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Factorizations of 400...007

Table of contents

  1. About 400...007
  2. Prime numbers of the form 400...007
  3. Factorizations of 400...007
  4. References

1. About 400...007

First ten terms

47, 407, 4007, 40007, 400007, 4000007, 40000007, 400000007, 4000000007, 40000000007

General term

4·10n+7

2. Prime numbers of the form 400...007

Last update

Jan 18, 2009

Searched up to

n≤10000

Difficulty of search

9.44%

Results

  1. 4·101+7 = 47 is prime. (Makoto Kamada / Dec 1, 2004)
  2. 4·103+7 = 4007 is prime. (Makoto Kamada / Dec 1, 2004)
  3. 4·109+7 = 4000000007<10> is prime. (Makoto Kamada / Dec 1, 2004)
  4. 4·1039+7 = 4(0)387<40> is prime. (Makoto Kamada / PPSIQS / Dec 1, 2004)
  5. 4·102323+7 = 4(0)23227<2324> is PRP. (Makoto Kamada / PFGW / Dec 17, 2004)

3. Factorizations of 400...007

Last update

May 20, 2009

Completed up to

Range

n≤200

Terms which have not been factored yet

n=171, 174, 176, 178, 179, 184, 186, 187, 188, 192, 193, 196, 197, 199 (14/200)

