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News and updates, January 2006

Jan 31, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000
(85·10¹⁹⁵+41)/9 = 9(4)₁₉₄9_<196> = 11 · 251 · 2161031 · 27117551 · 1356870133_<10> · 1739134559_<10> · C161
C161 = P32 · C129
P32 = 25433652459414927499870617826399_<32>
C129 = [972564350491546545147205599284218262224405374403653035025318106240841093313007765387765814323889960983051835806443072289350847213_<129>]
(85·10¹⁵³+41)/9 = 9(4)₁₅₂9_<154> = 11 · 677 · C151
C151 = P30 · P121
P30 = 532169908190609312922547459373_<30>
P121 = 2383113620910345920040953299352597741758366084543329896306152414094100094570766140265306051858235710984214902514068075779_<121>
(85·10¹⁹¹+41)/9 = 9(4)₁₉₀9_<192> = 11 · 994241 · 3853279 · 101912461631_<12> · C168
C168 = P29 · C140
P29 = 14619811588998591301047585107_<29>
C140 = [15041548193948732237377921782760162860444904346066707049385208315027780859557363470765425247552446374119213069706352597065891744437122468593_<140>]

Jan 31, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000
(35·10¹⁹⁵-53)/9 = 3(8)₁₉₄3_<196> = 11 · 353 · C193
C193 = P32 · C161
P32 = 13489623807653598428959653177019_<32>
C161 = [74243477544933195199721018884564753532476736984037248212062263178045358729126496935286755527092585387779607938542329058870850264718140427333783944788315471979579_<161>]

Jan 31, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(2·10¹⁵⁴+7)/9 = (2)₁₅₃3_<154> = 3 · 13 · 83 · 227 · 62851 · 910523 · 11950907 · 226326480869_<12> · C119
C119 = P34 · P85
P34 = 2678614065727037627558566220314891_<34>
P85 = 7294061730828789765648309600745906429764528886149847086345196093357863550959590237333_<85>

Number: 22223_154 N=19537976348479297709241108486263881541684093534372921346678597304513214562602235530128310041656777831832213020684025703 ( 119 digits) SNFS difficulty: 155 digits. Divisors found: r1=2678614065727037627558566220314891 (pp34) r2=7294061730828789765648309600745906429764528886149847086345196093357863550959590237333 (pp85) Version: GGNFS-0.77.1 Total time: 44.63 hours. Scaled time: 26.60 units (timescale=0.596). Factorization parameters were as follows: name: 22223_154 n: 19537976348479297709241108486263881541684093534372921346678597304513214562602235530128310041656777831832213020684025703 m: 10000000000000000000000000000000 c5: 1 c0: 35 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2600001) Relations: rels:5734822, finalFF:622092 Initial matrix: 433711 x 622092 with sparse part having weight 48174864. Pruned matrix : 382626 x 384858 with weight 19449566. Total sieving time: 39.59 hours. Total relation processing time: 0.39 hours. Matrix solve time: 4.49 hours. Time per square root: 0.16 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: 44.63 hours. --------- CPU info (if available) ----------

Jan 30, 2006 (2nd)

By CWI, GMP-ECM
(10³⁸³-1)/9 = (1)_383<383> = 852559 · 1628675880394909638591813700831880313095925587_<46> · C331
C331 = P47 · C285
P47 = 23181229247696012268805890210990826546682789683_<47>
C285 = [345192952476958960147823998139683616642758281269013129543194636356033777495389903234686281133559196454018224515556815842464194616108378684266847054423006039422253677029609403326167675526846676838304378980263488424464689785323765671486102372923974370891369373572968024442734473362642049_<285>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 30, 2006

By Patrick Keller / GMP-ECM B1=1000000, Msieve v. 1.03
(29·10¹⁹⁷+7)/9 = 3(2)₁₉₆3_<198> = 11 · 21487 · 43969 · 344695237 · 1684161325078097_<16> · 4370874144876529_<16> · 1167476286104917223_<19> · C131
C131 = P32 · P41 · P58
P32 = 58538086613548548979322909890333_<32>
P41 = 27331887467833258552502650566280944366953_<41>
P58 = 6541795177200537912720111371200600941834147753875171749613_<58>

Mon Jan 30 00:27:51 2006 Msieve v. 1.03 Mon Jan 30 00:27:51 2006 random seeds: f48bdf24 eb4aed3e Mon Jan 30 00:27:51 2006 factoring 178799609620859433102456092550449953189558502392026811425674771874894588929096911710737173707739189 (99 digits) Mon Jan 30 00:27:52 2006 using multiplier of 1 Mon Jan 30 00:27:52 2006 sieve interval: 9 blocks of size 65536 Mon Jan 30 00:27:52 2006 processing polynomials in batches of 6 Mon Jan 30 00:27:52 2006 using a sieve bound of 2572489 (94118 primes) Mon Jan 30 00:27:52 2006 using large prime bound of 385873350 (28 bits) Mon Jan 30 00:27:52 2006 using double large prime bound of 2854963469885100 (43-52 bits) Mon Jan 30 00:27:52 2006 using trial factoring cutoff of 56 bits Mon Jan 30 00:27:52 2006 polynomial 'A' values have 13 factors Mon Jan 30 00:28:08 2006 restarting with 15020 full and 918731 partial relations Mon Jan 30 03:21:36 2006 94326 relations (22749 full + 71577 combined from 1400538 partial), need 94214 Mon Jan 30 03:21:37 2006 begin with 1400538 relations Mon Jan 30 03:21:38 2006 reduce to 224123 relations in 10 passes Mon Jan 30 03:21:38 2006 attempting to read 22749 full and 224123 partial relations Mon Jan 30 03:21:43 2006 recovered 22749 full and 224123 partial relations Mon Jan 30 03:21:43 2006 recovered 235484 polynomials Mon Jan 30 03:21:43 2006 attempting to build 71577 cycles Mon Jan 30 03:21:43 2006 found 71577 cycles in 6 passes Mon Jan 30 03:21:45 2006 distribution of cycle lengths: Mon Jan 30 03:21:45 2006 length 2 : 16449 Mon Jan 30 03:21:45 2006 length 3 : 15837 Mon Jan 30 03:21:45 2006 length 4 : 12749 Mon Jan 30 03:21:45 2006 length 5 : 9690 Mon Jan 30 03:21:45 2006 length 6 : 6646 Mon Jan 30 03:21:45 2006 length 7 : 4252 Mon Jan 30 03:21:45 2006 length 8 : 2620 Mon Jan 30 03:21:45 2006 length 9+: 3334 Mon Jan 30 03:21:45 2006 largest cycle: 21 relations Mon Jan 30 03:21:45 2006 94118 x 94182 system, weight 6188121 (avg 65.70/col) Mon Jan 30 03:21:45 2006 reduce to 92662 x 92726 in 3 passes Mon Jan 30 03:25:00 2006 lanczos halted after 1467 iterations Mon Jan 30 03:25:00 2006 recovered 64 nontrivial dependencies Mon Jan 30 03:26:02 2006 prp41 factor: 27331887467833258552502650566280944366953 Mon Jan 30 03:26:02 2006 prp58 factor: 6541795177200537912720111371200600941834147753875171749613 Mon Jan 30 03:26:02 2006 elapsed time 02:58:11

