News and updates, January 2008

Since June 16, 2000

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News and updates, January 2008	2008-02-01(Fri) 02:54

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News and updates, January 2008

Jan 31, 2008 (3rd): By Sinkiti Sibata / GGNFS
(11·10¹⁰⁷+7)/9 = 1(2)₁₀₆3_<108> = 3² · 41 · C105
C105 = P46 · P60
P46 = 1292550447331944890025042849241722436631493391_<46>
P60 = 256257336153707341238146911505259598651293150772733923813137_<60>

Number: 12223_107 N=331225534477566997892201144233664558867810900331225534477566997892201144233664558867810900331225534477567 ( 105 digits) SNFS difficulty: 108 digits. Divisors found: r1=1292550447331944890025042849241722436631493391 (pp46) r2=256257336153707341238146911505259598651293150772733923813137 (pp60) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.02 hours. Scaled time: 1.37 units (timescale=0.676). Factorization parameters were as follows: name: 12223_107 n: 331225534477566997892201144233664558867810900331225534477566997892201144233664558867810900331225534477567 m: 1000000000000000000000 c5: 1100 c0: 7 skew: 0.36 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:64124, largePrimes:2429252 encountered Relations: rels:3033429, finalFF:718930 Max relations in full relation-set: 28 Initial matrix: 113289 x 718930 with sparse part having weight 53214391. Pruned matrix : 57627 x 58257 with weight 4923663. Total sieving time: 1.84 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,108,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.02 hours. --------- CPU info (if available) ----------
(11·10¹¹¹+7)/9 = 1(2)₁₁₀3_<112> = 1666104019_<10> · C102
C102 = P39 · P64
P39 = 235975824491022308928990780915762844819_<39>
P64 = 3108712443286375789320997869432868788061093950925051865679921143_<64>

Number: 12223_111 N=733580981910002956557433418100543110341193062221538415376826614702633534804661090144229597601266108117 ( 102 digits) SNFS difficulty: 112 digits. Divisors found: r1=235975824491022308928990780915762844819 (pp39) r2=3108712443286375789320997869432868788061093950925051865679921143 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.79 hours. Scaled time: 1.21 units (timescale=0.676). Factorization parameters were as follows: name: 12223_111 n: 733580981910002956557433418100543110341193062221538415376826614702633534804661090144229597601266108117 m: 10000000000000000000000 c5: 110 c0: 7 skew: 0.58 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:64059, largePrimes:2021282 encountered Relations: rels:2053022, finalFF:193864 Max relations in full relation-set: 28 Initial matrix: 113224 x 193864 with sparse part having weight 15557092. Pruned matrix : 89133 x 89763 with weight 4789183. Total sieving time: 1.58 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.11 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.79 hours. --------- CPU info (if available) ----------
(11·10¹¹⁴+7)/9 = 1(2)₁₁₃3_<115> = 151 · 122621323170953_<15> · C98
C98 = P43 · P55
P43 = 6707176161219300156417206391262616855238919_<43>
P55 = 9841640960702845903948148581547115321867466062969048439_<55>

Number: 12223_114 N=66009619638905539253901637431935754347497426208831751373830011892396353837800790236691341428997441 ( 98 digits) SNFS difficulty: 116 digits. Divisors found: r1=6707176161219300156417206391262616855238919 (pp43) r2=9841640960702845903948148581547115321867466062969048439 (pp55) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.23 hours. Scaled time: 1.51 units (timescale=0.676). Factorization parameters were as follows: name: 12223_114 n: 66009619638905539253901637431935754347497426208831751373830011892396353837800790236691341428997441 m: 100000000000000000000000 c5: 11 c0: 70 skew: 1.45 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63989, largePrimes:2303070 encountered Relations: rels:2648109, finalFF:464927 Max relations in full relation-set: 28 Initial matrix: 113152 x 464927 with sparse part having weight 38989712. Pruned matrix : 65830 x 66459 with weight 5847898. Total sieving time: 2.03 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.23 hours. --------- CPU info (if available) ----------
Jan 31, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, GGNFS
(11·10¹⁴⁹+7)/9 = 1(2)₁₄₈3_<150> = 3 · 5455414187_<10> · C139
C139 = P31 · P109
P31 = 2490019097316894784751546161679_<31>
P109 = 2999152258909011442964542293733101419514316878763530379221746764878442585998011725357379568000480610857964417_<109>
(11·10¹⁵⁰+7)/9 = 1(2)₁₄₉3_<151> = 14281 · 81937 · 44143109464746506290891_<23> · C119
C119 = P32 · P33 · P55
P32 = 68241356669473223079132276622237_<32>
P33 = 151148305752490290170716101146479_<33>
P55 = 2294022325606514181685656134858589548523107480053902263_<55>

Thu Jan 31 18:17:58 2008 Thu Jan 31 18:17:58 2008 Thu Jan 31 18:17:58 2008 Msieve v. 1.32 Thu Jan 31 18:17:58 2008 random seeds: 83626f43 2e9ca7e0 Thu Jan 31 18:17:58 2008 factoring 156547195729448570330739228648254921953631297430761643676132908131266366819040570422331 (87 digits) Thu Jan 31 18:17:59 2008 no P-1/P+1/ECM available, skipping Thu Jan 31 18:17:59 2008 commencing quadratic sieve (86-digit input) Thu Jan 31 18:17:59 2008 using multiplier of 3 Thu Jan 31 18:17:59 2008 using 32kb Intel Core sieve core Thu Jan 31 18:17:59 2008 sieve interval: 19 blocks of size 32768 Thu Jan 31 18:17:59 2008 processing polynomials in batches of 11 Thu Jan 31 18:17:59 2008 using a sieve bound of 1474127 (56333 primes) Thu Jan 31 18:17:59 2008 using large prime bound of 117930160 (26 bits) Thu Jan 31 18:17:59 2008 using double large prime bound of 338006235664960 (41-49 bits) Thu Jan 31 18:17:59 2008 using trial factoring cutoff of 49 bits Thu Jan 31 18:17:59 2008 polynomial 'A' values have 11 factors Thu Jan 31 18:56:57 2008 56548 relations (15649 full + 40899 combined from 592255 partial), need 56429 Thu Jan 31 18:56:57 2008 begin with 607904 relations Thu Jan 31 18:56:57 2008 reduce to 135305 relations in 10 passes Thu Jan 31 18:56:57 2008 attempting to read 135305 relations Thu Jan 31 18:56:58 2008 recovered 135305 relations Thu Jan 31 18:56:58 2008 recovered 114562 polynomials Thu Jan 31 18:56:58 2008 attempting to build 56548 cycles Thu Jan 31 18:56:58 2008 found 56548 cycles in 5 passes Thu Jan 31 18:56:59 2008 distribution of cycle lengths: Thu Jan 31 18:56:59 2008 length 1 : 15649 Thu Jan 31 18:56:59 2008 length 2 : 10984 Thu Jan 31 18:56:59 2008 length 3 : 10147 Thu Jan 31 18:56:59 2008 length 4 : 7618 Thu Jan 31 18:56:59 2008 length 5 : 5079 Thu Jan 31 18:56:59 2008 length 6 : 3170 Thu Jan 31 18:56:59 2008 length 7 : 1835 Thu Jan 31 18:56:59 2008 length 9+: 2066 Thu Jan 31 18:56:59 2008 largest cycle: 20 relations Thu Jan 31 18:56:59 2008 matrix is 56333 x 56548 with weight 3176684 (avg 56.18/col) Thu Jan 31 18:56:59 2008 filtering completed in 3 passes Thu Jan 31 18:56:59 2008 matrix is 51951 x 52015 with weight 2948955 (avg 56.69/col) Thu Jan 31 18:57:00 2008 saving the first 48 matrix rows for later Thu Jan 31 18:57:00 2008 matrix is 51903 x 52015 with weight 2312723 (avg 44.46/col) Thu Jan 31 18:57:00 2008 matrix includes 64 packed rows Thu Jan 31 18:57:00 2008 using block size 20806 for processor cache size 4096 kB Thu Jan 31 18:57:01 2008 commencing Lanczos iteration Thu Jan 31 18:57:11 2008 lanczos halted after 822 iterations (dim = 51901) Thu Jan 31 18:57:11 2008 recovered 16 nontrivial dependencies Thu Jan 31 18:57:11 2008 prp32 factor: 68241356669473223079132276622237 Thu Jan 31 18:57:11 2008 prp55 factor: 2294022325606514181685656134858589548523107480053902263 Thu Jan 31 18:57:11 2008 elapsed time 00:39:13
(11·10¹²²+7)/9 = 1(2)₁₂₁3_<123> = 3 · 41 · 15619 · 1095251 · C110
C110 = P38 · P73
P38 = 48431758142731886716282698692789115637_<38>
P73 = 1199355541668143121502827815414108595405173439839162449118989915332245617_<73>

Number: 12223_122 N=58086897521216703275912831000039986472494161953461626501002431196310592545468815762540152169182614030699413029 ( 110 digits) SNFS difficulty: 123 digits. Divisors found: r1=48431758142731886716282698692789115637 (pp38) r2=1199355541668143121502827815414108595405173439839162449118989915332245617 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.53 hours. Scaled time: 2.85 units (timescale=1.857). Factorization parameters were as follows: n: 58086897521216703275912831000039986472494161953461626501002431196310592545468815762540152169182614030699413029 m: 1000000000000000000000000 c5: 1100 c0: 7 skew: 0.36 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [400000, 720001) Primes: RFBsize:63951, AFBsize:64124, largePrimes:1449343 encountered Relations: rels:1472423, finalFF:194913 Max relations in full relation-set: 28 Initial matrix: 128142 x 194913 with sparse part having weight 9661941. Pruned matrix : 101275 x 101979 with weight 3961287. Total sieving time: 1.48 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000 total time: 1.53 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Jan 31, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(85·10¹⁹⁵+41)/9 = 9(4)₁₉₄9_<196> = 11 · 251 · 2161031 · 27117551 · 1356870133_<10> · 1739134559_<10> · 25433652459414927499870617826399_<32> · C129
C129 = P34 · P96
P34 = 7002080819084472935961485898736537_<34>
P96 = 138896476007643400498736213707955873126885773149612346584374896337109150206915149170156100613749_<96>
(11·10¹³⁴+7)/9 = 1(2)₁₃₃3_<135> = 3² · 1909319 · 112657579 · 12870442303_<11> · 35009213055361_<14> · C96
C96 = P45 · P51
P45 = 250936660198033341179351798590647701228125319_<45>
P51 = 558378674753209903140848242317261829328091333759211_<51>

Number: n N=140117679768374411977764694698883397854653689968283909022051675788789766936274055898866478563309 ( 96 digits) Divisors found: r1=250936660198033341179351798590647701228125319 (pp45) r2=558378674753209903140848242317261829328091333759211 (pp51) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.95 hours. Scaled time: 10.00 units (timescale=1.438). Factorization parameters were as follows: name: KA_1_2_133_3 n: 140117679768374411977764694698883397854653689968283909022051675788789766936274055898866478563309 m: 7035295626774042355948 deg: 4 c4: 57195720 c3: 96456981219 c2: -312182490713950436 c1: -140354032571367830 c0: 208626920336365938460725 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.220 # E(F1,F2) = 3.549845e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1201709066. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 1060001) Primes: RFBsize:92938, AFBsize:92678, largePrimes:1805383 encountered Relations: rels:1837680, finalFF:208790 Max relations in full relation-set: 28 Initial matrix: 185697 x 208790 with sparse part having weight 14018467. Pruned matrix : 172473 x 173465 with weight 9746709. Total sieving time: 6.36 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.47 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 6.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(11·10¹¹³+7)/9 = 1(2)₁₁₂3_<114> = 3 · 332779 · C108
C108 = P49 · P59
P49 = 2619324426169291429122454074993428764646076844357_<49>
P59 = 46739462714767849044740338669006128168735950121361654313347_<59>

Number: n N=122425816354820288361767842143707207307975385287956093205222507251781935581093580847171067707820327426732879 ( 108 digits) SNFS difficulty: 114 digits. Divisors found: r1=2619324426169291429122454074993428764646076844357 (pp49) r2=46739462714767849044740338669006128168735950121361654313347 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.28 hours. Scaled time: 1.86 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_2_112_3 n: 122425816354820288361767842143707207307975385287956093205222507251781935581093580847171067707820327426732879 skew: 0.23 deg: 5 c5: 11000 c0: 7 m: 10000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:78498, AFBsize:78252, largePrimes:4124095 encountered Relations: rels:3582159, finalFF:227837 Max relations in full relation-set: 28 Initial matrix: 156817 x 227837 with sparse part having weight 11132713. Pruned matrix : 101119 x 101967 with weight 3888696. Total sieving time: 1.12 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.07 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,114,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 1.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(11·10¹¹⁷+7)/9 = 1(2)₁₁₆3_<118> = 23 · 41 · 49742129 · C107
C107 = P30 · P78
P30 = 199547644984836153697911566023_<30>
P78 = 130577246643745005872051606673712223079810458974387218354742399714928811490183_<78>
Jan 30, 2008 (4th): By Sinkiti Sibata / PRIMO
10²⁷³⁰+9 is prime.
Jan 30, 2008 (3rd): By Tyler Cadigan / GGNFS, Msieve
9·10¹⁷⁰+7 = 9(0)₁₆₉7_<171> = 11593 · C167
C167 = P45 · P51 · P72
P45 = 647317419452212964571902174202614495944617659_<45>
P51 = 439565483361516384512985467534108059954554466647701_<51>
P72 = 272838590381901265341010790500512053115606212399648275844615354818716361_<72>

Number: 90007_170 N=77633054429397049943931682912102130596049340119037350125075476580695247131889933580608988182523936858449064090399378935564564823600448546536703182955231605279047701199 ( 167 digits) SNFS difficulty: 170 digits. Divisors found: r1=647317419452212964571902174202614495944617659 r2=439565483361516384512985467534108059954554466647701 r3=272838590381901265341010790500512053115606212399648275844615354818716361 Version: Total time: 93.71 hours. Scaled time: 242.25 units (timescale=2.585). Factorization parameters were as follows: n: 77633054429397049943931682912102130596049340119037350125075476580695247131889933580608988182523936858449064090399378935564564823600448546536703182955231605279047701199 m: 10000000000000000000000000000000000 c5: 9 c4: 0 c3: 0 c2: 0 c1: 0 c0: 7 skew: 0.95 type: snfs Y1: 1 Y0: -10000000000000000000000000000000000 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, 7700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 745800 x 746047 Total sieving time: 93.71 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 93.71 hours. --------- CPU info (if available) ----------
Jan 30, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(32·10¹⁶⁷-23)/9 = 3(5)₁₆₆3_<168> = 11 · 5867 · 8724407193127_<13> · C150
C150 = P47 · P104
P47 = 35370681682761663696088257679173159323507380621_<47>
P104 = 17853334356291297197483708874035153373989805242165023362167712280044355742973131910508838734976772818507_<104>

Number: n N=631484606492292083872367262096114628708262907358211747146704361754234279408840465950023789885761252373596395216832756065677361490571843403991001952847 ( 150 digits) SNFS difficulty: 168 digits. Divisors found: Wed Jan 30 04:47:13 2008 prp47 factor: 35370681682761663696088257679173159323507380621 Wed Jan 30 04:47:13 2008 prp104 factor: 17853334356291297197483708874035153373989805242165023362167712280044355742973131910508838734976772818507 Wed Jan 30 04:47:13 2008 elapsed time 01:47:22 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 75.58 hours. Scaled time: 99.02 units (timescale=1.310). Factorization parameters were as follows: name: KA_3_5_166_3 n: 631484606492292083872367262096114628708262907358211747146704361754234279408840465950023789885761252373596395216832756065677361490571843403991001952847 skew: 0.75 deg: 5 c5: 100 c0: -23 m: 2000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3600133) Primes: RFBsize:230209, AFBsize:230357, largePrimes:7604437 encountered Relations: rels:7042468, finalFF:511197 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 75.25 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 75.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁶⁴-1 = 7(9)₁₆₄_<165> = 12954394367_<11> · 506888062514609_<15> · C141
C141 = P51 · P90
P51 = 136719084005415749015513821637101935561368136069713_<51>
P90 = 891110722536656448479198244649382601120593416934422175200192460737138401437174420855050241_<90>

Number: n N=121831841732615858077060884495408980012801655561808302844196831596094254357569474806622403580182271741991617248312179184985155377588893450833 ( 141 digits) SNFS difficulty: 165 digits. Divisors found: Wed Jan 30 06:26:42 2008 prp51 factor: 136719084005415749015513821637101935561368136069713 Wed Jan 30 06:26:42 2008 prp90 factor: 891110722536656448479198244649382601120593416934422175200192460737138401437174420855050241 Wed Jan 30 06:26:42 2008 elapsed time 00:50:07 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 30.94 hours. Scaled time: 56.59 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_9_164 n: 121831841732615858077060884495408980012801655561808302844196831596094254357569474806622403580182271741991617248312179184985155377588893450833 skew: 1.05 deg: 5 c5: 4 c0: -5 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2199990) Primes: RFBsize:230209, AFBsize:230262, largePrimes:7266385 encountered Relations: rels:6749996, finalFF:527344 Max relations in full relation-set: 28 Initial matrix: 460535 x 527344 with sparse part having weight 44818095. Pruned matrix : Total sieving time: 30.78 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 30.94 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(88·10¹⁸⁴-7)/9 = 9(7)₁₈₄_<185> = 6277698227_<10> · 177693190297546087_<18> · 242984284590355995633538751051_<30> · C129
C129 = P33 · P97
P33 = 319127484177447982424141312841577_<33>
P97 = 1130385423636183718748628040572882785884593902791426607982038309444292046269569228004421072395199_<97>
Jan 30, 2008: The factor table of 122...223 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jan 29, 2008 (2nd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(28·10¹⁹⁰-1)/9 = 3(1)₁₉₀_<191> = 83 · 197 · 306898684974258906701022611_<27> · 3903025884228757387157019754586401_<34> · C127
C127 = P42 · P85
P42 = 566411654175336073779051055434185692429273_<42>
P85 = 2804416823774290398535475890197371140903510729229348762350392625035735079960933230587_<85>
8·10¹⁶⁶-1 = 7(9)₁₆₆_<167> = 3099809 · 66319073 · 769195169 · C144
C144 = P71 · P74
P71 = 36016936302058360187537361721146449943796609862852885565964670381174623_<71>
P74 = 14046667079478560713957129015435981397074694852066792830046818073901232961_<74>

