Since June 16, 2000

STUDIO KAMADA

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Last update

Sequence

General term

Room for prime numbers

Prime numbers

1. (13·10¹+23)/9 = 17 is prime. (Makoto Kamada / Sep 23, 2004)
2. (13·10³+23)/9 = 1447 is prime. (Makoto Kamada / Sep 23, 2004)
3. (13·10⁴+23)/9 = 14447 is prime. (Makoto Kamada / Sep 23, 2004)
4. (13·10⁶+23)/9 = 1444447 is prime. (Makoto Kamada / Sep 23, 2004)
5. (13·10⁹+23)/9 = 1444444447_<10> is prime. (Makoto Kamada / Sep 23, 2004)
6. (13·10²²+23)/9 = 1(4)₂₁7_<23> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
7. (13·10²⁸+23)/9 = 1(4)₂₇7_<29> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
8. (13·10³⁴+23)/9 = 1(4)₃₃7_<35> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
9. (13·10³⁷+23)/9 = 1(4)₃₆7_<38> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
10. (13·10⁶¹+23)/9 = 1(4)₆₀7_<62> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
11. (13·10⁸²+23)/9 = 1(4)₈₁7_<83> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
12. (13·10²⁷⁴+23)/9 = 1(4)₂₇₃7_<275> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
13. (13·10²⁷⁶+23)/9 = 1(4)₂₇₅7_<277> is prime. (Makoto Kamada / PPSIQS / Sep 23, 2004)
14. (13·10⁷³⁵+23)/9 = 1(4)₇₃₄7_<736> is prime. (searched by Makoto Kamada / Sep 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 28, 2006)
15. (13·10¹⁴⁴³+23)/9 = 1(4)₁₄₄₂7_<1444> is prime. (searched by Makoto Kamada / Sep 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Aug 23, 2006)
16. (13·10²²¹⁵+23)/9 = 1(4)₂₂₁₄7_<2216> is prime. (searched by Makoto Kamada / Sep 23, 2004) (certified by Sinkiti Sibata / PRIMO 3.0.4 / Oct 16, 2007)
17. (13·10²⁹⁶⁸+23)/9 = 1(4)₂₉₆₇7_<2969> is PRP. (Makoto Kamada / Sep 23, 2004)
18. (13·10³³⁰¹+23)/9 = 1(4)₃₃₀₀7_<3302> is PRP. (Makoto Kamada / PFGW / Dec 17, 2004)
19. (13·10³⁸⁸³+23)/9 = 1(4)₃₈₈₂7_<3884> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 5 / May 4, 2006)
20. (13·10³⁹⁹¹+23)/9 = 1(4)₃₉₉₀7_<3992> is PRP. (Makoto Kamada / PFGW / Dec 17, 2004)
21. (13·10⁵¹⁵²+23)/9 = 1(4)₅₁₅₁7_<5153> is PRP. (Makoto Kamada / PFGW / Dec 20, 2004)
22. (13·10⁸⁰³²+23)/9 = 1(4)₈₀₃₁7_<8033> is PRP. (Makoto Kamada / PFGW / Dec 30, 2004)
23. (13·10⁸⁹⁴⁶+23)/9 = 1(4)₈₉₄₅7_<8947> is PRP. (Makoto Kamada / PFGW / Dec 30, 2004)

• 1-10000

• A102934 (On-Line Encyclopedia of Integer Sequences)