(29·10¹⁸⁴+7)/9 = 3(2)₁₈₃3_<185> = 3 · 1609 · 141209 · 51361763 · C168
C168 = P32 · C137
P32 = 40099719731363732494892431187567_<32>
C137 = [22952740803469060968111049404977261126816846627377021815399203618706658891312214574568337698722128170320166788147251434819194627650881241_<137>]

Jan 29, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000
(29·10²⁰⁰+7)/9 = 3(2)₁₉₉3_<201> = 19 · 31469 · 200361424120519799_<18> · 58874401726386398612126252576411_<32> · C146
C146 = P36 · P110
P36 = 606815175214790313738987778416739217_<36>
P110 = 75287329942185691582016605126251222192589334987378940003905961066870448780390121188605939719076412292159168861_<110>

Jan 29, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000, GGNFS-0.77.1-20050930-pentium4 gnfs
(29·10¹⁸⁶+7)/9 = 3(2)₁₈₅3_<187> = 367 · 6869 · 24173692225247190029_<20> · 817085648520860204729531_<24> · C137
C137 = P33 · P34 · P71
P33 = 148875337781562336091206119274899_<33>
P34 = 5595198805825978240661829971576263_<34>
P71 = 77686768150478058338957220040145869488476905274432941974964154046333127_<71>

Number: 32223_186 N=434672912384034472276489075857058056092971658726960112621499647289367910737488108932999434401951383764401 ( 105 digits) Divisors found: r1=5595198805825978240661829971576263 (pp34) r2=77686768150478058338957220040145869488476905274432941974964154046333127 (pp71) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 9.48 hours. Scaled time: 4.83 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 434672912384034472276489075857058056092971658726960112621499647289367910737488108932999434401951383764401 skew: 43423.78 # norm 3.55e+014 c5: 2700 c4: -32793540 c3: -22483127152441 c2: 82849481010709582 c1: 14402080289847793642392 c0: -46281243702985892444165040 # alpha -6.74 Y1: 17831828861 Y0: -174325078919840638189 # Murphy_E 2.18e-009 # M 75917951504007049919756011760453746537937058616496215661199923963867940747621339656342162085021060087616 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Sieved special-q in [1250000, 1950001) Relations: rels:4463965, finalFF:492216 Initial matrix: 366964 x 492216 with sparse part having weight 33506857. Pruned matrix : 311533 x 313431 with weight 13262973. Total sieving time: 7.31 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.80 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 9.48 hours. --------- CPU info (if available) ----------

Jan 29, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(4·10¹⁵³+23)/9 = (4)₁₅₂7_<153> = 3 · 17 · 19 · 81017 · 241784369429_<12> · C134
C134 = P46 · P89
P46 = 1470703507530817065767950099767404004845089349_<46>
P89 = 15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559_<89>

Number: 44447_153 N=23414739239786028749269162319365649597012527790011081766399867486328722607760076327047273100135171383472611229438026705790715508501091 ( 134 digits) SNFS difficulty: 155 digits. Divisors found: r1=1470703507530817065767950099767404004845089349 (pp46) r2=15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559 (pp89) Version: GGNFS-0.77.1 Total time: 41.25 hours. Scaled time: 24.59 units (timescale=0.596). Factorization parameters were as follows: name: 44447_153 n: 23414739239786028749269162319365649597012527790011081766399867486328722607760076327047273100135171383472611229438026705790715508501091 m: 10000000000000000000000000000000 c5: 1 c0: 575 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2500001) Relations: rels:5624531, finalFF:597924 Initial matrix: 433646 x 597924 with sparse part having weight 43829030. Pruned matrix : 383560 x 385792 with weight 18604471. Total sieving time: 36.47 hours. Total relation processing time: 0.33 hours. Matrix solve time: 4.29 hours. Time per square root: 0.16 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: 41.25 hours. --------- CPU info (if available) ----------

Jan 28, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000
(29·10²⁰⁰+7)/9 = 3(2)₁₉₉3_<201> = 19 · 31469 · 200361424120519799_<18> · C178
C178 = P32 · C146
P32 = 58874401726386398612126252576411_<32>
C146 = [45685494310321139538690186388518699890739761704723675271383671232036884261792667410604433223602786884855278216669151772545738533720768128503921837_<146>]

Jan 28, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000
(35·10¹⁷¹-53)/9 = 3(8)₁₇₀3_<172> = 11 · 257 · 313 · 14547037 · C159
C159 = P36 · P123
P36 = 451637800707841604043591937013618243_<36>
P123 = 668945230356071257795118498826470672455372523944031278211962172797587051335478238590834313058838878619295303466223808615463_<123>

Jan 28, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
(10¹⁶⁶+11)/3 = (3)₁₆₅7_<166> = 2269 · 5764399 · 19537095989_<11> · 87732744049_<11> · 301816485953164436063353_<24> · C111
C111 = P53 · P59
P53 = 11206452347884993130940717654027456951433829993441411_<53>
P59 = 43959969732682098946597196186987599511353917863039376632629_<59>

Divisors found: r1=11206452347884993130940717654027456951433829993441411 (pp53) r2=43959969732682098946597196186987599511353917863039376632629 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 37.53 hours. Scaled time: 20.19 units (timescale=0.538). Factorization parameters were as follows: name: c111 n: 492635306023768541594765890513052108909476061496811112954272759376577034953854526502589831415278876920382399519 skew: 25890.51 # norm 6.53e+014 c5: 14280 c4: -898725224 c3: -24028726065267 c2: 149970026802419081 c1: 8622273537997815680117 c0: 2369636294795826677063373 # alpha -5.25 Y1: 598043715709 Y0: -2030304024354184370578 # Murphy_E 9.11e-010 # M 344700207265714400774493844422343622305068913230711086885117440445706540058613325752159815816366332677658325980 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:231093, largePrimes:7527070 encountered Relations: rels:7440978, finalFF:621380 Max relations in full relation-set: 28 Initial matrix: 461385 x 621380 with sparse part having weight 53695434. Pruned matrix : 332381 x 334751 with weight 28979305. Total sieving time: 32.00 hours. Total relation processing time: 0.41 hours. Matrix solve time: 4.82 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 37.53 hours. --------- CPU info (if available) ----------

Jan 27, 2006

A very improvised snfs poly file for GGNFS is available on each contribution pages. Default parameters are required and the skew is not adjusted.

