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Factorizations of 400...009

Table of contents

  1. About 400...009
  2. Prime numbers of the form 400...009
  3. Factorizations of 400...009
  4. References

1. About 400...009

First ten terms

49, 409, 4009, 40009, 400009, 4000009, 40000009, 400000009, 4000000009, 40000000009

General term

4·10n+9

2. Prime numbers of the form 400...009

Last update

Aug 9, 2009

Searched up to

n≤30000

Difficulty of search

21.55%

Results

  1. 4·102+9 = 409 is prime.
  2. 4·104+9 = 40009 is prime.
  3. 4·105+9 = 400009 is prime.
  4. 4·108+9 = 400000009 is prime.
  5. 4·109+9 = 4000000009<10> is prime.
  6. 4·1028+9 = 4(0)279<29> is prime.
  7. 4·10191+9 = 4(0)1909<192> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PPSIQS / Jan 1, 2005)
  8. 4·10196+9 = 4(0)1959<197> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PPSIQS / Jan 1, 2005)
  9. 4·102038+9 = 4(0)20379<2039> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Jo Yeong Uk / PRIMO 3.0.4 / Oct 1, 2007)

3. Factorizations of 400...009

Last update

Nov 4, 2009

Completed up to

Range

n≤250

Terms which have not been factored yet

n=184, 186, 190, 197, 201, 204, 207, 208, 209, 211, 214, 215, 218, 220, 221, 223, 224, 225, 226, 227, 228, 230, 231, 232, 233, 234, 235, 238, 239, 240, 241, 244, 245, 246, 247, 248, 249 (37/250)

