Table of contents 目次

  1. About 400...007 400...007 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...007 400...007 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...007 400...007 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...007 400...007 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

40w7 = { 47, 407, 4007, 40007, 400007, 4000007, 40000007, 400000007, 4000000007, 40000000007, … }

1.3. General term 一般項

4×10n+7 (1≤n)

2. Prime numbers of the form 400...007 400...007 の形の素数

2.1. Last updated 最終更新日

May 25, 2015 2015 年 5 月 25 日

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

  1. 4×101+7 = 47 is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
  2. 4×103+7 = 4007 is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
  3. 4×109+7 = 4000000007<10> is prime. は素数です。 (Makoto Kamada / December 1, 2004 2004 年 12 月 1 日)
  4. 4×1039+7 = 4(0)387<40> is prime. は素数です。 (Makoto Kamada / PPSIQS / December 1, 2004 2004 年 12 月 1 日)
  5. 4×102323+7 = 4(0)23227<2324> 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: Ray Chandler / Primo 3.0.9 / September 19, 2010 2010 年 9 月 19 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 / May 24, 2015 2015 年 5 月 24 日

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

  1. 4×102k+7 = 11×(4×100+711+36×102-19×11×k-1Σm=0102m)
  2. 4×103k+2+7 = 37×(4×102+737+36×102×103-19×37×k-1Σm=0103m)
  3. 4×1013k+6+7 = 79×(4×106+779+36×106×1013-19×79×k-1Σm=01013m)
  4. 4×1016k+13+7 = 17×(4×1013+717+36×1013×1016-19×17×k-1Σm=01016m)
  5. 4×1018k+5+7 = 19×(4×105+719+36×105×1018-19×19×k-1Σm=01018m)
  6. 4×1021k+17+7 = 43×(4×1017+743+36×1017×1021-19×43×k-1Σm=01021m)
  7. 4×1022k+16+7 = 23×(4×1016+723+36×1016×1022-19×23×k-1Σm=01022m)
  8. 4×1028k+12+7 = 29×(4×1012+729+36×1012×1028-19×29×k-1Σm=01028m)
  9. 4×1033k+24+7 = 67×(4×1024+767+36×1024×1033-19×67×k-1Σm=01033m)
  10. 4×1034k+31+7 = 103×(4×1031+7103+36×1031×1034-19×103×k-1Σm=01034m)

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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 9.44%. 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 9.44% です。

3. Factor table of 400...007 400...007 の素因数分解表

3.1. Last updated 最終更新日

October 24, 2017 2017 年 10 月 24 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, 197, 199, 201, 202, 203, 204, 209, 212, 214, 218, 220, 221, 223, 224, 226, 227, 230, 232, 235, 236, 238, 239, 240, 243, 244, 245, 246, 247, 249 (30/250)