Jan 27, 2006 (3rd)

By Patrick Keller / GMP-ECM
(35·10¹⁷⁹-53)/9 = 3(8)₁₇₈3_<180> = 11 · 1453 · C176
C176 = P28 · C148
P28 = 4823708954837782458566048329_<28>
C148 = [5044128471268801172062513142983485358949897775689870766059301754241680504722143167099125805317082288533122296651679099968127315184968035371550200469_<148>]

Jan 27, 2006 (2nd)

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(5·10¹⁷⁷+31)/9 = (5)₁₇₆9_<177> = 13 · 56345207 · 3866383109_<10> · 242143359684157_<15> · 272242916096747_<15> · 1691532864670216129_<19> · C112
C112 = P46 · P66
P46 = 5590949666318516260855679354188427787135841331_<46>
P66 = 314649542503316748079738255963456709156720035705251552887876749141_<66>

Number: 7638 N=1759189754666192572326725349064953542205081951959080946286724157353603060805175015430135904517498852334266546671 ( 112 digits) Divisors found: r1=5590949666318516260855679354188427787135841331 (pp46) r2=314649542503316748079738255963456709156720035705251552887876749141 (pp66) Version: GGNFS-0.77.1-20050930-athlon Total time: 23.44 hours. Scaled time: 15.47 units (timescale=%1.3lf). Factorization parameters were as follows: name: 7638 n: 1759189754666192572326725349064953542205081951959080946286724157353603060805175015430135904517498852334266546671 skew: 23920.37 # norm 1.64e+015 c5: 26760 c4: 2529054184 c3: -88766237821472 c2: -1536599333403767721 c1: 11040733049224213553472 c0: -20360395729652409608835548 # alpha -5.47 Y1: 739415148989 Y0: -2309737831355081448027 # Murphy_E 8.07e-010 # M 79677056783275846577819398475589618451768605930335261907244912079153872042265783015618928186592278468264372413 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2650001) Relations: rels:7206433, finalFF:570022 Initial matrix: 499190 x 570022 with sparse part having weight 44320846. Pruned matrix : 465373 x 467932 with weight 28459747. Total sieving time: 20.25 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.65 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 23.44 hours. --------- CPU info (if available) ----------

Jan 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(8·10¹⁵²+1)/9 = (8)₁₅₁9_<152> = 276553 · 96941219 · 17522761249341089058283_<23> · C117
C117 = P52 · P65
P52 = 9275450587465013271141450209568903221034440958615769_<52>
P65 = 20399666486620694433547638703203893366675685859664738168665270201_<65>

Number: 88889_152 N=189216098497416263473135181856600180019937737923795853280762266113886314312612554827066663044652111065432137324399569 ( 117 digits) SNFS difficulty: 152 digits. Divisors found: r1=9275450587465013271141450209568903221034440958615769 (pp52) r2=20399666486620694433547638703203893366675685859664738168665270201 (pp65) Version: GGNFS-0.77.1 Total time: 39.61 hours. Scaled time: 23.61 units (timescale=0.596). Factorization parameters were as follows: name: 88889_152 n: 189216098497416263473135181856600180019937737923795853280762266113886314312612554827066663044652111065432137324399569 m: 1000000000000000000000000000000 c5: 800 c0: 1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5656806, finalFF:560541 Initial matrix: 352461 x 560541 with sparse part having weight 49911832. Pruned matrix : 311880 x 313706 with weight 17483011. Total sieving time: 35.95 hours. Total relation processing time: 0.37 hours. Matrix solve time: 3.15 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 39.61 hours. --------- CPU info (if available) ----------

Jan 26, 2006 (2nd)

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(8·10¹⁶⁶+1)/9 = (8)₁₆₅9_<166> = 3 · 557461665979_<12> · 1225671932987_<13> · 1106648171488609_<16> · 8449459157386939_<16> · C111
C111 = P48 · P64
P48 = 333087075628896812713251964530979547595195984979_<48>
P64 = 1392325284264560906132614928910781331907389357350433733048086539_<64>

Number: 3254 N=463765557259855051917117131486710479266089943564208828987238225638693593801271651567757735109441644551336097681 ( 111 digits) Divisors found: r1=333087075628896812713251964530979547595195984979 (pp48) r2=1392325284264560906132614928910781331907389357350433733048086539 (pp64) Version: GGNFS-0.77.1-20050930-athlon Total time: 19.29 hours. Scaled time: 11.85 units (timescale=%1.3lf). Factorization parameters were as follows: name: 3254 n: 463765557259855051917117131486710479266089943564208828987238225638693593801271651567757735109441644551336097681 skew: 36628.95 # norm 5.55e+015 c5: 16800 c4: -2384216080 c3: -58737157009298 c2: -3097661265535552497 c1: 9175246943003298098750 c0: 479467956148092230621982685 # alpha -6.74 Y1: 604398104101 Y0: -1941787400956269041544 # Murphy_E 9.07e-010 # M 391675059068029791990482987611213515275710334411496631346201367720880232500594510316273613195473518983785111212 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2350001) Relations: rels:7130922, finalFF:535065 Initial matrix: 460667 x 535065 with sparse part having weight 42098767. Pruned matrix : 426581 x 428948 with weight 25847979. Total sieving time: 16.52 hours. Total relation processing time: 0.36 hours. Matrix solve time: 2.21 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.29 hours. --------- CPU info (if available) ----------

Jan 26, 2006

By Anton Korobeynikov / GGNFS-0.77.1-20050930-athlon
2·10¹⁵⁵-1 = 1(9)_155<156> = 5012795239_<10> · C146
C146 = P72 · P75
P72 = 136754115856816167695867638454568058370179471864695591167031691027321981_<72>
P75 = 291749166878241872177396255297205394204088421236507456460074010898849116061_<75>

Number: snfs N=39897899368396683078640308292073846665253745067243908623573443351652528969376480849310828991552990102095809942178250620541654244896237621885436841 ( 146 digits) SNFS difficulty: 155 digits. Divisors found: r1=136754115856816167695867638454568058370179471864695591167031691027321981 (pp72) r2=291749166878241872177396255297205394204088421236507456460074010898849116061 (pp75) Version: GGNFS-0.77.1-20050930-athlon Total time: 141.14 hours. Scaled time: 66.90 units (timescale=0.474). Factorization parameters were as follows: n: 39897899368396683078640308292073846665253745067243908623573443351652528969376480849310828991552990102095809942178250620541654244896237621885436841 c5: 2 c0: -1 m: 10000000000000000000000000000000 skew: 100.0 type: snfs lss: 1 qintsize: 50000Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved rational special-q in [1500000, 3550001) Primes: RFBsize:216816, AFBsize:216491, largePrimes:5779940 encountered Relations: rels:5731745, finalFF:497024 Max relations in full relation-set: 28 Initial matrix: 433372 x 497024 with sparse part having weight 47577503. Pruned matrix : 403451 x 405681 with weight 35625976. Total sieving time: 129.13 hours. Total relation processing time: 0.88 hours. Matrix solve time: 10.85 hours. Time per square root: 0.28 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: 141.14 hours. --------- CPU info (if available) ----------

Jan 25, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
(28·10¹⁵¹+17)/9 = 3(1)₁₅₀3_<152> = 3 · 11 · 19 · 47 · 53 · 743 · 5279 · 6760674071_<10> · C129
C129 = P64 · P66
P64 = 1183424773474736884406097266107576876938774299229979351789940959_<64>
P66 = 634750602886514005931448326915798097467522134045896246417437275273_<66>

Number: 31113_151 N=751179588433925505819980439132160983509357836200324681542769367407649269891006424737915625504962455505240739186983603374500606807 ( 129 digits) SNFS difficulty: 152 digits. Divisors found: r1=1183424773474736884406097266107576876938774299229979351789940959 (pp64) r2=634750602886514005931448326915798097467522134045896246417437275273 (pp66) Version: GGNFS-0.77.1 Total time: 36.25 hours. Scaled time: 21.61 units (timescale=0.596). Factorization parameters were as follows: name: 31113_151 n: 751179588433925505819980439132160983509357836200324681542769367407649269891006424737915625504962455505240739186983603374500606807 m: 1000000000000000000000000000000 c5: 280 c0: 17 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5476607, finalFF:488877 Initial matrix: 352462 x 488877 with sparse part having weight 42762285. Pruned matrix : 322831 x 324657 with weight 19033619. Total sieving time: 32.22 hours. Total relation processing time: 0.38 hours. Matrix solve time: 3.50 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.25 hours. --------- CPU info (if available) ----------

