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Factorizations of 800...003

Table of contents

  1. About 800...003
  2. Prime numbers of the form 800...003
  3. Factorizations of 800...003
  4. References

1. About 800...003

First ten terms

83, 803, 8003, 80003, 800003, 8000003, 80000003, 800000003, 8000000003, 80000000003

General term

8·10n+3

2. Prime numbers of the form 800...003

Last update

Aug 9, 2009

Searched up to

n≤10000

Difficulty of search

13.93%

Results

  1. 8·101+3 = 83 is prime.
  2. 8·1031+3 = 8(0)303<32> is prime.
  3. 8·10105+3 = 8(0)1043<106> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PPSIQS / Jan 6, 2005)
  4. 8·10113+3 = 8(0)1123<114> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PPSIQS / Jan 6, 2005)
  5. 8·10369+3 = 8(0)3683<370> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PPSIQS / Jan 6, 2005)
  6. 8·101359+3 = 8(0)13583<1360> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 6, 2006)
  7. 8·106219+3 = 8(0)62183<6220> is PRP. (Makoto Kamada / PFGW / Dec 25, 2004)

3. Factorizations of 800...003

Last update

Oct 22, 2009

Completed up to

Range

n≤200

Terms which have not been factored yet

n=173, 174, 179, 180, 182, 183, 184, 186, 188, 190, 191, 192, 193, 195, 197, 199, 200 (17/200)