Number: n N=505917913457799458734266811971710885068794540173797125115673787463148323314430390867563858141920290003653553739065318013688362034376483144348703 ( 144 digits) SNFS difficulty: 167 digits. Divisors found: Tue Jan 29 15:17:36 2008 prp71 factor: 36016936302058360187537361721146449943796609862852885565964670381174623 Tue Jan 29 15:17:36 2008 prp74 factor: 14046667079478560713957129015435981397074694852066792830046818073901232961 Tue Jan 29 15:17:36 2008 elapsed time 01:05:44 (Msieve 1.33, sqrts: 5) Version: GGNFS-0.77.1-20050930-k8 Total time: 47.31 hours. Scaled time: 39.65 units (timescale=0.838). Factorization parameters were as follows: name: KA_7_9_166 n: 505917913457799458734266811971710885068794540173797125115673787463148323314430390867563858141920290003653553739065318013688362034376483144348703 type: snfs deg: 5 c5: 5 c0: -2 skew: 0.83 m: 2000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000317) Primes: RFBsize:216816, AFBsize:216391, largePrimes:5650975 encountered Relations: rels:5543339, finalFF:475811 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 47.14 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 47.31 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
2·10²⁰⁰-7 = 1(9)₁₉₉3_<201> = 1301 · 77494184407_<11> · 29804123292653_<14> · 19122300006570627091_<20> · 348311486605878509660662409_<27> · C127
C127 = P36 · P92
P36 = 182349040760987799564918359076342409_<36>
P92 = 54801926834354290860267834669391833266360484125455715191587135759479195271787329085245083573_<92>
5·10¹⁶⁵+9 = 5(0)₁₆₄9_<166> = 521 · 291041 · 51554521 · 247260059 · C142
C142 = P34 · P47 · P62
P34 = 2818939442454687157524932103668483_<34>
P47 = 54054662364681162784830736490034092875986992681_<47>
P62 = 16976121589164324923231167526328949052941343024340689600524177_<62>

Number: n N=917638520764052206896551340018795507931530546527901174784162865815188938411283681136417866187149051462548537 ( 108 digits) Divisors found: Tue Jan 29 22:25:04 2008 prp47 factor: 54054662364681162784830736490034092875986992681 Tue Jan 29 22:25:04 2008 prp62 factor: 16976121589164324923231167526328949052941343024340689600524177 Tue Jan 29 22:25:04 2008 elapsed time 00:34:55 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 10.53 hours. Scaled time: 6.85 units (timescale=0.651). Factorization parameters were as follows: name: KA_5_0_164_9 n: 917638520764052206896551340018795507931530546527901174784162865815188938411283681136417866187149051462548537 skew: 12661.24 # norm 8.65e+14 c5: 38640 c4: 1501673822 c3: -9563743305193 c2: 326542209276603545 c1: -784249620915261605303 c0: -3465551045340897498365887 # alpha -5.89 Y1: 180905640823 Y0: -473288130946733068878 # Murphy_E 1.29e-09 # M 615124226853032890747798413252407572674371891804947226660272403689813790259428441717994802080173114188169006 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 special-q in [100000, 1600253) Primes: RFBsize:183072, AFBsize:182897, largePrimes:4231691 encountered Relations: rels:4183086, finalFF:395397 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 10.38 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 10.53 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
(5·10¹⁶⁷+31)/9 = (5)₁₆₆9_<167> = 7 · 139 · 599 · 266019989 · 23813862167_<11> · 1214077141347307_<16> · C128
C128 = P34 · P94
P34 = 3086469830114575503416081453035859_<34>
P94 = 4015460952029460285580689768666475042854516300138580007649352832352944445338548114829366485943_<94>
8·10¹⁶⁶-3 = 7(9)₁₆₅7_<167> = 73 · 263 · 4871 · 38923 · 10018333847_<11> · 23260492026164711_<17> · C128
C128 = P29 · P46 · P54
P29 = 18999269464663877966125576661_<29>
P46 = 5307586564792536865694064565220881786182872779_<46>
P54 = 935273344920036478019602994707096223631982392496166617_<54>

Number: n N=4964044239906161870476855656801449522869998195582208895845589159358843507206718978911380698097818643 ( 100 digits) Divisors found: r1=5307586564792536865694064565220881786182872779 (pp46) r2=935273344920036478019602994707096223631982392496166617 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.17 hours. Scaled time: 7.63 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_9_165_7 n: 4964044239906161870476855656801449522869998195582208895845589159358843507206718978911380698097818643 skew: 11740.72 # norm 9.09e+13 c5: 18900 c4: -286790748 c3: -9341293608541 c2: 21518992260573429 c1: 507960725404261725909 c0: -1621065082208637890886413 # alpha -5.89 Y1: 14187730073 Y0: -12130433167648029208 # Murphy_E 3.39e-09 # M 2833834172188564969898722875963018176226523725892070100671241162145110381032161315411329682313695471 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:135072, AFBsize:135007, largePrimes:3475063 encountered Relations: rels:3445984, finalFF:390014 Max relations in full relation-set: 48 Initial matrix: 270160 x 390014 with sparse part having weight 22376727. Pruned matrix : 161780 x 163194 with weight 7262992. Total sieving time: 3.89 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.10 hours. Total square root time: 0.08 hours, sqrts: 3. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 4.17 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jan 29, 2008: By Alban Nonymous / Jan 24, 2008
10¹²⁶⁸+1 is divisible by 1068836516672887538001262066480057_<34>
10¹³⁷⁶+1 is divisible by 8316321056168357161591149746561_<31>
10¹³⁹³+1 is divisible by 2313690662340499476839285921303291_<34>
10¹⁴⁹⁶+1 is divisible by 3112019096332789739503121888657089_<34>
10¹⁵¹³+1 is divisible by 9788270089405071134464024815801247_<34>
10¹⁶⁷⁸+1 is divisible by 204080546955445025527141472026009_<33>
10¹⁷⁰⁹+1 is divisible by 830662208135423938663117541699_<30>
10¹⁷⁴⁵+1 is divisible by 5038152633461836859451917395541171_<34>
10¹⁷⁹²+1 is divisible by 8803929888324104650587958648444417_<34>
10¹⁸³⁹+1 is divisible by 2397103947161858599012200785150611_<34>
10¹⁸⁶²+1 is divisible by 123202615416316140277937805321161_<33>
References: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)
Jan 28, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(2·10¹⁶⁴+7)/9 = (2)₁₆₃3_<164> = 59 · 697437560875820935427_<21> · C141
C141 = P48 · P93
P48 = 544113926826738557075513436540781338666336584873_<48>
P93 = 992522360499429901684593984914140940525360628309658561254022439588152781604125217695717239207_<93>

Number: n N=540045239034688628751879697373871298969883014741235343144711185616205145128356800782052470756952541880048918185633946948049410617464398715711 ( 141 digits) SNFS difficulty: 165 digits. Divisors found: Mon Jan 28 03:37:34 2008 prp48 factor: 544113926826738557075513436540781338666336584873 Mon Jan 28 03:37:34 2008 prp93 factor: 992522360499429901684593984914140940525360628309658561254022439588152781604125217695717239207 Mon Jan 28 03:37:34 2008 elapsed time 00:57:20 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 37.52 hours. Scaled time: 68.41 units (timescale=1.823). Factorization parameters were as follows: name: KA_2_163_3 n: 540045239034688628751879697373871298969883014741235343144711185616205145128356800782052470756952541880048918185633946948049410617464398715711 skew: 2.04 deg: 5 c5: 1 c0: 35 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2516603) Primes: RFBsize:250150, AFBsize:249871, largePrimes:7416724 encountered Relations: rels:6907833, finalFF:557563 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 37.37 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 37.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
7·10¹⁹³-3 = 6(9)₁₉₂7_<194> = 135391 · 308941571 · 784047751 · 6463670201813352033221_<22> · 32665964050477191352790761_<26> · C125
C125 = P36 · P42 · P47
P36 = 569756699704183297346120295651615869_<36>
P42 = 296810751027062020613622711817064044961881_<42>
P47 = 59778586616800168827028392336187139434362916103_<47>

Mon Jan 28 09:08:45 2008 Mon Jan 28 09:08:45 2008 Mon Jan 28 09:08:45 2008 Msieve v. 1.33 Mon Jan 28 09:08:45 2008 random seeds: eaf4fd80 85d2fd47 Mon Jan 28 09:08:45 2008 factoring 17742927189068736669754163160818939750150478560748635115421055932744873894014336636069743 (89 digits) Mon Jan 28 09:08:46 2008 searching for 15-digit factors Mon Jan 28 09:08:47 2008 commencing quadratic sieve (89-digit input) Mon Jan 28 09:08:47 2008 using multiplier of 23 Mon Jan 28 09:08:47 2008 using 64kb Opteron sieve core Mon Jan 28 09:08:47 2008 sieve interval: 15 blocks of size 65536 Mon Jan 28 09:08:47 2008 processing polynomials in batches of 7 Mon Jan 28 09:08:47 2008 using a sieve bound of 1543813 (58667 primes) Mon Jan 28 09:08:47 2008 using large prime bound of 123505040 (26 bits) Mon Jan 28 09:08:47 2008 using double large prime bound of 367309670191840 (42-49 bits) Mon Jan 28 09:08:47 2008 using trial factoring cutoff of 49 bits Mon Jan 28 09:08:47 2008 polynomial 'A' values have 11 factors Mon Jan 28 10:14:23 2008 58789 relations (15537 full + 43252 combined from 619377 partial), need 58763 Mon Jan 28 10:14:24 2008 begin with 634913 relations Mon Jan 28 10:14:24 2008 reduce to 142871 relations in 9 passes Mon Jan 28 10:14:24 2008 attempting to read 142871 relations Mon Jan 28 10:14:26 2008 recovered 142871 relations Mon Jan 28 10:14:26 2008 recovered 122497 polynomials Mon Jan 28 10:14:26 2008 attempting to build 58789 cycles Mon Jan 28 10:14:26 2008 found 58789 cycles in 6 passes Mon Jan 28 10:14:27 2008 distribution of cycle lengths: Mon Jan 28 10:14:27 2008 length 1 : 15537 Mon Jan 28 10:14:27 2008 length 2 : 11431 Mon Jan 28 10:14:27 2008 length 3 : 10411 Mon Jan 28 10:14:27 2008 length 4 : 7960 Mon Jan 28 10:14:27 2008 length 5 : 5547 Mon Jan 28 10:14:27 2008 length 6 : 3403 Mon Jan 28 10:14:27 2008 length 7 : 2090 Mon Jan 28 10:14:27 2008 length 9+: 2410 Mon Jan 28 10:14:27 2008 largest cycle: 18 relations Mon Jan 28 10:14:27 2008 matrix is 58667 x 58789 (14.5 MB) with weight 3552843 (60.43/col) Mon Jan 28 10:14:27 2008 sparse part has weight 3552843 (60.43/col) Mon Jan 28 10:14:28 2008 filtering completed in 3 passes Mon Jan 28 10:14:28 2008 matrix is 54808 x 54872 (13.6 MB) with weight 3353779 (61.12/col) Mon Jan 28 10:14:28 2008 sparse part has weight 3353779 (61.12/col) Mon Jan 28 10:14:29 2008 saving the first 48 matrix rows for later Mon Jan 28 10:14:29 2008 matrix is 54760 x 54872 (10.2 MB) with weight 2800225 (51.03/col) Mon Jan 28 10:14:29 2008 sparse part has weight 2340902 (42.66/col) Mon Jan 28 10:14:29 2008 matrix includes 64 packed rows Mon Jan 28 10:14:29 2008 using block size 21845 for processor cache size 512 kB Mon Jan 28 10:14:29 2008 commencing Lanczos iteration Mon Jan 28 10:14:29 2008 memory use: 9.1 MB Mon Jan 28 10:14:58 2008 lanczos halted after 868 iterations (dim = 54760) Mon Jan 28 10:14:58 2008 recovered 18 nontrivial dependencies Mon Jan 28 10:14:59 2008 prp42 factor: 296810751027062020613622711817064044961881 Mon Jan 28 10:14:59 2008 prp47 factor: 59778586616800168827028392336187139434362916103 Mon Jan 28 10:14:59 2008 elapsed time 01:06:14
8·10¹⁶⁶-7 = 7(9)₁₆₅3_<167> = 189105069674903884763_<21> · C147
C147 = P46 · P102
P46 = 1522772221419401839524691150172700628024852433_<46>
P102 = 277812555442990950898376801343060528596613057168376742703741533699762175389406425410348927877185643467_<102>

Number: n N=423045242190124065978268840790986080931372264092805157767902165882183318614229422370170273292031889136860171886007619487987078786024585708825505211 ( 147 digits) SNFS difficulty: 167 digits. Divisors found: Mon Jan 28 11:47:25 2008 prp46 factor: 1522772221419401839524691150172700628024852433 Mon Jan 28 11:47:25 2008 prp102 factor: 277812555442990950898376801343060528596613057168376742703741533699762175389406425410348927877185643467 Mon Jan 28 11:47:25 2008 elapsed time 02:35:34 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 73.65 hours. Scaled time: 129.10 units (timescale=1.753). Factorization parameters were as follows: name: KA_7_9_165_3 n: 423045242190124065978268840790986080931372264092805157767902165882183318614229422370170273292031889136860171886007619487987078786024585708825505211 type: snfs skew: 1.23 deg: 5 c5: 5 c0: -14 m: 2000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300001) Primes: RFBsize:230209, AFBsize:230867, largePrimes:7595197 encountered Relations: rels:7039683, finalFF:510104 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 73.33 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000 total time: 73.65 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(14·10¹⁷⁹-41)/9 = 1(5)₁₇₈1_<180> = 11 · 4208178866231_<13> · 15619110457642458343_<20> · 351430029612999360197_<21> · C126
C126 = P35 · P92
P35 = 20107693569497065346641840555374563_<35>
P92 = 30446770005100168171382797846562982573356796889366415814698830439233930405861605026830253107_<92>
5·10¹⁶⁴-9 = 4(9)₁₆₃1_<165> = 2671 · 77632909 · 12338521168499_<14> · C141
C141 = P34 · P49 · P59
P34 = 4339455695928017012813559346271651_<34>
P49 = 2130438876068504052547916867650293287718131453411_<49>
P59 = 21138920651137598568207584663615217929520666173979820026871_<59>

Number: n N=45035178353310875346083151105578272111290713326972753456419802659112470613730247332180443661058076304606981 ( 107 digits) Divisors found: Mon Jan 28 16:51:00 2008 prp49 factor: 2130438876068504052547916867650293287718131453411 Mon Jan 28 16:51:00 2008 prp59 factor: 21138920651137598568207584663615217929520666173979820026871 Mon Jan 28 16:51:00 2008 elapsed time 00:37:13 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 8.58 hours. Scaled time: 7.17 units (timescale=0.836). Factorization parameters were as follows: name: KA_4_9_163_1 n: 45035178353310875346083151105578272111290713326972753456419802659112470613730247332180443661058076304606981 skew: 8115.52 # norm 1.71e+15 c5: 154560 c4: 307703758 c3: 145805345482189 c2: -157159415040315452 c1: -3632690209768005682794 c0: -1184546233994452070467176 # alpha -7.03 Y1: 323870616509 Y0: -196286607975166774105 # Murphy_E 1.51e-09 # M 37232403993864362254878977070445837812503056159276185148333904982476946194988434481797403305406657484158305 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 special-q in [100000, 1300289) Primes: RFBsize:183072, AFBsize:183409, largePrimes:4088051 encountered Relations: rels:4006302, finalFF:403691 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 8.44 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 8.58 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 27, 2008 (3rd): By Bruce Dodson
(10³⁸¹-1)/9 is divisible by 82548590511975869997227448819484483748713764399174373_<53>, cofactor is prime.
References: The ECMNET Project (Paul Zimmermann)
Jan 27, 2008 (2nd): By Sinkiti Sibata / PFGW
(43·10¹⁰⁷³²-7)/9, (43·10¹⁵⁹⁷²-7)/9 and (43·10¹⁸¹¹⁴-7)/9 are PRPs.
Jan 27, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
4·10¹⁶⁴-3 = 3(9)₁₆₃7_<165> = 21347 · 59377 · 1751822150967709_<16> · 3934065255006277_<16> · C125
C125 = P36 · P89
P36 = 618354792441051937903025593120469857_<36>
P89 = 74051794299396180801895939838809464335023542105428143074269478481756813823421500448195263_<89>
(46·10¹⁷⁷-1)/9 = 5(1)₁₇₇_<178> = 17 · 23920583 · 143176470892200291319_<21> · 2722757562808167831264949_<25> · C125
C125 = P33 · P93
P33 = 181438620433318013127689602298557_<33>
P93 = 177698711659907069705725103293869509281941495123735028737953271728984627792031730189561210103_<93>
9·10¹⁶⁷-7 = 8(9)₁₆₆3_<168> = 4102069211_<10> · C159
C159 = P73 · P87
P73 = 1475840225808026944863592821406727235005191165802606042142091249608358711_<73>
P87 = 148662072304606973843025284582176600459246392524700966245732210436802333527066765202333_<87>

