Factorizations of 500...003

Table of contents

1. About 500...003
   • First ten terms
   • General term
2. Prime numbers of the form 500...003
   • Last update
   • Searched up to
   • Difficulty of search
   • Results
3. Factorizations of 500...003
   • Last update
   • Completed up to
   • Range
   • Terms which have not been factored yet
   • Results
4. References

1. About 500...003

First ten terms

53, 503, 5003, 50003, 500003, 5000003, 50000003, 500000003, 5000000003, 50000000003

General term

5·10ⁿ+3

2. Prime numbers of the form 500...003

Last update

Aug 9, 2009

Searched up to

n≤10000

Difficulty of search

24.96%

Results

1. 5·10¹+3 = 53 is prime.
2. 5·10²+3 = 503 is prime.
3. 5·10³+3 = 5003 is prime.
4. 5·10⁸+3 = 500000003 is prime.
5. 5·10¹⁸+3 = 5(0)₁₇3_<19> is prime.
6. 5·10²⁰+3 = 5(0)₁₉3_<21> is prime.
7. 5·10³¹+3 = 5(0)₃₀3_<32> is prime.
8. 5·10⁴²+3 = 5(0)₄₁3_<43> is prime.
9. 5·10¹⁰³+3 = 5(0)₁₀₂3_<104> is prime. (searched by Makoto Kamada / Dec 3, 2004) (certified by Makoto Kamada / PFGW / Jan 2, 2005)
10. 5·10¹⁷⁵+3 = 5(0)₁₇₄3_<176> is prime. (searched by Makoto Kamada / Dec 3, 2004) (certified by Makoto Kamada / PFGW / Jan 2, 2005)
11. 5·10¹⁸¹+3 = 5(0)₁₈₀3_<182> is prime. (searched by Makoto Kamada / Dec 3, 2004) (certified by Makoto Kamada / PPSIQS / Jan 4, 2005)
12. 5·10⁵³¹+3 = 5(0)₅₃₀3_<532> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 30, 2006)
13. 5·10⁷⁰⁶+3 = 5(0)₇₀₅3_<707> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006)
14. 5·10¹⁰⁷⁷+3 = 5(0)₁₀₇₆3_<1078> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 14, 2006)
15. 5·10¹¹⁷⁷+3 = 5(0)₁₁₇₆3_<1178> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 11, 2006)
16. 5·10¹⁵⁵²+3 = 5(0)₁₅₅₁3_<1553> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 4, 2006)

3. Factorizations of 500...003

Last update

Nov 4, 2009

Completed up to

• n≤100 / Jan 4, 2005
• n≤150 / Jul 15, 2007

Range

n≤200

Terms which have not been factored yet

n=174, 177, 178, 182, 184, 190, 193, 194, 195, 197, 199, 200 (12/200)