Results

8·101+3 =
83
= definitely prime number
8·102+3 =
803
= 11 · 73
8·103+3 =
8003
= 53 · 151
8·104+3 =
80003
= 7 · 11 · 1039
8·105+3 =
800003
= 17 · 47059
8·106+3 =
8000003
= 11 · 727273
8·107+3 =
80000003
= 23 · 3478261
8·108+3 =
800000003
= 11 · 29 · 2507837
8·109+3 =
8000000003<10>
= 677 · 11816839
8·1010+3 =
80000000003<11>
= 7 · 11 · 73 · 389 · 36587
8·1011+3 =
800000000003<12>
= 31 · 6983 · 3695611
8·1012+3 =
8000000000003<13>
= 11 · 51679 · 14072887
8·1013+3 =
80000000000003<14>
= 227 · 352422907489<12>
8·1014+3 =
800000000000003<15>
= 11 · 313 · 232355503921<12>
8·1015+3 =
8000000000000003<16>
= 443 · 112939 · 159897739
8·1016+3 =
80000000000000003<17>
= 7 · 11 · 53 · 2267 · 56843 · 152123
8·1017+3 =
800000000000000003<18>
= 19 · 42105263157894737<17>
8·1018+3 =
8000000000000000003<19>
= 112 · 73 · 905694554511491<15>
8·1019+3 =
80000000000000000003<20>
= 109 · 16253 · 1287743 · 35067173
8·1020+3 =
800000000000000000003<21>
= 11 · 150413 · 675151 · 716161571
8·1021+3 =
8000000000000000000003<22>
= 17 · 439 · 1071954977890928581<19>
8·1022+3 =
80000000000000000000003<23>
= 7 · 11 · 1038961038961038961039<22>
8·1023+3 =
800000000000000000000003<24>
= 661 · 229689653 · 5269229272891<13>
8·1024+3 =
8000000000000000000000003<25>
= 11 · 103 · 2383 · 12583 · 235478813120119<15>
8·1025+3 =
80000000000000000000000003<26>
= 18649609621<11> · 4289634025900343<16>
8·1026+3 =
800000000000000000000000003<27>
= 11 · 31 · 73 · 23603 · 1987537 · 685062695861<12>
8·1027+3 =
8000000000000000000000000003<28>
= 784495495981<12> · 10197636622497263<17>
8·1028+3 =
80000000000000000000000000003<29>
= 72 · 11 · 66221 · 654967 · 3529441 · 969572171
8·1029+3 =
800000000000000000000000000003<30>
= 23 · 53 · 107 · 229 · 262288283 · 102114668361413<15>
8·1030+3 =
8000000000000000000000000000003<31>
= 11 · 981482123 · 740994369871703993051<21>
8·1031+3 =
80000000000000000000000000000003<32>
= definitely prime number
8·1032+3 =
800000000000000000000000000000003<33>
= 11 · 8693 · 11399091131<11> · 733934658021984031<18>
8·1033+3 =
8000000000000000000000000000000003<34>
= 43874627 · 98517337073<11> · 1850818727789393<16>
8·1034+3 =
80000000000000000000000000000000003<35>
= 7 · 11 · 73 · 199 · 262436075963<12> · 272520884534145539<18>
8·1035+3 =
800000000000000000000000000000000003<36>
= 19 · 263 · 13411 · 41894466829<11> · 284946159087225121<18>
8·1036+3 =
8000000000000000000000000000000000003<37>
= 11 · 29 · 2871563 · 25551370127189<14> · 341795831706491<15>
8·1037+3 =
80000000000000000000000000000000000003<38>
= 17 · 475053005483611<15> · 9906015325911933748969<22>
8·1038+3 =
800000000000000000000000000000000000003<39>
= 11 · 227699 · 4429417 · 503895548843<12> · 143103115325617<15>
8·1039+3 =
8000000000000000000000000000000000000003<40>
= 33493639 · 668392133 · 357352086579892684476769<24>
8·1040+3 =
80000000000000000000000000000000000000003<41>
= 7 · 112 · 132040897 · 715316282211507793844536899917<30>
8·1041+3 =
800000000000000000000000000000000000000003<42>
= 31 · 1163 · 22189554267328655035641971541896652151<38>
8·1042+3 =
8000000000000000000000000000000000000000003<43>
= 11 · 53 · 73 · 83 · 293 · 7729525946888643630815885058146243<34>
8·1043+3 =
80000000000000000000000000000000000000000003<44>
= 47 · 161569 · 252798042738519287<18> · 41673539165929557083<20>
8·1044+3 =
800000000000000000000000000000000000000000003<45>
= 11 · 59 · 1335106159<10> · 923271629851945325532435651049733<33>
8·1045+3 =
8000000000000000000000000000000000000000000003<46>
= 3319 · 2410364567640855679421512503766194636938837<43>
8·1046+3 =
80000000000000000000000000000000000000000000003<47>
= 7 · 11 · 808187 · 3874279 · 252890311 · 2404909901<10> · 545588877436513<15>
8·1047+3 =
800000000000000000000000000000000000000000000003<48>
= 892704843854221<15> · 896152861169688318559696303598543<33>
8·1048+3 =
8000000000000000000000000000000000000000000000003<49>
= 11 · 367 · 1751623 · 1131333372878431437831391824390899576353<40>
8·1049+3 =
80000000000000000000000000000000000000000000000003<50>
= 2089 · 4493 · 8523444319587823279593372041845423714800439<43>
8·1050+3 =
800000000000000000000000000000000000000000000000003<51>
= 11 · 73 · 1511298750851<13> · 659210503152769736257238319497783051<36>
8·1051+3 =
8000000000000000000000000000000000000000000000000003<52>
= 23 · 61 · 1075355269<10> · 5302495987758294626525975386152930218629<40>
8·1052+3 =
80000000000000000000000000000000000000000000000000003<53>
= 7 · 11 · 3923 · 8243 · 32128884983556876429528803078113287760113751<44>
8·1053+3 =
800000000000000000000000000000000000000000000000000003<54>
= 17 · 19 · 57424087729<11> · 43131380640248358587703649188273670155409<41>
8·1054+3 =
8000000000000000000000000000000000000000000000000000003<55>
= 11 · 11721890915948123<17> · 62043976734439859046741982481053751051<38>
8·1055+3 =
80000000000000000000000000000000000000000000000000000003<56>
= 53 · 4129 · 17431 · 19392167 · 121477320301<12> · 8902774761774115679578460147<28>
8·1056+3 =
800000000000000000000000000000000000000000000000000000003<57>
= 11 · 31 · 15050214077<11> · 793606044487<12> · 2756979091572917<16> · 71245016449508401<17>
8·1057+3 =
8000000000000000000000000000000000000000000000000000000003<58>
= 71865389213<11> · 1307075859827<13> · 85166619881691312524283341358054053<35>
8·1058+3 =
80000000000000000000000000000000000000000000000000000000003<59>
= 7 · 11 · 73 · 103 · 4447099404637863059<19> · 31071508594872805524194675855096459<35>
8·1059+3 =
800000000000000000000000000000000000000000000000000000000003<60>