3.4. Factor table 素因数分解表

4×101+7 = 47 = definitely prime number 素数
4×102+7 = 407 = 11 × 37
4×103+7 = 4007 = definitely prime number 素数
4×104+7 = 40007 = 11 × 3637
4×105+7 = 400007 = 19 × 37 × 569
4×106+7 = 4000007 = 11 × 79 × 4603
4×107+7 = 40000007 = 167 × 239521
4×108+7 = 400000007 = 11 × 37 × 982801
4×109+7 = 4000000007<10> = definitely prime number 素数
4×1010+7 = 40000000007<11> = 11 × 3636363637<10>
4×1011+7 = 400000000007<12> = 37 × 71 × 373 × 408217
4×1012+7 = 4000000000007<13> = 11 × 29 × 191 × 65650183
4×1013+7 = 40000000000007<14> = 17 × 107 × 229 × 8861 × 10837
4×1014+7 = 400000000000007<15> = 112 × 37 × 89345543891<11>
4×1015+7 = 4000000000000007<16> = 911 × 468883 × 9364339
4×1016+7 = 40000000000000007<17> = 11 × 23 × 8597 × 18390457927<11>
4×1017+7 = 400000000000000007<18> = 37 × 43 × 167611 × 1499986307<10>
4×1018+7 = 4000000000000000007<19> = 11 × 379 × 5821 × 42179 × 3907817
4×1019+7 = 40000000000000000007<20> = 61 × 79 × 181 × 45858990483113<14>
4×1020+7 = 400000000000000000007<21> = 11 × 37 × 28639363 × 34316440027<11>
4×1021+7 = 4000000000000000000007<22> = 19732764797<11> × 202708542931<12>
4×1022+7 = 40000000000000000000007<23> = 11 × 809 × 3761 × 1481153 × 806892221
4×1023+7 = 400000000000000000000007<24> = 19 × 37 × 59 × 4561 × 10211 × 33941 × 6100981
4×1024+7 = 4000000000000000000000007<25> = 11 × 67 × 113 × 9787 × 4907547046319381<16>
4×1025+7 = 40000000000000000000000007<26> = 972 × 2913929 × 3153907 × 462581941
4×1026+7 = 400000000000000000000000007<27> = 11 × 37 × 149 × 24725317 × 266770280451497<15>
4×1027+7 = 4000000000000000000000000007<28> = 4861 × 822875951450318864431187<24>
4×1028+7 = 40000000000000000000000000007<29> = 11 × 3636363636363636363636363637<28>
4×1029+7 = 400000000000000000000000000007<30> = 172 × 37 × 21017 × 1779875808364527251347<22>
4×1030+7 = 4000000000000000000000000000007<31> = 11 × 1163 × 312670991948721957320409599<27>
4×1031+7 = 40000000000000000000000000000007<32> = 103 × 197 × 233754349 × 8433286230784303873<19>
4×1032+7 = 400000000000000000000000000000007<33> = 11 × 37 × 79 × 2531 × 4943 × 23856778201<11> × 41681557843<11>
4×1033+7 = 4000000000000000000000000000000007<34> = 1931 × 280338770951<12> × 7389151186109402147<19>
4×1034+7 = 40000000000000000000000000000000007<35> = 11 × 617 × 5009 × 1176606140183855887162059229<28>
4×1035+7 = 400000000000000000000000000000000007<36> = 37 × 5099 × 372354229009991<15> × 5693993467871879<16>
4×1036+7 = 4000000000000000000000000000000000007<37> = 112 × 8017 × 4123469033262993824074255430351<31>
4×1037+7 = 40000000000000000000000000000000000007<38> = 321611 × 16979782660843<14> × 7324820220383636959<19>
4×1038+7 = 400000000000000000000000000000000000007<39> = 11 × 23 × 372 × 43 × 541 × 1733 × 909451 × 1298819 × 24251790094001<14>
4×1039+7 = 4000000000000000000000000000000000000007<40> = definitely prime number 素数
4×1040+7 = 40000000000000000000000000000000000000007<41> = 11 × 29 × 7417 × 16906006408221729036446391265004609<35>
4×1041+7 = 400000000000000000000000000000000000000007<42> = 192 × 37 × 139 × 49507282789<11> × 637994864249<12> × 6821030503069<13>
4×1042+7 = 4000000000000000000000000000000000000000007<43> = 11 × 821 × 442918835123463625290665485549773004097<39>
4×1043+7 = 40000000000000000000000000000000000000000007<44> = 313 × 8311 × 4300691 × 3575395847256589475193131177539<31>
4×1044+7 = 400000000000000000000000000000000000000000007<45> = 11 × 37 × 3593 × 8671167943<10> × 31545017101546775617494197999<29>
4×1045+7 = 4000000000000000000000000000000000000000000007<46> = 17 × 79 × 16176055410143<14> × 184124403445529845525013703143<30>
4×1046+7 = 40000000000000000000000000000000000000000000007<47> = 11 × 71 × 51216389244558258642765685019206145966709347<44>
4×1047+7 = 400000000000000000000000000000000000000000000007<48> = 37 × 47 × 814183 × 19985749387<11> × 349255373309<12> × 40473880535441117<17>
4×1048+7 = 4000000000000000000000000000000000000000000000007<49> = 11 × 26765991761191<14> × 13585760874499462042803360122658307<35>
4×1049+7 = 40000000000000000000000000000000000000000000000007<50> = 383 × 151651 × 688677570854462750316864854584956151812979<42>
4×1050+7 = 400000000000000000000000000000000000000000000000007<51> = 11 × 37 × 163 × 17697411929<11> × 3879665637899<13> × 87816054281462107996537<23>
4×1051+7 = 4(0)507<52> = 293726003 × 13618133768020531706210566587119629309768669<44>
4×1052+7 = 4(0)517<53> = 11 × 359 × 21402239576867<14> × 101169725523491<15> × 4678030667952838283819<22>
4×1053+7 = 4(0)527<54> = 37 × 1117 × 763381 × 2045598455107<13> × 6197882814782076847015901073449<31>
4×1054+7 = 4(0)537<55> = 11 × 13043 × 577336267038310565760409<24> × 48290418825607786730203151<26>
4×1055+7 = 4(0)547<56> = 1470550312631893493087<22> × 27200701435648706832827738636099161<35>
4×1056+7 = 4(0)557<57> = 11 × 37 × 629059 × 1562335143128041727378196612401989004183710880539<49>
4×1057+7 = 4(0)567<58> = 67 × 502543 × 1324733 × 2931961 × 193797509 × 157825518923074612759993793291<30>
4×1058+7 = 4(0)577<59> = 112 × 79 × 4184538131603724238937127314572654043309969662098545873<55>
4×1059+7 = 4(0)587<60> = 19 × 37 × 43 × 13232326573819841873697442852889609315557907969168679083<56>
4×1060+7 = 4(0)597<61> = 11 × 23 × 991 × 383681 × 638719 × 1033951 × 82093733 × 104111942923<12> × 7366737139333341659<19>
4×1061+7 = 4(0)607<62> = 17 × 151 × 8052659 × 62729456462801<14> × 704330527370990953<18> × 43797243442267264723<20>
4×1062+7 = 4(0)617<63> = 11 × 37 × 653 × 1505055103829988975471364445330754672255437952222025728917<58>
4×1063+7 = 4(0)627<64> = 6043 × 1598418601445003512233029<25> × 414111100424751623088561805087078081<36>
4×1064+7 = 4(0)637<65> = 11 × 109 × 5304713159<10> × 13992883878265521385669<23> × 449439949233244394558007490883<30>
4×1065+7 = 4(0)647<66> = 37 × 103 × 2663 × 22646287 × 1740415206617799769883336667850378627527240764581477<52>
4×1066+7 = 4(0)657<67> = 11 × 107 × 17977839608332151<17> × 189036656363050007031246075025764542395649039641<48>
4×1067+7 = 4(0)667<68> = 131 × 907 × 6841 × 24061702249445748790073<23> × 2045198520361163897657403157850284247<37>
4×1068+7 = 4(0)677<69> = 11 × 29 × 37 × 3367687 × 10063194430510571560333095731744408274394992076993054989587<59>
4×1069+7 = 4(0)687<70> = 1263181 × 611296385494902797<18> × 5180152900055810738981213242360687746036720751<46>
4×1070+7 = 4(0)697<71> = 11 × 40673663 × 89403396895028519158364557339318968238399468382369111029817099<62>
4×1071+7 = 4(0)707<72> = 37 × 79 × 433 × 9283 × 8383819 × 94924377175597<14> × 42779458125998770235026845079920320682617<41>
4×1072+7 = 4(0)717<73> = 11 × 3823 × 514229 × 471601181 × 10259125517856492047234983<26> × 38231489258848639514635789357<29>
4×1073+7 = 4(0)727<74> = 146790974159<12> × 272496318177390698489369509464459633568143762454121612203449673<63>
4×1074+7 = 4(0)737<75> = 11 × 37 × 703880603552928673<18> × 1396260925276484853508489215529546940513201783302740337<55>
4×1075+7 = 4(0)747<76> = 10993 × 9220291 × 2869649389<10> × 6328435783<10> × 7110600253<10> × 285344538395817133<18> × 1071021258705139103<19>
4×1076+7 = 4(0)757<77> = 11 × 10837 × 2784091 × 8807229953535427<16> × 13684705972013322259021613988313510537123675098193<50>
4×1077+7 = 4(0)767<78> = 17 × 19 × 37 × 2368237 × 14132877119245323955653137822485254557789564500170956175143093977261<68>
4×1078+7 = 4(0)777<79> = 11 × 2531 × 2032991 × 2212654511<10> × 453429131723<12> × 70439567130453085647831818617221157189417367749<47>
4×1079+7 = 4(0)787<80> = 61 × 683 × 17785367 × 3724812792031498033<19> × 14492462031904437756685564671665582469990744895199<50>
4×1080+7 = 4(0)797<81> = 112 × 37 × 43 × 7788237588337642668791180521<28> × 266787360135707563054997859536524418277944983697<48>
4×1081+7 = 4(0)807<82> = 592 × 71 × 5551192261<10> × 2915488618091243626268858856710257620291820460972259471439169530837<67>