Results

5·10¹+3 =

53

= definitely prime number

5·10²+3 =

503

= definitely prime number

5·10³+3 =

5003

= definitely prime number

5·10⁴+3 =

50003

= 31 · 1613

5·10⁵+3 =

500003

= 7 · 71429

5·10⁶+3 =

5000003

= 83 · 107 · 563

5·10⁷+3 =

50000003

= 491 · 101833

5·10⁸+3 =

500000003

= definitely prime number

5·10⁹+3 =

5000000003_<10>

= 149 · 33557047

5·10¹⁰+3 =

50000000003_<11>

= 3947 · 12667849

5·10¹¹+3 =

500000000003_<12>

= 7 · 607 · 117674747

5·10¹²+3 =

5000000000003_<13>

= 17 · 19 · 2447 · 6326063

5·10¹³+3 =

50000000000003_<14>

= 131 · 197 · 29363 · 65983

5·10¹⁴+3 =

500000000000003_<15>

= 53 · 349 · 27031410499_<11>

5·10¹⁵+3 =

5000000000000003_<16>

= 35855291 · 139449433

5·10¹⁶+3 =

50000000000000003_<17>

= 23 · 2297 · 252829 · 3743297

5·10¹⁷+3 =

500000000000000003_<18>

= 7 · 919 · 77724234416291_<14>

5·10¹⁸+3 =

5000000000000000003_<19>

= definitely prime number

5·10¹⁹+3 =

50000000000000000003_<20>

= 31 · 6079 · 265323774602147_<15>

5·10²⁰+3 =

500000000000000000003_<21>

= definitely prime number

5·10²¹+3 =

5000000000000000000003_<22>

= 57179 · 5077207 · 17222991151_<11>

5·10²²+3 =

50000000000000000000003_<23>

= 811 · 4943 · 12472644372729511_<17>

5·10²³+3 =

500000000000000000000003_<24>

= 7 · 29 · 2463054187192118226601_<22>

5·10²⁴+3 =

5000000000000000000000003_<25>

= 47 · 106382978723404255319149_<24>

5·10²⁵+3 =

50000000000000000000000003_<26>

= 199 · 991 · 253538124527785243067_<21>

5·10²⁶+3 =

500000000000000000000000003_<27>

= 46853 · 10671675239579109128551_<23>

5·10²⁷+3 =

5000000000000000000000000003_<28>

= 53 · 59 · 2104591 · 759756482347799579_<18>

5·10²⁸+3 =

50000000000000000000000000003_<29>

= 17 · 353 · 8331944675887352107982003_<25>

5·10²⁹+3 =

500000000000000000000000000003_<30>

= 7 · 3919 · 758405810021_<12> · 24032284101871_<14>

5·10³⁰+3 =

5000000000000000000000000000003_<31>

= 19 · 953 · 11815707734539_<14> · 23370271767211_<14>

5·10³¹+3 =

50000000000000000000000000000003_<32>

= definitely prime number

5·10³²+3 =

500000000000000000000000000000003_<33>

= 139 · 1399 · 2571209651292547091704763423_<28>

5·10³³+3 =

5000000000000000000000000000000003_<34>

= 11056091 · 491616683 · 919902475321705451_<18>

5·10³⁴+3 =

50000000000000000000000000000000003_<35>

= 31 · 79283 · 15393925741_<11> · 1321535543256512971_<19>

5·10³⁵+3 =

500000000000000000000000000000000003_<36>

= 7² · 179 · 69149 · 366893806043_<12> · 2246956213564399_<16>

5·10³⁶+3 =

5000000000000000000000000000000000003_<37>

= 1381 · 188603 · 952741 · 5302163 · 11131999 · 341371013

5·10³⁷+3 =

50000000000000000000000000000000000003_<38>

= 823 · 15972841 · 320859611 · 11854219044193544311_<20>

5·10³⁸+3 =

500000000000000000000000000000000000003_<39>

= 23 · 257 · 2011 · 4454299 · 17548455863_<11> · 538119463428139_<15>

5·10³⁹+3 =

5000000000000000000000000000000000000003_<40>

= 97 · 1559965879_<10> · 97759865719_<11> · 338004571812645299_<18>

5·10⁴⁰+3 =

50000000000000000000000000000000000000003_<41>

= 53 · 347 · 653 · 40193 · 79861 · 1649506973_<10> · 786343236668809_<15>

5·10⁴¹+3 =

500000000000000000000000000000000000000003_<42>

= 7 · 389 · 409 · 5743 · 418493 · 186797921971643578708178771_<27>

5·10⁴²+3 =

5000000000000000000000000000000000000000003_<43>

= definitely prime number

5·10⁴³+3 =

50000000000000000000000000000000000000000003_<44>

= 223 · 3847 · 58283141834356979581084089751375773563_<38>

5·10⁴⁴+3 =

500000000000000000000000000000000000000000003_<45>

= 17 · 970699463 · 315264813713_<12> · 96108276943703779480261_<23>

5·10⁴⁵+3 =

5000000000000000000000000000000000000000000003_<46>

= 95383 · 166277281610172003269_<21> · 315257996121076539889_<21>

5·10⁴⁶+3 =

50000000000000000000000000000000000000000000003_<47>

= 317 · 101207 · 173779 · 8968150684572007656776936763178403_<34>

5·10⁴⁷+3 =

500000000000000000000000000000000000000000000003_<48>

= 7 · 83 · 64811 · 13278381724315247796777873202130351695733_<41>

5·10⁴⁸+3 =

5000000000000000000000000000000000000000000000003_<49>

= 19 · 863 · 304933829359029090687320851375251570409221199_<45>

5·10⁴⁹+3 =

50000000000000000000000000000000000000000000000003_<50>

= 31 · 193 · 8357011532675915092762828012702657529667390941_<46>

5·10⁵⁰+3 =

500000000000000000000000000000000000000000000000003_<51>

= 227 · 683 · 58534097027240535143_<20> · 55095295959251801328567781_<26>

5·10⁵¹+3 =

5000000000000000000000000000000000000000000000000003_<52>

= 29 · 5861 · 29417129005877542375374332966599791726726638387_<47>

5·10⁵²+3 =

50000000000000000000000000000000000000000000000000003_<53>

= 32749 · 3558972331_<10> · 29085384481_<11> · 14749338414541363898106228077_<29>

5·10⁵³+3 =

500000000000000000000000000000000000000000000000000003_<54>

= 7 · 53 · 3809891 · 91510157 · 240221858056469_<15> · 16091692378493428511531_<23>

5·10⁵⁴+3 =

5000000000000000000000000000000000000000000000000000003_<55>

= 46261 · 392684768327_<12> · 35295194285332489_<17> · 7798217700500651888041_<22>

5·10⁵⁵+3 =

50000000000000000000000000000000000000000000000000000003_<56>

= 10102595440132567406550851_<26> · 4949223226476531491438676389953_<31>

5·10⁵⁶+3 =

500000000000000000000000000000000000000000000000000000003_<57>

= 379 · 977 · 1087621 · 6727485300773_<13> · 184546532145417521101908247004177_<33>

5·10⁵⁷+3 =

5000000000000000000000000000000000000000000000000000000003_<58>

= 433 · 21613517 · 534264928324922938927673513586476428661285292223_<48>

5·10⁵⁸+3 =

50000000000000000000000000000000000000000000000000000000003_<59>

= 61 · 1009 · 3623 · 9137 · 89867 · 928148539 · 829575336381901_<15> · 354652873447672069_<18>

5·10⁵⁹+3 =

500000000000000000000000000000000000000000000000000000000003_<60>

= 7 · 107 · 1679641 · 8255453 · 152778774688461206737_<21> · 315114064590027073770947_<24>

5·10⁶⁰+3 =

5000000000000000000000000000000000000000000000000000000000003_<61>

= 17 · 23 · 353 · 55547 · 1801549 · 20071516765709788013_<20> · 18035644307512020473625799_<26>

5·10⁶¹+3 =

50000000000000000000000000000000000000000000000000000000000003_<62>

= 487 · 68659499 · 1495341591663140431129087408437897497393539829257231_<52>

5·10⁶²+3 =

500000000000000000000000000000000000000000000000000000000000003_<63>

= 964061489687_<12> · 9379273348781507513_<19> · 55296300467873121298489939248413_<32>

5·10⁶³+3 =

5000000000000000000000000000000000000000000000000000000000000003_<64>

= 269 · 18587360594795539033457249070631970260223048327137546468401487_<62>

5·10⁶⁴+3 =

50000000000000000000000000000000000000000000000000000000000000003_<65>

= 31 · 97039 · 16621185562572281380715236208654385383462385758436332050067_<59>

5·10⁶⁵+3 =

500000000000000000000000000000000000000000000000000000000000000003_<66>

= 7 · 77383 · 923052497687753493292177499303095364245746112564405988026163_<60>

5·10⁶⁶+3 =

5000000000000000000000000000000000000000000000000000000000000000003_<67>

= 19 · 53 · 109 · 161814173 · 281512366641983858237678980579702094481390934249786997_<54>

5·10⁶⁷+3 =

50000000000000000000000000000000000000000000000000000000000000000003_<68>

= 151 · 2952913 · 2940403168993_<13> · 87780946932937_<14> · 434445458499472845535660211291741_<33>

5·10⁶⁸+3 =

500000000000000000000000000000000000000000000000000000000000000000003_<69>

= 6240836117_<10> · 102789413199797_<15> · 779433089899991989110704703313079188033682747_<45>

5·10⁶⁹+3 =

5000000000000000000000000000000000000000000000000000000000000000000003_<70>

= 1663 · 147227767 · 2384032997_<10> · 8565954590598526685670743287535875319826645623119_<49>

