Table of contents 目次

  1. About 400...003 400...003 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 400...003 400...003 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 400...003 400...003 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 400...003 400...003 について

1.1. Classification 分類

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

1.2. Sequence 数列

40w3 = { 43, 403, 4003, 40003, 400003, 4000003, 40000003, 400000003, 4000000003, 40000000003, … }

1.3. General term 一般項

4×10n+3 (1≤n)

2. Prime numbers of the form 400...003 400...003 の形の素数

2.1. Last updated 最終更新日

December 11, 2018 2018 年 12 月 11 日

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

  1. 4×101+3 = 43 is prime. は素数です。 (Makoto Kamada / November 24, 2004 2004 年 11 月 24 日)
  2. 4×103+3 = 4003 is prime. は素数です。 (Makoto Kamada / November 24, 2004 2004 年 11 月 24 日)
  3. 4×107+3 = 40000003 is prime. は素数です。 (Makoto Kamada / November 24, 2004 2004 年 11 月 24 日)
  4. 4×1010+3 = 40000000003<11> is prime. は素数です。 (Makoto Kamada / November 24, 2004 2004 年 11 月 24 日)
  5. 4×1040+3 = 4(0)393<41> is prime. は素数です。 (Makoto Kamada / PPSIQS / November 24, 2004 2004 年 11 月 24 日)
  6. 4×10419+3 = 4(0)4183<420> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Makoto Kamada / PPSIQS / January 17, 2005 2005 年 1 月 17 日)
  7. 4×10449+3 = 4(0)4483<450> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Makoto Kamada / PFGW / January 17, 2005 2005 年 1 月 17 日)
  8. 4×101737+3 = 4(0)17363<1738> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / July 29, 2006 2006 年 7 月 29 日) [certificate証明]
  9. 4×102245+3 = 4(0)22443<2246> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by:証明: Serge Batalov / PRIMO 3.0.6 / July 1, 2008 2008 年 7 月 1 日) [certificate証明]
  10. 4×103131+3 = 4(0)31303<3132> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by:証明: Maksym Voznyy / Primo 3.0.9 / December 29, 2012 2012 年 12 月 29 日) [certificate証明]
  11. 4×103813+3 = 4(0)38123<3814> is prime. は素数です。 (discovered by:発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by:証明: Youcef L / Primo 4.0.0 - alpha 14 - LG64 / November 2, 2012 2012 年 11 月 2 日) [certificate証明]
  12. 4×105345+3 = 4(0)53443<5346> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 21, 2004 2004 年 12 月 21 日)
  13. 4×105659+3 = 4(0)56583<5660> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 21, 2004 2004 年 12 月 21 日)
  14. 4×105681+3 = 4(0)56803<5682> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 21, 2004 2004 年 12 月 21 日)
  15. 4×108410+3 = 4(0)84093<8411> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 31, 2004 2004 年 12 月 31 日)
  16. 4×109097+3 = 4(0)90963<9098> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / January 4, 2005 2005 年 1 月 4 日)
  17. 4×1011293+3 = 4(0)112923<11294> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / August 29, 2010 2010 年 8 月 29 日)
  18. 4×1021061+3 = 4(0)210603<21062> is PRP. はおそらく素数です。 (Ray Chandler / srsieve, PFGW / August 29, 2010 2010 年 8 月 29 日)

2.3. Range of search 捜索範囲

  1. n≤50000 / Completed 終了 / Ray Chandler / September 7, 2010 2010 年 9 月 7 日
  2. n≤200000 / Completed 終了 / Bob Price / August 10, 2015 2015 年 8 月 10 日

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

Cofactors are written verbosely to clarify that they are integers. 補因子はそれらが整数であることを明確にするために冗長に書かれています。

  1. 4×106k+3 = 7×(4×100+37+36×106-19×7×k-1Σm=0106m)
  2. 4×106k+2+3 = 13×(4×102+313+36×102×106-19×13×k-1Σm=0106m)
  3. 4×1015k+2+3 = 31×(4×102+331+36×102×1015-19×31×k-1Σm=01015m)
  4. 4×1016k+15+3 = 17×(4×1015+317+36×1015×1016-19×17×k-1Σm=01016m)
  5. 4×1018k+16+3 = 19×(4×1016+319+36×1016×1018-19×19×k-1Σm=01018m)
  6. 4×1021k+1+3 = 43×(4×101+343+36×10×1021-19×43×k-1Σm=01021m)
  7. 4×1022k+15+3 = 23×(4×1015+323+36×1015×1022-19×23×k-1Σm=01022m)
  8. 4×1028k+19+3 = 29×(4×1019+329+36×1019×1028-19×29×k-1Σm=01028m)
  9. 4×1033k+25+3 = 67×(4×1025+367+36×1025×1033-19×67×k-1Σm=01033m)
  10. 4×1046k+6+3 = 139×(4×106+3139+36×106×1046-19×139×k-1Σm=01046m)

— Read more続きを読む —— Hide more続きを隠す —

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 18.95%. 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 18.95% です。

3. Factor table of 400...003 400...003 の素因数分解表

3.1. Last updated 最終更新日

August 19, 2024 2024 年 8 月 19 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=214, 216, 225, 229, 230, 233, 236, 237, 238, 239, 243, 245, 247, 249, 252, 253, 255, 257, 259, 260, 261, 265, 266, 268, 269, 271, 272, 273, 275, 276, 277, 281, 282, 289, 290, 292, 293, 294, 295, 296, 299, 300 (42/300)