Number: n N=219401466359120384914441659331622622883141792996919768450976533267468558077432204495293680211871978578374113151939210418163761206222124856293654573347958072763 ( 159 digits) SNFS difficulty: 167 digits. Divisors found: Sun Jan 27 14:19:56 2008 prp73 factor: 1475840225808026944863592821406727235005191165802606042142091249608358711 Sun Jan 27 14:19:56 2008 prp87 factor: 148662072304606973843025284582176600459246392524700966245732210436802333527066765202333 Sun Jan 27 14:19:56 2008 elapsed time 01:34:48 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 92.12 hours. Scaled time: 77.29 units (timescale=0.839). Factorization parameters were as follows: name: KA_8_9_166_3 n: 219401466359120384914441659331622622883141792996919768450976533267468558077432204495293680211871978578374113151939210418163761206222124856293654573347958072763 type: snfs deg: 5 c5: 900 c0: -7 skew: 0.38 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5900001) Primes: RFBsize:216816, AFBsize:216321, largePrimes:6047622 encountered Relations: rels:5989690, finalFF:470608 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 91.85 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 92.12 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
7·10¹⁹⁰+1 = 7(0)₁₈₉1_<191> = 29 · 18168419302228497779_<20> · 102557119002802823101_<21> · 73316966906831314464051823_<26> · C125
C125 = P39 · P86
P39 = 355098879311614202406460897590438184483_<39>
P86 = 49758043313543013512337916205691953866857075376389549242886554315519833104914284256879_<86>
Jan 26, 2008 (3rd): By Sinkiti Sibata / PRIMO
(7·10²²²⁷-1)/3 is prime.
Jan 26, 2008 (2nd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
8·10¹⁸⁴-9 = 7(9)₁₈₃1_<185> = 17 · 41 · 53881 · 525199 · 19560201548737_<14> · 47291522362212610363688449301629559_<35> · C124
C124 = P38 · P87
P38 = 16036893578982114464326470006735731329_<38>
P87 = 273414034698599650866625624274832254903897139353621479873467317551382470700435628639391_<87>
3·10¹⁶⁶-7 = 2(9)₁₆₅3_<167> = 25411 · 4718927 · 954512749 · C147
C147 = P54 · P93
P54 = 611255532829942634147397320551746694935812453256656449_<54>
P93 = 428796965068732802120208918501494985696065115728677764830252574676814510715480757019757325969_<93>

Number: n N=262104517358950568229392646975475073832192212584139002189008516545530131509021579305206164560915839602751144638772767618539909590293230081939024081 ( 147 digits) SNFS difficulty: 166 digits. Divisors found: Sat Jan 26 19:52:25 2008 prp54 factor: 611255532829942634147397320551746694935812453256656449 Sat Jan 26 19:52:25 2008 prp93 factor: 428796965068732802120208918501494985696065115728677764830252574676814510715480757019757325969 Sat Jan 26 19:52:25 2008 elapsed time 01:02:35 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 65.89 hours. Scaled time: 55.08 units (timescale=0.836). Factorization parameters were as follows: name: KA_2_9_165_3 n: 262104517358950568229392646975475073832192212584139002189008516545530131509021579305206164560915839602751144638772767618539909590293230081939024081 type: snfs deg: 5 c5: 30 c0: -7 skew: 0.75 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 4125767) Primes: RFBsize:216816, AFBsize:216451, largePrimes:5784372 encountered Relations: rels:5641483, finalFF:469726 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 65.66 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 65.89 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 26, 2008: By Robert Backstrom / GMP-ECM
(5·10¹⁷⁷-17)/3 = 1(6)₁₇₆1_<178> = 11 · 187325868787_<12> · 388369379195020879_<18> · 379285042374911888951809_<24> · C124
C124 = P34 · P90
P34 = 8697916583198815476581493494469319_<34>
P90 = 631295035191337832585938232859170493922975996573273470112711910425120192821369762271447597_<90>
Jan 25, 2008 (4th): By Yousuke Koide
10¹¹⁰³+1 is divisible by 28335885146165932870615739992009_<32>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jan 25, 2008 (3rd): By Sinkiti Sibata / PRIMO
(2·10²⁷⁵⁹+61)/9 is prime.
Jan 25, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(16·10¹⁶⁷-1)/3 = 5(3)₁₆₇_<168> = 41 · 1867 · C163
C163 = P50 · P56 · P58
P50 = 40597113862788129876743745080216984123131298311427_<50>
P56 = 90647476731104016968844622707762569866503500594961277609_<56>
P58 = 1893301042298636909272719039593617589762226489198375358373_<58>

Number: n N=6967396936958121589785796090419393749374022931445168763417682382501382592829677627252973118911692598447141407675458650676490696347777618108264639154158011853284039 ( 163 digits) SNFS difficulty: 168 digits. Divisors found: Fri Jan 25 16:25:02 2008 prp50 factor: 40597113862788129876743745080216984123131298311427 Fri Jan 25 16:25:02 2008 prp56 factor: 90647476731104016968844622707762569866503500594961277609 Fri Jan 25 16:25:02 2008 prp58 factor: 1893301042298636909272719039593617589762226489198375358373 Fri Jan 25 16:25:02 2008 elapsed time 01:52:38 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 65.44 hours. Scaled time: 85.59 units (timescale=1.308). Factorization parameters were as follows: name: KA_5_3_167 n: 6967396936958121589785796090419393749374022931445168763417682382501382592829677627252973118911692598447141407675458650676490696347777618108264639154158011853284039 skew: 0.46 deg: 5 c5: 50 c0: -1 m: 2000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3002683) Primes: RFBsize:230209, AFBsize:230262, largePrimes:7515348 encountered Relations: rels:6996341, finalFF:506931 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 65.16 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 65.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁶⁶+9 = 8(0)₁₆₅9_<167> = 19 · 233 · C164
C164 = P39 · P125
P39 = 247318002448511232349795071846013961161_<39>
P125 = 73067581878550869883137762289663789192178328142338528983715149951558468070091483340423029109213779504121706037391601196627747_<125>

Number: n N=18070928393946238988028009939010616670431443415405466455839168737293878473006550711542805511633160153602891348543031398238084481590241698667269030946464874632934267 ( 164 digits) SNFS difficulty: 166 digits. Divisors found: Fri Jan 25 17:43:51 2008 prp39 factor: 247318002448511232349795071846013961161 Fri Jan 25 17:43:51 2008 prp125 factor: 73067581878550869883137762289663789192178328142338528983715149951558468070091483340423029109213779504121706037391601196627747 Fri Jan 25 17:43:51 2008 elapsed time 01:14:29 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 38.49 hours. Scaled time: 70.60 units (timescale=1.834). Factorization parameters were as follows: name: KA_8_0_165_9 n: 18070928393946238988028009939010616670431443415405466455839168737293878473006550711542805511633160153602891348543031398238084481590241698667269030946464874632934267 skew: 0.65 deg: 5 c5: 80 c0: 9 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2800001) Primes: RFBsize:250150, AFBsize:249916, largePrimes:7433182 encountered Relations: rels:6924228, finalFF:559097 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 38.31 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 38.49 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jan 25, 2008: By Robert Backstrom / GMP-ECM
(28·10¹⁷⁹-1)/9 = 3(1)₁₇₉_<180> = 17 · 158980370820846386325091_<24> · 130636323549165510465523960184309_<33> · C123
C123 = P34 · P90
P34 = 7681520532229285847327407805697901_<34>
P90 = 114712818212665930084237933685466980822542837060511859279956130473398076525563656416693357_<90>
Jan 24, 2008: By Robert Backstrom / GGNFS, Msieve
3·10¹⁶⁵-7 = 2(9)₁₆₄3_<166> = 389 · 72612871 · 4893118907011_<13> · C143
C143 = P43 · P45 · P55
P43 = 9586550427068758139277418251508130186850823_<43>
P45 = 763966565598162182661254838642609221002481461_<45>
P55 = 2963709019423440832352969589339376348532317934047934059_<55>

Number: n N=21705623988186509688790428902323610401675410826005059910283930842779622114834229639699870079593155974739505331652907856358417153429937020853777 ( 143 digits) SNFS difficulty: 165 digits. Divisors found: Thu Jan 24 15:26:22 2008 prp43 factor: 9586550427068758139277418251508130186850823 Thu Jan 24 15:26:22 2008 prp45 factor: 763966565598162182661254838642609221002481461 Thu Jan 24 15:26:22 2008 prp55 factor: 2963709019423440832352969589339376348532317934047934059 Thu Jan 24 15:26:22 2008 elapsed time 02:15:02 (Msieve 1.33, sqrts: 6) Version: GGNFS-0.77.1-20051202-athlon Total time: 49.56 hours. Scaled time: 86.88 units (timescale=1.753). Factorization parameters were as follows: name: KA_2_9_164_3 n: 21705623988186509688790428902323610401675410826005059910283930842779622114834229639699870079593155974739505331652907856358417153429937020853777 type: snfs skew: 1.18 deg: 5 c5: 3 c0: -7 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2400109) Primes: RFBsize:230209, AFBsize:229717, largePrimes:7315297 encountered Relations: rels:6790830, finalFF:500470 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 49.24 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 49.56 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 23, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
7·10¹⁶⁴+1 = 7(0)₁₆₃1_<165> = 1493 · 4603 · 119429 · 79514415457_<11> · C143
C143 = P61 · P82
P61 = 4011137403054399824497281514214954974908736320403030763817761_<61>
P82 = 2674077881194096559726374285341983014251581688108917524458192840920208139039746043_<82>

Number: n N=10726093807938100380941104602089661772874937656392292672836679543626950747738348408334379189320094232984694581540360379030131023025802572869723 ( 143 digits) SNFS difficulty: 165 digits. Divisors found: r1=4011137403054399824497281514214954974908736320403030763817761 (pp61) r2=2674077881194096559726374285341983014251581688108917524458192840920208139039746043 (pp82) Version: GGNFS-0.77.1-20051202-athlon Total time: 51.39 hours. Scaled time: 93.99 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_0_163_1 n: 10726093807938100380941104602089661772874937656392292672836679543626950747738348408334379189320094232984694581540360379030131023025802572869723 skew: 1.07 deg: 5 c5: 7 c0: 10 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3400001) Primes: RFBsize:250150, AFBsize:250406, largePrimes:7753552 encountered Relations: rels:7254296, finalFF:580211 Max relations in full relation-set: 48 Initial matrix: 500621 x 580211 with sparse part having weight 54263099. Pruned matrix : 464913 x 467480 with weight 37063090. Total sieving time: 48.91 hours. Total relation processing time: 0.18 hours. Matrix solve time: 2.16 hours. Total square root time: 0.14 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 51.39 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(4·10¹⁶⁵-31)/9 = (4)₁₆₄1_<165> = 3² · 7 · 79 · 337 · 29959 · 213283087187_<12> · C143
C143 = P43 · P101
P43 = 1430726570423886205441057904508188264305283_<43>
P101 = 28985417905225412247112454549094232344842096588627794290356131149243691637467494402561338794411644631_<101>

Number: n N=41470207551846257950116491850868348405236653748523626812527085979082127700219902135132902454773983973407894491568655258286753201587180691885573 ( 143 digits) SNFS difficulty: 165 digits. Divisors found: Wed Jan 23 16:28:15 2008 prp43 factor: 1430726570423886205441057904508188264305283 Wed Jan 23 16:28:15 2008 prp101 factor: 28985417905225412247112454549094232344842096588627794290356131149243691637467494402561338794411644631 Wed Jan 23 16:28:15 2008 elapsed time 00:55:20 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-k8 Total time: 49.93 hours. Scaled time: 41.89 units (timescale=0.839). Factorization parameters were as follows: name: KA_4_164_1 n: 41470207551846257950116491850868348405236653748523626812527085979082127700219902135132902454773983973407894491568655258286753201587180691885573 type: snfs deg: 5 c5: 4 c0: -31 skew: 1.51 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 100000) Primes: RFBsize:216816, AFBsize:217657, largePrimes:5723795 encountered Relations: rels:5649683, finalFF:500595 Max relations in full relation-set: 28 Initial matrix: 434537 x 500595 with sparse part having weight 44325199. Pruned matrix : 409247 x 411483 with weight 32710677. Total sieving time: 47.78 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.96 hours. Total square root time: 0.00 hours, sqrts: 32. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 49.93 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 23, 2008: By JMB / GGNFS, Msieve
(8·10¹⁸¹+7)/3 = 2(6)₁₈₀9_<182> = 73 · 383 · 1063 · 73679 · 808737119 · 238190255383_<12> · 28997879660064605217042319409_<29> · C121
C121 = P49 · P73
P49 = 1081148321083352502456169169103040048126155984589_<49>
P73 = 2016448909088811437437590767002243563539760000671212660803839912919962279_<73>
Jan 22, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
2·10¹⁶⁴+9 = 2(0)₁₆₃9_<165> = 11 · 17 · 19 · 2124275874910691323_<19> · C143
C143 = P62 · P81
P62 = 67130200642296191884709171155818744379421413745297802772910633_<62>
P81 = 394735263859854699241113017883444812425244047937865162764408227983060854002018867_<81>

Number: n N=26498657463501774710786304364562173257102193262370047211443501109678795224636984084060517451881873318073703378052692450542514081851319770912811 ( 143 digits) SNFS difficulty: 165 digits. Divisors found: Tue Jan 22 22:48:01 2008 prp62 factor: 67130200642296191884709171155818744379421413745297802772910633 Tue Jan 22 22:48:01 2008 prp81 factor: 394735263859854699241113017883444812425244047937865162764408227983060854002018867 Tue Jan 22 22:48:01 2008 elapsed time 00:36:37 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-k8 Total time: 30.93 hours. Scaled time: 25.89 units (timescale=0.837). Factorization parameters were as follows: name: KA_2_0_163_9 n: 26498657463501774710786304364562173257102193262370047211443501109678795224636984084060517451881873318073703378052692450542514081851319770912811 type: snfs deg: 5 c5: 1 c0: 45 skew: 2.14 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 100000) Primes: RFBsize:216816, AFBsize:216986, largePrimes:5519473 encountered Relations: rels:5435506, finalFF:523534 Max relations in full relation-set: 28 Initial matrix: 433866 x 523534 with sparse part having weight 39663812. Pruned matrix : 365732 x 367965 with weight 25276057. Total sieving time: 29.39 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.38 hours. Total square root time: 0.01 hours, sqrts: 32. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 30.93 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 22, 2008 (3rd): By Jo Yeong Uk / GMP-ECM
(2·10¹⁶⁵+7)/9 = (2)₁₆₄3_<165> = 1867 · 11462603 · 4855604094401_<13> · C142
C142 = P36 · P107
P36 = 135175420835923295308837910165690077_<36>
P107 = 15820453108988154482791229654640228746372406550518557422884079078297050679566535405743149235122673945634099_<107>
Jan 22, 2008 (2nd): By JMB / GMP-ECM
6·10¹⁶⁷-1 = 5(9)₁₆₇_<168> = 173 · 1559 · 8623 · 92761 · 1458366583_<10> · 919553016868249730947567_<24> · C121
C121 = P34 · P87
P34 = 7293628624498449156699219017293493_<34>
P87 = 284346639497725940029917594329688361811266078086355525897345582582328575687665394870903_<87>
Jan 22, 2008: By Yousuke Koide
(10¹⁷²⁹-1)/9 is divisible by 940468712658622180120548555277_<30>
(10¹⁹¹⁷-1)/9 is divisible by 1510552624688788386453049_<25>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jan 21, 2008: By Robert Backstrom / GGNFS, Msieve
(86·10¹⁶⁶+31)/9 = 9(5)₁₆₅9_<167> = 3 · 5524823 · 25729399 · 191756229961403_<15> · 170453805976796449_<18> · C121
C121 = P43 · P79
P43 = 4207775080549597799925358625476582357997273_<43>
P79 = 1629213400252065933172781543589693668667463228952759374791851515131060589281919_<79>

Number: n N=6855363546478120852508823668140569336220438309449632211103825793414564211312811099648902774037863458800459081558030206887 ( 121 digits) SNFS difficulty: 167 digits. Divisors found: Mon Jan 21 21:03:17 2008 prp43 factor: 4207775080549597799925358625476582357997273 Mon Jan 21 21:03:17 2008 prp79 factor: 1629213400252065933172781543589693668667463228952759374791851515131060589281919 Mon Jan 21 21:03:17 2008 elapsed time 02:50:05 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 117.31 hours. Scaled time: 153.56 units (timescale=1.309). Factorization parameters were as follows: name: KA_9_5_165_9 n: 6855363546478120852508823668140569336220438309449632211103825793414564211312811099648902774037863458800459081558030206887 skew: 0.51 deg: 5 c5: 860 c0: 31 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5110037) Primes: RFBsize:230209, AFBsize:230038, largePrimes:7978220 encountered Relations: rels:7387955, finalFF:484643 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 116.89 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 117.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 20, 2008 (2nd): By Sinkiti Sibata / PFGW
8·10¹³⁴⁴⁷-9 is PRP.
Jan 20, 2008: By Robert Backstrom / GGNFS, Msieve
8·10¹⁵⁸+9 = 8(0)₁₅₇9_<159> = 43 · 133397260513579219_<18> · 167167903992258454388890478299_<30> · C111
C111 = P49 · P63
P49 = 2033479913775371639587434065835085127837961461819_<49>
P63 = 410281407262533748598335324491991573466072616789247908444678817_<63>