4×1082+7 = 4(0)817<83> = 11 × 23 × 15331 × 15541951819<11> × 232264505495580393435499<24> × 2856804899028143449862156634895027177513529<43>
4×1083+7 = 4(0)827<84> = 37 × 431 × 402529 × 78429691649464676560988636280123823<35> × 794517221528963735243507356427906547643<39> (Makoto Kamada / msieve 0.81 / 7.1 minutes)
4×1084+7 = 4(0)837<85> = 11 × 79 × 219529 × 299261 × 70064526755527318709119264297445795885361854037852271322826483687595487<71>
4×1085+7 = 4(0)847<86> = 727 × 109363 × 405600257 × 527263309483<12> × 1573146293161<13> × 1495410002787932321774884951732147371634594777<46>
4×1086+7 = 4(0)857<87> = 11 × 37 × 982800982800982800982800982800982800982800982800982800982800982800982800982800982801<84>
4×1087+7 = 4(0)867<88> = 139 × 1021 × 1996751 × 620421690731<12> × 127951996936870189116075461<27> × 177812176198176712983269019679635512833<39>
4×1088+7 = 4(0)877<89> = 11 × 98564172565667<14> × 6600385411457737116253<22> × 5589576830400854269359997695214744049518229574878387<52>
4×1089+7 = 4(0)887<90> = 37 × 71621061916609515028109134134598055288291<41> × 150944575820422101425306447211855858408857883721<48> (Makoto Kamada / GGNFS-0.70.3 / 0.14 hours)
4×1090+7 = 4(0)897<91> = 11 × 67 × 827 × 24007 × 7304333 × 466617148584043867<18> × 80206181704276071954216073396464378435409872098081220109<56>
4×1091+7 = 4(0)907<92> = 6011 × 6654466810846780901680252869738812177674263849609050074862751622026285143902844784561637<88>
4×1092+7 = 4(0)917<93> = 11 × 37 × 982800982800982800982800982800982800982800982800982800982800982800982800982800982800982801<90>
4×1093+7 = 4(0)927<94> = 17 × 47 × 79229 × 258648812837<12> × 244297233079982019882109113648688601383119314216076577299443411078500917641<75>
4×1094+7 = 4(0)937<95> = 11 × 5657 × 1285323498480793419257<22> × 500113617437201615164372127533421256220455364772280183599472658205413<69>
4×1095+7 = 4(0)947<96> = 19 × 37 × 347 × 1639740756986320462734841621539634583772305598484879540544639892433006341697377644594389627<91>
4×1096+7 = 4(0)957<97> = 11 × 29 × 491 × 56779 × 2156617 × 208558095562637864311029230806040851686450569040429895330559173222553105670027481<81>
4×1097+7 = 4(0)967<98> = 79 × 6863 × 24782773097<11> × 1687044182687<13> × 519316238625664028708070091<27> × 3397900371838217543632382864452418362655059<43>
4×1098+7 = 4(0)977<99> = 11 × 37 × 5839 × 331937 × 4044670901230701768151111939<28> × 125368448621667014758040059473623770992595554122825927806613<60>
4×1099+7 = 4(0)987<100> = 103 × 72983566771<11> × 152542758044569<15> × 3488237835151771350219863893321200172484965538972254487293303117277173331<73>
4×10100+7 = 4(0)997<101> = 11 × 5711413 × 692417046755257677464549<24> × 919509010020646173072830953434241040757909925975245062048028099750701<69>
4×10101+7 = 4(0)1007<102> = 37 × 43 × 66232193194023511<17> × 3795951678152543181210276286750395575158529346643899548133792628475736284012158007<82>
4×10102+7 = 4(0)1017<103> = 112 × 2585280752085942635036731470745668477195362783<46> × 12786948269736886765489577885313149519498166924858577249<56> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 0.61 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 10, 2007 2007 年 9 月 10 日)
4×10103+7 = 4(0)1027<104> = 8317 × 2307718947388501051<19> × 10171046590108803317<20> × 106617820257402683732969545553<30> × 1921829834019223280013982246911221<34> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3468208765 for P34 / September 3, 2007 2007 年 9 月 3 日)
4×10104+7 = 4(0)1037<105> = 11 × 23 × 37 × 49055043907<11> × 167494769929345967445792325103<30> × 5200592516379921787336332002431463118753363515375654106032947<61> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3576232874 for P30 / September 3, 2007 2007 年 9 月 3 日)
4×10105+7 = 4(0)1047<106> = 1043329248228030997017608973380352553<37> × 3833880826012994445256424591562881885990352920890139603449554354425519<70> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.37 hours on Core 2 Quad Q6600 / September 10, 2007 2007 年 9 月 10 日)
4×10106+7 = 4(0)1057<107> = 11 × 11887 × 96607700155906921<17> × 64819024777953578883539736640240237<35> × 48851826656369687093848975611401730998510732736463<50> (Sinkiti Sibata / Msieve v. 1.26 for P35 x P50 / September 10, 2007 2007 年 9 月 10 日)
4×10107+7 = 4(0)1067<108> = 37 × 191 × 1669 × 5669 × 338683055591887<15> × 17663169519531815152997626916124684395778439292892087431971825974455617056062504003<83>
4×10108+7 = 4(0)1077<109> = 11 × 193 × 771305081 × 3140421473261381<16> × 47585436920124691429<20> × 50621651376769961308361<23> × 322912975691329944501147679823361799901<39>
4×10109+7 = 4(0)1087<110> = 17 × 5627173061<10> × 33220302370681537<17> × 6255658824026110951<19> × 111043568406709692293<21> × 18119689558658990205009446225821551458457721<44>
4×10110+7 = 4(0)1097<111> = 11 × 37 × 79 × 5612461 × 130073407 × 803734927 × 5263248413831741<16> × 4028375343967278809846441625067003287895580724930191835702762067271<67>
4×10111+7 = 4(0)1107<112> = 269 × 14549 × 53117 × 717756842186126207<18> × 26807955119273081898538566441813530701394514789617989561408161845821706464763702813<83>
4×10112+7 = 4(0)1117<113> = 11 × 14431 × 251982789575471995262723555981126489060797147554822005657013625969346293648143831776289679414895962605754027<108>
4×10113+7 = 4(0)1127<114> = 19 × 37 × 144731 × 38839309 × 101221229638636170475464137626705953548059560941890172908875708369075110285096578516806567744787111<99>
4×10114+7 = 4(0)1137<115> = 11 × 3149444390934098454862201223<28> × 115460480801984307984195261076010964393508890162939814589228437328801138345465858294819<87>
4×10115+7 = 4(0)1147<116> = 11369 × 74831 × 616137941 × 1088289150861427535771593<25> × 262090130323693780634432290545289<33> × 267536632629551162276076355325135275466509<42> (Makoto Kamada / Msieve 1.26 for P33 x P42 / 4.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / September 10, 2007 2007 年 9 月 10 日)
4×10116+7 = 4(0)1157<117> = 11 × 37 × 71 × 953 × 10173367 × 47836812629<11> × 29846086003884875638111513937870552788454646736588769417201287129343109293888257611194387189<92>
4×10117+7 = 4(0)1167<118> = 3372533359686783953<19> × 7571231308415109663829195119389645559083504639<46> × 156652461213639440290493125833595279391925366872158121<54> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.85 hours on Core 2 Quad Q6600 / September 10, 2007 2007 年 9 月 10 日)
4×10118+7 = 4(0)1177<119> = 11 × 1355872409785589112231313<25> × 8329037256949978677503257<25> × 321998373465336952204972552124124490115114711147122577135548131176557<69>
4×10119+7 = 4(0)1187<120> = 37 × 107 × 1471 × 3433 × 20007278310726802875139347248430978053753975490528967422935362808528879482644166665278620052030180703031217911<110>
4×10120+7 = 4(0)1197<121> = 11 × 1250831 × 51158077863472778717<20> × 16163441146585422712119803589901420539893<41> × 351577137058775393064141868807182275859318715677825467<54> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 2.14 hours on Pentium 4 3.4GHz, Windows XP and Cygwin / September 10, 2007 2007 年 9 月 10 日)
4×10121+7 = 4(0)1207<122> = 97 × 83115187 × 39877614167<11> × 124416707343569232606494712914782307903872357741083875347758940814369726259927321031411346632458820939<102>
4×10122+7 = 4(0)1217<123> = 11 × 37 × 43 × 617 × 12329 × 165018011 × 1407942961189307<16> × 310525128173251414960402600541<30> × 41645775254403590505222927813301936708406854066436238480407<59> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3576028625 for P30 / September 4, 2007 2007 年 9 月 4 日)
4×10123+7 = 4(0)1227<124> = 67 × 79 × 1459 × 2333 × 19949 × 33829 × 46451 × 893003465557677469001745507020861686789619767<45> × 7931029477391238937468273562091619341494204808802031281<55> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 2.59 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 10, 2007 2007 年 9 月 10 日)