3.4. Factor table 素因数分解表

4×101+3 = 43 = definitely prime number 素数
4×102+3 = 403 = 13 × 31
4×103+3 = 4003 = definitely prime number 素数
4×104+3 = 40003 = 109 × 367
4×105+3 = 400003 = 269 × 1487
4×106+3 = 4000003 = 7 × 139 × 4111
4×107+3 = 40000003 = definitely prime number 素数
4×108+3 = 400000003 = 13 × 1783 × 17257
4×109+3 = 4000000003<10> = 23687 × 168869
4×1010+3 = 40000000003<11> = definitely prime number 素数
4×1011+3 = 400000000003<12> = 59 × 5521 × 1227977
4×1012+3 = 4000000000003<13> = 7 × 571428571429<12>
4×1013+3 = 40000000000003<14> = 1620733 × 24680191
4×1014+3 = 400000000000003<15> = 13 × 12799 × 15193 × 158233
4×1015+3 = 4000000000000003<16> = 172 × 23 × 601775236949<12>
4×1016+3 = 40000000000000003<17> = 192 × 110803324099723<15>
4×1017+3 = 400000000000000003<18> = 31 × 277 × 46582042622569<14>
4×1018+3 = 4000000000000000003<19> = 7 × 571428571428571429<18>
4×1019+3 = 40000000000000000003<20> = 29 × 1193 × 10723 × 25943 × 4156091
4×1020+3 = 400000000000000000003<21> = 132 × 9342079 × 253355158453<12>
4×1021+3 = 4000000000000000000003<22> = 3637 × 1099807533681605719<19>
4×1022+3 = 40000000000000000000003<23> = 43 × 1597 × 552317869 × 1054623697<10>
4×1023+3 = 400000000000000000000003<24> = 5529864491<10> × 72334503069833<14>
4×1024+3 = 4000000000000000000000003<25> = 7 × 36313 × 15736198370516658733<20>
4×1025+3 = 40000000000000000000000003<26> = 67 × 131 × 4557365842543010140139<22>
4×1026+3 = 400000000000000000000000003<27> = 13 × 30769230769230769230769231<26>
4×1027+3 = 4000000000000000000000000003<28> = 47 × 85106382978723404255319149<26>
4×1028+3 = 40000000000000000000000000003<29> = 1831772893<10> × 21836768167526322271<20>
4×1029+3 = 400000000000000000000000000003<30> = 3461 × 115573533660791678705576423<27>
4×1030+3 = 4000000000000000000000000000003<31> = 72 × 17918827 × 929224609 × 4902680951929<13>
4×1031+3 = 40000000000000000000000000000003<32> = 17 × 113 × 157 × 15460147 × 8578658012253554917<19>
4×1032+3 = 400000000000000000000000000000003<33> = 13 × 31 × 199 × 5232 × 607 × 8179 × 59809 × 61410559003<11>
4×1033+3 = 4000000000000000000000000000000003<34> = 1252548654233<13> × 3193488721162217725691<22>
4×1034+3 = 40000000000000000000000000000000003<35> = 19 × 2105263157894736842105263157894737<34>
4×1035+3 = 400000000000000000000000000000000003<36> = 703217 × 568814462676528013401268740659<30>
4×1036+3 = 4000000000000000000000000000000000003<37> = 7 × 11149 × 719839 × 71201749258188406897696039<26>
4×1037+3 = 40000000000000000000000000000000000003<38> = 23 × 3417863 × 11106131 × 28767319337<11> × 1592631563401<13>
4×1038+3 = 400000000000000000000000000000000000003<39> = 13 × 61 × 151 × 3340487544157069724326265418437821<34>
4×1039+3 = 4000000000000000000000000000000000000003<40> = 3559 × 5959039 × 188606117700241577197335460603<30>
4×1040+3 = 40000000000000000000000000000000000000003<41> = definitely prime number 素数
4×1041+3 = 400000000000000000000000000000000000000003<42> = 233 × 1937339 × 1239445849<10> × 174437176759<12> × 4098565147759<13>
4×1042+3 = 4000000000000000000000000000000000000000003<43> = 7 × 514081 × 1533793 × 588702187 × 645627007 × 1906717307857<13>
4×1043+3 = 40000000000000000000000000000000000000000003<44> = 43 × 1949 × 6597728841459523<16> × 72341120951148076950623<23>
4×1044+3 = 400000000000000000000000000000000000000000003<45> = 13 × 94138981 × 326848989041327834542517841458585251<36>
4×1045+3 = 4000000000000000000000000000000000000000000003<46> = 85554671991781313<17> × 46753729596254594601616296131<29>
4×1046+3 = 40000000000000000000000000000000000000000000003<47> = 11056524438627739261<20> × 3617773399048763681664977023<28>
4×1047+3 = 400000000000000000000000000000000000000000000003<48> = 17 × 29 × 31 × 503 × 1483 × 53342777 × 2087124133<10> × 315150747280807479049<21>
4×1048+3 = 4000000000000000000000000000000000000000000000003<49> = 7 × 5743 × 370561 × 629509 × 29265534253<11> × 14574881252350104917899<23>
4×1049+3 = 40000000000000000000000000000000000000000000000003<50> = 96737 × 413492252188924610025119654320477170059026019<45>
4×1050+3 = 400000000000000000000000000000000000000000000000003<51> = 13 × 619 × 947203 × 420238111 × 124878447097068053404902022142353<33>
4×1051+3 = 4(0)503<52> = 997 × 16703 × 19334827 × 12423102295978191365878024219063375979<38>
4×1052+3 = 4(0)513<53> = 19 × 139 × 1717151534304991<16> × 8820292101058400274622073281224013<34>
4×1053+3 = 4(0)523<54> = 113736971 × 205345229454254982049<21> × 17126700982101592925834057<26>
4×1054+3 = 4(0)533<55> = 7 × 506224025651386627704835321<27> × 1128805711450147951504196749<28>
4×1055+3 = 4(0)543<56> = 167 × 257 × 373 × 655043214941420453112883<24> × 3814447242350040082886443<25>
4×1056+3 = 4(0)553<57> = 13 × 229 × 7237 × 94026330103<11> × 6772499207780011<16> × 29155744481593836839059<23>
4×1057+3 = 4(0)563<58> = 1913 × 758192900771<12> × 2757816131651999470095997764009837314313961<43>
4×1058+3 = 4(0)573<59> = 67 × 1231334149<10> × 484852081669290509020235867123571992329212476941<48>
4×1059+3 = 4(0)583<60> = 23 × 163315541 × 15789751463<11> × 255568626556589<15> × 26388931651976961368052403<26>
4×1060+3 = 4(0)593<61> = 7 × 631 × 1291 × 1505223991<10> × 466020710964249919277261248950521303496753439<45>
4×1061+3 = 4(0)603<62> = 11715631 × 8527688325586767640299523<25> × 400371345601809272177979841231<30>
4×1062+3 = 4(0)613<63> = 13 × 31 × 1092463 × 3279390781699<13> × 277048011019479194194042226938639674113173<42>
4×1063+3 = 4(0)623<64> = 17 × 74204163711511347990420743<26> × 3170901818418546091021277212217881813<37>
4×1064+3 = 4(0)633<65> = 43 × 29077 × 239383 × 732801400264626147547<21> × 182373756375451621296178240918873<33>
4×1065+3 = 4(0)643<66> = 4897007 × 91140629 × 896225393550567626004411111430780045971410451574201<51>
4×1066+3 = 4(0)653<67> = 7 × 727 × 786009039103949695421497347219493024169777952446453134211043427<63>
4×1067+3 = 4(0)663<68> = 857 × 4984984436833854319<19> × 9363007313740275447130543099248941684370785141<46>
4×1068+3 = 4(0)673<69> = 13 × 5119 × 14437 × 1854533283495367<16> × 28694593629301657<17> × 7823837871411872332717728883<28>
4×1069+3 = 4(0)683<70> = 59 × 32533 × 1205901887<10> × 328729116101154124253440727<27> × 5256948467486007993654347501<28>
4×1070+3 = 4(0)693<71> = 19 × 97 × 601 × 2971761873163904493819043<25> × 12151955698323834928541791881818181870547<41>
4×1071+3 = 4(0)703<72> = 14202971 × 16572542984479<14> × 1699384437973117568257322220194835951205844123659367<52>
4×1072+3 = 4(0)713<73> = 72 × 163 × 181 × 17406058021883851<17> × 158963459299121978057868223270123375968989113977799<51>
4×1073+3 = 4(0)723<74> = 47 × 38651 × 98408142554574728256715931<26> × 223753771364935104631412998476650404951829<42>
4×1074+3 = 4(0)733<75> = 13 × 4423 × 907267 × 393959963360490547<18> × 19463121630578963076845880068289883893278245153<47>
4×1075+3 = 4(0)743<76> = 29 × 192703981903169033189<21> × 692627876009531473013076623<27> × 1033406855356254553510513181<28>
4×1076+3 = 4(0)753<77> = 28191931 × 109289310103<12> × 759865446779947<15> × 358896508908960601<18> × 47604888563333520693755893<26>
4×1077+3 = 4(0)763<78> = 31 × 643 × 20067225204434856770180103346209802839512366427532232980484623488687101791<74>
4×1078+3 = 4(0)773<79> = 7 × 752484841 × 759388814622740590958201869515895574793949332766122033508750206741469<69>
4×1079+3 = 4(0)783<80> = 17 × 40217863089699709946201623753351<32> × 58504878074270570805668029332137033440247501909<47> (Makoto Kamada / GGNFS-0.61.3 for P32 x P47)
4×1080+3 = 4(0)793<81> = 13 × 193 × 11779 × 963181 × 27229732902193<14> × 2571702684596833<16> × 200668341681534899665756229395868014057<39>
4×1081+3 = 4(0)803<82> = 23 × 919 × 489989436803651256409361574497<30> × 386215701843389652460659709818016609033839909427<48> (Makoto Kamada / GGNFS-0.61.3 for P30 x P48)
4×1082+3 = 4(0)813<83> = 1965571 × 46275720811<11> × 5329642249540100939055458167<28> × 82512549255444045959336643292923146389<38>
4×1083+3 = 4(0)823<84> = 283 × 3251 × 7839769653287083<16> × 9169875801760125509<19> × 6047694299909460387623389320225188893148053<43>
4×1084+3 = 4(0)833<85> = 7 × 9601 × 1222159 × 572412223 × 6617846398437817<16> × 12855595223112980416462018000648398107630718754141<50>
4×1085+3 = 4(0)843<86> = 43 × 540190215440868360530293<24> × 1722046293230874531237050233554512421861689939541840263312197<61>
4×1086+3 = 4(0)853<87> = 13 × 277 × 9657356773<10> × 11502138534960762244536108377341140842644974426073563733983487373329613911<74>
4×1087+3 = 4(0)863<88> = 1093 × 3989 × 2182577 × 132941281143903049<18> × 3161887102397275282347510972596922724350016430622109923043<58>
4×1088+3 = 4(0)873<89> = 19 × 421 × 2398867 × 191350477 × 46950909538681<14> × 44817686757153901<17> × 5177202217027806290251487898457694674543<40>
4×1089+3 = 4(0)883<90> = 662321331848557<15> × 603936459186040453832931240163982225177904975175429595185517268200687052079<75>
4×1090+3 = 4(0)893<91> = 7 × 4003 × 102259 × 6789687919875078991<19> × 205600897865496745909841816785723349111998355974436881793309347<63>
4×1091+3 = 4(0)903<92> = 67 × 159879252529<12> × 3734161349452416593104154486986109200706503217569395159008782357606671488251921<79>
4×1092+3 = 4(0)913<93> = 13 × 31 × 302987593 × 3275895958107791842366045573361126228793353623179096721538696776127830638625142857<82>
4×1093+3 = 4(0)923<94> = 515653 × 2016409 × 67424191 × 57056886754417315955593031668936021807225920337545087601534033689526854529<74>
4×1094+3 = 4(0)933<95> = 160235387265042924361213310800063<33> × 249632747689101949347527741384205376473772244328443516301352381<63> (Makoto Kamada / GGNFS-0.61.3 for P33 x P63)
4×1095+3 = 4(0)943<96> = 17 × 3168862859<10> × 3569949433698210893189<22> × 2079914875457913598243792445576833817624632341729556601502275909<64>
4×1096+3 = 4(0)953<97> = 7 × 164122388870399209<18> × 3481722240100985764537026367513513312245513315581946229602357470585591903759581<79>
4×1097+3 = 4(0)963<98> = 1397189 × 28628911335545871031048770066182885779948167356026994200498286201795175885295403843001913127<92>
4×1098+3 = 4(0)973<99> = 132 × 61 × 139 × 43633 × 825301 × 19224409609812811<17> × 403225690931051006827034621383764292357940500078338504752008096531<66>
4×1099+3 = 4(0)983<100> = 3679453 × 13739741 × 79122169216533028312084450587495254858902508500825650977748500951465581521073834159211<86>
4×10100+3 = 4(0)993<101> = 263073848445071927083549627052866428045181<42> × 152048560647227291488352660711022861393906946872917710945663<60> (Makoto Kamada / GGNFS-0.61.3 for P42 x P60 / 0.57 hours)
4×10101+3 = 4(0)1003<102> = 27409 × 299006143979<12> × 48807514071067393196893297461566367062600793161528567545868321932515556736365597510073<86>