Results

4·101+9 =
49
= 72
4·102+9 =
409
= definitely prime number
4·103+9 =
4009
= 19 · 211
4·104+9 =
40009
= definitely prime number
4·105+9 =
400009
= definitely prime number
4·106+9 =
4000009
= 13 · 307693
4·107+9 =
40000009
= 7 · 1051 · 5437
4·108+9 =
400000009
= definitely prime number
4·109+9 =
4000000009<10>
= definitely prime number
4·1010+9 =
40000000009<11>
= 17 · 2352941177<10>
4·1011+9 =
400000000009<12>
= 379 · 383 · 2755637
4·1012+9 =
4000000000009<13>
= 13 · 307692307693<12>
4·1013+9 =
40000000000009<14>
= 7 · 23 · 248447204969<12>
4·1014+9 =
400000000000009<15>
= 157 · 1009 · 2525045293<10>
4·1015+9 =
4000000000000009<16>
= 16049939 · 249222131
4·1016+9 =
40000000000000009<17>
= 15811657 · 2529779137<10>
4·1017+9 =
400000000000000009<18>
= 589451 · 678597542459<12>
4·1018+9 =
4000000000000000009<19>
= 13 · 29 · 2549 · 238949 · 17419817
4·1019+9 =
40000000000000000009<20>
= 7 · 6299 · 907173474247613<15>
4·1020+9 =
400000000000000000009<21>
= 61 · 11353 · 577589804384773<15>
4·1021+9 =
4000000000000000000009<22>
= 192 · 131 · 3539 · 23900166756841<14>
4·1022+9 =
40000000000000000000009<23>
= 277 · 80657 · 1790350894900181<16>
4·1023+9 =
400000000000000000000009<24>
= 241 · 21048023413<11> · 78855434773<11>
4·1024+9 =
4000000000000000000000009<25>
= 13 · 54409 · 2464093 · 2295032289289<13>
4·1025+9 =
40000000000000000000000009<26>
= 7 · 5714285714285714285714287<25>
4·1026+9 =
400000000000000000000000009<27>
= 17 · 1022981 · 3987718793<10> · 5767916669<10>
4·1027+9 =
4000000000000000000000000009<28>
= 7019 · 76367 · 7462408494990913333<19>
4·1028+9 =
40000000000000000000000000009<29>
= definitely prime number
4·1029+9 =
400000000000000000000000000009<30>
= 2287 · 125887 · 357103 · 3890625634969687<16>
4·1030+9 =
4000000000000000000000000000009<31>
= 13 · 9277 · 127636573 · 259856717052784933<18>
4·1031+9 =
40000000000000000000000000000009<32>
= 7 · 571 · 3169 · 343615357 · 9190328573803009<16>
4·1032+9 =
400000000000000000000000000000009<33>
= 109 · 313 · 2017 · 33637 · 1333413721<10> · 129598830553<12>
4·1033+9 =
4000000000000000000000000000000009<34>
= 167 · 211 · 463 · 1297134327053<13> · 189014499795463<15>
4·1034+9 =
40000000000000000000000000000000009<35>
= 977 · 3853 · 1658413 · 6407280323676719495153<22>
4·1035+9 =
400000000000000000000000000000000009<36>
= 23 · 17391304347826086956521739130434783<35>
4·1036+9 =
4000000000000000000000000000000000009<37>
= 13 · 673 · 5007481 · 746382589 · 122326560499727449<18>
4·1037+9 =
40000000000000000000000000000000000009<38>
= 7 · 89 · 4528956463<10> · 448619261063<12> · 31600640349007<14>
4·1038+9 =
400000000000000000000000000000000000009<39>
= 904681 · 1286773 · 343607458511598560508359293<27>
4·1039+9 =
4000000000000000000000000000000000000009<40>
= 19 · 263 · 519769 · 1283603623<10> · 1199801315721338023931<22>
4·1040+9 =
40000000000000000000000000000000000000009<41>
= 4583989 · 53282040853<11> · 163770461681236137270577<24>
4·1041+9 =
400000000000000000000000000000000000000009<42>
= 62819 · 6127387209188263<16> · 1039186860760131986597<22>
4·1042+9 =
4000000000000000000000000000000000000000009<43>
= 13 · 17 · 45833 · 394902090443833421215502710854762613<36>
4·1043+9 =
40000000000000000000000000000000000000000009<44>
= 72 · 59 · 1711627703<10> · 8083558631051769306511133155933<31>
4·1044+9 =
400000000000000000000000000000000000000000009<45>
= 193 · 2355253 · 3497454495313<13> · 251601394578025584961717<24>
4·1045+9 =
4000000000000000000000000000000000000000000009<46>
= 47 · 929 · 66624257486510533<17> · 1375035901286364383510971<25>
4·1046+9 =
40000000000000000000000000000000000000000000009<47>
= 29 · 15749 · 15174253 · 5771672627053216076534421888239293<34>
4·1047+9 =
400000000000000000000000000000000000000000000009<48>
= 179 · 125598986305571<15> · 17791838431495856399012139229201<32>
4·1048+9 =
4000000000000000000000000000000000000000000000009<49>
= 132 · 19273 · 1228072383814374403041689680231442521453657<43>
4·1049+9 =
40000000000000000000000000000000000000000000000009<50>
= 7 · 397 · 249317 · 1718251 · 33599510223775788866714735067436013<35>
4·1050+9 =
400000000000000000000000000000000000000000000000009<51>
= 31922437 · 869065517089313<15> · 14418212915647076935693405589<29>
4·1051+9 =
4000000000000000000000000000000000000000000000000009<52>
= 4007 · 27798720260849<14> · 35910036425522125848807593285603263<35>
4·1052+9 =
40000000000000000000000000000000000000000000000000009<53>
= 229 · 174672489082969432314410480349344978165938864628821<51>
4·1053+9 =
400000000000000000000000000000000000000000000000000009<54>
= 197 · 241 · 8425132169260905280451587084272384523032205067717<49>
4·1054+9 =
4000000000000000000000000000000000000000000000000000009<55>
= 13 · 997 · 475193993 · 25247442031965497<17> · 25723683351603508297888489<26>
4·1055+9 =
40000000000000000000000000000000000000000000000000000009<56>
= 7 · 677 · 122431502244020573213<21> · 68941400929034921180003690681887<32>
4·1056+9 =
400000000000000000000000000000000000000000000000000000009<57>
= 3793 · 172993 · 84752742673813<14> · 146959922063821<15> · 48943603822015947817<20>
4·1057+9 =
4000000000000000000000000000000000000000000000000000000009<58>
= 19 · 23 · 487 · 53462532493<11> · 5987021575531<13> · 58720432098028690323400449917<29>
4·1058+9 =
40000000000000000000000000000000000000000000000000000000009<59>
= 17 · 3037 · 45377 · 425501 · 147091452241<12> · 7711552449617<13> · 35375343067509032209<20>
4·1059+9 =
400000000000000000000000000000000000000000000000000000000009<60>
= 213215086383851<15> · 1876039856203609462964493535094492291509072859<46>
4·1060+9 =
4000000000000000000000000000000000000000000000000000000000009<61>
= 13 · 1489 · 934393 · 4136898509025393647125969<25> · 53458589846946159335647861<26>
4·1061+9 =
40000000000000000000000000000000000000000000000000000000000009<62>
= 7 · 24700762903<11> · 2567700548529169<16> · 90096352763492210148648083325153241<35>
4·1062+9 =
400000000000000000000000000000000000000000000000000000000000009<63>
= 403527973 · 10826954736233<14> · 91554569382040361567203501448605749162701<41>
4·1063+9 =
4000000000000000000000000000000000000000000000000000000000000009<64>
= 211 · 37361 · 4240968143<10> · 419984477169421934009<21> · 284879235313752456517988117<27>
4·1064+9 =
40000000000000000000000000000000000000000000000000000000000000009<65>
= 1597 · 5700138373<10> · 144238295165635283803033<24> · 30464152178623676841281024833<29>
4·1065+9 =
400000000000000000000000000000000000000000000000000000000000000009<66>
= 1560967 · 19109364969489013<17> · 2326000573697615609<19> · 5765144496937827306805931<25>
4·1066+9 =
4000000000000000000000000000000000000000000000000000000000000000009<67>
= 13 · 31489 · 233437 · 41858925579992246364265263179325757684603546066726770001<56>
4·1067+9 =
40000000000000000000000000000000000000000000000000000000000000000009<68>
= 7 · 167877046243575356903<21> · 34038517129940267875217471598280286468835644729<47>
4·1068+9 =
400000000000000000000000000000000000000000000000000000000000000000009<69>
= 15961331320453<14> · 25129811447748016546609<23> · 997244497429145435634148422533317<33>
4·1069+9 =
4000000000000000000000000000000000000000000000000000000000000000000009<70>
= 69070887333625876615877<23> · 57911518939654252993752435202349130212411571317<47>
4·1070+9 =
40000000000000000000000000000000000000000000000000000000000000000000009<71>
= 149 · 617 · 12049 · 155626061 · 53732793159025489<17> · 4318329850917723450333923623115539313<37>
4·1071+9 =
400000000000000000000000000000000000000000000000000000000000000000000009<72>
= 19037 · 229637 · 68581343 · 1222634490013<13> · 9859196657767<13> · 110681607761504959695884947637<30>
4·1072+9 =
4000000000000000000000000000000000000000000000000000000000000000000000009<73>