4×10124+7 = 4(0)1237<125> = 113 × 29 × 709 × 1801 × 2531 × 260722306516963<15> × 67816150798627989304720548529530399180885482189<47> × 18135123580998002481347196781299085919725495181681<50> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 2.58 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 10, 2007 2007 年 9 月 10 日)
4×10125+7 = 4(0)1247<126> = 17 × 37 × 2142420593<10> × 17465135037676903<17> × 3547813266353285192996701<25> × 4790401454391193668772785329790653149871725010030322071359207145873681777<73>
4×10126+7 = 4(0)1257<127> = 11 × 23 × 10988333105569<14> × 16031070312247<14> × 1622183750793132481252673<25> × 459469579294610231208790237<27> × 120417144744420185476389760127899782258554005033<48>
4×10127+7 = 4(0)1267<128> = 606497 × 2268865117<10> × 211856473010664580779859<24> × 377275926509092007527238672431385514979<39> × 363682014571282571218438761205122109617347029045963<51> (Jo Yeong Uk / Msieve v. 1.25 for P39 x P51 / 48.38 minutes on Core 2 Quad Q6600 / September 10, 2007 2007 年 9 月 10 日)
4×10128+7 = 4(0)1277<129> = 11 × 37 × 65837 × 14927791102282649588875571225921333003976502313303807904108646852088989488931770627473651609016221620076595242535367389173<122>
4×10129+7 = 4(0)1287<130> = 197 × 27838762934579403199<20> × 49110419612123801773199<23> × 14851495486534557710460390047007879790580145713586559299045498094087341703678410717131<86>
4×10130+7 = 4(0)1297<131> = 11 × 1444520412397380043861<22> × 408504680191109431162215803581538597<36> × 6162353197057531640657105318413959662898339394094871838459411864184198861<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 1.80 hours on Core 2 Quad Q6600 / September 10, 2007 2007 年 9 月 10 日)
4×10131+7 = 4(0)1307<132> = 19 × 37 × 163 × 3490736458124252764226932777142657672202392899842044175269877562418731291834294740332841721282147501069038040300552409044498163<127>
4×10132+7 = 4(0)1317<133> = 11 × 1383665436911<13> × 15993881312447791<17> × 105178237608324529255932346205701327687403<42> × 156227130243012416024084470042988923198135605773570637061345279<63> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.47 hours on Core 2 Quad Q6600 / September 11, 2007 2007 年 9 月 11 日)
4×10133+7 = 4(0)1327<134> = 103 × 139 × 581182594323229533763<21> × 26266897688914103600761963556264623<35> × 183014957204357914443774593629154442488846573682381077826399652046581216079<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.48 hours on Core 2 Quad Q6600 / September 11, 2007 2007 年 9 月 11 日)
4×10134+7 = 4(0)1337<135> = 11 × 37 × 32796773 × 2156909495539<13> × 13893208258178951698628396862381371357700064112584363134228481760768390394861609195360876402283980223326913050383<113>
4×10135+7 = 4(0)1347<136> = 11423 × 5609791559<10> × 1201105787235845761<19> × 51969893924012452340420135609947484266265891445603617284629421123235169233684939622556868792712533080991<104>
4×10136+7 = 4(0)1357<137> = 11 × 79 × 113 × 151 × 967 × 8035637264791904171821<22> × 151132305869278356285433<24> × 13843131922546324190310604226546490969103<41> × 165938194222088675576956806070665609433217<42> (Sinkiti Sibata / Msieve v. 1.26 for P41 x P42 / 1.9 hours on Celeron 750MHz, Windows 2000 / September 10, 2007 2007 年 9 月 10 日)
4×10137+7 = 4(0)1367<138> = 37 × 1107462891089<13> × 33316615015951<14> × 44362108741514166069517<23> × 6604744653496085875408845180964624010370390597872832959019173358460247859286555601902297<88>
4×10138+7 = 4(0)1377<139> = 11 × 38795278363<11> × 9373211869596287664189026858777681310270235671678086378050725874523959949750557319808646023186065510854745155412054843937133999<127>
4×10139+7 = 4(0)1387<140> = 47 × 59 × 61 × 7229 × 8623 × 10837 × 31986300717986806917050274578788541806841309083879<50> × 10943861459545403346659982155635581621711169730625226161155822473142568559<74> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 8.92 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 11, 2007 2007 年 9 月 11 日)
4×10140+7 = 4(0)1397<141> = 11 × 37 × 84263 × 21289799939<11> × 339012053851<12> × 5722935804716380853<19> × 246523695335114998234346215684034044871<39> × 1145419047714673326600757462103639786711752383269528461<55> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 8.01 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 11, 2007 2007 年 9 月 11 日)
4×10141+7 = 4(0)1407<142> = 17 × 1569667180412083523<19> × 149900641730489159482299282930224487646429481017768782812152110616771590274226758405195984136016153848547689705791000232477<123>
4×10142+7 = 4(0)1417<143> = 11 × 128425333 × 330484919 × 1110686627<10> × 2229599509718725418315923215401<31> × 34597646459065868838026205405922156262284783213861761567480768713986485734911023224453<86> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=2936475969 for P31 / September 10, 2007 2007 年 9 月 10 日)
4×10143+7 = 4(0)1427<144> = 37 × 43 × 2953 × 85208610560597464386908162003<29> × 1000749795659211467211625369787<31> × 998429423289612292605918747746093298336322693193270765403387192272005415284169<78> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 12.96 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 12, 2007 2007 年 9 月 12 日)
4×10144+7 = 4(0)1437<145> = 11 × 179 × 18849577301<11> × 752837899459199<15> × 48338648874827112317609973195674549<35> × 2961533694098241796253566194687162650499134657877589080508209090117714412844440753<82> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 13.12 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 12, 2007 2007 年 9 月 12 日)
4×10145+7 = 4(0)1447<146> = 4392151 × 3232273843<10> × 1211897590658056825345729619<28> × 245205770243078049098016147103<30> × 9481520166803148988611378706542788658592969110039776211044688806734040407<73> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1428234538 for P30 / September 5, 2007 2007 年 9 月 5 日)
4×10146+7 = 4(0)1457<147> = 112 × 37 × 27631 × 7504421 × 2195747147917<13> × 196235138726596894036664375923931616765414137799105075997570607987500909290641898214529430953865551282337655353744654973<120>
4×10147+7 = 4(0)1467<148> = 1129 × 4188853 × 67490216069<11> × 19051007484473<14> × 11295665509210916966706874055352683<35> × 58237180376655904757848126410332579800623520950059240684705186957430254159852941<80> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3103559510 for P35 / September 5, 2007 2007 年 9 月 5 日)
4×10148+7 = 4(0)1477<149> = 11 × 23 × 2447 × 245114463615524143538086032433891970756683404064249115073005692163<66> × 263594632206945158216136499659187321494630614449650644664224883579346714068479<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 11.66 hours on Cygwin on AMD 64 3400+ / September 12, 2007 2007 年 9 月 12 日)
4×10149+7 = 4(0)1487<150> = 19 × 372 × 79 × 156593 × 156967 × 6118218475309117<16> × 458151166462975414839515281092455846471073253<45> × 2825279191259063103973675923003172457201413683427285242607338783549973213<73> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 26.65 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / September 14, 2007 2007 年 9 月 14 日)
4×10150+7 = 4(0)1497<151> = 11 × 263 × 27917 × 31193 × 10283467867<11> × 716791221934667531<18> × 215403815786187551588952232631938752820158787098171733028717332478281418449176598915770376006370808708839334127<111>
4×10151+7 = 4(0)1507<152> = 71 × 23656444037<11> × 393219896051<12> × 4236889707807204032029321<25> × 14294518672550366026672832710717908458334046339696793614943542097834107842824477366490326297608385033671<104>
4×10152+7 = 4(0)1517<153> = 11 × 29 × 37 × 631 × 162153046213<12> × 88985318329249787<17> × 255038398132349509211<21> × 14594498721865977989252951886791372184677151972974646593244336472337992395227769334766869109365439<98>