5·10⁷⁰+3 =

50000000000000000000000000000000000000000000000000000000000000000000003_<71>

= 47 · 751 · 11423 · 2176374330047_<13> · 6532322710476609889_<19> · 8722697390504230048895798797411_<31>

5·10⁷¹+3 =

500000000000000000000000000000000000000000000000000000000000000000000003_<72>

= 7 · 27107 · 19694704307_<11> · 83887747003342561_<17> · 1594933254404032348498814610541821137261_<40>

5·10⁷²+3 =

5000000000000000000000000000000000000000000000000000000000000000000000003_<73>

= 1951 · 28236083 · 3257582762131_<13> · 27862034580050919463307956209849711034004812471861_<50>

5·10⁷³+3 =

50000000000000000000000000000000000000000000000000000000000000000000000003_<74>

= 2458369 · 186255721 · 109197655021346519032188868746864673772325722708428922430347_<60>

5·10⁷⁴+3 =

500000000000000000000000000000000000000000000000000000000000000000000000003_<75>

= 113 · 1367 · 3236853519430831677143282557891125195020424545707608547882774112940293_<70>

5·10⁷⁵+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000003_<76>

= 1391278548773_<13> · 3593816640391396113855304555439641249068664080681220038212949511_<64>

5·10⁷⁶+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000003_<77>

= 17 · 914237 · 51585917 · 615543491473607_<15> · 101314683185894239551114563306314916300880780653_<48>

5·10⁷⁷+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000003_<78>

= 7³ · 75337 · 19349402651046177697715969421906797719912830167080930927624681649115533_<71>

5·10⁷⁸+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000003_<79>

= 139 · 35971223021582733812949640287769784172661870503597122302158273381294964028777_<77>

5·10⁷⁹+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000003_<80>

= 29 · 31 · 53² · 6217 · 59353297 · 8427422669_<10> · 6367047377656506462904155066986354326719808015871093_<52>

5·10⁸⁰+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000003_<81>

= 631 · 1075771 · 59752210914727863661279_<23> · 12327267863683037631960515363901872892062001409457_<50>

5·10⁸¹+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000003_<82>

= 4259 · 1552251396894823280891_<22> · 148457018476693417664950589_<27> · 5094476587689179975610939251983_<31>

5·10⁸²+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000003_<83>

= 23 · 4398173539_<10> · 874965724061328499_<18> · 1405617153215469079_<19> · 401894181192586916650815560145826219_<36>

5·10⁸³+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000000003_<84>

= 7 · 36071941452443329_<17> · 2300363559615287218357043_<25> · 860807352173688904077437529359880857107207_<42>

5·10⁸⁴+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<85>

= 19² · 421 · 24181 · 1010117135473163_<16> · 1346898009406529223327940117955488165597586573906124580504921_<61>

5·10⁸⁵+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<86>

= 59 · 114414247 · 41171227740870361_<17> · 93013262654070633768573203_<26> · 1934190248802853050684809734724717_<34>

5·10⁸⁶+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<87>

= 8191 · 61042607740202661457697472836039555609815651324624587962397753632035160542058356733_<83>

5·10⁸⁷+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<88>

= 1015349 · 1532507 · 3330409 · 78384201665678636303903501861_<29> · 12309093795615004924776021889954551509929_<41>

5·10⁸⁸+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<89>

= 83 · 999828754498801_<15> · 137688575402049362965673005049117_<33> · 4375910015802456779964680584557999666773_<40> (Makoto Kamada / msieve 0.81 / 5.8 minutes)

5·10⁸⁹+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<90>

= 7 · 4729 · 147487 · 1799897942758773045413_<22> · 56898527585042673029472232819497892488272923031472385106071_<59>

5·10⁹⁰+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<91>

= 1172507923409530160430980839447069_<34> · 4264363506781706010639612444247484405646223517613650045087_<58> (Makoto Kamada / GGNFS-0.70.3 / 0.22 hours)

5·10⁹¹+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<92>

= 4211 · 309172364789_<12> · 63965188254948038831773448357514251_<35> · 600399625571213025489918330607991148393607_<42> (Makoto Kamada / msieve 0.83 / 14 minutes)

5·10⁹²+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<93>

= 17 · 53 · 353 · 1021 · 10651 · 4796118223711_<13> · 30141475017152446658517232590409850398172859190985867927921020636471_<68>

5·10⁹³+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<94>

= 90128760589243643561619256691730383092807_<41> · 55476187260437282036868709902133261637660094894409829_<53> (Makoto Kamada / GGNFS-0.70.7 / 0.39 hours)

5·10⁹⁴+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<95>

= 31 · 72620645868563173343_<20> · 19286687324592734936063_<23> · 17927430443998405953241699_<26> · 64235116700341599654502943_<26>

5·10⁹⁵+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<96>

= 7 · 176507 · 446041 · 31830437 · 10225181741_<11> · 2787543241477667783403610272474345922702013146942423703332326626551_<67>

5·10⁹⁶+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<97>

= 762667462116924669758247090489861920682702481277_<48> · 6555937218196741695801550898218372577739396832639_<49> (Makoto Kamada / GGNFS-0.70.7 / 0.46 hours)

5·10⁹⁷+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<98>

= 941 · 40927 · 390491 · 70228999 · 253795301693352795581_<21> · 186534593164781287357321331812963179886263954927271847401_<57>

5·10⁹⁸+3 =

500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<99>

= 420785350832911_<15> · 44186432061632719_<17> · 44648887351839256399_<20> · 1627023998074869019103_<22> · 370182477871326723400149811_<27>

5·10⁹⁹+3 =

5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<100>

= 859493 · 2698836149_<10> · 46606393157_<11> · 201991350982876187_<18> · 6930035321787863868408416051_<28> · 33039801179985499802003182831_<29>

5·10¹⁰⁰+3 =

50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<101>

= 28903494311221_<14> · 35433579205312085193587_<23> · 881356810145768386810291_<24> · 55392742297889665879812947278570656198079_<41>

5·10¹⁰¹+3 =

5(0)₁₀₀3_<102>

= 7 · 19999297 · 49766137 · 69229464001_<11> · 12612692590259314008604763383_<29> · 82191049054613077031122732232691363349783303067_<47>