Results

4·101+7 =
47
= definitely prime number
4·102+7 =
407
= 11 · 37
4·103+7 =
4007
= definitely prime number
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
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
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 =
4000000000000000000000000000000000000000000000000007<52>
= 293726003 · 13618133768020531706210566587119629309768669<44>
4·1052+7 =
40000000000000000000000000000000000000000000000000007<53>
= 11 · 359 · 21402239576867<14> · 101169725523491<15> · 4678030667952838283819<22>
4·1053+7 =
400000000000000000000000000000000000000000000000000007<54>
= 37 · 1117 · 763381 · 2045598455107<13> · 6197882814782076847015901073449<31>
4·1054+7 =
4000000000000000000000000000000000000000000000000000007<55>
= 11 · 13043 · 577336267038310565760409<24> · 48290418825607786730203151<26>
4·1055+7 =
40000000000000000000000000000000000000000000000000000007<56>
= 1470550312631893493087<22> · 27200701435648706832827738636099161<35>
4·1056+7 =
400000000000000000000000000000000000000000000000000000007<57>
= 11 · 37 · 629059 · 1562335143128041727378196612401989004183710880539<49>
4·1057+7 =
4000000000000000000000000000000000000000000000000000000007<58>
= 67 · 502543 · 1324733 · 2931961 · 193797509 · 157825518923074612759993793291<30>
4·1058+7 =
40000000000000000000000000000000000000000000000000000000007<59>
= 112 · 79 · 4184538131603724238937127314572654043309969662098545873<55>
4·1059+7 =
400000000000000000000000000000000000000000000000000000000007<60>
= 19 · 37 · 43 · 13232326573819841873697442852889609315557907969168679083<56>
4·1060+7 =
4000000000000000000000000000000000000000000000000000000000007<61>
= 11 · 23 · 991 · 383681 · 638719 · 1033951 · 82093733 · 104111942923<12> · 7366737139333341659<19>
4·1061+7 =
40000000000000000000000000000000000000000000000000000000000007<62>
= 17 · 151 · 8052659 · 62729456462801<14> · 704330527370990953<18> · 43797243442267264723<20>
4·1062+7 =
400000000000000000000000000000000000000000000000000000000000007<63>
= 11 · 37 · 653 · 1505055103829988975471364445330754672255437952222025728917<58>
4·1063+7 =
4000000000000000000000000000000000000000000000000000000000000007<64>
= 6043 · 1598418601445003512233029<25> · 414111100424751623088561805087078081<36>
4·1064+7 =
40000000000000000000000000000000000000000000000000000000000000007<65>
= 11 · 109 · 5304713159<10> · 13992883878265521385669<23> · 449439949233244394558007490883<30>
4·1065+7 =
400000000000000000000000000000000000000000000000000000000000000007<66>
= 37 · 103 · 2663 · 22646287 · 1740415206617799769883336667850378627527240764581477<52>
4·1066+7 =
4000000000000000000000000000000000000000000000000000000000000000007<67>
= 11 · 107 · 17977839608332151<17> · 189036656363050007031246075025764542395649039641<48>
4·1067+7 =
40000000000000000000000000000000000000000000000000000000000000000007<68>
= 131 · 907 · 6841 · 24061702249445748790073<23> · 2045198520361163897657403157850284247<37>
4·1068+7 =
400000000000000000000000000000000000000000000000000000000000000000007<69>
= 11 · 29 · 37 · 3367687 · 10063194430510571560333095731744408274394992076993054989587<59>
4·1069+7 =
4000000000000000000000000000000000000000000000000000000000000000000007<70>
= 1263181 · 611296385494902797<18> · 5180152900055810738981213242360687746036720751<46>
4·1070+7 =
40000000000000000000000000000000000000000000000000000000000000000000007<71>
= 11 · 40673663 · 89403396895028519158364557339318968238399468382369111029817099<62>
4·1071+7 =
400000000000000000000000000000000000000000000000000000000000000000000007<72>
= 37 · 79 · 433 · 9283 · 8383819 · 94924377175597<14> · 42779458125998770235026845079920320682617<41>
4·1072+7 =
4000000000000000000000000000000000000000000000000000000000000000000000007<73>
= 11 · 3823 · 514229 · 471601181 · 10259125517856492047234983<26> · 38231489258848639514635789357<29>
4·1073+7 =
40000000000000000000000000000000000000000000000000000000000000000000000007<74>
= 146790974159<12> · 272496318177390698489369509464459633568143762454121612203449673<63>
4·1074+7 =
400000000000000000000000000000000000000000000000000000000000000000000000007<75>
= 11 · 37 · 703880603552928673<18> · 1396260925276484853508489215529546940513201783302740337<55>
4·1075+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000007<76>
= 10993 · 9220291 · 2869649389<10> · 6328435783<10> · 7110600253<10> · 285344538395817133<18> · 1071021258705139103<19>
4·1076+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000007<77>
= 11 · 10837 · 2784091 · 8807229953535427<16> · 13684705972013322259021613988313510537123675098193<50>
4·1077+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000007<78>
= 17 · 19 · 37 · 2368237 · 14132877119245323955653137822485254557789564500170956175143093977261<68>
4·1078+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000007<79>
= 11 · 2531 · 2032991 · 2212654511<10> · 453429131723<12> · 70439567130453085647831818617221157189417367749<47>
4·1079+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000007<80>
= 61 · 683 · 17785367 · 3724812792031498033<19> · 14492462031904437756685564671665582469990744895199<50>
4·1080+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000007<81>
= 112 · 37 · 43 · 7788237588337642668791180521<28> · 266787360135707563054997859536524418277944983697<48>
4·1081+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000007<82>
= 592 · 71 · 5551192261<10> · 2915488618091243626268858856710257620291820460972259471439169530837<67>
4·1082+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000007<83>
= 11 · 23 · 15331 · 15541951819<11> · 232264505495580393435499<24> · 2856804899028143449862156634895027177513529<43>
4·1083+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000007<84>
= 37 · 431 · 402529 · 78429691649464676560988636280123823<35> · 794517221528963735243507356427906547643<39> (Makoto Kamada / msieve 0.81 / 7.1 minutes)
4·1084+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000007<85>
= 11 · 79 · 219529 · 299261 · 70064526755527318709119264297445795885361854037852271322826483687595487<71>
4·1085+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000007<86>
= 727 · 109363 · 405600257 · 527263309483<12> · 1573146293161<13> · 1495410002787932321774884951732147371634594777<46>
4·1086+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000007<87>
= 11 · 37 · 982800982800982800982800982800982800982800982800982800982800982800982800982800982801<84>
4·1087+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<88>
= 139 · 1021 · 1996751 · 620421690731<12> · 127951996936870189116075461<27> · 177812176198176712983269019679635512833<39>
4·1088+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<89>
= 11 · 98564172565667<14> · 6600385411457737116253<22> · 5589576830400854269359997695214744049518229574878387<52>
4·1089+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<90>
= 37 · 71621061916609515028109134134598055288291<41> · 150944575820422101425306447211855858408857883721<48> (Makoto Kamada / GGNFS-0.70.3 / 0.14 hours)
4·1090+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<91>
= 11 · 67 · 827 · 24007 · 7304333 · 466617148584043867<18> · 80206181704276071954216073396464378435409872098081220109<56>
4·1091+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<92>
= 6011 · 6654466810846780901680252869738812177674263849609050074862751622026285143902844784561637<88>
4·1092+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<93>