= 13 · 97 · 12637 · 251015719420151177982256577349207483757557220445205245199371431537<66>
4·1073+9 =
40000000000000000000000000000000000000000000000000000000000000000000000009<74>
= 7 · 1713527371<10> · 340600150189835637263<21> · 9790977897241649225111881493361677824490819<43>
4·1074+9 =
400000000000000000000000000000000000000000000000000000000000000000000000009<75>
= 17 · 29 · 773533 · 891355313 · 13449275209940041<17> · 87495252332015317829606877480592687626617<41>
4·1075+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000009<76>
= 19 · 523264691 · 594425449 · 676842413772890773564250466145830931111773051905671410329<57>
4·1076+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000009<77>
= 26394552178453<14> · 1212653972086849<16> · 1249708718647360341792282910050980386773415815397<49>
4·1077+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000009<78>
= 280375220670188124973<21> · 167275912846527789937393693<27> · 8528780833485390011481371994481<31>
4·1078+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000009<79>
= 13 · 2297 · 25908900351533158191833<23> · 5170191902706730568983218736959359584557656302590493<52>
4·1079+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000009<80>
= 7 · 23 · 1373 · 21165307905757<14> · 228952072338551443223<21> · 37341727758086475203174398794805115602823<41>
4·1080+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000009<81>
= 61 · 6557377049180327868852459016393442622950819672131147540983606557377049180327869<79>
4·1081+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000009<82>
= 892 · 34296992681708836771<20> · 14723936549902970214724395162795722124772868939644951294099<59>
4·1082+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000009<83>
= 1731521829941<13> · 23101065957316266056825665141832323444266427229053022800477270532146949<71>
4·1083+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000009<84>
= 241 · 1510423 · 1881823 · 24014942053<11> · 296504111296141409<18> · 82007452975672193441598211869098496220253<41>
4·1084+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000009<85>
= 13 · 2340397 · 161235647917<12> · 804751742812242961168447141<27> · 1013220838694846677506606443514254189377<40>
4·1085+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000009<86>
= 72 · 11427939927179945352419<23> · 71432518530370723066022585835435015818776257106487682609128339<62>
4·1086+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000009<87>
= 6581 · 129517 · 661217 · 5939487721517107421<19> · 935158874428412604506761<24> · 127780012112319901067893338821<30>
4·1087+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<88>
= 7087203689<10> · 564397493782826142221802876138558235249276183178146553761339199460956821950881<78>
4·1088+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<89>
= 39709 · 227066013979431575629775037253704301<36> · 4436279546316510561053538117916593800255543972401<49> (Makoto Kamada / GGNFS-0.70.3 / 0.14 hours)
4·1089+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<90>
= 120597493 · 393261610875202721<18> · 8434127417487660929933523595618508935578844027530225186128214053<64>
4·1090+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<91>
= 13 · 17 · 708427940710019381<18> · 6191433608351527831077953<25> · 4126490178135686653661208549277346519074674953<46>
4·1091+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<92>
= 7 · 47 · 277 · 7717 · 73009 · 360985277 · 142832331115207891119797<24> · 15109267513556344459821913417914464701403941289<47>
4·1092+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<93>
= 157 · 11689 · 2637190441<10> · 37888645549<11> · 12825589219153<14> · 170080718155863190539989016654763752295474602135072529<54>
4·1093+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<94>
= 19 · 211 · 6619 · 28463 · 14882677 · 64542503754065251<17> · 2061698683044393167<19> · 7486363660015639579<19> · 357213532352044923703<21>
4·1094+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<95>
= 269 · 79059613 · 17597633788453<14> · 424533421492688455002213933013<30> · 251760078702864752532178096774092670676873<42> (Makoto Kamada / msieve 0.81 / 2.9 minutes)
4·1095+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<96>
= 331 · 4099 · 4889 · 34693 · 88169 · 272887 · 72242609324325654720653718868360903335894524888506429179407105334472531<71>
4·1096+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<97>
= 13 · 2547471757<10> · 399733992462149249766148608632773681<36> · 302159449066235946897726987287804354073508327774129<51> (Makoto Kamada / GGNFS-0.70.5 / 0.35 hours)
4·1097+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<98>
= 7 · 6601354341023269328787238886180533176329<40> · 865623237155293890321262656296684879904072617420643595703<57> (Makoto Kamada / GGNFS-0.70.5 / 0.36 hours)
4·1098+9 =
400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<99>
= 492812940973<12> · 534245715799090304732940984466061<33> · 1519276567383994276568017830452390519397881383785065153<55> (Makoto Kamada / GGNFS-0.70.5 / 0.44 hours)
4·1099+9 =
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<100>
= 1316299 · 23733644234291195486041<23> · 129584034370431955586616801502452527<36> · 988074099247265431730733375219977213<36> (Makoto Kamada / msieve 0.81 / 4.3 minutes)
4·10100+9 =
40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009<101>
= 252457 · 3825781 · 10271377715017<14> · 48957260176284394201<20> · 82358165261737491066942986862344637371473106120272751581<56>
4·10101+9 =
4(0)1009<102>
= 23 · 59 · 1499 · 81649 · 6412969 · 375550634611270931868287759153559145368061864762321629151337933025837844916175163823<84>
4·10102+9 =
4(0)1019<103>
= 13 · 29 · 762397 · 139157598651276497<18> · 94240010293401725751188992794810989<35> · 1061195040716664263009908396266920779032617<43> (Makoto Kamada / Msieve 1.30 for P35 x P43 / 11 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Nov 25, 2007)
4·10103+9 =
4(0)1029<104>
= 7 · 367 · 3169 · 568241 · 666051610994839819<18> · 1496329584881976087324454469014561<34> · 8675728169628497526212806700903471333651<40> (Makoto Kamada / Msieve 1.30 for P34 x P40 / 4.3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Nov 25, 2007)
4·10104+9 =
4(0)1039<105>
= 6961 · 57463008188478666858210027294928889527366757649762965091222525499209883637408418330699612124694727769<101>
4·10105+9 =
4(0)1049<106>
= 293 · 5643331 · 19768913443163251<17> · 8953380387844556721529<22> · 2095769500190024736613561<25> · 6521439887479099964996594817625517<34>
4·10106+9 =
4(0)1059<107>
= 17 · 6037 · 54277 · 65033 · 393637 · 280507422006808725959915242330927724994392904816732535909164558725741506632948525385813<87>
4·10107+9 =
4(0)1069<108>
= 203011 · 55710113896285389095562461197<29> · 35367663875448023865453351769377203005505502624744560709320766733028552527<74>
4·10108+9 =
4(0)1079<109>
= 13 · 2521 · 2372437 · 358672215493<12> · 92423592503653<14> · 193356441377348233<18> · 934976288415640021<18> · 8584386883329884351795149483500680797<37>
4·10109+9 =
4(0)1089<110>
= 7 · 40423 · 15317212331<11> · 4650625584472051961707336921<28> · 7801469023564348490753986729<28> · 254370012959068487857734251326987346411<39>
4·10110+9 =
4(0)1099<111>
= 113 · 2393 · 251419167001<12> · 165181848872234857617062189249532241<36> · 35618706443028798016568330143685321380313564206887456692761<59> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.95 hours on Cygwin on AMD XP 2700+ / Nov 26, 2007)
4·10111+9 =
4(0)1109<112>
= 19 · 653 · 123493 · 2610663324445005887897525533088460379846644819648266753109036179251775289078407266234168559870215728659<103>
4·10112+9 =
4(0)1119<113>
= 47869 · 402422281 · 20200221739295708137<20> · 102793932584885084256697806937410407330622008971214709546957362708559810928828813<81>