Number: n N=834299000663855262700697358741077630803654699409180671446600595711970677159208132513234866970546095185263588123 ( 111 digits) Divisors found: Sun Jan 20 13:47:42 2008 prp49 factor: 2033479913775371639587434065835085127837961461819 Sun Jan 20 13:47:42 2008 prp63 factor: 410281407262533748598335324491991573466072616789247908444678817 Sun Jan 20 13:47:42 2008 elapsed time 00:38:14 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 17.62 hours. Scaled time: 14.80 units (timescale=0.840). Factorization parameters were as follows: name: n n: 834299000663855262700697358741077630803654699409180671446600595711970677159208132513234866970546095185263588123 skew: 58678.97 # norm 7.16e+15 c5: 1080 c4: 182319978 c3: 218777671087271 c2: 720093217709119301 c1: -192584130922452106377951 c0: 1924021866441673318910186961 # alpha -6.76 Y1: 160325997587 Y0: -3780758800577929514024 # Murphy_E 8.64e-10 # M 33078737459182277151461009133502300498047025913472764694038857216187874729045379963943227488355847412005621263 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 special-q in [100000, 1099990) Primes: RFBsize:230209, AFBsize:230298, largePrimes:8164286 encountered Relations: rels:9063518, finalFF:1450544 Max relations in full relation-set: 28 Initial matrix: 460588 x 1450544 with sparse part having weight 132062689. Pruned matrix : Total sieving time: 17.36 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 17.62 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
8·10¹⁶⁵+9 = 8(0)₁₆₄9_<166> = 3089 · C163
C163 = P72 · P91
P72 = 314438682222884322729688296198134025767975025422514323112159291576842309_<72>
P91 = 8236374989606056257892776904055137083699957579463131990199160763315628777145426750588217509_<91>

Number: n N=2589834898025250890255746196179993525412754936872774360634509550016186468112657818064098413726124959533829718355454839753965684687601165425704111362900615085788281 ( 163 digits) SNFS difficulty: 165 digits. Divisors found: Sun Jan 20 15:06:59 2008 prp72 factor: 314438682222884322729688296198134025767975025422514323112159291576842309 Sun Jan 20 15:06:59 2008 prp91 factor: 8236374989606056257892776904055137083699957579463131990199160763315628777145426750588217509 Sun Jan 20 15:06:59 2008 elapsed time 00:53:55 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.69 hours. Scaled time: 59.79 units (timescale=1.829). Factorization parameters were as follows: name: KA_8_0_164_9 n: 2589834898025250890255746196179993525412754936872774360634509550016186468112657818064098413726124959533829718355454839753965684687601165425704111362900615085788281 skew: 1.02 deg: 5 c5: 8 c0: 9 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2399990) Primes: RFBsize:250150, AFBsize:250351, largePrimes:7431294 encountered Relations: rels:6960850, finalFF:588566 Max relations in full relation-set: 28 Initial matrix: 500566 x 588566 with sparse part having weight 45969560. Pruned matrix : Total sieving time: 32.52 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 32.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
8·10¹⁶²+9 = 8(0)₁₆₁9_<163> = 4339 · 31891930524271969_<17> · C143
C143 = P44 · P100
P44 = 21467718354271832026587974954408013867919721_<44>
P100 = 2692983165965493372324419233124120624401536996288557907855362716504013533241417008457888322335917819_<100>

Number: n N=57812204139742489271285991377047918106956344241296136018020163264497892626415364960802382490255087006871059445557673759660623134031508745408499 ( 143 digits) SNFS difficulty: 162 digits. Divisors found: Sun Jan 20 17:58:22 2008 prp44 factor: 21467718354271832026587974954408013867919721 Sun Jan 20 17:58:22 2008 prp100 factor: 2692983165965493372324419233124120624401536996288557907855362716504013533241417008457888322335917819 Sun Jan 20 17:58:22 2008 elapsed time 01:03:41 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 39.20 hours. Scaled time: 32.89 units (timescale=0.839). Factorization parameters were as follows: name: KA_8_0_161_9 n: 57812204139742489271285991377047918106956344241296136018020163264497892626415364960802382490255087006871059445557673759660623134031508745408499 type: snfs deg: 5 c5: 25 c0: 9 skew: 0.82 m: 200000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3700187) Primes: RFBsize:216816, AFBsize:216596, largePrimes:5557225 encountered Relations: rels:5370833, finalFF:450084 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 39.08 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 39.20 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
8·10¹⁵³+9 = 8(0)₁₅₂9_<154> = 47 · 61 · C151
C151 = P53 · P98
P53 = 48895464172194500888865555728935598425504411122071941_<53>
P98 = 57068140361452359856128021667726448531461834024720351768797284045710734038067945628429182751862647_<98>

Number: n N=2790373212417160795256365538890826648064178583885594698290896407394489012905476107429368678060690617370073247296825950470875479595395884199511684687827 ( 151 digits) SNFS difficulty: 153 digits. Divisors found: Mon Jan 21 00:02:56 2008 prp53 factor: 48895464172194500888865555728935598425504411122071941 Mon Jan 21 00:02:56 2008 prp98 factor: 57068140361452359856128021667726448531461834024720351768797284045710734038067945628429182751862647 Mon Jan 21 00:02:56 2008 elapsed time 00:50:57 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.84 hours. Scaled time: 38.38 units (timescale=1.757). Factorization parameters were as follows: name: KA_8_0_152_9 n: 2790373212417160795256365538890826648064178583885594698290896407394489012905476107429368678060690617370073247296825950470875479595395884199511684687827 type: snfs skew: 0.51 deg: 5 c5: 250 c0: 9 m: 2000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1199990) Primes: RFBsize:216816, AFBsize:216231, largePrimes:6128293 encountered Relations: rels:5616787, finalFF:504996 Max relations in full relation-set: 28 Initial matrix: 433114 x 504996 with sparse part having weight 23765859. Pruned matrix : Total sieving time: 21.68 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 21.84 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 19, 2008 (5th): By Kurt Beschorner / Jan 11, 2008
10⁷²³+1 is divisible by 1432840997383099816903558298765841755281_<40>
By Yousuke Koide / Jan 19, 2008
(10¹⁵¹⁹-1)/9 is divisible by 1949428804182808888625531087089_<31>
By Yousuke Koide / Jan 10, 2008
10¹⁰⁷⁶+1 is divisible by 2943022282018927015773940725270857_<34>
By Yousuke Koide / Jan 14, 2008
10¹⁰⁸⁸+1 is divisible by 6618913490111218105668231761297491201_<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jan 19, 2008 (4th): By Sinkiti Sibata / PRIMO
8·10²⁸⁶⁵-9 is prime.
Jan 19, 2008 (3rd): By Robert Backstrom / GGNFS
8·10¹³⁵+9 = 8(0)₁₃₄9_<136> = C136
C136 = P68 · P69
P68 = 14801185105213067737040565827661608911957391220799504238072333395727_<68>
P69 = 540497260397233405983441758896201567297916533811770073388400426116967_<69>

Number: n N=8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 136 digits) SNFS difficulty: 135 digits. Divisors found: r1=14801185105213067737040565827661608911957391220799504238072333395727 (pp68) r2=540497260397233405983441758896201567297916533811770073388400426116967 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.58 hours. Scaled time: 6.27 units (timescale=1.752). Factorization parameters were as follows: name: KA_8_0_134_9 n: 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 type: snfs skew: 1.02 deg: 5 c5: 8 c0: 9 m: 1000000000000000000000000000 rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 20000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 520001) Primes: RFBsize:114155, AFBsize:114197, largePrimes:4737996 encountered Relations: rels:4119531, finalFF:278781 Max relations in full relation-set: 28 Initial matrix: 228417 x 278781 with sparse part having weight 12620096. Pruned matrix : 181742 x 182948 with weight 6381214. Total sieving time: 3.06 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.35 hours. Total square root time: 0.05 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.3,2.3,75000 total time: 3.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 19, 2008 (2nd): By Jo Yeong Uk / GGNFS
8·10¹⁶¹+9 = 8(0)₁₆₀9_<162> = 7 · 361469 · 2281823 · 93410043703_<11> · 104070924106063664505185233829029_<33> · C107
C107 = P42 · P65
P42 = 379610134970967214429953242481364208742167_<42>
P65 = 37547251435502570973405299828344898136743364461002377728913347569_<65>

Number: 80009_161 N=14253317185219973460389890832990183114112816437488046262223139768008252805218662703888332623114842777242023 ( 107 digits) Divisors found: r1=379610134970967214429953242481364208742167 (pp42) r2=37547251435502570973405299828344898136743364461002377728913347569 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.59 hours. Scaled time: 22.76 units (timescale=2.150). Factorization parameters were as follows: name: 80009_161 n: 14253317185219973460389890832990183114112816437488046262223139768008252805218662703888332623114842777242023 skew: 17252.92 # norm 1.36e+15 c5: 25740 c4: 1525971078 c3: -78399570652366 c2: -924627151537472927 c1: 5307909918257896333150 c0: -6383666319595918601313427 # alpha -6.14 Y1: 1794392251 Y0: -223183169083949077020 # Murphy_E 1.50e-09 # M 3259513081427069279902873066038332939958046926443042510831308470696793387168947203008701013843850761293813 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1440001) Primes: RFBsize:135072, AFBsize:134778, largePrimes:4529531 encountered Relations: rels:4544044, finalFF:350991 Max relations in full relation-set: 28 Initial matrix: 269934 x 350991 with sparse part having weight 32490968. Pruned matrix : 221679 x 223092 with weight 18081436. Polynomial selection time: 0.55 hours. Total sieving time: 9.69 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.20 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 10.59 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹⁵⁷+9 = 8(0)₁₅₆9_<158> = 11489 · 716402649541_<12> · 10593937852386983_<17> · C126
C126 = P40 · P87
P40 = 3790480017172792738294451504361484879367_<40>
P87 = 242046575091074164088712317063624793945838546238186463919115736744802008317537350438981_<87>

Number: 80009_157 N=917472706107830464548023335426499676786648020601531299604889262480796085192109512368398576216119494573875335431375851279405027 ( 126 digits) SNFS difficulty: 157 digits. Divisors found: r1=3790480017172792738294451504361484879367 (pp40) r2=242046575091074164088712317063624793945838546238186463919115736744802008317537350438981 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 22.81 hours. Scaled time: 49.09 units (timescale=2.152). Factorization parameters were as follows: n: 917472706107830464548023335426499676786648020601531299604889262480796085192109512368398576216119494573875335431375851279405027 m: 20000000000000000000000000000000 c5: 25 c0: 9 skew: 0.82 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, 2900001) Primes: RFBsize:216816, AFBsize:216596, largePrimes:5641343 encountered Relations: rels:5610183, finalFF:554682 Max relations in full relation-set: 28 Initial matrix: 433476 x 554682 with sparse part having weight 45050664. Pruned matrix : 370085 x 372316 with weight 28747141. Total sieving time: 21.92 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.77 hours. Time per square root: 0.04 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: 22.81 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Jan 19, 2008: By Sinkiti Sibata / GGNFS
8·10¹⁶⁹-9 = 7(9)₁₆₈1_<170> = 41 · 311 · 6744493062860975247569_<22> · 153259559622294960992443672324849_<33> · C112
C112 = P37 · P76
P37 = 4793749476605961545931498988840397341_<37>
P76 = 1266174380191027066904884727886512981316500532551514322249230638281825634221_<76>

Number: 79991_169 N=6069722772332613766716520417588435051267558844262481968159500137499985223028918430208947236222098739972967006361 ( 112 digits) SNFS difficulty: 170 digits. Divisors found: r1=4793749476605961545931498988840397341 (pp37) r2=1266174380191027066904884727886512981316500532551514322249230638281825634221 (pp76) Version: GGNFS-0.77.1-20060513-k8 Total time: 146.83 hours. Scaled time: 292.79 units (timescale=1.994). Factorization parameters were as follows: name: 79991_169 n: 6069722772332613766716520417588435051267558844262481968159500137499985223028918430208947236222098739972967006361 m: 10000000000000000000000000000000000 c5: 4 c0: -45 skew: 1.62 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, 7300001) Primes: RFBsize:412849, AFBsize:412326, largePrimes:6069244 encountered Relations: rels:6343174, finalFF:937345 Max relations in full relation-set: 28 Initial matrix: 825239 x 937345 with sparse part having weight 55828427. Pruned matrix : 731366 x 735556 with weight 41378296. Total sieving time: 140.28 hours. Total relation processing time: 0.29 hours. Matrix solve time: 6.01 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 146.83 hours. --------- CPU info (if available) ----------
Jan 18, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
(82·10¹⁶⁶+71)/9 = 9(1)₁₆₅9_<167> = 3 · 7 · 103 · 3559 · 657277553 · C152
C152 = P59 · P94
P59 = 13107171807510682605279428504965984440896588003160354566801_<59>
P94 = 1373817494916889709450680140394462103187938380492405920907074652881504931172026794650480415619_<94>

Number: n N=18006861938039607305322991457173802411519321448085804024087657304778709212270954053562588283400455269971589526621315846889887965055791590110119179264819 ( 152 digits) SNFS difficulty: 167 digits. Divisors found: Sat Jan 19 00:19:19 2008 prp59 factor: 13107171807510682605279428504965984440896588003160354566801 Sat Jan 19 00:19:19 2008 prp94 factor: 1373817494916889709450680140394462103187938380492405920907074652881504931172026794650480415619 Sat Jan 19 00:19:19 2008 elapsed time 01:14:13 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 69.08 hours. Scaled time: 57.96 units (timescale=0.839). Factorization parameters were as follows: name: KA_9_1_165_9 n: 18006861938039607305322991457173802411519321448085804024087657304778709212270954053562588283400455269971589526621315846889887965055791590110119179264819 type: snfs deg: 5 c5: 820 c0: 71 skew: 0.61 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5502187) Primes: RFBsize:216816, AFBsize:217798, largePrimes:5905376 encountered Relations: rels:5864793, finalFF:364046 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 68.91 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 69.08 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 18, 2008 (3rd): By matsui / GMP-ECM
(5·10²⁰⁰+7)/3 = 1(6)₁₉₉9_<201> = 13 · C200
C200 = P43 · C157
P43 = 1715594718690854847659598110202544048758877_<43>
C157 = [7472926257488112167078933876668962989538550274994875554580903056006003718702207791126018309714959671296814070741865292739422577672509829862325988145378354069_<157>]
Jan 18, 2008 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁴⁴+9 = 8(0)₁₄₃9_<145> = 17 · 5659 · C140
C140 = P49 · P92
P49 = 1783403562694297290006912071546504111216735779123_<49>
P92 = 46628531887385325172139496576332321929456019180371596843235469372553694072124836083262715161_<92>

Number: 80009_144 N=83157489891167635104934357556417159548039042441503903204681766680872737856407804330426286082554598089456669750423583464133135141315759383803 ( 140 digits) SNFS difficulty: 145 digits. Divisors found: r1=1783403562694297290006912071546504111216735779123 (pp49) r2=46628531887385325172139496576332321929456019180371596843235469372553694072124836083262715161 (pp92) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 17.72 hours. Scaled time: 11.96 units (timescale=0.675). Factorization parameters were as follows: name: 80009_144 n: 83157489891167635104934357556417159548039042441503903204681766680872737856407804330426286082554598089456669750423583464133135141315759383803 m: 100000000000000000000000000000 c5: 4 c0: 45 skew: 1.62 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2350001) Primes: RFBsize:100021, AFBsize:100108, largePrimes:2772356 encountered Relations: rels:2756638, finalFF:246870 Max relations in full relation-set: 28 Initial matrix: 200193 x 246870 with sparse part having weight 25827334. Pruned matrix : 187239 x 188303 with weight 17819215. Total sieving time: 16.37 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.10 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 17.72 hours. --------- CPU info (if available) ----------
Jan 18, 2008: By Jo Yeong Uk / Msieve
8·10¹⁴²+9 = 8(0)₁₄₁9_<143> = 3329 · 29281922233_<11> · 1795510682849862934729054445135297_<34> · C96
C96 = P33 · P63
P33 = 627552504355594804282068645958259_<33>
P63 = 728347356775380943407963675027056892979696390562810902400314219_<63>

Fri Jan 18 00:19:37 2008 Fri Jan 18 00:19:37 2008 Fri Jan 18 00:19:37 2008 Msieve v. 1.32 Fri Jan 18 00:19:37 2008 random seeds: 181d3ee3 28f57196 Fri Jan 18 00:19:37 2008 factoring 457076207785168212371453509113670437822360245086692204469952475655630982399330567850785958184721 (96 digits) Fri Jan 18 00:19:38 2008 no P-1/P+1/ECM available, skipping Fri Jan 18 00:19:38 2008 commencing quadratic sieve (96-digit input) Fri Jan 18 00:19:38 2008 using multiplier of 41 Fri Jan 18 00:19:38 2008 using 32kb Intel Core sieve core Fri Jan 18 00:19:38 2008 sieve interval: 36 blocks of size 32768 Fri Jan 18 00:19:38 2008 processing polynomials in batches of 6 Fri Jan 18 00:19:38 2008 using a sieve bound of 2265589 (83442 primes) Fri Jan 18 00:19:38 2008 using large prime bound of 339838350 (28 bits) Fri Jan 18 00:19:38 2008 using double large prime bound of 2271382337631900 (43-52 bits) Fri Jan 18 00:19:38 2008 using trial factoring cutoff of 52 bits Fri Jan 18 00:19:38 2008 polynomial 'A' values have 13 factors Fri Jan 18 04:56:17 2008 84020 relations (20540 full + 63480 combined from 1255479 partial), need 83538 Fri Jan 18 04:56:17 2008 begin with 1276019 relations Fri Jan 18 04:56:18 2008 reduce to 218047 relations in 13 passes Fri Jan 18 04:56:18 2008 attempting to read 218047 relations Fri Jan 18 04:56:20 2008 recovered 218047 relations Fri Jan 18 04:56:20 2008 recovered 204713 polynomials Fri Jan 18 04:56:21 2008 attempting to build 84020 cycles Fri Jan 18 04:56:21 2008 found 84020 cycles in 6 passes Fri Jan 18 04:56:21 2008 distribution of cycle lengths: Fri Jan 18 04:56:21 2008 length 1 : 20540 Fri Jan 18 04:56:21 2008 length 2 : 14920 Fri Jan 18 04:56:21 2008 length 3 : 14308 Fri Jan 18 04:56:21 2008 length 4 : 11504 Fri Jan 18 04:56:21 2008 length 5 : 8432 Fri Jan 18 04:56:21 2008 length 6 : 5715 Fri Jan 18 04:56:21 2008 length 7 : 3656 Fri Jan 18 04:56:21 2008 length 9+: 4945 Fri Jan 18 04:56:21 2008 largest cycle: 22 relations Fri Jan 18 04:56:21 2008 matrix is 83442 x 84020 with weight 5533587 (avg 65.86/col) Fri Jan 18 04:56:22 2008 filtering completed in 4 passes Fri Jan 18 04:56:22 2008 matrix is 79418 x 79482 with weight 5234465 (avg 65.86/col) Fri Jan 18 04:56:23 2008 saving the first 48 matrix rows for later Fri Jan 18 04:56:23 2008 matrix is 79370 x 79482 with weight 4121997 (avg 51.86/col) Fri Jan 18 04:56:23 2008 matrix includes 64 packed rows Fri Jan 18 04:56:23 2008 using block size 31792 for processor cache size 4096 kB Fri Jan 18 04:56:25 2008 commencing Lanczos iteration Fri Jan 18 04:56:52 2008 lanczos halted after 1256 iterations (dim = 79365) Fri Jan 18 04:56:52 2008 recovered 15 nontrivial dependencies Fri Jan 18 04:56:53 2008 prp33 factor: 627552504355594804282068645958259 Fri Jan 18 04:56:53 2008 prp63 factor: 728347356775380943407963675027056892979696390562810902400314219 Fri Jan 18 04:56:53 2008 elapsed time 04:37:16
Jan 17, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
7·10¹⁶⁴+9 = 7(0)₁₆₃9_<165> = 4967 · 340656502544310619_<18> · C144
C144 = P50 · P95
P50 = 12939677343964955884740014469294611585657994552577_<50>
P95 = 31971554264779842589165734337945281912004539206121203124090877304667512724759902380130148456029_<95>