Jan 25, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(52·10¹⁷⁷-7)/9 = 5(7)_177<178> = 5209 · 687901 · 3591592130707531_<16> · 20758583474340401_<17> · 163882620580891776606591883_<27> · C111
C111 = P55 · P56
P55 = 5990130956546303578954044839627845137546757129595421161_<55>
P56 = 22030613574269288396243921906995869107155224693130054301_<56>

Number: 7205 N=131966260362939672544609184922691216201854675825526623713085165777457266196327622856980876044228227484894463461 ( 111 digits) Divisors found: r1=5990130956546303578954044839627845137546757129595421161 (pp55) r2=22030613574269288396243921906995869107155224693130054301 (pp56) Version: GGNFS-0.77.1-20050930-athlon Total time: 19.89 hours. Scaled time: 12.93 units (timescale=%1.3lf). Factorization parameters were as follows: name: 7205 n: 131966260362939672544609184922691216201854675825526623713085165777457266196327622856980876044228227484894463461 skew: 38293.48 # norm 4.68e+015 c5: 26460 c4: -1421202454 c3: -176948763340345 c2: -2446403972040051259 c1: 106057665132258845107595 c0: -6358896990066060629975025 # alpha -6.46 Y1: 616825309463 Y0: -1379039484047520995828 # Murphy_E 8.87e-010 # M 73243177485515507332517433451890715278931353287625047006678691986437432307082725942451292464863658852031109008 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2400001) Relations: rels:7208189, finalFF:557042 Initial matrix: 460412 x 557042 with sparse part having weight 47165794. Pruned matrix : 419163 x 421529 with weight 26297790. Total sieving time: 17.25 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.10 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.89 hours. --------- CPU info (if available) ----------

Jan 24, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(13·10¹⁶⁴-1)/3 = 4(3)_164<165> = 17 · 23 · 121291 · 1720324112526590653_<19> · 22830290549856975884476811953_<29> · C111
C111 = P45 · P66
P45 = 250560538262323237800920263917376214890034701_<45>
P66 = 928500998327696518716189155494288425648796690706977226894213494177_<66>

Number: 2007 N=232645709918092128212963626281842374753128885585849987283506411402099491993298681298998317099407771797991436077 ( 111 digits) Divisors found: r1=250560538262323237800920263917376214890034701 (pp45) r2=928500998327696518716189155494288425648796690706977226894213494177 (pp66) Version: GGNFS-0.77.1-20050930-athlon Total time: 23.62 hours. Scaled time: 15.31 units (timescale=%1.3lf). Factorization parameters were as follows: name: 2007 n: 232645709918092128212963626281842374753128885585849987283506411402099491993298681298998317099407771797991436077 skew: 14212.24 # norm 1.41e+014 c5: 17520 c4: -731536343 c3: -7203612784458 c2: 137854935490016143 c1: 757017358734400134189 c0: -3936459434010134648132846 # alpha -3.52 Y1: 140945592403 Y0: -1677383992046597419989 # Murphy_E 8.77e-010 # M 30919382169914387085751545851925427078681855413600291588789589589734820051013111462667174408849572806160572640 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2500001) Relations: rels:7297886, finalFF:584279 Initial matrix: 460506 x 584279 with sparse part having weight 46858369. Pruned matrix : 409772 x 412138 with weight 22844098. Total sieving time: 21.23 hours. Total relation processing time: 0.28 hours. Matrix solve time: 1.92 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 23.62 hours. --------- CPU info (if available) ----------

Jan 23, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
(4·10¹⁵²+41)/9 = (4)₁₅₁9_<152> = 7 · 227 · 971 · 674759 · C140
C140 = P67 · P74
P67 = 1749054437074730839738212413266980681168427109942203394836261055113_<67>
P74 = 24407446290192717863936113799240790417381456561254089477520149077854868713_<74>

Number: 44449_152 N=42689952231524751722138041230328646463026795672759687658152146679145117324025601300082106418039877056208737757403079020376978414617472379569 ( 140 digits) SNFS difficulty: 152 digits. Divisors found: r1=1749054437074730839738212413266980681168427109942203394836261055113 (pp67) r2=24407446290192717863936113799240790417381456561254089477520149077854868713 (pp74) Version: GGNFS-0.77.1 Total time: 40.18 hours. Scaled time: 23.99 units (timescale=0.597). Factorization parameters were as follows: name: 44449_152 n: 42689952231524751722138041230328646463026795672759687658152146679145117324025601300082106418039877056208737757403079020376978414617472379569 m: 1000000000000000000000000000000 c5: 400 c0: 41 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5353614, finalFF:451285 Initial matrix: 352740 x 451285 with sparse part having weight 39087828. Pruned matrix : 333599 x 335426 with weight 20667424. Total sieving time: 35.74 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.00 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 40.18 hours. --------- CPU info (if available) ----------

Jan 23, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(10¹⁶⁷+11)/3 = (3)₁₆₆7_<167> = 37 · 1223 · 1659737 · 2908723 · 447435816063229601_<18> · 1294695630404312613929_<22> · C111
C111 = P49 · P62
P49 = 8084500782190389840478406072564528309399381768737_<49>
P62 = 32580465758870391821055101253905389293574411343938722240893569_<62>

Number: 3051 N=263396800911714895792509875297859568219343048500407357011345512027494719081492325733089149289256654778588552353 ( 111 digits) Divisors found: r1=8084500782190389840478406072564528309399381768737 (pp49) r2=32580465758870391821055101253905389293574411343938722240893569 (pp62) Version: GGNFS-0.77.1-20050930-athlon Total time: 19.92 hours. Scaled time: 13.26 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 263396800911714895792509875297859568219343048500407357011345512027494719081492325733089149289256654778588552353 skew: 44063.22 # norm 5.82e+015 c5: 31440 c4: -2042808076 c3: -259462411933762 c2: 3562919922588584576 c1: 78571915379339780403777 c0: -1247587394058679282894357380 # alpha -7.13 Y1: 449769722723 Y0: -1529773914367355424991 # Murphy_E 9.78e-010 # M 37620472442472730250295197130900633958251966432039131133767733126942109554102128164093057823374055476852748918 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1600000, 2300001) Relations: rels:7226550, finalFF:590752 Initial matrix: 460667 x 590752 with sparse part having weight 46800960. Pruned matrix : 405019 x 407386 with weight 21906508. Total sieving time: 17.67 hours. Total relation processing time: 0.25 hours. Matrix solve time: 1.81 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 19.92 hours. --------- CPU info (if available) ----------

Jan 22, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
2·10¹⁶¹-9 = 1(9)₁₆₀1_<162> = 11 · 8009 · 46649 · 5470052140709707519_<19> · 21260817950106947166511_<23> · C111
C111 = P44 · P68
P44 = 38623719592924262442438059227864671483234091_<44>
P68 = 10834057799333342211229610150242910516634871944815694724812226195039_<68>

