28×1098-19 = 3(1)98<99> = 19 × 29 × 402391688632643<15> × 55595659588064421068401<23> × 3202490101316072490493490623<28> × 7881089111598699997944712095749<31>
28×1099-19 = 3(1)99<100> = 3 × 17 × 281 × 877 × 247536606310081167872050591390148165069043308058696551973320716746133431796322849017619593753<93>
28×10100-19 = 3(1)100<101> = 227 × 938916864227<12> × 252859943470456145235023<24> × 577274652536697313408534518709215227893942109925114737865360833<63>
28×10101-19 = 3(1)101<102> = 69946777 × 7208030643628691<16> × 2420496479236717648348371161<28> × 254933397828800907311455975438132515762408790122893<51>
28×10102-19 = 3(1)102<103> = 3 × 24331858729047739003458111435677466330688702357<47> × 42620543238606207295474826005379456202911549357812117241<56> (Makoto Kamada / SNFS for P47 x P56 / 3:45:40:71)
28×10103-19 = 3(1)103<104> = 577 × 82581831656109167<17> × 730304554386214631<18> × 894028139605035891186715304871148987235575188988266025430247082159<66>
28×10104-19 = 3(1)104<105> = 3911 × 19211 × 29851 × 3466363 × 19986055100473507<17> × 1652685057802047135722941<25> × 1211511743225061976785787265741749639510388861<46>
28×10105-19 = 3(1)105<106> = 35 × 38839237833796301461061<23> × 329638970722353329129881974771130289752812021249279640723146078451881875240662457<81>
28×10106-19 = 3(1)106<107> = 31 × 24094121473<11> × 3035893958548414331482156002773<31> × 13720063917000835559846074880276981672558895819344012864493270389<65>
28×10107-19 = 3(1)107<108> = 24077 × 12921506463060643398725385683893803676168588740753046937372227067787145869963496744241853682398600785443<104>
28×10108-19 = 3(1)108<109> = 3 × 53 × 83 × 225767 × 9723127465647490740903656178329<31> × 107392478101279201565968868184871485812597446568363928944263227421741<69> (Naoki Yamamoto / for P31 x P69 / March 22, 2004 2004 年 3 月 22 日)
28×10109-19 = 3(1)109<110> = 3207047 × 2242853921901389<16> × 472822819904586097207827991<27> × 9147676121067983676277009780561200861687804266274025797097987<61>
28×10110-19 = 3(1)110<111> = 1297 × 148082057 × 6150889000757<13> × 22373649646422047424049423207769<32> × 11770594120008843084370431262503020511457320038362364923<56>
28×10111-19 = 3(1)111<112> = 3 × 1021 × 538558537586002690399<21> × 697163546658203060591059<24> × 151798326082341931516445732281<30> × 17821077422612290701371023154876957<35>
28×10112-19 = 3(1)112<113> = 46957 × 815491 × 4713493 × 41288194750989795233<20> × 4174718972936197924563741364356300720419129825475478565896378974379325879837<76>
28×10113-19 = 3(1)113<114> = 1503583 × 206913160837220899086456225636437171151250786362383128241747287054396804906088397588367992396236929461899417<108>
28×10114-19 = 3(1)114<115> = 32 × 154229053021<12> × 2582423522467<13> × 18098087181960493<17> × 47956411224583441402506973175977858617052264655183235256497837320642594029<74>
28×10115-19 = 3(1)115<116> = 17 × 124759 × 788872477 × 150174906317267122652035663<27> × 123819926417258767891112587554921845113083880349101106022166816974760240187<75>
28×10116-19 = 3(1)116<117> = 19 × 2377 × 9286769221<10> × 12579336305407044447861116109751<32> × 58967179855832066531899593904791884143237262604567839338096201001532407<71>
28×10117-19 = 3(1)117<118> = 3 × 23 × 8699827 × 926101118905389803<18> × 1463855444535956575845516883<28> × 3822955241064540531891749189885465169931529305737301651160196553<64>
28×10118-19 = 3(1)118<119> = 6514689720223<13> × 1339329241954225991443969<25> × 3565614890880189564008736133317966426511007030308323118463570237281167464393934553<82>
28×10119-19 = 3(1)119<120> = 593 × 60625711 × 8653742806810943483199162580082727599068238985079828370122472556843289293939928228695649763117359886802623257<109>
28×10120-19 = 3(1)120<121> = 3 × 971 × 3593 × 5465308488713658787<19> × 54388006325955704237490276774368544985109843622074910664548492406784802234100779656094047651717<95>
28×10121-19 = 3(1)121<122> = 31 × 53 × 1451 × 8618763293292161<16> × 620212768724971039979<21> × 108348934237081755551508989<27> × 22532026108157476919386005394254281176916730456685697<53>
28×10122-19 = 3(1)122<123> = 110581 × 1529369 × 16754389 × 109797924668335514555365610461632313114777523259087853779246219211602619595737909213490061092937051279991<105>
28×10123-19 = 3(1)123<124> = 32 × 61 × 269 × 3083 × 357809 × 35447719693<11> × 328339709977<12> × 16255098875508742295339572855971809959<38> × 100940344807386664704798695248019486320254351137527<51>
28×10124-19 = 3(1)124<125> = 1162367 × 26765308298593397017560814365093908473925284450703702970844071718408309175252834183275257393844724696340408073449359033<119>
28×10125-19 = 3(1)125<126> = 257 × 2087 × 116349679 × 4256013934461701<16> × 225063260416102750225001751763<30> × 5204597068991878300139972119622046965779245555044591966878220075377<67> (Naoki Yamamoto / for P30 x P67 / March 22, 2004 2004 年 3 月 22 日)
28×10126-19 = 3(1)126<127> = 3 × 29 × 165479 × 3403427 × 905725712473<12> × 7520548355520711934404450344729246962997<40> × 9321605873732438542588728464618640784227803490462063002278561<61> (Sinkiti Sibata / GGNFS-0.73.4 for P40 x P61 / 3.75 hours / April 15, 2005 2005 年 4 月 15 日)
28×10127-19 = 3(1)127<128> = 281 × 307 × 238599056062709776815461419063<30> × 107554330787428224166772754609776501813<39> × 14053166861603880222824059670432645508929757889981227607<56> (Tetsuya Kobayashi / GMP-ECM B1=1e6 for P30 / May 7, 2004 2004 年 5 月 7 日) (Naoki Yamamoto / for P39 x P56 / May 8, 2004 2004 年 5 月 8 日)
28×10128-19 = 3(1)128<129> = 317 × 12990488583482872691<20> × 520969341590184715621338111312366954921214789141<48> × 145016896897054672966641097051971115808459317464238937158493<60> (Sinkiti Sibata / GGNFS-0.73.4 for P48 x P60 / 4.86 hours / April 15, 2005 2005 年 4 月 15 日)
28×10129-19 = 3(1)129<130> = 3 × 614450203 × 1081754037011<13> × 1560195606220382648756045164943646139274333821321140427626098396528639966911545544813494978756638114074942189<109>
28×10130-19 = 3(1)130<131> = 4324003 × 311483563 × 4726352074551879480881<22> × 4887292495763365534157039840001944172280177518979533693161618668680051847551410212245787726679<94>
28×10131-19 = 3(1)131<132> = 17 × 23821830687990493<17> × 768230361237405223056954483572215097460072618636766862238734377843352800812555289792842175994751946715740878747331<114>
28×10132-19 = 3(1)132<133> = 33 × 47 × 14843 × 1490595172789<13> × 1494381030698527<16> × 6665858183644351<16> × 728364077874015308293<21> × 15272374579791904768747229452041750217245610999246259611207177<62>
28×10133-19 = 3(1)133<134> = 23772479 × 4661149798387950069326780910128942201<37> × 280768246138105278818027047217392733347706647719771405121039131873453130761157349833137409<90> (Sinkiti Sibata / GGNFS-0.73.4 for P37 x P90 / 8.09 hours / April 17, 2005 2005 年 4 月 17 日)
28×10134-19 = 3(1)134<135> = 19 × 53 × 277 × 701 × 5796859 × 3611192237<10> × 1358769123518944026535129296500716906585653961788989197<55> × 55937010190050826723396184986190224689858976124054556499<56> (Sinkiti Sibata / GGNFS-0.73.4 for P55 x P56 / 14.54 hours / April 17, 2005 2005 年 4 月 17 日)
28×10135-19 = 3(1)135<136> = 3 × 10300469367242916451<20> × 7683930573457486564648081513<28> × 13102489491397317646769416780137888945330964323802773376155529927060182429351919042059799<89> (Tetsuya Kobayashi / GMP-ECM B1=1e6 for P28 x P89 / May 7, 2004 2004 年 5 月 7 日)
28×10136-19 = 3(1)136<137> = 31 × 6469 × 16381 × 1749001 × 303639927086451348390224610638032524907346867513043503<54> × 17833119933549804907843420188189974329012488534323956272603491728943<68> (Sinkiti Sibata / GGNFS-0.73.4 for P54 x P68 / 10.14 hours / April 17, 2005 2005 年 4 月 17 日)
28×10137-19 = 3(1)137<138> = 2447 × 1837103 × 115040363843<12> × 11687623785883<14> × 44120481248292503323<20> × 1166625151057184344712303221425970670660272795387750793788611823073645734275741361333<85>
28×10138-19 = 3(1)138<139> = 3 × 59 × 126131 × 139354313632898623026589255942676364193998066448944463986398461572174562798112782262971016149209012722317224537071564556709473972653<132>