4×10153+7 = 4(0)1527<154> = 15122759 × 24745976488388042357<20> × 309312185819485412279995450362993507710825827912972995314067713<63> × 34556307836253073852792654157706035652442377990012162822070317853<65> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 34.45 hours on Pentium 2.4GHz, Windows XP and Cygwin / September 15, 2007 2007 年 9 月 15 日)
4×10154+7 = 4(0)1537<155> = 11 × 342802429 × 25012593481129<14> × 9378914296479408781<19> × 4999642122681669494026196348160121217<37> × 9044263464946840747038283509739191493041103507550062570873462979319591737141<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P37 x P76 / 19.99 hours on Core 2 Quad Q6600 / September 14, 2007 2007 年 9 月 14 日)
4×10155+7 = 4(0)1547<156> = 37 × 10810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810810811<155>
4×10156+7 = 4(0)1557<157> = 11 × 67 × 1009 × 47149 × 1932911 × 59022417468377137149358618496962530424591010921559077722252918019981657625005802043519520181263421074465058849612926160470447374514953084061<140>
4×10157+7 = 4(0)1567<158> = 17 × 19875157 × 1469183047<10> × 42169567669<11> × 46007753657<11> × 292957231827292399177<21> × 8814970410242325051502600691310445528441<40> × 16083084130339877401016180137996623124776743395012266452129<59> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P40 x P59 / 3.05 hours on Core 2 Quad Q6600 / September 12, 2007 2007 年 9 月 12 日)
4×10158+7 = 4(0)1577<159> = 11 × 37 × 12007 × 64184521 × 801992267819<12> × 40168232933255472863199410867005086259141899511<47> × 39586568659768781756154959633375249919813838935426658359620291935490219828230564916987<86> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 24.50 hours on Core 2 Quad Q6600 / October 2, 2007 2007 年 10 月 2 日)
4×10159+7 = 4(0)1587<160> = 1759 × 665251 × 380206966797325875839<21> × 38552289465776278156018648781010077<35> × 233205275767539960164870481835449750381744466297103083038069953484504186782020869825210096921041<96> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=3980882931 for P35 / September 13, 2007 2007 年 9 月 13 日)
4×10160+7 = 4(0)1597<161> = 11 × 1136957848708636651<19> × 25817512708582211180172834678179339<35> × 123882095407939278236523043249249576804371883991910405477004505369234945547803086828965151030213745119507133<108> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=246460385 for P35 / September 13, 2007 2007 年 9 月 13 日)
4×10161+7 = 4(0)1607<162> = 37 × 135634950176910695018973466825893607656590609530685636796371<60> × 79705199852324998153571878460082630852438535935125517735082254432468091835256979745543882602791947641<101> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 35.22 hours on Cygwin on AMD 64 3400+ / September 13, 2007 2007 年 9 月 13 日)
4×10162+7 = 4(0)1617<163> = 11 × 79 × 1139323553<10> × 234034230184541159881265925110454036781626436280873469868669<60> × 17262900077839710421537401417208645828242546967978794855357928428513665188571039974636777079<92> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 39.72 hours on Cygwin on AMD 64 3200+ / September 23, 2007 2007 年 9 月 23 日)
4×10163+7 = 4(0)1627<164> = 90119551 × 443854852317229143762600415086400064287936809627469182575044121114185311464767506442636404169390502178600512556925633151456779894520335548498238745108705657<156>
4×10164+7 = 4(0)1637<165> = 11 × 37 × 43 × 6449 × 238291 × 18515813 × 196948146026549213753598998945340356169909690257113074987708892318543<69> × 4078518408615435716369982093154238241123860446542160172985649100147392724947<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.32 / January 12, 2008 2008 年 1 月 12 日)
4×10165+7 = 4(0)1647<166> = 401 × 13708301987<11> × 669762803603041<15> × 52363354231220831<17> × 20748345568086422841621539254080697783777055725165024369020103747155341733030184821335971451122704328458933448036969842691<122>
4×10166+7 = 4(0)1657<167> = 11 × 1723 × 5093575211835090988967<22> × 414342331396989202589915715309045161963937785133108032430074856006606243627232768172860765847842632417133382481988126021821260380507596701657<141>
4×10167+7 = 4(0)1667<168> = 19 × 37 × 103 × 3181 × 2195243 × 49677996456074056607500961<26> × 15924180782199724146635402764921837022814435560705638178719358476215437250397765586730249580866157703182682122958337710789421521<128>
4×10168+7 = 4(0)1677<169> = 112 × 2618693672249983639196789<25> × 434600913422969283935715734532476163912699428553621729133663787<63> × 29046866416543146278620690212890391220410722501413452500320961183706650069675369<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 / 47.09 hours on Cygwin on AMD 64 X2 6000+ / July 13, 2008 2008 年 7 月 13 日)
4×10169+7 = 4(0)1687<170> = 2711 × 2209171 × 6678841548074316239975853409770873790106418659244262119691482315469229524152137090517404964147593701692862641336290287797211448106589754801561990891475708892747<160>
4×10170+7 = 4(0)1697<171> = 11 × 23 × 37 × 2381 × 2531 × 23039 × 1367480531<10> × 22070578087533539660066827927884256765089556891<47> × 10197359262644066179879009668764560198414918046657958570180948390548824665266349600950111435706326543<101> (Robert Backstrom / GGNFS-0.77.1-20060513-pentium-m snfs / 37.67 hours / May 20, 2009 2009 年 5 月 20 日)
4×10171+7 = 4(0)1707<172> = 3335301202024415353546067887<28> × 410037667471288976241689296388276289281<39> × 51426660780166300926755648189998830408613787<44> × 56873879204227560921875844575762314754395742118690775665543563<62> (Sinkiti Sibata / Msieve 1.40 snfs / 57.66 hours on Core i7 2.93GHz,Windows 7 64bit,and Cygwin / January 29, 2010 2010 年 1 月 29 日)
4×10172+7 = 4(0)1717<173> = 11 × 107 × 109 × 28109 × 4110437 × 37009237580533<14> × 100305578557150326645901431665213886002442319<45> × 726923004900429115307541442670226086141573640361924923419646985297364567603919585356657165361801089<99> (Serge Batalov / Msieve-1.38 snfs / 37.00 hours on Opteron-2.6GHz; Linux x86_64 / November 24, 2008 2008 年 11 月 24 日)
4×10173+7 = 4(0)1727<174> = 17 × 37 × 167 × 3014699489<10> × 1263132319273635646332498569514968770517938711272790738423318550296842169903618227351117268447868862664426998223244731345982783648261191883280374030379536131741<160>
4×10174+7 = 4(0)1737<175> = 11 × 149 × 4789 × 2663581 × 152629135649<12> × 76982944784946368920484345557544894861183<41> × 16283146405519833518143913288935446051211681948850296589711890188256730869928049433790754073851412297997719871<110> (Wataru Sakai / August 3, 2010 2010 年 8 月 3 日)
4×10175+7 = 4(0)1747<176> = 79 × 11304493 × 44790077177636417034482873762077710096375514506835826306665092579124361538305212478712130128315609677710009930665553997541430113146218314381052300469480518985356451981<167>
4×10176+7 = 4(0)1757<177> = 11 × 37 × 7135210354090040619550238567081980993<37> × 86406086830766213721042664242352923897087065103767310682979<59> × 1594095969696754347682904756547583137063074286784180958958904570542532322797883<79> (matsuix / GMP-ECM 6.0 B1=6700417, sigma=1265699576 for P37 / November 11, 2007 2007 年 11 月 11 日) (Warut Roonguthai / Msieve 1.48 snfs / October 14, 2011 2011 年 10 月 14 日)
4×10177+7 = 4(0)1767<178> = 419 × 173767929557963321729<21> × 272757861127713014089301<24> × 55596506082506498754154195877<29> × 2168624917890105707938720036681408679<37> × 1670579402649688089552461215114367735067686171584466742428310437779<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P37 x P67 / 5.70 hours on Core 2 Quad Q6600 / September 17, 2007 2007 年 9 月 17 日)
4×10178+7 = 4(0)1777<179> = 11 × 233 × 63179 × 12192793 × 16845706020390628754706680461<29> × 1563362006220667088154890552346111754498073<43> × 769283940315576237259252254305122932469351279083047996175021132544870432641839950287392894579<93> (Robert Backstrom / Msieve 1.44 gnfs for P43 x P93 / May 29, 2012 2012 年 5 月 29 日)
4×10179+7 = 4(0)1787<180> = 37 × 139 × 37468593467<11> × 599510744974290683<18> × 50908443942493453887015118513597866765285027457390712482503402327903932359<74> × 68012585140279758528459181985230163401345685666640474962991190006186613951<74> (Dmitry Domanov / Msieve 1.40 snfs / December 2, 2012 2012 年 12 月 2 日)