= 567383 · 27898757 · 2340629520184369<16> · 21592162274488674956986804816577<32>
8·1060+3 =
8000000000000000000000000000000000000000000000000000000000003<61>
= 11 · 727272727272727272727272727272727272727272727272727272727273<60>
8·1061+3 =
80000000000000000000000000000000000000000000000000000000000003<62>
= 1669 · 47932893948472139005392450569203115638106650689035350509287<59>
8·1062+3 =
800000000000000000000000000000000000000000000000000000000000003<63>
= 112 · 409 · 231559 · 111039989 · 110409209191<12> · 5694229067442353566241963036625847<34>
8·1063+3 =
8000000000000000000000000000000000000000000000000000000000000003<64>
= 1193 · 14042761 · 477526017744974382138745095755344510601420905299813811<54>
8·1064+3 =
80000000000000000000000000000000000000000000000000000000000000003<65>
= 7 · 11 · 29 · 5870523053<10> · 6844629419<10> · 891609170101262599464086175914257228297013<42>
8·1065+3 =
800000000000000000000000000000000000000000000000000000000000000003<66>
= 1394389 · 148466510419<12> · 5272065747354949486171<22> · 732987756330063899024306423<27>
8·1066+3 =
8000000000000000000000000000000000000000000000000000000000000000003<67>
= 11 · 73 · 1202269643<10> · 1676262932271402143218087<25> · 4943453107172608935036406237061<31>
8·1067+3 =
80000000000000000000000000000000000000000000000000000000000000000003<68>
= 1613 · 1027787 · 789075952717253<15> · 61155242278618976517684297186637893855471721<44>
8·1068+3 =
800000000000000000000000000000000000000000000000000000000000000000003<69>
= 11 · 532 · 204583 · 7496894159791<13> · 16880862804494345582361142441843437935407200649<47>
8·1069+3 =
8000000000000000000000000000000000000000000000000000000000000000000003<70>
= 17 · 317 · 51962327 · 15712673005300727<17> · 1818206220473972652653184549099598068790463<43>
8·1070+3 =
80000000000000000000000000000000000000000000000000000000000000000000003<71>
= 72 · 11 · 5171 · 1150477396992224280429460523647<31> · 24948738636797438946308049673214621<35> (Makoto Kamada / msieve 0.81 / 47 seconds)
8·1071+3 =
800000000000000000000000000000000000000000000000000000000000000000000003<72>
= 19 · 31 · 1103 · 266821 · 3098783 · 6508081816133<13> · 228841614712619592877279682697858576632311<42>
8·1072+3 =
8000000000000000000000000000000000000000000000000000000000000000000000003<73>
= 11 · 131 · 587 · 7705057 · 42702809047<11> · 12935088148959819721<20> · 2222215702120388264670955570951<31>
8·1073+3 =
80000000000000000000000000000000000000000000000000000000000000000000000003<74>
= 23 · 233 · 1942757 · 1320873538247<13> · 37677163045049972333<20> · 154400361613164759255471946730731<33>
8·1074+3 =
800000000000000000000000000000000000000000000000000000000000000000000000003<75>
= 11 · 73 · 9439 · 2389619 · 4315068851<10> · 10236042095082544689857584995848601999525929187167911<53>
8·1075+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000003<76>
= 188779 · 3909267091<10> · 701492506592451927206719<24> · 15453182230628394947646365908854574733<38>
8·1076+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000003<77>
= 7 · 11 · 3232238695369<13> · 415036967988709934528267<24> · 774477945246471710078538349910933433893<39>
8·1077+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000003<78>
= 8169308075963<13> · 97927510207857573992866361114049392028488341159366269518918869081<65>
8·1078+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000003<79>
= 11 · 151 · 28181 · 4112490633703<13> · 89516675599707971<17> · 464253394020511340773358308194601595000791<42>
8·1079+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000003<80>
= 762917 · 463929885844279024771<21> · 403260075284126100029633029<27> · 560499355568344229708718601<27>
8·1080+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000003<81>
= 11 · 97 · 1801 · 140421419311<12> · 1794707887841403001<19> · 1651903695809972440677960373793941442033690119<46>
8·1081+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000003<82>
= 53 · 1009 · 34330441972126526344107580271537<32> · 4357561814692112077426598342166795767977005047<46> (Makoto Kamada / GGNFS-0.70.1 / 0.10 hours)
8·1082+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000003<83>
= 7 · 11 · 73 · 107 · 461 · 216317 · 31845991 · 107411984579<12> · 11034870330762312227<20> · 35336725616889405113813031847859<32>
8·1083+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000000003<84>
= 83 · 33536059111<11> · 287408672109179772000016984618101405815598080263717980858338163868549831<72>
8·1084+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000000003<85>
= 112 · 55787 · 172352981 · 6876268239228814677307933716672056455100832624154722455550862026057869<70>
8·1085+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000000003<86>
= 17 · 4705882352941176470588235294117647058823529411764705882352941176470588235294117647059<85>
8·1086+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000000000003<87>
= 11 · 31 · 51992894757193071098834645121805421870281<41> · 45122339632645802553442119914381794587095743<44> (Makoto Kamada / GGNFS-0.70.3 / 0.13 hours)
8·1087+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<88>
= 2237 · 2783233637<10> · 452322196859180670722705119853<30> · 2840706977234826416475037502646911280607974079<46> (Makoto Kamada / msieve 0.83 / 11 minutes)
8·1088+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<89>
= 7 · 11 · 197 · 2209987429321358015127649757841903166192063<43> · 2386399955666281289040005203830649017037949<43> (Makoto Kamada / GGNFS-0.70.3 / 0.15 hours)
8·1089+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<90>