28×10139-19 = 3(1)139<140> = 23 × 401 × 6869442431<10> × 8201790277<10> × 151723915832626286918993436841007<33> × 1046070491078451817587498267478589<34> × 377223005511673979186119699372574922813654796022657<51> (Tetsuya Kobayashi / GMP-ECM B1=1e6 for P33 / May 7, 2004 2004 年 5 月 7 日) (Naoki Yamamoto / for P34 x P51 / May 7, 2004 2004 年 5 月 7 日)
28×10140-19 = 3(1)140<141> = 28061244394528078097445236936881<32> × 11086860822600495496089798493845024271017940020968874041788390705256335001099077800139750826481064002684323831<110> (Tetsuya Kobayashi / GMP-ECM 5.0.3 (B1=1000000) for P32 x P110 / August 14, 2004 2004 年 8 月 14 日)
28×10141-19 = 3(1)141<142> = 32 × 1109 × 311703347471306593639025259103407585523605962439746629707555466497456278039385944405481526010531120239566287056518496253993699139476115731<138>
28×10142-19 = 3(1)142<143> = 7301597 × 11562898307297<14> × 4916511500456033<16> × 193191252769849956505439432831<30> × 33595572112247073555344073339779<32> × 11547936770994507682778259324179946656817378287<47> (Tetsuya Kobayashi / GMP-ECM B1=1e6 for P30 x P32 x P47 / May 7, 2004 2004 年 5 月 7 日)
28×10143-19 = 3(1)143<144> = 263 × 5456111 × 138052796555701<15> × 107253664497452549<18> × 116573850967584096912312262096761599241450013841771<51> × 125608226798127591346038863148280844795094728289902213<54> (Anton Korobeynikov / GGNFS-0.73.3 gnfs for P51 x P54 / 19.75 hours / March 6, 2005 2005 年 3 月 6 日)
28×10144-19 = 3(1)144<145> = 3 × 68259441937979744951640698797<29> × 130522260397986637978317952371613<33> × 116398383092931351479137105146603590908252840941503083126928866253479361451337974517<84> (Tetsuya Kobayashi / GMP-ECM B1=1e6 for P29 x P33 x P84 / May 7, 2004 2004 年 5 月 7 日)
28×10145-19 = 3(1)145<146> = 188711 × 105090087887<12> × 9428392735439<13> × 166386806413820526766866366722575299607978682416747712092511296870633145786853990616678038262240339157638267155629057<117>
28×10146-19 = 3(1)146<147> = 557 × 13348403 × 135946790369989487351394815094401985653072460527854961951072789406649<69> × 307795352666770994437375124491141669602934981887147533997871263854009<69> (Sinkiti Sibata / GGNFS-0.73.4 for P69(1359...) x P69(3077...) / 25.20 hours / April 19, 2005 2005 年 4 月 19 日)
28×10147-19 = 3(1)147<148> = 3 × 17 × 53 × 5335755289<10> × 188537518563012513122387659479595807159890697208441<51> × 1144131086843924892396284393693892007671045374707891235617520596889136021659017349113<85> (Sinkiti Sibata / GGNFS-0.73.4 for P51 x P85 / 41.12 hours / April 20, 2005 2005 年 4 月 20 日)
28×10148-19 = 3(1)148<149> = 20297 × 5832655002086973292533748447156252349399054005111269643<55> × 262795171406053605652617712159477735923385859363447375812037122013872356413610009393027341<90> (Sinkiti Sibata / GGNFS-0.73.4 for P55 x P90 / 36.05 hours / April 22, 2005 2005 年 4 月 22 日)
28×10149-19 = 3(1)149<150> = 83 × 18131 × 109712637690850034608956265910417297400012012734563892169318853345141<69> × 1884338906467129357869775163361615341452520042565997407540228991425036222227<76> (Sinkiti Sibata / GGNFS-0.73.4 for P69 x P76 / 44.12 hours / April 24, 2005 2005 年 4 月 24 日)
28×10150-19 = 3(1)150<151> = 32 × 6971 × 125197 × 846913 × 93685696889<11> × 1199903662141<13> × 1403106237540005447447<22> × 567366079746132403265113884152652067<36> × 5226026584128553669613574839501952755233031877382069609<55> (Naoki Yamamoto / for P36 x P55 / March 20, 2004 2004 年 3 月 20 日)
28×10151-19 = 3(1)151<152> = 31 × 19843 × 434831 × 974853410034804062561219744184438708636042947181325656020147<60> × 119312702335017997752212094830142486881715593155366467314651908260291633099814831<81> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 for P60 x P81 / 36.44 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / June 16, 2006 2006 年 6 月 16 日)
28×10152-19 = 3(1)152<153> = 192 × 373 × 138725048447172782047588804984691<33> × 4614801318243737710787835047153093<34> × 2086846457343354311267623487016180553<37> × 1729422474912842686429904181234071831567075333<46> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=3672784463 for P33 / February 27, 2005 2005 年 2 月 27 日) (Makoto Kamada / GMP-ECM 6.0.1 B1=11000000, sigma=1701688029 for P34, msieve-0.88 for P37 x P46 / April 14, 2005 2005 年 4 月 14 日)
28×10153-19 = 3(1)153<154> = 3 × 2156207 × 8622287 × 599155396153<12> × 758789025710646472692249434850475074640894740293827<51> × 122693293575279404068194860876165197135028729140976454096131624341950993818503<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 for P51 x P78 / 19.61 hours on Core 2 Duo E6300@2.33GHz / February 24, 2007 2007 年 2 月 24 日)
28×10154-19 = 3(1)154<155> = 29 × 523 × 356947 × 1279301069<10> × 329796478307462684783<21> × 300621016513776590359526923103344706640342409501697<51> × 45307905222633353862121896072140996414543098670746516403110579681<65> (Sinkiti Sibata / GGNFS-0.77.1 for P51 x P65 / 48.44 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / June 9, 2006 2006 年 6 月 9 日)
28×10155-19 = 3(1)155<156> = 281 × 503771 × 1832323937877638424687563602099971871<37> × 528132257091941690986148848873348959257<39> × 2271072974612884347124933126129315615770172419175193664363341850801604363<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P37 x P39 x P73 / 32.07 hours on Cygwin on AMD XP 2700+ / April 4, 2007 2007 年 4 月 4 日)
28×10156-19 = 3(1)156<157> = 3 × 4341599 × 21062551 × 73627823 × 86138002801<11> × 24107648562718188155071<23> × 74172339841965699483511894781354151963288316193024144432415423575797981917148051617613394660815486661<101>
28×10157-19 = 3(1)157<158> = 311 × 487 × 480670490093480346271<21> × 6438097168233354220222049<25> × 2963884335817527111335736587670265958585892914749<49> × 22395457197128163961438045327803254457295208979708748555213<59> (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P49 x P59 / 21.35 hours / July 13, 2005 2005 年 7 月 13 日)
28×10158-19 = 3(1)158<159> = 109 × 2854230377166156982670744138634046890927624872579001019367991845056065239551478083588175331294597349643221202854230377166156982670744138634046890927624872579<157>
28×10159-19 = 3(1)159<160> = 33 × 97 × 717667 × 31119047 × 4319493713<10> × 691407189640250229701631872793975317289967702892453<51> × 17810004148297787657731990085303963501623195591076357396769870762158063825273702029<83> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P51 x P83 / 31.18 hours on Core 2 Quad Q6600 / October 24, 2007 2007 年 10 月 24 日)
28×10160-19 = 3(1)160<161> = 53 × 113 × 367 × 10608547 × 331545143 × 633091035242735539801967600647466189684568802167457<51> × 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001<88> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.26 for P51 x P88 / October 2, 2007 2007 年 10 月 2 日)
28×10161-19 = 3(1)161<162> = 232 × 479 × 3931 × 12601 × 601567974625494115295565539<27> × 1322387510050293446984064653<28> × 31158233996408307678317475367043667268790534787517902330960185252755444619162581289959014726373<95>
28×10162-19 = 3(1)162<163> = 3 × 6299 × 100970377 × 1630529576681281444153203265064420153031262683353946217961079138719402742564921507667008939331613371962287341031643290829841956615458245691794283625119<151>
28×10163-19 = 3(1)163<164> = 17 × 5807 × 52652550737<11> × 145695234831457<15> × 132116509176428263<18> × 153121853039728981621<21> × 1616403486191862757573<22> × 1256336469003318205849513668967961402483023628881650713131955229984427354679<76>
28×10164-19 = 3(1)164<165> = 1737265539857<13> × 252249696241091<15> × 26106630115401509928704918723<29> × 27193671615382449140729179756297345921271319139648222513354703536214203678797979436152365081608209288658796511<110> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=1831496342 for P29 x P110 / June 26, 2005 2005 年 6 月 26 日)
28×10165-19 = 3(1)165<166> = 3 × 1997 × 41029853253616558862159<23> × 1479931381061176239842955946643233<34> × 2662130344631855481640471681171550281616064848447<49> × 3212516327124022069219127196505956546984798871424714788369<58> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=3650039559 for P34 / July 21, 2005 2005 年 7 月 21 日) (Tyler Cadigan / GGNFS-0.77.1-20050930-pentium4 gnfs for P49 x P58 / 23.43 hours on P4 3.2 gig, 1024 Mb RAM / October 3, 2005 2005 年 10 月 3 日)