4×10102+3 = 4(0)1013<103> = 7 × 1444687 × 24759043 × 329892728386250840772201577591<30> × 48426333618294308227066708262511191032340613776828454629359<59> (Makoto Kamada / Msieve 1.21 for P30 x P59 / 1.3 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10103+3 = 4(0)1023<104> = 23 × 29 × 149 × 132989 × 4359474767<10> × 5000294302747<13> × 21003151917471131<17> × 6610251148158616292841851334549385279275052480122459151<55>
4×10104+3 = 4(0)1033<105> = 13 × 1957086243885661507<19> × 2020383526373258068932229669873<31> × 7781670830487480975075498692612523765954523835636334421<55> (Makoto Kamada / Msieve 1.21 for P31 x P55 / 44 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10105+3 = 4(0)1043<106> = 26641774879<11> × 1243681713696752480448523<25> × 2558877519422687531398902976661<31> × 47177843937382527807444728801342373334619<41> (Makoto Kamada / Msieve 1.21 for P31 x P41 / 2.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10106+3 = 4(0)1053<107> = 19 × 43 × 1422695689<10> × 728719273889174277348190729<27> × 9593307103955838393068505521701<31> × 4922631375855969255378368432000495239<37> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1841835567 for P31 x P37 / May 22, 2007 2007 年 5 月 22 日)
4×10107+3 = 4(0)1063<108> = 31 × 593 × 47074377439<11> × 102347646395347<15> × 2321802954514236535820271610129681<34> × 1945162101718577957824273238473005486437700017<46> (Makoto Kamada / Msieve 1.21 for P34 x P46 / 12 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10108+3 = 4(0)1073<109> = 7 × 53887 × 458210225212357<15> × 232931499453707914944074233<27> × 2305828604173231223727905635771<31> × 43088157532196592153119605021717<32> (Makoto Kamada / Msieve 1.21 for P31 x P32 / 27 seconds on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10109+3 = 4(0)1083<110> = 157 × 659 × 3015622139<10> × 8789691551616868774948328182836667117193493269<46> × 14585602253855018384156891160085996096225659769091<50> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P46 x P50 / 0.62 hours on Core 2 Quad Q6600 / May 25, 2007 2007 年 5 月 25 日)
4×10110+3 = 4(0)1093<111> = 13 × 349 × 12865806673<11> × 6852581206364793317702827753475558688893946919349263338168095404246296488637765897286437688853803<97>
4×10111+3 = 4(0)1103<112> = 17 × 1061 × 5431 × 3916426088914262500957<22> × 24037074049042231771482129505828138857389<41> × 433754853110404164185779637213028415023113<42> (Makoto Kamada / Msieve 1.21 for P41 x P42 / 26 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10112+3 = 4(0)1113<113> = 109 × 366972477064220183486238532110091743119266055045871559633027522935779816513761467889908256880733944954128440367<111>
4×10113+3 = 4(0)1123<114> = 151 × 2521 × 9341 × 9946673530747<13> × 213150967517384807318120724304052423803<39> × 53058095146024700376361296298594029717899946692445353<53> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P39 x P53 / 0.67 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10114+3 = 4(0)1133<115> = 72 × 1021 × 3207018465358387<16> × 24930828356632241332212356615093313483098762503430413270723591402599025343424553441072571395861<95>
4×10115+3 = 4(0)1143<116> = 389 × 810028972969<12> × 126943315520245226648235215122992574872963405537941034496704303318529050817247431492844231711375283983<102>
4×10116+3 = 4(0)1153<117> = 13 × 11303513240301787<17> × 29633428267406760787<20> × 91858911340652280678247707831211883422979867000931894281093394331335203035192399<80>
4×10117+3 = 4(0)1163<118> = 27919 × 157747 × 78066983 × 1030466172731<13> × 52782015879397236339899<23> × 213900556969295705920721918800059799987549750820302658466495339473<66>
4×10118+3 = 4(0)1173<119> = 211621276763532507670415744223334748617<39> × 189016910831212661627315911618686407924531685546937547055501093534558399895914859<81> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P39 x P81 / 0.96 hours on Core 2 Quad Q6600 / May 25, 2007 2007 年 5 月 25 日)
4×10119+3 = 4(0)1183<120> = 47 × 977 × 141871 × 23360919038493371193241<23> × 979342115367401422202381<24> × 3492073820802070530525307<25> × 768539455491897698431689459718814113301<39>
4×10120+3 = 4(0)1193<121> = 7 × 5612274364620889506308759859628576707925837<43> × 101817647232428482152474928700295254049026878546996061124502636639930949090617<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P43 x P78 / 0.81 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10121+3 = 4(0)1203<122> = 6961 × 170977595876812450723<21> × 34585230048100307623332840382749782681057<41> × 971758800986673748132478129675100273134597913849135461393<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P41 x P57 / 0.97 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10122+3 = 4(0)1213<123> = 13 × 31 × 751 × 140302808583575220937569935644682059<36> × 9419950992110895877545261702594558645655155927342812397620420321479963685240471389<82> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P36 x P82 / 1.17 hours on Core 2 Quad Q6600 / May 26, 2007 2007 年 5 月 26 日)
4×10123+3 = 4(0)1223<124> = 69654799971724406209<20> × 57426049627933116630888947965849336670461929170721643555957933746420337327757344197684310249267708176067<104>
4×10124+3 = 4(0)1233<125> = 19 × 67 × 98926811115971491993<20> × 317627120727642727863108477985491134969102581502737558321771738632117212679241276544314298617036257427<102>
4×10125+3 = 4(0)1243<126> = 23 × 12973 × 552011 × 270424717701619708607<21> × 16607592862206514667866399723<29> × 2002436999818684619322552805837<31> × 270042468531600274446420277679962091<36> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=159528211 for P31 x P36 / May 22, 2007 2007 年 5 月 22 日)
4×10126+3 = 4(0)1253<127> = 7 × 2689657 × 19582464016673805247755977616241<32> × 179063494877062505880412645812193<33> × 60588563744576868591308703969643081921575538027488700669<56> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=808262192 for P33 / May 22, 2007 2007 年 5 月 22 日) (Makoto Kamada / Msieve 1.21 for P32 x P56 / 1.1 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10127+3 = 4(0)1263<128> = 17 × 432 × 59 × 11285195303<11> × 521293731281094645703485420673506602610925860757394203<54> × 3666321666068084664903157915264085011548958113765261075461<58> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P54 x P58 / 1.62 hours on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10128+3 = 4(0)1273<129> = 13 × 543248403613<12> × 56639339507659545043474209085859160935513261169699453555031372526642361564268534316030299853532486056871768250567387<116>
4×10129+3 = 4(0)1283<130> = 2125328766779684187720000305302944444700439100557051<52> × 1882061760289836591422460816044047312356413460440607394774696364308476485811353<79> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P52 x P79 / 2.58 hours on Core 2 Quad Q6600 / May 25, 2007 2007 年 5 月 25 日)
4×10130+3 = 4(0)1293<131> = 18775423254242536747470151<26> × 9216558447751648739364061213<28> × 27215602876078480656252573412258483<35> × 8493437875015212423615891593770534705445107<43> (Makoto Kamada / Msieve 1.21 for P35 x P43 / 9.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10131+3 = 4(0)1303<132> = 29 × 199 × 122709869 × 17745113024976168939376435372018500870859981957<47> × 31831027271271917917211409577687106292138046864406391959013403689139371721<74> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P47 x P74 / 2.30 hours on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10132+3 = 4(0)1313<133> = 7 × 367699 × 75669648215166599173<20> × 1112013696695243458462948812197952325199534586937<49> × 18468756317073684462309916330756661620043623970152551745171<59> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P49 x P59 / 2.52 hours on Core 2 Quad Q6600 / May 27, 2007 2007 年 5 月 27 日)
4×10133+3 = 4(0)1323<134> = 1610513 × 3981084129240481<16> × 6238704295353856503164400656259624529816029641133765294703451212944892292858742856759609095297487297601471595251<112>
4×10134+3 = 4(0)1333<135> = 13 × 14847271921<11> × 119228841896299<15> × 1378915574100727281289807<25> × 1246929404598807676544463133134304025759071<43> × 10109021211106208981114442276532687402729837<44> (Makoto Kamada / Msieve 1.21 for P43 x P44 / 38 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10135+3 = 4(0)1343<136> = 11328523 × 167209353214438072108071764699<30> × 2111670406352169953615950969505952926778362473341224768552933956228839776053527035084886239827494539<100> (suberi / GMP-ECM 6.1.2 B1=1000000, sigma=1914283015 for P30 x P100 / May 26, 2007 2007 年 5 月 26 日)
4×10136+3 = 4(0)1353<137> = 27739 × 176431 × 85693987 × 615417073 × 1652141749<10> × 507844181944179043<18> × 3545607390121939838871483707257<31> × 52096191387344066342417246282819807171507372224926283<53> (Makoto Kamada / Msieve 1.21 for P31 x P53 / 42 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / May 24, 2007 2007 年 5 月 24 日)
4×10137+3 = 4(0)1363<138> = 31 × 2677 × 9857 × 211632281186902167467053<24> × 2310591953058840359849977453840662508890967017970212612238759050240365837713869843964234869344035186557389<106>
4×10138+3 = 4(0)1373<139> = 7 × 1033 × 930729119481891694801482963283168394796716926087<48> × 594344609294641138185135993021839496344619029158623927721993187831394871362972952598299<87> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P48 x P87 / 4.68 hours on Core 2 Quad Q6600 / May 28, 2007 2007 年 5 月 28 日)
4×10139+3 = 4(0)1383<140> = 730085207 × 4622218820599<13> × 1090080139886653<16> × 2443464119454710007355153216679458364521<40> × 4450118210277028673112750346091921480847013205495714394729918167<64> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P40 x P64 / 8.54 hours on Core 2 Quad Q6600 / May 28, 2007 2007 年 5 月 28 日)
4×10140+3 = 4(0)1393<141> = 13 × 6271 × 3583081 × 106008901 × 663715681652299<15> × 15998791042740433<17> × 341804726631197143<18> × 881016660147692389<18> × 7275799489711586311<19> × 555224635685842824645369750125550019<36>
4×10141+3 = 4(0)1403<142> = 2203 × 4052041277140292797<19> × 112337436097652014259149829<27> × 3988844679446693555912397892920017310079394614551388692329952864369366285112034054096432643977<94>
4×10142+3 = 4(0)1413<143> = 19 × 397523109523<12> × 1792722597263327053<19> × 361944429343387970109181659326070203309043443208301<51> × 8161857721768944819535587526816743204330570033059102272751923<61> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P51 x P61 / 6.94 hours on Cygwin on AMD 64 3400+ / May 29, 2007 2007 年 5 月 29 日)
4×10143+3 = 4(0)1423<144> = 17 × 113 × 78787 × 2262548272661<13> × 668738863741807343<18> × 29265125636007894785323<23> × 59686106943410752640846922736381784765660417207930297289703128003378037852368088441<83>
4×10144+3 = 4(0)1433<145> = 7 × 139 × 193770466069024922717310499<27> × 21215807548751484962253067138510843971444743670553328791941361291829629575242899926689208262680512641632556871780389<116>