= 19 · 472 · 3109501 · 14296927638194957491<20> · 428753077450911004740266186056240330736025446540684248842023<60>
8·1090+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<91>
= 11 · 73 · 193 · 170085607 · 938130909964865534091552476961419737<36> · 323508818017133291941816792568731577689423<42> (Makoto Kamada / GGNFS-0.70.3 / 0.21 hours)
8·1091+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<92>
= 113 · 77573 · 12149329 · 1074573224735595634039887047<28> · 699057095784542323854892532766371206825997051691169<51>
8·1092+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<93>
= 11 · 29 · 103 · 3491 · 66248925079<11> · 24290370549213544581361<23> · 4334103262048748903730959906132907155843386084534351<52>
8·1093+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<94>
= 2053937786051542486210180283<28> · 3894957312888757681393174562958023891479027822449758422495835754841<67>
8·1094+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<95>
= 7 · 11 · 53 · 601 · 21433 · 26261246527<11> · 369459993133008966638741<24> · 1970926442135483927984839<25> · 79581621853365472371143407<26>
8·1095+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<96>
= 23 · 54751 · 79231 · 25642081 · 490826459119<12> · 267423707733290178422117579389<30> · 2382285558188963882135861228559133111<37> (Makoto Kamada / msieve 0.81 / 1.4 minutes)
8·1096+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<97>
= 11 · 232701226253<12> · 267430733679223334492428286586361<33> · 11686576711987162822836634581578879259881985725704181<53> (Makoto Kamada / GGNFS-0.71.4 / 0.31 hours)
8·1097+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<98>
= 3511 · 25981 · 5878069 · 5775687991<10> · 677628322879<12> · 38121794928848640593468164444529611540856155116816184893745613<62>
8·1098+3 =
800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<99>
= 11 · 73 · 8311 · 222796787 · 295089888774096271<18> · 1823299056393473406307522267792201685796264235812755890403426181683<67>
8·1099+3 =
8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<100>
= 2131 · 2752211938103<13> · 1364032326697768990154089754568863333576918442246231127582930452520001873599418846071<85>
8·10100+3 =
80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003<101>
= 7 · 11 · 179 · 36408319 · 6115017566381<13> · 2455669220460404089924466119<28> · 10616418433959711373400277784445293578937077817201<50>
8·10101+3 =
8(0)1003<102>
= 17 · 31 · 557 · 922283 · 309525393822366661<18> · 9546928899824104087628266915435753352884151337437783966611208571902614279<73>
8·10102+3 =
8(0)1013<103>
= 11 · 59 · 2909 · 250321394839<12> · 73893077891192132187902179374341<32> · 229086681980295270219691452305688749689507823847518717<54> (Robert Backstrom / Msieve v. 1.25 for P32 x P54 / 41.33 minutes / Aug 9, 2007)
8·10103+3 =
8(0)1023<104>
= 8447 · 4354457 · 12301281430605925812079463<26> · 92650460140163238877679901473<29> · 1908339112582881881543260411801319113043<40>
8·10104+3 =
8(0)1033<105>
= 11 · 21107 · 237845132143<12> · 77926895668201<14> · 1712194848032429<16> · 108576531164926624074615159282254415664503512696871914972137<60>
8·10105+3 =
8(0)1043<106>
= definitely prime number
8·10106+3 =
8(0)1053<107>
= 7 · 112 · 73 · 10499 · 106273 · 47189860490284841929338677754779<32> · 24573337579454995751875650980653118980652254383713835857903861<62> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4256974982 for P32 / Aug 1, 2007)
8·10107+3 =
8(0)1063<108>
= 192 · 53 · 4311041529493168981918983158515670589329095421550917<52> · 9698949742404051679952742591797529833940595342191923<52> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.82 hours on Cygwin on AMD XP 2700+ / Aug 9, 2007)
8·10108+3 =
8(0)1073<109>
= 11 · 5527 · 9958256083822556593072164658877<31> · 13213703178894954610665804924839486965167161792188153823634168464500913387<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.96 hours on Cygwin on AMD 64 3200+ / Aug 9, 2007)
8·10109+3 =
8(0)1083<110>
= 41389 · 296676938035337991737<21> · 6515102690147474147803980219580376568939662956483643880211324239313109630254913501671<85>
8·10110+3 =
8(0)1093<111>
= 11 · 14747 · 67853 · 229991531503<12> · 3428025182905969<16> · 203471506518364613<18> · 453069803603611603225742588679081501394410587616941028533<57>
8·10111+3 =
8(0)1103<112>
= 61 · 1270823 · 157003159 · 9770136203<10> · 242125581741895343<18> · 277859595771752157056080803440560953539521517341413915037994444184691<69>
8·10112+3 =
8(0)1113<113>
= 72 · 11 · 147858293717<12> · 3840117103591<13> · 454057872231532423<18> · 5215142530978054082743<22> · 110391000996324009180070685590142723852019595619<48>
8·10113+3 =
8(0)1123<114>
= definitely prime number
8·10114+3 =
8(0)1133<115>
= 11 · 73 · 1229 · 652743731 · 20457301024193281<17> · 607059854616891932209263404593988019400899404926677156356776277950084265934947019079<84>
8·10115+3 =
8(0)1143<116>
= 1583 · 1488167 · 33959196211481846962456934024507853554622045456700995229980508257619816127584031170371932845565540728475723<107>
8·10116+3 =
8(0)1153<117>
= 11 · 31 · 501077 · 30244611063283188190841459<26> · 47772235073471907793622686848045341<35> · 3240466788618869376438883648133185467425146712141<49> (Robert Backstrom / Msieve v. 1.25 for P35 x P49 / 27.1 minutes / Aug 9, 2007)
8·10117+3 =
8(0)1163<118>
= 17 · 23 · 95569 · 3626149 · 743563094142647141671434594596447952314537<42> · 79402233062151798302517520827673963545042250342272076178284489<62> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.14 hours on Cygwin on AMD 64 3400+ / Aug 9, 2007)