Number: c111 N=418451610494985126825836635808849111611795791400042430454732256218470337626978790680198450889274838215059874549 ( 111 digits) Divisors found: r1=38623719592924262442438059227864671483234091 (pp44) r2=10834057799333342211229610150242910516634871944815694724812226195039 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 38.14 hours. Scaled time: 21.67 units (timescale=0.568). Factorization parameters were as follows: name: c111 n: 418451610494985126825836635808849111611795791400042430454732256218470337626978790680198450889274838215059874549 skew: 3675.70 # norm 1.93e+014 c5: 32760 c4: -178083787 c3: 21650278439078 c2: 8917979542614550 c1: -49383796745086078804 c0: 13429828240883863427696 # alpha -3.65 Y1: 795881887993 Y0: -1664410687743954876989 # Murphy_E 8.91e-010 # M 10948574208808051795460323832426812352113482816811172364528579270127779274130082656672732319498982550206267293 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2500001) Primes: RFBsize:230209, AFBsize:230091, largePrimes:7793681 encountered Relations: rels:7932693, finalFF:773618 Max relations in full relation-set: 28 Initial matrix: 460383 x 773618 with sparse part having weight 72578266. Pruned matrix : 260552 x 262917 with weight 44454129. Total sieving time: 33.38 hours. Total relation processing time: 0.46 hours. Matrix solve time: 4.05 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 38.14 hours. --------- CPU info (if available) ----------

Jan 21, 2006 (3rd)

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs
(7·10¹⁵⁸-1)/3 = 2(3)_158<159> = 1567 · 6272477 · 94340496413_<11> · 411102666467_<12> · 48861300224203_<14> · C113
C113 = P37 · P76
P37 = 1447531832598287194675337087588890669_<37>
P76 = 8654203791135258006846208256907995285539701724907372088440732832849802487071_<76>

Number: 1 N=12527235473461064690789740751463629224250685860494368593748060178562891242691247493191763713705069665306105040499 ( 113 digits) Divisors found: r1=1447531832598287194675337087588890669 (pp37) r2=8654203791135258006846208256907995285539701724907372088440732832849802487071 (pp76) Version: GGNFS-0.77.1-20050930-athlon Total time: 26.10 hours. Scaled time: 17.25 units (timescale=%1.3lf). Factorization parameters were as follows: name: 1 n: 12527235473461064690789740751463629224250685860494368593748060178562891242691247493191763713705069665306105040499 skew: 89208.53 # norm 3.49e+015 c5: 2760 c4: -1034197276 c3: -28219325036870 c2: 7094204249441952635 c1: -225125126489700920174112 c0: -346886755808856710520625020 # alpha -6.18 Y1: 434919627923 Y0: -5387556766897775617289 # Murphy_E 7.50e-010 # M 12155549874620238031766711571075608703631898509942543672223711551128349335307687833438143686070227069253819519139 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 5000Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1750000, 2655001) Relations: rels:7505319, finalFF:659459 Initial matrix: 501526 x 659459 with sparse part having weight 55260502. Pruned matrix : 438001 x 440572 with weight 25312097. Total sieving time: 22.64 hours. Total relation processing time: 0.54 hours. Matrix solve time: 2.73 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 26.10 hours. --------- CPU info (if available) ----------

Jan 21, 2006 (2nd)

By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 gnfs
By Torbjorn Granlund / GMP-ECM
10⁸¹⁰+1 = 1(0)₈₀₉1_<811> = 61 · 101 · 109 · 181 · 541 · 1621 · 3541 · 8101 · 9901 · 19441 · 27541 · 27961 · 68041 · 119881 · 153469 · 329941 · 2925721 · 4188901 · 39526741 · 49229101 · 68189581 · 999999000001_<12> · 29639179139212862101_<20> · 4999437541453012143121_<22> · 13029637224192121671301_<23> · 1105097795002994798105101_<25> · 67128593062302476037266041_<26> · 7997499229153265919258822361_<28> · 59779577156334533866654838281_<29> · 292833529380862495499652402770042860551961_<42> · 141849229571534821256183437819902857798933927761_<48> · 902957305935680526667861848839993076071896366838581_<51> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681_<102> · C108 · [21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701_<185>]
C108 = P43 · P65
P43 = 2187911623791867750065408022595894263802921_<43>
P65 = 79802900676249574386310013540996547368285959759708473463717727701_<65>

Number: 10001_810a N=174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621 ( 108 digits) Divisors found: r1=2187911623791867750065408022595894263802921 (pp43) r2=79802900676249574386310013540996547368285959759708473463717727701 (pp65) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 18.72 hours. Scaled time: 11.51 units (timescale=0.615). Factorization parameters were as follows: name: 10001_810a n: 174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621 skew: 5126.41 # norm 1.93e+14 c5: 103740 c4: 5489741268 c3: -13075289527817 c2: -139084549632406609 c1: 119742151420102586749 c0: 271623207935125340303085 # alpha -5.35 Y1: 259012632439 Y0: -278750831169188009758 # Murphy_E 1.45e-09 # M 134662390696672647263499356795199525153224044769487875113261803659845520946252776074226595599860047310328984 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2600001) Primes: RFBsize:183072, AFBsize:182575, largePrimes:4597622 encountered Relations: rels:4798738, finalFF:516298 Max relations in full relation-set: 28 Initial matrix: 365731 x 516298 with sparse part having weight 45217492. Pruned matrix : 265981 x 267873 with weight 25469744. Total sieving time: 15.82 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.37 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 18.72 hours. --------- CPU info (if available) ----------

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 21, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(34·10¹⁵¹-7)/9 = 3(7)_151<152> = 37 · C151
C151 = P44 · P49 · P59
P44 = 36244743842331203919950327303612252533187707_<44>
P49 = 1236569276238851873641077650635328609093214576107_<49>
P59 = 22780916748875701195796464739236626157318164712696869631829_<59>

Number: 37777_151 N=1021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021 ( 151 digits) SNFS difficulty: 152 digits. Divisors found: r1=36244743842331203919950327303612252533187707 (pp44) r2=1236569276238851873641077650635328609093214576107 (pp49) r3=22780916748875701195796464739236626157318164712696869631829 (pp59) Version: GGNFS-0.77.1 Total time: 46.75 hours. Scaled time: 31.09 units (timescale=0.665). Factorization parameters were as follows: name: 37777_151 n: 1021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021 m: 1000000000000000000000000000000 c5: 340 c0: -7 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2400001) Relations: rels:5359277, finalFF:399435 Initial matrix: 352217 x 399435 with sparse part having weight 36448166. Pruned matrix : 346243 x 348068 with weight 26257292. Total sieving time: 41.64 hours. Total relation processing time: 0.43 hours. Matrix solve time: 4.52 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 46.75 hours. --------- CPU info (if available) ----------

Jan 20, 2006 (2nd)

By Yousuke Koide / GMP-ECM
10⁸¹⁰+1 = 1(0)₈₀₉1_<811> = 61 · 101 · 109 · 181 · 541 · 1621 · 3541 · 8101 · 9901 · 19441 · 27541 · 27961 · 68041 · 119881 · 153469 · 329941 · 2925721 · 4188901 · 39526741 · 49229101 · 68189581 · 999999000001_<12> · 29639179139212862101_<20> · 4999437541453012143121_<22> · 13029637224192121671301_<23> · 1105097795002994798105101_<25> · 67128593062302476037266041_<26> · 7997499229153265919258822361_<28> · 59779577156334533866654838281_<29> · 141849229571534821256183437819902857798933927761_<48> · 902957305935680526667861848839993076071896366838581_<51> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681_<102> · C149 · [21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701_<185>]
C149 = P42 · C108
P42 = 292833529380862495499652402770042860551961_<42>
C108 = [174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621_<108>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 20, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
(28·10¹⁵⁹+17)/9 = 3(1)₁₅₈3_<160> = 11 · 31 · 60558053 · 7212362800961_<13> · 33539753385806481216611969_<26> · C111
C111 = P51 · P61
P51 = 462536132185574572774501768659198144654440616697393_<51>
P61 = 1346499340514681298574411447231016501419631070503438624796113_<61>