28×10166-19 = 3(1)166<167> = 31 × 1381 × 8839 × 20642682679<11> × 33269787928489054315540705663<29> × 119712871023092847484095658440638447607367789413552968677064234286977758025807179489059501287109911175570047882248570267<120>
28×10167-19 = 3(1)167<168> = 2699 × 35083 × 201517 × 132211486382868061681<21> × 622034512368604087851615654481<30> × 14957629796921962305112256643833653651<38> × 13254329882974026588044639224501407408503731822345782359808742685209<68> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=3922410115 for P38 / January 24, 2005 2005 年 1 月 24 日) (Kenichiro Yamaguchi / msieve 0.88 for P30 x P68 / 13:35:40 on Pentium M 1.3GHz / May 12, 2005 2005 年 5 月 12 日)
28×10168-19 = 3(1)168<169> = 32 × 12377 × 41984093 × 149519217696375701284876859610392404589<39> × 4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751<118> (suberi / GGNFS-0.77.1-20060513-pentium4 for P39 x P118 / 197.02 hours on Pentium 4 2.26GHz, Windows XP and Cygwin / July 4, 2006 2006 年 7 月 4 日)
28×10169-19 = 3(1)169<170> = 569 × 66874311668453<14> × 44747666732132274776543864200416504217245710983578615464026424207<65> × 18271471956786769290650039107080148906269339162611613818652179674703425122513940651184189<89> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs for P65 x P89 / 48.38 hours on Cygwin on AMD 64 X2 6000+ / July 28, 2008 2008 年 7 月 28 日)
28×10170-19 = 3(1)170<171> = 19 × 194022611 × 5328187985291<13> × 523160083277781738962657179<27> × 2034416473796509875496633128017420031802765447<46> × 14881803754980492436345625472473603610295959695851442433011508052049006779313<77> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=2513232389 for P27 / June 26, 2005 2005 年 6 月 26 日) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=11000000, sigma=5560633114 for P46 x P77 / September 15, 2009 2009 年 9 月 15 日)
28×10171-19 = 3(1)171<172> = 3 × 3891659 × 3102239807<10> × 106533181187<12> × 806304764865949735396587402932351730383339316825806920766223553583036549444226240887185025314069701684103245337248512992809307593833633336994227<144>
28×10172-19 = 3(1)172<173> = 149 × 19009 × 6877246441372402649<19> × 1724230517504569670736836635964441<34> × 9768844483733605983857894729980673<34> × 94823694499320570244033199429122419011801625776673637024727322019611784153183003<80> (Sinkiti Sibata / Msieve 1.40 snfs for P34(1724...) x P34(9768...) x P80 / 79.64 hours / October 9, 2009 2009 年 10 月 9 日)
28×10173-19 = 3(1)173<174> = 53 × 103612676339<12> × 9737493193419986671<19> × 4029058309486985448887299<25> × 8534554809469539304814207677240295290372836899<46> × 169197978104796095779666677633728972685095582295334772633741546037171823<72> (JMB / GGNFS-0.77.1-20060513-pentium4 gnfs for P46 x P72 / 5.55 hours on Half dozen Win32 systems using a distributed version of GGNFS for stage-1 sieving. / October 17, 2006 2006 年 10 月 17 日)
28×10174-19 = 3(1)174<175> = 3 × 2971 × 10799 × 451939 × 605286277 × 5324553890743<13> × 168517515354625529559054637391101<33> × 131685862319569826123767299065424365952891770022473676802466204675977540215100361667406077973313830273073557<108> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=277564547 for P33 x P108 / June 26, 2005 2005 年 6 月 26 日)
28×10175-19 = 3(1)175<176> = 1129 × 4813 × 2021783 × 48989426767<11> × 35877664818871918379<20> × 1479040098898126552607950872991118425537418096925300001<55> × 1089343141261345549990530760606706805181401799514742667325043273654986775853897<79> (Dmitry Domanov / Msieve 1.40 snfs for P55 x P79 / May 17, 2011 2011 年 5 月 17 日)
28×10176-19 = 3(1)176<177> = 3457458712067567520813625719941<31> × 270178976470481648584113208793532043856912004359925161424173<60> × 333048105221143013142611194354689907341134869483745075418238821043779116346132714245927<87> (Makoto Kamada / GMP-ECM 5.0.3 B1=82280, sigma=3486448619 for P31) (Warut Roonguthai / Msieve 1.48 snfs for P60 x P87 / February 2, 2012 2012 年 2 月 2 日)
28×10177-19 = 3(1)177<178> = 32 × 244261 × 67159548244381<14> × 162757680668801<15> × 159600220063738292747896500529315636639369649<45> × 811215307770605991737684691618215811310801779281031684567784011504376693880106071174307096542314031<99> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P45 x P99 / December 19, 2012 2012 年 12 月 19 日)
28×10178-19 = 3(1)178<179> = 47 × 2874415202149<13> × 960299372213330711602381265026795313701482333286721815910703856162140683939593<78> × 239806813289433465100483117940345025105357455776354812060090736732232561128644715976909<87> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P78 x P87 / December 20, 2012 2012 年 12 月 20 日)
28×10179-19 = 3(1)179<180> = 17 × 158980370820846386325091<24> × 130636323549165510465523960184309<33> × 7681520532229285847327407805697901<34> × 114712818212665930084237933685466980822542837060511859279956130473398076525563656416693357<90> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=698854403 for P33 / July 8, 2005 2005 年 7 月 8 日) (Robert Backstrom / GMP-ECM 6.0.1 B1=1060000, sigma=1014459517 for P34 x P90 / January 25, 2008 2008 年 1 月 25 日)
28×10180-19 = 3(1)180<181> = 3 × 212832660449380219<18> × 429592807049600257003<21> × 550672806996146042970197534192003347369925634590341414266499<60> × 20597066033906815850781114480658202241082988085779509084563390462202477930781863159<83> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P60 x P83 / December 23, 2012 2012 年 12 月 23 日)
28×10181-19 = 3(1)181<182> = 31 × 30763 × 131778108005165319031015081<27> × 7563928137750457967474580790773668005253377255374658229968638820769147<70> × 32729131465645542025078220639122168362578291227157689536679633954404750525012041<80> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P70 x P80 / December 25, 2012 2012 年 12 月 25 日)
28×10182-19 = 3(1)182<183> = 29 × 12840007 × 580260502196602261861<21> × 2896032052036682153468178837130972357090552404416820269983597<61> × 497194012334052982862758872105915406506803949572603257202540316538701666764740742583793908661<93> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P61 x P93 / December 29, 2012 2012 年 12 月 29 日)
28×10183-19 = 3(1)183<184> = 3 × 23 × 61 × 281 × 20563656587141<14> × 11568206262492886403<20> × 11057677262918100992208967203352309452597507292684467280964699437181609297158699371682443367837677917123804761863003339830173712770295837704829633<146>
28×10184-19 = 3(1)184<185> = 525778616898163<15> × 8929000795771058884423<22> × 120051971280213158742792176985886666860528334687<48> × 55200173775971551789404940786961459935369493318477328847189718797724435334312457263687136545737112997<101> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P48 x P101 / January 1, 2013 2013 年 1 月 1 日)
28×10185-19 = 3(1)185<186> = 126719 × 56709157 × 64762787405822827<17> × 6107627265368785837854331<25> × 109451706111920927229745139138608495806623501109277114055036835640847661563231457459215759855673567399710907857070087728550735300541<132>
28×10186-19 = 3(1)186<187> = 34 × 53 × 131 × 199 × 4067309 × 916625868678918833697444587<27> × 7456430668834257789935629689706953845490417530837617773240220206737721146056877271697384437834443068299796703587179227184524836846837788764124001<145> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=1736394442 for P27 x P145 / June 23, 2005 2005 年 6 月 23 日)
28×10187-19 = 3(1)187<188> = 179 × 1858889 × 48572115197<11> × 440201725980094243625218327<27> × 603671770861716180601638184485785997811411<42> × 64651837698675086080094974611581348858089499083<47> × 112043981813773783541314219659012496043499596950513823<54> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=3001683282 for P27 / June 23, 2005 2005 年 6 月 23 日) (Jo Yeong Uk / GMP-ECM 6.3 B1=3000000, sigma=7924915071 for P42, GGNFS/Msieve v1.39 gnfs for P47 x P54 / December 11, 2012 2012 年 12 月 11 日)
28×10188-19 = 3(1)188<189> = 19 × 503 × 2416629624381304027373196419958393926957531<43> × 13470503866653980725975346962207094079095769556923068819279584548159094120699797381682796572270886434971475080102868213043108034624212177560433<143> (Dmitry Domanov / GGNFS/msieve snfs for P43 x P143 / 215.19 hours / December 14, 2009 2009 年 12 月 14 日)