4×10145+3 = 4(0)1443<146> = 15679 × 8391654179<10> × 1630535804362988309<19> × 646714525652426822605941812765336474593578059<45> × 288304285235034063465342910556093561504177705697017827218911974846793<69> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P45 x P69 / 7.95 hours on Cygwin on AMD 64 3400+ / May 29, 2007 2007 年 5 月 29 日)
4×10146+3 = 4(0)1453<147> = 13 × 41023 × 2958721 × 248105437 × 1101807494113<13> × 7014417751034503<16> × 41503832743290556850451533494303423483207<41> × 3185395578251891000053013244421171035550838420033010094357<58> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 for P41 x P58 / 14.41 hours on Core 2 Duo E6300 1.86GHz,Windows Vista and Cygwin / May 29, 2007 2007 年 5 月 29 日)
4×10147+3 = 4(0)1463<148> = 23 × 3072 × 1103 × 2153 × 196831 × 28317379524667<14> × 139408515201118856613189939218865096249315247658508700780453385868737486171830996595382150641497936563719363478187823<117>
4×10148+3 = 4(0)1473<149> = 43 × 433 × 100065703 × 12687175129<11> × 6739023729247306489<19> × 653001312242351067783538309652220151840959811<45> × 384540790042736112351657990250185253692610846424727214146899269<63> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 for P45 x P63 / 20.03 hours on Core 2 Duo E6300 1.86GHz, Windows Vista and Cygwin / May 30, 2007 2007 年 5 月 30 日)
4×10149+3 = 4(0)1483<150> = 49117 × 64969 × 8868841 × 45712301 × 301046889247463311050153637<27> × 1027041235264873861644509788687464071137204921399808014538536862534968482016607090799630357456517583<100>
4×10150+3 = 4(0)1493<151> = 7 × 310940527 × 63337149079<11> × 344795380705680471706981<24> × 84152044367076220359093655691449270624041787994387478180495810213978219492706082301246050226372104299252873<107>
4×10151+3 = 4(0)1503<152> = 87523 × 4494503443<10> × 1297415475912073088053509540386798385058609<43> × 78374900853242505310466623601273918272208107442148395944232718006339250364736934925355798428203<95> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P43 x P95 / 16.66 hours on Cygwin on AMD 64 3200+ / May 30, 2007 2007 年 5 月 30 日)
4×10152+3 = 4(0)1513<153> = 13 × 31 × 1051 × 2801114324800249062766187692606357600549569364661409619095961178167<67> × 337148626424781873328036805457958920928175121942812922349685550558244211164690453<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P67 x P81 / 17.49 hours on Cygwin on AMD 64 3400+ / May 30, 2007 2007 年 5 月 30 日)
4×10153+3 = 4(0)1523<154> = 163 × 647531 × 11061581 × 4124679348155700834063553597<28> × 3535740861654872658270519573725613482190542128854473<52> × 234922167135062332183441254151884253123634863112124506309891<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P52 x P60 / 17.10 hours on Core 2 Quad Q6600 / May 30, 2007 2007 年 5 月 30 日)
4×10154+3 = 4(0)1533<155> = 1327 × 870755550325850941<18> × 22208856755600059957457268067062121<35> × 1894425688430070080563866230389466204449<40> × 822790066767611381874600814825665810874654564700976063637801<60> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P35 x P40 x P60 / 28.57 hours on Cygwin on AMD 64 3200+ / May 31, 2007 2007 年 5 月 31 日)
4×10155+3 = 4(0)1543<156> = 131 × 277 × 1597 × 131311 × 823553 × 667849372139<12> × 492825456187630481531157139782940959270957733499511907<54> × 193927631621634265976915268190761855606404319236001612241209942831445103<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona for P54 x P72 / 17.81 hours on Core 2 Quad Q6600 / May 31, 2007 2007 年 5 月 31 日)
4×10156+3 = 4(0)1553<157> = 72 × 14407 × 33849273943<11> × 167394427925483075428243819528602166918331276032774336793883340354052175803147302279104909498258848880017372300728159607027092114374437257747<141>
4×10157+3 = 4(0)1563<158> = 67 × 3613 × 289830419 × 570129170832163809741740595369391519907158357251093181381631732983630766970106185378605214139011991612182614437265356998465394693599732942364247<144>
4×10158+3 = 4(0)1573<159> = 13 × 61 × 504413619167717528373266078184110970996216897856242118537200504413619167717528373266078184110970996216897856242118537200504413619167717528373266078184110971<156>
4×10159+3 = 4(0)1583<160> = 17 × 29 × 409 × 4108499 × 39134819 × 417437569 × 3210493232143522115233150147270451<34> × 2111007970395248522288822270407200076593257339<46> × 43610401448779057354383384061999544768111674794916639<53> (suberi / GMP-ECM 6.1.2 B1=5000000, sigma=1671372949 for P34 / June 6, 2007 2007 年 6 月 6 日) (suberi / Msieve 1.22 for P46 x P53 / 08:04:32 on Sempron 3400+ 1.80GHz, Windows Vista / June 6, 2007 2007 年 6 月 6 日)
4×10160+3 = 4(0)1593<161> = 19 × 2105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894737<160>
4×10161+3 = 4(0)1603<162> = 93187 × 34563163 × 1429384127<10> × 174991800857<12> × 5565980346411937268388128381439563107<37> × 700131433832122433345260550981903682611<39> × 127409931013861119158868865095362078118650478133953821<54> (suberi / GMP-ECM 6.1.2 B1=5000000, sigma=883745355 for P37 / June 6, 2007 2007 年 6 月 6 日) (suberi / Msieve 1.22 for P39 x P54 / 04:45:41 on Pentium 4 2.26GHz, Windows XP / June 6, 2007 2007 年 6 月 6 日)
4×10162+3 = 4(0)1613<163> = 7 × 16111 × 898857769272037<15> × 52633384675921297349532423419308829377260438229<47> × 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643<96> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 for P47 x P96 / October 9, 2007 2007 年 10 月 9 日)
4×10163+3 = 4(0)1623<164> = 1316989799426812351<19> × 9122825587223042642884812944337703070033<40> × 3329263796544560932998781161768664065173476621162459775686753155158211188126981055831370511645586167117741<106> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=2575813498 for P40 x P106 / June 8, 2007 2007 年 6 月 8 日)
4×10164+3 = 4(0)1633<165> = 13 × 11467 × 9523399993242554891943426601<28> × 31445722457122043977687400352333915199796312519950578127<56> × 8960107578000945594964516537852622453791282510444775001014858922521752127659<76> (Justin Card / GGNFS-0.77.1-20060722-k8 for P56 x P76 / May 3, 2008 2008 年 5 月 3 日)
4×10165+3 = 4(0)1643<166> = 47 × 2239 × 64301 × 5622060993572083<16> × 17162193244336712083651773667387<32> × 6126634498248786631325750859569676596678356085694049608225501662771812141931771359526911934006293383097455871<109> (suberi / GMP-ECM 6.1.2 B1=5000000, sigma=943201141 for P32 x P109 / June 5, 2007 2007 年 6 月 5 日)
4×10166+3 = 4(0)1653<167> = 97 × 52318521292866967<17> × 7881934042291838479932765365505117965273182241769017501103032161886510234435138139324129256880163852351188419822271536920099308299032115075306792597<148>
4×10167+3 = 4(0)1663<168> = 31 × 28775130387762169<17> × 6041416682842093129<19> × 9040172761574724472563661611963885082577<40> × 8210421944564469678826128815336450569971653908303104793893829949559207978039441352980000269<91> (suberi / GMP-ECM 6.2.1 B1=1000000, sigma=4208089882 for P40 x P91 / September 1, 2008 2008 年 9 月 1 日)
4×10168+3 = 4(0)1673<169> = 7 × 2547542022769<13> × 224305847095495028562474049923259277322508553763735462624339784362722529566381749832436665082137269640064005279132291137107176906459348048196470504526769141<156>
4×10169+3 = 4(0)1683<170> = 23 × 43 × 2695744223<10> × 1095863878505531791352248008590604473<37> × 13690786705166299346121105341688039593329430814257896520268003985603036085194932170203623925361810203165403423559971573513<122> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=1598264602 for P37 x P122 / June 8, 2007 2007 年 6 月 8 日)
4×10170+3 = 4(0)1693<171> = 13 × 2332022449008725190543961<25> × 9091674957193157331925985427613<31> × 5519848976962319518553726010848147162459426482482457<52> × 262913457234491688131920560141939578410279343647748980394630731<63> (suberi / GMP-ECM 6.1.2 B1=5000000, sigma=1435742688 for P31 / June 6, 2007 2007 年 6 月 6 日) (honeycrack7 / GGNFS-0.77.1-20060513-k8 for P52 x P63 / 226.94 hours on DualCore Intel Core 2 Duo E6400, 1600 MHz, Windows XP and Cygwin / July 28, 2007 2007 年 7 月 28 日)
4×10171+3 = 4(0)1703<172> = 439 × 36277 × 1268563 × 15218882404130261<17> × 756250231338276927304375103001690458827<39> × 17202983946086459938373724428120076924823810662429126159556894474473395321848053399384538121207658238541<104> (Erik Branger / GMP-ECM B1=3000000, sigma=3099713956 for P39 x P104 / September 25, 2009 2009 年 9 月 25 日)
4×10172+3 = 4(0)1713<173> = 4297 × 304933 × 9172777578559994863<19> × 5526492335788471398452047<25> × 602198648126887280513574836358871919550787524058802489496528115892764759974094786609751416324263314911652342664866295823<120>
4×10173+3 = 4(0)1723<174> = 179 × 769 × 1534843 × 3663690269<10> × 516770735432063961884535453306912440046755002754711793504756148013469177780667065588262761178299758254636079664852862964306313644724812107747307995148959<153>
4×10174+3 = 4(0)1733<175> = 7 × 571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429<174>
4×10175+3 = 4(0)1743<176> = 17 × 6883 × 19412177 × 169757677820354209<18> × 7869296226745426570552208159293<31> × 13182377316446225748087882274614574555076488881805882086115583209285537401151576878380413502502112486527863046837877<116> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=1958534315 for P31 x P116 / June 10, 2007 2007 年 6 月 10 日)
4×10176+3 = 4(0)1753<177> = 132 × 14479 × 1727839 × 3661730251935283360279392267311779<34> × 30175961085952909008534878737421283007<38> × 856217277330621580192849824402420828954681540263284216581477838361242201893253167019116379159<93> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=1337949521 for P38 / June 8, 2007 2007 年 6 月 8 日) (Robert Backstrom / GMP-ECM 6.0.1 B1=1178000, sigma=1375184272 for P34 x P93 / February 11, 2008 2008 年 2 月 11 日)
4×10177+3 = 4(0)1763<178> = 4003 × 36482783222777<14> × 50658903671601877607<20> × 540667982031990222482833145305316014107462605980191475513186809952744748995369725009518989792884573064584708322426776457165694335234652899759<141>
4×10178+3 = 4(0)1773<179> = 19 × 2851 × 1750141 × 421925850077734778458472888293811439505113004562393105404304970874418011511629520756037200371809088337426866070440373903570871723599361920857626823069384258132891918807<168>
4×10179+3 = 4(0)1783<180> = 9679838127597185553923930374350132743<37> × 191036532994880646588869280641375529254981954340701<51> × 216309437884752288522244329757285002058432970681423732981110681293149999573768732312881302121<93> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=2524219083 for P37 / May 25, 2007 2007 年 5 月 25 日) (matsui / Msieve 1.43 snfs for P51 x P93 / December 24, 2009 2009 年 12 月 24 日)
4×10180+3 = 4(0)1793<181> = 7 × 83826283922298951250679670902394172492665030066721447476491438645405060824416416839171<86> × 6816818600216674079721080459803918316770769056707557617751767138646831184079876164364702748599<94> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 for P86 x P94 / 402.02 hours on Core 2 Duo E6300 1.86GHz, Windows Vista and Cygwin / June 17, 2007 2007 年 6 月 17 日)