5·10¹⁰²+3 =

5(0)₁₀₁3_<103>

= 19 · 162623 · 676909 · 181097177 · 346247253640091932231_<21> · 38124673116508318887370655005740219912736845196103157426773093_<62>

5·10¹⁰³+3 =

5(0)₁₀₂3_<104>

= definitely prime number

5·10¹⁰⁴+3 =

5(0)₁₀₃3_<105>

= 23 · 4937 · 103177537189_<12> · 42677000098645109324308290726585519293533411209782702927345171483821485714344207412464777_<89>

5·10¹⁰⁵+3 =

5(0)₁₀₄3_<106>

= 53 · 1901 · 710051 · 11430203 · 1112199245327374990611151_<25> · 5497761996707844977724388584029597517146142849063721507614356717_<64>

5·10¹⁰⁶+3 =

5(0)₁₀₅3_<107>

= 1621 · 11717 · 96703376493620307418141_<23> · 27222557349131022163291502450760695089748925325604647937096952630760247896519_<77>

5·10¹⁰⁷+3 =

5(0)₁₀₆3_<108>

= 7 · 29 · 2463054187192118226600985221674876847290640394088669950738916256157635467980295566502463054187192118226601_<106>

5·10¹⁰⁸+3 =

5(0)₁₀₇3_<109>

= 17 · 587 · 1279 · 42083 · 31574329 · 33785145833_<11> · 8726615021574227019550590292567300416626509252436250133495291885139609885644493_<79>

5·10¹⁰⁹+3 =

5(0)₁₀₈3_<110>

= 31 · 30391 · 53071739192736389487125326789234079274318266974199704708843131614728893634681744701582917693162555552843_<104>

5·10¹¹⁰+3 =

5(0)₁₀₉3_<111>

= 181 · 140869 · 11063288894785937_<17> · 6039261878537983804809377055481_<31> · 293499849169094259922144875395852639709254512750131598291_<57> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.51 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹¹¹+3 =

5(0)₁₁₀3_<112>

= 197 · 1283 · 1568123 · 187503779304601503581_<21> · 514518939710253831299_<21> · 130763219671540435495217673836027799045080694557054765098369_<60>

5·10¹¹²+3 =

5(0)₁₁₁3_<113>

= 107 · 1307 · 13028359 · 16956931 · 19979299 · 1885793599_<10> · 257539314091_<12> · 1285526516447_<13> · 7683151853911_<13> · 10915764011597_<14> · 1546967309963728120162537277_<28>

5·10¹¹³+3 =

5(0)₁₁₂3_<114>

= 7 · 337 · 370704791593_<12> · 571760124756203207111421010779436699943573302892601652250624532679408487285021037322799934126403469_<99>

5·10¹¹⁴+3 =

5(0)₁₁₃3_<115>

= 316469363851_<12> · 1081354250785203149101117499513_<31> · 33280544906954346861035663714839_<32> · 439015556833735689338180321004768868727479_<42> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.54 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹¹⁵+3 =

5(0)₁₁₄3_<116>

= 1801 · 53693 · 95436841 · 10577844127_<11> · 10231135104177199_<17> · 13047158872579191461385245774333_<32> · 3836945517031630316195569878396294937246859_<43> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3062116458 for P32 / Jul 5, 2007)

5·10¹¹⁶+3 =

5(0)₁₁₅3_<117>

= 47 · 80071 · 306437 · 1987703 · 63855381214883_<14> · 21154501478439364069_<20> · 161474482564732608964784497483670363380086179206807934842681777127_<66>

5·10¹¹⁷+3 =

5(0)₁₁₆3_<118>

= 67639007175241_<14> · 959920477452168131953_<21> · 8882987148662865123217_<22> · 8669189372599413963937258433861366490975991382760707781192683_<61>

5·10¹¹⁸+3 =

5(0)₁₁₇3_<119>

= 53 · 61 · 7417037 · 116452580393_<12> · 100025451298640466942990019_<27> · 69193464626049628817643522282497_<32> · 2587075728644263778201293352077733123357_<40> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=580784386 for P32 / Jul 5, 2007)

5·10¹¹⁹+3 =

5(0)₁₁₈3_<120>

= 7² · 71843 · 90543020753040293576959578835244863827338385803_<47> · 1568680455115318344001740770037613906724896970510571219229245382643_<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 0.79 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹²⁰+3 =

5(0)₁₁₉3_<121>

= 19 · 134597 · 558083 · 1698377 · 14830426043_<11> · 178545183437_<12> · 6615705888443_<13> · 869534162635048412617189_<24> · 135420222955486281342936174320416216393490783_<45>

5·10¹²¹+3 =

5(0)₁₂₀3_<122>

= 25471 · 548719 · 3577453604054472240686475872076060031580119080879340748916182043557349462446802287368512689896452336202696942547_<112>

5·10¹²²+3 =

5(0)₁₂₁3_<123>

= 10429 · 13016717839_<11> · 156557721619969_<15> · 1754709718977289_<16> · 2222035728477287_<16> · 1377019286670908784926607287_<28> · 4381824822381470268103344915542062697_<37>

5·10¹²³+3 =

5(0)₁₂₂3_<124>

= 29103572282156559112182740936226932631374490509_<47> · 171800215847231475291585450337672992777067604341481417436023086954002453065167_<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.06 hours on Core 2 Quad Q6600 / Jul 13, 2007)

5·10¹²⁴+3 =

5(0)₁₂₃3_<125>

= 17 · 31 · 139 · 199 · 353 · 17749 · 4211985913711273004737734377_<28> · 128040753937687879477084697015491_<33> · 1015097562328485295738336683852546474132803693053831_<52> (Jo Yeong Uk / Msieve v. 1.21 for P33 x P52 / 00:21:25 on Core 2 Quad Q6600 / Jul 13, 2007)

5·10¹²⁵+3 =

5(0)₁₂₄3_<126>

= 7 · 317 · 8380969 · 114941807971087_<15> · 4767017037828203_<16> · 49067478362324376456479774885211551370446703191142766443539812337024088376179137517293_<86>

5·10¹²⁶+3 =

5(0)₁₂₅3_<127>

= 23 · 32869 · 1771845148714035530042375961149100976639_<40> · 3732758672015730547173100481173208742246650750942529540645311897013388939508906671_<82> (Jo Yeong Uk / GMP-ECM B1=1000000, sigma=1186508037 for P40 / Jul 14, 2007)

