Since June 16, 2000

STUDIO KAMADA

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News and updates, February 2007

Feb 28, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
(10¹⁵³+11)/3 = (3)₁₅₂7_<153> = 21713 · 1958639 · C142
C142 = P47 · P96
P47 = 56012047933977242644746128635736463158657930621_<47>
P96 = 139933940296037326170860171696111127188198457902149369986513673643425230148449166105666454124371_<96>

Number: 33337_153 N=7837986571451952337344021664199398173461416743422190003615130300703792594977381173662233460335937902016270973969313815005514673204533423264391 ( 142 digits) SNFS difficulty: 153 digits. Divisors found: r1=56012047933977242644746128635736463158657930621 (pp47) r2=139933940296037326170860171696111127188198457902149369986513673643425230148449166105666454124371 (pp96) Version: GGNFS-0.77.1-20050930-k8 Total time: 23.71 hours. Scaled time: 21.41 units (timescale=0.903). Factorization parameters were as follows: n: 7837986571451952337344021664199398173461416743422190003615130300703792594977381173662233460335937902016270973969313815005514673204533423264391 m: 2000000000000000000000000000000 c5: 125 c0: 44 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2400001) Primes: RFBsize:176302, AFBsize:176309, largePrimes:5522255 encountered Relations: rels:5355675, finalFF:397759 Max relations in full relation-set: 28 Initial matrix: 352677 x 397759 with sparse part having weight 36285588. Pruned matrix : 338033 x 339860 with weight 27748899. Total sieving time: 22.55 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.02 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 23.71 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 27, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
10¹⁹⁰+3 = 1(0)₁₈₉3_<191> = 7 · 109 · 1999 · 9733 · 3233311 · 754010347 · 2866919243941_<13> · 17720582280902798851_<20> · C133
C133 = P33 · C100
P33 = 655722163172284079918744219522347_<33>
C100 = [8294263879886669337889452986894589163143089933573829537603544076933357431118781123536752128389983027_<100>]

Feb 27, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs
10¹⁷⁸+3 = 1(0)₁₇₇3_<179> = 7 · 157 · 24245477791_<11> · 5078466902270143_<16> · 4569709099059178801353087954144739_<34> · C116
C116 = P57 · P59
P57 = 841050813852720381404892919400005717849954152346218888253_<57>
P59 = 19227735730244777938096884405431184217580235872014168819807_<59>

Number: 10003_178 N=16171502784467401319287662621859897744129487788677630030766407486502790213752219467024595149277155013321436626027171 ( 116 digits) Divisors found: r1=841050813852720381404892919400005717849954152346218888253 (pp57) r2=19227735730244777938096884405431184217580235872014168819807 (pp59) Version: GGNFS-0.77.1-20050930-k8 Total time: 31.02 hours. Scaled time: 28.04 units (timescale=0.904). Factorization parameters were as follows: name: 10003_178 n: 16171502784467401319287662621859897744129487788677630030766407486502790213752219467024595149277155013321436626027171 skew: 59320.44 # norm 8.29e+15 c5: 18360 c4: -5896211018 c3: -169978952505995 c2: 19216375200484044757 c1: 295044772439832950255035 c0: -5091579523182641313914445475 # alpha -6.33 Y1: 648790286489 Y0: -15451715806320998022694 # Murphy_E 5.24e-10 # M 2075202453831472643899126093394648510121006128741731540160248918241614765343065675054342930282131187537282500185585 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3075001) Primes: RFBsize:256726, AFBsize:257167, largePrimes:7603714 encountered Relations: rels:7597769, finalFF:672489 Max relations in full relation-set: 28 Initial matrix: 513974 x 672489 with sparse part having weight 59145054. Pruned matrix : 388056 x 390689 with weight 34744662. Total sieving time: 29.17 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.52 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 31.02 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 25, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
10¹⁷⁸+3 = 1(0)₁₇₇3_<179> = 7 · 157 · 24245477791_<11> · 5078466902270143_<16> · C149
C149 = P34 · C116
P34 = 4569709099059178801353087954144739_<34>
C116 = [16171502784467401319287662621859897744129487788677630030766407486502790213752219467024595149277155013321436626027171_<116>]

Feb 25, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
(55·10¹⁵³-1)/9 = 6(1)_153<154> = 3 · 7² · 59 · 499 · 4433601500999501_<16> · C132
C132 = P36 · P96
P36 = 443171310398193925665075725975649587_<36>
P96 = 718657553936836885321598272947467364542248403492347369865271322934439134580238588061966073028939_<96>

Number: 61111_153 N=318488409905748732335262453779275118109518084807264340557733279354756102540104018347999743339896897734455486744819880964471174398193 ( 132 digits) SNFS difficulty: 156 digits. Divisors found: r1=443171310398193925665075725975649587 (pp36) r2=718657553936836885321598272947467364542248403492347369865271322934439134580238588061966073028939 (pp96) Version: GGNFS-0.77.1-20050930-k8 Total time: 23.26 hours. Scaled time: 21.07 units (timescale=0.906). Factorization parameters were as follows: n: 318488409905748732335262453779275118109518084807264340557733279354756102540104018347999743339896897734455486744819880964471174398193 m: 10000000000000000000000000000000 c5: 11 c0: -20 skew: 1.13 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2600001) Primes: RFBsize:216816, AFBsize:217532, largePrimes:5648529 encountered Relations: rels:5672716, finalFF:610597 Max relations in full relation-set: 28 Initial matrix: 434414 x 610597 with sparse part having weight 46505927. Pruned matrix : 319951 x 322187 with weight 28817513. Total sieving time: 22.20 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.91 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 23.26 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 24, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
10¹⁸⁰+3 = 1(0)₁₇₉3_<181>