Number: c111 N=622804596952087616912505747405171660214728457594249079875162518181585744977322568358844642895637638988043633409 ( 111 digits) Divisors found: r1=462536132185574572774501768659198144654440616697393 (pp51) r2=1346499340514681298574411447231016501419631070503438624796113 (pp61) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 35.69 hours. Scaled time: 21.20 units (timescale=0.594). Factorization parameters were as follows: name: c111 n: 622804596952087616912505747405171660214728457594249079875162518181585744977322568358844642895637638988043633409 skew: 40274.04 # norm 3.24e+015 c5: 24960 c4: 3358680112 c3: -154095379278068 c2: -5133738171144417744 c1: 97735448881250080837173 c0: 973118633560276453861668837 # alpha -6.68 Y1: 255538396069 Y0: -1902917132300748293272 # Murphy_E 9.18e-010 # M 204503118033941889104818766711331234716892044883651475030150490804811943446656433575566145287157210501727805036 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:230053, largePrimes:7688165 encountered Relations: rels:7775371, finalFF:751041 Max relations in full relation-set: 28 Initial matrix: 460347 x 751041 with sparse part having weight 67651935. Pruned matrix : 260052 x 262417 with weight 38209459. Total sieving time: 31.54 hours. Total relation processing time: 0.46 hours. Matrix solve time: 3.42 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 35.69 hours. --------- CPU info (if available) ----------

Jan 19, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(85·10¹⁵¹+41)/9 = 9(4)₁₅₀9_<152> = 3 · 11 · 263 · C149
C149 = P34 · P56 · P60
P34 = 4943181161334121867022094443412343_<34>
P56 = 15942446963562877289932971560669341883979707656772226419_<56>
P60 = 138084591641348859848844692898664238439608537558881691144443_<60>

Number: 94449_151 N=10881950045448144307459896813508980809361037497919627197193737117691490315064459551151566360691835977007079668676626851531794497573965254573619592631 ( 149 digits) SNFS difficulty: 152 digits. Divisors found: r1=4943181161334121867022094443412343 (pp34) r2=15942446963562877289932971560669341883979707656772226419 (pp56) r3=138084591641348859848844692898664238439608537558881691144443 (pp60) Version: GGNFS-0.77.1 Total time: 45.03 hours. Scaled time: 26.84 units (timescale=0.596). Factorization parameters were as follows: name: 94449_151 n: 10881950045448144307459896813508980809361037497919627197193737117691490315064459551151566360691835977007079668676626851531794497573965254573619592631 m: 1000000000000000000000000000000 c5: 850 c0: 41 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5470422, finalFF:459583 Initial matrix: 352868 x 459583 with sparse part having weight 41964979. Pruned matrix : 334801 x 336629 with weight 21806643. Total sieving time: 40.36 hours. Total relation processing time: 0.41 hours. Matrix solve time: 4.10 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 45.03 hours. --------- CPU info (if available) ----------

Jan 17, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(89·10¹⁵¹+1)/9 = 9(8)₁₅₀9_<152> = 3 · 11² · 683 · 106781 · C142
C142 = P61 · P81
P61 = 9592561240368708557394631004994331725705539077245555042315551_<61>
P81 = 389396106087029426819397405054446679770014664080460923953210556844866305408789611_<81>

Number: 98889_151 N=3735305994400940222977603340946986263067520786719671553018228690399643253656412142170867746660925810754124002709470582364123614636317632540661 ( 142 digits) SNFS difficulty: 152 digits. Divisors found: r1=9592561240368708557394631004994331725705539077245555042315551 (pp61) r2=389396106087029426819397405054446679770014664080460923953210556844866305408789611 (pp81) Version: GGNFS-0.77.1 Total time: 40.47 hours. Scaled time: 24.20 units (timescale=0.598). Factorization parameters were as follows: name: 98889_151 n: 3735305994400940222977603340946986263067520786719671553018228690399643253656412142170867746660925810754124002709470582364123614636317632540661 m: 1000000000000000000000000000000 c5: 890 c0: 1 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5400256, finalFF:457265 Initial matrix: 353142 x 457265 with sparse part having weight 41226568. Pruned matrix : 332763 x 334592 with weight 21288107. Total sieving time: 36.15 hours. Total relation processing time: 0.31 hours. Matrix solve time: 3.84 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 40.47 hours. --------- CPU info (if available) ----------

Jan 15, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(4·10¹⁵²-31)/9 = (4)₁₅₁1_<152> = 41 · 79 · 4231 · 19037823664438599021743461_<26> · C120
C120 = P51 · P70
P51 = 166866328854011532118907641869784764648724705750463_<51>
P70 = 1020886585728828363510597287873903676785706217228771834142475438673643_<70>

Number: 44441_152 N=170351596736875709959179822326526166723291839274113159290765004032671542668674951513691570325256153664621191583653146709 ( 120 digits) SNFS difficulty: 152 digits. Divisors found: r1=166866328854011532118907641869784764648724705750463 (pp51) r2=1020886585728828363510597287873903676785706217228771834142475438673643 (pp70) Version: GGNFS-0.77.1 Total time: 42.82 hours. Scaled time: 25.60 units (timescale=0.598). Factorization parameters were as follows: name: 44441_152 n: 170351596736875709959179822326526166723291839274113159290765004032671542668674951513691570325256153664621191583653146709 m: 1000000000000000000000000000000 c5: 400 c0: -31 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5546011, finalFF:491989 Initial matrix: 352175 x 491989 with sparse part having weight 44706048. Pruned matrix : 327635 x 329459 with weight 20162990. Total sieving time: 38.40 hours. Total relation processing time: 0.40 hours. Matrix solve time: 3.86 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 42.82 hours. --------- CPU info (if available) ----------

Jan 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(5·10¹⁵¹+13)/9 = (5)₁₅₀7_<151> = 7 · 337 · 709 · C145
C145 = P66 · P80
P66 = 244675379719578289333919494527112794313295764375089268344563909567_<66>
P80 = 13575725494988365411487737203669177049217503397028681709211591765872759556449241_<80>

Number: 55557_151 N=3321645790455038235796858506990636081217959819910994508057282977448881698190081711822116035849592955559900268249470745567977846482699307549788647 ( 145 digits) SNFS difficulty: 151 digits. Divisors found: r1=244675379719578289333919494527112794313295764375089268344563909567 (pp66) r2=13575725494988365411487737203669177049217503397028681709211591765872759556449241 (pp80) Version: GGNFS-0.77.1 Total time: 43.12 hours. Scaled time: 25.78 units (timescale=0.598). Factorization parameters were as follows: name: 55557_151 n: 3321645790455038235796858506990636081217959819910994508057282977448881698190081711822116035849592955559900268249470745567977846482699307549788647 m: 1000000000000000000000000000000 c5: 50 c0: 13 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5749297, finalFF:559546 Initial matrix: 352970 x 559546 with sparse part having weight 51636734. Pruned matrix : 313574 x 315402 with weight 18663720. Total sieving time: 39.14 hours. Total relation processing time: 0.42 hours. Matrix solve time: 3.40 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 43.12 hours. --------- CPU info (if available) ----------