Condition

Status

Factorization results

(13·10¹+23)/9 =

17

= definitely prime number

(13·10²+23)/9 =

147

= 3 · 7²

(13·10³+23)/9 =

1447

= definitely prime number

(13·10⁴+23)/9 =

14447

= definitely prime number

(13·10⁵+23)/9 =

144447

= 3 · 89 · 541

(13·10⁶+23)/9 =

1444447

= definitely prime number

(13·10⁷+23)/9 =

14444447

= 433 · 33359

(13·10⁸+23)/9 =

144444447

= 3² · 7 · 29 · 173 · 457

(13·10⁹+23)/9 =

1444444447_<10>

= definitely prime number

(13·10¹⁰+23)/9 =

14444444447_<11>

= 100393 · 143879

(13·10¹¹+23)/9 =

144444444447_<12>

= 3 · 2207 · 21816107

(13·10¹²+23)/9 =

1444444444447_<13>

= 19 · 46271 · 1643003

(13·10¹³+23)/9 =

14444444444447_<14>

= 47 · 1889 · 162693809

(13·10¹⁴+23)/9 =

144444444444447_<15>

= 3 · 7 · 233 · 1259 · 23447681

(13·10¹⁵+23)/9 =

1444444444444447_<16>

= 67 · 185833 · 116012077

(13·10¹⁶+23)/9 =

14444444444444447_<17>

= 491 · 29418420457117_<14>

(13·10¹⁷+23)/9 =

144444444444444447_<18>

= 3² · 17 · 107453 · 8785993283_<10>

(13·10¹⁸+23)/9 =

1444444444444444447_<19>

= 127 · 14831 · 766878720431_<12>

(13·10¹⁹+23)/9 =

14444444444444444447_<20>

= 13007 · 19531 · 56859000691_<11>

(13·10²⁰+23)/9 =

144444444444444444447_<21>

= 3 · 7 · 179 · 82465597 · 465967589

(13·10²¹+23)/9 =

1444444444444444444447_<22>

= 222011 · 6506184128013677_<16>

(13·10²²+23)/9 =

14444444444444444444447_<23>

= definitely prime number

(13·10²³+23)/9 =

144444444444444444444447_<24>

= 3 · 117634809157_<12> · 409301876657_<12>

(13·10²⁴+23)/9 =

1444444444444444444444447_<25>

= 2063 · 205063 · 3414399296270663_<16>

(13·10²⁵+23)/9 =

14444444444444444444444447_<26>

= 103 · 16069 · 8727196757940389621_<19>

(13·10²⁶+23)/9 =

144444444444444444444444447_<27>

= 3³ · 7 · 227 · 39383 · 392549 · 217776247747_<12>

(13·10²⁷+23)/9 =

1444444444444444444444444447_<28>

= 3659 · 394764811272053688014333_<24>

(13·10²⁸+23)/9 =

14444444444444444444444444447_<29>

= definitely prime number

(13·10²⁹+23)/9 =

144444444444444444444444444447_<30>

= 3 · 349 · 828055457 · 166607572854967193_<18>

(13·10³⁰+23)/9 =

1444444444444444444444444444447_<31>

= 19 · 6113 · 295186039 · 42130540684643459_<17>

(13·10³¹+23)/9 =

14444444444444444444444444444447_<32>

= 7993 · 42372848065451_<14> · 42648461993029_<14>

(13·10³²+23)/9 =

144444444444444444444444444444447_<33>

= 3 · 7 · 932307119 · 1761411577_<10> · 4188530683189_<13>

(13·10³³+23)/9 =

1444444444444444444444444444444447_<34>

= 17 · 59 · 1440124072227761160961559765149_<31>

(13·10³⁴+23)/9 =

14444444444444444444444444444444447_<35>

= definitely prime number

(13·10³⁵+23)/9 =

144444444444444444444444444444444447_<36>

= 3² · 169409 · 1633157 · 23719735867_<11> · 2445592361473_<13>

(13·10³⁶+23)/9 =

1444444444444444444444444444444444447_<37>

= 29 · 83 · 600101555647878871809075381987721_<33>

(13·10³⁷+23)/9 =

14444444444444444444444444444444444447_<38>

= definitely prime number

(13·10³⁸+23)/9 =

144444444444444444444444444444444444447_<39>

= 3 · 7 · 7789 · 883079583811385069569688904648463_<33>

(13·10³⁹+23)/9 =

1444444444444444444444444444444444444447_<40>

= 47669387 · 1170670957_<10> · 25883704407899341180433_<23>

(13·10⁴⁰+23)/9 =

14444444444444444444444444444444444444447_<41>

= 277 · 101009 · 516251114501769007910345067526579_<33>

(13·10⁴¹+23)/9 =

144444444444444444444444444444444444444447_<42>

= 3 · 81847567 · 588266089181956357336170397687547_<33>

(13·10⁴²+23)/9 =

1444444444444444444444444444444444444444447_<43>

= 5087 · 270379 · 458069 · 2292636730796519129035272631_<28>

(13·10⁴³+23)/9 =

14444444444444444444444444444444444444444447_<44>

= 153947 · 4783959373_<10> · 25694498834447_<14> · 763311804330671_<15>

(13·10⁴⁴+23)/9 =

144444444444444444444444444444444444444444447_<45>

= 3² · 7² · 97 · 109 · 479 · 10993 · 4848582033787_<13> · 1213381954827619111_<19>

(13·10⁴⁵+23)/9 =

1444444444444444444444444444444444444444444447_<46>

= 337 · 132137 · 32437434595059462820463233464136290263_<38>

(13·10⁴⁶+23)/9 =

14444444444444444444444444444444444444444444447_<47>

= 8863 · 1629746637080496947359183622299948600298369_<43>

(13·10⁴⁷+23)/9 =

144444444444444444444444444444444444444444444447_<48>

= 3 · 31991 · 480902321 · 13359561380655023_<17> · 234262460002208333_<18>

(13·10⁴⁸+23)/9 =

1444444444444444444444444444444444444444444444447_<49>

= 19 · 67 · 261637 · 814776633106182689_<18> · 5322733385935553003723_<22>

(13·10⁴⁹+23)/9 =

14444444444444444444444444444444444444444444444447_<50>

= 17 · 61 · 89 · 38959 · 105656233 · 38021492121936765909400889923157_<32>

(13·10⁵⁰+23)/9 =

144444444444444444444444444444444444444444444444447_<51>

= 3 · 7 · 2502169 · 6443407 · 634433232821_<12> · 672455299107309140298049_<24>

(13·10⁵¹+23)/9 =

1444444444444444444444444444444444444444444444444447_<52>

= 173 · 8349389852280025690430314707771355170199100834939_<49>

(13·10⁵²+23)/9 =

14444444444444444444444444444444444444444444444444447_<53>

= 1381 · 11489 · 608897 · 2412303146188339_<16> · 619796639626892745162401_<24>

(13·10⁵³+23)/9 =

144444444444444444444444444444444444444444444444444447_<54>

= 3⁵ · 59911193 · 820185439 · 24090434911_<11> · 502145882844539591523757_<24>

(13·10⁵⁴+23)/9 =

1444444444444444444444444444444444444444444444444444447_<55>

= 697913917 · 692243678939_<12> · 64186504391881_<14> · 46579654288161040649_<20>

(13·10⁵⁵+23)/9 =

14444444444444444444444444444444444444444444444444444447_<56>

= 137777 · 15830671 · 6622543132390658354813934334496616294834241_<43>

(13·10⁵⁶+23)/9 =

144444444444444444444444444444444444444444444444444444447_<57>

= 3 · 7 · 1020913 · 154021723 · 8516775431_<10> · 46071912353_<11> · 111480626673780595951_<21>

(13·10⁵⁷+23)/9 =

1444444444444444444444444444444444444444444444444444444447_<58>

= 84659 · 13437897463_<11> · 13711028531_<11> · 68881136113_<11> · 1344392402451686090497_<22>

(13·10⁵⁸+23)/9 =

14444444444444444444444444444444444444444444444444444444447_<59>

= 169331759337080876182002901_<27> · 85302630179909482442518017818147_<32>

(13·10⁵⁹+23)/9 =

144444444444444444444444444444444444444444444444444444444447_<60>

= 3 · 47 · 103 · 22195373 · 6320432791_<10> · 70898205033058458698981464245901774823_<38>

(13·10⁶⁰+23)/9 =

1444444444444444444444444444444444444444444444444444444444447_<61>

= 127 · 2273 · 26437 · 1237493 · 1734049 · 65014567 · 1252747883_<10> · 1082946611570881296893_<22>

(13·10⁶¹+23)/9 =

14444444444444444444444444444444444444444444444444444444444447_<62>

= definitely prime number

(13·10⁶²+23)/9 =

144444444444444444444444444444444444444444444444444444444444447_<63>

= 3² · 7 · 85577 · 105107 · 254901032843943236455470726599327223028428627508771_<51>

(13·10⁶³+23)/9 =

1444444444444444444444444444444444444444444444444444444444444447_<64>

= 7219 · 11689 · 681470441 · 2603654606153790877_<19> · 9647528009620603816417613081_<28>