4×10180+7 = 4(0)1797<181> = 11 × 29 × 232676903 × 53890974098869007321849596739964853732378437419004278392537276678165948273186887329390572062724154689416389079242875767928275225679074939553090887794435619440333202664351<170>
4×10181+7 = 4(0)1807<182> = 497589058207<12> × 80387619744161984190895269390117254620670795163508489773008116703778723048845266868567334449316933671381887039051307641327553706466745461998048376229374372859540462037401<170>
4×10182+7 = 4(0)1817<183> = 11 × 37 × 5902703 × 37760843933<11> × 1674936332852367533987873251<28> × 2330176577666875374606105976962270839<37> × 47627606812357868080621344383726803782953<41> × 23720676061967159486831460421686709294636997657176676784247<59> (Serge Batalov / GMP-ECM 6.2.1 B1=2000000, sigma=55071172 for P37, pol51+Msieve 1.36 gnfs for P41 x P59 / 4.3 hours on Opteron-2.2GHz; Linux x86_64 / August 7, 2008 2008 年 8 月 7 日)
4×10183+7 = 4(0)1827<184> = 1745568479<10> × 4905502945797010451<19> × 3220431844647571889539380037<28> × 145052576410231048487799324832131995302321473505142134087440561835535473534451099556622068192772175145591541720499246666603613959<129>
4×10184+7 = 4(0)1837<185> = 11 × 877 × 39841 × 64969 × 4038202389358957263240913752263127880894201201820861105035375813467577<70> × 396682661688521283105637723961070218244715551697892154840685638111923776709128236756171755229780106057<102> (Robert Backstrom / Msieve 1.44 snfs / February 28, 2012 2012 年 2 月 28 日)
4×10185+7 = 4(0)1847<186> = 19 × 37 × 43 × 47 × 44971 × 1735813 × 1955926054382106295429<22> × 1843955514422604372985505288952739568244057452342131975947059716006842801211578522652953245387647388314322505782954470166899698378443450761414966567<148>
4×10186+7 = 4(0)1857<187> = 11 × 71 × 142573 × 918307021 × 23108858389027622915323<23> × 14038470155619240766222618912594529<35> × 120582835016219274964161752375016768028631861368533092320829475404326979424480003910475628535256587019987262671377<114> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2575416615 for P35 / April 7, 2011 2011 年 4 月 7 日)
4×10187+7 = 4(0)1867<188> = 15373 × 20563 × 7205969922799<13> × 688590332230738485620370006435189093461031505528861888524463689810963977188483<78> × 25501253156328634670229558189358974347407586032777004325563164831960617947093393905354229<89> (Dmitry Domanov / Msieve 1.50 snfs / August 11, 2014 2014 年 8 月 11 日)
4×10188+7 = 4(0)1877<189> = 11 × 37 × 79 × 599 × 16823 × 2802193 × 272256877 × 1439838199<10> × 243199590896994738362770572662158973938218516947373908668520401926648208873<75> × 4621200267912612430795333791515436481001624072764157228446067146299921603854101<79> (Daniel Morel / GGNFS-0.77.1 for P75 x P79 / December 11, 2014 2014 年 12 月 11 日)
4×10189+7 = 4(0)1887<190> = 17 × 67 × 156437 × 471871 × 1631297 × 29163555035768599318382908646206098728584596197104654002741759972144843699002662755483391357558501413418259684574177298472144489214243066747181225465917960613071138639127<170>
4×10190+7 = 4(0)1897<191> = 112 × 443 × 3511 × 124097 × 1712690081318315526635520038966752925689941631530305674797343350838419822528609061990825512602380991288480287731212598400492488110866672851846045327443523385179528900925161735707<178>
4×10191+7 = 4(0)1907<192> = 37 × 261310102124981081093875787<27> × 41371576234125638535444336317417534313847704890572039740377784097061953215846813356243971391689253143703182812380612753622136141157015830070447298521340937935734353<164>
4×10192+7 = 4(0)1917<193> = 11 × 23 × 99912271190751785316079<23> × 510911950705809060308785244330301179<36> × 2473421093870358016194945591927342186877<40> × 125220812436161176621503688920180892705596314382512360883490984977999696574944794407138861267<93> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1937866668 for P36 / April 7, 2011 2011 年 4 月 7 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=85038718 for P40 / April 11, 2011 2011 年 4 月 11 日)
4×10193+7 = 4(0)1927<194> = 6131 × 9463 × 101924881 × 183946145712468019<18> × [36772988818547455108124111168505856091807688738273109715320356222025361295418506493438548041780529643458294038227899850094127194760761182324630025435299851499321<161>] Free to factor
4×10194+7 = 4(0)1937<195> = 11 × 37 × 982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982800982801<192>
4×10195+7 = 4(0)1947<196> = 257 × 2141 × 4743194187258232961246655821<28> × 1532636963883079379479780537157925951709735522818826906505452595980676230521599783299850324012280982244973624686594592247004843058335415045248528732787484164910591<163>
4×10196+7 = 4(0)1957<197> = 11 × 1067789 × 239682331904859805861970201199983371009733444205017707<54> × 14208421828248700902749113805654452031722484299404367220663206740298549292027313504104977551440016026904929687743143349558675496264509019<137> (matsui / Msieve 1.42 snfs / 814.38 hours / September 29, 2009 2009 年 9 月 29 日)
4×10197+7 = 4(0)1967<198> = 37 × 59 × 131 × 373 × 133519 × 3371089 × [8331301256832907309157708500822099215961394744994684193364126409085955631213297568779219155903110142294652586003443136961815829046123663126752993517701723128283492081000802999713<178>] Free to factor
4×10198+7 = 4(0)1977<199> = 11 × 1481 × 174241 × 1409165145496084613329616303273583884490907760163985759863404493085934912681967771920347598230956763903057863388274299692825496110654701505070917238215800192255994171151838812323542777188397<190>
4×10199+7 = 4(0)1987<200> = 61 × 181 × 367 × 530443 × 492415691 × 12112733671975183715669217933907<32> × [3120130385171184912799198326020246600170409090267934947127747564622203526474452817726170719298760804796691535391906369965963888868583353217178446091<148>] (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3736815856 for P32 / September 10, 2007 2007 年 9 月 10 日) Free to factor
4×10200+7 = 4(0)1997<201> = 11 × 37 × 1283 × 3862363 × 850829939689<12> × 7902206235541<13> × 2427955288687425440124619<25> × 744937326890658098750633812878347827267331909<45> × 16309261376519004401367144323776493633648587766960444190910507407496460267050598624335377069811<95> (Tyler Cadigan / GGNFS + msieve gnfs for P45 x P95 / March 6, 2008 2008 年 3 月 6 日)
4×10201+7 = 4(0)2007<202> = 79 × 103 × 1091 × 6571 × 17038664496296129<17> × [4024425629416166856637861322296640306153677436865968742695778608651559832318277879711870523254498093767760234562475004394613023542574945082582505347790721158720980853002003919<175>] Free to factor
4×10202+7 = 4(0)2017<203> = 11 × 191 × 10837 × 667483556982998291724745572340957<33> × [2631990357926825704109591989700457485982690486980541663068287960866830986737653056453435830249760864785372089333960850315705084012387899337174340799478682311786923<163>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=314212603 for P33 / November 25, 2012 2012 年 11 月 25 日) Free to factor
4×10203+7 = 4(0)2027<204> = 19 × 37 × 5291563 × [107527783884317960604265704230348046610989993443194988053433369814221847225288642065539652569380737350051997976588399811974874071987812046129508534433029083137288655353823184993394308825207726763<195>] Free to factor
4×10204+7 = 4(0)2037<205> = 11 × 35897 × 230260073 × 8020011658658341060484790559369<31> × [5485491083950963755543831884431324707217897674618846721423912237607045084565923162312121953582387064379509874121477250244168926132424870388413525491057880175533<160>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3309664432 for P31 / November 25, 2012 2012 年 11 月 25 日) Free to factor
4×10205+7 = 4(0)2047<206> = 17 × 505657 × 1377527182681503588797779<25> × 23367118133193453510408592101248483<35> × 144560524258458772923419907478227052853921513060423854371522522854900906191049868924492682802978185489987412548201089903749252849941007344679<141> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=1324322346 for P35 / November 25, 2012 2012 年 11 月 25 日)