= 28123846354801856041_<20> · 846519155191153820587_<21> · C140
C140 = P35 · P105
P35 = 77061435151581887669779157560546231_<35>
P105 = 545068896844122913071888795078742584270297590744667404658731433888121502839542622364777079658746154067239_<105>

Feb 24, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
(28·10¹⁵³-1)/9 = 3(1)_153<154> = 3 · 2156207 · 8622287 · 599155396153_<12> · C128
C128 = P51 · P78
P51 = 758789025710646472692249434850475074640894740293827_<51>
P78 = 122693293575279404068194860876165197135028729140976454096131624341950993818503_<78>

Number: 31111_153 N=93098324693216579417753550046991752832637021075594278760522148525511109448795692087399923815341074215583301555795522034929280981 ( 128 digits) SNFS difficulty: 155 digits. Divisors found: r1=758789025710646472692249434850475074640894740293827 (pp51) r2=122693293575279404068194860876165197135028729140976454096131624341950993818503 (pp78) Version: GGNFS-0.77.1-20050930-k8 Total time: 19.61 hours. Scaled time: 17.77 units (timescale=0.906). Factorization parameters were as follows: n: 93098324693216579417753550046991752832637021075594278760522148525511109448795692087399923815341074215583301555795522034929280981 m: 10000000000000000000000000000000 c5: 7 c0: -25 skew: 1.29 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2400001) Primes: RFBsize:216816, AFBsize:216906, largePrimes:5406288 encountered Relations: rels:5274106, finalFF:488668 Max relations in full relation-set: 28 Initial matrix: 433788 x 488668 with sparse part having weight 34023429. Pruned matrix : 393569 x 395801 with weight 23880608. Total sieving time: 18.36 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.12 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 19.61 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 23, 2007 (2nd)

By Yousuke Koide / GMP-ECM
10⁸¹²+1 = 1(0)₈₁₁1_<813> = 73 · 137 · 233 · 7841 · 355193 · 17456377 · 21591416633_<11> · 127522001020150503761_<21> · 17468739848498438039329935679794457_<35> · 320326994163169943384295066992439316655840979654890345228609_<60> · C665
C665 = P33 · C633
P33 = 144919694966021542240510318821809_<33>
C633 = [395331939737645320291413064117561097049246687109905814427194810304353495921929416126294305229072789125855534815576659488174603154390875860634149548209175383448724590281810799154139648183136729921980128112325848586411749334562196253224749514725985439259582812608720279719207754040268684455927656154375997917489451629418896999620634088684149924321190877325892101533587902648474485664803938673414481754826326389029692982503772120395159833178519597418300782371333265894526366450300708586722070814774924029567261873002611140424872633891019926511850875956451902172967028046865109519247953630446750690804572155699886510959628554374758738857_<633>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 23, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
(86·10¹⁵³+31)/9 = 9(5)₁₅₂9_<154> = 11 · 157 · 593447 · 355701609695516717_<18> · C128
C128 = P43 · P86
P43 = 2333147258247029252947881169964585045658781_<43>
P86 = 11234498342156787134685645268358398193131468455122513168368272096894919519757431168343_<86>

Number: 95559_153 N=26211739004783903442088690574964455578189548285351447620659647136122658039301734190181588545726298787223130741712855492947169883 ( 128 digits) SNFS difficulty: 155 digits. Divisors found: r1=2333147258247029252947881169964585045658781 (pp43) r2=11234498342156787134685645268358398193131468455122513168368272096894919519757431168343 (pp86) Version: GGNFS-0.77.1-20050930-k8 Total time: 28.68 hours. Scaled time: 25.98 units (timescale=0.906). Factorization parameters were as follows: n: 26211739004783903442088690574964455578189548285351447620659647136122658039301734190181588545726298787223130741712855492947169883 m: 2000000000000000000000000000000 c5: 5375 c0: 62 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216097, largePrimes:5600692 encountered Relations: rels:5519089, finalFF:512518 Max relations in full relation-set: 28 Initial matrix: 432979 x 512518 with sparse part having weight 41128559. Pruned matrix : 389202 x 391430 with weight 27957400. Total sieving time: 27.31 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.20 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 28.68 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 22, 2007 (2nd)

By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
10¹⁹⁹+3 = 1(0)₁₉₈3_<200> = 13 · 4533299 · 259556761 · 111011352372742720485057131_<27> · 505135145839533539009957298516389_<33> · C125
C125 = P41 · P84
P41 = 16093036459190114862200718359175889466551_<41>
P84 = 724430892695841602220008780254282449815290128891715782166558993784367540920500492781_<84>

Feb 22, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs
(52·10¹⁹⁹-7)/9 = 5(7)_199<200> = 3 · 19 · 13119178847_<11> · 21322941493829819_<17> · 27313233753447177563_<20> · 411351101494831873367498992021260976263151_<42> · C111
C111 = P46 · P66
P46 = 1272101379026747903707298354196236477819089199_<46>
P66 = 253527282351532668908867579235496341067847640059655454647818415871_<66>