28×10189-19 = 3(1)189<190> = 3 × 37337 × 25300129 × 1097822460553225227275285900695448767217872604693559801950186490312369606077222877344944547689224969194247318714855670979235984124680518656731272716891625683302639322927780014869<178>
28×10190-19 = 3(1)190<191> = 83 × 197 × 306898684974258906701022611<27> × 3903025884228757387157019754586401<34> × 566411654175336073779051055434185692429273<42> × 2804416823774290398535475890197371140903510729229348762350392625035735079960933230587<85> (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=3598967002 for P34 / March 21, 2005 2005 年 3 月 21 日) (Robert Backstrom / GMP-ECM 6.0.1 B1=2328000, sigma=500482026 for P42 x P85 / January 29, 2008 2008 年 1 月 29 日)
28×10191-19 = 3(1)191<192> = 6197 × 17839635938857<14> × 257151644189669463738913<24> × 6640250143350598462463268599219<31> × 1648064835818731819503175566093799461463906092440925968516339312383305952539020121973929333839216181356636543190133684097<121> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=2082117885 for P31 x P121 / July 2, 2005 2005 年 7 月 2 日)
28×10192-19 = 3(1)192<193> = 3 × 953 × 1291 × 297561836163749702555893<24> × 2832682466060203033799901405980658043023379813871295738626291526747066244229303756202182465086669361209283324208716858339813680230143046278051348284824984707404483<163>
28×10193-19 = 3(1)193<194> = 26740702564061<14> × 1163436564038667323052939380669477978226027620178398669027588709553713137805212626338869932651049999735504221628245374981606565662005809616907294834248011873822283556768256338104051<181>
28×10194-19 = 3(1)194<195> = 68711 × 88337 × 6983867049876129211051936820597921994926448841288461842847937<61> × 7339232455694647062603795354941115636271084095536001041829548564143692027854067676349447431085465657472466954675490150046929<124> (matsui / Msieve 1.48 snfs for P61 x P124 / December 27, 2010 2010 年 12 月 27 日)
28×10195-19 = 3(1)195<196> = 32 × 17 × 1213 × 47041 × 5287450731049160105331481<25> × 1707625350432798558548917787<28> × 39468245208345508959526022554968922207359861894313369022677879146318768751749288964947270916620642732883484805395587925040324724060537<134>
28×10196-19 = 3(1)196<197> = 31 × 59 × 217473341 × 1942944437014644587<19> × 313103321868850900243<21> × 244473869388239300149683099080893014032473258915007<51> × 525914672266947949730846370666001151872850812010507485852635658665589663679558681856930889573177<96> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P51 x P96 / January 9, 2013 2013 年 1 月 9 日)
28×10197-19 = 3(1)197<198> = 12421 × 10273447 × 72375231568337205881256773<26> × 4177240849049899311583039641602719171031742224309<49> × 6383872830522353817383869843235528566867561352034422827<55> × 1263220211218358051729777565891527308022345673393713669327<58> (Jo Yeong Uk / GMP-ECM v6.3 B1=11000000, sigma=5283046705 for P49, GGNFS/Msieve v1.39 gnfs for P55 x P58 / January 8, 2013 2013 年 1 月 8 日)
28×10198-19 = 3(1)198<199> = 3 × 7681 × 316768767781<12> × 285079978661287<15> × 11677129665096260974090620195773<32> × 37372288595954645332787364142970066370599<41> × 3425954829813547496322385057911265268910960458106209163395919512377952502103000289354283313996333<97> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3448535475 for P32, B1=3000000, sigma=80390821 for P41 x P97 / September 8, 2010 2010 年 9 月 8 日)
28×10199-19 = 3(1)199<200> = 53 × 86423 × 1686453450565791786260563<25> × 129788055635717129060443309006877407646875937495784717097132897171<66> × 31031390020768791310619114222088110006504935770084369487978389644026009875299893719346861201492880250853<104> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P66 x P104 / January 20, 2013 2013 年 1 月 20 日)
28×10200-19 = 3(1)200<201> = 1704023 × 8739212203807295182262848218418072616613215494473923<52> × 20891411554682040882505879096746006799492064955579448890853550439847309304822422247355291185317884580441859522081321587495869998526968664482459<143> (Robert Backstrom / Msieve 1.42 snfs for P52 x P143 / April 25, 2010 2010 年 4 月 25 日)
28×10201-19 = 3(1)201<202> = 3 × 1423 × 465664409819295204536418479658396523<36> × [1565007130098198547993163466898016739854197536465941252087255300810070900575518192002024509099192406250403851413239698370841215240924086784197537126352958925574153<163>] (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=413114658 for P36 / January 6, 2013 2013 年 1 月 6 日) Free to factor
28×10202-19 = 3(1)202<203> = 1828960261<10> × 17010271778185513627795060721175019073370184674073195246482783537696071960259562529177943200325833165333662277482972119704852959137700538104316478153983855809489953216162913181584491031820789851<194>
28×10203-19 = 3(1)203<204> = 277 × 1453 × 10657 × 7052333 × 188151621736279<15> × [54663117448603443453415646953122872585083673211882419904996845400471902463390934905024378304695813148853968494021216869048153719829964637721343144056624828222171361864272869<173>] Free to factor
28×10204-19 = 3(1)204<205> = 32 × 11996741 × 7393918085238246999651865447<28> × 274253494021193202811878603342987811<36> × 158539863928713775111950047670699085600521460918271446241<57> × 89628152486541748276368185176744795863066145626385809230767990397717259765527<77> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3230854732 for P36 / January 4, 2013 2013 年 1 月 4 日) (Dmitry Domanov / for P57 x P77 / February 1, 2013 2013 年 2 月 1 日)
28×10205-19 = 3(1)205<206> = 23 × 441053 × 72142989371911<14> × 77703414220814361634760543<26> × [547094904103780383248138003361459407551504443850965268348224998599325952669134488664809244255411177109946353463360861241286923802236161342638426552785322715853<159>] Free to factor
28×10206-19 = 3(1)206<207> = 19 × 6428255374913<13> × 171418705280871514585591<24> × 21027689072253691684699054343<29> × 2233307340414219729577544728861855871263245211<46> × 316424825107398796806476322146502768315695070231055605731533095545077686080635673706035961611591<96> (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=2775275096 for P46 x P96 / January 5, 2013 2013 年 1 月 5 日)
28×10207-19 = 3(1)207<208> = 3 × 317 × 37861 × 3968587692536329<16> × 34891314548077854334367<23> × 624007215019805100302298507506955238719174061861343873871484698132964769629068551846856914935555994551650847751657586131577057196168359149108514998373963652937707<162>
28×10208-19 = 3(1)208<209> = 23209 × 408866897427433<15> × 557761274435224577<18> × [5877989214813694915846133062257514715334128072129503160235493365070506233679438856974578033531063932567727140135777374658391230016864476561878087633739099404640501296650519<172>] Free to factor
28×10209-19 = 3(1)209<210> = 73847 × 39624731941895735396453387224531<32> × 2376927267350671487969812469603518472531<40> × 44730158272530920584279713790372872758382852215252146225715298287952697370549994217001706831020733178086759594437893213510990436042633<134> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1866622188 for P32, B1=1000000, sigma=654300476 for P40 x P134 / January 4, 2013 2013 年 1 月 4 日)
28×10210-19 = 3(1)210<211> = 3 × 29 × 6661 × [5368547940078568699103049852911373134597357945824832333537146421201316137874281261677790106264654458205183217995832856395369013853346225517743722010452179371622967645103702131486092680694298966381961065373<205>] Free to factor
28×10211-19 = 3(1)211<212> = 172 × 31 × 281 × 67419041 × 171740119 × 157921672757<12> × 16320433877514203<17> × 109052237318420021789543<24> × 9776745219573102210870607<25> × 9385182500696685373701770119<28> × 7497821736227014333372387930329571<34> × 5519696375766100761939483051252243654377800414664549<52> (Ignacio Santos / Yafu 1.33 for P34 x P52 / January 4, 2013 2013 年 1 月 4 日)
28×10212-19 = 3(1)212<213> = 53 × 719 × 11813 × 3759193621039<13> × 12457833067328574379<20> × 14757519161174034089616006521487767564842751364006870585865701875074362789281258450467846105989021611424445795726137896601689946007081797862202637596238402467763659468891341<173>