(13·10⁶⁴+23)/9 =

14444444444444444444444444444444444444444444444444444444444444447_<65>

= 29 · 22639 · 451349504080060294404187027_<27> · 48745287463384204445252173833031_<32>

(13·10⁶⁵+23)/9 =

144444444444444444444444444444444444444444444444444444444444444447_<66>

= 3 · 17 · 6737839 · 6822623 · 61611057542063142116467486434725930176324349435701_<50>

(13·10⁶⁶+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444447_<67>

= 19² · 2753 · 377796007 · 16313086006663_<14> · 1020175457996881_<16> · 231163397345759159858279_<24>

(13·10⁶⁷+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444447_<68>

= 52315240611271155788050960824067_<32> · 276103947447628365472267171058153141_<36>

(13·10⁶⁸+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444447_<69>

= 3 · 7 · 3923 · 10427 · 56463670327_<11> · 227510554005245179_<18> · 13089806093708825442667169175599_<32>

(13·10⁶⁹+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444447_<70>

= 155659780327_<12> · 1171925778936327367_<19> · 1601615231911272637_<19> · 4943859632405825098459_<22>

(13·10⁷⁰+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444447_<71>

= 108823341701_<12> · 132732961685109799222048100781878455618704511707029668734547_<60>

(13·10⁷¹+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444447_<72>

= 3² · 487 · 1283 · 746413 · 34413078177548084191504769910208311215692293061766591596471_<59>

(13·10⁷²+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444447_<73>

= 2633 · 13760077 · 828504247 · 10685745260460920319053_<23> · 4503286355883367368027934714537_<31>

(13·10⁷³+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444447_<74>

= 219042524326333964045351_<24> · 65943562734534688862562838341124025464973959655497_<50>

(13·10⁷⁴+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444447_<75>

= 3 · 7 · 1033 · 6243210420049_<13> · 2281607848599053137488631379_<28> · 467446865497595394863499409049_<30>

(13·10⁷⁵+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444447_<76>

= 3719 · 5113 · 10531 · 1131275569_<10> · 2952264692353_<13> · 3757338188022730387_<19> · 574811266249970437254569_<24>

(13·10⁷⁶+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444447_<77>

= 855739 · 1978069903421_<13> · 368748731811168197_<18> · 23141278397400146239179802163870122903229_<41>

(13·10⁷⁷+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444447_<78>

= 3 · 83 · 4561 · 108439 · 1172886316392029700100055685192302304915174312018853750046633692657_<67>

(13·10⁷⁸+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444447_<79>

= 401 · 190367 · 6334127 · 9351385892243_<13> · 319449386716173729217070437292344257782109590850181_<51>

(13·10⁷⁹+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444447_<80>

= 1801 · 1442559293921_<13> · 45732093561459359_<17> · 52542833988069409_<17> · 2313763043808849453612731123897_<31>

(13·10⁸⁰+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444447_<81>

= 3³ · 7 · 154727 · 4939385626373389049299236632769600871842597950876115356494059342014485949_<73>

(13·10⁸¹+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444447_<82>

= 17 · 67 · 2237 · 566906106001760810365241469076994440002953144730649172467533396329684158729_<75>

(13·10⁸²+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444447_<83>

= definitely prime number

(13·10⁸³+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444444447_<84>

= 3 · 223 · 184463 · 19940359 · 66369319308375491280867779569_<29> · 884433371791299222384005443214325909731_<39>

(13·10⁸⁴+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<85>

= 19 · 8059 · 14321 · 658707701853650023382762931051131945232097345799897679375649482532157829167_<75>

(13·10⁸⁵+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<86>

= 331 · 175900891 · 248087458341016044437010232004070762052237680302003714985114402056920480007_<75>

(13·10⁸⁶+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<87>

= 3 · 7² · 1623917 · 21259291850369_<14> · 10619333794252097_<17> · 2680239564601333323233779294171193961668605488121_<49>

(13·10⁸⁷+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<88>

= 181² · 773 · 866057 · 573610307 · 643763165187659919330524673589_<30> · 178350632108951009518877102889493709_<36>

(13·10⁸⁸+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<89>

= 269 · 24205439387_<11> · 2107063509924817_<16> · 1052829308498781649195092990327355145696592234066120542822897_<61>

(13·10⁸⁹+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<90>

= 3² · 70877440289_<11> · 226438520502555542226282876648107371890778677102535659208580010857753321482247_<78>

(13·10⁹⁰+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<91>

= 131 · 1571 · 15991 · 2233441879_<10> · 22765880899_<11> · 8632142957780623446764252586995614801453479315126766140830077_<61>

(13·10⁹¹+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<92>

= 59 · 167 · 1465994564543229924332126707037901597934075352120617522018110671312741748142133811473099_<88>

(13·10⁹²+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<93>

= 3 · 7 · 29 · 941 · 6151 · 26487403 · 1547065924461744094101086683727222674748826165884757471697258237106749728871_<76>

(13·10⁹³+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<94>

= 89 · 103 · 439 · 50989 · 94399 · 74570181980851647159554277087172700402742565810099729718387982039139873846829_<77>

(13·10⁹⁴+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<95>

= 173 · 31477 · 483308361719346223_<18> · 896893850800496713074168659_<27> · 6119219759491400144211587722613183233001051_<43>

(13·10⁹⁵+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<96>

= 3 · 48148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149_<95>

(13·10⁹⁶+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<97>

= 809 · 112095814741_<12> · 15928061481197167812933353348182042979889728516074354469238728288440096891573597163_<83>

(13·10⁹⁷+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<98>

= 17 · 8999 · 11786513 · 17819779242989_<14> · 42985002303185499839_<20> · 10458106405568460638101308987218816210963583746945683_<53>

(13·10⁹⁸+23)/9 =

144444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<99>

= 3² · 7 · 15773 · 280589 · 5302089229_<10> · 33303189578035579_<17> · 2933880948652689566090701079327181046116592633220259054153047_<61>

(13·10⁹⁹+23)/9 =

1444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<100>

= 20269977874978493_<17> · 48380102173899798200419254467118286241867_<41> · 1472925520515835862540213121130580422441537_<43> (Makoto Kamada / GGNFS 0.53.3 / Total time: 0.59 hours (actual time: 0.62 hours))

(13·10¹⁰⁰+23)/9 =

14444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447_<101>

= 2678798056108829_<16> · 5392136376799589418058664563875784012672288853613133994597232410768339843237864731243_<85>