Number: n N=413701596371317891466218325717451870444516473623608643198379811850920699346023699901441617183278752045530834118946731942880940904318389213136733 ( 144 digits) SNFS difficulty: 165 digits. Divisors found: Thu Jan 17 05:01:38 2008 prp50 factor: 12939677343964955884740014469294611585657994552577 Thu Jan 17 05:01:38 2008 prp95 factor: 31971554264779842589165734337945281912004539206121203124090877304667512724759902380130148456029 Thu Jan 17 05:01:38 2008 elapsed time 01:15:29 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 50.52 hours. Scaled time: 92.41 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_0_163_9 n: 413701596371317891466218325717451870444516473623608643198379811850920699346023699901441617183278752045530834118946731942880940904318389213136733 skew: 1.67 deg: 5 c5: 7 c0: 90 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200001) Primes: RFBsize:250150, AFBsize:250726, largePrimes:7700483 encountered Relations: rels:7192174, finalFF:570722 Max relations in full relation-set: 28 Initial matrix: 500942 x 570722 with sparse part having weight 52231117. Pruned matrix : Total sieving time: 50.35 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 50.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
8·10¹³⁸+9 = 8(0)₁₃₇9_<139> = C139
C139 = P55 · P85
P55 = 2546678620364651588556275988984437932502588301075923203_<55>
P85 = 3141346511502304521005861647877216134965756685545711187785868781031519564330138156803_<85>

Number: n N=8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 ( 139 digits) SNFS difficulty: 138 digits. Divisors found: r1=2546678620364651588556275988984437932502588301075923203 (pp55) r2=3141346511502304521005861647877216134965756685545711187785868781031519564330138156803 (pp85) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.84 hours. Scaled time: 7.00 units (timescale=1.823). Factorization parameters were as follows: name: KA_8_0_137_9 n: 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009 skew: 0.51 deg: 5 c5: 250 c0: 9 m: 2000000000000000000000000000 type: snfs rlim: 2200000 alim: 2200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:162662, AFBsize:162140, largePrimes:5837421 encountered Relations: rels:5298457, finalFF:413705 Max relations in full relation-set: 48 Initial matrix: 324869 x 413705 with sparse part having weight 21736846. Pruned matrix : 244542 x 246230 with weight 9611405. Total sieving time: 3.39 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.25 hours. Total square root time: 0.10 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,75000 total time: 3.84 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(68·10¹⁶⁶+13)/9 = 7(5)₁₆₅7_<167> = 23 · 2477 · 47387 · 270272371 · C150
C150 = P35 · P57 · P59
P35 = 17985186201587473669314610148901419_<35>
P57 = 397989410018895033644398024474036815977092109203982240519_<57>
P59 = 14466558893742234502005420987466649404111592901097703772811_<59>

Number: n N=5757537239124070718550706302077403581327869498093808787670412687981204498446980968064332802066081638503147134728909 ( 115 digits) SNFS difficulty: 168 digits. Divisors found: Thu Jan 17 18:45:16 2008 prp57 factor: 397989410018895033644398024474036815977092109203982240519 Thu Jan 17 18:45:16 2008 prp59 factor: 14466558893742234502005420987466649404111592901097703772811 Thu Jan 17 18:45:16 2008 elapsed time 02:21:00 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 92.58 hours. Scaled time: 162.30 units (timescale=1.753). Factorization parameters were as follows: name: KA_7_5_165_7 n: 5757537239124070718550706302077403581327869498093808787670412687981204498446980968064332802066081638503147134728909 # n: 103550379308220275542310045522274995058308499116008352769830405684729022693055150581242133006534481024514566056854884998045901353617827387408730421871 type: snfs skew: 0.91 deg: 5 c5: 85 c0: 52 m: 2000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4100263) Primes: RFBsize:230209, AFBsize:229927, largePrimes:7782959 encountered Relations: rels:7221963, finalFF:514347 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 92.26 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000 total time: 92.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁷¹+9 = 8(0)₁₇₀9_<172> = 1609 · 47441 · 179947 · 2675683 · 717143003 · 8834088052212443456467_<22> · 113402724882979773257549023_<27> · C96
C96 = P47 · P49
P47 = 66045585799722886585090670007395970328026662921_<47>
P49 = 4587394211090038825215575348339222477208606014167_<49>

Number: n N=302977137965699242280736032700812694716266941721901019359481957770507344407132716999451859601807 ( 96 digits) Divisors found: r1=66045585799722886585090670007395970328026662921 (pp47) r2=4587394211090038825215575348339222477208606014167 (pp49) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.94 hours. Scaled time: 9.03 units (timescale=1.829). Factorization parameters were as follows: name: KA_8_0_170_9 n: 302977137965699242280736032700812694716266941721901019359481957770507344407132716999451859601807 m: 10512455641630070932636 deg: 4 c4: 24808080 c3: 107490494716 c2: 237883365092106694 c1: -567116283863032245 c0: -93029552726751959402373 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.436 # E(F1,F2) = 3.324346e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1200539918. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 1060001) Primes: RFBsize:92938, AFBsize:93341, largePrimes:1857869 encountered Relations: rels:1936762, finalFF:252332 Max relations in full relation-set: 48 Initial matrix: 186357 x 252332 with sparse part having weight 18488619. Pruned matrix : 154570 x 155565 with weight 8634865. Total sieving time: 4.69 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.11 hours. Total square root time: 0.06 hours, sqrts: 3. Prototype def-par.txt line would be: gnfs,95,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 4.94 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(83·10¹⁶⁶+61)/9 = 9(2)₁₆₅9_<167> = 3 · 131 · 3571 · 20201 · C157
C157 = P78 · P79
P78 = 934362002948337010399886026756338182492289458726612819250096628684686778943023_<78>
P79 = 3481489941299881313436648358877533150389619165412918752742979918506381341113641_<79>

Number: n N=3252971914797445349054660398728776863568519850605226649656754557340236386460735898302316013890979678288381293137596702958878519747398343478609039579707076743 ( 157 digits) SNFS difficulty: 167 digits. Divisors found: Thu Jan 17 19:55:51 2008 prp78 factor: 934362002948337010399886026756338182492289458726612819250096628684686778943023 Thu Jan 17 19:55:51 2008 prp79 factor: 3481489941299881313436648358877533150389619165412918752742979918506381341113641 Thu Jan 17 19:55:51 2008 elapsed time 01:31:24 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 119.15 hours. Scaled time: 99.73 units (timescale=0.837). Factorization parameters were as follows: name: KA_9_2_165_9 n: 3252971914797445349054660398728776863568519850605226649656754557340236386460735898302316013890979678288381293137596702958878519747398343478609039579707076743 type: snfs deg: 5 c5: 830 c0: 61 skew: 0.59 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 8900713) Primes: RFBsize:216816, AFBsize:216337, largePrimes:6552860 encountered Relations: rels:6849372, finalFF:293088 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 118.83 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 119.15 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 17, 2008 (2nd): By Sinkiti Sibata / Msieve, GGNFS
8·10¹²⁶+9 = 8(0)₁₂₅9_<127> = 401 · 389297 · 232424285281_<12> · 9781973560753067_<16> · C92
C92 = P46 · P46
P46 = 2728784228720769076664362884053977424213249851_<46>
P46 = 8260139316381217641035166733618289230331842561_<46>

Wed Jan 16 20:51:56 2008 Msieve v. 1.30 Wed Jan 16 20:51:56 2008 random seeds: cfffcf7b 8fc00eba Wed Jan 16 20:51:56 2008 factoring 22540137893577421722479220457850357073538436377154439147119377080504418319859512970688708411 (92 digits) Wed Jan 16 20:51:57 2008 commencing quadratic sieve (92-digit input) Wed Jan 16 20:51:57 2008 using multiplier of 1 Wed Jan 16 20:51:57 2008 using 64kb Pentium 4 sieve core Wed Jan 16 20:51:57 2008 sieve interval: 18 blocks of size 65536 Wed Jan 16 20:51:57 2008 processing polynomials in batches of 6 Wed Jan 16 20:51:57 2008 using a sieve bound of 1787701 (66803 primes) Wed Jan 16 20:51:57 2008 using large prime bound of 187708605 (27 bits) Wed Jan 16 20:51:57 2008 using double large prime bound of 780317810587350 (42-50 bits) Wed Jan 16 20:51:57 2008 using trial factoring cutoff of 50 bits Wed Jan 16 20:51:57 2008 polynomial 'A' values have 12 factors Thu Jan 17 03:35:28 2008 67110 relations (16704 full + 50406 combined from 841445 partial), need 66899 Thu Jan 17 03:35:31 2008 begin with 858149 relations Thu Jan 17 03:35:33 2008 reduce to 171422 relations in 10 passes Thu Jan 17 03:35:33 2008 attempting to read 171422 relations Thu Jan 17 03:35:38 2008 recovered 171422 relations Thu Jan 17 03:35:38 2008 recovered 153847 polynomials Thu Jan 17 03:35:39 2008 attempting to build 67110 cycles Thu Jan 17 03:35:39 2008 found 67110 cycles in 6 passes Thu Jan 17 03:35:39 2008 distribution of cycle lengths: Thu Jan 17 03:35:39 2008 length 1 : 16704 Thu Jan 17 03:35:39 2008 length 2 : 12264 Thu Jan 17 03:35:39 2008 length 3 : 11271 Thu Jan 17 03:35:39 2008 length 4 : 8988 Thu Jan 17 03:35:39 2008 length 5 : 6855 Thu Jan 17 03:35:39 2008 length 6 : 4505 Thu Jan 17 03:35:39 2008 length 7 : 2786 Thu Jan 17 03:35:39 2008 length 9+: 3737 Thu Jan 17 03:35:39 2008 largest cycle: 23 relations Thu Jan 17 03:35:39 2008 matrix is 66803 x 67110 with weight 4164343 (avg 62.05/col) Thu Jan 17 03:35:41 2008 filtering completed in 3 passes Thu Jan 17 03:35:41 2008 matrix is 63419 x 63483 with weight 3955932 (avg 62.31/col) Thu Jan 17 03:35:41 2008 saving the first 48 matrix rows for later Thu Jan 17 03:35:41 2008 matrix is 63371 x 63483 with weight 3075316 (avg 48.44/col) Thu Jan 17 03:35:41 2008 matrix includes 64 packed rows Thu Jan 17 03:35:42 2008 using block size 21845 for processor cache size 512 kB Thu Jan 17 03:35:42 2008 commencing Lanczos iteration Thu Jan 17 03:36:22 2008 lanczos halted after 1003 iterations (dim = 63369) Thu Jan 17 03:36:22 2008 recovered 17 nontrivial dependencies Thu Jan 17 03:36:23 2008 prp46 factor: 2728784228720769076664362884053977424213249851 Thu Jan 17 03:36:23 2008 prp46 factor: 8260139316381217641035166733618289230331842561 Thu Jan 17 03:36:23 2008 elapsed time 06:44:27
8·10¹²¹+9 = 8(0)₁₂₀9_<122> = 107 · 17321 · C116
C116 = P56 · P61
P56 = 39837349575609258121788494808572654717964321457787972441_<56>
P61 = 1083534667380804556636556284146554026394969807509139591856667_<61>

Number: 80009_121 N=43165149321740613063824529351492192233834246905733249089350240402903503769126882337738156966828122310608860618114147 ( 116 digits) SNFS difficulty: 122 digits. Divisors found: r1=39837349575609258121788494808572654717964321457787972441 (pp56) r2=1083534667380804556636556284146554026394969807509139591856667 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.09 hours. Scaled time: 1.41 units (timescale=0.675). Factorization parameters were as follows: name: 80009_121 n: 43165149321740613063824529351492192233834246905733249089350240402903503769126882337738156966828122310608860618114147 m: 2000000000000000000000000 c5: 5 c0: 18 skew: 1.29 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63758, largePrimes:1975769 encountered Relations: rels:1935048, finalFF:135159 Max relations in full relation-set: 28 Initial matrix: 112922 x 135159 with sparse part having weight 10397305. Pruned matrix : 104434 x 105062 with weight 6434318. Total sieving time: 1.80 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.19 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.09 hours. --------- CPU info (if available) ----------
8·10¹¹⁷+9 = 8(0)₁₁₆9_<118> = 570407 · 540758209 · 1090020499081_<13> · C92
C92 = P31 · P61
P31 = 8959752026870266003989106938343_<31>
P61 = 2655653222978175541447519201124671928388493948927052821291921_<61>

Wed Jan 16 21:03:16 2008 Msieve v. 1.30 Wed Jan 16 21:03:16 2008 random seeds: 2dab32f1 b486c163 Wed Jan 16 21:03:16 2008 factoring 23793994347243262779610066748319237664501818933229988395230398510229558410776055302151026903 (92 digits) Wed Jan 16 21:03:17 2008 commencing quadratic sieve (92-digit input) Wed Jan 16 21:03:18 2008 using multiplier of 7 Wed Jan 16 21:03:18 2008 using 64kb Pentium 2 sieve core Wed Jan 16 21:03:18 2008 sieve interval: 18 blocks of size 65536 Wed Jan 16 21:03:18 2008 processing polynomials in batches of 6 Wed Jan 16 21:03:18 2008 using a sieve bound of 1777823 (67059 primes) Wed Jan 16 21:03:18 2008 using large prime bound of 186671415 (27 bits) Wed Jan 16 21:03:18 2008 using double large prime bound of 772573811846445 (42-50 bits) Wed Jan 16 21:03:18 2008 using trial factoring cutoff of 50 bits Wed Jan 16 21:03:18 2008 polynomial 'A' values have 12 factors Thu Jan 17 09:34:51 2008 67313 relations (18203 full + 49110 combined from 814645 partial), need 67155 Thu Jan 17 09:34:59 2008 begin with 832848 relations Thu Jan 17 09:35:08 2008 reduce to 165375 relations in 10 passes Thu Jan 17 09:35:08 2008 attempting to read 165375 relations Thu Jan 17 09:35:23 2008 recovered 165375 relations Thu Jan 17 09:35:23 2008 recovered 140039 polynomials Thu Jan 17 09:35:35 2008 attempting to build 67313 cycles Thu Jan 17 09:35:36 2008 found 67313 cycles in 5 passes Thu Jan 17 09:35:39 2008 distribution of cycle lengths: Thu Jan 17 09:35:39 2008 length 1 : 18203 Thu Jan 17 09:35:39 2008 length 2 : 12779 Thu Jan 17 09:35:39 2008 length 3 : 11589 Thu Jan 17 09:35:39 2008 length 4 : 9025 Thu Jan 17 09:35:39 2008 length 5 : 6318 Thu Jan 17 09:35:39 2008 length 6 : 4096 Thu Jan 17 09:35:39 2008 length 7 : 2477 Thu Jan 17 09:35:39 2008 length 9+: 2826 Thu Jan 17 09:35:39 2008 largest cycle: 18 relations Thu Jan 17 09:35:40 2008 matrix is 67059 x 67313 with weight 3998972 (avg 59.41/col) Thu Jan 17 09:35:45 2008 filtering completed in 3 passes Thu Jan 17 09:35:45 2008 matrix is 62553 x 62617 with weight 3752163 (avg 59.92/col) Thu Jan 17 09:35:47 2008 saving the first 48 matrix rows for later Thu Jan 17 09:35:48 2008 matrix is 62505 x 62617 with weight 2858139 (avg 45.64/col) Thu Jan 17 09:35:48 2008 matrix includes 64 packed rows Thu Jan 17 09:35:48 2008 using block size 10922 for processor cache size 256 kB Thu Jan 17 09:35:50 2008 commencing Lanczos iteration Thu Jan 17 09:38:48 2008 lanczos halted after 990 iterations (dim = 62503) Thu Jan 17 09:38:49 2008 recovered 16 nontrivial dependencies Thu Jan 17 09:39:30 2008 prp31 factor: 8959752026870266003989106938343 Thu Jan 17 09:39:30 2008 prp61 factor: 2655653222978175541447519201124671928388493948927052821291921 Thu Jan 17 09:39:30 2008 elapsed time 12:36:14
8·10¹³³+9 = 8(0)₁₃₂9_<134> = 89 · 683 · 48247 · 28063523 · C117
C117 = P57 · P61
P57 = 419570597518623739301843398921438222427110769704939738021_<57>
P61 = 2316656939278359599773662465108090166954145351342952510252907_<61>