Jan 12, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs
(13·10¹⁶⁴-31)/9 = 1(4)₁₆₃1_<165> = 3 · 43 · 112428709734049_<15> · 12667023571737990991217609155379403223_<38> · C111
C111 = P40 · P72
P40 = 1676745044461232317729000675458505147939_<40>
P72 = 468913024426091623245443201751896636676035669103202976763622771817695493_<72>

Number: c111 N=786247589989777914636073830302682947375520031653629043043502213698140564149219934257068310767319486956018538927 ( 111 digits) Divisors found: r1=1676745044461232317729000675458505147939 (pp40) r2=468913024426091623245443201751896636676035669103202976763622771817695493 (pp72) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 34.26 hours. Scaled time: 20.14 units (timescale=0.588). Factorization parameters were as follows: name: c111 n: 786247589989777914636073830302682947375520031653629043043502213698140564149219934257068310767319486956018538927 skew: 33636.57 # norm 3.04e+015 c5: 25920 c4: 3144008652 c3: -165915269317612 c2: -3366808236145090300 c1: 65987022536508996805519 c0: -83913059230236699400938539 # alpha -6.22 Y1: 168306501707 Y0: -1978718297937859459848 # Murphy_E 8.62e-010 # M 382289855528369169824421895336199655196115297917391454091611178216699183661511295281539641929425741668177499676 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:230419, largePrimes:7530904 encountered Relations: rels:7451513, finalFF:629444 Max relations in full relation-set: 28 Initial matrix: 460708 x 629444 with sparse part having weight 52954694. Pruned matrix : 325045 x 327412 with weight 28218188. Total sieving time: 29.63 hours. Total relation processing time: 0.40 hours. Matrix solve time: 3.93 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 34.26 hours. --------- CPU info (if available) ----------

Jan 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(5·10¹⁵¹-41)/9 = (5)₁₅₀1_<151> = 8807 · 2090089 · C141
C141 = P41 · P101
P41 = 11985535893412477734546646139854999516751_<41>
P101 = 25181248688759856231710588775652390270239456503420879894844818915001826111432510170224977191479409487_<101>

Number: 55551_151 N=301810760000077146934882355719805754244522020140143157553847294497017706100796642885120166592755779952215374038834393599733412999151844816737 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=11985535893412477734546646139854999516751 (pp41) r2=25181248688759856231710588775652390270239456503420879894844818915001826111432510170224977191479409487 (pp101) Version: GGNFS-0.77.1 Total time: 36.08 hours. Scaled time: 21.54 units (timescale=0.597). Factorization parameters were as follows: name: 55551_151 n: 301810760000077146934882355719805754244522020140143157553847294497017706100796642885120166592755779952215374038834393599733412999151844816737 m: 1000000000000000000000000000000 c5: 50 c0: -41 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5700417, finalFF:582235 Initial matrix: 353156 x 582235 with sparse part having weight 52139676. Pruned matrix : 306424 x 308253 with weight 17013977. Total sieving time: 32.85 hours. Total relation processing time: 0.30 hours. Matrix solve time: 2.80 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 36.08 hours. --------- CPU info (if available) ----------

Jan 9, 2006 (2nd)

By Yousuke Koide / GMP-ECM
(10⁶¹³-1)/9 = (1)_613<613> = 116511326129882791_<18> · 1338285489332902166657911_<25> · 1167883827993965201733843631_<28> · C544
C544 = P36(1578...) · P36(4178...) · C473
P36(1578...) = 157818501697366913685542354577959717_<36>
P36(4178...) = 417832220121515364538149502380148831_<36>
C473 = [92529686120873990343331646774569359605383200587531417818236454390368869356415580228140609613497955460838507350423994235002078982421038981440839145461968437684528151941016349039119710736708391988071730726458391973172748638236782424739028612908524572972797032173010469396535113785013391541941058401658302567269148785675157132157433612203464707174823357971319412397911253267576408572089565418449213549477068089648406765856499332638101600661504414922416754050898040460592701003_<473>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 9, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(4·10¹⁵¹-13)/9 = (4)₁₅₀3_<151> = 3² · 569 · 739 · 296843 · 2093219419_<10> · C130
C130 = P57 · P73
P57 = 608858606877851551008985766196261799773945455000342152507_<57>
P73 = 3104275453960187109937984286123825972776995247295782410574851825856126963_<73>

Number: 44443_151 N=1890064828263309725274083499046605546833450559934940425099723669089227887530971292896451763065906695772892072780173366261700746241 ( 130 digits) SNFS difficulty: 151 digits. Divisors found: r1=608858606877851551008985766196261799773945455000342152507 (pp57) r2=3104275453960187109937984286123825972776995247295782410574851825856126963 (pp73) Version: GGNFS-0.77.1 Total time: 35.91 hours. Scaled time: 23.92 units (timescale=0.666). Factorization parameters were as follows: name: 44443_151 n: 1890064828263309725274083499046605546833450559934940425099723669089227887530971292896451763065906695772892072780173366261700746241 m: 1000000000000000000000000000000 c5: 40 c0: -13 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2100001) Relations: rels:5703153, finalFF:584406 Initial matrix: 352876 x 584406 with sparse part having weight 52535784. Pruned matrix : 305996 x 307824 with weight 17082130. Total sieving time: 32.57 hours. Total relation processing time: 0.36 hours. Matrix solve time: 2.85 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 35.91 hours. --------- CPU info (if available) ----------

Jan 7, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(7·10¹⁵¹-43)/9 = (7)₁₅₀3_<151> = 3³ · 29 · C148
C148 = P59 · P90
P59 = 45315988862875285213569229229556178268002361973050983850023_<59>
P90 = 219200886965523354035724320238357087792206973888306661944263918310909301395050880685320197_<90>

Number: 77773_151 N=9933304952462040584645948630622960124875833688094224492691925642117212998439052078898822193841350929473534837519511849013764722576983113381580814531 ( 148 digits) SNFS difficulty: 151 digits. Divisors found: r1=45315988862875285213569229229556178268002361973050983850023 (pp59) r2=219200886965523354035724320238357087792206973888306661944263918310909301395050880685320197 (pp90) Version: GGNFS-0.77.1 Total time: 45.55 hours. Scaled time: 30.33 units (timescale=0.666). Factorization parameters were as follows: name: 77773_151 n: 9933304952462040584645948630622960124875833688094224492691925642117212998439052078898822193841350929473534837519511849013764722576983113381580814531 m: 1000000000000000000000000000000 c5: 70 c0: -43 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2300001) Relations: rels:5323814, finalFF:394816 Initial matrix: 351642 x 394816 with sparse part having weight 35764287. Pruned matrix : 344365 x 346187 with weight 26333968. Total sieving time: 40.55 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.55 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 45.55 hours. --------- CPU info (if available) ----------

Jan 5, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
(2·10¹⁵³+61)/9 = (2)₁₅₂9_<153> = 47 · 45584453 · 28080199986351056858875439_<26> · C118
C118 = P39 · P79
P39 = 671616835389977570079621109237856169919_<39>
P79 = 5499853356503855968659112953597044134358448571426698521260112204765203148087759_<79>