4·10113+9 =
4(0)1129<114>
= 241 · 6299 · 263494370113414564256066463819917407689687950204833935966915646888559667312008294802771170290482780972281051<108>
4·10114+9 =
4(0)1139<115>
= 13 · 307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307693<114>
4·10115+9 =
4(0)1149<116>
= 7 · 1065570921703<13> · 666712140118867142401<21> · 8043428905639068320907024160786814258414902143560784208015289845368078367045948729<82>
4·10116+9 =
4(0)1159<117>
= 3486469281397<13> · 2874109277349469<16> · 39918192825796476484273263602828739918551745682615894520536911408198521623282926063109513<89>
4·10117+9 =
4(0)1169<118>
= 163890451 · 119008224119929<15> · 1049848161996414833607686052033851<34> · 195345258444219449654150537877637812726731604913236518703820721<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.75 hours on Cygwin on AMD XP 2700+ / Nov 26, 2007)
4·10118+9 =
4(0)1179<119>
= 3728574790867178284745181738866780429302431068160529<52> · 10727959674558907354142285722781332734722136495462711094331511744121<68> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.90 hours on Core 2 Quad Q6600 / Nov 25, 2007)
4·10119+9 =
4(0)1189<120>
= 59011 · 10299709529696676595537272509874674618354731<44> · 658115379703367141596436109463234164314654145602057711013672694021719049<72> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.09 hours on Cygwin on AMD XP 2700+ / Nov 26, 2007)
4·10120+9 =
4(0)1199<121>
= 13 · 2557 · 8521 · 18757 · 2782921 · 20807569 · 42423481 · 5260604677<10> · 9084332713196797189069<22> · 6413199442442194033714618165934461275077708047821501061<55>
4·10121+9 =
4(0)1209<122>
= 7 · 7681 · 21529 · 5126081 · 160536083470159087<18> · 25197118973989779612749487725434152433845493<44> · 1666523008134979471401647272922628239564300453<46> (Makoto Kamada / Msieve 1.30 for P44 x P46 / 1.3 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Nov 25, 2007)
4·10122+9 =
4(0)1219<123>
= 17 · 2706797501<10> · 6953571473897<13> · 17434028941619909<17> · 1172523685438153707688897631706842320781<40> · 61154439922943106826214876293148089769296229<44> (Makoto Kamada / Msieve 1.30 for P40 x P44 / 31 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Nov 25, 2007)
4·10123+9 =
4(0)1229<124>
= 23 · 211 · 10289 · 15773 · 28999255687<11> · 4155424942588126939<19> · 34052378043650525917<20> · 1237691732108335720395890820493788321462836023188447935046340529<64>
4·10124+9 =
4(0)1239<125>
= 5131897 · 10621340399206741<17> · 733842284467151960541788077521714305018167316607261871506456893259617021807177370441055990594693293517<102>
4·10125+9 =
4(0)1249<126>
= 89 · 1704513258290743<16> · 218192536144132173623<21> · 767414207295499894139<21> · 8209262080507660256729<22> · 13019490676902258793481<23> · 147333586169105084996339<24>
4·10126+9 =
4(0)1259<127>
= 132 · 1093 · 157478185310284045321<21> · 51219530045909995936125110786993<32> · 2684708475243401264102954877320619544959453611256556529626076156285909<70> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.80 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Nov 26, 2007)
4·10127+9 =
4(0)1269<128>
= 72 · 223 · 557 · 1247945470942529<16> · 5266332114282325726310265118334367446631931663513799714242971304507693394428854385705650075423382761675139<106>
4·10128+9 =
4(0)1279<129>
= 1993 · 51913 · 1430797079340329352472921<25> · 181803558476376236283955641729897094029004670893<48> · 14862646249026576411818998493115073085499220973317<50> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 3.78 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Nov 26, 2007)
4·10129+9 =
4(0)1289<130>
= 19 · 13921 · 42456366769<11> · 1961107985919825167<19> · 90496029963707513725625363116699<32> · 2007068038467510110982557191892561779029831762757164209225700983<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 4.35 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Nov 26, 2007)
4·10130+9 =
4(0)1299<131>
= 29 · 29327982001<11> · 329323186569671308148482561<27> · 142809633071539376801441849555115905105958179055428369664898581960137530212268159989282516461<93>
4·10131+9 =
4(0)1309<132>
= 619 · 194167 · 14543527 · 80094272947449979071432758202536808045156517<44> · 2857082077051308573674020837361541499660528541802562865615658481450429087<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.68 hours on Cygwin on AMD XP 2700+ / Nov 26, 2007)
4·10132+9 =
4(0)1319<133>
= 13 · 37897 · 74413 · 4795671157<10> · 238753385743005127820360651581<30> · 95293671318403094554219044478411340076428386781973958525263323355023354847784827289<83> (Makoto Kamada / GMP-ECM 6.1.3 B1=50000, sigma=200747974 for P30 / Nov 18, 2007)
4·10133+9 =
4(0)1329<134>
= 7 · 14039910954930703<17> · 212045331507039776360742002829387808898620546351104409<54> · 1919414992157459171757261776221197366678153779688615271444343881<64> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.87 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Nov 26, 2007)
4·10134+9 =
4(0)1339<135>
= 233 · 940913 · 20129983336618458257<20> · 90638182001720257986508099682792568767343035039944010471235455177949468770983476603141594355101924799589153<107>
4·10135+9 =
4(0)1349<136>
= 4432543729<10> · 350104414826237<15> · 50076108520827966913691944342129<32> · 4390119913201648970056724078503841<34> · 11724718391352138352586053521568560187634367997<47> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / Nov 27, 2007)
4·10136+9 =
4(0)1359<137>
= 15397849 · 2597765441134018134610879740410494998359835844604009300260055803898323720410558643613143628048307266813695861025783536388751441841<130>
4·10137+9 =
4(0)1369<138>
= 47 · 210996161 · 27663076039007<14> · 144128879329630272184991648078450696106391196441<48> · 10116635425360137333667412655105196323996222926944429943963917753921<68> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / Nov 27, 2007)
4·10138+9 =
4(0)1379<139>
= 13 · 17 · 151237 · 23622629 · 2358576581457354735036391367836589<34> · 9655958096615738258431632197488338493<37> · 222451879743848962799083986064899346768400423382735149<54> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=193689354 for P34 / Nov 20, 2007) (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3022877036 for P37 / Nov 20, 2007)
4·10139+9 =
4(0)1389<140>
= 7 · 1609 · 16477 · 12613903 · 79168561468111998367<20> · 215836815580611127367881401108630068848301320097806396732865375805443310325317266878546524937161202815859<105>
4·10140+9 =
4(0)1399<141>
= 61 · 109 · 181 · 332372499831736421960183436382657135331279825238539588472989333335549149998878242813067889575884380902208532168256930589819928888903661<135>
4·10141+9 =
4(0)1409<142>
= 3264208176022063<16> · 1989887208412614157281179<25> · 12560245906602427344287633654384461339<38> · 49029282824428429410597115467691293631272803877265436025347251103<65> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 8.54 hours on Core2 Duo E6300 1.86GHz, Windows Vista / Nov 27, 2007)
4·10142+9 =
4(0)1419<143>
= 257 · 3989 · 6279116232481<13> · 6213900707545681120308304861181972524657170097039234485897815848245930015477488248356291397342887327051188390965392632031493<124>
4·10143+9 =
4(0)1429<144>
= 241 · 56854471504091<14> · 343717243907717<15> · 84933104950680254110902658606958111217295042787312058537647957343210132528078258529488349178237267769702479147167<113>
4·10144+9 =
4(0)1439<145>
= 13 · 6170977 · 33845281 · 260772951042433<15> · 4957419885753409<16> · 16811608672680433<17> · 67785541316170185933535335881094717003677525321680844690099265573069837995189233789<83>
4·10145+9 =
4(0)1449<146>
= 7 · 23 · 16196138573250129419<20> · 270390616492056889150461299<27> · 1605173021880918410125104138533069730893<40> · 35343468163557001022907513872788192718182385124531802470493<59> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 11.67 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Nov 27, 2007)