28×10213-19 = 3(1)213<214> = 33 × 227 × 349 × 1454455618299732032135781327584493612316621066885790794532223438251008807819610518602253606257774519797192786378025793627603988512086188546587953606398025597276095518048261850216108729699760362853432065936291<208>
28×10214-19 = 3(1)214<215> = 56843 × 3964302337<10> × 36208355057227<14> × 3812966305578766665452211325248603396723676260472539851859050235480391458343431810631754058718925124456017936787899165552746105678319304921846093346317241856093675753486052287520352929023<187>
28×10215-19 = 3(1)215<216> = 65053 × 180060264457<12> × [26560136878379484645203617180818249507058941694410181548767603456735692737130653089565753505413243928686403609584818827435883810900065051522354672447361189994640102783876618464268965843625936758880091<200>] Free to factor
28×10216-19 = 3(1)216<217> = 3 × 92767 × 328533425249<12> × 3459813473299495222362119<25> × [9834867377294291784229477564719769367807390751002050288504692047434391376247838874789169138168774717182931882205356839768170605634692710867726663565447888052745932504493765781<175>] Free to factor
28×10217-19 = 3(1)217<218> = 809 × 433416857 × 53577406900410268397<20> × [1656073133027918825912645778021480834766522163764948180275410933037826159827875931402597969703059428722189411746417337093842658170999899546989620565351830324104599473475488662984510622851<187>] Free to factor
28×10218-19 = 3(1)218<219> = 1427 × 6553 × 106557305761057<15> × 3701636701609387926125351832973409057<37> × 84347916069481647894268302158954223260128558351316579210166165451913071110579662567179259912732372736185579210040495555492942340569022787224203226037990021849669<161> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1598690375 for P37 x P161 / January 4, 2013 2013 年 1 月 4 日)
28×10219-19 = 3(1)219<220> = 3 × 18221003 × 387904002681162439<18> × 285301069000648941613<21> × 25513616252162509996404023<26> × 63846372655084681913264383563293<32> × 315708358475618952552935814264357622283722072764730079230901413220507657578513798457880557377348249573508038364513023<117> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2678719152 for P26 / January 4, 2013 2013 年 1 月 4 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2760527677 for P32 x P117 / January 5, 2013 2013 年 1 月 5 日)
28×10220-19 = 3(1)220<221> = 193 × 1951 × 3448895727444700739<19> × 3491486313186765099971579<25> × 32044307384035905885521059094895033319<38> × 6074612084991743987696516208865512406747666657<46> × 35248537021263094619636993967511409024084458362471130555161085525196612609107637245331599<89> (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=3467035402 for P38 / January 6, 2013 2013 年 1 月 6 日) (Dmitry Domanov / for P46 x P89 / February 7, 2013 2013 年 2 月 7 日)
28×10221-19 = 3(1)221<222> = 229 × 7462135777<10> × 2469954554959544927<19> × [73710257761336629111741847670181859922188774406081035819928876438895758450598126413815877789675641508279963177144559221002141366396975071513749724023935478381120011470213515432076836134596421<191>] Free to factor
28×10222-19 = 3(1)222<223> = 32 × 49081 × 2469161 × 2821751557<10> × [1010860968197685817818980601184837465656542469501041829307733697441749728220782880337723896976868010969751998678046591484658277723870516156094371091133873197351580646771919831078405716752191196848160867<202>] Free to factor
28×10223-19 = 3(1)223<224> = 277103779072150517821031319575967383053690384115168582319071040267829786000848323192717284755067<96> × 112272417270103696666129659133164734324599692680892959476257867256368451563452061118606154152322817101943440878936918610043741733<129> (matsui / Msieve 1.52 snfs for P96 x P129 / May 9, 2013 2013 年 5 月 9 日)
28×10224-19 = 3(1)224<225> = 19 × 47 × 5189 × 50372987082231229176171564381777593293<38> × 1332854330451672326348791491900002008052559135441858559196776502460297608315761751520877735995558898906561531380146468150147742318919211345326591171941638050050273921001783158346451<181> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=501057529 for P38 x P181 / January 5, 2013 2013 年 1 月 5 日)
28×10225-19 = 3(1)225<226> = 3 × 53 × 7219 × 1828907973626161<16> × 28240833340576533104959639<26> × 4689250826481740507527754950360181<34> × 11190990599030674482190224556416279560429375377743645892985969766792910444678115062277840599463112698958496618162402322561464268360434742528955409<146> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1163357452 for P34 x P146 / December 28, 2012 2012 年 12 月 28 日)
28×10226-19 = 3(1)226<227> = 31 × 5431 × 198453728201<12> × 5447819793995293101221<22> × [170919663799015719723983214254676421074313864514007929049582985168333748425763055041869373165371963798861542367830750886532146615721111901444079972154790774187120619703860380352855333882731<189>] Free to factor
28×10227-19 = 3(1)227<228> = 17 × 23 × 795680591077010514350667803353225348110258596192100028417163967036089798238135834043762432509235578289286729184427394146064222790565501562944018186984938903097470872406933788007956805910770105143506678033532253481102585961921<225>
28×10228-19 = 3(1)228<229> = 3 × 8167 × 199811 × 14883390854077<14> × 42698284961096541200301999425264596133614933571802335611224020249100451675735537107842751795747356760969040676137118005738572551559741084734099647749298463167103473582665705347613795220435436960887495790413<206>
28×10229-19 = 3(1)229<230> = 3772753 × 218135718595278405360250428259079<33> × 37803356677757057585096239333372074947023210933662595104679374531599381280287802017484351092134116219176426348482913076011531357786237868785469791586555497468299100369408675614121603197875953<191> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=813115774 for P33 x P191 / December 28, 2012 2012 年 12 月 28 日)
28×10230-19 = 3(1)230<231> = 167 × 5813191 × 13213815889<11> × 248171230242227<15> × 67202546406808465825974162834714089<35> × 1454182934881533020301415884039831917687558994490914182104161643629697775933075573976405306869598704871213791555105268494112194667988512398014164142437434400863989<163> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2029712269 for P35 x P163 / January 5, 2013 2013 年 1 月 5 日)
28×10231-19 = 3(1)231<232> = 32 × 83 × 1327 × 3279820403<10> × [956916259611796258632060897300051622201507137248462782491370851984306509188688375494295018429372983493668893441917588722602276420885386568488990702403682246091600654644453739983747706998233990811156560314891857421273<216>] Free to factor
28×10232-19 = 3(1)232<233> = 363179 × 85663298569331131786560101523246418738724185900371748121755693779406604212003202583605084851026934682652661941111989159921446755211923352151724386903183034016589921529359106972350028804284143937593063230834137191608300896007509<227>
28×10233-19 = 3(1)233<234> = 283 × 2897 × 6118729 × [62018230749017066065241161425025076339662544548154717890233559934648106988931597498985109826622469357274337733783654564060262949101588850624565923990417397251280002254376064173168189466708403671878596783913154683960967309<221>] Free to factor
28×10234-19 = 3(1)234<235> = 3 × 1493 × 166237 × 190933171181<12> × [21883933224801798964571302597382456542953720225499218542851785556564931317084729750336614808773381269300968790637910961443252833159777768119898253261906873214172831966546869354808011971215304134499442095304057985697<215>] Free to factor
28×10235-19 = 3(1)235<236> = 707436689 × 171858824067136659090673535089<30> × [255891645297538064414339770129613443750506456520344856783405701060648080543471613908003600935509452181323530936978625125570540101174323689975609100074987717731380838608074942507994476091733049153991<198>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3040236256 for P30 / December 28, 2012 2012 年 12 月 28 日) Free to factor
28×10236-19 = 3(1)236<237> = 3914851 × 180370873 × 4942484692588816930724637586231<31> × [89143266563089357653005357658334087718484254645488939221765412229975115404685173714499307020072730024711418854580058655976400399309723907258372878158114529594008288616242488156080263049749747<191>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=79160468 for P31 / January 5, 2013 2013 年 1 月 5 日) Free to factor