= 11 · 37 · 982800982800982800982800982800982800982800982800982800982800982800982800982800982800982801<90>
4·1093+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<94>
= 17 · 47 · 79229 · 258648812837<12> · 244297233079982019882109113648688601383119314216076577299443411078500917641<75>
4·1094+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<95>
= 11 · 5657 · 1285323498480793419257<22> · 500113617437201615164372127533421256220455364772280183599472658205413<69>
4·1095+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<96>
= 19 · 37 · 347 · 1639740756986320462734841621539634583772305598484879540544639892433006341697377644594389627<91>
4·1096+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<97>
= 11 · 29 · 491 · 56779 · 2156617 · 208558095562637864311029230806040851686450569040429895330559173222553105670027481<81>
4·1097+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<98>
= 79 · 6863 · 24782773097<11> · 1687044182687<13> · 519316238625664028708070091<27> · 3397900371838217543632382864452418362655059<43>
4·1098+7 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<99>
= 11 · 37 · 5839 · 331937 · 4044670901230701768151111939<28> · 125368448621667014758040059473623770992595554122825927806613<60>
4·1099+7 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<100>
= 103 · 72983566771<11> · 152542758044569<15> · 3488237835151771350219863893321200172484965538972254487293303117277173331<73>
4·10100+7 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007<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 / Sep 10, 2007)
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 / Sep 3, 2007)
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 / Sep 3, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 4, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 10, 2007)
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 / Sep 11, 2007)
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 / Sep 11, 2007)
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 / Sep 10, 2007)
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 / Sep 11, 2007)
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 / Sep 11, 2007)
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 / Sep 10, 2007)
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 / Sep 12, 2007)
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 / Sep 12, 2007)
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 / Sep 5, 2007)
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 / Sep 5, 2007)
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+ / Sep 12, 2007)
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 / Sep 14, 2007)
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 / Sep 15, 2007)
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 / Sep 14, 2007)
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 / Sep 12, 2007)
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 / Oct 2, 2007)
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 / Sep 13, 2007)
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 / Sep 13, 2007)
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+ / Sep 13, 2007)
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+ / Sep 23, 2007)
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 / Jan 12, 2008)
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+ / Jul 13, 2008)
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)
4·10171+7 =
4(0)1707<172>
= 3335301202024415353546067887<28> · [1199291985255225192754578703725735635034737485447419639459131108568918655877742516064449398215741509247520027186101646141132386513584233490174761<145>] SUBMIT/RESERVE
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 / Nov 24, 2008)
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> · [1253524560661331280230025695397313591564814112191226797483239336720470519760464369879894033179678585353101136612796379296031321969935429744959065667393<151>] SUBMIT/RESERVE
4·10175+7 =
4(0)1747<176>
= 79 · 11304493 · 44790077177636417034482873762077710096375514506835826306665092579124361538305212478712130128315609677710009930665553997541430113146218314381052300469480518985356451981<167>
4·10176+7 =
4(0)1757<177>
= 11 · 37 · 7135210354090040619550238567081980993<37> · [137739594774192223139709541988016487305378968971069153072936288397790444184230544651923302551708474913403317389091953092751175896905333457<138>] (matsuix / GMP-ECM 6.0 B1=6700417, sigma=1265699576 for P37 / Nov 11, 2007) SUBMIT/RESERVE
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 / Sep 17, 2007)
4·10178+7 =
4(0)1777<179>
= 11 · 233 · 63179 · 12192793 · 16845706020390628754706680461<29> · [1202669284285099186401315370094948291673818003955856973023257116448103151001600737001206766822582016522733090012680625997367422747646267<136>] SUBMIT/RESERVE
4·10179+7 =
4(0)1787<180>
= 37 · 139 · 37468593467<11> · 599510744974290683<18> · [3462414877997995367746778414036825019585800042496066102169580153296211560858747211182421457625668826164835800136218835966761586319693554519949740409<148>] SUBMIT/RESERVE
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 / Aug 7, 2008)
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 · [1601884872247857541929364463054070741377582346397858650448855896531225418310224802752039645714551698780134263721690562350826500942648593168613713388597206843067491990813889<172>] SUBMIT/RESERVE
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> · [1692798530655153039668862721170821641348422631632051347799737269598742160572646433341229099254655125172317824517000297100962149848948168570575096433<148>] SUBMIT/RESERVE
4·10187+7 =
4(0)1867<188>
= 15373 · 20563 · 7205969922799<13> · [17559916383216502983393031900448239143457951770613533572095560721644049769781888887818902733641044520141191139969311929620026981478625487631415257526412307071614144607<167>] SUBMIT/RESERVE
4·10188+7 =
4(0)1877<189>
= 11 · 37 · 79 · 599 · 16823 · 2802193 · 272256877 · 1439838199<10> · [1123874014609429824236567613843684082091542950341300616058217918866484619157645274086664251736828389608087706521971124081256789273727549486221145265638173<154>] SUBMIT/RESERVE
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> · [158241590261290641462898297613779972867217868813765931658183723391123131104584724918341966851238155716034170786130229666993153953870783778726149345265625298408498634461<168>] SUBMIT/RESERVE
4·10193+7 =
4(0)1927<194>
= 6131 · 9463 · 101924881 · 183946145712468019<18> · [36772988818547455108124111168505856091807688738273109715320356222025361295418506493438548041780529643458294038227899850094127194760761182324630025435299851499321<161>] SUBMIT/RESERVE
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 · [3405507676482560097206811117518195414671216538439369916375204873213374893013847901002572946187274486217442175969562934590669470875204404956069376661834535066044287435404968925168140556199433<190>] SUBMIT/RESERVE
4·10197+7 =
4(0)1967<198>
= 37 · 59 · 131 · 373 · 133519 · 3371089 · [8331301256832907309157708500822099215961394744994684193364126409085955631213297568779219155903110142294652586003443136961815829046123663126752993517701723128283492081000802999713<178>] SUBMIT/RESERVE
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 / Sep 10, 2007) SUBMIT/RESERVE
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 / Mar 6, 2008)

4. References

Copyright (C) 1999-2009 Makoto Kamada All Rights Reserved.