4·10146+9 =
4(0)1459<147>
= 220681 · 486209806553<12> · 764412203911204700836054966106935734613<39> · 4876898556751362048961362794806390789746536739262210158192817562689449702712780913893826501<91> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 10.26 hours on Cygwin on AMD XP 2700+ / Nov 27, 2007)
4·10147+9 =
4(0)1469<148>
= 19 · 4057594903<10> · 44338326960703<14> · 256008644002393841860575255628769<33> · 404664799012214157417672549706061106703<39> · 11295575051062064761509401409725052595688718501423797<53> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2766072150 for P33 / Nov 20, 2007) (Sinkiti Sibata / Msieve v. 1.28 for P39 x P53 / 11.94 hours on Pentium3 750MHz, Windows Me / Nov 26, 2007)
4·10148+9 =
4(0)1479<149>
= 397 · 853 · 7321 · 29011093 · 4493636292960215751289<22> · 92434815990640075017640402187985349<35> · 1338913300569270255707383411990054108086821389860006097017974083996576133953<76> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1573321121 for P35 / Nov 20, 2007)
4·10149+9 =
4(0)1489<150>
= 18493 · 15208906085724863<17> · 35274210892827613264081<23> · 40317847369951035346198806666122621921229309916638852314732468437701852182835351772288656466406535552362771<107>
4·10150+9 =
4(0)1499<151>
= 13 · 461 · 346705813 · 880078819597<12> · 70157489449933<14> · 1211697258811082095589<22> · 25731485325266264685316538802440540399877528238993196754275086696533047049847435968257497009<92>
4·10151+9 =
4(0)1509<152>
= 7 · 131 · 197 · 1531 · 47933 · 2296496011<10> · 1404598779340570579<19> · 6104431168415592413869608635611<31> · 153232696611883288817148088275635599149717352290249536018399392505789557880036813<81> (Robert Backstrom / GMP-ECM 6.0.1 B1=1448000, sigma=536718007 for P31 / Dec 1, 2007)
4·10152+9 =
4(0)1519<153>
= 26713 · 1234873 · 1996467668952176494127953<25> · 35974049014171230767387935670841612478177<41> · 168835367899724431687288680957130059518243845115630566914418157002167566445961<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / Dec 6, 2007)
4·10153+9 =
4(0)1529<154>
= 211 · 499 · 823 · 7213 · 5983931 · 20484293 · 1674567153955540249123309372823653<34> · 31178204285060110569074580607563260199102302136786304734413870091585370032227633400052324234081<95> (Robert Backstrom / GMP-ECM 6.0.1 B1=1155000, sigma=3343519632 for P34 / Nov 29, 2007)
4·10154+9 =
4(0)1539<155>
= 17 · 13913 · 1396989572897<13> · 61059519554988608394921409<26> · 42618868918024524866536599051397923694814520254443166653<56> · 46520226216352324323002797548303105981922548494168073941<56> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / Dec 10, 2007)
4·10155+9 =
4(0)1549<156>
= 1975423 · 3095912878954409<16> · 34448312105302906122201979845692525321041884536529688865372252369<65> · 1898642540091341888277141518857734481586769553402869501770427156234223<70> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 26.75 hours on Cygwin on AMD XP 2700+ / Dec 1, 2007)
4·10156+9 =
4(0)1559<157>
= 13 · 1213 · 1237 · 205062448436406520514216646323617354906654804487566115337476654281065666481409833041743075925448111433805354621412938712524645302201299244913925806253<150>
4·10157+9 =
4(0)1569<158>
= 7 · 87972114341735599736283329579<29> · 22156740177008454467142813185853133375535106690625343<53> · 2931642819433829612544003364072511581602586787125479620745479951967818422771<76> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / Dec 1, 2007)
4·10158+9 =
4(0)1579<159>
= 29 · 617 · 16694516335098246170350962150521377733606416852014894432101<59> · 1339069098410419305684551449267723355927167683871174848884295909043052511734794797656249685854513<97> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.30 / Nov 29, 2007)
4·10159+9 =
4(0)1589<160>
= 59 · 5613936607<10> · 78918344807<11> · 2118843795331<13> · 3878257691504423440325364853<28> · 392955123090102563686734374525767<33> · 47389698841229495008237336545522944129176490198562383160258074779<65> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=4262207878 for P33 / Nov 21, 2007)
4·10160+9 =
4(0)1599<161>
= 277 · 138637 · 247609 · 15173733529<11> · 60797126856307127135595444344471160234256633836042739865882569<62> · 4559940072470123498850798447077277366305328269178339465898539108054593612449<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve / Dec 1, 2007)
4·10161+9 =
4(0)1609<162>
= 4051 · 127235411 · 1969369859<10> · 3315928709727846416041854024938819789689<40> · 118838532278963278232537809676524506390734233220677222531873601915306217550488799630909789562805027619<102> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / Dec 4, 2007)
4·10162+9 =
4(0)1619<163>
= 13 · 14484959608208348655122569360348676482871487639034491862149522347733039174529<77> · 21242193006733989503775579532646316990712184952355071124010335682117913659526189758317<86> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.30 / Dec 1, 2007)
4·10163+9 =
4(0)1629<164>
= 7 · 1303 · 257837 · 959561 · 5915543 · 878200471969328827561876462072079282958405245015115821377184281733<66> · 3412018883530127490227807989559980166714774210829016758904628027464337410663<76> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.32 / Jan 9, 2008)
4·10164+9 =
4(0)1639<165>
= 433 · 325501909 · 155697059191893120469<21> · 2480292169582768150613622571493155466576298122188305452881<58> · 7349119396569529045017568501654084454037447639806748910113839336437017179473<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 46.42 hours on Cygwin on AMD 64 X2 6000+ / Apr 9, 2008)
4·10165+9 =
4(0)1649<166>
= 19 · 1877 · 8893 · 11427643437022285783<20> · 128867463506675408316022657357<30> · 467807742471873906594101709631462254293<39> · 18307391061578173853638901084078048550027933080852242492899530687116597<71> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=366089251 for P30 / Nov 22, 2007) (JMB / GMP-ECM 6.1.3 B1=44000000, sigma=3065949829 for P39 / Nov 28, 2007)
4·10166+9 =
4(0)1659<167>
= 95273 · 8165188054910845523309<22> · 14974400622659504557368769453<29> · 16787178947577077116058498947766265186683375867777<50> · 204548731765952768246248790510940164302339098214505480636361977<63> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P50 x P63 / 17.28 hours on Core 2 Quad Q6600 / Dec 9, 2007)
4·10167+9 =
4(0)1669<168>
= 23 · 23041 · 82571 · 9141201602713997050786878892618917530515110570413840519864945246628360383497926678911136034798895190617262127600989109943630852760886838694749338794680669053<157>
4·10168+9 =
4(0)1679<169>
= 13 · 97 · 373 · 8504251062499867121077148439576233169555631621356725693255916301161042876307794358705057690713145233473582607105726975271763973016011378687921624822208001224612153<163>
4·10169+9 =
4(0)1689<170>
= 73 · 89 · 7481 · 207246019 · 845142638547421004330094762180574773307401004688254872802529628697418322901667891284028031254706560428688361394220866920309297472989125841285693158433253<153>
4·10170+9 =
4(0)1699<171>
= 17 · 157 · 460710007049003831439916489<27> · 325299781750580975452236640340504586671040660826393559465921119070610988900472254166029502281750728082670126640485912086213508796918658218149<141>
4·10171+9 =
4(0)1709<172>
= 4727579 · 42758299609<11> · 70786206663533<14> · 52842317195285609<17> · 1749706642519018677552131<25> · 13309174465738976322573197980572388901369971<44> · 227171538029579664285228640378502521594404174584065064527<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P44 x P57, Msieve 1.30 / Nov 28, 2007)
4·10172+9 =
4(0)1719<173>
= 379417 · 2183353693<10> · 369214042069<12> · 10392906827609765461<20> · 1432364659536702101368956541<28> · 521485688834094616003641826229481656646415453<45> · 16846429736694498814138730507079319979241737624177166277<56> (Sinkiti Sibata / Msieve v. 1.30 for P45 x P56 / 41.96 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Dec 1, 2007)