28×10237-19 = 3(1)237<238> = 3 × 2999 × 22968949 × 3485329496264591<16> × 194081544316857366845677<24> × [22256076067857169213168780317955834828770913745138442494218817502431433712516553377946405036165091775443493383877323089901833176795230762001156806103355136056069030383319120444001427839941<188>] Free to factor
28×10238-19 = 3(1)238<239> = 29 × 53 × 8105776919364303511941205155846456139<37> × [2497163665198775495980444731973814086249411894193222424269816809150125594493514330031572275299418313105936084007286799192995806970464362851557176949603657654946593625769087636956976160871078552716277<199>] (Ignacio Santos / GMP-ECM 6.4 B1=1000000, sigma=1155665703 for P37 / January 6, 2013 2013 年 1 月 6 日) Free to factor
28×10239-19 = 3(1)239<240> = 281 × 16987 × 20339116885520371<17> × 14303569955173795605457491219306680258156333333<47> × 224035055290398483237682319614037585720728884770822231892131764133727477347693538042040345873527335981586319647745419174671691957355614892497127103465967258947143168037891<171> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3138683912 for P47 x P171 / February 11, 2013 2013 年 2 月 11 日)
28×10240-19 = 3(1)240<241> = 33 × 14251 × 22568971 × 207876350224625653<18> × 1723413839177000844248845592603253524970709510269747799394882408444604463028318041054226733496619217240187979213135580174584736421588422728475776028383069998458859220619357979155865684760908846769560508861607161<211>
28×10241-19 = 3(1)241<242> = 31 × 2239 × 10211137 × 21187799 × 269735101 × 2329693512257<13> × 3944819521688647823737<22> × 835750014302686501172449139608678614740841456347012915006558167702416662393631787364723161216234216800391599614342059067949150504434333350114104700931426084999202946723192901339437<180>
28×10242-19 = 3(1)242<243> = 19 × 21470483 × 16462995831485766635960942323669<32> × [46324553098678440573909813932687166677039918251362218566692783680582722976866200053393026735648736344987640197431225104549788278703107694595906454386219961511656214280822270120093713615049940247467320947<203>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=4105959296 for P32 / January 5, 2013 2013 年 1 月 5 日) Free to factor
28×10243-19 = 3(1)243<244> = 3 × 17 × 61 × 166807 × 574373 × 5672837 × 7940707 × 1014582197124291915960990117625253437<37> × [228381283113231430608789891059631270025561765921740183986487459422155770681305564635030434726142933813991595755469887241236136061306803217924492735133012061435846114622203694975577<180>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1231443411 for P37 / January 5, 2013 2013 年 1 月 5 日) Free to factor
28×10244-19 = 3(1)244<245> = 1009 × 979186966927391<15> × [31488990024207298739081897043740598463484344977880925957090362206667470138213554373708001476871613170601081409421697441943998240481815315108201389612709418547628563992531252294930466884142124445207965068413294294490035689761769<227>] Free to factor
28×10245-19 = 3(1)245<246> = 6067 × [51279233741735802062157756899804040071058366756405325714704320275442741241323736791018808490375986667399227148691463838983206050949581524824643334615314176876728384887277255828434335109792502243466476200941340219401864366426753108803545592733<242>] Free to factor
28×10246-19 = 3(1)246<247> = 3 × 1037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037<247>
28×10247-19 = 3(1)247<248> = 7829114507385116798162128077524194285901<40> × [3973771373731262378001058673014213920557120090005553966081167599317853576982872351817637640895453020876592480138777372865502465187591796234106410234202876880909587307799896089768049434234886425362403659386211<208>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2422811890 for P40 / January 9, 2013 2013 年 1 月 9 日) Free to factor
28×10248-19 = 3(1)248<249> = 1187117 × 1642813 × 380988017 × 3614204976287221970362008347<28> × 79170748666404898630475491736689991<35> × 1463339241984853818405348268999368941789916908649665950015293490827118081942414407237363719780064875284669840190553376572013087916798858467922869665011320718297031899<166> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=388368575 for P28 / January 4, 2013 2013 年 1 月 4 日) (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=910401038 for P35 x P166 / January 5, 2013 2013 年 1 月 5 日)
28×10249-19 = 3(1)249<250> = 32 × 23 × 28759 × 613040891 × 93648336670552099024153543206145473835159<41> × [9102944267810099070371593868323161409168327022750931183601200978040752054141275785366150137547860971289006114457856583377512936909687727646517517442917340159501266224885960936513779367549625563<193>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=2209327258 for P41 / February 12, 2013 2013 年 2 月 12 日) Free to factor
28×10250-19 = 3(1)250<251> = 2137 × 9719 × 307537483530446451232791412379<30> × 4870699778614766771625640446555251272555939916674001013163474580946737972353185747251600946903082085525556288746847371921632419661499143951727767808948878391224915691986122609795091746665247267002174101605637408603<214> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2560468764 for P30 x P214 / December 30, 2012 2012 年 12 月 30 日)
28×10251-19 = 3(1)251<252> = 53 × 23410665018703<14> × 25457545902554846663691371<26> × 41230523237229923850829739<26> × 238885901696126937718106533019364774598454831123532771067339855394565068623609457654793173860090549625597130963522174921946582374074877661029644514595274988916211379334196046015108354541<186>
28×10252-19 = 3(1)252<253> = 3 × 473203 × 6156379 × 27165844512318120536003<23> × [13103829063658512213897054572420945956212465948908043850043957444382953710966959567461550051651807564073203921215057089866266639338257212425965872553832958970545572724113375752057095530981521285275732633356235792166767<218>] Free to factor
28×10253-19 = 3(1)253<254> = 8059 × 685666249 × 95101327693<11> × 1814775432839<13> × 55561903873392207463<20> × 809595431073184212059<21> × [725215294819502125351172735747790571786678119839541065209797513552189647189579487891435196755207461436862545105460860728846292810339225114604615962124111594091707300596091159219<177>] Free to factor
28×10254-19 = 3(1)254<255> = 59 × 419 × 5349791 × 14193286854275356159<20> × 14533981693471300057<20> × 11403681587426083967902592656477169565523767101946639458441135315657527453939522865502340877984625122526693319388039901423497445032685245981557283058289455642928397452682038856631575938683288337520523459727<206>
28×10255-19 = 3(1)255<256> = 3 × 97 × 787 × 1314088819393091227<19> × 25542098152553843811335591<26> × 1930540237869362292273337183<28> × 209646517644929544837482877112539703639949305906020527101788234866414410809409406975512803412813662911684446774804597766596022119032980143379843521768565693034382421550916791818293<180>
28×10256-19 = 3(1)256<257> = 31 × 1847 × 6299 × 76491763739<11> × 290655695509<12> × 3879911430722882704959339147660739472944120961346800047213493764756217345161712319133131270222026149588233206277162478424309824359283256554063461474121257772183359519537776309533811109912612346535713018666918727568582253024427<226>
28×10257-19 = 3(1)257<258> = 379 × 820873644092641454119026678393433010847258868367047786572852535913221929053063617707417179712694224567575491058340662562298446203459396071533274699501612430372324831427733802403987100557021401348578129580768103195543828789211374963353855174435649369686309<255>
28×10258-19 = 3(1)258<259> = 32 × 9645889564790725182553<22> × 606055951416654850040836594343911<33> × [59131378926742805274830983366670150952962413520753393170615839831013406056668811760344294296386966561364391815402204337364806670934502878816687181614613172601970442865992372562701110236554924710266944513<203>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=547781861 for P33 / September 21, 2015 2015 年 9 月 21 日) Free to factor
28×10259-19 = 3(1)259<260> = 17 × 181 × 1903991 × 38795663762367791<17> × [136879984634150642597201878880407028319666921211659840889781151126343767120657775046346294818410564496504395253562998339364829249740760509504553341536310845177614373979179027898583946596500790152507587649049151889643079485603315518803<234>] Free to factor