(13·10¹⁰¹+23)/9 =

1(4)₁₀₀7_<102>

= 3 · 113 · 691 · 161348975116031_<15> · 2638979885325029_<16> · 1448174200546308221383716357185100221888828279859617821802170696997_<67>

(13·10¹⁰²+23)/9 =

1(4)₁₀₁7_<103>

= 19 · 127 · 719 · 70434883300550025768921698856829_<32> · 11820254604073182658618421398181422566578014985987820143827603769_<65> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 0.99 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Mar 5, 2008)

(13·10¹⁰³+23)/9 =

1(4)₁₀₂7_<104>

= 293 · 226027 · 395429 · 5818259 · 393252429137_<12> · 8672424885112801921_<19> · 21725174650026677719_<20> · 1279487648864061335422494680603489_<34>

(13·10¹⁰⁴+23)/9 =

1(4)₁₀₃7_<105>

= 3 · 7 · 149 · 52751654539_<11> · 108747064013621259854420041_<27> · 351593252544047084723547244879_<30> · 22887645677548015958529420565162483_<35> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=611463270 for P30 / Feb 26, 2008)

(13·10¹⁰⁵+23)/9 =

1(4)₁₀₄7_<106>

= 47 · 17627 · 3545372653_<10> · 1055357511369673_<16> · 335068087266999290179_<21> · 1784084621539071672608341_<25> · 779497215627901270440801981193_<30>

(13·10¹⁰⁶+23)/9 =

1(4)₁₀₅7_<107>

= 1182185754731_<13> · 2172029727110878635738586779067649_<34> · 5625347506338151318885368500376703770981780047991444353962013_<61> (Makoto Kamada / GMP-ECM 6.1.3 B1=50000, sigma=2076058315 for P34 / Jan 21, 2008)

(13·10¹⁰⁷+23)/9 =

1(4)₁₀₆7_<108>

= 3³ · 35216147 · 108637347988459_<15> · 23732641770407504929_<20> · 34022056488563625861441521_<26> · 1731846675308785518622951843549442964173_<40>

(13·10¹⁰⁸+23)/9 =

1(4)₁₀₇7_<109>

= 13441 · 107465549024956807115872661590986120411014392116988649984706825715679223602741198158205821326124874967967_<105>

(13·10¹⁰⁹+23)/9 =

1(4)₁₀₈7_<110>

= 61 · 277 · 503 · 1831601 · 2156071 · 51656325972977006306990866008287770891019_<41> · 8331166415227273953870412449749267635633640111533_<49> (Robert Backstrom / Msieve v. 1.33 for P41 x P49 / Mar 5, 2008)

(13·10¹¹⁰+23)/9 =

1(4)₁₀₉7_<111>

= 3 · 7 · 8753 · 3711679 · 249417913 · 2537235671983_<13> · 1240465707151710983651_<22> · 16138801360122815192117753_<26> · 16711280210341400465353722380753_<32>

(13·10¹¹¹+23)/9 =

1(4)₁₁₀7_<112>

= 863 · 386881426812688222963_<21> · 536034555099477259492189339343_<30> · 8070851920836102438701243831587152825693030353472471416341_<58> (Robert Backstrom / Msieve v. 1.33 for P30 x P58 / Mar 5, 2008)

(13·10¹¹²+23)/9 =

1(4)₁₁₁7_<113>

= 4215060217_<10> · 1836768886313390835854431_<25> · 1865703152448774944771719391090768939193139031744626454511303651661702393741961_<79>

(13·10¹¹³+23)/9 =

1(4)₁₁₂7_<114>

= 3 · 17 · 1058632741_<10> · 3726222878100481201794626013271269800973447843967_<49> · 717986894749436893374924732971774453291142110739897151_<54> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.39 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Mar 5, 2008)

(13·10¹¹⁴+23)/9 =

1(4)₁₁₃7_<115>

= 67 · 245563 · 275904691 · 341712991 · 25425790294979881117_<20> · 36624193903242864651740851922561324301537351916910970698087296215444391_<71>

(13·10¹¹⁵+23)/9 =

1(4)₁₁₄7_<116>

= 11447053 · 275027587711008053_<18> · 4588079025725865009229759024281788945772161972265588741466412350504819778001217996403800783_<91>

(13·10¹¹⁶+23)/9 =

1(4)₁₁₅7_<117>

= 3² · 7 · 1103 · 61600920917936257129108063_<26> · 33744078768778850689964053052637328204725152037846966278481450851524000786252468365521_<86>

(13·10¹¹⁷+23)/9 =

1(4)₁₁₆7_<118>

= 137089 · 2938981 · 118824907 · 30171296508404213725820751270457193651174221926177012710635271935586868876523739292954377529546169_<98>

(13·10¹¹⁸+23)/9 =

1(4)₁₁₇7_<119>

= 83 · 146894591 · 120347382739_<12> · 1650165537080777_<16> · 8238817863322481_<16> · 724082216757997374424060385163820474469708770041041122628722484993_<66>

(13·10¹¹⁹+23)/9 =

1(4)₁₁₈7_<120>

= 3 · 443 · 11059 · 116341 · 15648638539_<11> · 31868005109_<11> · 5581887904138474171_<19> · 30346923055543112170165556176750563351584609378253261738971650867957_<68>

(13·10¹²⁰+23)/9 =

1(4)₁₁₉7_<121>

= 19 · 29 · 1741 · 22441 · 76702542741648809846780802317_<29> · 874779316283849878292104906255438129819684224118598047597761358345503878142800761_<81> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.18 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 5, 2008)

(13·10¹²¹+23)/9 =

1(4)₁₂₀7_<122>

= 6599 · 2188883837618494384671078109477867016888080685625768214039164183125389368759576366789580912932935966728965668198885353_<118>

(13·10¹²²+23)/9 =

1(4)₁₂₁7_<123>

= 3 · 7 · 275974403633615893708374712313364033866417253364443479869_<57> · 24923713169568184598667917122586887747016051523773565479357462303_<65> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.80 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 5, 2008)

(13·10¹²³+23)/9 =

1(4)₁₂₂7_<124>

= 24686158607887409_<17> · 947104076875960805980958443_<27> · 61780244369598875229413331596854885386917318786279903982560551596066801140231981_<80>

