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

August 11, 2015 2015 年 8 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)
  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)
  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)
  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)
  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

  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)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 18.95%. 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

July 19, 2014 2014 年 7 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=193, 200, 204, 205, 214, 216, 219, 220, 221, 223, 224, 225, 226, 229, 230, 233, 236, 237, 238, 239, 243, 245, 247, 249, 250 (25/250)

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)
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)
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)
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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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 / 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> × [4335547469834061658147640270649033830947751346180887685982242725322739227885527197088689212274797976410149229278074449718558275634579825277633238195596546383299247872616363363<175>] Free to factor
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 / 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 / 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 / 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 / November 4, 2012 2012 年 11 月 4 日)
4×10200+3 = 4(0)1993<201> = 13 × 991 × 87691 × 814976131 × 287615789104916661244746697<27> × [1510533456914556659284000396935645808300129721824648349906140727379221285272794845339437152159459642112098507021131327692168684883902682243075699276411538793<157>] Free to factor
4×10201+3 = 4(0)2003<202> = 2204443 × 4468091 × 71688345769<11> × 55666002587068831184719813551787647635352501345999778360804123<62> × 101765486562492975664464010218464694031797606985557466323154868219064829799187863546776410364117597258832751486743513<117> (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 snfs / 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 / February 19, 2013 2013 年 2 月 19 日)
4×10204+3 = 4(0)2033<205> = 7 × 2647 × 6733 × 1185445304240320581173227980358111768949628211<46> × [27046923637225036925607576082718640325076170892478783217466311435980784433816843293370872332964682149571857324094177865675107335525401497727742252283989<152>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1653578623 for P46 / November 18, 2012 2012 年 11 月 18 日) Free to factor
4×10205+3 = 4(0)2043<206> = 544042113731<12> × 243023367290327526806945861<27> × [302537656150620145033462389948283306434073008912523303684940773900164327016875621125645026517331542798449771462297991035960648741249636736937120097405573072364433357133<168>] Free to factor
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 / 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 / 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 / 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 / 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> × [726776310698164533654015319622307234195032645329537091172950440930029047255459749538850654453019997909136480915859750105787582721597320839712793449932515869562345256274997699341571757<183>] Free to factor
4×10220+3 = 4(0)2193<221> = 109 × 7273112341009<13> × [50456044105776872268620790750917146599661989289005346566724573410061575089462916040238170526613044298553468881209667519459713028315974240062532171893134828772820328909665545453401312153936283891489454195263<206>] Free to factor
4×10221+3 = 4(0)2203<222> = 167 × 947751774578523701533<21> × [2527254124006785496935897300421828041775488180446373620104067652768999602371856288415110302830606284916348732501653286167614439840018527358798216709765998485587368666947854307273136043735528887219273<199>] Free to factor
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> × [103188635587358061084206600902265939372824315276457080413201084880605241845779194121787497224997655745203172530226045869895228318051777636820734441028807910850535969769877573831911484288741127<192>] Free to factor
4×10224+3 = 4(0)2233<225> = 13 × 277 × 283 × 202009395725707<15> × 38964228161899290209200976212201111<35> × [49866947789544876656836053379654506842017782006392645051965526525548592563589069077149471328034354361262368322683502565467767362957442889554457127724956079670980894869533<170>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3048405199 for P35 / November 15, 2012 2012 年 11 月 15 日) Free to factor
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 × [4574098276559816112101085742272661312150989154469928905934011999918123640849579291593390565213319362512497294134988272583781185201465586828792530680478308882681583411026298434983709920750316784893765995764613700819438271<220>] Free to factor
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 / 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 / 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 / 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> × [284735840972928257427252310894822484528031658866536455450332799101470700003641780506112547935521828498901112400964496721474372084202450499027372347681899<153>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1339124700 for P33 / November 12, 2012 2012 年 11 月 12 日) Free to factor
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