28×10260-19 = 3(1)260<261> = 19 × 1712783588661211109<19> × [9560033803597347794659145508511654034893116515553598910745084814026723188214365708257076513209815382380134084812027920984896883657482223115595044737327884252403306150265248730927126688892489441466504435530677132914329596958855010441943133241<241>] Free to factor
28×10261-19 = 3(1)261<262> = 3 × 5828299 × [177931337605884158832111570981007844147501189804613153346634590476061203626827833822018574722579784777177189611761002144371288610456848050698331886719785144351214142760527048635809013408035009363287133525070871799308346575396532854103236130650990458285863<255>] Free to factor
28×10262-19 = 3(1)262<263> = 3023 × [10291469107215054949093983166096960341088690410556106884257727790642114161796596464145256735398978204138640790972911383099937516080420480023523357959348697026500532951078766493917006652699672878303377807181975226963649060903443966626235895174036093652368875657<260>] Free to factor
28×10263-19 = 3(1)263<264> = 1741 × 18728249 × 4641312757<10> × [2055789963101849110790921794936318539500024885016360005152589056415816050116306797705121293424919298619577463354808714918598324176801174271529958953219549889050077974620471980505035458688851856741767265931043464043079703445810373294608999852847<244>] Free to factor
28×10264-19 = 3(1)264<265> = 3 × 53 × 1549 × 5918879396601947<16> × 78516401166744507419<20> × 33708677441520222277661430034122010891<38> × [806353342130345875911307276957210353450558971918947364689508726002938136590369297824190383528446369701622361807728775684955235115132097744650045000552977546937488484316122762662056485167<186>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3667437401 for P38 / September 28, 2015 2015 年 9 月 28 日) Free to factor
28×10265-19 = 3(1)265<266> = 313 × 84088799857<11> × 2379086357865086947982333975447439386509<40> × [496847173542934070783190651777268139980254038873660631820404164723344865283547888919634313937872448272577799625190394052652037909635467930086822359335392622901125643888486024068966959406476479289859118632301520619<213>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3483236925 for P40 / September 29, 2015 2015 年 9 月 29 日) Free to factor
28×10266-19 = 3(1)266<267> = 29 × 109 × 28619 × 3439034807074341717367343540322316487271688175059733670262451452020740067246714665791324224315167220285560476286226990709279201628462570240950237938896239150264316047564067102835275277068264979710044682875675363028905145280115532310922778265389925485831004029<259>
28×10267-19 = 3(1)267<268> = 34 × 281 × [136686046795444449326088972853174777519050617772115070124823650591411234616717679851988537898647296301177940824705026629370902469623966921976675502443263086468569531703840389750499148153029792676556878481222754321475818773828527354295114938320421383555692241602351<264>] Free to factor
28×10268-19 = 3(1)268<269> = 1402267074867695145565063723<28> × [22186295085083179074709133622905489861576054218407322198325672276941804265526927261423013692604387759931015146333337368195211637212372533370220209191242825006862399310054345504307575240134969956180713641372255450907430354218139799475605894357<242>] Free to factor
28×10269-19 = 3(1)269<270> = 2766494227817<13> × 405162426707443<15> × [277559815305043696616612168545749328711703795020851938055026126703063895642771810977028415870720104591349062853165791710911794846687784107113165473325494546617760421943297023090892799131034585292399795156078199752394271576377189834611818973781<243>] Free to factor
28×10270-19 = 3(1)270<271> = 3 × 47 × 389 × 1174093 × 1936399 × 6925256993<10> × 11820371060010816993957254273776245619<38> × 304777186075184326819013016533894859281898162762609010070711579005351255101559397362502810413684838731915705492511504300612557892665871465444772523031553331377216541570449332134346824710122989375797157650431<207> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2878339613 for P38 x P207 / September 28, 2015 2015 年 9 月 28 日)
28×10271-19 = 3(1)271<272> = 23 × 31 × 2959219 × 1015550677<10> × 3428160409<10> × 4235319231254998672251102140211557295424894422350044201702630141649336243907477543645553771028708947353825202516595297384284675922846446313204793174052583267731929569370701002329370147281671881159100002094194216836507311339102775937523372628041<244>
28×10272-19 = 3(1)272<273> = 83 × 113 × 277 × 129640189908659<15> × 7271587518177379<16> × [127031177260232769682324174647092414300321545166680736241523412909823045502332424126798593270310961530972646273641804040302160953758184414428386593042651244309734150020508625219813407464505984786797068090802573384413467997504326150752097<237>] Free to factor
28×10273-19 = 3(1)273<274> = 3 × 443837 × 43229414375465011153626527041<29> × [54049466435469321168351077380065397865263728261121420883183524881645498225998698330967241129006665475298678527768717870980114583482261517419031124156556004834934553837117507695956444042298213720405794063603040595735194396934208866176490161<239>] Free to factor
28×10274-19 = 3(1)274<275> = 385533827842431286151675845742489<33> × 80696190228542814193420935131011090088614249309834868547219141788358202657415073396649260755390255226354261630073257253444939901550258494918813773011150352239847587956176368248716090237805716607159809131491650303760326663789262755030765922399<242> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3889476600 for P33 x P242 / September 14, 2015 2015 年 9 月 14 日)
28×10275-19 = 3(1)275<276> = 17 × 128393 × 74263756911980325293<20> × 668320169691820411126237<24> × [2871863340451882296334612744694748885558741917375992171996787949887713045451269865612152966686643927040024375661079234810426844596690945360476190201369315418423607718737862298945513717303843483354831943090743177693170604319991<226>] Free to factor
28×10276-19 = 3(1)276<277> = 32 × 223 × 23580031 × [65739103574750967052766419929372775551159040150168010100949193944077651300006385171278069371776158494333827979158097883694919378111980483870941655704908099827952972808930445262733913059914604702120828991225658541675670853368123085456143178397470193502302627368006383<266>] Free to factor
28×10277-19 = 3(1)277<278> = 53 × 238031 × 2586620583780187<16> × 953396167687491502810476903083068848766391650810707408568588731881443959917339075433456753389055410560881036826412354566182300850561789301993610355253056339655659537131353126396072686507519326955087133226126753707065709034794096267678711053525300873319071<255>
28×10278-19 = 3(1)278<279> = 19 × [16374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269005847953216374269<278>] Free to factor
28×10279-19 = 3(1)279<280> = 3 × 1978315215736060230746550414639836867<37> × [524202123497893990092648339421171993669448184796398503509255095105486289212127112557364518545700418030289036450089954738267402415510487179771643646876312211788021140044561882667205692489441342762076982948098187020110317952287252951682424794511<243>] (Serge Batalov / GMP-ECM B1=3000000, sigma=1:3673062555 for P37 / September 26, 2015 2015 年 9 月 26 日) Free to factor
28×10280-19 = 3(1)280<281> = 307 × 12338526744217<14> × [8213227254860404240564696761559511202719467279270649088097553717984585894601189455751622348888947477697188616145462065141884149424682446750103832609050392934250644045963064243551830486992262288238159269446513327680605710936513545342219318312791222848551260687589669<265>] Free to factor
28×10281-19 = 3(1)281<282> = 1330559 × 2825222159407<13> × 249099877106309113004848752116479888099073<42> × [332242562537515694491638799897973811785852777419366729831015737392698067212701062546109105781329440957544061059381430972409536728351359464285804071559202917764427446918666945866979074316143427848549241137476885959881068439<222>] (KTakahashi / GMP-ECM 6.4.4 B1=30000000, x0=2270268000 for P42 / September 21, 2015 2015 年 9 月 21 日) Free to factor