(13·10¹²⁴+23)/9 =

1(4)₁₂₃7_<125>

= 4861 · 20399 · 31723 · 62521993 · 19608773125447472591_<20> · 3745491858604408275520766856865934309677475795901080194375712005457568413198718905177_<85>

(13·10¹²⁵+23)/9 =

1(4)₁₂₄7_<126>

= 3² · 464247637731423992081446576515259298176781598923_<48> · 34570736416615334709852602535504361723332346937596499346376073111611171864021_<77> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 2.83 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 5, 2008)

(13·10¹²⁶+23)/9 =

1(4)₁₂₅7_<127>

= 1747 · 10391 · 49005667 · 69676172561239_<14> · 987823085251644979_<18> · 23590700178236558387342072945647676700896672023438959042642296676949997496411293_<80>

(13·10¹²⁷+23)/9 =

1(4)₁₂₆7_<128>

= 103 · 67089542389_<11> · 202509386109599571491_<21> · 14549579140164833600801209324805687_<35> · 709435963265061108754917795311933782934023902804157269931073_<60> (Sinkiti Sibata / Msieve v. 1.33 for P35 x P60 / 2.04 hours on Pentium4 2.4GHz, Windows XP and Cygwin / Mar 5, 2008)

(13·10¹²⁸+23)/9 =

1(4)₁₂₇7_<129>

= 3 · 7⁴ · 359 · 66612700003_<11> · 1331167551723961827044232908143687891357_<40> · 629945850433649252006066469143506208365518616550926335658920273196015541_<72> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.14 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 5, 2008)

(13·10¹²⁹+23)/9 =

1(4)₁₂₈7_<130>

= 17 · 71986679 · 388579423 · 131638082375417_<15> · 13768205563065773942619038565998211282092437391_<47> · 1675950144686658660252724258618579568960643440587009_<52> (Robert Backstrom / Msieve v. 1.33 for P47 x P52 / Mar 5, 2008)

(13·10¹³⁰+23)/9 =

1(4)₁₂₉7_<131>

= 1543 · 82463 · 113520889770516569499901909655480944300048928987995035794363443491009561627897977319802897241900915647358886157340506854583_<123>

(13·10¹³¹+23)/9 =

1(4)₁₃₀7_<132>

= 3 · 1889 · 20360833 · 31771542433_<11> · 538393284151_<12> · 73183665039437320193043726110049992237027494104384933540602444384006934454838477242314308512754419_<98>

(13·10¹³²+23)/9 =

1(4)₁₃₁7_<133>

= 6343 · 8219 · 66713 · 4317193 · 49382761427_<11> · 8854773201383480311_<19> · 219999859009701701463206070734734476452579594282387515890331729201725585074357861567_<84>

(13·10¹³³+23)/9 =

1(4)₁₃₂7_<134>

= 11657957 · 1239020219790178025570384626092242787003284061216252937323790475847907523114422573736070946602774778157480289594861642090843571_<127>

(13·10¹³⁴+23)/9 =

1(4)₁₃₃7_<135>

= 3⁴ · 7 · 6190141 · 3699678316581991_<16> · 11123802722920956998465879182436097069507538391595156962039136510681595340684861594423767936765942600301837611_<110>

(13·10¹³⁵+23)/9 =

1(4)₁₃₄7_<136>

= 193 · 4328774092087433_<16> · 1728934785395725845090032768516301891640913475376965627015397447604500542301840590575708616030824462490497925764551463_<118>

(13·10¹³⁶+23)/9 =

1(4)₁₃₅7_<137>

= 28351 · 741778358369_<12> · 1020170085864367_<16> · 16493851895001413_<17> · 40819119005601628491301335501942890589222314071502663352586701798620627130330629648801603_<89>

(13·10¹³⁷+23)/9 =

1(4)₁₃₆7_<138>

= 3 · 89 · 173 · 347 · 545161 · 16530623101836969024451362824188351845753342403082319109306168938020114764600593274984051493360927430036090611681112066851051_<125>

(13·10¹³⁸+23)/9 =

1(4)₁₃₇7_<139>

= 19 · 599 · 1429883584413769044754647369821_<31> · 586128798116731777961115493247664079920542415073_<48> · 151435145516772344278889031078601478025961666278540775039_<57> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3647572132 for P31 / Feb 26, 2008) (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.33 / Mar 6, 2008)

(13·10¹³⁹+23)/9 =

1(4)₁₃₈7_<140>

= 227 · 389 · 26347 · 24967667047_<11> · 248665908539458972633642469295245807528016711238770087204991988984808196244932987117310321721102769310250040735221112661_<120>

(13·10¹⁴⁰+23)/9 =

1(4)₁₃₉7_<141>

= 3 · 7 · 97 · 116639 · 361213 · 235765177 · 1745882905442085615069163292717_<31> · 1274538776841461345684727695080517503_<37> · 3208151205533195406082282981411310434662624665968979_<52> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 10.31 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Mar 6, 2008)

(13·10¹⁴¹+23)/9 =

1(4)₁₄₀7_<142>

= 311 · 1361 · 1399 · 101922108984892127_<18> · 78182239713204452989_<20> · 306117462680173936119739906937960618473972651887945591258360226801871517199720332527340032752181_<96>

(13·10¹⁴²+23)/9 =

1(4)₁₄₁7_<143>

= 1819523 · 7938588544604516922536535369129406138006743769902575809398641536515034129518804898011426315822577919841873086761994459231592260413550389_<136>

(13·10¹⁴³+23)/9 =

1(4)₁₄₂7_<144>

= 3² · 2389 · 72881353 · 6508800369946252997_<19> · 8247464312828826073_<19> · 123511028190274527084942581597557283_<36> · 13902683100663382375897508514348828772415433347065218804613_<59> (Robert Backstrom / Msieve v. 1.33 for P36 x P59 / Mar 5, 2008)

(13·10¹⁴⁴+23)/9 =

1(4)₁₄₃7_<145>

= 127 · 5309 · 698531 · 18250784633_<11> · 489889502898266347_<18> · 7974072093667475428695114878478870116137528321_<46> · 43016877271613784214536967602395329942184013449106489386429_<59> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 19.57 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 6, 2008)

(13·10¹⁴⁵+23)/9 =

1(4)₁₄₄7_<146>

= 17 · 349 · 649123 · 1775611609_<10> · 9343080165895605403209672061982422960039_<40> · 89613447463680659731752405803506450728307_<41> · 2522831592649101185126932192574929950666412669_<46> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 14.85 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 6, 2008)