4×10181+3 = 4(0)1803<182> = 684195100951<12> × 58462856492836361259109602571820183971207927451367688826987109269761299203190733838587286169549432395465108989983531525621363729635133448218188190392627820539215996529653<170>
4×10182+3 = 4(0)1813<183> = 13 × 31 × 26041856359<11> × 361844469631<12> × 105332178576577671647313782376139506954454126740931473679707225542479919248058581178576852982066796279456661813720362879251252880665382416977701665986539669369<159>
4×10183+3 = 4(0)1823<184> = 247811 × 12355093 × 354318850535269817<18> × 1535067212949415823<19> × 358545789680150774171<21> × 6699264286447980099506742287099132028978595797521871835704810763880430688611776436093231786071444095178728900347601<115>
4×10184+3 = 4(0)1833<185> = 643 × 44017 × 49859134658930905291<20> × 3260581655841388369657396033<28> × 5986920270178566508580072759197219<34> × 598460262591086976314911215354850882063724060041<48> × 2426330557371719231339466672548563551076810498249<49> (suberi / GMP-ECM 6.1.2 B1=11000000, sigma=3847881528 for P34 / June 10, 2007 2007 年 6 月 10 日) (suberi / Msieve v. 1.23 for P48 x P49 / 09:44:48 on Pentium 4 2.26GHz, Windows XP / June 11, 2007 2007 年 6 月 11 日)
4×10185+3 = 4(0)1843<186> = 59 × 11020580464970018963281153740355391062570795450373519356122648057289<68> × 615181844413636911986288389296689173200938369983514842349545281535581167010170014581500501046126500380108078763742353<117> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs for P68 x P117 / 676.35 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / November 21, 2007 2007 年 11 月 21 日)
4×10186+3 = 4(0)1853<187> = 7 × 1447 × 8011 × 88882471 × 84750025669<11> × 3526320744211<13> × 1855790376396659490972052841574130847984609734208039206281273992842996381600157241574818780760615341594861483032615065929831833505368029925834276833<148>
4×10187+3 = 4(0)1863<188> = 29 × 157 × 18289 × 724558778467<12> × 12789947662689371<17> × 1226050020366609411992546893<28> × 42278717264163328182462252178030159259398428803154456142915805295906566483370986771666957936474890142243664317413128579035959<125>
4×10188+3 = 4(0)1873<189> = 13 × 151 × 50311 × 24875180711963832920631823391799924802362043<44> × 1752874383582602263485228831981881536452332411343350533<55> × 92888019522893020037527962353614086664215590109173413876816904217403183939544249209<83> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.38 snfs for P44 x P55 x P83 / 69.83 hours, 6.8 hours / October 5, 2008 2008 年 10 月 5 日)
4×10189+3 = 4(0)1883<190> = 4073 × 2740957 × 3428923 × 667970431 × 1742817889<10> × 1937455415981<13> × 83854417267246524902406054576857546895613097<44> × 3818365928839740457687318687141989113011278407<46> × 144690884061596303738959983223805952509795639618444761<54> (Youcef Lemsafer / GMP-ECM 6.4.2 [configured with GMP 5.0.5, --enable-asm-redc] B1=11000000, sigma=3223465856 for P44, GGNFS-SVN 430, msieve 1.50 (SVN 408) gnfs for P46 x P54 / November 2, 2012 2012 年 11 月 2 日)
4×10190+3 = 4(0)1893<191> = 43 × 67 × 139 × 3643 × 359510878809739<15> × 1210334710134169237<19> × 629589472322495446334663675031264845997425910079012360357<57> × 100084720178780115237981541387311663053886915308400483818855627013027077953155995355273351769<93> (Youcef Lemsafer / GGNFS-SVN430, msieve 1.50 (SVN 408) snfs for P57 x P93 / November 7, 2012 2012 年 11 月 7 日)
4×10191+3 = 4(0)1903<192> = 17 × 23 × 263 × 771973 × 290812553 × 3939201304198453<16> × 496857887136613356073364815759143715926429945989<48> × 8852620808892333828220623190726176571486957207475902564329512905997388043044240977592574442388795812594875367<109> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 snfs for P48 x P109 / January 9, 2014 2014 年 1 月 9 日)
4×10192+3 = 4(0)1913<193> = 7 × 2287 × 88741 × 456553 × 5088649 × 11725447 × 103359015490664326725355445054887187173102054677430133066642497451076692216819215517603496425587705969764037478529511187729270407381470703373657296591145732618953993<165>
4×10193+3 = 4(0)1923<194> = 9226055135669165281<19> × 269425138015309831058086976915810358735031420146135064645409746829<66> × 16091844665168913209987577377995010161597650476066713168848866293234817097876780567727234264626032821889385647<110> (Eric Jeancolas / cado-nfs-3.0.0 for P66 x P110 / January 6, 2021 2021 年 1 月 6 日)
4×10194+3 = 4(0)1933<195> = 13 × 487 × 10747520347<11> × 1061459829998311<16> × 56889821479343939004524558081383<32> × 1097437743804222790112801602356295333<37> × 88707711400317344925950831681572035023026603223066152620648506409066689217254920192657566027207151<98> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1395551294 for P32 / May 24, 2007 2007 年 5 月 24 日) (Robert Backstrom / GMP-ECM 6.0.1 B1=3962000, sigma=529594722 for P37 x P98 / April 15, 2008 2008 年 4 月 15 日)
4×10195+3 = 4(0)1943<196> = 334619 × 1899148878726749048488989889567829<34> × 32601858539276085142790225160966382602241<41> × 193066989304746770344432769201893486686057553632642714382109333422062514555086259523145588633095270924396313597858133<117> (matsui / GMP-ECM B1=80000000, sigma=1533119823 for P34 / May 17, 2008 2008 年 5 月 17 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=545160739 for P41 x P117 / November 18, 2012 2012 年 11 月 18 日)
4×10196+3 = 4(0)1953<197> = 19 × 1999 × 67219 × 232417 × 105162433573<12> × 879893400439<12> × 728522501185067418692213792158887231189645499390755057215334878391600133103008264202971419245285496432026575387763290483756122592128121062099652085597870759623<159>
4×10197+3 = 4(0)1963<198> = 31 × 1697 × 241373051 × 50647276074597052651963<23> × 506225605061761913883409<24> × 1228647988633267077039506055160330792161688659957583837888735937413053436384998321717851570266417684443725172201007549189750660741686747637<139>
4×10198+3 = 4(0)1973<199> = 73 × 499 × 6623605628946997<16> × 1337219835698580307<19> × 22355415272513896662048780081754279783<38> × 118028070472771437685486920896484037107828428621451610964475648743976065340805709497284979806314122890506877033820039746847<123> (matsui / GMP-ECM 6.2.1 for P38 x P123 / September 30, 2008 2008 年 9 月 30 日)
4×10199+3 = 4(0)1983<200> = 45491 × 69341177 × 642372473 × 215197013955613<15> × 4991400986540152551808517427177441442627<40> × 18377975781051058172783152369408940453134121073012417417787451223164907643698737199603426353365174187001561474880862157637223<125> (Youcef Lemsafer / GMP-ECM 6.4.2 B1=3000000, sigma=3465487454 for P40 x P125 / November 4, 2012 2012 年 11 月 4 日)
4×10200+3 = 4(0)1993<201> = 13 × 991 × 87691 × 814976131 × 287615789104916661244746697<27> × 91411332317318462584478045153997760981495491017113267<53> × 16524575439629342518710831485015416686955712259196821814738208614902744274813214754072691374556403192179<104> (Eric Jeancolas / cado-nfs-3.0.0 for P53 x P104 / October 18, 2020 2020 年 10 月 18 日)
4×10201+3 = 4(0)2003<202> = 2204443 × 4468091 × 71688345769<11> × 55666002587068831184719813551787647635352501345999778360804123<62> × 101765486562492975664464010218464694031797606985557466323154868219064829799187863546776410364117597258832751486743513<117> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 snfs for P62 x P117 / January 11, 2014 2014 年 1 月 11 日)
4×10202+3 = 4(0)2013<203> = 1935408417379470350634773280499850478044062847264770421674284584576922879097177760442893509<91> × 20667472374724774699183660392381951388966816047820142983688470223957706120195325118454188853859825490527108976167<113> (Markus Tervooren / Msieve 1.51 for P91 x P113 / March 15, 2013 2013 年 3 月 15 日)
4×10203+3 = 4(0)2023<204> = 9896088083509053881090350733303341204003835574556922907569044035648109238086645674926237903<91> × 40420012092107813948890213218430549985946501942513337640305126159736863950316376207107962721816976355668689410701<113> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P91 x P113 / February 19, 2013 2013 年 2 月 19 日)
4×10204+3 = 4(0)2033<205> = 7 × 2647 × 6733 × 1185445304240320581173227980358111768949628211<46> × 752755928093336406131299491375783839572478130977047901389201773229543897<72> × 35930535553180538840872232460421218300976363254673030171459553247522344369033437<80> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1653578623 for P46 / November 18, 2012 2012 年 11 月 18 日) (ebina / Msieve 1.53 for P72 x P80 / August 29, 2022 2022 年 8 月 29 日)
4×10205+3 = 4(0)2043<206> = 544042113731<12> × 243023367290327526806945861<27> × 32494200552335699648978400282039001227799506734400830616987140219<65> × 9310512368610145251359034266441719339376583540554750411033922152321523984571242845150089916091166152407<103> (Bob Backstrom / Msieve 1.44 snfs for P65 x P103 / October 28, 2023 2023 年 10 月 28 日)
4×10206+3 = 4(0)2053<207> = 13 × 6709 × 866312595789617760669426916944551384531202932191<48> × 5294003428912673529266570585609495497354764027914788498546054399779378241104358759547273015549120607126864090024554790755276735041006354519268387991018349<154> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 for P48 x P154 / January 7, 2014 2014 年 1 月 7 日)
4×10207+3 = 4(0)2063<208> = 17 × 8467 × 1368167 × 3008021 × 6752452459067916195975979165594044111714085371231591620332695177988761420881045642726368053920160986320440906257409235520848277969843898466694821075648613149601203732849588271740170995660411<190>
4×10208+3 = 4(0)2073<209> = 7717 × 1593521023<10> × 4854732424700303185200088823854916154542218011789913375796818755559<67> × 670020970389119662358800621319621735065052739737946123244511313431686131877002715722478883422393858963285149176604600699366281887<129> (Youcef Lemsafer / Msieve 1.52 for P67 x P129 / March 11, 2014 2014 年 3 月 11 日)
4×10209+3 = 4(0)2083<210> = 1470493 × 2178257 × 2670734441985263<16> × 6363890556851987151593512352053<31> × 7347413842076466604219717222806593727461772937973763770623204947731611207034902363460681472254749927736622033418038169846124076440722295464774877848477<151> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1762452215 for P31 x P151 / November 9, 2012 2012 年 11 月 9 日)
4×10210+3 = 4(0)2093<211> = 7 × 337 × 1074566161<10> × 3562571137<10> × 235912505430739<15> × 1877519180262009013920995978662675069840000980698051795356820073480985389378297177176660810250048492121248952663206145040165461225871916311435236628638751601646649131941775879<175>
4×10211+3 = 4(0)2103<212> = 43 × 47 × 23628503 × 414708602177<12> × 149528473660720489<18> × 1367189621974279281567896797<28> × 12608789500338438498039692636829511<35> × 547537132141098581614384437938530709<36> × 1431115883533622852243182912912449320404780896252482479061754714077393530159<76> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=2412633238 for P35 / November 9, 2012 2012 年 11 月 9 日) (Warut Roonguthai / GMP-ECM 6.3 B1=3000000, sigma=1281610126 for P36 x P76 / November 13, 2012 2012 年 11 月 13 日)