Number: 22229_153 N=3693794106404065858730314506980409104367505481133478480581009263807454409922295169004251243400306482394846724627921521 ( 118 digits) SNFS difficulty: 153 digits. Divisors found: r1=671616835389977570079621109237856169919 (pp39) r2=5499853356503855968659112953597044134358448571426698521260112204765203148087759 (pp79) Version: GGNFS-0.77.1 Total time: 56.97 hours. Scaled time: 37.88 units (timescale=0.665). Factorization parameters were as follows: name: 22229_153 n: 3693794106404065858730314506980409104367505481133478480581009263807454409922295169004251243400306482394846724627921521 m: 1000000000000000000000000000000 c5: 2000 c0: 61 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2700001) Relations: rels:5744016, finalFF:475866 Initial matrix: 352137 x 475866 with sparse part having weight 49699157. Pruned matrix : 333291 x 335115 with weight 25753267. Total sieving time: 51.98 hours. Total relation processing time: 0.44 hours. Matrix solve time: 4.41 hours. Time per square root: 0.15 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: 56.97 hours. --------- CPU info (if available) ----------

Jan 5, 2006

By Wataru Sakai / GMP-ECM 6.0.1
3·10¹⁶²-1 = 2(9)_162<163> = 1586308304691323221318531843777_<31> · C133
C133 = P36 · P98
P36 = 152512406662190891155427973892329217_<36>
P98 = 12400194079641198397538641885769926694273799859212033454948583982801438301040530455353496340235711_<98>
3·10¹⁶⁷-1 = 2(9)_167<168> = 7 · 7643 · 5308447 · C157
C157 = P38 · C119
P38 = 22854213927330216399615920416772214007_<38>
C119 = [46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531_<119>]

Jan 3, 2006

By Sinkiti Sibata / GGNFS-0.77.1
(2·10¹⁵²+61)/9 = (2)₁₅₁9_<152> = 19 · 661 · 3110104741_<10> · C138
C138 = P36 · P103
P36 = 212106865486264043300787031493682199_<36>
P103 = 2682271187373818595628680353095781651261120492663158413594580075578341939139175919064741649056564506009_<103>

Number: 22229_152 N=568928133937980278199098064552428646633330057246257057269990790106201631376496707972280571278537623830907316340729803882559809990871833791 ( 138 digits) SNFS difficulty: 152 digits. Divisors found: r1=212106865486264043300787031493682199 (pp36) r2=2682271187373818595628680353095781651261120492663158413594580075578341939139175919064741649056564506009 (pp103) Version: GGNFS-0.77.1 Total time: 40.24 hours. Scaled time: 26.76 units (timescale=0.665). Factorization parameters were as follows: name: 22229_152 n: 568928133937980278199098064552428646633330057246257057269990790106201631376496707972280571278537623830907316340729803882559809990871833791 m: 1000000000000000000000000000000 c5: 200 c0: 61 skew: 2 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1200000, 2200001) Relations: rels:5449459, finalFF:461888 Initial matrix: 352626 x 461888 with sparse part having weight 40268875. Pruned matrix : 331996 x 333823 with weight 20373572. Total sieving time: 35.71 hours. Total relation processing time: 0.34 hours. Matrix solve time: 4.04 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 40.24 hours. --------- CPU info (if available) ----------

Jan 1, 2006 (3rd)

By Yousuke Koide / GMP-ECM
(10⁸⁶⁷-1)/9 = (1)_867<867> = 3 · 37 · 613 · 42773 · 210631 · 2071723 · 52986961 · 93101929 · 1112647111_<10> · 5363222357_<10> · 234771432523_<12> · 6270681177984151_<16> · 13168164561429877_<17> · 93195753455238027770502373_<26> · 74451201112778571232641337987561693_<35> · 25086158646798685749029022942725879293529996353937930044688310225209792405267161387550045665503080767367139652501504645587640324255739525766942448322852994756555563269219516158897234150632016254115138596672215506548424356751044570760748443769_<242> · C465
C465 = P35 · C431
P35 = 20086446755059947304637543254330027_<35>
C431 = [43847928340273007036683492466629425347593144386187849570352692715343015468508233711269987298844088842010811958146922848088904584451385409058136753439089940818345804415994995588939268929792742826083627766997939694984246400007687684923922833991165782358300738461285079416521540204902744071543408565874874731448917358285646695823461539103120712047524782671709937412975148617883482385473395336582811704194633808078648898999907547620693_<431>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 1, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁵³+71)/9 = (1)₁₅₂9_<153> = 7 · 5113880010251_<13> · C139
C139 = P51 · P89
P51 = 102810924599828884362050857164373075486103832573319_<51>
P89 = 30190454557728793269250249717674139102743562662711596919033095611883027825428747426710493_<89>

Number: 11119_153 N=3103908547169215253162254552873669619616617637161201595918077528854736573322626119479853392157234575315036994281948666107068847843409136267 ( 139 digits) SNFS difficulty: 155 digits. Divisors found: r1=102810924599828884362050857164373075486103832573319 (pp51) r2=30190454557728793269250249717674139102743562662711596919033095611883027825428747426710493 (pp89) Version: GGNFS-0.77.1 Total time: 53.43 hours. Scaled time: 35.48 units (timescale=0.664). Factorization parameters were as follows: name: 11119_153 n: 3103908547169215253162254552873669619616617637161201595918077528854736573322626119479853392157234575315036994281948666107068847843409136267 m: 10000000000000000000000000000000 c5: 1 c0: 7100 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2800001) Relations: rels:5486477, finalFF:518137 Initial matrix: 434532 x 518137 with sparse part having weight 39785945. Pruned matrix : 414550 x 416786 with weight 23920260. Total sieving time: 47.55 hours. Total relation processing time: 0.32 hours. Matrix solve time: 5.41 hours. Time per square root: 0.16 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: 53.43 hours. --------- CPU info (if available) ----------

Jan 1, 2006

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹⁷⁹-3 = (9)₁₇₈7_<179> = C179
C179 = P44 · P62 · P74
P44 = 47527552610960667080491218952801922312569073_<44>
P62 = 38918563279240249010933742596447312973214118388632853991466677_<62>
P74 = 54062702222061890579230284912359478718122077297383163210696543917211696057_<74>

Number: 99997_179 N=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 179 digits) SNFS difficulty: 180 digits. Divisors found: r1=47527552610960667080491218952801922312569073 (pp44) r2=38918563279240249010933742596447312973214118388632853991466677 (pp62) r3=54062702222061890579230284912359478718122077297383163210696543917211696057 (pp74) Version: GGNFS-0.77.1 Total time: 623.03 hours. Scaled time: 484.09 units (timescale=0.777). Factorization parameters were as follows: name: 99997_175 n: 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 1000000000000000000000000000000000000 c5: 1 c0: -30 type: snfs skew: 1 qintsize: 100000 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [3700000, 8100001) Relations: rels:6798472, finalFF:1134568 Initial matrix: 1002617 x 1134568 with sparse part having weight 56588036. Pruned matrix : 947705 x 952782 with weight 39508237. Total sieving time: 606.40 hours. Total relation processing time: 0.97 hours. Matrix solve time: 15.38 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 623.03 hours. --------- CPU info (if available) ----------

Note: This is the second largest number factored by GGNFS in our tables. Congratulations!