(13·10¹⁴⁶+23)/9 =

1(4)₁₄₅7_<147>

= 3 · 7 · 3479557 · 19622489662095236649338844058215831256042080388367537519_<56> · 100740356624526186007814934359778825461356811979856485445035129252550852026602460329_<84> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 29.62 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 7, 2008)

(13·10¹⁴⁷+23)/9 =

1(4)₁₄₆7_<148>

= 67 · 490258807 · 10213739034520031_<17> · 1480241574680768294011_<22> · 2908595186300017626049029243087862480743338606729481643763608861788246141018988019990986048409644343_<100>

(13·10¹⁴⁸+23)/9 =

1(4)₁₄₇7_<149>

= 29 · 82893068831154629_<17> · 10326766722762193030677743410047854627737_<41> · 18781709518265729197727134979077408403048257_<44> · 30980265889559158971246250118179234976988163463_<47> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 50.14 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 8, 2008)

(13·10¹⁴⁹+23)/9 =

1(4)₁₄₈7_<150>

= 3 · 59 · 642789047 · 8628460657_<10> · 384131451857134907_<18> · 1869299252728233162593593784842467695639821_<43> · 204911855236147914759409599454283650327219283947887580206394976351047_<69> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 26.05 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 9, 2008)

(13·10¹⁵⁰+23)/9 =

1(4)₁₄₉7_<151>

= 1410361 · 1024166468332890972201049550040340341546912063255042109392165867068392024768441870162635271710182318175590819970521337759938373540139329181992727_<145>

(13·10¹⁵¹+23)/9 =

1(4)₁₅₀7_<152>

= 47 · 1459 · 1489 · 6550441069_<10> · 2731118671267928548408841950780937_<34> · 926226113280928870632802667563416935974873_<42> · 8537384850979962295167735815770595423638734296748278114279_<58> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 30.82 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Mar 10, 2008)

(13·10¹⁵²+23)/9 =

1(4)₁₅₁7_<153>

= 3² · 7 · 109 · 9437669376050991528449453_<25> · 2228789415200160909185838366456712820256148511635322352255893876677738266774336837655685740300914770158640941361893356000697_<124>

(13·10¹⁵³+23)/9 =

1(4)₁₅₂7_<154>

= 580549 · 2385293 · 12984149 · 254011988467_<12> · 20988808355170947443_<20> · 15068316749714303315015928309384057890021142497785694123926956556402961494016494219567366227752724510059_<104>

(13·10¹⁵⁴+23)/9 =

1(4)₁₅₃7_<155>

= 19919 · 3679468548146533_<16> · 7630751612715717403_<19> · 2262802058462321464484841458672901509492655613223530140187_<58> · 11413907115688684242996799010354104342118227296131335025701_<59> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / Mar 9, 2008)

(13·10¹⁵⁵+23)/9 =

1(4)₁₅₄7_<156>

= 3 · 769 · 62611376005394210855849347396811636083417617877955979386408515147136733612676395511245966382507344796031402013196551558060010595771323989789529451428021_<152>

(13·10¹⁵⁶+23)/9 =

1(4)₁₅₅7_<157>

= 19 · 389980758750449231614133227379820419633329_<42> · 91675205847127951535304492278434084611246814323398249_<53> · 2126435275612637276891658087461597168753509864505325623463053_<61> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.33 / Mar 10, 2008)

(13·10¹⁵⁷+23)/9 =

1(4)₁₅₆7_<158>

= 16927 · 2524139 · 1130777445877727136149_<22> · 29470374557264323160093526813499099303_<38> · 8608324398240878863428561563214391554918361_<43> · 1178490710904896662118258002202295955986767897_<46> (Robert Backstrom / GMP-ECM 6.0 B1=1258000, sigma=2973888295 for P38, Msieve v. 1.33 for P43 x P46 / Mar 8, 2008)

(13·10¹⁵⁸+23)/9 =

1(4)₁₅₇7_<159>

= 3 · 7 · 229 · 106765482187099_<15> · 281329451827162966482826282822933803850988587116937414690641391820035888396838934695584578450619301006587642269846846174714619020579112938917_<141>

(13·10¹⁵⁹+23)/9 =

1(4)₁₅₈7_<160>

= 83 · 5008661201_<10> · 3474570232523197426477955556499999124059374370418938201380817378999393901925388405152040650349200716130912965651076166076064645152890186170785973109_<148>

(13·10¹⁶⁰+23)/9 =

1(4)₁₅₉7_<161>

= 457 · 14293 · 161047 · 347071 · 302954513 · 101632852910485879_<18> · 1284927842389889594548698708086994904856107541149912956575920987443843910775978854115770722525304630822164499389416053_<118>

(13·10¹⁶¹+23)/9 =

1(4)₁₆₀7_<162>

= 3³ · 17 · 103 · 1724029 · 46124385028404659193551_<23> · 19676012510318678785250017004699445567484314567847182516372343_<62> · 1952714211361224583977547309784021653764745429767765757488007042063_<67> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / Mar 14, 2008)

(13·10¹⁶²+23)/9 =

1(4)₁₆₁7_<163>

= 48440917801958347097_<20> · 170569706737281090797_<21> · 4896627844567999141056381026425997699_<37> · 35701747916582274558191451115278830078250818431335984974373036683747660077947671049617_<86> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 134.15 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / May 2, 2008)

(13·10¹⁶³+23)/9 =

1(4)₁₆₂7_<164>

= 3517 · 18983905542455313683_<20> · 290489182949177909802781675636329039795637507570364531197_<57> · 744754172766735844931657694994085417458424028852613801213846101237458452241664067741_<84> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.34 / Apr 4, 2008)

(13·10¹⁶⁴+23)/9 =

1(4)₁₆₃7_<165>

= 3 · 7 · 839545558995717980676973391993_<30> · 20177046110532699947312283019200501521_<38> · 406050166580568139538183636120785029941680983190292244345051790690796540227700452076761314334219_<96> (Robert Backstrom / GMP-ECM 6.0 B1=228000, sigma=1811189061 for P30, GMP-ECM 6.0 B1=228000, sigma=1811189061 for P38 / Mar 9, 2008)