Number: 57777_199 N=322512405500288394218032710154255774087278705689799529635356287413030666368619768153870436563708339820226277329 ( 111 digits) Divisors found: r1=1272101379026747903707298354196236477819089199 (pp46) r2=253527282351532668908867579235496341067847640059655454647818415871 (pp66) Version: GGNFS-0.77.1-20050930-k8 Total time: 19.89 hours. Scaled time: 17.98 units (timescale=0.904). Factorization parameters were as follows: name: 57777_199 n: 322512405500288394218032710154255774087278705689799529635356287413030666368619768153870436563708339820226277329 skew: 19049.31 # norm 4.62e+15 c5: 56940 c4: 8333311569 c3: 130378450823455 c2: -3457389236060032737 c1: 7122233774699597553648 c0: 26218571313762820195500400 # alpha -5.75 Y1: 129261245377 Y0: -1414570610242647704179 # Murphy_E 8.37e-10 # M 244908670307495451176391156578070089225011585752165573221271866723377090566827216829777892597738977141074837489 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1200000, 2040001) Primes: RFBsize:176302, AFBsize:176810, largePrimes:7526749 encountered Relations: rels:7290349, finalFF:434299 Max relations in full relation-set: 28 Initial matrix: 353195 x 434299 with sparse part having weight 42494161. Pruned matrix : 299074 x 300903 with weight 27376589. Total sieving time: 18.86 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.75 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 19.89 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 21, 2007 (2nd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
(2·10¹⁵⁷-17)/3 = (6)₁₅₆1_<157> = C157
C157 = P60 · P98
P60 = 628486628437275763243226019561267587348336747741014522686317_<60>
P98 = 10607491655380562300466288136354207234632798963479344661061680154739676571597744074392683606884633_<98>

Number: 66661_157 N=6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 ( 157 digits) SNFS difficulty: 157 digits. Divisors found: r1=628486628437275763243226019561267587348336747741014522686317 (pp60) r2=10607491655380562300466288136354207234632798963479344661061680154739676571597744074392683606884633 (pp98) Version: GGNFS-0.77.1-20050930-k8 Total time: 27.11 hours. Scaled time: 24.59 units (timescale=0.907). Factorization parameters were as follows: n: 6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 m: 10000000000000000000000000000000 c5: 200 c0: -17 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216541, largePrimes:5667132 encountered Relations: rels:5652586, finalFF:569599 Max relations in full relation-set: 28 Initial matrix: 433422 x 569599 with sparse part having weight 46045150. Pruned matrix : 356719 x 358950 with weight 28863014. Total sieving time: 25.81 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.15 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 27.11 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.63 BogoMIPS (lpj=2335816) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.10 BogoMIPS).

Feb 21, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(52·10¹⁹⁹-7)/9 = 5(7)_199<200> = 3 · 19 · 13119178847_<11> · 21322941493829819_<17> · 27313233753447177563_<20> · C153
C153 = P42 · C111
P42 = 411351101494831873367498992021260976263151_<42>
C111 = [322512405500288394218032710154255774087278705689799529635356287413030666368619768153870436563708339820226277329_<111>]

Feb 17, 2007 (2nd)

By Yousuke Koide / GMP-ECM
(10¹⁴⁸⁵-1)/9 = (1)_1485<1485> = 3³ · 31 · 37 · 41 · 67 · 199 · 271 · 397 · 757 · 991 · 1321 · 21649 · 34849 · 55243 · 62921 · 198397 · 238681 · 333667 · 471241 · 513239 · 1577071 · 2906161 · 16357951 · 18679321 · 60834511 · 83251631 · 310362841 · 1981560241_<10> · 31351842721_<11> · 258360989311_<12> · 31600574312077_<14> · 440334654777631_<15> · 545431981101481_<15> · 596298133647227881_<18> · 1344628210313298373_<19> · 4185502830133110721_<19> · 165426670443186506567467_<24> · 1300635692678058358830121_<25> · 138267770127916457629034873443951_<33> · 483418418597220677238517353915231961831_<39> · 16860090181450569942798606214497570829921_<41> · 1703548913892494075097664562023844278044121_<43> · 362853724342990469324766235474268869786311886053883_<51> · 7907009307594694001053552000588658391100974093457603716419437_<61> · 1113954903312329460800701782039373182801635744784098645224633477_<64> · [88415092713367678139008031849456036531214635443710603842417450647749425991456343388066542975721610469026836129783834813518385505575072089337317444944320083700084281_<164>] · C695
C695 = P34 · C662
P34 = 4035237932666608861051093768608241_<34>
C662 = [14491961854759997987318745440205865717215092235131607457539451297044985828137745987618751910779935337450743029169715116165130001535712858818542505553012159022658570403931283147158358096058156927519056819695880820440205164069148370546551136152026451401191468202488142651601966386910139935847132556803499130069122366612387262070859275372869822375695150111399077632325143331047045000707169517942466827613230622811019760241780737321155276049750304376977883406746688008002436878234529678022439754363890579416396792468847348438177735168318288241130782120589812040887053417704682926423525859672694505398099632321848048462247957579965155055393914376032729548547886567561_<662>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 17, 2007

By Thomas Womack / gmp-ecm 6.1.2 B1=10^7
(52·10¹⁸⁰-7)/9 = 5(7)_180<181> = C181
C181 = P40 · C142
P40 = 1907145664709063958354268537876114943171_<40>
C142 = [3029541940446998167772966488018297475181566383829140811226747765285330708447334102021603405973003072683807287017514072821950182110331738508987_<142>]

Feb 16, 2007 (2nd)

By Thomas Womack / gmp-ecm 6.1.2 B1=10000000
(4·10¹⁷⁴-13)/9 = (4)₁₇₃3_<174> = C174
C174 = P35 · P139
P35 = 87397362083737992740080811306657947_<35>
P139 = 5085330195877183357332537501058300188350678694002609720879352861143821239003179780252075511657845817249891108582299028154671201878554346369_<139>

Feb 16, 2007

By Thomas Womack / ggnfs-0.77.0
8·10¹⁶¹-3 = 7(9)₁₆₀7_<162> = 11² · C160
C160 = P51 · P110
P51 = 250747836796484155922888159263112237486391376320671_<51>
P110 = 26367406923235271511544763325616291041131768180892905671230128715401910040795595415317934691655387997292702267_<110>

r1 = 26367406923235271511544763325616291041131768180892905671230128715401910040795595415317934691655387997292702267 r2 = 250747836796484155922888159263112237486391376320671 Total time: 42.61 hours. Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2250000, 3850001) Relations: rels:5942000, finalFF:809129 Initial matrix: 631709 x 809129 with sparse part having weight 46075762. Pruned matrix : 557525 x 560747 with weight 22467359. Total sieving time: 39.60 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.76 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 42.61 hours.