8·10118+3 =
8(0)1173<119>
= 7 · 11 · 17483 · 22901138627205461270741<23> · 5535500757107990826350590321<28> · 34034286784005507880536617237<29> · 13773764714661578982854007624838469<35>
8·10119+3 =
8(0)1183<120>
= 181 · 7879 · 5340576803<10> · 7656422875069<13> · 14906395578079<14> · 920351219985499557329425477239335493763008845217762342623031845746947655049449<78>
8·10120+3 =
8(0)1193<121>
= 11 · 29 · 53 · 967 · 50671 · 2402101204589<13> · 4020186343903541310162314350309733821840427310675442992491335802827098230138099978328162594451973<97>
8·10121+3 =
8(0)1203<122>
= 268643 · 14246316379<11> · 791708730619<12> · 26402584382264426724108231728453509277741367521807668516494911008472968065215131360301307538921<95>
8·10122+3 =
8(0)1213<123>
= 11 · 73 · 81135620752009<14> · 5586942927233741<16> · 2197802401562353589182156357544860335050188368321982663784948515492198227650802517969668029<91>
8·10123+3 =
8(0)1223<124>
= 3167 · 316094792597854896892960037<27> · 7991431521932828511913808110150837880640721341059920292042849101514929681722100481673801255257<94>
8·10124+3 =
8(0)1233<125>
= 7 · 11 · 83 · 3559 · 101267 · 209717 · 176677715696117<15> · 937367355983571473432402332509988855496923996553784249014018921332426151398109873328705702649<93>
8·10125+3 =
8(0)1243<126>
= 19 · 14029 · 949651 · 4975503961<10> · 418225494423564917<18> · 221118619773890855246685841<27> · 6868671502290063230111711508454885225930210859465739472430659<61>
8·10126+3 =
8(0)1253<127>
= 11 · 103 · 227 · 60103 · 2949429481414692226044768697960391260971797<43> · 175468859339115509595120669476348065354330998690902949927637469395852909063<75> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 2.10 hours on Cygwin on AMD 64 3200+ / Aug 9, 2007)
8·10127+3 =
8(0)1263<128>
= 109 · 733944954128440366972477064220183486238532110091743119266055045871559633027522935779816513761467889908256880733944954128440367<126>
8·10128+3 =
8(0)1273<129>
= 112 · 78881689 · 10518172897<11> · 31189870538527<14> · 15581864538979112551<20> · 16396649515932494065701296267925360926143309101983646833808095861719319963723<77>
8·10129+3 =
8(0)1283<130>
= 4373 · 82883 · 9383621683393851037733688168129743757022677767<46> · 2352201687843988988161223366148433683159763965903221828415227547320810905051<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.89 hours on Cygwin on AMD XP 2700+ / Aug 9, 2007)
8·10130+3 =
8(0)1293<131>
= 7 · 11 · 73 · 1301 · 1879 · 3920377 · 125920165279<12> · 15660751854468820254646065544043536489389591847<47> · 753072171293408570603918263199513415256851689104201069517<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.27 hours on Cygwin on AMD 64 3200+ / Aug 9, 2007)
8·10131+3 =
8(0)1303<132>
= 31 · 18556133 · 140515311157889484872449865329<30> · 9897309858587474462533808559524778559507284816320764852168510088136599686173598612238548962409<94> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.46 hours on Cygwin on AMD 64 3400+ / Aug 9, 2007)
8·10132+3 =
8(0)1313<133>
= 11 · 10091 · 41507 · 72923 · 59137933926855043059088194258782854822196623669244767645811<59> · 402634584408763303069783264206996096355933083613814946383593<60> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 2.77 hours on Cygwin on AMD 64 3200+ / Aug 9, 2007)
8·10133+3 =
8(0)1323<134>
= 17 · 53 · 199 · 571 · 781404686078041874871538290553591912711548591811568479537585023300852847539770299645938699447036043629300874590125160421161107<126>
8·10134+3 =
8(0)1333<135>
= 11 · 149 · 43405903 · 643534253 · 99025999314875960050767509377639719951680928982163689<53> · 176457993407320655445898143590093815879839497274040644855506527<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.16 hours on Cygwin on AMD 64 3200+ / Aug 9, 2007)
8·10135+3 =
8(0)1343<136>
= 47 · 107 · 167 · 445141 · 64394703446581<14> · 671518907669361327306106053768429944141723<42> · 494864033010832382214144161118931762517426636975925163439107088158187<69> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.65 hours on Cygwin on AMD XP 2700+ / Aug 9, 2007)
8·10136+3 =
8(0)1353<137>
= 7 · 11 · 525529 · 3285647117<10> · 143530513309195232999340064204983398299225538897530547<54> · 4192155846886791687644896239201840126733252957278980362790474381809<67> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 2.95 hours on Cygwin on AMD 64 3400+ / Aug 9, 2007)
8·10137+3 =
8(0)1363<138>
= 234197724741713<15> · 3415917045659973707995573522830132950656230966488448714185425810779379160872606705826467649195998166540203490196881882061331<124>
8·10138+3 =
8(0)1373<139>
= 11 · 73 · 114702851 · 1670593388520748238821421178145481837<37> · 104636458414847985111598726280566932595983083<45> · 496874190989597803112505558533083407730421846981<48> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 5.54 hours on Cygwin on AMD 64 3200+ / Aug 10, 2007)
8·10139+3 =
8(0)1383<140>
= 23 · 8543458983547141<16> · 407125600563378075866452671220053277190892468365831516466241632483837061786795743263207884948689538425917458131593362006321<123>
8·10140+3 =
8(0)1393<141>
= 11 · 25554223 · 15891364671711296496697<23> · 179090862327462564452009054626614549314357041631189636105018439331780893059507069609327444017287416114796903583<111>
8·10141+3 =
8(0)1403<142>
= 56055709 · 364100444483<12> · 531838425845359<15> · 737002931992221038534166527565828073535776760460419692699121627832970580889326908528540386492382636610843611<108>
8·10142+3 =
8(0)1413<143>