5·10¹²⁷+3 =

5(0)₁₂₆3_<128>

= 1063 · 19759 · 9528013351973_<13> · 231486198826356536297596881484840829_<36> · 1079305320539789652825036330387473369897040690627974500945419108513238427_<73> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=1941662947 for P36 / Jul 14, 2007)

5·10¹²⁸+3 =

5(0)₁₂₇3_<129>

= 824220383604228418854258476629_<30> · 778977109190834486013530928931812523699_<39> · 778756989881128479103802248680558442310201163296540906795693_<60> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2699720113 for P30 / Jul 6, 2007) (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 2.38 hours on Cygwin on AMD 64 3400+ / Jul 14, 2007)

5·10¹²⁹+3 =

5(0)₁₂₈3_<130>

= 83 · 9112993 · 6610447726166549973975394451332171072956009338494889024590216395372856347981022975220555572196990459083946973373390231537_<121>

5·10¹³⁰+3 =

5(0)₁₂₉3_<131>

= 349 · 223050252687486781077222133508703494233225969_<45> · 642305820856559171936319435779114051384175861818268799381835937621892642342986131663_<84> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 1.97 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹³¹+3 =

5(0)₁₃₀3_<132>

= 7 · 53 · 4048842607_<10> · 523541404697611061806834745219853229328170446317_<48> · 635790693115827427508005325491084683125703813484245526914108384957137147_<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.42 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹³²+3 =

5(0)₁₃₁3_<133>

= 16187 · 18572566704029876782615951371188489713635855833627934104693_<59> · 16631511131550278291805996309948604657716454712748581690326108061640533_<71> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.52 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹³³+3 =

5(0)₁₃₂3_<134>

= 11057031539_<11> · 886544732452880113982144287654486535090287_<42> · 5100711993689431955514377563639991758308507294250704290195426082082810455667928671_<82> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 2.78 hours on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹³⁴+3 =

5(0)₁₃₃3_<135>

= 263 · 5903 · 11971 · 278147 · 16482571679993_<14> · 5868291632963730471838954369553973220736366210274717393253287404971603430766504804331656302563208217332747_<106>

5·10¹³⁵+3 =

5(0)₁₃₄3_<136>

= 29 · 97 · 293 · 12415969 · 8179360663_<10> · 3544624710199_<13> · 502246085292724499_<18> · 103888204664039275506234925332227_<33> · 322982960901345113517889401979443805784667940709243_<51> (Jo Yeong Uk / Msieve v. 1.21 for P33 x P51 / 00:17:15 on Core 2 Quad Q6600 / Jul 13, 2007)

5·10¹³⁶+3 =

5(0)₁₃₅3_<137>

= 229 · 82132721813_<11> · 5824999790723064946307734440392437977214744000689735893063_<58> · 456375574500296265791802787296814526424506695836333278231520021053_<66> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 5.26 hours on Cygwin on AMD 64 3200+ / Jul 15, 2007)

5·10¹³⁷+3 =

5(0)₁₃₆3_<138>

= 7 · 3343 · 1231884389_<10> · 14133656423605033089328341238732583072598888641345800951_<56> · 1227188017945406154897963678957290689881567366655657179710045847933577_<70> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 6.48 hours on Cygwin on AMD XP 2700+ / Jul 15, 2007)

5·10¹³⁸+3 =

5(0)₁₃₇3_<139>

= 19 · 1847 · 2243 · 1854888679869283637_<19> · 34245411060208811631845963850057003813261211150174679440970851907502195211520682605734863208860691750207700435881_<113>

5·10¹³⁹+3 =

5(0)₁₃₈3_<140>

= 31² · 13757 · 1676267 · 5477477407_<10> · 914935539886441_<15> · 17576529389171235892873769570959_<32> · 25613885676592741147760266044980021990273525624421672846346548400112549_<71> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3401522408 for P32 / Jul 7, 2007)

5·10¹⁴⁰+3 =

5(0)₁₃₉3_<141>

= 17² · 1373153 · 15490764900917_<14> · 319431831015906441432555931_<27> · 254625665901514898141664498789886532707133045914495460376688572293867265692738371876322076917_<93>

5·10¹⁴¹+3 =

5(0)₁₄₀3_<142>

= 419 · 8814679 · 820452221 · 1264532627_<10> · 1304866692393062556786750201496972923992670107959398922183378289671457073707297377923507000277567238580923722862209_<115>

5·10¹⁴²+3 =

5(0)₁₄₁3_<143>

= 151 · 1207221004937_<13> · 450592298232999465856873727_<27> · 608726921836642240976758217841530281701416949077763948523572993771478344517382951480137814937359007347_<102>

5·10¹⁴³+3 =

5(0)₁₄₂3_<144>

= 7 · 59 · 131 · 19163 · 23789 · 96365852833312759_<17> · 81671235362417718269737_<23> · 137584931502707732683063_<24> · 45841742692394767309895959_<26> · 408399015003123572141614553519801012571413_<42>

5·10¹⁴⁴+3 =

5(0)₁₄₃3_<145>

= 53 · 8915485535218874463020966252542555006448848732763244901456195853393_<67> · 10581546262269091742312886939766011985159784242637011168380827339866200032807_<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 7.42 hours on Cygwin on AMD 64 3200+ / Jul 15, 2007)

5·10¹⁴⁵+3 =

5(0)₁₄₄3_<146>

= 10903 · 323797439456498340561904697913457873787_<39> · 2465188889777582684991267296272427043966702509_<46> · 5745136880246153704523428561631148137811827694096870119147_<58> (JMB / GMP-ECM B1=1000000, sigma=3545776710 for P39 / Jul 14, 2007) (JMB / GGNFS / Jul 15, 2007)

5·10¹⁴⁶+3 =

5(0)₁₄₅3_<147>

= 167 · 218145541 · 410197723711_<12> · 93608508393331353137_<20> · 357436272055582929707974317324577158309861213723960622293612294882451166203030222793037973760928293170607_<105>

5·10¹⁴⁷+3 =

5(0)₁₄₆3_<148>

= 82106351993586265631239_<23> · 138949891016035954229041_<24> · 2969683976039291151435611_<25> · 147579080976547109286694585045799451429111810694887599444933015273486191902127_<78>