4×10212+3 = 4(0)2113<213> = 13 × 31 × 223 × 2111023 × 3889607709523<13> × 6885162880115627766614886699397<31> × 13172134203721447991809798666141279729<38> × 5976968255494908613149824165626636098792982465473980149747406702545319769592165236194992254738446246620064123122728853231<121> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=4189573765 for P31 / November 12, 2012 2012 年 11 月 12 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=359660146 for P38 x P121 / November 13, 2012 2012 年 11 月 13 日)
4×10213+3 = 4(0)2123<214> = 23 × 52859 × 3290131169304392242857742131034409014301377660173866981641890608073817382914513344360756302451888000644865709183660879600117457682744166803070021394077928401810559182468207051244615494708235280570048126393679<208>
4×10214+3 = 4(0)2133<215> = 19 × 2083 × 27337 × 1365321773113<13> × [27078914535957693288348889552849449689471465878225564090845800692438321012989500399963729663489732245260045975799517342331589656605765755174678930379016352213378969231094623187652113029387833019<194>] Free to factor
4×10215+3 = 4(0)2143<216> = 29 × 509 × 407813521 × 34318587939301853671275636720973<32> × 79559650917036464525130975647656407670223<41> × 24336622822923244695728408198999044559436821571037487563080120158375447090272196962709447592778289276135511000668845129957953188297<131> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3341727408 for P32 / November 9, 2012 2012 年 11 月 9 日) (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1541059630 for P41 x P131 / November 13, 2012 2012 年 11 月 13 日)
4×10216+3 = 4(0)2153<217> = 7 × 379 × 1087 × 1453 × 2341 × 558834863533<12> × [729697195390724512987370355096402664404101470410197133129990900401820080887399731219745633721959198801672102659002625287484588604935334764020447827546569456421662291884740664756921220778241797<192>] Free to factor
4×10217+3 = 4(0)2163<218> = 997 × 7385406667<10> × 10377037775569<14> × 3293484143075337140822719<25> × 158950333837046908790452690989586242632808420102291932910978826460907879457870783001377798395162685055627085609280127671044884785899348675906878022226019249142632632027<168>
4×10218+3 = 4(0)2173<219> = 13 × 61 × 12877691311<11> × 39169569062185258990423868080255070418826635737816539011244863067180813223760025044607018077867249183117016885459224469874731695932614013904379888748842130946169944099248033181652066734620858137568411331061<206>
4×10219+3 = 4(0)2183<220> = 55837 × 491531 × 267898695283<12> × 748541080971179<15> × 1196941162972636524501118602258185023120446907593938710231<58> × 607194683565895118689991726848110464792506823454436787001072071654128285812016167478361680528887826483221542719179168936593947<126> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P58 x P126 / January 6, 2021 2021 年 1 月 6 日)
4×10220+3 = 4(0)2193<221> = 109 × 7273112341009<13> × 437667338233489953014117097940287281219257<42> × 1695672299782584909714502297209011812363001602468719867046231862684741413<73> × 67987196670768537260478268857916235331809766693280058741723993040526139448545156829060451243<92> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P42 x P73 x P92 / December 4, 2018 2018 年 12 月 4 日)
4×10221+3 = 4(0)2203<222> = 167 × 947751774578523701533<21> × 226388192311970151388017908864763506261<39> × 11163365448513095099781081247561534215880201818165844886950242119363550896731913719174840730012590381045266968707323310434188443851615413561386144409895172717093<161> (Dmitry Domanov / factordb.com for P39 x P161 / August 8, 2021 2021 年 8 月 8 日)
4×10222+3 = 4(0)2213<223> = 7 × 6571 × 148908031 × 583999349145326915489010551680162022143580857092948957642738359776113037849268284121208857947495262253321271442345143901520045271016544988918604857985771430483357702224810762947011662198373097560099263968522129<210>
4×10223+3 = 4(0)2223<224> = 17 × 67 × 99559 × 129976453 × 26300208433284013<17> × 40098031686256231223095275397773029007633072072608824055667582591983826787<74> × 2573408999093748517739759792504885751922922636910115576809921381286753613120755263329227170691270405636248980495127821<118> (Mehrshad Alipour / yafu 2.11 for P74 x P118 / August 15, 2024 2024 年 8 月 15 日)
4×10224+3 = 4(0)2233<225> = 13 × 277 × 283 × 202009395725707<15> × 38964228161899290209200976212201111<35> × 2705761647651954828879432325875664482174688177<46> × 18429911530758498787508802186051653582703380589339910023255814591225864381953336165312711255965034945364429313116937750301229<125> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3048405199 for P35 / November 15, 2012 2012 年 11 月 15 日) (Dmitry Domanov / factordb.com for P46 x P125 / August 8, 2021 2021 年 8 月 8 日)
4×10225+3 = 4(0)2243<226> = 877 × 1399 × 26740111 × 397476522618278484299<21> × [306738292776977543989929206125053013156366088740669613411988820123603807662439935719519125926528398753527975885341701673308490724281254943488570488216422113698798754984165720805823585233259349<192>] Free to factor
4×10226+3 = 4(0)2253<227> = 349 × 25057 × 14278845318591903262180338322157012141629123525270963331968662043910409137191459910979922562870650453<101> × 320340908140805260844743259174756369399086165280889578082178054170581301354733223491897366204255570791447879142571456707<120> (Bob Backstrom / Msieve 1.54 snfs for P101 x P120 / June 9, 2020 2020 年 6 月 9 日)
4×10227+3 = 4(0)2263<228> = 31 × 82007 × 10720487 × 14676850086749587061423443825298067670791951776153475077244363477718060838807281577539512066812271906327834726615808089120375550528468444008003622838319462172519546100849442670224672857768415104798549582622501417757<215>
4×10228+3 = 4(0)2273<229> = 7 × 421 × 30329513178733133779<20> × 23441390904371133348373<23> × 278056612429794606627984798199<30> × 37635681547262713872561260075603056075831<41> × 182430742741342074398495203790393781209274230241582506726513847300833155308269026632975854256330834779184929785663<114> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=235058780 for P30 / November 11, 2012 2012 年 11 月 11 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=2937954692 for P41 x P114 / November 8, 2013 2013 年 11 月 8 日)
4×10229+3 = 4(0)2283<230> = 592223 × 210218219 × [321295297336705630000884462398868098844659352117530566796418167956713602823933564992198969908959120108478883178513574448750251727426643815838903278227999414547301238217141748483697527389885287286754920666784780639319<216>] Free to factor
4×10230+3 = 4(0)2293<231> = 13 × 199 × 6379 × [24238791361755295706285960898102969173165743098019308984780644694889062990740842296787881428438028651826911033273619050914369016086255678164115160194475094732771264040244150073749552567060706598338321777590546580503419093611<224>] Free to factor
4×10231+3 = 4(0)2303<232> = 56338254721451307043371061741100902240009948361674152187800504974183<68> × 70999714488439119583106494321955650859298420103679844265377294091692079810671374033164800530385005016837314507585797819716507939054639835730410533537638889678049541<164> (matsui / Msieve 1.53 snfs for P68 x P164 / July 18, 2014 2014 年 7 月 18 日)
4×10232+3 = 4(0)2313<233> = 19 × 43 × 62316514651<11> × 2604687828058380269246941<25> × 301633170402257444577177741054052090814555483599958851742064356650547291879427529496948470548076114934494501641039052072263678210677246706852130481166906388405658462798728439194331782425988963549<195>
4×10233+3 = 4(0)2323<234> = 383 × 596434723 × [1751048996147230189820837645340497477686088345479874471319100434519035321110723359789345241328151650862778831968427298317697994237335042267838400566515543922080326828870580277050108815707210241607841081772475787211524895967<223>] Free to factor
4×10234+3 = 4(0)2333<235> = 7 × 163 × 607 × 5369251078969207<16> × 228704729160632401<18> × 413677807625338153<18> × 84357510781662998374813<23> × 134775458657001919418503791812891346795751372530546370246316709997189622708751263278658966775235161776969414836180037399582517499249226204360514356713952803<156>
4×10235+3 = 4(0)2343<236> = 23 × 24928771709<11> × 269184779065741426338140819<27> × 259167640934429990039478830221642971067041695940272917270515648501923038515838730311589620080055219067978563941838284136736453360170896753151746200006118769020557504939185989223139834616481670504291<198>
4×10236+3 = 4(0)2353<237> = 13 × 139 × 2929537987<10> × 457459548048484363<18> × [165177165185247641209548705631774770640178150750308279276515111291661587102875550614399953969456665008174488161653812640502666720067243540249725438920384368493904443688880588603315052139885869327487218467309<207>] Free to factor
4×10237+3 = 4(0)2363<238> = 441079 × 5346200033<10> × 41316164359<11> × 159215264248938533117401<24> × [257865776647840616835410246396971710705757152425943018182996425105622772109676267166780423672277922496828587785100006839570672237170911987951984259232676989937778151529641069264086952541531<189>] Free to factor
4×10238+3 = 4(0)2373<239> = 1615650823<10> × [24757824791452478342840543336881647477117028027534387608206603191263933147515253671863477892091538890640604711900672859682627104383927887863923676533168825675150230155888083250770578167186066540319522988910085802617760310452922661<230>] Free to factor
4×10239+3 = 4(0)2383<240> = 17 × 411667 × 413071924161991<15> × [138369170600614965574794383507418857780442606339794334101709054069233287045698986402927419634152044996701523341778301827715589059732476248079645965749790887473900069037035712436189354511160939606421116672223643602718647<219>] Free to factor
4×10240+3 = 4(0)2393<241> = 72 × 872184097 × 48617460721<11> × 1715745426229<13> × 4744948822741<13> × 45982244099633329<17> × 69219244948850989<17> × 2478728759293106448748854625123302953535308503<46> × 29973196937473811552413113073914261720238907936405144396898407226787396141025175835517884241393390414646059256843553<116> (Erik Branger / GMP-ECM B1=43000000, sigma=1:286669524 for P46 x P116 / March 15, 2014 2014 年 3 月 15 日)
4×10241+3 = 4(0)2403<242> = 373 × 20327 × 24733 × 280321 × 340111 × 28722836537<11> × 77892821618989913360754609569224775398450027579526804055368362637758591813910622998720900502659707637484897481712204465786675957689756276658502978783287710937692835519824506632538378164363020502985440432146243<209>
4×10242+3 = 4(0)2413<243> = 13 × 31 × 95793249500688206893<20> × 637223337762668892754291<24> × 16260292977891064620059113718444618886644517620863692295098204546608111465802315159257310625352035240950542919819126950317500429329020199882801310208300751930814211836066591627674067210544786774327<197>
4×10243+3 = 4(0)2423<244> = 29 × 59 × 3547 × 45013 × 171131 × 1992049729<10> × 23242923419<11> × [1847954268672667804884239460921812065743751063896879367153217575727995768252225058969390601295212887059228747116891925863738882951610034421934488062662525918764555694087534249046438561645455281706589923877203<208>] Free to factor