Feb 15, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8
2·10¹⁶⁶-9 = 1(9)₁₆₅1_<167> = C167
C167 = P43 · P124
P43 = 4342608369450320053307697679764984011450663_<43>
P124 = 4605526977909722451833107953713650779997398871974627226660275324682668177795505331963035514480056136584527504258436835169457_<124>

Number: 19991_166 N=19999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 ( 167 digits) SNFS difficulty: 166 digits. Divisors found: r1=4342608369450320053307697679764984011450663 (pp43) r2=4605526977909722451833107953713650779997398871974627226660275324682668177795505331963035514480056136584527504258436835169457 (pp124) Version: GGNFS-0.77.1-20050930-k8 Total time: 69.64 hours. Scaled time: 63.03 units (timescale=0.905). Factorization parameters were as follows: n: 19999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991 m: 1000000000000000000000000000000000 c5: 20 c0: -9 skew: 1 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 5700001) Primes: RFBsize:412849, AFBsize:412306, largePrimes:5923360 encountered Relations: rels:6223470, finalFF:960819 Max relations in full relation-set: 28 Initial matrix: 825222 x 960819 with sparse part having weight 43152556. Pruned matrix : 703215 x 707405 with weight 28666743. Total sieving time: 66.35 hours. Total relation processing time: 0.12 hours. Matrix solve time: 3.11 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.5,2.5,100000 total time: 69.64 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.60 BogoMIPS (lpj=2335804) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.08 BogoMIPS).

Feb 14, 2007 (3rd)

(10³⁹⁵-1)/9 =

(1)_395<395> = 41 · 271 · 317 · 6163 · 10271 · 307627 · 870801991 · 25439781075319591_<17> · 49172195536083790769_<20> · 4706625334158237778391951_<25> · 3660574762725521461527140564875080461079917_<43> · C262
C262 = P54 · P209
P54 = 388603184868446209952357338208961774763421470820867551_<54>
P209 = 22212532982654486103266742473370118653419410820133470750925842805231785671919088995453275587554965715421794773862472837122581772057977997807066409510062713778700204701764277608437512924874155027264480537635511_<209>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 14, 2007 (2nd)

By Shusuke Kubota / GGNFS-0.77.0
(73·10¹⁵⁴-1)/9 = 8(1)_154<155> = 3² · C154
C154 = P41 · P113
P41 = 93458549042255332010768816824559015680981_<41>
P113 = 96431474395537659290440617511664931557542477458136745046691918305873367117076472604700705384745959369588944243859_<113>

Number: 88881-155 N=9012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679 ( 154 digits) SNFS difficulty: 156 digits. Divisors found: r1=93458549042255332010768816824559015680981 (pp41) r2=96431474395537659290440617511664931557542477458136745046691918305873367117076472604700705384745959369588944243859 (pp113) Version: GGNFS-0.77.0 Total time: 56.41 hours. Scaled time: 46.48 units (timescale=0.824). Factorization parameters were as follows: n: 9012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679 m: 10000000000000000000000000000000 c5: 73 c0: -10 skew: 1 type: snfs qintsize: 25000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2875000) Relations: rels:5526542, finalFF:505041 Initial matrix: 433502 x 505041 with sparse part having weight 40814331. Pruned matrix : 418963 x 421194 with weight 26453378. Total sieving time: 51.15 hours. Total relation processing time: 0.43 hours. Matrix solve time: 4.69 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 56.41 hours. --------- CPU info (if available) ----------

Feb 14, 2007

By Thomas Womack / GGNFS-0.77.0
(5·10¹⁵³+13)/9 = (5)₁₅₂7_<153> = 109 · 1756903 · 1035843636655735339_<19> · C127
C127 = P35 · P92
P35 = 50145955190901622584127136372141099_<35>
P92 = 55849990274513738302544705045190770656055373081642160005471409653566216764003101702841243831_<92>

r1 = 50145955190901622584127136372141099 r2 = 55849990274513738302544705045190770656055373081642160005471409653566216764003101702841243831 SNFS difficulty: 154 digits. Divisors found: r1=50145955190901622584127136372141099 (pp35) r2=55849990274513738302544705045190770656055373081642160005471409653566216764003101702841243831 (pp92) Version: GGNFS-0.77.0 Total time: 26.69 hours. Scaled time: 42.86 units (timescale=1.606). Sieved special-q in [1200000, 2300001) Relations: rels:5620503, finalFF:527326 Initial matrix: 352875 x 527326 with sparse part having weight 48316105. Pruned matrix : 321712 x 323540 with weight 19282768. Total sieving time: 24.69 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.79 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 26.69 hours.