(13·10¹⁶⁵+23)/9 =

1(4)₁₆₄7_<166>

= 1051 · 618500551 · 40014887286079_<14> · 46629831888067_<14> · 3282821361484088048052437_<25> · 362764965293200023818281683244621133455373831880868477799823218502676270572651156415177348059793765067_<102>

(13·10¹⁶⁶+23)/9 =

1(4)₁₆₅7_<167>

= 17395527517317667_<17> · 830353918848661058750779982563391694568952892479610619097106624289312943313044760117752021755611270949042107099204623988670812158379879360719037360341_<150>

(13·10¹⁶⁷+23)/9 =

1(4)₁₆₆7_<168>

= 3 · 571 · 1120864826830189595009_<22> · 2196722081660400619860435665895112903415321030329429_<52> · 34246415634863136312265358406712864250373833913675284562837241961141882980145948561830479379_<92> (Serge Batalov / Msieve-1.38 snfs / 40.00 hours on Opteron-2.2GHz; Linux x86_64 / Oct 18, 2008)

(13·10¹⁶⁸+23)/9 =

1(4)₁₆₇7_<169>

= 6197231736504198581_<19> · 6827481749527884299_<19> · 125991706661408379069740433560492000863719150637957632449_<57> · 270957140149426777544289571433775011527741409316792143226462515238075645737_<75> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.35 / May 15, 2008)

(13·10¹⁶⁹+23)/9 =

1(4)₁₆₈7_<170>

= 61 · 2598593 · 5174929 · 13697428917972497_<17> · 1285550946979232054281168380768012120658065422741060174335927873021846048400284919415880530736985672083393371231108913494068423957985194603_<139>

(13·10¹⁷⁰+23)/9 =

1(4)₁₆₉7_<171>

= 3² · 7² · 446315784615474862410026239878656530619417_<42> · 733871474114925252241865494143887940469879995924979497675057972980625973036265099361056138544027803999139735087936933070351151_<126> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.35 / May 13, 2008)

(13·10¹⁷¹+23)/9 =

1(4)₁₇₀7_<172>

= 3983898590622918946099742220376300090916709488135066216815900242393474298893881_<79> · 362570585467285289874408318951946873117767996253948597783388693466115940756746792298079012887_<93> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 131.74 hours on Core 2 Quad Q6600 / Mar 12, 2008)

(13·10¹⁷²+23)/9 =

1(4)₁₇₁7_<173>

= 149371 · 167722932457097_<15> · 44064556377957406403542099_<26> · [13084366643374336218427068763076664376928546378329855179938464251636991069258127603734260770465527458131984491027921287413301319_<128>] SUBMIT/RESERVE

(13·10¹⁷³+23)/9 =

1(4)₁₇₂7_<174>

= 3 · 16916841312338544799_<20> · 2846166566156212298699859853179869807885870627547993249249727838951282711902622697585005273319040444781492878373151878077945642349463302356123869201316651_<154>

(13·10¹⁷⁴+23)/9 =

1(4)₁₇₃7_<175>

= 19 · 233584627 · 327017448697_<12> · 1508884939339678464343119204491325903774757813009_<49> · 659592843928901000722573606753947216311128546998729114026951853355308952821337342212632003472349819672303_<105> (Serge Batalov / Msieve-1.38 snfs / 32.00 hours on Opteron-2.6GHz; Linux x86_64 / Oct 6, 2008)

(13·10¹⁷⁵+23)/9 =

1(4)₁₇₄7_<176>

= 509 · 43613 · 270494197 · 1625095091_<10> · 507932858971_<12> · [2914231574374914644040391582107685995370916144611328381628442237813950091096767052130793232979910564293120444648813473231739771966502569323_<139>] SUBMIT/RESERVE

(13·10¹⁷⁶+23)/9 =

1(4)₁₇₅7_<177>

= 3 · 7 · 29² · 21292969 · 9728508841_<10> · [39482355320255808647284070457658369801488167286535850306814506925810162039107635323134557403435573668326821325904197541413859830228659345018738328830087963_<155>] SUBMIT/RESERVE

(13·10¹⁷⁷+23)/9 =

1(4)₁₇₆7_<178>

= 17 · 15569 · 206069 · 6322067 · [4189087628720144335030104745744544192155403838318079784769849137972237981462630931982336575255594813405411929343533880067746634058974765770857672602451569820593_<160>] SUBMIT/RESERVE

(13·10¹⁷⁸+23)/9 =

1(4)₁₇₇7_<179>

= 277 · 4761758900615140831294272937064147828242820480788864164772892249_<64> · 10950997291772328108097594654307473313103101691401224343725196196487050663817487869687697193902016189467940704539_<113> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.36 snfs / 55.55 hours, 4.72 hours / Sep 19, 2008)

(13·10¹⁷⁹+23)/9 =

1(4)₁₇₈7_<180>

= 3² · 3229 · 4597 · 60089 · 9879095759527441932587_<22> · [1821392789543283208015779931781060988466531101782531745919385953070492792750885981972199805456529782001287277526518265512467687177712098940606237_<145>] SUBMIT/RESERVE

(13·10¹⁸⁰+23)/9 =

1(4)₁₇₉7_<181>

= 67 · 173 · 1201 · 8629 · 31183 · 7190848943_<10> · 21741426124657_<14> · [2466552547341160226913723237776553992923422935263438317170959617269747315880981227453378058085526624209134301860096715548697828332522814400581_<142>] SUBMIT/RESERVE

(13·10¹⁸¹+23)/9 =

1(4)₁₈₀7_<182>

= 89 · 2351 · 4179597741403657136125578561199_<31> · 16516716760333096667117988980295045301374057590810905188798934704363204087310377384973228139433525404697961018840872069367433826397908079799882327_<146> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3984167826 for P31 / Mar 1, 2008)

(13·10¹⁸²+23)/9 =

1(4)₁₈₁7_<183>

= 3 · 7 · 431 · 504877 · 302900359194380622368791_<24> · 620741362332478637843569_<24> · 1652669751954615254434527463_<28> · 102018902795014993632340869013035640829170549_<45> · 997106370883333600948149656195325748620925984243486157_<54> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P45 x P54 / 4.25 hours on Cygwin on AMD 64 3400+ / Mar 5, 2008)