4×10206+7 = 4(0)2057<207> = 11 × 37 × 43 × 1033 × 3607 × 37013 × 4317611 × 385978789152483152523868521293<30> × 99446482085066987637357495828790063221358550958625309399032256413424532995748334553591545632952083087605915816463865604823886802985116047661805410039715303<155> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3359828010 for P30 / November 25, 2012 2012 年 11 月 25 日)
4×10207+7 = 4(0)2067<208> = 223 × 557 × 25257949 × 346151451517<12> × 3683288135023566546635832319471695369603828699021216382298752544545416916728099803391678127176908527415394681525031126854535878220352346248041233063589594254174652058819196604340498389<184>
4×10208+7 = 4(0)2077<209> = 11 × 29 × 477043711 × 17584854059039<14> × 14947630892776692774498541130780380518605806223040565387408619347922655227324967491195274568809079879226636009290074892479039682384938508613224642626964236454994973868225457335342765657<185>
4×10209+7 = 4(0)2087<210> = 37 × 39847 × 229771 × 200021766371299<15> × 527642406535972591832831<24> × [11187948857779994582061457858794505171353022075017032367629157564124468663708904493721419631943257063711487608061105653119725489971685873753474869434357776892787<161>] Free to factor
4×10210+7 = 4(0)2097<211> = 11 × 617 × 1539711202997406119<19> × 239134959998275532563155055329089<33> × 1600662610885979260036167251593112898709958565203575526751274558994845010555075286933089777809669581515130471896374897092603053239606908920866796200380452171<157> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=2361596253 for P33 / November 25, 2012 2012 年 11 月 25 日)
4×10211+7 = 4(0)2107<212> = 151 × 49789 × 165709 × 253061041 × 3701075711<10> × 88999810855772821225927574153<29> × 9960518138127405257115350927806321957<37> × 2444835524866616974792934968996806853645121<43> × 15817200597764909530409915610732344832737412154556891020195727939800670227<74> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3965772522 for P37, Msieve 1.49 gnfs for P43 x P74 / November 27, 2012 2012 年 11 月 27 日)
4×10212+7 = 4(0)2117<213> = 112 × 37 × 163 × 10954137099129631391861300997868886835431849<44> × [50038826988387070647357693383670188700600076330765973114934918196116278996331877319991187031933796690756345331060427564935698726391101162338363099029474541600202793<164>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=4143726657 for P44 / December 20, 2012 2012 年 12 月 20 日) Free to factor
4×10213+7 = 4(0)2127<214> = 13147 × 14988877759<11> × 506462080614860197<18> × 768203392232273212090877767<27> × 52172428825361509419654047369583966703420018943348059748703875802616598882217736172797157818974058085691910237236033114281504377756835802092867269876785641<155>
4×10214+7 = 4(0)2137<215> = 11 × 23 × 79 × 337 × 3567869 × [1664460824291773607169645620087736573787227763038432851206629919992655905450431471683300697440461034868873656509123092303903131314098478562147955486432989185433545033174885317001497230415173923244788337<202>] Free to factor
4×10215+7 = 4(0)2147<216> = 37 × 318679 × 5153521 × 3309781427<10> × 791350078581401324915406424303479060683<39> × 10881711427814197674723710857193753889019<41> × 230959378614034602822324353339795939932665300843875352754489720741842104552789876689771525659845592126336871202951<114> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1633987327 for P39 / November 30, 2012 2012 年 11 月 30 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2385643195 for P41 / December 17, 2012 2012 年 12 月 17 日)
4×10216+7 = 4(0)2157<217> = 11 × 2531 × 3686059338701499210797226449<28> × 8470334325077456080418360382776195530187921<43> × 45187711066280119656912828411566736086098420441<47> × 101833798396522228631754742416211211593372183134190072868300802322398058703856732370950853830143<96> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1575178505 for P47 / December 19, 2012 2012 年 12 月 19 日) (Erik Branger / GGNFS, Msieve gnfs for P43 x P96 / December 11, 2013 2013 年 12 月 11 日)
4×10217+7 = 4(0)2167<218> = 97 × 33769 × 5094704418889<13> × 670939679465615176031<21> × 3572461750821194359098746522685482120158014343564223936161213437123354340196755595217755806732895771194606529506856734926526597941119007377275893843931160702220208439523081597961<178>
4×10218+7 = 4(0)2177<219> = 11 × 37 × 907 × 78649 × 240181264705164533<18> × 596523827644508110284715605362058416999<39> × [96160821926728023672336380648355715094558804463914926808994858396459082265725451735037824958372702734401737402095634784703678196386742339114956442958921<152>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=401686332 for P39 / November 29, 2012 2012 年 11 月 29 日) Free to factor
4×10219+7 = 4(0)2187<220> = 125863 × 18364219 × 886529150008375207<18> × 7661118779609415243353<22> × 23405376451659015768423078038846795626181<41> × 518054582825344690889517638759031347080138026607<48> × 21014210694657699013634719687401676955903481563100005358698206274329744257027383<80> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3712335133 for P41 / December 17, 2012 2012 年 12 月 17 日) (Warut Roonguthai / Msieve 1.49 gnfs for P48 x P80 / December 19, 2012 2012 年 12 月 19 日)
4×10220+7 = 4(0)2197<221> = 11 × 2657687 × 30545629531<11> × [44793437701358422519647963522532153201452550644498668337619957627497516810441391612115633505026860008392483679775684280882945616686853312054685540760061961132098009601808770308785736868598909119070815721<203>] Free to factor
4×10221+7 = 4(0)2207<222> = 17 × 19 × 37 × 71 × 61157797 × 206706098219<12> × [37289990595938037612506892434102325113605317100391961835716763297807120069490719110785128981424558414927736432837425843952344247048834973319168678182318218014798712924090302852301842057060544388969<197>] Free to factor
4×10222+7 = 4(0)2217<223> = 11 × 67 × 25673 × 200730376304051360382250382582927<33> × 1053180438173673662779141731732941226160007736863208127816335937053169951738536383513019226352331373617260792148309071277276805201135878746654670130182603942243044545297919873073539041<184> (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=797832978 for P33 / November 25, 2012 2012 年 11 月 25 日)
4×10223+7 = 4(0)2227<224> = 5297 × 233124021774321037206538531633<30> × [32392389922888994288521317032204250341689830193003171667224059632003848231092884539177524756446372481046847681828737599452045836381912758143602907866942325588900655139901210866600462985580007<191>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=1695162968 for P30 / November 23, 2012 2012 年 11 月 23 日) Free to factor
4×10224+7 = 4(0)2237<225> = 11 × 37 × 809 × 548837 × 35600616903974009733220967<26> × [62175051694091315062710242693576695207726759752820442141530397967845770220761600483985824120566884397180107069075558879059853851866799675754846048648479683799877296779220030684364534084291<188>] Free to factor
4×10225+7 = 4(0)2247<226> = 107 × 139 × 7727 × 301901 × 689280631497050399<18> × 167259145770563619478419895010176479554523045556403969442700448264046364564713092391942444523766475749111265963384457148522777979024294689525461467848302561182698813909774715917524900429782559883<195>
4×10226+7 = 4(0)2257<227> = 11 × 413071 × 24545333 × 5845336513<10> × 23215682562745765263859120211<29> × [2642911961553744812246720006789359332429864078762296274447071330071210905137677766780900323476425160749394427356942500979693879748833505321943163859593523973517601563803466613<175>] Free to factor
4×10227+7 = 4(0)2267<228> = 37 × 43 × 79 × 197 × 28933 × 1233377 × 79737139 × 147355911177911<15> × [38528222256794578406983213483628219800916006290343134890635979435910551992153756876145075016611089313954977258192901869071050901425783649122948347080124711414486263316165448492734744961211<188>] Free to factor