Feb 12, 2007 (2nd)

By Yousuke Koide / GMP-ECM
(10⁸²⁵-1)/9 = (1)_825<825> = 3 · 31 · 37 · 41 · 67 · 151 · 271 · 1321 · 4201 · 7151 · 15401 · 21401 · 21649 · 25601 · 59951 · 62921 · 143551 · 471241 · 513239 · 2906161 · 83251631 · 182521213001_<12> · 1344628210313298373_<19> · 155460646275454423201_<21> · 1300635692678058358830121_<25> · 138267770127916457629034873443951_<33> · 2495283264895779020253203931608951_<34> · 15763985553739191709164170940063151_<35> · 1703548913892494075097664562023844278044121_<43> · 6069650333889644423896816835276507778804898705650161138729963603757211141984131085449988328049514249213169785004014797295919583814686411189300687347453551_<154> · C375
C375 = P43 · P333
P43 = 2088776436021648629103222560680031099644951_<43>
P333 = 214528843968953631928063476651039061041063809962416030964828547787541153707714846521305533494862873734486298787721809249575564868485587852627557513243818964260757025571864734011221992206979184553651791551471337682785524853615509168758324340944481464694072720676919519406523000680246989690635604205812979868199506676258154640779755801_<333>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 12, 2007

By Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs
(7·10¹⁸⁴-43)/9 = (7)₁₈₃3_<184> = 3 · 2087 · 173267 · 92637580320041260534335543461_<29> · 54923797941083258665408610502743_<32> · C115
C115 = P49 · P67
P49 = 1383615489945228484659595198563915740434096933951_<49>
P67 = 1018433770708324513989795221242712535071162592913196540345250819023_<67>

Number: 77773_184 N=1409120740635364908607465067802764562290036915063588145837948055243262006073639575459991601899495173541955885349873 ( 115 digits) Divisors found: r1=1383615489945228484659595198563915740434096933951 (pp49) r2=1018433770708324513989795221242712535071162592913196540345250819023 (pp67) Version: GGNFS-0.77.1-20050930-k8 Total time: 31.91 hours. Scaled time: 28.94 units (timescale=0.907). Factorization parameters were as follows: name: 77773_184 n: 1409120740635364908607465067802764562290036915063588145837948055243262006073639575459991601899495173541955885349873 skew: 57408.89 # norm 1.21e+16 c5: 14280 c4: -8199350774 c3: -148304488649521 c2: 21405458101595154052 c1: 142537809412331697636336 c0: -11062522908965943983877268608 # alpha -6.44 Y1: 1229138586269 Y0: -9973558664403551923037 # Murphy_E 5.60e-10 # M 936351327745923239120694157973164494754818427960473456494344742826592099052997543653036754399328806873797529005227 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3075001) Primes: RFBsize:256726, AFBsize:256781, largePrimes:7532171 encountered Relations: rels:7446703, finalFF:614994 Max relations in full relation-set: 28 Initial matrix: 513590 x 614994 with sparse part having weight 53608083. Pruned matrix : 430894 x 433525 with weight 34153324. Polynomial selection time: 1.31 hours. Total sieving time: 28.56 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.72 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 31.91 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 06 Memory: 4037276k/5242880k available (2106k kernel code, 0k reserved, 1297k data, 196k init) Calibrating delay using timer specific routine.. 4671.60 BogoMIPS (lpj=2335804) Calibrating delay using timer specific routine.. 4668.47 BogoMIPS (lpj=2334238) Total of 2 processors activated (9340.08 BogoMIPS).

Feb 11, 2007

By Yousuke Koide / GMP-ECM
(10⁷⁶⁵-1)/9 = (1)_765<765> = 3² · 31 · 37 · 41 · 271 · 307 · 613 · 18973 · 210631 · 238681 · 333667 · 2071723 · 2906161 · 11910133 · 52986961 · 262533041 · 5363222357_<10> · 8119594779271_<13> · 25332185271529_<14> · 77967508765681_<14> · 13168164561429877_<17> · 41331541464123787_<17> · 4185502830133110721_<19> · 17452955481423492661946457391_<29> · 34194473116159546979818689031_<29> · 4222100119405530170179331190291488789678081_<43> · 13753721844250167674053932561585423251305429858083649_<53> · 2385503624916094046163570223793978575506412147454036200711_<58> · C385
C385 = P39 · P346
P39 = 513179642980665929403935269209265889161_<39>
P346 = 1950585947224940419950248867026805880899314052934810675053013776673117345436439511928719471294613511792179585771032825256940078928817403205519252806576240803441065824757216160174665670758508088069382574508854177932682656221426002932789572902329615434652326605290218636214671926683628663404694204326895954873066839725116831163068208522081531521441_<346>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 10, 2007 (2nd)

By Philippe STROHL / GMP-ECM, GGNFS-0.77.1-20060722-pentium-m
(7·10¹⁸¹-43)/9 = (7)₁₈₀3_<181> = 3 · 60487457 · 63749185262142707_<17> · C156
C156 = P35 · P122
P35 = 64777876741657802572555583806019627_<35>
P122 = 10379288937582466970916981607412631488017397024321519329007965704922134757985272848817679210368742928554294200964291659967_<122>
(7·10¹⁸⁴-43)/9 = (7)₁₈₃3_<184> = 3 · 2087 · 173267 · 92637580320041260534335543461_<29> · C146
C146 = P32 · C115
P32 = 54923797941083258665408610502743_<32>
C115 = [1409120740635364908607465067802764562290036915063588145837948055243262006073639575459991601899495173541955885349873_<115>]
(7·10¹⁹⁰-43)/9 = (7)₁₈₉3_<190> = 3 · 379853 · 1653502611689_<13> · 223033235529943_<15> · C158
C158 = P32 · P126
P32 = 30617702251306471516292760426167_<32>
P126 = 604465682901527770286687448552777681175592272944031753571377173281664702601341986824877637011967643421219608087996220150348483_<126>
(7·10¹⁷¹-43)/9 = (7)₁₇₀3_<171> = 199 · 151305076042521491_<18> · C152
C152 = P42 · P43 · P68
P42 = 121495956675387278043299989858967591123701_<42>
P43 = 7068538249965126094045281972629883093163147_<43>
P68 = 30078593090070246841437934832118520753770865013385674443419876087151_<68>

Feb 10, 2007

By Philippe STROHL / GMP-ECM
(7·10¹⁹¹-43)/9 = (7)₁₉₀3_<191> = 896542069 · 151215945352530419_<18> · 834957171990917126025520458563_<30> · C152
C152 = P37 · P99
P37 = 1555638964216566815934684090827554843_<37>
P99 = 441686633572614353856740837849121421170592905576897104142793452892615860092900755744822879464359827_<99>