4×10244+3 = 4(0)2433<245> = 157257482519577791419<21> × 466085068237100708797<21> × 545737104777798584849773895249894034773936681425106854949927491446550064381613510317154318602732434423404121699218903964642915399395895104117925482651489995950236121153781383924835831127385572537910857421<204>
4×10245+3 = 4(0)2443<246> = 1214413 × 7089167 × 384263198078393<15> × 253551396397483607<18> × 2098022401468511471046539<25> × [227296870325827258125582336287111751093458091426442334641649146885132950662046112951248331616842034482839711728912812369594657949734546731650644266462503857270983846579427819837<177>] Free to factor
4×10246+3 = 4(0)2453<247> = 7 × 104198366467681<15> × 13126057757522765593<20> × 21055993577705779790389<23> × 19842253345979207640889093209867701443038643351764186704945066574158014293063021812109797617966981557053002142661132462427754542036741089062542678701812360172472136618576677596760564446583417<191>
4×10247+3 = 4(0)2463<248> = 751 × 342319 × 266183359081365726373<21> × [584531807226909313062495067977102710457042430167041129776707163342513452069022611090495586657154669269401907591053652766715599224517966469285941517504617248250414370211568977080244918055962524367361885143720812810268519<219>] Free to factor
4×10248+3 = 4(0)2473<249> = 13 × 25804213 × 122606185516471<15> × 786268619856765304496329<24> × 79052193523044972403102921<26> × 156469167369593280417181895414732727968914242162337580871255784075056785782276210591377922949980813727688538269874373644007273274125284794908010888404415112832065847101814470933<177>
4×10249+3 = 4(0)2483<250> = 14431 × 202231 × 15602929 × 102687325924457<15> × [855446509185101219008659899599024512726151301660807871764325081953039544418498230663876584752086775223984322333400200351971493601186545189540020168738030403682996368224124522010443249249403054195617373454135205690970691<219>] Free to factor
4×10250+3 = 4(0)2493<251> = 19 × 134503 × 663661 × 87566137 × 3008584834951<13> × 185612673741343<15> × 10610461033722048547<20> × 159641445028726199077868609267443<33> × 76726817853520239037649304234848477795120773537969<50> × 3711034146059851616226553455458471907374496901584533520195444698194629604418108218714150923882870506971<103> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1339124700 for P33 / November 12, 2012 2012 年 11 月 12 日) (Mehrshad Alipour / ecmpi for P50 x P103 / May 31, 2024 2024 年 5 月 31 日)
4×10251+3 = 4(0)2503<252> = 149 × 461 × 5033236638525911432746508022742294846313<40> × 86839045935334124751438171016340560506031<41> × 13323256984343140063438389408997365260168965801438398270051155465965546940622414926462813827456764391064185009134919478016445676802868986402932074571744262518782465109<167> (Erik Branger / GMP-ECM B1=3e6, sigma=3:3698481290 for P40, B1=3e6, sigma=3:3815176130 for P41 x P167 / March 6, 2019 2019 年 3 月 6 日)
4×10252+3 = 4(0)2513<253> = 7 × 181 × [3157063930544593528018942383583267561168113654301499605367008681925808997632202052091554853985793212312549329123914759273875295974743488555643251775848460931333859510655090765588003157063930544593528018942383583267561168113654301499605367008681925809<250>] Free to factor
4×10253+3 = 4(0)2523<254> = 43 × 1451 × 278207929 × 76982845224650903<17> × [29933717917438101724532446567119482545440630116492783584978606239184558537263669580504132108815757336095157207138829415129877680467065036737669518164491811164671088029420578376743373178738589686036969700141748669512421558533<224>] Free to factor
4×10254+3 = 4(0)2533<255> = 132 × 93909151105608859355000751460147<32> × 25203762119665028364164946192135101409419504917349641466456869407755806572957841598857195223757924343997313355588464857244964883196002573969790344734573519470240728346691401519867123530386619005863143894873836744125978121<221> (Erik Branger / GMP-ECM B1=3e6, sigma=3:4186858466 for P32 x P221 / March 6, 2019 2019 年 3 月 6 日)
4×10255+3 = 4(0)2543<256> = 17 × 113 × 16264457613149<14> × [128024486168640500370083844968405915598948438849364777928338664471228635531158444654053460284496213510036553334353897242134536877936053722839722240815105739693920106672512845957703105615130897283801458450354764856334522810282845340989312607<240>] Free to factor
4×10256+3 = 4(0)2553<257> = 67 × 5176886339570839<16> × 7462549113476074124594987957814886221787<40> × 15453588949628981301951850832903539886892523918662174890792632877807338542589798298145482371648736183528586309989040167151537111864201232807067214712782535637577309304693137646237466846883612863011813<200> (Erik Branger / GMP-ECM B1=3e6, sigma=3:3884025202 for P40 x P200 / March 6, 2019 2019 年 3 月 6 日)
4×10257+3 = 4(0)2563<258> = 23 × 31 × 47 × 74209 × 528833 × 567319 × 111794087 × 312892340529411251377950749<27> × 1265160481082705133910061442315779865623<40> × [12114647009580859025702937149515421298885359241708610812123104648484956587828021666626922004191404087831846687694024857954581342475359068443736482446891281206544639<164>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:3724714493 for P40 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10258+3 = 4(0)2573<259> = 7 × 772310827426725502720771<24> × 3653086054367997345500971121149<31> × 202539589293632437122294622014531336918886452030211363944951466475924010616323763202897458244794592587395361463503690861158922917391553600473982301374139472381451682102260911372836207925549020125242560451<204> (Erik Branger / GMP-ECM B1=3e6, sigma=3:4212245965 for P31 x P204 / March 6, 2019 2019 年 3 月 6 日)
4×10259+3 = 4(0)2583<260> = 705128451933396016106135809<27> × [56727252871904055626766084450373487334684240081636645320094841724098434651705210971763591929045576128051170599436227681200307504441536012460486086692001045598325791603023411466725085022668859025543523018073895147002821470257817771267<233>] Free to factor
4×10260+3 = 4(0)2593<261> = 13 × 2593 × 4243147 × 280965428503099897<18> × 210451481124459439213<21> × 1384345765266353250931<22> × [34164620118209942140875513310041907715305306627654406188202385774718353161804425220026610405242983847409096152898711987747057859698001127087952686384022232646001764748779639874943075456466771<191>] Free to factor
4×10261+3 = 4(0)2603<262> = 82549387 × 736318237 × 486656556924763<15> × [135225315195216239266757269925397885760263913462748779826445548409417752199975801061756085132159535908203145516970629221238908632173134306157813473575553228199093753786700358450226189442347094227541201269063040822420597553940121799<231>] Free to factor
4×10262+3 = 4(0)2613<263> = 97 × 1715492548507<13> × 474072578839976409628303<24> × 1582834085021498819123049931219<31> × 320345915880155345132420895150667737173874283345494759024037883816613978718338939656693143421303839324840336497259246357444777340210645783393982298721925929130564002392724552989816277689259510701<195> (Erik Branger / GMP-ECM B1=3e6, sigma=3:1306003443 for P31 x P195 / March 6, 2019 2019 年 3 月 6 日)
4×10263+3 = 4(0)2623<264> = 151 × 4139 × 69257 × 89481508372480193<17> × 97813198861762278797039513<26> × 1055828021198081555127650516208102554106284391146783692571695232923368095990478888782595126484382435886420260103064317281799616912195387688183669037615652874876137062530090096993567643618834686054948840576766079<211>
4×10264+3 = 4(0)2633<265> = 7 × 4003 × 17100037 × 94004413 × 156188437 × 7092573127<10> × 1771329636179773<16> × 77994952311978128001301<23> × 580246437049871645071056993464146083120242713034322085179026882511796832226511981256137728551037998485033043808006744728763194794517027913213826621108508491077690501504568049656889983120189<189>
4×10265+3 = 4(0)2643<266> = 157 × 2803 × 135762257 × 18199149568167419<17> × [36788077910644821785374032316950822926561562383408278138824012721383511763194115520832800289544348308028656330507646442055749147213551724135499800787771988922331541268640045156937425343467806676270505728071501910932070887256206831761071<236>] Free to factor
4×10266+3 = 4(0)2653<267> = 13 × 1747 × 30696859 × 91950346115911<14> × 1408526404520461<16> × [4430078619171873841821743678990264172629324351644410039334115168896155509473857234906513884746794010094433914936837334542262407923837812292479621112381907882849382162319747092290243255966190625032193086342233872767244549516957<226>] Free to factor
4×10267+3 = 4(0)2663<268> = 4127 × 19249 × 196583170415060900431<21> × 256136231212742629781744033891065682064341266015481949260276615524004894777307225193199841548533636965836979376491731895303201652648943963196946071097146410216758988036067488731749078211376267083895827925001531676785198025666941920016129731<240>
4×10268+3 = 4(0)2673<269> = 19 × 51829 × 1386100244686615153<19> × 1622464027100949733963<22> × 706747417374673546926544280871095959<36> × [25556396295466287657510291168639869276928164619164193304358812922835965601945674170958790524279364031515380299299737746950092162501978883158568786024294402476078120897556157240698503165953<188>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:3742213531 for P36 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10269+3 = 4(0)2683<270> = 43807580057<11> × 881265093503083<15> × [10361059310575385578609187239103438560035779902296336907242620099683295281264051703533068604532673585306996861222187821702357459094377433153103369823654345999776909325923074730994535134492744248840249464540187688201076180611259421464305887630513<245>] Free to factor
4×10270+3 = 4(0)2693<271> = 7 × 81202153 × 27596552145523811853277460480307792063709<41> × 254999648258327281275186099734784014941463373313147767817880680813446456886906011038310254129975846509693231630501138700331990271411318648638933494907094569693411627705955785859262780937132018242357476868965234382467666177<222> (Erik Branger / GMP-ECM B1=3e6, sigma=3:1690305265 for P41 x P222 / March 6, 2019 2019 年 3 月 6 日)
4×10271+3 = 4(0)2703<272> = 17 × 29 × 10711 × 145682691691800032409750944232404141<36> × [51996617857393908461429471857879926390479696802632964149857002528920504980153348250023144935596809269626335319422649066822324376965221986946771457431643955705921045560786895313794601168362266760630137349939861502404917696419515821<230>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:4126798493 for P36 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10272+3 = 4(0)2713<273> = 13 × 31 × 193 × 28513 × 259411 × 3265621 × 794796317494010804219719<24> × [267882724846667637760398358214997625045554611096977474710299316086279022979579845574846948096447463588095285370751215172520386524167129311260082045105024359741805822305077883415832159601428171654601752462782004355441778015251401<228>] Free to factor
4×10273+3 = 4(0)2723<274> = 233 × 269 × 6389 × 81475217 × 4092445603<10> × [29957837511808802581102345155845183824737421691673327009927637971144831862856805597689154868333703755758569198204685218754995105394035594468556410666114816339169460770810808423704741760650073510955694039979539400045263686561603720416645908276622201<248>] Free to factor