Number: 80009_133 N=972001136258687370985823047469769423820780268765457967270853419909277049455757306026026401291609436357811577033677047 ( 117 digits) SNFS difficulty: 133 digits. Divisors found: r1=419570597518623739301843398921438222427110769704939738021 (pp57) r2=2316656939278359599773662465108090166954145351342952510252907 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.79 hours. Scaled time: 4.59 units (timescale=0.675). Factorization parameters were as follows: name: 80009_133 n: 972001136258687370985823047469769423820780268765457967270853419909277049455757306026026401291609436357811577033677047 m: 200000000000000000000000000 c5: 250 c0: 9 skew: 0.51 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:63828, largePrimes:1528267 encountered Relations: rels:1544425, finalFF:190502 Max relations in full relation-set: 28 Initial matrix: 142393 x 190502 with sparse part having weight 13662880. Pruned matrix : 125537 x 126312 with weight 7340552. Total sieving time: 6.39 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.27 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.79 hours. --------- CPU info (if available) ----------
Jan 17, 2008: By Jo Yeong Uk / GGNFS, GMP-ECM
8·10¹³⁴+9 = 8(0)₁₃₃9_<135> = 59 · 16301584241_<11> · C123
C123 = P41 · P83
P41 = 28571873631885209731492091721987844825451_<41>
P83 = 29111825682462786935908160354061235293752365551347558913693510861695423975494302961_<83>

Number: 80009_134 N=831779404592797152588463117329260488018172917231409494936913348568290837598995454362795783479947855559771496090953957460411 ( 123 digits) SNFS difficulty: 135 digits. Divisors found: r1=28571873631885209731492091721987844825451 (pp41) r2=29111825682462786935908160354061235293752365551347558913693510861695423975494302961 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.83 hours. Scaled time: 6.03 units (timescale=2.130). Factorization parameters were as follows: n: 831779404592797152588463117329260488018172917231409494936913348568290837598995454362795783479947855559771496090953957460411 m: 1000000000000000000000000000 c5: 4 c0: 45 skew: 1.62 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1200001) Primes: RFBsize:107126, AFBsize:107233, largePrimes:2282220 encountered Relations: rels:2420613, finalFF:301201 Max relations in full relation-set: 28 Initial matrix: 214423 x 301201 with sparse part having weight 21861579. Pruned matrix : 178535 x 179671 with weight 10032422. Total sieving time: 2.69 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.83 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹⁴¹+9 = 8(0)₁₄₀9_<142> = 389 · 32563 · C135
C135 = P55 · P81
P55 = 4990867357422239873844609760866802279933879758965510129_<55>
P81 = 126543531026932811719775808439501974442746850624376305592456058350578392937456103_<81>

Number: 80009_141 N=631561978295267382421119685178985059375115210720259331979527602692569760165128194845080609807825952886897433624217622994919004939367287 ( 135 digits) SNFS difficulty: 142 digits. Divisors found: r1=4990867357422239873844609760866802279933879758965510129 (pp55) r2=126543531026932811719775808439501974442746850624376305592456058350578392937456103 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.10 hours. Scaled time: 13.13 units (timescale=2.152). Factorization parameters were as follows: n: 631561978295267382421119685178985059375115210720259331979527602692569760165128194845080609807825952886897433624217622994919004939367287 m: 20000000000000000000000000000 c5: 5 c0: 18 skew: 1.29 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:113902, largePrimes:3363009 encountered Relations: rels:3471113, finalFF:400013 Max relations in full relation-set: 28 Initial matrix: 228123 x 400013 with sparse part having weight 33816000. Pruned matrix : 169664 x 170868 with weight 12859155. Total sieving time: 5.93 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.10 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹⁵⁸+9 = 8(0)₁₅₇9_<159> = 43 · 133397260513579219_<18> · C141
C141 = P30 · C111
P30 = 167167903992258454388890478299_<30>
C111 = [834299000663855262700697358741077630803654699409180671446600595711970677159208132513234866970546095185263588123_<111>]
8·10¹⁶¹+9 = 8(0)₁₆₀9_<162> = 7 · 361469 · 2281823 · 93410043703_<11> · C139
C139 = P33 · C107
P33 = 104070924106063664505185233829029_<33>
C107 = [14253317185219973460389890832990183114112816437488046262223139768008252805218662703888332623114842777242023_<107>]
8·10¹⁴³+9 = 8(0)₁₄₂9_<144> = 7 · 383 · C141
C141 = P69 · P72
P69 = 341296326661470018931101663238896398460963020877249035438454385737449_<69>
P72 = 874302175383230664843059392215687849285838943004522735011833597504969961_<72>

Number: 80009_143 N=298396120850428944423722491607609101081685938082804923535994032077582991421111525550167847817978366281238343901529280119358448340171577769489 ( 141 digits) SNFS difficulty: 145 digits. Divisors found: r1=341296326661470018931101663238896398460963020877249035438454385737449 (pp69) r2=874302175383230664843059392215687849285838943004522735011833597504969961 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.48 hours. Scaled time: 16.07 units (timescale=2.150). Factorization parameters were as follows: n: 298396120850428944423722491607609101081685938082804923535994032077582991421111525550167847817978366281238343901529280119358448340171577769489 m: 100000000000000000000000000000 c5: 2 c0: 225 skew: 2.57 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1250001) Primes: RFBsize:114155, AFBsize:113882, largePrimes:3338731 encountered Relations: rels:3372927, finalFF:333484 Max relations in full relation-set: 28 Initial matrix: 228102 x 333484 with sparse part having weight 29484204. Pruned matrix : 191664 x 192868 with weight 13878389. Total sieving time: 7.28 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 7.48 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Jan 16, 2008 (4th): By Jo Yeong Uk / GGNFS, GMP-ECM
(64·10¹⁷³-1)/9 = 7(1)₁₇₃_<174> = 3² · 1383089 · 2544133 · 4732520529573831035803_<22> · C139
C139 = P61 · P79
P61 = 1909861565401470161137659936941982422346862092020573206552679_<61>
P79 = 2484337649409539669664989360715143924562307337363563977630662091731238984022991_<79>

Number: 71111_173 N=4744740992087112195864762816440374455308257317012861173239758256887368325321090061827164414472315846815098000336885604806637133029988642889 ( 139 digits) SNFS difficulty: 176 digits. Divisors found: r1=1909861565401470161137659936941982422346862092020573206552679 (pp61) r2=2484337649409539669664989360715143924562307337363563977630662091731238984022991 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 130.26 hours. Scaled time: 279.55 units (timescale=2.146). Factorization parameters were as follows: n: 4744740992087112195864762816440374455308257317012861173239758256887368325321090061827164414472315846815098000336885604806637133029988642889 m: 200000000000000000000000000000000000 c5: 1 c0: -50 skew: 2.19 type: snfs Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [4500000, 6500001) Primes: RFBsize:602489, AFBsize:602205, largePrimes:10863804 encountered Relations: rels:11191485, finalFF:1513162 Max relations in full relation-set: 28 Initial matrix: 1204758 x 1513162 with sparse part having weight 89597218. Pruned matrix : 913804 x 919891 with weight 49944003. Total sieving time: 124.75 hours. Total relation processing time: 0.17 hours. Matrix solve time: 5.25 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.6,2.6,100000 total time: 130.26 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹¹⁵+9 = 8(0)₁₁₄9_<116> = 23 · 164754409 · 1219038421_<10> · C98
C98 = P45 · P53
P45 = 562467957547373531345562723972322221908786381_<45>
P53 = 30790016732270191561933012796406982113872329442024087_<53>

Number: 80009_115 N=17318397824249470808770799132908237419565642366974059924207959257121120487219216176994046339559147 ( 98 digits) SNFS difficulty: 116 digits. Divisors found: r1=562467957547373531345562723972322221908786381 (pp45) r2=30790016732270191561933012796406982113872329442024087 (pp53) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.61 hours. Scaled time: 1.31 units (timescale=2.147). Factorization parameters were as follows: n: 17318397824249470808770799132908237419565642366974059924207959257121120487219216176994046339559147 m: 200000000000000000000000 c5: 1 c0: 36 skew: 2.05 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [300000, 390001) Primes: RFBsize:49098, AFBsize:49231, largePrimes:1769889 encountered Relations: rels:1784790, finalFF:176199 Max relations in full relation-set: 28 Initial matrix: 98393 x 176199 with sparse part having weight 13245210. Pruned matrix : 77376 x 77931 with weight 3716378. Total sieving time: 0.57 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 0.61 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹⁴²+9 = 8(0)₁₄₁9_<143> = 3329 · 29281922233_<11> · C129
C129 = P34 · C96
P34 = 1795510682849862934729054445135297_<34>
C96 = [457076207785168212371453509113670437822360245086692204469952475655630982399330567850785958184721_<96>]
8·10¹⁷⁵+9 = 8(0)₁₇₄9_<176> = 29 · 9907 · 828349 · 149397358667_<12> · 3432767866354222343_<19> · 75056191036086198203_<20> · C115
C115 = P30 · P86
P30 = 266890443093272218468549330943_<30>
P86 = 32721226544458263861906681169586495852149103259513363783751003948859549712960564477403_<86>
Jan 16, 2008 (3rd): By Jo Yeong Uk / GGNFS, GMP-ECM
8·10¹⁶⁴-9 = 7(9)₁₆₃1_<165> = 7 · 41 · 1143403361_<10> · 261891714717420247_<18> · 11046278788929908087_<20> · C117
C117 = P39 · P79
P39 = 308636832720759777975330569373913552783_<39>
P79 = 2730380120299666574824672795496309223735144601900062623583012669777090797192599_<79>

Number: 79991_164 N=842695872453016151605622018022638106849233137887964461947572705754837909988138005741669220163798173899089414403453017 ( 117 digits) Divisors found: r1=308636832720759777975330569373913552783 (pp39) r2=2730380120299666574824672795496309223735144601900062623583012669777090797192599 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 32.49 hours. Scaled time: 69.91 units (timescale=2.152). Factorization parameters were as follows: name: 79991_164 n: 842695872453016151605622018022638106849233137887964461947572705754837909988138005741669220163798173899089414403453017 skew: 39822.29 # norm 1.28e+16 c5: 53100 c4: -1234949190 c3: -584057431279291 c2: 113539236838916353 c1: 172914044835050143787073 c0: 1186521124802802637136030280 # alpha -5.74 Y1: 3702589636013 Y0: -27549615417740198203969 # Murphy_E 4.20e-10 # M 398711343419018151458526581075477856479282773180178871103100914140391572713644277776727739442770855281441383627371216 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3825001) Primes: RFBsize:315948, AFBsize:317384, largePrimes:7631001 encountered Relations: rels:7736677, finalFF:795523 Max relations in full relation-set: 28 Initial matrix: 633411 x 795523 with sparse part having weight 61742503. Pruned matrix : 492974 x 496205 with weight 35425385. Polynomial selection time: 1.75 hours. Total sieving time: 29.00 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.41 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 32.49 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
7·10¹⁶¹-9 = 6(9)₁₆₀1_<162> = 31 · 238529 · 16165785424707406853881795571381_<32> · C124
C124 = P34 · P91
P34 = 1154734515303355813588848626575829_<34>
P91 = 5071263789375496111006719685471610072718773087775179235920085143775708329815366365895324241_<91>
Jan 16, 2008 (2nd): By Robert Backstrom / GMP-ECM
8·10¹⁵⁶-9 = 7(9)₁₅₅1_<157> = 13001 · C153
C153 = P34 · P120
P34 = 1295988165151587695336675852925431_<34>
P120 = 474801621105532083834700125189778681342962201400810891482867919304452802278015894667986382020302929101025045361916944761_<120>
Jan 16, 2008: The factor table of 800...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jan 15, 2008 (4th): By Jo Yeong Uk / GMP-ECM
8·10¹⁸⁰-9 = 7(9)₁₇₉1_<181> = C181
C181 = P39 · C142
P39 = 826115977894170609050375729157582021497_<39>
C142 = [9683870320959750397301131599191235511655411576027658067144718311274518875633720728729028560156827649352670707054841461900759820696819277771503_<142>]
8·10¹⁹⁵-9 = 7(9)₁₉₄1_<196> = 3889 · 15610275261869941441_<20> · 435897677914358674687851179_<27> · 1045513792226296340499906371_<28> · C120
C120 = P32 · P89
P32 = 19119580804026448034824934992231_<32>
P89 = 15123377562818027057411188140424291585847836807190418568871815626881749196170735312717121_<89>
Jan 15, 2008 (3rd): By matsui / GMP-ECM
(14·10¹⁹³-41)/9 = 1(5)₁₉₂1_<194> = 11 · 331 · C190
C190 = P32 · C158
P32 = 62526939757042506698769902098831_<32>
C158 = [68327837135788697792225797137899512369957580856225051975788498022627748463669114687246453722274284444945237019649575567790089868646790503352013257536766804281_<158>]
(8·10¹⁹⁵-53)/9 = (8)₁₉₄3_<195> = 23 · 29 · C193
C193 = P33 · C160
P33 = 144590681557580521442564517528323_<33>
C160 = [9216824939736569669228358640580173977056399699297573655614497386963756277829507934369338603231828859333521137520519483912139878643422967809749001298287897524163_<160>]
Jan 15, 2008 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁵¹-9 = 7(9)₁₅₀1_<152> = 81001 · 1259231 · 1739471 · 87802863301_<11> · C124
C124 = P47 · P78
P47 = 30791592289433442832144020953926711999042958399_<47>
P78 = 166777008939323811795992782279128050360042974145183252503836734575392545775709_<78>

Number: 79991_151 N=5135329662510855451262747808996030428811545227752914475018951225716569545596080341020197792116773744210930101595349671729891 ( 124 digits) SNFS difficulty: 152 digits. Divisors found: r1=30791592289433442832144020953926711999042958399 (pp47) r2=166777008939323811795992782279128050360042974145183252503836734575392545775709 (pp78) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.10 hours. Scaled time: 42.15 units (timescale=1.998). Factorization parameters were as follows: name: 79991_151 n: 5135329662510855451262747808996030428811545227752914475018951225716569545596080341020197792116773744210930101595349671729891 m: 2000000000000000000000000000000 c5: 5 c0: -18 skew: 1.29 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, 1900001) Primes: RFBsize:176302, AFBsize:176263, largePrimes:5423196 encountered Relations: rels:5343061, finalFF:492291 Max relations in full relation-set: 28 Initial matrix: 352631 x 492291 with sparse part having weight 42349212. Pruned matrix : 286234 x 288061 with weight 22574991. Total sieving time: 19.86 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.98 hours. Time per square root: 0.13 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: 21.10 hours. --------- CPU info (if available) ----------
8·10¹⁵²-9 = 7(9)₁₅₁1_<153> = 7 · 17 · 4660787009_<10> · 138804112174759_<15> · C128
C128 = P49 · P79
P49 = 8716632273706955002066316578892953673433856501001_<49>
P79 = 1192154963555103648416832707448716501053570407831671868210179818737805091325919_<79>

Number: 79991_152 N=10391576430584355190373677199759407351446517692328060162305724930882541948962841610590261491446581131649370344311873473040744919 ( 128 digits) SNFS difficulty: 152 digits. Divisors found: r1=8716632273706955002066316578892953673433856501001 (pp49) r2=1192154963555103648416832707448716501053570407831671868210179818737805091325919 (pp79) Version: GGNFS-0.77.1-20060513-k8 Total time: 25.77 hours. Scaled time: 51.56 units (timescale=2.001). Factorization parameters were as follows: name: 79991_152 n: 10391576430584355190373677199759407351446517692328060162305724930882541948962841610590261491446581131649370344311873473040744919 m: 2000000000000000000000000000000 c5: 25 c0: -9 skew: 0.82 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, 2100001) Primes: RFBsize:176302, AFBsize:176228, largePrimes:5853695 encountered Relations: rels:6051618, finalFF:728881 Max relations in full relation-set: 28 Initial matrix: 352594 x 728881 with sparse part having weight 65846116. Pruned matrix : 233861 x 235687 with weight 30991348. Total sieving time: 24.73 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.78 hours. Time per square root: 0.12 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: 25.77 hours. --------- CPU info (if available) ----------
Jan 15, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(71·10¹⁶⁶-17)/9 = 7(8)₁₆₅7_<167> = 134850917 · C159
C159 = P42 · P117
P42 = 651848668311457681434595316282892913713581_<42>
P117 = 897460106491496446614435004796283119759388322955462991597812172002637625312740762585824492525266076716658116988493431_<117>

Number: n N=585008175279140956000239055763253644681473607546093949727378486339020511732144089823941567181844887928265915232069863409893526262701564638888505955720633986411 ( 159 digits) SNFS difficulty: 167 digits. Divisors found: Tue Jan 15 05:36:06 2008 prp42 factor: 651848668311457681434595316282892913713581 Tue Jan 15 05:36:06 2008 prp117 factor: 897460106491496446614435004796283119759388322955462991597812172002637625312740762585824492525266076716658116988493431 Tue Jan 15 05:36:06 2008 elapsed time 03:06:55 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 124.47 hours. Scaled time: 162.43 units (timescale=1.305). Factorization parameters were as follows: name: KA_7_8_165_7 n: 585008175279140956000239055763253644681473607546093949727378486339020511732144089823941567181844887928265915232069863409893526262701564638888505955720633986411 skew: 0.47 deg: 5 c5: 710 c0: -17 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5001307) Primes: RFBsize:230209, AFBsize:229783, largePrimes:8029739 encountered Relations: rels:7472162, finalFF:393297 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 124.03 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 124.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
2·10¹⁶⁵-3 = 1(9)₁₆₄7_<166> = 53 · 71881 · 238245737904007_<15> · C145
C145 = P37 · P52 · P57
P37 = 1403781958927021896724841424949479359_<37>
P52 = 2551589809127749396488652666886417210600862321179209_<52>
P57 = 615183048749711493044799857844699363803138896771654939937_<57>