= 7 · 11 · 2052821 · 555623953052671<15> · 66874197333983887<17> · 7352063485952674581275466674908134761977993<43> · 1852675630827404483230700868124109595424698262269677635106219<61> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 10.17 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 12, 2007)
8·10143+3 =
8(0)1423<144>
= 19 · 379 · 11813 · 221087 · 4516212432004069217<19> · 8406016943441479893959693<25> · 1120492986465098726033974583382789488826987710649084441975785272765641292908005564346173<88>
8·10144+3 =
8(0)1433<145>
= 11 · 683 · 393806677683834962330167370796793978219439105832001<51> · 2703918032157216794192284740946405968077357310935054868472060871084932805552853385839924731<91> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 6.79 hours on Cygwin on AMD 64 3200+ / Aug 10, 2007)
8·10145+3 =
8(0)1443<146>
= 11766775508491<14> · 605396612359960159<18> · 51046027337556414770008979411652470215926317473591<50> · 220004003518038430086171786263037474229055943495226606880307715457<66> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 7.75 hours on Cygwin on AMD 64 3200+ / Aug 11, 2007)
8·10146+3 =
8(0)1453<147>
= 11 · 31 · 53 · 73 · 1663 · 273919 · 1623467 · 423225567534437<15> · 1030135101140839<16> · 1880671419246688595464604866691528974862487144051760955949638153504473954417737826119959617250051<97>
8·10147+3 =
8(0)1463<148>
= 31466053047841<14> · 446393418652404001<18> · 2323850000470988610164769082031528440943605820371041061<55> · 245087883633789932212635585467307279310123198991773916587660103<63> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 18.83 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 17, 2007)
8·10148+3 =
8(0)1473<149>
= 7 · 11 · 29 · 317 · 509 · 13229 · 1633127480251888041774589540737718105895353<43> · 10277254618113551226936717541671467485926625997768564715394439356053800695383219974495822267431<95> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 17.86 hours on Cygwin on AMD XP 2700+ / Aug 16, 2007)
8·10149+3 =
8(0)1483<150>
= 17 · 65286080108845637650879<23> · 7385100750797983107672043705537569949<37> · 97603197957078940502415021668837796258378802054006942074636790201088264247159331747210129<89> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3224045903 for P37 / Aug 3, 2007)
8·10150+3 =
8(0)1493<151>
= 112 · 333847094812043<15> · 123915190735934296426572399348483454050629019309155367871597523<63> · 1598204928807240823149342852972588765245266509250337333568977262671359787<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 16.97 hours on Cygwin on AMD XP 2700+ / Aug 13, 2007)
8·10151+3 =
8(0)1503<152>
= 1131077 · 70729048508633806540138292972096506250237605397333691693845777077953136700684391955631667870534013157371248818603861629225950134252575200450544039<146>
8·10152+3 =
8(0)1513<153>
= 11 · 2579 · 28371454403<11> · 336678847633<12> · 3422844640710287449<19> · 20918851613784488258393673803<29> · 41230965182166976497662730773979766302299982947056022070519379750159227452766779<80>
8·10153+3 =
8(0)1523<154>
= 151 · 347 · 2843 · 1902048496423825078608398414836733249964757502655492013897910231644363411<73> · 28234826233775491249880369404044758618051858710202572340818371819411450863<74> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 26.88 hours on Cygwin on AMD XP 2700+ / Aug 11, 2007)
8·10154+3 =
8(0)1533<155>
= 72 · 11 · 73 · 6763250917489964555182738767583283902011275699423252245547421266789261<70> · 300623454884502196692218573721100636698457518684754797248879483662802680386190709<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 17.23 hours on Cygwin on AMD 64 3400+ / Aug 10, 2007)
8·10155+3 =
8(0)1543<156>
= 773 · 266449 · 3103527589<10> · 1251528627155639164199916747969826060711425922321229282587770871616682700815026262721404787403918692705714299304471900518721084606042891051<139>
8·10156+3 =
8(0)1553<157>
= 11 · 217489 · 350411 · 747131311 · 101603729565571469689<21> · 21328690499264043747847<23> · 5894018504747416231693659414080884214710672916599792947454431000326270305908773811988954517099<94>
8·10157+3 =
8(0)1563<158>
= 1243523 · 2355211711<10> · 1447349903160164528341<22> · 18872640887254146082294006254212089368658493319806297325592949968676605353833020130022985287385535952949960034686075647811<122>
8·10158+3 =
8(0)1573<159>
= 11 · 631 · 1250671907<10> · 40979175159967469<17> · 2248854384424882488961561751344764306410287459803078696649448310882043257096537712187210405199786375583248400385713503467823016201<130>
8·10159+3 =
8(0)1583<160>
= 53 · 1249 · 15803 · 153231313845746405825884701365885833226325571486615400562069271<63> · 49907361884479263130985185256128895476821348429200465525031812515377456758530477125109523<89> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 29.43 hours on Cygwin on AMD 64 3400+ / Aug 13, 2007)
8·10160+3 =
8(0)1593<161>
= 7 · 11 · 59 · 103 · 17191 · 15416167801<11> · 110265275957<12> · 5850509482617685466678711858680214178216504239137200505416320587381515785453594912361067953600933779570707101802765601106684653761<130>
8·10161+3 =
8(0)1603<162>
= 19 · 23 · 31 · 129126249073062336423461145334519<33> · 2631015527810085421291051911982281677569752486170207<52> · 173823667706511661436246647779256732900511330139840852735400152888111969953<75> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1730702291 for P33 / Aug 3, 2007) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 snfs / 65.82 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 16, 2007)
8·10162+3 =
8(0)1613<163>
= 11 · 73 · 563 · 1519506206599<13> · 11645645572705370842511370232719758223630265958429311476732548901555870142467162509939957997664258756251989201839808616696129890956171898763439373<146>