5·10¹⁴⁸+3 =

5(0)₁₄₇3_<149>

= 23 · 122117 · 553249 · 2522659 · 13292482722648700239840631_<26> · 15947741321569901709147142457_<29> · 7037119119859597676550832006219_<31> · 8550404596993401489765767474006096463155418031_<46> (Makoto Kamada / Msieve 1.25 for P31 x P46 / 10 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Jul 13, 2007)

5·10¹⁴⁹+3 =

5(0)₁₄₈3_<150>

= 7 · 1931 · 5243209539041849099760187057760329315540666673453359958582230909941313_<70> · 7054926221581529213954354507669417037749392705948230321975121930804768049743_<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 10.32 hours on Core 2 Quad Q6600 / Jul 15, 2007)

5·10¹⁵⁰+3 =

5(0)₁₄₉3_<151>

= 1245381079_<10> · 232068384169_<12> · 3281330425711817_<16> · 3983269107490187761662938933_<28> · 1323616429220128741691304002012098418070492757816238358912574567043595352601660216811473_<88>

5·10¹⁵¹+3 =

5(0)₁₅₀3_<152>

= 443 · 947 · 16270985621257205906905273044911329_<35> · 1985841848915255165882503532099473704607_<40> · 3688567872296026104787199609577180339676172266118012744852132484083849981_<73> (Robert Backstrom / GMP-ECM 5.0 B1=891500, sigma=1474273551 for P35, GGNFS-0.77.1-20060513-athlon-xp / 19.96 hours on Cygwin on AMD 64 3200+ / Jul 16, 2007)

5·10¹⁵²+3 =

5(0)₁₅₁3_<153>

= 14869 · 135268966532217716081858222979343678676268459159986363363_<57> · 248593672856895851344394797338957581879512075361661154360125070884478563005695290561420504349_<93> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 24.70 hours on Cygwin on AMD XP 2700+ / Jul 16, 2007)

5·10¹⁵³+3 =

5(0)₁₅₂3_<154>

= 1109 · 4508566275924256086564472497745716862037871956717763751127141568981064021641118124436429215509467989179440937781785392245266005410279531109107303877367_<151>

5·10¹⁵⁴+3 =

5(0)₁₅₃3_<155>

= 31 · 4021 · 167160802616143494509108495516497129_<36> · 2399605173928420299498820740137566306845129879546122780196166540333527775067120892884179276851300720910497809301857_<115> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 18.03 hours on Cygwin on AMD 64 3400+ / Jul 15, 2007)

5·10¹⁵⁵+3 =

5(0)₁₅₄3_<156>

= 7 · 55469 · 1287720554337944231398232732311226605336829065398176072606835735790647543157954378636200915311770023410759677863826126819871073418099685023552408938841_<151>

5·10¹⁵⁶+3 =

5(0)₁₅₅3_<157>

= 17 · 19 · 353 · 9781 · 2903959 · 3738923 · 48999199953669556762469285191647229_<35> · 16220542161012079506892689114089790259652611_<44> · 519539008028015605717126723388083053475004321678810798119_<57> (JMB / GMP-ECM B1=1000000, sigma=2562771777 for P35 / Jul 14, 2007) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P44 x P57 / 3.73 hours on Core 2 Quad Q6600 / Jul 15, 2007)

5·10¹⁵⁷+3 =

5(0)₁₅₆3_<158>

= 53 · 149 · 13437119575793745653860491268913351112372015271429983467581637225087533319599_<77> · 471196096929417376262628665137399248660726397583286864726053838970722199918901_<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 29.27 hours on Cygwin on AMD 64 3200+ / Jul 16, 2007)

5·10¹⁵⁸+3 =

5(0)₁₅₇3_<159>

= 23535093831695777_<17> · 3336615942677038549001641449007892174836007_<43> · 6367190586858022590177464026314548769045456613292917746979423848926661873487443619330012203341779877_<100> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 29.31 hours on Cygwin on AMD 64 3400+ / Jul 16, 2007)

5·10¹⁵⁹+3 =

5(0)₁₅₈3_<160>

= 83066365779588590821426749068056416859826527_<44> · 60192834405048939466899798943567903902651745875844194867985009267232595787118690954252254004124505688435636777703389_<116> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 24.58 hours on Core 2 Quad Q6600 / Jul 15, 2007)

5·10¹⁶⁰+3 =

5(0)₁₅₉3_<161>

= 2207 · 7760503636757_<13> · 120355074834623_<15> · 82551714075637674821552052888550681_<35> · 1770092901260328461943147499208826822490849_<43> · 165993545605717346668480035353143215370070055379374031_<54> (JMB / GMP-ECM B1=1000000, sigma=2567545950 for P35 / Jul 14, 2007) (Jo Yeong Uk / Msieve v. 1.21 for P43 x P54 / 03:16:10 on Core 2 Quad Q6600 / Jul 15, 2007)

5·10¹⁶¹+3 =

5(0)₁₆₀3_<162>

= 7² · 1447 · 180463 · 26314542158435393005535533221629_<32> · 11706943567107084998551285511603272813010623152246453284257_<59> · 126846321501220363453898438705886991913400990993746411945018359_<63> (JMB / GMP-ECM B1=1000000, sigma=1129548668 for P32 / Jul 14, 2007) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 80.52 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jul 19, 2007)

5·10¹⁶²+3 =

5(0)₁₆₁3_<163>

= 47 · 11117 · 5487049 · 1743996874287927570615560828385603584978842879167210331182020108181733721422878319766121326268352912079842952192701661035149571920584229278614898636153_<151>

5·10¹⁶³+3 =

5(0)₁₆₂3_<164>

= 29 · 227 · 1372379 · 3452401427_<10> · 1652368488234263596749387089016071429414818510198454291329_<58> · 970161182233720701578804573039325030395254397715312007695070136323727969873955547645013_<87> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.31 / Dec 18, 2007)

5·10¹⁶⁴+3 =

5(0)₁₆₃3_<165>

= 557 · 217837300066202477_<18> · 1196687247426772242533735797290481529635161715296376005028120547_<64> · 3443514377361480174374528664126918435300112338137700545497427175846407441531435641_<82> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.32 / Jan 9, 2008)