28×10282-19 = 3(1)282<283> = 3 × 24328164040495428640090757791693753981<38> × 42627015968440436103071655177054425409410074382415513342583700487958376369888604244590016563622740311279370508813828652312544583216279094393793238171772480448773689973396722812999650982904581578686652179647495954349859472198984419616868416790577<245> (Serge Batalov / GMP-ECM B1=3000000, sigma=1:1374701821 for P38 x P245 / September 28, 2015 2015 年 9 月 28 日)
28×10283-19 = 3(1)283<284> = 1123 × 1607 × 339586934741<12> × 1451389586204025194693<22> × 407829509003410572569465392421<30> × [85764244619761670213984217309592054754161248896078570681259934274532568130225258518469954531837122201099922858619339436485109036703287582338339263671570070981950180472319110228776000123590535672115463003103909657687<215>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2578001563 for P30 / September 21, 2015 2015 年 9 月 21 日) Free to factor
28×10284-19 = 3(1)284<285> = 135909259 × [2289109023183704585653808259753009992579763172066967940065886983543270669374417758477449362821639040141563211017956555197693419188689058418831575787718120890579729458396290065205278700777193635579391328379703042241670312624624869090862390112149100239823330293568233722112421429<277>] Free to factor
28×10285-19 = 3(1)285<286> = 32 × 199 × 4657286302517802481117<22> × 11823340164366709959858719141<29> × [31546182740330756269595382051221523901597777185691021203539861839727801543130876816895179378689278341958280559622446339828012066956248242659631902506745868663512940625465930668979454233570988221518340207923946174562332636840280305993<233>] Free to factor
28×10286-19 = 3(1)286<287> = 31 × 317 × 1531 × 2857 × [723784260692137049647711760294864464092405671021001223422097554991755787193784447128441882724297900288034677248062698478787467428243155026486177895730778054891524797309895557574175538037339235454255625292389568948092572292351337869865070640224394870945187290218925159228497279<276>] Free to factor
28×10287-19 = 3(1)287<288> = 2738426465902615115336612500243194007966547<43> × 113609445053535702212396432836603749231701718276355102909370939218786467522450706655664485565312568535146059424482779933881969212683013422325010168784250695582776885801026364050005081723150106002143091186457897553472898356911657597506862265118013<246> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=286569100 for P43 x P246 / September 22, 2015 2015 年 9 月 22 日)
28×10288-19 = 3(1)288<289> = 3 × 197 × 383 × 26666279232742159139<20> × 744745332422358714370577027369<30> × [692084391202613815802957115958909759088018107967381970733712637101728292200459854686915275584259138627431234659470215279915383290681030282894380380067226445084707612983296356462715365500108750230417605285613779029739189313780631574357<234>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1596298729 for P30 / September 21, 2015 2015 年 9 月 21 日) Free to factor
28×10289-19 = 3(1)289<290> = 1240332493<10> × 208286363953<12> × [120424974287392079326870317636234982445229084718597915484053877241880507508903741380732260582739887690419065137621831702331314145408303194267725607213808777830970730407761202641495213434117282211264652657253696175675215427398820294811334878573711149784390901879602827859<270>] Free to factor
28×10290-19 = 3(1)290<291> = 53 × 1801 × 4451 × 4379714834589277230489581459911<31> × 460781691231933928442711454837632693<36> × 362850141240883940812095438639952968993915006224358345014123385705306236404426278226441358661437967713646185292719755366037800705890166518023858308828693773550802298088371177727806007834519803958547794822906005953419<216> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=972449901 for P31 / September 14, 2015 2015 年 9 月 14 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=325840790 for P36 x P216 / September 30, 2015 2015 年 9 月 30 日)
28×10291-19 = 3(1)291<292> = 3 × 17 × 7487 × 723493 × 49974546041590177750681<23> × 311296709105738140488713922706427088714719<42> × [723902025540233727408145769430748998839525650619663325195387001954192352507995405861805410726233470716857295265895184219571051055374331773673953047254948183723041620066866569776752702136567764747785821419206945856289<216>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3518330838 for P42 / September 30, 2015 2015 年 9 月 30 日) Free to factor
28×10292-19 = 3(1)292<293> = 3923 × 269921131187717<15> × 2309318062111419349<19> × 67646341929133030440493741425534191<35> × 188075514967011516236062192957925393718910528591217081839408774568474505830680115492254192240300859386614362878240566831901055495732566381586636409614421863787319815533944840193871945165214131283267801058435288963848285019<222> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1355759420 for P35 x P222 / September 23, 2015 2015 年 9 月 23 日)
28×10293-19 = 3(1)293<294> = 23 × 653 × [20714502371070717831487523211339710440848998675751455563693395772761908989354225388581870371603376463886484527006532466283448372801858386784147487256882023510960191165264738738338844870571350363613496977902064792004202084766702917045816040422871769832286511159938152414349231713903130109269<290>] Free to factor
28×10294-19 = 3(1)294<295> = 33 × 29 × 5121156479<10> × 18829797627890360611<20> × 19698262013157495019003100101<29> × [2091761433142545119428111246933588829997484051556132181293671972507724071957411759796219936346609767291485465830614758629198469203683829075730999574542662957170460638547537532878486329659877791106236955987965901912815117732425003742393<235>] Free to factor
28×10295-19 = 3(1)295<296> = 281 × 524171 × 38841163811<11> × 84290937371099<14> × 216716367160477<15> × [297694891716055283222535375472159491942666972444569606795924449195091139893991743541473083852153587035713953207193480357671411273438030209632010494557909676814526042508930783434511830364066963089987370873921127583957013715049562263350944447474279537<249>] Free to factor
28×10296-19 = 3(1)296<297> = 19 × 467 × 18713 × 50207 × 50503 × 127588303 × 35576003882347<14> × 111082629221743959053232281<27> × [1465568082911936318169261565216644848147460927818744998700558889010005454103148473852200282652349515995675585799712172273156709000778812885464159682677497241951255030157165599505877767472921551072269063653614270732490149955198250379<232>] Free to factor
28×10297-19 = 3(1)297<298> = 3 × 587 × 149012887 × 3352240823309876423<19> × [3536691075087655408489495529186603363147873429677701956268343346076170803372231463852647209455372671520254657214501096966104699440835152581050116026563374186608105807804944620333561317731918152102497539385849975364159296844933572611843048169436322962115047453053670151<268>] Free to factor
28×10298-19 = 3(1)298<299> = 233 × 177928035834443<15> × 6423149479910145538241676541230862711873<40> × [116833446234284071155868294601677097278840309282348385007656938355114785774786591690539212754379906951023429265231007407973802640133412455358347848085473978545949237227395983259110919167312664730751584400344965642971543465080764073977136572653<243>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=35641354 for P40 / September 23, 2015 2015 年 9 月 23 日) Free to factor
28×10299-19 = 3(1)299<300> = 1399 × 20542805450537843832532488543951103133<38> × [10825252976090349681922557884271702740521564608111605447227220950503928027926233706921811541621609930852775768143620508581913667422382545717001365493481724153299862264208988938672802618448626527466456896840873453840347171636141896628386244557553920803309069733<260>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=3607260267 for P38 / September 21, 2015 2015 年 9 月 21 日) Free to factor
28×10300-19 = 3(1)300<301> = 3 × 1117 × 205823763712702181<18> × 32041290578881094286845356523<29> × [140778255122991742209716858817689310806225664606528447613872113350257164931407727774723876292097006740400323757914915101348014246731885247996650754181827880983853012332872134947174266101783591079549515291774721172456461791532886328758510991050927752247<252>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2141133357 for P18, B1=3000000, sigma=3826725582 for P29 / September 21, 2015 2015 年 9 月 21 日) Free to factor
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