Feb 9, 2007

By Shusuke Kubota / GMP-ECM 6.0.1 B1=1000000, GGNFS-0.77.0 gnfs
(17·10¹⁵³-71)/9 = 1(8)₁₅₂1_<154> = 3 · 11 · 458033732131576820267_<21> · C132
C132 = P34 · P45 · P53
P34 = 2487441325075200197121778501595359_<34>
P45 = 935061187428302940375031505062267678199121469_<45>
P53 = 53728180464604315513396648915975156149011893915038001_<53>

Number: 18881-153 N=50239136223595060423269539592167071615943681788416865006866027868792606935588881818866205949943469 ( 98 digits) Divisors found: r1=935061187428302940375031505062267678199121469 (pp45) r2=53728180464604315513396648915975156149011893915038001 (pp53) Version: GGNFS-0.77.0 Total time: 16.77 hours. Scaled time: 13.76 units (timescale=0.820). Factorization parameters were as follows: name: 18881-153 n: 50239136223595060423269539592167071615943681788416865006866027868792606935588881818866205949943469 m: 1709282966443362906 deg: 5 c5: 3443280 c4: 4131057000 c3: -144180038412326 c2: -1723950652316668 c1: 5865605519247624248 c0: -848169666955669766435 skew: 725.838 type: gnfs # adj. I(F,S) = 47.844 # E(F1,F2) = 2.926012e-03 # GGNFS version 0.77.0 polyselect. # Options were: # lcd=1, enumLCD=2, maxS1=58.00000000, seed=1170826781. # maxskew=1500.0 # These parameters should be manually set: rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 type: gnfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [900000, 1950001) Relations: rels:3911307, finalFF:340161 Initial matrix: 270265 x 340161 with sparse part having weight 28787639. Pruned matrix : 247996 x 249411 with weight 15276957. Total sieving time: 14.69 hours. Total relation processing time: 0.35 hours. Matrix solve time: 1.51 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 16.77 hours. --------- CPU info (if available) ----------

Feb 8, 2007

By Bruce Dodson / GMP-ECM
10²⁶⁶+1 = 1(0)₂₆₅1_<267> = 29 · 101 · 281 · 2129 · 121499449 · 14691812549_<11> · 722817036322379041_<18> · 1369778187490592461_<19> · 1728095716605342484009_<22> · C182
C182 = P52 · P130
P52 = 3845225778323318739662926792353902964405172909187389_<52>
P130 = 4859378131018035310593858490137688922829468686775068797577396520148545290055799616742354372616293735785798821073310265896384033181_<130>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 6, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(13·10¹⁵³-1)/3 = 4(3)_153<154> = 7 · 661 · 797 · 460916575998112074071727299_<27> · C121
C121 = P54 · P68
P54 = 199795892670038144209829374746205946009729446983267859_<54>
P68 = 12760138661362256349935504330320109597229231443037841109860164508027_<68>

Number: trial N=2549423294440337571087290903497700361859461239948612878825560392658318637774911572584694853772175150748353008237496604193 ( 121 digits) SNFS difficulty: 154 digits. Divisors found: r1=199795892670038144209829374746205946009729446983267859 (pp54) r2=12760138661362256349935504330320109597229231443037841109860164508027 (pp68) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 70.94 hours. Scaled time: 38.88 units (timescale=0.548). Factorization parameters were as follows: n: 2549423294440337571087290903497700361859461239948612878825560392658318637774911572584694853772175150748353008237496604193 m: 1000000000000000000000000000000 c5: 13000 c0: -1 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2600001) Primes: RFBsize:176302, AFBsize:176953, largePrimes:5649921 encountered Relations: rels:5555582, finalFF:412943 Max relations in full relation-set: 0 Initial matrix: 353322 x 412943 with sparse part having weight 38504182. Pruned matrix : 331910 x 333740 with weight 28482681. Total sieving time: 59.58 hours. Total relation processing time: 0.57 hours. Matrix solve time: 10.38 hours. Time per square root: 0.41 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 70.94 hours. --------- CPU info (if available) ----------

Feb 6, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4
(8·10¹⁵⁴-53)/9 = (8)₁₅₃3_<154> = 3 · 7 · 19 · C152
C152 = P49 · P104
P49 = 2109117000218396790445988790435409265621492648171_<49>
P104 = 10562674812469988978662532655660065618933586481087912099926424984662629593973290757990833266941366306327_<104>

Number: 88883_154 N=22277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917 ( 152 digits) SNFS difficulty: 155 digits. Divisors found: r1=2109117000218396790445988790435409265621492648171 (pp49) r2=10562674812469988978662532655660065618933586481087912099926424984662629593973290757990833266941366306327 (pp104) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 53.54 hours. Scaled time: 33.84 units (timescale=0.632). Factorization parameters were as follows: n: 22277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917014759120022277917 m: 10000000000000000000000000000000 c5: 4 c0: -265 skew: 2.31 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216371, largePrimes:5634709 encountered Relations: rels:5587850, finalFF:541403 Max relations in full relation-set: 28 Initial matrix: 433251 x 541403 with sparse part having weight 43022066. Pruned matrix : 372854 x 375084 with weight 27680522. Total sieving time: 46.09 hours. Total relation processing time: 0.35 hours. Matrix solve time: 6.91 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 53.54 hours. --------- CPU info (if available) ----------

Feb 2, 2007 (3rd)