8·10163+3 =
8(0)1623<164>
= 263814841588028840292075635769021187187588777<45> · 2946574066938041203271903376456481181720414869700453<52> · 102913749296606783576701454837580698830029182185894558528664578737263<69> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 62.05 hours on Cygwin on AMD 64 3200+ / Aug 13, 2007)
8·10164+3 =
8(0)1633<165>
= 11 · 269 · 270361608651571476850287259209192294694153430212909766813112538019601216627238932071645826292666441365326123690435958093950659006421088205474822575194322406218317<162>
8·10165+3 =
8(0)1643<166>
= 17 · 83 · 2221 · 12653 · 1033040033209816345546009288939<31> · 19558081525904346337653953996359<32> · 31235192130845769254279459512560137999028121<44> · 319693142674609372256180538787347658839023974155301<51> (JMB / GMP-ECM B1=1000000, sigma=2461535803 for P32 / Aug 10, 2007) (JMB / GMP-ECM B1=1000000, sigma=3313357411 for P31 / Aug 14, 2007) (JMB / MSieve, version 1.25 / Aug 15, 2007)
8·10166+3 =
8(0)1653<167>
= 7 · 11 · 7207 · 213557 · 675042207726840501923943437063716431944375391927644166365098739719847433933733106431880955429652535398774532475286500174046221017501050758866213895714122261<156>
8·10167+3 =
8(0)1663<168>
= 251467910385709<15> · 126974570731714215575127079<27> · 837436146854618446845679601742976105039316057<45> · 29918440904777602878053870979485087624956432150490430623595618437356372457311766689<83> (Jo Yeong Uk / GMP-ECM 6.2 B1=1000000, sigma=127447873 for P45 / Jul 18, 2008)
8·10168+3 =
8(0)1673<169>
= 11 · 7508952959070127<16> · 67190157772167649<17> · 13469805809745432155725685004278020183984235651737<50> · 107016544227351834704803055140285312688017262106116130497648324056315093035478326557023<87> (Erik Branger / GGNFS, Msieve snfs / 78.19 hours / Nov 26, 2008)
8·10169+3 =
8(0)1683<170>
= 1224246060187948513536044665977519421<37> · 65346340577741579518249257770472291479731205704109850662463019782005485937532123816920926149530479698626097812995924318713137169466943<134> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=605871003 for P37 / Aug 12, 2007)
8·10170+3 =
8(0)1693<171>
= 11 · 73 · 25087 · 32666806785659<14> · 518810619846876503372769619770433<33> · 2343204381484500438488187466170885890773141731069741607646382933532921328434754372068190854059489563670232771599467309<118> (JMB / GMP-ECM B1=1000000, sigma=650741743 for P33 / Aug 14, 2007)
8·10171+3 =
8(0)1703<172>
= 612 · 4127 · 852049508559867811<18> · 41830988536643648556938375963<29> · 14616146588079515322204221559487489982957819195442464500318341681782225823320505611257273099132714329208444985035252613<119>
8·10172+3 =
8(0)1713<173>
= 7 · 112 · 53 · 261587 · 13420331 · 14742878852145643127878371424312249<35> · 14102707670245966200868549502313038790457<41> · 2441555056445183184204788723617272663411410204503080174188931011979879367292787673<82> (JMB / GMP-ECM B1=3000000, sigma=3195193927 for p35 / Aug 15, 2007) (Robert Backstrom / GMP-ECM 6.0.1 B1=2302000, sigma=733154304 for P41 / Apr 24, 2008)
8·10173+3 =
8(0)1723<174>
= 10399 · 18679 · 27631 · 28669 · 1023782077690866407<19> · [5078414167660249712387604108103770106232569588807573760842807059492552797592615923563863371986917242189753154173080121449260817395309242191<139>] SUBMIT/RESERVE
8·10174+3 =
8(0)1733<175>
= 11 · 28860413 · 78072669179616838037<20> · [322771910399903277511783412965868608527179674343956826500304757533948887978327882307645196978712434265037603027119954605083171829549768684013381033<147>] SUBMIT/RESERVE
8·10175+3 =
8(0)1743<176>
= 2311 · 8719 · 10144789 · 189170845637<12> · 64291971599470835512165635997396471<35> · 32178766751417498825847425179242872864738948414927779187900762406084025362150026649375978793241187540045915304472389<116> (JMB / GMP-ECM B1=1000000, sigma=3854916441 for P35 / Aug 11, 2007)
8·10176+3 =
8(0)1753<177>
= 11 · 29 · 31 · 97 · 62483 · 122288966750943559327954013<27> · 13203393905721557635469906716094551<35> · 4919037198222532817308550055704182012037503<43> · 1680548460217191645379213872474567141004274448100352481467434493<64> (JMB / GMP-ECM B1=1000000, sigma=265324565 for P35 / Aug 11, 2007) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P43 x P64 / 10.56 hours on Core 2 Quad Q6600 / Aug 12, 2007)
8·10177+3 =
8(0)1763<178>
= 385193 · 2734184657326888957539301452070127<34> · 7595979059565388610562921211099574234745355573365762780772087213624892584821367744840306376847974198287155385422756473803526652906088908773<139> (JMB / GMP-ECM B1=1000000, sigma=2128350113 for P34 / Aug 10, 2007)
8·10178+3 =
8(0)1773<179>
= 7 · 11 · 73 · 120504276263123<15> · 1521121596498992083430684328800554217699357191<46> · 77644377170813478936009808463885244242858683928639274087657213019286395263296774458233906745544656020639399572401451<116> (matsui / GGNFS-0.77.1-20060722-nocona snfs / 118.65 hours / May 16, 2009)
8·10179+3 =
8(0)1783<180>
= 19 · 7459 · 51407 · 2954417 · 836674876807247<15> · [44422704641645354838019828754369819311769539730617619841098627846322462375966966506075706508894195236760510406647593071916451097751211699429610824651<149>] SUBMIT/RESERVE
8·10180+3 =
8(0)1793<181>
= 11 · 5171 · 58979 · 2987999523284992099934311763<28> · [798077074490870019814933589592530611416215471014531931398466926930872807477792836399144022108346231914504813515112259796348416682854616465671019<144>] SUBMIT/RESERVE
8·10181+3 =
8(0)1803<182>