Number: n N=1569694797937903300551110733526778314018254369305286389639105161479391032809561453871065828543212923908169833 ( 109 digits) Divisors found: Tue Jan 15 14:40:26 2008 prp52 factor: 2551589809127749396488652666886417210600862321179209 Tue Jan 15 14:40:26 2008 prp57 factor: 615183048749711493044799857844699363803138896771654939937 Tue Jan 15 14:40:26 2008 elapsed time 00:47:23 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 11.42 hours. Scaled time: 9.56 units (timescale=0.837). Factorization parameters were as follows: name: KA_1_9_164_7 n: 1569694797937903300551110733526778314018254369305286389639105161479391032809561453871065828543212923908169833 skew: 8306.36 # norm 2.76e+14 c5: 66240 c4: -3742036824 c3: -9666955114689 c2: 233645416862500981 c1: 389670328960034369953 c0: -1807187513145699342603261 # alpha -5.10 Y1: 357931261909 Y0: -473088827202633755566 # Murphy_E 1.24e-09 # M 794377935712316731005078895413010160819638922615293091642026246376800976490609919453234209027858723238419702 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 special-q in [100000, 2800001) Primes: RFBsize:230209, AFBsize:230661, largePrimes:7168024 encountered Relations: rels:6884920, finalFF:517695 Max relations in full relation-set: 28 Initial matrix: 460952 x 517695 with sparse part having weight 37788957. Pruned matrix : 413293 x 415661 with weight 25450233. Total sieving time: 11.25 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 11.42 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
8·10¹⁴⁹-9 = 7(9)₁₄₈1_<150> = 41 · 387128561 · C140
C140 = P42 · P47 · P52
P42 = 506448962913497763293952892565556348977959_<42>
P47 = 51909484898783796991431617515193618122604873161_<47>
P52 = 1917204817158045773364919500838723218822870408926609_<52>

Number: n N=50402365228617734335016222043145796714084216637046821048037371523707138598899480824205970221639614758238464126637047456747868817464881438991 ( 140 digits) SNFS difficulty: 150 digits. Divisors found: Tue Jan 15 21:21:09 2008 prp42 factor: 506448962913497763293952892565556348977959 Tue Jan 15 21:21:09 2008 prp47 factor: 51909484898783796991431617515193618122604873161 Tue Jan 15 21:21:09 2008 prp52 factor: 1917204817158045773364919500838723218822870408926609 Tue Jan 15 21:21:09 2008 elapsed time 00:47:51 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 14.51 hours. Scaled time: 19.05 units (timescale=1.313). Factorization parameters were as follows: name: KA_7_9_148_1 n: 50402365228617734335016222043145796714084216637046821048037371523707138598899480824205970221639614758238464126637047456747868817464881438991 skew: 1.62 deg: 5 c5: 4 c0: -45 m: 1000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 799990) Primes: RFBsize:203362, AFBsize:203002, largePrimes:6263890 encountered Relations: rels:5792386, finalFF:494582 Max relations in full relation-set: 28 Initial matrix: 406428 x 494582 with sparse part having weight 27219008. Pruned matrix : Total sieving time: 14.35 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 14.51 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 14, 2008 (6th): By Irvine
10³⁷⁵+1 is divisible by 4709825349852110182615878875374419529306990314325041101342026868334001_<70>, cofactor is prime.
Reference: The Cunningham Project (Sam Wagstaff)
Jan 14, 2008 (5th): By Yousuke Koide
(10¹²⁷⁹-1)/9 is divisible by 2320223789459953862122440032213_<31>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jan 14, 2008 (4th): By Jo Yeong Uk / Msieve, GGNFS
8·10¹⁵⁸-9 = 7(9)₁₅₇1_<159> = 7 · 4323841 · 4714903 · 462997341128773543_<18> · 410562561244534563981430142949031_<33> · C95
C95 = P47 · P48
P47 = 46763860302718914140271163284841847599644741791_<47>
P48 = 630639651843465146374746113429199687582690077977_<48>

Sun Jan 13 22:37:33 2008 Sun Jan 13 22:37:33 2008 Sun Jan 13 22:37:33 2008 Msieve v. 1.32 Sun Jan 13 22:37:33 2008 random seeds: 22de54b1 e3793a1d Sun Jan 13 22:37:33 2008 factoring 29491144580163096639800559468991908217808992070869327114070748537704128510842764288695820636807 (95 digits) Sun Jan 13 22:37:34 2008 no P-1/P+1/ECM available, skipping Sun Jan 13 22:37:34 2008 commencing quadratic sieve (95-digit input) Sun Jan 13 22:37:34 2008 using multiplier of 23 Sun Jan 13 22:37:34 2008 using 32kb Intel Core sieve core Sun Jan 13 22:37:34 2008 sieve interval: 36 blocks of size 32768 Sun Jan 13 22:37:34 2008 processing polynomials in batches of 6 Sun Jan 13 22:37:34 2008 using a sieve bound of 2117419 (78824 primes) Sun Jan 13 22:37:34 2008 using large prime bound of 309143174 (28 bits) Sun Jan 13 22:37:34 2008 using double large prime bound of 1915522827320368 (43-51 bits) Sun Jan 13 22:37:34 2008 using trial factoring cutoff of 51 bits Sun Jan 13 22:37:34 2008 polynomial 'A' values have 12 factors Mon Jan 14 02:03:04 2008 79124 relations (19503 full + 59621 combined from 1162555 partial), need 78920 Mon Jan 14 02:03:05 2008 begin with 1182058 relations Mon Jan 14 02:03:06 2008 reduce to 205345 relations in 12 passes Mon Jan 14 02:03:06 2008 attempting to read 205345 relations Mon Jan 14 02:03:07 2008 recovered 205345 relations Mon Jan 14 02:03:07 2008 recovered 189496 polynomials Mon Jan 14 02:03:08 2008 attempting to build 79124 cycles Mon Jan 14 02:03:08 2008 found 79122 cycles in 5 passes Mon Jan 14 02:03:08 2008 distribution of cycle lengths: Mon Jan 14 02:03:08 2008 length 1 : 19503 Mon Jan 14 02:03:08 2008 length 2 : 13950 Mon Jan 14 02:03:08 2008 length 3 : 13238 Mon Jan 14 02:03:08 2008 length 4 : 10765 Mon Jan 14 02:03:08 2008 length 5 : 8092 Mon Jan 14 02:03:08 2008 length 6 : 5469 Mon Jan 14 02:03:08 2008 length 7 : 3396 Mon Jan 14 02:03:08 2008 length 9+: 4709 Mon Jan 14 02:03:08 2008 largest cycle: 21 relations Mon Jan 14 02:03:08 2008 matrix is 78824 x 79122 with weight 5358756 (avg 67.73/col) Mon Jan 14 02:03:08 2008 filtering completed in 3 passes Mon Jan 14 02:03:08 2008 matrix is 75111 x 75175 with weight 5115448 (avg 68.05/col) Mon Jan 14 02:03:10 2008 saving the first 48 matrix rows for later Mon Jan 14 02:03:10 2008 matrix is 75063 x 75175 with weight 4227524 (avg 56.24/col) Mon Jan 14 02:03:10 2008 matrix includes 64 packed rows Mon Jan 14 02:03:10 2008 using block size 30070 for processor cache size 4096 kB Mon Jan 14 02:03:12 2008 commencing Lanczos iteration Mon Jan 14 02:03:40 2008 lanczos halted after 1188 iterations (dim = 75062) Mon Jan 14 02:03:40 2008 recovered 17 nontrivial dependencies Mon Jan 14 02:03:41 2008 prp47 factor: 46763860302718914140271163284841847599644741791 Mon Jan 14 02:03:41 2008 prp48 factor: 630639651843465146374746113429199687582690077977 Mon Jan 14 02:03:41 2008 elapsed time 03:26:08
8·10¹⁵⁴-9 = 7(9)₁₅₃1_<155> = 41 · 59281 · 547957391 · 12119965852433_<14> · C127
C127 = P39 · P89
P39 = 461939553236586484114536733702650233023_<39>
P89 = 10728951295727690102209746621884683736435695534177888595486933153914001471840926288450159_<89>

Number: 79991_154 N=4956126968245544840829612126947542016537069480457201107807317941718490806281289773378008927417668578515244674558217734871400657 ( 127 digits) SNFS difficulty: 155 digits. Divisors found: r1=461939553236586484114536733702650233023 (pp39) r2=10728951295727690102209746621884683736435695534177888595486933153914001471840926288450159 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 18.01 hours. Scaled time: 38.75 units (timescale=2.151). Factorization parameters were as follows: n: 4956126968245544840829612126947542016537069480457201107807317941718490806281289773378008927417668578515244674558217734871400657 m: 10000000000000000000000000000000 c5: 4 c0: -45 skew: 1.62 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:216516, largePrimes:5592938 encountered Relations: rels:5575870, finalFF:574005 Max relations in full relation-set: 28 Initial matrix: 433396 x 574005 with sparse part having weight 43815050. Pruned matrix : 340472 x 342702 with weight 27481926. Total sieving time: 17.33 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.57 hours. Time per square root: 0.04 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: 18.01 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
3·10¹⁶⁴+1 = 3(0)₁₆₃1_<165> = 7 · 153643579 · 3358957632992895950040793_<25> · C131
C131 = P37 · P94
P37 = 9126754553793380350961701881130062943_<37>
P94 = 9098879264948989983429360562774153133639098883364585761384303273204226621258077428446473075683_<94>
Jan 14, 2008 (3rd): By Sinkiti Sibata / GGNFS
8·10¹⁴⁵-9 = 7(9)₁₄₄1_<146> = 31 · 3769 · 7489 · 279971682391_<12> · C126
C126 = P55 · P71
P55 = 7742337301078104200488978966281420202696958368400348371_<55>
P71 = 42178597070720342821424007221144098406947930977765023595765919575211661_<71>

Number: 79991_145 N=326560925407781770767774075639791745382030213521430418350721109651781264744036225782582623040049517265875742904382248461554231 ( 126 digits) SNFS difficulty: 145 digits. Divisors found: r1=7742337301078104200488978966281420202696958368400348371 (pp55) r2=42178597070720342821424007221144098406947930977765023595765919575211661 (pp71) Version: GGNFS-0.77.1-20060513-k8 Total time: 13.98 hours. Scaled time: 27.74 units (timescale=1.985). Factorization parameters were as follows: name: 79991_145 n: 326560925407781770767774075639791745382030213521430418350721109651781264744036225782582623040049517265875742904382248461554231 m: 100000000000000000000000000000 c5: 8 c0: -9 skew: 1.02 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2150001) Primes: RFBsize:100021, AFBsize:99978, largePrimes:2778825 encountered Relations: rels:2779522, finalFF:267636 Max relations in full relation-set: 28 Initial matrix: 200064 x 267636 with sparse part having weight 27367024. Pruned matrix : 181507 x 182571 with weight 16750604. Total sieving time: 13.45 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.36 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 13.98 hours. --------- CPU info (if available) ----------
8·10¹⁴⁸-9 = 7(9)₁₄₇1_<149> = 23 · 2351 · 5417 · 18204143 · 1811121196799_<13> · 1947542272318766199929_<22> · C100
C100 = P37 · P64
P37 = 1698869895271211983854184427647893889_<37>
P64 = 2503720935946036989300856832502895816091759303149812092199359903_<64>

Sat Jan 12 20:55:23 2008 Msieve v. 1.30 Sat Jan 12 20:55:23 2008 random seeds: 45d02a07 42588f3f Sat Jan 12 20:55:23 2008 factoring 4253496124238984707734842877964977170209510988448548351661975134912047668525960763545100431865332767 (100 digits) Sat Jan 12 20:55:24 2008 commencing quadratic sieve (100-digit input) Sat Jan 12 20:55:24 2008 using multiplier of 3 Sat Jan 12 20:55:24 2008 using 64kb Pentium 4 sieve core Sat Jan 12 20:55:24 2008 sieve interval: 18 blocks of size 65536 Sat Jan 12 20:55:24 2008 processing polynomials in batches of 6 Sat Jan 12 20:55:24 2008 using a sieve bound of 2704027 (98824 primes) Sat Jan 12 20:55:24 2008 using large prime bound of 405604050 (28 bits) Sat Jan 12 20:55:24 2008 using double large prime bound of 3123087099560100 (43-52 bits) Sat Jan 12 20:55:24 2008 using trial factoring cutoff of 52 bits Sat Jan 12 20:55:24 2008 polynomial 'A' values have 13 factors Sun Jan 13 07:55:59 2008 9287 relations (6915 full + 2372 combined from 447278 partial), need 98920 Sun Jan 13 07:55:59 2008 elapsed time 11:00:36 Sun Jan 13 08:10:19 2008 Sun Jan 13 08:10:19 2008 Sun Jan 13 08:10:19 2008 Msieve v. 1.30 Sun Jan 13 08:10:19 2008 random seeds: 8ded5200 352a1059 Sun Jan 13 08:10:19 2008 factoring 4253496124238984707734842877964977170209510988448548351661975134912047668525960763545100431865332767 (100 digits) Sun Jan 13 08:10:20 2008 commencing quadratic sieve (100-digit input) Sun Jan 13 08:10:20 2008 using multiplier of 3 Sun Jan 13 08:10:20 2008 using 64kb Pentium 4 sieve core Sun Jan 13 08:10:20 2008 sieve interval: 18 blocks of size 65536 Sun Jan 13 08:10:20 2008 processing polynomials in batches of 6 Sun Jan 13 08:10:20 2008 using a sieve bound of 2704027 (98824 primes) Sun Jan 13 08:10:20 2008 using large prime bound of 405604050 (28 bits) Sun Jan 13 08:10:20 2008 using double large prime bound of 3123087099560100 (43-52 bits) Sun Jan 13 08:10:20 2008 using trial factoring cutoff of 52 bits Sun Jan 13 08:10:20 2008 polynomial 'A' values have 13 factors Sun Jan 13 08:10:22 2008 restarting with 6915 full and 447278 partial relations Mon Jan 14 09:57:41 2008 98999 relations (23067 full + 75932 combined from 1497061 partial), need 98920 Mon Jan 14 09:57:47 2008 begin with 1520128 relations Mon Jan 14 09:57:50 2008 reduce to 263703 relations in 11 passes Mon Jan 14 09:57:50 2008 attempting to read 263703 relations Mon Jan 14 09:58:00 2008 recovered 263703 relations Mon Jan 14 09:58:00 2008 recovered 255071 polynomials Mon Jan 14 09:58:01 2008 attempting to build 98999 cycles Mon Jan 14 09:58:01 2008 found 98999 cycles in 6 passes Mon Jan 14 09:58:01 2008 distribution of cycle lengths: Mon Jan 14 09:58:01 2008 length 1 : 23067 Mon Jan 14 09:58:01 2008 length 2 : 16643 Mon Jan 14 09:58:01 2008 length 3 : 16544 Mon Jan 14 09:58:01 2008 length 4 : 13575 Mon Jan 14 09:58:01 2008 length 5 : 10481 Mon Jan 14 09:58:01 2008 length 6 : 7268 Mon Jan 14 09:58:01 2008 length 7 : 4607 Mon Jan 14 09:58:01 2008 length 9+: 6814 Mon Jan 14 09:58:01 2008 largest cycle: 21 relations Mon Jan 14 09:58:02 2008 matrix is 98824 x 98999 with weight 6671927 (avg 67.39/col) Mon Jan 14 09:58:04 2008 filtering completed in 3 passes Mon Jan 14 09:58:04 2008 matrix is 95182 x 95246 with weight 6452945 (avg 67.75/col) Mon Jan 14 09:58:05 2008 saving the first 48 matrix rows for later Mon Jan 14 09:58:05 2008 matrix is 95134 x 95246 with weight 5001470 (avg 52.51/col) Mon Jan 14 09:58:05 2008 matrix includes 64 packed rows Mon Jan 14 09:58:05 2008 using block size 21845 for processor cache size 512 kB Mon Jan 14 09:58:07 2008 commencing Lanczos iteration Mon Jan 14 09:59:41 2008 lanczos halted after 1506 iterations (dim = 95134) Mon Jan 14 09:59:41 2008 recovered 18 nontrivial dependencies Mon Jan 14 09:59:43 2008 prp37 factor: 1698869895271211983854184427647893889 Mon Jan 14 09:59:43 2008 prp64 factor: 2503720935946036989300856832502895816091759303149812092199359903 Mon Jan 14 09:59:43 2008 elapsed time 25:49:24
8·10¹⁴⁴-9 = 7(9)₁₄₃1_<145> = 41 · 356977 · 12418519760749442070754470311_<29> · C110
C110 = P34 · P77
P34 = 1202396689032442891861982410658929_<34>
P77 = 36605664115474603832272688375093831327326195191011201019483886504026399481577_<77>

Number: 79991_144 N=44014529332280370913945784430768068918614841536502394721741885965309300374132997959530907498071104444566051033 ( 110 digits) SNFS difficulty: 145 digits. Divisors found: r1=1202396689032442891861982410658929 (pp34) r2=36605664115474603832272688375093831327326195191011201019483886504026399481577 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 15.54 hours. Scaled time: 30.96 units (timescale=1.992). Factorization parameters were as follows: name: 79991_144 n: 44014529332280370913945784430768068918614841536502394721741885965309300374132997959530907498071104444566051033 m: 100000000000000000000000000000 c5: 4 c0: -45 skew: 1.62 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2350001) Primes: RFBsize:100021, AFBsize:100108, largePrimes:2834967 encountered Relations: rels:2856600, finalFF:275497 Max relations in full relation-set: 28 Initial matrix: 200193 x 275497 with sparse part having weight 29783015. Pruned matrix : 180481 x 181545 with weight 17934606. Total sieving time: 14.99 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.35 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 15.54 hours. --------- CPU info (if available) ----------
Jan 14, 2008 (2nd): By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(2·10¹⁶³-11)/9 = (2)₁₆₂1_<163> = 17 · 37877640361436692050097_<23> · C139
C139 = P64 · P76
P64 = 2220078767826668361325983014056277664531569885622229234531374787_<64>
P76 = 1554487611393771714900494781481020302062202220737078357519127682939670142767_<76>