4×10228+7 = 4(0)2277<229> = 11 × 179916251 × 2021142401618648869932468544135924866307026170950858888025831327690146435763806370311504747637479193785355367168229642781760922550772601616535664494456165809966973820704854706891576812793657179771027819139937705591899887<220>
4×10229+7 = 4(0)2287<230> = 3719 × 5101 × 71999 × 630101 × 3550960484632177786903<22> × 193406403693914145060428953627298958515928281473<48> × 1496175740538277970655032961452537656569472796770651129<55> × 45231663311041421600515439556707130330131140673611638849814713579313719888706200089984497<89> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=486705012 for P48 / December 19, 2012 2012 年 12 月 19 日) (Youcef Lemsafer / Msieve 1.54 gnfs for P55 x P89 / October 23, 2017 2017 年 10 月 23 日)
4×10230+7 = 4(0)2297<231> = 11 × 37 × 5185287916033<13> × [189536434372746236266757835516915931348785446510290342236024334488892052864103206155788591157502074431152037214392737989075598445353808209304095528240277496782084535150656041473094033961521433453623248236426999937297<216>] Free to factor
4×10231+7 = 4(0)2307<232> = 472 × 359 × 15091 × 2423690533245343441<19> × 9722176385275092941<19> × 14184405726881984753488950795026412524679045493083197241838380335346543708680831087303504778392495538780987904942758619315540566880902013571457110323958777671725213290638636704715169207<185>
4×10232+7 = 4(0)2317<233> = 11 × 34759 × 1147351 × 9250789811<10> × 429578116434295122707641<24> × [22944720480471415059588400733755310548037605198859497034138806875491483709522315819566336354703009859654692274624543216901503574819965242225074393051782705515872201023735739270740999660943<188>] Free to factor
4×10233+7 = 4(0)2327<234> = 37 × 12057979 × 911352624107<12> × 983778428999076650769328377746045934991388186116896814076708796442451098797617834620383224295181967757161304187356386648699961759380389169019820116708689062007141907317116635882386190274152144662459199387953469187<213>
4×10234+7 = 4(0)2337<235> = 112 × 232841617 × 1477726049<10> × 96077144142317262069010198174263161898059318355078474106765612444280100581308346588785493656595028843479937733199846085626383200435757726965140695240902363593321362063508153929471903495710059399384975503491372364399<215>
4×10235+7 = 4(0)2347<236> = 103 × 52851589471<11> × [7347924981067913209449913279201934388970601415702493729272943721817850935738901631414308028702876044111629883786189125417240090602552164799300203364562678086016752653913837548039059827350961697031298907940999917227694815039<223>] Free to factor
4×10236+7 = 4(0)2357<237> = 11 × 23 × 29 × 37 × 8243 × [178753456487996957662646472978659790749317986184812992202697810890924088055960067303661550454204109179363272564154835623735408951377941285510853874797585339499872952544893900432314653567487056116998091297851523282905614304515121<228>] Free to factor
4×10237+7 = 4(0)2367<238> = 17 × 130279 × 1806078628536132634802322436508434612955092306421106196068798953196826900457524868573915799711298331228499198326848758524126727119128494818586174558402487331487219961864649758459559416148961753124403147453225949918342670007310103249<232>
4×10238+7 = 4(0)2377<239> = 11 × 14351941 × 33177786313807<14> × [7636762072653719033538539792050253666098867483610920936436178169426928732945519391388810965707267774144071941255346639486163958301976825661618320459975949170553951087472725981686023816710953937244544946684599230002751<217>] Free to factor
4×10239+7 = 4(0)2387<240> = 19 × 37 × 254252167271<12> × [2237896529187824940579914442881017358440977765734237482644589160483220338012054509147945349035695153330118181515943639856695790395467832834956399292820416613789835138958706895093606027828566907402834199182556451032048709187039<226>] Free to factor
4×10240+7 = 4(0)2397<241> = 11 × 79 × 22080902891394212989<20> × 502576024103937856223379279326851451425673<42> × [414783642192337809933161863467664125085603659260321223706012799052536153998637821981979580883510460744351430567640823992146035371828718832010806169526557794374249574307634229599<177>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=567881304 for P42 / December 20, 2012 2012 年 12 月 20 日) Free to factor
4×10241+7 = 4(0)2407<242> = 229 × 593 × 12421 × 26501 × 340297 × 12602848882852690164987287153729147<35> × 208652764178139122175886160498500400511754181127846445927301032762546054971735032509222997721810842160735232714414518644295062097386401137399864846523302059529423828813263283899741658845329<189> (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3369716444 for P35 / November 23, 2012 2012 年 11 月 23 日)
4×10242+7 = 4(0)2417<243> = 11 × 37 × 190006447 × 10108635144763<14> × 119528890089667<15> × 4280868000297343792188543676806175305293258699921819329556341706153407342669720264474639904131879378168660240052490396205059192091342661227897548388124280505900548018782336320951380655333782879365111999023<205>
4×10243+7 = 4(0)2427<244> = 94693 × 5923367774150069950172581<25> × [7131377349111513036272294747729796281722196155409508986702808118178371671560693232036628555669357254027552741436477288096881218360124629091576077089225541690306643671622633948481019045983462579682337003944526994079<214>] Free to factor
4×10244+7 = 4(0)2437<245> = 11 × 253200847 × 18214275698123<14> × 179169831173741<15> × [4400736462041805903971874040794948381880377450504713494837296695790166426883739786147441935842549414070398170346232888400898775868210047949186148189483904626408260447075880844127479300630489810566572766434997<208>] Free to factor
4×10245+7 = 4(0)2447<246> = 37 × 2521 × 3089 × 9421 × 26113 × 572331416483<12> × 107555246625709491341<21> × [91671545745013031069058510251961984569736731529435544856331762952547837029715144697915297259910540365984095042665831545393165380114641703984631038218178868189494077534779211851619849084649437220601<197>] Free to factor
4×10246+7 = 4(0)2457<247> = 11 × 18236398886763939466196902516579238629<38> × [19940140917859202378216503263466281731056729638143549770270827074044910027394794992510250545493858288217246805799013606070095836608824558756516719350861964691783693831301198582576244470207642031100992930044753<209>] (Makoto Kamada / GMP-ECM 6.4.3 B1=1e6, sigma=3389661263 for P38 / November 24, 2012 2012 年 11 月 24 日) Free to factor
4×10247+7 = 4(0)2467<248> = 32797 × 8329468572487574623<19> × 98686807828838508721182607<26> × [1483711545874357530448953158221473318906865727187679690462429995292749056460529324394539073425597610802380539538931015644432609392634901196913604976423605568360487315755015157718491696122708656565571<199>] Free to factor
4×10248+7 = 4(0)2477<249> = 11 × 37 × 43 × 113 × 202264042560399835559333398394933690261947104918909817037003700926318748915991146902857131299197567977152253752377234575217699317308290348010455028359947067500061943363034122449640045853258448442642721300881416131467582383408685116855522288739<243>
4×10249+7 = 4(0)2487<250> = 29947 × 249583 × 5755660803668697169427<22> × 32444432929019326518846307<26> × [2865868693661424718000393245766717191381177359245100300129197164253460141503310718422644625380098230592712156416402782574869052962255833110836346925316839371075983373074400306129994530091675363<193>] (Warut Roonguthai / GMP-ECM 6.3 B1=1000000, sigma=3125937694 for P26 / November 25, 2012 2012 年 11 月 25 日) Free to factor
4×10250+7 = 4(0)2497<251> = 11 × 2713 × 176857 × 5076677 × 7538731 × 14054025667879<14> × 183278982136027<15> × 93226797304003773559<20> × 31937514022329499199026746195384994575133471<44> × 25820354427786934363120414560875629111674006291862742174205611484619556134046638114384717630497229001103114841697425538342347749852056903<137> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=925369814 for P44 / December 28, 2012 2012 年 12 月 28 日)
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