4×10274+3 = 4(0)2733<275> = 43 × 244147 × 9395883139<10> × 405510904252303803308689729998825681707233794239855830159181965410588447586532751087884043496531072423954864223704241032565697813835029004560358816293753027674014413810082307087327979690443669281544393540036594517091059589591325912955284408632776788476173937<258>
4×10275+3 = 4(0)2743<276> = 6084497 × 12687047 × 14948584661683<14> × 53704383184089257<17> × [6454534893357273623487774582123601054454450312840427473322743286866208123619414901367276100877712638051174791888080886522738094348022109296859991236722049770559514898514936807213520001930301662057271064254618549651036273179591753407<232>] Free to factor
4×10276+3 = 4(0)2753<277> = 7 × 14236309 × 556352302573<12> × 4265904840144590107<19> × 190792941483071253583370385351229<33> × [88642335209542692208908760749593370171051182384218006549813355345234499497591495443214266590791672090956972776166449707507171137857498270899203899774268300516770522221349404877314609381472178632155339659099<206>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:2044892549 for P33 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10277+3 = 4(0)2763<278> = 35839 × 525570974437681811<18> × [2123600092300199764288839697984427290155671798142519814966200786820908170708733504376896040534044790570383780866476081225566955910197625591438560434927117770053764304462735597686072529987287794843236550699103637501653924593167505085104088493553128595401007<256>] Free to factor
4×10278+3 = 4(0)2773<279> = 13 × 61 × 3069939236599<13> × 12775677203983<14> × 12860951316391410315647222812086632061888483653484341478193144543008804668187849715674803249792286037853964875463422943584961477241065115644268190532401782735252152644777882340505707511215826708765537022490926393598349903078337475667068822539674556563<251>
4×10279+3 = 4(0)2783<280> = 23 × 1123 × 65504641 × 1077180118534656662087<22> × 2887404455381952477334342608173947<34> × 760123880671118304802128331561765487909346382505532896556574554820106419418256396228393494475345355840762185725488440813179703498676022224748923796567646207551923034318918606216425781550058944711141649202104696243<213> (Erik Branger / GMP-ECM B1=3e6, sigma=3:306716144 for P34 x P213 / March 6, 2019 2019 年 3 月 6 日)
4×10280+3 = 4(0)2793<281> = 709 × 3853 × 33898719424666699<17> × 3576131467289492557429<22> × 10378441400008414743269228812069<32> × 11638200668055362300703974986218687428714758158636546641936113593367991916966553252437752579671341119543217840033926431464406418343081771974201798965214746925948292781772828690539543632289426957013690352961<206> (Erik Branger / GMP-ECM for P32 x P206 / March 6, 2019 2019 年 3 月 6 日)
4×10281+3 = 4(0)2803<282> = 2668091 × [149919924020582506368785772299370598678980589492637245131444167384095969740162535685626914524279719095038362634557816806098442669309255194069467645593797213063572419381497857456885840850255857090331626619931629018650413347970515248542872038472450902161882784357804887464483033<276>] Free to factor
4×10282+3 = 4(0)2813<283> = 72 × 139 × 57457 × 6320113 × 436697711609859992381606217404310289<36> × [3703398149089342864123605663655815991200637734775978575171569532214079719436744068472662239378328003041298831909702334386208741846492305944021201381617144286380754101264169177786761459558107862986685517318701600163131915227827890377<232>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:3746827418 for P36 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10283+3 = 4(0)2823<284> = 12089739117349436141<20> × 49252669373818104467350696483<29> × 24450506751324486255355779299188651085839<41> × 2747422333187943210181228591618649682329193596462913242346817934966517330824546701293068791710697936473215406536696149855511720326033032892054014437093637205685793408867086550319163883956376793259<196> (Erik Branger / GMP-ECM B1=3e6, sigma=3:3655304093 for P41 x P196 / March 6, 2019 2019 年 3 月 6 日)
4×10284+3 = 4(0)2833<285> = 13 × 229 × 237581779 × 35262789829<11> × 2170776387827128819<19> × 7388159607870366605835847491562492202101719952706942952335991704579666941888296877208138542940517938606846639328031407157863485894845374634274126351457205395567988470791952448691604596795179474776726040910305798165188200961341258881414989275791<244>
4×10285+3 = 4(0)2843<286> = 131 × 357593 × 9410939 × 156325951003483<15> × 1077798885574331<16> × 39985231475407748778705421355244134881<38> × 1346785104504773102055364824320979962421378244949486140561129783145661500487358615865153528688033642429498949837832341077451692418322177820323148757162850174379140632376940427765173121072249488859651060963<205> (Seth Troisi / GMP-ECM 7.0.6 B1=4000000000 for P38 x P205 / November 18, 2023 2023 年 11 月 18 日)
4×10286+3 = 4(0)2853<287> = 19 × 48679 × 996708045757<12> × 365478040192374496771<21> × 118723171850786139300700593611444222267879927241227327971725385554915402408005707988659011258864951145965663298403558852880718056346826463629249478232260049804150002894121679706772202364300996138266282844178694671751545079155401200240092523295748849<249>
4×10287+3 = 4(0)2863<288> = 172 × 31 × 8499767281<10> × 60759016996507<14> × 28666615974094375867091<23> × 775047198731712522953629581877492413121<39> × 3891151151087274901605364373609500345247577321364539180126270742096403636859153520106673212334110858835516701653644631584887604217161898139208944642044342847255529558412662300182567094250436052536141<199> (Erik Branger / GMP-ECM B1=3e6, sigma=3:1862157377 for P39 x P199 / March 6, 2019 2019 年 3 月 6 日)
4×10288+3 = 4(0)2873<289> = 7 × 313 × 571 × 1597 × 892979539 × 2241997280392776333609934321015234583931166132814070868463756569600817623910711669477622934621032055228498425942120992891221955939769776367462444940983223995387750425148703775882072783131603210713039868357217864854168070718126052977717179741261297670229035276511402770481<271>
4×10289+3 = 4(0)2883<290> = 67 × 2437 × 14276791 × 501722897099<12> × 56508654713057<14> × 1123229136944868624978899<25> × [538830049227481938384887792292632313502300802142312886888861176714877871838890997362523764463823271700851276380070231080487835382564369891900902305522577007565297731405602147342493148308051068530214615157943368730088878707320011<228>] Free to factor
4×10290+3 = 4(0)2893<291> = 13 × 4547066927807135437417918879<28> × [6766830411284381917087259810952980102271140647003858376705799550333963203794377848162251171191674343802948631844777759411015928652062776604704732877916793804675389960830848221527513768118593738186117251074555222149420829382246897041242198639583233922944542091089<262>] Free to factor
4×10291+3 = 4(0)2903<292> = 643 × 30851447743311097072061<23> × 3045057246176393363507872351<28> × 66218297105972698000939455799221145384857372303693295401614294193040897955012950525080355464069388632088171227482774412527371924347998179272564957313094013095421851689129326310768007011099776241464241034094177202839581069263398591617856011<239>
4×10292+3 = 4(0)2913<293> = 1279 × 5113 × 4527840313<10> × 411159366607875708303133141<27> × 1787671543599247770344464783274772373<37> × [1837911676445808332725397756961805780189005859348347258730014079371716043158823480828111444355692467653483309852707852411787550494065854851819013274154239624291835272776477390744447556010837227655914319418787378421<214>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:1344747953 for P37 / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10293+3 = 4(0)2923<294> = 277 × 523 × 612786020239<12> × 169058470814046181992748279<27> × [26652180637953401277790229918862342257446428350634037490430600607285918749518019916753382473283018438422036515900509891690106041896887837586200426701698924397168486406760450239428085591542622286764700795540173841143548590976238743951792046590417987053<251>] Free to factor
4×10294+3 = 4(0)2933<295> = 7 × 1483 × 354550310941<12> × [1086783233597765573572416654514212245201336206434313588957155673527479675705242862100233626836409365798808554364663172839248002529595298160170890888637376845529922159009106078453196898732220546509035853459062544739259903647999398924987204576109174031462318737962931142706234791643<280>] Free to factor
4×10295+3 = 4(0)2943<296> = 43 × 294382095407<12> × 530390549947<12> × 61363145920931<14> × 346390135158402984595314971773<30> × 979748039245458665997117084527<30> × [286086148542885105424595423619620897197147645301498965262261238833950578490052762337083494532714017528888250512300685499601801000865961554108765831073005134603738149482751910183356472489629520764749<198>] (Erik Branger / GMP-ECM B1=3e6, sigma=3:233830791 for P30(3463...), B1=3e6, sigma=3:538024693 for P30(9797...) / March 6, 2019 2019 年 3 月 6 日) Free to factor
4×10296+3 = 4(0)2953<297> = 13 × 27733 × 2446829311<10> × 132395646559588784508833299<27> × [3424856726449481395996857825572682618163464333717076242981688848781161288957851459546138200736206263620528406372969759383016554859344467645688211687800242411056609061447415222456564848119190164236636304603426515765945670825583308368510276654912683100689663<256>] Free to factor
4×10297+3 = 4(0)2963<298> = 954131 × 59300147756146085522329772153<29> × 258133244212134669407094181111768811<36> × 975373997423310574241616981970832701363<39> × 280789650478825995227360890196948015348471380187012917027355509952011089574260749483487173650823637770605704867363739918494966559640758911169687940913034848279312932927089141479612428132297<189> (Erik Branger / GMP-ECM B1=3e6, sigma=3:923685529 for P36, B1=3e6, sigma=3:1778598048 for P39 x P189 / March 6, 2019 2019 年 3 月 6 日)
4×10298+3 = 4(0)2973<299> = 3919 × 60467822809<11> × 32084748590286649<17> × 5260920699138312340565993194934975750852479618533741586659279066479462211945128167521259430116355300248721061284643118710925232343837348296655880847950329445598955438313947706862253163445180794882672576555757794092068551846363679658345626674699738358976011731951125757<268>
4×10299+3 = 4(0)2983<300> = 29 × 421433 × [32729054080425268237099413765365574942701654134575488213163020063646555017498997877275374978818165312324771712802223153727466966770273214779426222043557952558745174612367311300843255896118636929811807120811202697004972443363803809940091921184837578387107305558530717485505324730719661987421079<293>] Free to factor
4×10300+3 = 4(0)2993<301> = 7 × 307 × 13339 × 10235325553<11> × 8385518778208801363<19> × [1625805942919604555873836887661231516484509230737651495302659656109631203135264463566704918146431381560393743040311441745480471058798783213646456077421498697904947406761637118184410424933049768642492044832852618389733298964549897775985609879612716316494216163676407<265>] Free to factor
plain text versionプレーンテキスト版

4. Related links 関連リンク