= 17 · 47 · 120077 · 766223541469<12> · 752719880879203667<18> · 148057738580234774662331071<27> · 147863869707137044125193702898663252618158313<45> · 66039126656639520936203017529360818061007971819918535640380875386612837009<74> (JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs for P45 x P74 / Sep 26, 2007)
8·10182+3 =
8(0)1813<183>
= 11 · 1973 · 84420643883<11> · [436638027434265521382407497695755974120320420083662072563992989339483058638184905637205373550580914558968285612117246429863833474833077545624178757503028310500667859247<168>] SUBMIT/RESERVE
8·10183+3 =
8(0)1823<184>
= 23 · 2515879 · [138252311401510859278381346085680452904894489551469235827803082463166084731005156344613725374951933559671952841721824010441367566287706136140472781774930525189251428885162566659<177>] SUBMIT/RESERVE
8·10184+3 =
8(0)1833<185>
= 7 · 11 · 2376827 · 2051700983727498703133<22> · 1110318608754654894718951253<28> · [191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693<129>] SUBMIT/RESERVE
8·10185+3 =
8(0)1843<186>
= 53 · 73691670258525152691437<23> · 204831015088781947568739792176466994498276644848090684973300137421436242140325974678514325315436546927563999424400488904909084698669115778137936077456388472890323<162>
8·10186+3 =
8(0)1853<187>
= 11 · 73 · 197 · 17401 · 3020497 · 220323797 · [4367110614744097463182398269261274287191734054762856708648451493363747023027729004417999049202068134236319131352234778728841221858194591240480790066971632465855537<163>] SUBMIT/RESERVE
8·10187+3 =
8(0)1863<188>
= 29837 · 17836048919020313496807619<26> · 150326718700801571261482640187071400500823957169070799823400912320987712536122844384584486226701092179304845411964672665222944185167552771742197754990530647301<159>
8·10188+3 =
8(0)1873<189>
= 11 · 107 · 293 · 5441115131<10> · 106511956593119726957069<24> · [4002760687156585027520347299378057399958901798137202599120195394771669507861856389534719265662524368421912847665684764903872596233232980770053434113057<151>] SUBMIT/RESERVE
8·10189+3 =
8(0)1883<190>
= 619 · 1847 · 2087 · 17854618292333<14> · 66686803592942902296799<23> · 921080685636059212526826174467963<33> · 17588503812768618802899470677477549249528890421<47> · 173817279856071866628575928062476489118502849448260284689789701413<66> (JMB / GMP-ECM B1=1000000, sigma=1799117052 for P33 / Aug 11, 2007) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs / 44.29 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Aug 14, 2007)
8·10190+3 =
8(0)1893<191>
= 7 · 11 · 4733 · 1676294884572518313001<22> · 811922358971434495608319<24> · [161286432681930695395431578191458011974762265535989812126587463390765928300135205920780808715841822754273284625937069221092684154285156421757<141>] SUBMIT/RESERVE
8·10191+3 =
8(0)1903<192>
= 31 · 2842729 · 66328803526681337<17> · [136864454205284996693790358712278009271559052224549185024306843802769166435276362177338276909574040689759318164705442311644374383283586162563996534995180590662998006781<168>] SUBMIT/RESERVE
8·10192+3 =
8(0)1913<193>
= 11 · 8191 · 54851 · 31110721 · 31559061199575423197<20> · [1648700138747607315730707585949407831903483228636011124338761685890251082645070982493556140316636906525975673773401372784932731939732245485766720763283402369<157>] SUBMIT/RESERVE
8·10193+3 =
8(0)1923<194>
= 8129428296305567387872785743237<31> · [9840790407900656066067629265440156194052735351485740152553562788802520276246454755383145153441343986651954238576587064493418247128625236538534767814847098071980519<163>] (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2872125755 for P31 / Aug 7, 2007) SUBMIT/RESERVE
8·10194+3 =
8(0)1933<195>
= 112 · 73 · 103 · 223 · 1447 · 2027 · 6271 · 214378184259679859014420218347192295318775051793914037272297999880788819147087705064389099351363290877973395753601856563888270455996778458050773433660857868551510312782551402361<177>
8·10195+3 =
8(0)1943<196>
= 499 · 237362465057<12> · [67542541422488969201470977999545917764885665583557500429379430951208203195002814115238183825696879910681007365148275294727350351492337354818545199496158280781987537154505038380683921<182>] SUBMIT/RESERVE
8·10196+3 =
8(0)1953<197>
= 72 · 11 · 3621665081282620076674432630274353389234788872072180469<55> · 40981979900057019772289486633568158426513623345700595433142245023700808306621864377405722307822200045704430796237062488553288170254983146933<140> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 38.35 hours, 3.85 hours / May 6, 2009)
8·10197+3 =
8(0)1963<198>
= 17 · 19 · 49701979 · 780808607 · 26076920319273076996675767301<29> · [2447444719548378339619829614249789627085695960053062447396841606685367979050190055438702256834046939845645421862753151405036735916578790278144353058537<151>] (JMB / GMP-ECM B1=1000000, sigma=2545770276 for P29 / Aug 10, 2007) SUBMIT/RESERVE
8·10198+3 =
8(0)1973<199>
= 11 · 53 · 1350678383321052486001773788083398163612589<43> · 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969<155> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=184675988 for P43 / Aug 25, 2009)
8·10199+3 =
8(0)1983<200>
= 1999 · 30221347231<11> · 178809515026945537373<21> · [7405813087236729613785003129716865196208350579008137252289697673195442592799136251425223509600217375085569541005574931526013112543150733301888712775050032951631902319<166>] SUBMIT/RESERVE
8·10200+3 =
8(0)1993<201>
= 11 · 607472219 · 147010366511382569644373<24> · 7546527715304377195290179372975899421<37> · [107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499<132>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4043050459 for P37 / Oct 21, 2008) SUBMIT/RESERVE

4. References

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