4·10173+9 =
4(0)1729<174>
= 241 · 2609 · 49277 · 37490161253921<14> · 817315416761140501205161<24> · 192750975747012200555324918025716343881<39> · 2185853367735352411488999932909611191071596551799121040574783002059359617054726183998413<88> (Robert Backstrom / GMP-ECM 6.0 B1=2442000, sigma=3323678714 for P39 / Feb 11, 2008)
4·10174+9 =
4(0)1739<175>
= 13 · 358073 · 217328021421685514569<21> · 3953933292618172077127265772121748539513833728170513039266006786871318220832367759947355161281839742703467990288076776537526836881557524261264927789<148>
4·10175+9 =
4(0)1749<176>
= 7 · 401 · 3169 · 1891223 · 193971539 · 12257858029676611496353462983004900423146023624367849810522129522038355641907452161755324282656343366460821500502010627996593854818607457321748280042339459<155>
4·10176+9 =
4(0)1759<177>
= 5949217 · 260808949 · 37078796641<11> · 25253318745384671209<20> · 30659586774476168038113800824694868364850678869<47> · 8979813218286857062544785990149537754786720685038107462329302196640845737147656966793<85> (Sinkiti Sibata / Msieve / 80.41 hours / Mar 6, 2009)
4·10177+9 =
4(0)1769<178>
= 769 · 1583 · 4447 · 133051 · 27471971 · 202151814940210900000057206424771165643787269558489323119112883608470657437185553048798123972788401866993683733316406001935656948253709753290720354776020041<156>
4·10178+9 =
4(0)1779<179>
= 1599137 · 25013491652059829770682561906828495619824943078673059281349878090495060773404655135863906594619472878183670317177327521031656449697555619062031583285234473344059952336791657<173>
4·10179+9 =
4(0)1789<180>
= 921163045658547580756150590548571589420901651<45> · 434233659160780244149695889605425366477201748488030257510308420904369547799589597822903126508104998452818212276951470860768875906012659<135> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 514.08 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Dec 10, 2007)
4·10180+9 =
4(0)1799<181>
= 13 · 2293 · 3697 · 15493021 · 356679403981<12> · 7613777314732978779697<22> · 425332272985269084222506529751921<33> · 2028245328547010720335723720294520432822986427659668208529742591478467559455377267252935084340950609<100> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=1221583337 for P33 / Nov 23, 2007)
4·10181+9 =
4(0)1809<182>
= 7 · 4463 · 9013 · 44939 · 54440369 · 646495019927<12> · 17375472304230114852745301318776299103<38> · 96680330851377897032675335617773667304146317489<47> · 53466443788604542141782787390935555045766340238599979694824022367<65> (Serge Batalov / GMP-ECM 6.2.1 B1=11000000, sigma=2640071409 for P38 / Feb 13, 2009) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P47 x P65 / 11.56 hours on Core 2 Quad Q6700 / Feb 16, 2009)
4·10182+9 =
4(0)1819<183>
= 593 · 1328642261<10> · 23666791403837444777<20> · 30538114624651788954583755347034152657<38> · 702450347822345188677038220687379849426066288977031773444331177142414305322712815983768134833633739828814217175997<114> (matsui / GMP-ECM 6.2.1 for P38 / Sep 22, 2008)
4·10183+9 =
4(0)1829<184>
= 19 · 47 · 211 · 507371 · 12800256361540851179<20> · 3268750472332670260412090654062890935923767473781061060416941374621087285908953975000009434301764465129758225750004661863496951777328826637592647516829287<154>
4·10184+9 =
4(0)1839<185>
= 86629 · 17315047017625261<17> · [26666929636551284865749676559985064929619556026911197840995261892026232694863092865560797017860538142122468810446558611395066656624799409134739874379357033093116361<164>] SUBMIT/RESERVE
4·10185+9 =
4(0)1849<186>
= 160201 · 2496863315459953433499166671868465240541569653123263899725969251128270110673466457762435939850562730569721787005074874688672355353587056260572655601400740319973033876193032502918209<181>
4·10186+9 =
4(0)1859<187>
= 13 · 17 · 29 · 9257 · 23480381 · [2871404101451399791889619424614834268252941424871914610671253916513288061367543296597396226954575583071335430001878843184061841095705726085505222908586859291143018455741453<172>] SUBMIT/RESERVE
4·10187+9 =
4(0)1869<188>
= 7 · 463 · 659 · 31187419 · 1422552580681<13> · 313608486641729<15> · 1346046230331284293142797595459864282652758756687789596472452823720928516243501240585875399693070043664898447095535892488549047787841115893960827481<148>
4·10188+9 =
4(0)1879<189>
= 337 · 1201 · 58693 · 876529 · 2430640727175969638994585027337101361<37> · 7903395490385727731463723829241886338897947794113256415232279926080628572269461573229661036837524536596561491729907318379745124431713621<136> (matsui / GMP-ECM B1=88000000, sigma=101061817 for P37 / Sep 17, 2008)
4·10189+9 =
4(0)1889<190>
= 23 · 1567 · 66173 · 246030458809<12> · 427784512582518755165413<24> · 15935599295478703223668355222203651040533146833365702079354227555185016378027753764240941825049498083902107324559043430408906071605031955805229689<146>
4·10190+9 =
4(0)1899<191>
= 2789 · 17155258129<11> · 1411411376393248424585966404607993<34> · [592325740845773596110618934810993533587964947739141920784957245331142523666993635952898907996987364689434079735407153529578722036865973825841773<144>] (matsui / GMP-ECM B1=88000000, sigma=2898798771 for P34 / Sep 17, 2008) SUBMIT/RESERVE
4·10191+9 =
4(0)1909<192>
= definitely prime number
4·10192+9 =
4(0)1919<193>
= 13 · 3084049 · 20054833 · 362793721871669762743297557966121<33> · 34347828192180472650311406770836321<35> · 399224581811496883777327450848889939055934413354952004388681194427258371965399996716709123759572132028042808069<111> (matsui / GMP-ECM B1=88000000, sigma=2110858031 for P33 / Sep 17, 2008) (matsui / GMP-ECM 6.2.1 for P35 / Oct 15, 2008)
4·10193+9 =
4(0)1929<194>
= 7 · 11437 · 13853895929<11> · 284374155722383<15> · 1455040861595700679822195920931<31> · 40774884715492908428204364418823<32> · 9456466122140544011470454984220083014832730601<46> · 226042958165565708353120714503974059356275405880402226161<57> (matsui / GMP-ECM 6.2.1 for P32 / Oct 1, 2008) (matsui / GMP-ECM 6.2.1 for P31 / Oct 15, 2008) (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.38 gnfs for P46 x P57 / 5.56 hours, 0.61 hours / Oct 15, 2008)
4·10194+9 =
4(0)1939<195>
= 2665781 · 777716085741029<15> · 192936520219429395619375328945303785182939062000314233861188124429897927487161084950952612036074378745402564000772073633249122495281275480660949529437417156696207244582964641<174>
4·10195+9 =
4(0)1949<196>
= 569 · 325889 · 79087703 · 143864647583978940811727209<27> · 1895898028384615696251793941239978553891758796871307004276552920334711509119160356272879507632138997239520574377327997632182591163183607158544056351410687<154>
4·10196+9 =
4(0)1959<197>
= definitely prime number
4·10197+9 =
4(0)1969<198>
= 1597 · 94202005886838037<17> · [2658856658086202185064250938079472746663859126592014100054321408287948245172160493783340251826354249244908998126266481100787212802533174219203369159238971497004207867105641270281<178>] SUBMIT/RESERVE
4·10198+9 =
4(0)1979<199>
= 13 · 119161480369370553888738724548996511607859620678122425499095327719568445123612055947061<87> · 2582145729799085189864734222137758538649682303628164199071706577153193715726836851292948073706300167943278781913<112> (matsui / GGNFS-0.77.1-20060722-nocona / Feb 18, 2009)
4·10199+9 =
4(0)1989<200>
= 7 · 167 · 807609247 · 69410343209<11> · 3583758997367<13> · 4408808231743453<16> · 902378687429809728877943<24> · 34354547702604499771852060945580290335045785027459957891<56> · 1246197671815972306658825990912399156490027586001311061642622929565689<70> (Erik Branger / GGNFS, Msieve gnfs for P56 x P70 / 97.56 hours / Feb 20, 2009)
4·10200+9 =
4(0)1999<201>
= 61 · 7428301 · 66571867650574241377<20> · 13260195340912706189613478602151803601200846612924840571496471519038131433542401429752928656391236967769486953577322329150096781747532322298039868635523760934059181669090897<173>