5·10¹⁶⁵+3 =

5(0)₁₆₄3_<166>

= 107 · 3347 · 76127449 · 526115281 · 8629342554611_<13> · 669110924591646330515236469_<27> · 90824126989341694860705521906459719377905473_<44> · 664708541046310574292268644887995665738412289611807142993429_<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P44 x P60 / 6.17 hours on Core 2 Quad Q6600 / Jul 15, 2007)

5·10¹⁶⁶+3 =

5(0)₁₆₅3_<167>

= 58411 · 205212516206615635610167665320053000460472202204809200220862876866413_<69> · 4171300883176815364229387134807678863679793387097531618573030009987940624111825593896704727821_<94> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 80.81 hours on Cygwin on AMD XP 2700+ / Jul 20, 2007)

5·10¹⁶⁷+3 =

5(0)₁₆₆3_<168>

= 7 · 773 · 8329 · 66986389608208370945649030468786635518218514529828739674619854324867_<68> · 165620097981775245286549676152338224696848100622028775546996783901831190108848495803829997811_<93> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.32 / Dec 28, 2007)

5·10¹⁶⁸+3 =

5(0)₁₆₇3_<169>

= 30261601 · 890150258236321_<15> · 498727304848409587637_<21> · 142978063635046612431340573579_<30> · 12718944880656352612135685179437522176294183_<44> · 204659137232336784991399810699824456814839775637627027_<54> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1087748790 for P30 / Jul 9, 2007) (Jo Yeong Uk / Msieve v. 1.21 for P44 x P54 / 04:25:25 on Core 2 Quad Q6600 / Jul 14, 2007)

5·10¹⁶⁹+3 =

5(0)₁₆₈3_<170>

= 31 · 16244243 · 29298332253113065055747_<23> · 219470599991522042446043080605252718567618567796903842516245509_<63> · 15441503431769976028446348762595181204879730780351588237227771804855548607617_<77> (matsui / GGNFS-0.77.1-20060722-nocona / Apr 23, 2009)

5·10¹⁷⁰+3 =

5(0)₁₆₉3_<171>

= 23² · 53 · 83 · 139 · 16067 · 187471 · 10244358647_<11> · 21800705213641_<14> · 2297848350912936021727670498427026103832182756085324531838897331823600222770129524405223296299394736813992554953763915717858142333_<130>

5·10¹⁷¹+3 =

5(0)₁₇₀3_<172>

= 2141 · 3463 · 22115239687_<11> · 2126176738288566290549353_<25> · 147260649364933694278877144916097788377722854278739967_<54> · 97391963406433881857367240605552004713811188886749910103549282496731302376393_<77> (Markus Tervooren / Msieve 1.42 snfs / 30.58 hours / Sep 30, 2009)

5·10¹⁷²+3 =

5(0)₁₇₁3_<173>

= 17 · 9089719 · 870832992287_<12> · 13385200156201_<14> · 47347314846917_<14> · 724273923844727_<15> · 199380097814707075827853407010411667_<36> · 4060045237533688631179618384328067264911276818684333348445532508588775649451_<76> (JMB / GMP-ECM B1=1000000, sigma=3089909484 for P36 / Jul 14, 2007)

5·10¹⁷³+3 =

5(0)₁₇₂3_<174>

= 7 · 313 · 169061906987_<12> · 59249254073379949902901368057587_<32> · 22782373957682117221393919745453826568924577598689253992144435924521117243880060681895434415464594199441242777852408944634407357_<128> (suberi / GMP-ECM 6.1.2 B1=1000000, sigma=2699943498 for P32 / Jul 15, 2007)

5·10¹⁷⁴+3 =

5(0)₁₇₃3_<175>

= 19 · 109 · 22313393 · 2476448641_<10> · [43691299823166622677419713765955366740192160053158913276378951487613075749335919745960807708172852610403720149520728363974918064390555131663772617267686661_<155>] SUBMIT/RESERVE

5·10¹⁷⁵+3 =

5(0)₁₇₄3_<176>

= definitely prime number

5·10¹⁷⁶+3 =

5(0)₁₇₅3_<177>

= 233 · 167483 · 164607553791153072943705556256499_<33> · 77838344545335028846811880278194243230332959322516120862226515570460253216262769544776639596904080563916319548577503073466720983267686923_<137> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2250673457 for P33 / Jul 10, 2007)

5·10¹⁷⁷+3 =

5(0)₁₇₆3_<178>

= 176218992155079534631185354899_<30> · [28373786155806670640998399527341074498848269897625772403660234914777229704006772677455191720133985486886631783071384944023777763803864984794834905297_<149>] (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=3025299345 for P30 / Jul 14, 2007) SUBMIT/RESERVE

5·10¹⁷⁸+3 =

5(0)₁₇₇3_<179>

= 61 · 5813 · 1266095772152669053113048638910331_<34> · [111371299677925599229304910106423605557497863192994526047063490147240879819809490792264436773201047749707743497289808646191385677866285614841_<141>] (JMB / GMP-ECM B1=1000000, sigma=1453825301 for P34 / Jul 14, 2007) SUBMIT/RESERVE

5·10¹⁷⁹+3 =

5(0)₁₇₈3_<180>

= 7 · 6581 · 274649101458389267214457_<24> · 17442996660668102907927206569_<29> · 58420054131152676580667221137068677907_<38> · 38780985245897447564182837100518071852832635692767107596372080155550102208945138108939_<86> (JMB / GMP-ECM B1=1000000, sigma=557507828 for P38 / Jul 14, 2007)

5·10¹⁸⁰+3 =

5(0)₁₇₉3_<181>

= 3636511 · 10065320359_<11> · 170781899320909_<15> · 28365504652386968928074018263317721_<35> · 28198443896462682489337688478809235310463625892214771261649188513799597672988910349570886709139480460830651399289823_<116> (JMB / GMP-ECM B1=1000000, sigma=1565609571 for P35 / Jul 16, 2007)

5·10¹⁸¹+3 =

5(0)₁₈₀3_<182>

= definitely prime number

5·10¹⁸²+3 =

5(0)₁₈₁3_<183>

= 439 · 571 · 7643 · 63450664231189_<14> · 11951894979697246105009_<23> · [344137956109328156234359179916101627084221416585608027603674755253493544013700093827271881824770271572632587518940435222038574478095373209_<138>] SUBMIT/RESERVE