(13·10¹⁸³+23)/9 =

1(4)₁₈₂7_<184>

= 32797 · 194230109 · 226751500243661571246030543523786719607331695910187663819794246620911181291235943332796700323983784194557843856682728647178989148353288827983816328735168857123517123732839_<171>

(13·10¹⁸⁴+23)/9 =

1(4)₁₈₃7_<185>

= 130313823514075667946558550056804849533881379_<45> · 134178502432547024473255568544090457894328704524614680930133832431_<66> · 826090095056379329198269351883150800396104341540990784443107295090242772603_<75> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 360.94 hours on Cygwin on AMD 64 3200+ / Mar 28, 2008)

(13·10¹⁸⁵+23)/9 =

1(4)₁₈₄7_<186>

= 3 · 6699197 · 56662439 · 126841559960550153075538632626486274040210390451675498212320432112321953371322067366445757785835682518709324458090992856907018900429758723937835474992342037192138119163903_<171>

(13·10¹⁸⁶+23)/9 =

1(4)₁₈₅7_<187>

= 127 · 1422107 · 6477644772041_<13> · 12188549828209_<14> · [101296789867835711838715838690105224221262432556607006358844202323250939074384546949241956477676722382825313871920253963733662078627313214883543362997067_<153>] SUBMIT/RESERVE

(13·10¹⁸⁷+23)/9 =

1(4)₁₈₆7_<188>

= 1669 · 4027 · 311512763 · 3294371807_<10> · 510290097199_<12> · 1191107593453_<13> · 42103336104117427_<17> · 81833245643991275917541848002766588054252965890498015493532668769168512215639660989395325346677534909178697506170440128861_<122>

(13·10¹⁸⁸+23)/9 =

1(4)₁₈₇7_<189>

= 3³ · 7 · 21882899 · 39682621950481289503_<20> · 880103652261416918717838857429351550456909957445826138372197460059174974956276090100197603403822063807064276345251916195768413842972946988720327601506880363959_<159>

(13·10¹⁸⁹+23)/9 =

1(4)₁₈₈7_<190>

= 1481 · 516521 · 5724007 · [329881260214684829594791355574680799465151633821967866359448286743405552882146665435721608770125843057030604374326147530655554322570247227301010559318886394255915247607263321_<174>] SUBMIT/RESERVE

(13·10¹⁹⁰+23)/9 =

1(4)₁₈₉7_<191>

= 4102505843284003964542961_<25> · 1881580315956778183210367581_<28> · [1871237333044290490645956660703574247499490247718514170731094415373529604280586216238758938023498804568082632342152470849028226601249848667_<139>] SUBMIT/RESERVE

(13·10¹⁹¹+23)/9 =

1(4)₁₉₀7_<192>

= 3 · 787 · 151303795183_<12> · 239927831108970050531880906952823_<33> · [1685289077230009467477538807130226181158811156835053798339057727432760588816583828561885708429215857645462356028296583066530644331964269498237103_<145>] (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=899759065 for P33 / Mar 2, 2008) SUBMIT/RESERVE

(13·10¹⁹²+23)/9 =

1(4)₁₉₁7_<193>

= 19 · 31301420412352178317_<20> · [2428752140042345092889937649431367605772781656042124512518432210530648112769743226424130707529477577373645814055484657215476574930133345232859726043594705016237741210804889_<172>] SUBMIT/RESERVE

(13·10¹⁹³+23)/9 =

1(4)₁₉₂7_<194>

= 17 · 1196455461628544734772941131559603494899791069387129434425021729_<64> · 5746234301488081463418161619215684930851366835539570351147091267_<64> · 123586790714944675816525046385603864129642170689196698566797580037_<66> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, Msieve 1.38 snfs / 207.28 hours, 24.64 hours / Oct 1, 2008)

(13·10¹⁹⁴+23)/9 =

1(4)₁₉₃7_<195>

= 3 · 7 · 4357 · 115022837 · 71984333297_<11> · 22513090507837_<14> · 8469091189618167890062314493657595724221763604160485971763183173242421147974254450513919830321271503772120732615615489971694895495365472912609385627472918807_<157>

(13·10¹⁹⁵+23)/9 =

1(4)₁₉₄7_<196>

= 103 · 331 · 577 · 911725164517_<12> · 563220168489614860626764656859_<30> · 41654141427322616652855513644521_<32> · 37391517136576492214407196832292095434789606457973_<50> · 91809241027487944385754632122283696654344609873546408374196174673_<65> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2224965545 for P32 / Mar 3, 2008) (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=969132544 for P30 / Mar 3, 2008) (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P50 x P65, Msieve 1.33 / Mar 9, 2008)

(13·10¹⁹⁶+23)/9 =

1(4)₁₉₅7_<197>

= 85159 · 548323 · 860957 · [359295985912236483282775809568733069700515487252352971275333254567512886529014145497788637789396313035919971840592993740715620279639049200325491006299202050691275206302409836613503_<180>] SUBMIT/RESERVE

(13·10¹⁹⁷+23)/9 =

1(4)₁₉₆7_<198>

= 3² · 47 · 465067 · 4097767 · 3488972006228808849811_<22> · [51357066117492293940042807873871148801767084025610575557912798274680838279763264465704929474707800866886563622032559027983526986182936022780795747966608284404991_<161>] SUBMIT/RESERVE

(13·10¹⁹⁸+23)/9 =

1(4)₁₉₇7_<199>

= 179 · 266983 · 30224853402660405081436763888371869521549149844274696552759912390053927950687305377664274618293639486732420463245958652870192882668725658080095038471042031790161360564614955490427506441247571_<191>

(13·10¹⁹⁹+23)/9 =

1(4)₁₉₈7_<200>

= 88301 · 97171 · 14709557 · 9380701384113676637_<19> · 96637000536716385619_<20> · 57251133189500039825065474428151_<32> · 333670648710684229453163570612770033938844831_<45> · 6608731526570938248049146439234589449529372334618254009651625581707_<67> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=764502261 for P32 / Mar 4, 2008) (Robert Backstrom / GGNFS-0.77.1-20050930-k8 gnfs for P45 x P67, Msieve 1.33 / Mar 9, 2008)

(13·10²⁰⁰+23)/9 =

1(4)₁₉₉7_<201>

= 3 · 7 · 83 · 82871167208516606106967552750685280805762733473576847070822974437432268757569962389239497673232612991649136227449480461528654299738637088034678396124179256709377191304902148275642251545866003697329_<197>