4·10201+9 =
4(0)2009<202>
= 19 · 41969 · 1976453 · 8788979 · 21280979 · 869485926612010929713294429061619<33> · [15606254712063376725539740805651828004258104146302801666353687446609629914140730575528706598887037816965221011197626429846238635396925544675637<143>] (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3803940840 for P33 / Feb 27, 2009) SUBMIT/RESERVE
4·10202+9 =
4(0)2019<203>
= 17 · 1117 · 2574721 · 818140179270228523740581736159729356875726252823169381283765288333363879380977392449236189870510353981946255578886811984387553107314994126577073197717093330333497463305005196150532668891965261<192>
4·10203+9 =
4(0)2029<204>
= 241 · 10093 · 21504565484876647<17> · 26854677970110810209789011<26> · 284755456550999885678873494082877296058232996663262430689758616921765324930935277345456531034111703235800146701627398316294535586341742417321380828545176729<156>
4·10204+9 =
4(0)2039<205>
= 133 · 3163073222102835073<19> · 104371341092297168434106963028253<33> · [5514922642801281170779376780759437194775023248270464884245911662908683979158794827643748726590188350303750194354785166138207825960686703194983314150313<151>] (Serge Batalov / GMP-ECM 6.2.3 B1=3000000, sigma=3928819928 for P33 / Aug 27, 2009) SUBMIT/RESERVE
4·10205+9 =
4(0)2049<206>
= 7 · 331 · 60009389597450539<17> · 425671499713583193200939<24> · 675834215075137281305080765018530502788335171916363536343854997460864501058814335086316421493681275023788311584199763573974729615452377074097473531714553921380437<162>
4·10206+9 =
4(0)2059<207>
= 409 · 977995110024449877750611246943765281173594132029339853300733496332518337408312958435207823960880195599022004889975550122249388753056234718826405867970660146699266503667481662591687041564792176039119804401<204>
4·10207+9 =
4(0)2069<208>
= 4729 · 6299 · 672779 · [199593614015031885965678522461525277704984589327844858584170433570576450073980110630377240908325431940773119217247230833603250518299608272469290865559770772723407518884882554127225865675089455401<195>] SUBMIT/RESERVE
4·10208+9 =
4(0)2079<209>
= 56041 · 1840599613<10> · [387788377581688289371431249461030381022462384738758093566030054271723711277607755787221028097718270404721169014157843013308491791342913847779739566394836804064339457446263608159998580483142197173<195>] SUBMIT/RESERVE
4·10209+9 =
4(0)2089<210>
= 491 · 9108877 · 70880585949727<14> · 27616798594990984777138087<26> · [45689144864459737111365899608194961796501222629191342437683960705531070764599726160050139860377833806431617936602852332012561128838389454939164242865982232800063<161>] SUBMIT/RESERVE
4·10210+9 =
4(0)2099<211>
= 13 · 26309 · 5253679217<10> · 4887281314249<13> · 455492686613620588551112306594985520246460381216022000109454281426119716020385406579545280511243688843395042669031581045292878825971759840975571999135334756871574845542745235488860369<183>
4·10211+9 =
4(0)2109<212>
= 72 · 23 · 3943 · 346447 · 12214014041401<14> · 2249372628029918199931699321<28> · [945698439181680505663501238782708686449185274195678070924658785859662192872561948691998361332632995365532116027956875857279239144300667546020864392005717034887<159>] SUBMIT/RESERVE
4·10212+9 =
4(0)2119<213>
= 1057477 · 1719841 · 2162154127181111154546903829<28> · 77175797637606010161708971689<29> · 1746066645189561080367807342423137376428492594383633<52> · 754870008751017698161582119509494539523940082054318759700337322475860229316028590649214989769<93> (Markus Tervooren / msieve 1.41, lattice siever (64bit/asm) gnfs for P52 x P93 / 669.60 hours on Q6700 / May 12, 2009)
4·10213+9 =
4(0)2129<214>
= 89 · 211 · 4912330291777329830182920462792184153201<40> · 209197765948292508715840081366263723462559353816430654219<57> · 207273092529491319737806399512561945738725389466995842008096844701461670330893312911176031446241487096666609893809<114> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 120.93 hours, 44.52 hours / Aug 4, 2009)
4·10214+9 =
4(0)2139<215>
= 29 · 1217 · 7786148386377735821<19> · [145562242988025635613919280477381116593397869108726341544922296125944767249979828847843443562035046129275107091067705011606526702249585186860819550088210631870598859509081945793235530181311953<192>] SUBMIT/RESERVE
4·10215+9 =
4(0)2149<216>
= 843511914000515635859<21> · [474207884157704358649174657207698774419432418000250069661555478626132664205028001470344000184854278072993746126905336164598885848072423655305106019325631993089594887626596539899206037084975476851<195>] SUBMIT/RESERVE
4·10216+9 =
4(0)2159<217>
= 13 · 3078594054131367145950769<25> · 99945722716964004103276231613096872237723482435939148019947815682703620556233148110226160098164250446605754074221702698752812874667061106151582439391765728778357025656680126191009903902639997<191>
4·10217+9 =
4(0)2169<218>
= 7 · 59 · 10331 · 103801 · 2709378956041357<16> · 1746852043119607943<19> · 23516613293858822582041<23> · 1014018537142620832647766463<28> · 10240471134688208781527994263<29> · 9302958779121468396279950822681<31> · 8399983999392945602288689704976938270469713713532739350711371797<64> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1580648321 for P31 / Feb 28, 2009)
4·10218+9 =
4(0)2179<219>
= 17 · 149 · 423599432549<12> · [372794444622164148325945841252447484504212834373237605805219419948066373399815648516293118962690745283125366029168213890347983911020163431377105775781716813687401560559572612041418667246414827567559606577<204>] SUBMIT/RESERVE
4·10219+9 =
4(0)2189<220>
= 19 · 187290361394179498232863<24> · 9457269799406383426633156512971<31> · 118857114821080154967545816861734128831254596556026751501924605858763770033655810048872088003725641017149749577328038719567805266379972250629286861103129887452328807<165> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=734110824 for P31 / Feb 28, 2009)
4·10220+9 =
4(0)2199<221>
= 997 · 111121 · 709782838241307772064197157557<30> · [508678284043207491838639547329208587939624038234857803345666529198327364330853529788009362174703257997129512155060318466697378595895660342894182806227347292962993606597316990987670801<183>] (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1818859441 for P30 / Feb 28, 2009) SUBMIT/RESERVE
4·10221+9 =
4(0)2209<222>
= 1380329 · 6586109027452037<16> · [43999573131412731821244310394957477165025040198739128869945884369893758915884725692824645975690256003517293893303349646548705176793462967323476927059009461201813421610375868592425469990878490457169133<200>] SUBMIT/RESERVE
4·10222+9 =
4(0)2219<223>
= 13 · 113 · 5862761853228757<16> · 17589576864839190157<20> · 5274182050091317198581965547001<31> · 5006398706548685269808541408685382119276014206454662384624282431054279618619937841652442041715222856369255023664857400346225756316048000059634993308331989<154> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=3200907737 for P31 / Feb 28, 2009)
4·10223+9 =
4(0)2229<224>
= 7 · 849533 · 992539 · 1487466529<10> · 9123362680493<13> · [499380954823368629696796705151353215723452870181324733048397352617367205331038227787111897713991334784635822310237511116333018400381959894246044656091926067973774040951914432014443544920133<189>] SUBMIT/RESERVE
4·10224+9 =
4(0)2239<225>
= 577 · 102217 · 24814560283453144513<20> · [273309333925766620929415275177520748961346039031240296794006117360450186744666492862045272614581189615632172303790332429991958597045283761880165528665587854893129436252874776356075667618906762934977<198>] SUBMIT/RESERVE
4·10225+9 =
4(0)2249<226>
= 179 · 606401909035756925044903<24> · [36850755880067866288379311590761764982953232025155359751431764103391286411481397176164432861437842634276290368953298183122387998136182422936489729834091611069263439255415555787541474497332341413143157<200>] SUBMIT/RESERVE