5·10¹⁸³+3 =

5(0)₁₈₂3_<184>

= 53 · 2253971 · 22933567 · 872683629733718312183363_<24> · 2091304986012211451175800619436595563347769212985491802204880825094576779945718852668828426711262227533259301616642053664190545178039143082872561_<145>

5·10¹⁸⁴+3 =

5(0)₁₈₃3_<185>

= 31 · 2687 · 2535154133_<10> · [236775234410313783059816275856166824723594303413061163494337763868583633052680624207774178885519022968939697845523734434506250023251149816132015434062982894850965940300503_<171>] SUBMIT/RESERVE

5·10¹⁸⁵+3 =

5(0)₁₈₄3_<186>

= 7 · 505752502245677956259_<21> · 18507977608619856746602644452748137837_<38> · 7630885880694883788242610766381704283225279287936847958869670360168616422552526506424965632629458726936822609309848264083247763_<127> (suberi / GMP-ECM 6.1.2 B1=3000000, sigma=3614596123 for P38 / Jul 20, 2007)

5·10¹⁸⁶+3 =

5(0)₁₈₅3_<187>

= 113 · 1999 · 3079 · 3797 · 92099093 · 298400119 · 7063295315177_<13> · 6969354988860332281_<19> · 2731892341376794135045007_<25> · 7364382395306340008013769_<25> · 1147035865427337017136577429_<28> · 60645317696677687093610484674525646184452370191271_<50>

5·10¹⁸⁷+3 =

5(0)₁₈₆3_<188>

= 43951 · 881623824379321_<15> · 7538781648531214385240912695837561_<34> · 171165708092478089670945899225361876860032835861904429144861641040302889862809476562441735553451758084446668158294751605231000217623613_<135> (JMB / GMP-ECM B1=1000000, sigma=2383272046 for P34 / Jul 14, 2007)

5·10¹⁸⁸+3 =

5(0)₁₈₇3_<189>

= 17 · 353 · 694042304507_<12> · 534714061843976765275098162965857648543309727_<45> · 224511622860875644540507133498734394246496745568262356156954776102962010083439706705021118582845752441312785525001232938868447927_<129> (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=2524047625 for P45 / Jul 4, 2008)

5·10¹⁸⁹+3 =

5(0)₁₈₈3_<190>

= 91095965487358089320603_<23> · 494396890325323305718414399_<27> · 111018442640083081970947618984445439303130371746063567619735073193700750979768533007349526842130828718519132702632964174582139162807213505799_<141>

5·10¹⁹⁰+3 =

5(0)₁₈₉3_<191>

= 11187623 · 1206015527_<10> · 134932983931021_<15> · [27463833498036978931279122698566196103643363675090766798128022755411351207988997570033945512205280674454048735810379350567552531540854521806185942636303194251583_<161>] SUBMIT/RESERVE

5·10¹⁹¹+3 =

5(0)₁₉₀3_<192>

= 7 · 29 · 1862219 · 1322644751875111480766217733615045731619449911148296709860073523123561443621988373280727483817527432716882915071575833372600451608585601344814394148141349362228768778807682154562482779_<184>

5·10¹⁹²+3 =

5(0)₁₉₁3_<193>

= 19 · 23 · 119565829 · 95693290407027618038419981193806055270319420783109072461031121968017956783476298754817280453990453982954882558845432530233709987476182148868297139208013635532470628324933123639220011_<182>

5·10¹⁹³+3 =

5(0)₁₉₂3_<194>

= 68430913250627_<14> · 13104913306486423_<17> · [55754960965977667099262303619967816906897335637724058560887675987960359641171796316619144498801780827605775396781796574777058291468658191359929597537624685917709543_<164>] SUBMIT/RESERVE

5·10¹⁹⁴+3 =

5(0)₁₉₃3_<195>

= 10609553 · 438880348296833_<15> · [107380836487521405694796605699185745338872547707350981368154986200059602157936951155326031927046701272155542149104933319842923629084717875609048751712582358392809014192270547_<174>] SUBMIT/RESERVE

5·10¹⁹⁵+3 =

5(0)₁₉₄3_<196>

= 751 · 3001 · 614843 · 258585653 · 362881860749_<12> · [38452993426727927713660275047955049821820459632124227232403097193742746056235770847115386577975738570378773854145939115603126436028686901046880193882572448395338143_<164>] SUBMIT/RESERVE

5·10¹⁹⁶+3 =

5(0)₁₉₅3_<197>

= 53 · 4831 · 81435758513_<11> · 620177514568967_<15> · 8335212300603379_<16> · 35165888307807931_<17> · 1724266535012524133_<19> · 18149768500139575450781954504934682959012295193_<47> · 421514178392323250396382121254673947852157285795193589239114535798571_<69> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P47 x P69 / 23.37 hours on Core 2 Quad Q6600 / Jul 18, 2007)

5·10¹⁹⁷+3 =

5(0)₁₉₆3_<198>

= 7 · 17493029 · 7120436377_<10> · 24200822641_<11> · [23695736351380415244004256931680513817197336811220426535223782896597104693816923457593254159300559653260891100543204615906939847399894235465448190699889311959028229521593_<170>] SUBMIT/RESERVE

5·10¹⁹⁸+3 =

5(0)₁₉₇3_<199>

= 8689333129_<10> · 153432197600721917_<18> · 3750308994519522383522483020395659550858969331709345535904461838009283679890347744226122442593080577079421507856574382850972150298227915214840092134048508484762597128198471_<172>

5·10¹⁹⁹+3 =

5(0)₁₉₈3_<200>

= 31 · 577 · 9391 · 147844831 · 6158110597551295216831_<22> · [326939223792247766844779917877606712606767451167966562253639127137004867273204642400811592400034256527386422238848074153248332576298397531106070913260400033724819_<162>] SUBMIT/RESERVE

5·10²⁰⁰+3 =

5(0)₁₉₉3_<201>

= 15241 · 44657 · 932333 · 115950677407269228980611_<24> · [6795519300541856100090453542286624239470214656784601069980675786414162837826425989504861017459421939671772935664803067817722265435063030431314634930760154024385613_<163>] SUBMIT/RESERVE

4. References

• A096254 (On-Line Encyclopedia of Integer Sequences)