By Anonymous
10¹⁰⁰¹+1 = 1(0)₁₀₀₀1_<1002> = 11² · 23 · 463 · 859 · 4093 · 8009 · 8779 · 24179 · 51767 · 590437 · 909091 · 7444361 · 21705503 · 1058313049_<10> · 22144088539_<11> · 109313560357_<12> · 264752347289_<12> · 4539402627853030477_<19> · 104730101107272149081_<21> · 216031795247629116757_<21> · 4924630160315726207887_<22> · 50678387411703889101759125785290439894389920385627096501794498837_<65> · 34607524609209512562213651270561528862879196390936320471942325254862879783_<74> · C685
C685 = P32 · C653
P32 = 82618024434905595106111659338321_<32>
C653 = [58178503308788154426291302030707350928236341702129983308363771602879105119870038450937896434351306926832195838172811764529737671608235809780061534507676893306702862878665952965468559129218515193819486430054025214904255822372500866194419422851643203261474792811499761645758008369734627788354249782503720864053338330703456736872798891065209921648587941030445907386080167626025743023118127792717574879066917697833440606515276780249741342049676747757046612644216010177666746964557488809230177420595138964543098172211888391402341224671422980295129401586274555426919525435497071806104833893258096563326906555680874384650491265582875651844594074431054692116931_<653>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 2, 2007 (2nd)