4·10226+9 =
4(0)2259<227>
= 31337 · [1276446373296741870632160066375211411430577272872323451510993394390018189360819478571656508280945846762612885726138430609184031655870057759198391677569646105243003478316367233621597472636180872451096148323068577081405367457<223>] SUBMIT/RESERVE
4·10227+9 =
4(0)2269<228>
= 12659 · 42767 · 682259 · 1261349631343<13> · [858552874999075346368012799518845890480221472932243016924413500224002860125309346172222044539967500196212982186171084426983128756659730501650719441321687447072713201591069374405955348444760337854771969<201>] SUBMIT/RESERVE
4·10228+9 =
4(0)2279<229>
= 13 · 3709 · 150632969593<12> · 4403428148909407333<19> · [125068762717615453072552784419259101041847217761882153020627138105379041537855404135343604356436230123327708618669324962368940498132532367904187316334787007263739067493710719624375982749809158533<195>] SUBMIT/RESERVE
4·10229+9 =
4(0)2289<230>
= 7 · 47 · 277 · 1457422598837<13> · 551420791056445453796063<24> · 1638406192738208329601682412911049<34> · 333345124197251305675550256925290253496716079465791821716379169270916804717942808852818711966723328607977587292438599629740745367231278762393317263765016767<156> (Makoto Kamada / GMP-ECM 6.2.1 B1=1e6, sigma=1467685157 for P34 / Mar 1, 2009)
4·10230+9 =
4(0)2299<231>
= 857 · 191476712521<12> · 8028511193274445924646050673<28> · [303618471635148302875013276431116991069591797728221416774456900877195412292456052212417141607687467184408454701436005671448750185847346472867664341696586874423661292335225895959134470575289<189>] SUBMIT/RESERVE
4·10231+9 =
4(0)2309<232>
= 541531 · 563327077 · 344974725091<12> · [38009203123631100628260875115373462909570627247507581597846937241698038932991128761302797949815480281608468227351024708950725931512554168319349399262249588296729091658547310572038707875049320136138761605477<206>] SUBMIT/RESERVE
4·10232+9 =
4(0)2319<233>
= 6781 · 86869 · [67904948601819198358348975988027569864095494226722118685189278313149540860095860499224382037763303411691122682004950443910691554199279454139415979313395714972638320593552945621688300060030181474837730472727141115135982655881<224>] SUBMIT/RESERVE
4·10233+9 =
4(0)2329<234>
= 23 · 241 · 27435761 · [2630256495534832519671588725579347129934832765132385401880987530726835813648218261659450838411306287985736604149222639690330902569007746369148047095242274982762927550208536640183181644396978572408122581585106484958034907583<223>] SUBMIT/RESERVE
4·10234+9 =
4(0)2339<235>
= 13 · 17 · [18099547511312217194570135746606334841628959276018099547511312217194570135746606334841628959276018099547511312217194570135746606334841628959276018099547511312217194570135746606334841628959276018099547511312217194570135746606334841629<233>] SUBMIT/RESERVE
4·10235+9 =
4(0)2349<236>
= 7 · 5573 · 8768013343<10> · 46382191979<11> · [2521276274512363956994936859786933686545932824186770827157316924734926578993294376025507473889271656494230822506106074485173398660459088718421349979032185198698097682100266405762218916751620211417126949398671927<211>] SUBMIT/RESERVE
4·10236+9 =
4(0)2359<237>
= 193 · 355609 · 1104193 · 18648457 · 530224333 · 533804697044331114759261601310823323308616585540765221910067593417055899599861135187191821602666626954933164454857594632226846906361814501701071096132360386705581599307667050223485405435238108503423601188429<207>
4·10237+9 =
4(0)2369<238>
= 19 · 210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684211<237>
4·10238+9 =
4(0)2379<239>
= 13729 · 264609763147329391577993<24> · [11010707411765256858548653740610118023871093778797409212334316791131530420978652697027293273646597863356436417140752877085791009381027209760498750978639429609881935669897916419922021608892184845951587489960464097<212>] SUBMIT/RESERVE
4·10239+9 =
4(0)2389<240>
= 983 · 15389903 · 4267139508637<13> · 4298785922742343<16> · 4683933785766256278623<22> · [307735206107618533007178043551976557773308392564547725453111499852890428470219213622437527093012915272048008076083287455361528811183959201431237451388873164800706110104091958584237<180>] SUBMIT/RESERVE
4·10240+9 =
4(0)2399<241>
= 13 · 1490226374629<13> · [206473535115703058091169633368038883546960933024843422503449663774127952585655839101348618000599167338270994828011178351007134386489404705171227058245317212907807375024552379461007218096204591883823161619459382651519463716391017<228>] SUBMIT/RESERVE
4·10241+9 =
4(0)2409<242>
= 7 · 14106394181773<14> · [405084789256009500959754186387273499062936989362303996213362636163015709220544329198497499383315095188917840231821338736664669903204084046610233367209491272393457084603608806478998256689751057034715379700467431394672466073322219<228>] SUBMIT/RESERVE
4·10242+9 =
4(0)2419<243>
= 29 · 601 · 625969 · 517852967663401<15> · 70799179713688698262849292594179995807285084551686552728241575523541225198203701982092213878982229208841071044222232816034911143025108079862389175062848934863876184987776645670063173630755076343585771533822100108376109<218>
4·10243+9 =
4(0)2429<244>
= 211 · 761 · 127566948277192337869764297638109721127023<42> · 195278627055004260165165796713698923970426519764143364350420080659555185314378363696270057757429282480559027603944657848259735353558435498871600913917817557530384015450970490735110900823076695659173<198> (Serge Batalov / GMP-ECM 6.2.3 B1=11000000, sigma=3161935447 for P42 / Aug 27, 2009)
4·10244+9 =
4(0)2439<245>
= 829 · 6316202857<10> · 1689891773761<13> · [4520541901810601412828688084585610269711053287930096735843239402848347423859601728154320827801543215029968038993623272398634917346080013126137602777923239382485019101358635086637511611394830186880467634412467118783619573<220>] SUBMIT/RESERVE
4·10245+9 =
4(0)2449<246>
= 284957 · 82069760818893961<17> · [17103992351646896947820678886143627407011692156056123625751845024762478944067537148965053674138922458858308356979643268213517888423902840640814811396361041225592982387853888071093551960355253612128950692336805235956024526517<224>] SUBMIT/RESERVE
4·10246+9 =
4(0)2459<247>
= 13 · 389 · 617 · 50777 · [25247293880461782697257293776006595553265668303841196016434660636737328692147797578872494846335590484101524509724047825017096872684282247614713977077985155453305008960962275583155890044223894846623484113855736194731737883080211281448393<236>] SUBMIT/RESERVE
4·10247+9 =
4(0)2469<248>
= 7 · 397 · 3169 · 927184488768257538302423<24> · [4898724861250213278177986759898099678785991413557336755124446455783549052230461199942147081319260184539135489527953942339733897625012144994436896734403915473716608067444198319433546518584703621359801715592969602309933<217>] SUBMIT/RESERVE
4·10248+9 =
4(0)2479<249>
= 109 · 157 · 222437485156209239721584649092089<33> · [105081403472507701127044472851803774228799733560932737552951993501629404537657221649279921860005838295301318857627808513987051312269821710093470836004276067692676649441223404038410980976203789322509492454610415737<213>] (Serge Batalov / GMP-ECM 6.2.2 B1=1000000, sigma=566428965 for P33 / Mar 2, 2009) SUBMIT/RESERVE
4·10249+9 =
4(0)2489<250>
= 197 · 1259 · 2179 · 62971 · 1088579 · 1306928213<10> · 184515969747407<15> · [447738633412680088656693715678000489708733545251160348593789636545965027843678090916408361907688063879499626232841510058650075759683177342611595987651459963597616424012443765870345826158382980277456793734783<207>] SUBMIT/RESERVE
4·10250+9 =
4(0)2499<251>
= 172 · 6390680809561<13> · 25515781715614181<17> · 848801510394874251260023659751607386622798929408796565018046486638110030688061988932479753368130172131465836796733021998704961471009396587265763132158986835121915788572798426422377356074179066275604034230905886064881341<219>

4. References

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