By Kurt Beschorner / GMP-ECM
(10¹³⁶³-1)/9 = (1)_1363<1363> = 3191 · 16763 · 43037 · 62003 · 580639 · 35121409 · 569205157 · 77843839397_<11> · 509649121665126339920293_<24> · 221693470933128952318104031_<27> · 316362908763458525001406154038726382279_<39> · C1224
C1224 = P30 · C1194
P30 = 795287068884583505529998090507_<30>
C1194 = [303053550423437757744577970664347139058174265460996097827735855091960961366617190860861899538339427405302065921323308004694332410780453265553794004513756822368209038844441902309599726063212073788915315822866313526643695616771407660238952357090919109445769850894110083406400864937888101833288067278306468763556061991141637735812818752063838929845320254221932028730902118799572921376401194490286744053625633974823222256070386822901071470266212047977758083287736560454805962821410294269221218466138883248534724699124803763016999874119320088188873423380603419044661818905203746741225061226597240721791112435539530002691526296718763907292498223321401320012291219342972873336424886111381568035786397233783154826935657629585333161391381414575770495792384239420277817996166704389686399904195136501855409808019538835646562852044459239211575894673645778708008519647683157375573098405948287435014337255947307010911001292419835690084361858589494681751918742740383645957261693219402585237639569461609996150772869934210727941413121840947487571997838497930100990291001100537076969586874801586276569972001567327069012872244703569759943095969578175595127498839339587510269198005621059667948789447437782642986957_<1194>]
(10¹⁴¹⁷-1)/9 = (1)_1417<1417> = 53 · 79 · 592307 · 1192679 · 74383999 · 265371653 · 35224702898191_<14> · 712767480971213008079_<21> · 5295275348767234696493_<22> · 246829743984355435962408390910378218537282105150086881669547_<60> · C1269
C1269 = P27 · C1243
P27 = 320759296668278219098942271_<27>
C1243 = [1807962964739891266189097056530234806062431767311423328744246983012018469480509986030486092575806531205340633799701714501165255757647960636778704332848091002970907847614870031786506197311736491694548091615354728702238276470555753505102286480946750577799105829175873448773931411486194802387560478953556109800421252377051910887848432972004805875176348604596991067283393186015327300001219122275166001470317555037985576878046909924066826046595406861138007407044607947349804561692439601682308891050632770431801025387194322134807435474333209341495146357837941837551706663872277184691379667841049800124927701696945137899749848756941018168966978497219949386544439607730078717943844176715497535766483923175904691169486082589380849466712498419529363740988161052645728327293980736354239984569025476919263028684103495974518096875427430007362125003715323349166458392306648079506655261994595408652409837318999606971784596145004271200346154069050284165284502300089336496441994324497430903465478316042118552841508288916762534034593841431651854367051273254973426855748143399608480280391066558807548859322585665145716396172940250714548218710694760335882280800696008224923355890289479592821583051861272228680196273820468893343061082725120024319369835150920080067_<1243>]
(10¹⁵⁴¹-1)/9 = (1)_1541<1541> = 3083 · 416071 · 493121 · 73169879117_<11> · 79863595778924342083_<20> · 11111111111111111111111_<23> · 28213380943176667001263153660999177245677_<41> · C1432
C1432 = P27 · C1406
P27 = 453705568156105320101001973_<27>
C1406 = [21134651516625743546890394107470844907479101338767920175606829641381409740006066105359778875852557693330672741609769971903490143459321853791621927150388840080978939724048850901854316724028594840222545578756237289839719333944013510117329696331418528887043082498707522884927211722756355953420758843956706414456395748205730175240795380943328077101500432000606746309699225335852275849208810579013996932425337858730804408430076455488292782663754279650536042416841571872994763623564370557928084924692369433971807291184955462748659972340620316419998766214376110878039100970605546328475282329672793112780945215005900449423748649485575832923817067261319677247616470177480667543260307649641155900211417251124900673058337339052575004426303516852740850083831820888199155367665484662813601732714457812587267307725453146328707543884479978031437792448373540869436638720441463327503700034899467797981715427485727388369367494620211186531624606909762218646618344073281919148141141103101374642913607603429301308817846134680270940432922295257930326912840385952450105869326719027661322184642246076759572589955126651100077599548810133757709419575105659702183751467048010072475380106330080726264759988336691270828091597604129022525679595125180138288946082224994462694280827181587124958906971098972669340113833079048056605666830126595568874371693442218186856330033320899529202798532949224792235565371115950824730876872577562530307_<1406>]
(10¹⁷⁸⁹-1)/9 = (1)_1789<1789> = 39359 · 15367511 · 1553903933_<10> · 1036330801552389631_<19> · C1750
C1750 = P24 · C1726
P24 = 289319996763559834545559_<24>
C1726 = [3942837499439788061006944005045960718031486305577669627347253650039890321211994289379151938973310874850909435607956123122373090697532769795751167924693837794161082874840439638501132104303263899086924115533649057636244015830444657773516604004037438543727777073203302412364862600498176849479949473377539411452728745169933045051932389267734062359088160828713934870961080362842267605776193414549899550396053896313811933135608302426066443951706346413481958933433688342021908673459058683089585505795767461215484375046250361597762305765392896560557743728592263890398335486220705008931781533659816577900022386517954802174214486603572948890913445984059319713144031993677879920870496666548344818537213927754061002698478647910543381380073623428605053342609122482475738206920326824464327619038724816610030642905609614072435312429524191225206369486913501903002277803975049628855245626076186828913477216013920331439226922420525254233442729472850030206453751204580226244005963622625739486689341400829788024746459418073871675281540798930149401936448596412966292470988929859007344438577764846698397140012506376736645041912539548266216913362399399032412908581595079247559109902038049591748329385786055846889351909274757252136756090688205433305699729684759624710529568581942894558580807538053455910285653760969235114134103679010678018567507583541013942437863524408140562028399790265985729515306715849629150272650273129300704875740641586416956958650682921949181587381455061374245833631347378093122836134452241005704894394879066045192375148941067473715818860137578458100687319496055787232337883524420144853590949474086092966954941929991699950779540584381552340206530079269381878652437099530645734013689177173442931238693436585294711171175497278627_<1726>]
10¹¹⁷³+1 = 1(0)₁₁₇₂1_<1174> = 7 · 11 · 13 · 47 · 103 · 139 · 2531 · 4013 · 31051 · 2955961 · 2140571729_<10> · 21993833369_<11> · 37633218241_<11> · 291078844423_<12> · 837042695779_<12> · 9101279023169_<13> · 143574021480139_<15> · 549797184491917_<15> · 377526955309799110357_<21> · 24649445347649059192745899_<26> · 473608692432035450677211738101499095303_<39> · 10716938719047367538834654373404752406351326801836497222088230040131663586216274781916394062442922695303181507242106723273347077744999936956310904046369389147208937313522359019479619429347564668082983985444056247726866683751993403229947286059050999830315193876492518147194037_<275> · C693
C693 = P28 · C665
P28 = 5718695187661520881538869249_<28>
C665 = [19010644145695322442596197267125042884422868255022599767493290364039234062415429333907999864691739173795260320378861055964127145682409009427107712529810252464517289298080164319904869840576256342883389125818582402079952512042858297115608946297491656759114204785207287207243576094138786865390191547258635907677241328093726205037638267062013156683163911676808858057446736948956303893626662973050170317203867973298049356744746481831901972743222598577141036541608397443502337218886325093431887273649028091617509913303741217594022418581681618959379282154580275142153998626983832153956552170243293669205787041806706605636159791777704358392669878320221138319342230431351721_<665>]
10¹¹⁹³+1 = 1(0)₁₁₉₂1_<1194> = 11 · 59651 · 53979914146049857432194823_<26> · C1162
C1162 = P30 · C1133
P30 = 198967330445464802733582366889_<30>
C1133 = [14189778742392371822642464950295420598664613116648809753042689444870476667678262283972005038116540843336863837863764148879121448975368096535914316580611824820280358541845177484282962523673492504056748411707282673481645254762423336182533392931917615081877746791397835188974222778151311424184745536567736162654982777184515925485753546325716404087091870903092275328177951082186392981158347804800448785726152060403108870700513166920826189555108851673010918501338004327589779330197106265408955344060922120410917888447706962950356306376942817414547580241131328456968130947355118062783781411462622375933899030723810309604218581357118013526489734378995893972825454915362359640168679374586440064527973918906860115103631093524224684768949076317452365838495117769189761295766298889392238273398605877114850710885226216618560741198378653014548830718195754193150403671240372569916849086223167646058546438327863231841205948476087420301663949934620211238040821675676819201872339480134979460270733168740906651295908694282683598843883004034032243280079564829227845090271498824504246761717903627496937462197957747979655626804393725202656530686491589503_<1133>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 2, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(67·10¹⁵³+23)/9 = 7(4)₁₅₂7_<154> = 11 · 6030653 · 8193403 · 326176421242447441543_<21> · C119
C119 = P43 · P76
P43 = 5154315594748468038755725836892835668230311_<43>
P76 = 8146806128868512010643223189999358487179665174602492096290584650206693233411_<76>

Number: trial N=41991209877419369037432001482964525746811820171841723098290931984019537579033702205003427059699691239093343828828120821 ( 119 digits) SNFS difficulty: 154 digits. Divisors found: r1=5154315594748468038755725836892835668230311 (pp43) r2=8146806128868512010643223189999358487179665174602492096290584650206693233411 (pp76) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 67.72 hours. Scaled time: 34.88 units (timescale=0.515). Factorization parameters were as follows: n: 41991209877419369037432001482964525746811820171841723098290931984019537579033702205003427059699691239093343828828120821 m: 1000000000000000000000000000000 c5: 67000 c0: 23 skew: 1 type: snfsFactor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:217321, largePrimes:5617548 encountered Relations: rels:5590468, finalFF:508481 Max relations in full relation-set: 0 Initial matrix: 434204 x 508481 with sparse part having weight 32443032. Pruned matrix : 382267 x 384502 with weight 23492975. Total sieving time: 55.64 hours. Total relation processing time: 0.56 hours. Matrix solve time: 11.02 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 67.72 hours. --------- CPU info (if available) ----------