Number: n N=3451084940904905586708196728200554661963901726244208158350060888692051925846967926091130062961315383616227129749369913889451806441074215629 ( 139 digits) SNFS difficulty: 163 digits. Divisors found: r1=2220078767826668361325983014056277664531569885622229234531374787 (pp64) r2=1554487611393771714900494781481020302062202220737078357519127682939670142767 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 38.74 hours. Scaled time: 70.85 units (timescale=1.829). Factorization parameters were as follows: name: KA_2_162_1 n: 3451084940904905586708196728200554661963901726244208158350060888692051925846967926091130062961315383616227129749369913889451806441074215629 skew: 0.71 deg: 5 c5: 125 c0: -22 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2600001) Primes: RFBsize:216816, AFBsize:216697, largePrimes:7455704 encountered Relations: rels:6931886, finalFF:513994 Max relations in full relation-set: 48 Initial matrix: 433578 x 513994 with sparse part having weight 52499854. Pruned matrix : 395935 x 398166 with weight 33837805. Total sieving time: 36.93 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.57 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 38.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
8·10¹⁶⁰-9 = 7(9)₁₅₉1_<161> = 31 · 57073 · C155
C155 = P39 · P117
P39 = 162324131850327948485434438093621716953_<39>
P117 = 278557273407351934069599866763595027872975703442508848781459154897177077473859196381772941462840739464361826004563169_<117>
8·10¹⁶⁵-9 = 7(9)₁₆₄1_<166> = 281 · C164
C164 = P29 · P136
P29 = 18039899370116253132365185259_<29>
P136 = 1578154639645101849715900601142746848194561974023738373087552898239995805944710078341227436286841880064814566233260954631456666425083629_<136>
5·10¹⁶²-1 = 4(9)₁₆₂_<163> = 7898189142101_<13> · 456514351349672851_<18> · C133
C133 = P46 · P87
P46 = 7739832354657573536230860093069953953660396661_<46>
P87 = 179166366257503162309509372277349334970926729613420475526494728627218732934704149702509_<87>

Number: n N=1386717638426251931934033806378717686203165786751271889807208433424201191175011460788311942354451703713581361177260630054458086922449 ( 133 digits) SNFS difficulty: 162 digits. Divisors found: Mon Jan 14 10:32:34 2008 prp46 factor: 7739832354657573536230860093069953953660396661 Mon Jan 14 10:32:34 2008 prp87 factor: 179166366257503162309509372277349334970926729613420475526494728627218732934704149702509 Mon Jan 14 10:32:34 2008 elapsed time 00:57:29 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 39.69 hours. Scaled time: 33.26 units (timescale=0.838). Factorization parameters were as follows: name: KA_4_9_162 n: 1386717638426251931934033806378717686203165786751271889807208433424201191175011460788311942354451703713581361177260630054458086922449 type: snfs deg: 5 c5: 500 c0: -1 skew: 0.29 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3700000) Primes: RFBsize:216816, AFBsize:216391, largePrimes:5827763 encountered Relations: rels:5828091, finalFF:514396 Max relations in full relation-set: 28 Initial matrix: 433273 x 514396 with sparse part having weight 53218789. Pruned matrix : 400490 x 402720 with weight 39410526. Total sieving time: 39.57 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 39.69 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
8·10¹⁵⁵-9 = 7(9)₁₅₄1_<156> = 89 · 39076948619_<11> · 17285468921447286611_<20> · C125
C125 = P33 · P92
P33 = 630937457078491523522125157973689_<33>
P92 = 21091713323420107009957029361942912268853049172167108976864637180884556752573488461477765719_<92>
Jan 14, 2008: By matsui / GMP-ECM
5·10¹⁹⁰-9 = 4(9)₁₈₉1_<191> = 61 · 409 · C187
C187 = P32 · P155
P32 = 47568134021252279670958230004481_<32>
P155 = 42130900895096262260841447387806243682255781771378005956259860699611715275397274609349024640992587587106601079256289499605009903500893334162184491530113339_<155>
(34·10¹⁹⁷-43)/9 = 3(7)₁₉₆3_<198> = 11 · 433 · C194
C194 = P30 · C165
P30 = 175552370499658335275248396363_<30>
C165 = [451803018305522330975120918157248100722684575456134658825674860937758490095206379652486712157977804105105296752082281189878524588429897592043870795445824300265839717_<165>]
Jan 13, 2008 (3rd): By matsui / GMP-ECM
(73·10²⁰⁰-1)/9 = 8(1)₂₀₀_<201> = 487 · C199
C199 = P36 · C164
P36 = 116587695911853113400792854475193411_<36>
C164 = [14285606062277732309168156983256445884072165236631874368716790782839231122943523363577821850787245917630279558418605214545784622225512312628692589974007175489848523_<164>]
Jan 13, 2008 (2nd): By Sinkiti Sibata / GGNFS, Msieve
8·10¹³⁴-9 = 7(9)₁₃₃1_<135> = 7 · 41 · 2991559 · 51611423 · C119
C119 = P51 · P68
P51 = 547886259883585498357025117689672145168225517346471_<51>
P68 = 32951430664648770389924301340174201074562936491053050907418208102919_<68>

Number: 79991_134 N=18053636104667704643286239945614946302235180121774908791993905279361217947079393873400776543238916285526231963749448849 ( 119 digits) SNFS difficulty: 135 digits. Divisors found: r1=547886259883585498357025117689672145168225517346471 (pp51) r2=32951430664648770389924301340174201074562936491053050907418208102919 (pp68) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.77 hours. Scaled time: 11.57 units (timescale=2.004). Factorization parameters were as follows: name: 79991_134 n: 18053636104667704643286239945614946302235180121774908791993905279361217947079393873400776543238916285526231963749448849 m: 1000000000000000000000000000 c5: 4 c0: -45 skew: 1.62 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:64108, largePrimes:1539429 encountered Relations: rels:1553166, finalFF:188124 Max relations in full relation-set: 28 Initial matrix: 142670 x 188124 with sparse part having weight 14083615. Pruned matrix : 127526 x 128303 with weight 7818342. Total sieving time: 5.59 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.77 hours. --------- CPU info (if available) ----------
8·10¹²⁷-9 = 7(9)₁₂₆1_<128> = 379 · 162668538905134917251_<21> · C106
C106 = P42 · P64
P42 = 657946460633670262464217847012752777057361_<42>
P64 = 1972225892515966800861803327069244574222166958428213389132029239_<64>

Number: 79991_127 N=1297619045550961749053867427793399261073676933317173039733022282273362765727795424832044173656449032178279 ( 106 digits) SNFS difficulty: 127 digits. Divisors found: r1=657946460633670262464217847012752777057361 (pp42) r2=1972225892515966800861803327069244574222166958428213389132029239 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.10 hours. Scaled time: 6.18 units (timescale=1.996). Factorization parameters were as follows: name: 79991_127 n: 1297619045550961749053867427793399261073676933317173039733022282273362765727795424832044173656449032178279 m: 20000000000000000000000000 c5: 25 c0: -9 skew: 0.82 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 750001) Primes: RFBsize:63951, AFBsize:63968, largePrimes:1468206 encountered Relations: rels:1493823, finalFF:197352 Max relations in full relation-set: 28 Initial matrix: 127983 x 197352 with sparse part having weight 9951716. Pruned matrix : 104345 x 105048 with weight 4227563. Total sieving time: 2.98 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.04 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 3.10 hours. --------- CPU info (if available) ----------
8·10¹⁶²-9 = 7(9)₁₆₁1_<163> = 103 · 885679 · 27972713 · 20174793473_<11> · 128513348641_<12> · 6739247979073_<13> · 1849901488629672000658219697_<28> · C86
C86 = P32 · P55
P32 = 29004454390043890346738171836159_<32>
P55 = 3343949795648324158059774855467139266458728235931156713_<55>

Sun Jan 13 08:25:03 2008 Msieve v. 1.30 Sun Jan 13 08:25:03 2008 random seeds: 4905ce6d 0961e9c8 Sun Jan 13 08:25:03 2008 factoring 96989439330478405638385934491360121476455014414443770871154615953823073607951988985367 (86 digits) Sun Jan 13 08:25:04 2008 commencing quadratic sieve (86-digit input) Sun Jan 13 08:25:04 2008 using multiplier of 1 Sun Jan 13 08:25:04 2008 using 64kb Pentium 2 sieve core Sun Jan 13 08:25:04 2008 sieve interval: 9 blocks of size 65536 Sun Jan 13 08:25:05 2008 processing polynomials in batches of 12 Sun Jan 13 08:25:05 2008 using a sieve bound of 1466767 (56000 primes) Sun Jan 13 08:25:05 2008 using large prime bound of 117341360 (26 bits) Sun Jan 13 08:25:05 2008 using double large prime bound of 334974615074720 (41-49 bits) Sun Jan 13 08:25:05 2008 using trial factoring cutoff of 49 bits Sun Jan 13 08:25:05 2008 polynomial 'A' values have 11 factors Sun Jan 13 14:10:11 2008 56141 relations (16063 full + 40078 combined from 585521 partial), need 56096 Sun Jan 13 14:10:16 2008 begin with 601584 relations Sun Jan 13 14:10:23 2008 reduce to 133024 relations in 9 passes Sun Jan 13 14:10:23 2008 attempting to read 133024 relations Sun Jan 13 14:10:32 2008 recovered 133024 relations Sun Jan 13 14:10:32 2008 recovered 109251 polynomials Sun Jan 13 14:10:58 2008 attempting to build 56141 cycles Sun Jan 13 14:10:58 2008 found 56141 cycles in 5 passes Sun Jan 13 14:11:02 2008 distribution of cycle lengths: Sun Jan 13 14:11:02 2008 length 1 : 16063 Sun Jan 13 14:11:02 2008 length 2 : 11348 Sun Jan 13 14:11:02 2008 length 3 : 9829 Sun Jan 13 14:11:02 2008 length 4 : 7247 Sun Jan 13 14:11:02 2008 length 5 : 4933 Sun Jan 13 14:11:02 2008 length 6 : 3080 Sun Jan 13 14:11:02 2008 length 7 : 1688 Sun Jan 13 14:11:02 2008 length 9+: 1953 Sun Jan 13 14:11:02 2008 largest cycle: 20 relations Sun Jan 13 14:11:04 2008 matrix is 56000 x 56141 with weight 3038483 (avg 54.12/col) Sun Jan 13 14:11:08 2008 filtering completed in 4 passes Sun Jan 13 14:11:09 2008 matrix is 51087 x 51151 with weight 2800152 (avg 54.74/col) Sun Jan 13 14:11:11 2008 saving the first 48 matrix rows for later Sun Jan 13 14:11:12 2008 matrix is 51039 x 51151 with weight 2114035 (avg 41.33/col) Sun Jan 13 14:11:12 2008 matrix includes 64 packed rows Sun Jan 13 14:11:12 2008 using block size 10922 for processor cache size 256 kB Sun Jan 13 14:11:14 2008 commencing Lanczos iteration Sun Jan 13 14:13:38 2008 lanczos halted after 809 iterations (dim = 51034) Sun Jan 13 14:13:39 2008 recovered 15 nontrivial dependencies Sun Jan 13 14:14:05 2008 prp32 factor: 29004454390043890346738171836159 Sun Jan 13 14:14:05 2008 prp55 factor: 3343949795648324158059774855467139266458728235931156713 Sun Jan 13 14:14:05 2008 elapsed time 05:49:02
8·10¹⁴⁷-9 = 7(9)₁₄₆1_<148> = 71569 · 15914071 · 77519441 · 211293311 · 3128994342837361_<16> · C105
C105 = P45 · P60
P45 = 757574316234139695166249827153995203794288161_<45>
P60 = 180907822053975968030490364262581021587417735195779858011279_<60>

Number: 79991_147 N=137051119593948261370044705690083652684958246482044222007487026886745761271810395403932044275256914167919 ( 105 digits) SNFS difficulty: 147 digits. Divisors found: r1=757574316234139695166249827153995203794288161 (pp45) r2=180907822053975968030490364262581021587417735195779858011279 (pp60) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.13 hours. Scaled time: 42.15 units (timescale=1.995). Factorization parameters were as follows: name: 79991_147 n: 137051119593948261370044705690083652684958246482044222007487026886745761271810395403932044275256914167919 m: 200000000000000000000000000000 c5: 25 c0: -9 skew: 0.82 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3050001) Primes: RFBsize:114155, AFBsize:114087, largePrimes:2932834 encountered Relations: rels:2973016, finalFF:311516 Max relations in full relation-set: 28 Initial matrix: 228306 x 311516 with sparse part having weight 33697415. Pruned matrix : 204714 x 205919 with weight 20792624. Total sieving time: 20.36 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.57 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 21.13 hours. --------- CPU info (if available) ----------
Jan 13, 2008: By Jo Yeong Uk / GGNFS
8·10¹³⁶-9 = 7(9)₁₃₅1_<137> = 17 · 4337 · 31319 · 22064536663081199635553_<23> · C106
C106 = P45 · P61
P45 = 414874359200499062591640749476962066365515367_<45>
P61 = 3784707754227857968375340111961975566863294728841184192955991_<61>

Number: 79991_136 N=1570178204296442471478760889548334038176734874175207254303092147557263103549956249477642039440313865213697 ( 106 digits) SNFS difficulty: 137 digits. Divisors found: r1=414874359200499062591640749476962066365515367 (pp45) r2=3784707754227857968375340111961975566863294728841184192955991 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.02 hours. Scaled time: 6.42 units (timescale=2.126). Factorization parameters were as follows: n: 1570178204296442471478760889548334038176734874175207254303092147557263103549956249477642039440313865213697 m: 2000000000000000000000000000 c5: 5 c0: -18 skew: 1.29 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1250001) Primes: RFBsize:107126, AFBsize:106673, largePrimes:2293144 encountered Relations: rels:2442022, finalFF:309970 Max relations in full relation-set: 28 Initial matrix: 213865 x 309970 with sparse part having weight 23128338. Pruned matrix : 176160 x 177293 with weight 10368683. Total sieving time: 2.88 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.02 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹⁴⁰-9 = 7(9)₁₃₉1_<141> = 7 · 2445390769_<10> · 37242387217387908233_<20> · C112
C112 = P33 · P79
P33 = 388536296915994985391902206726511_<33>
P79 = 3229792119842628898676018383831983166364802105671842667810158223564146032892279_<79>

Number: 79991_140 N=1254891470052116520828269206319513146161103905631639479267954114925778079057809127052812483177258998970076508569 ( 112 digits) SNFS difficulty: 141 digits. Divisors found: r1=388536296915994985391902206726511 (pp33) r2=3229792119842628898676018383831983166364802105671842667810158223564146032892279 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.41 hours. Scaled time: 11.62 units (timescale=2.148). Factorization parameters were as follows: n: 1254891470052116520828269206319513146161103905631639479267954114925778079057809127052812483177258998970076508569 m: 20000000000000000000000000000 c5: 1 c0: -36 skew: 2.05 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1100001) Primes: RFBsize:114155, AFBsize:114197, largePrimes:3313249 encountered Relations: rels:3414814, finalFF:399605 Max relations in full relation-set: 28 Initial matrix: 228416 x 399605 with sparse part having weight 33303166. Pruned matrix : 167030 x 168236 with weight 12188509. Total sieving time: 5.25 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 5.41 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹⁶¹-9 = 7(9)₁₆₀1_<162> = 29 · 199 · 571 · 1692365724601_<13> · C144
C144 = P33 · P111
P33 = 428383815004193749871857607077279_<33>
P111 = 334869450332200636093078292799339933789697545275221769023019937305594987180395275406031737563279818152065360169_<111>
8·10¹⁵⁸-9 = 7(9)₁₅₇1_<159> = 7 · 4323841 · 4714903 · 462997341128773543_<18> · C128
C128 = P33 · C95
P33 = 410562561244534563981430142949031_<33>
C95 = [29491144580163096639800559468991908217808992070869327114070748537704128510842764288695820636807_<95>]
8·10¹⁵⁰-9 = 7(9)₁₄₉1_<151> = 193 · 247601 · 3624571477934606884159_<22> · C122
C122 = P53 · P69
P53 = 96315157891755373030439425392135709447474977307786081_<53>
P69 = 479544565961051555887991852543525630193846540227492360552478340319353_<69>

Number: 79991_150 N=46187410586671979793763904423352571432961215465785614036273142323402790039945056505520163118222449815563959534158948325593 ( 122 digits) SNFS difficulty: 151 digits. Divisors found: r1=96315157891755373030439425392135709447474977307786081 (pp53) r2=479544565961051555887991852543525630193846540227492360552478340319353 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.20 hours. Scaled time: 24.03 units (timescale=2.146). Factorization parameters were as follows: n: 46187410586671979793763904423352571432961215465785614036273142323402790039945056505520163118222449815563959534158948325593 m: 2000000000000000000000000000000 c5: 1 c0: -36 skew: 2.05 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, 1900001) Primes: RFBsize:176302, AFBsize:176388, largePrimes:5294283 encountered Relations: rels:5193470, finalFF:481776 Max relations in full relation-set: 28 Initial matrix: 352754 x 481776 with sparse part having weight 38435562. Pruned matrix : 281271 x 283098 with weight 21037307. Total sieving time: 10.76 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.34 hours. Time per square root: 0.03 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: 11.20 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
Jan 12, 2008 (8th): By Sinkiti Sibata / GGNFS, Msieve
8·10¹¹⁵-9 = 7(9)₁₁₄1_<116> = 31 · C115
C115 = P34 · P39 · P43
P34 = 1952641829846445891880391633628571_<34>
P39 = 183792537662905341244235989253778248189_<39>
P43 = 7190810275475399982758739592384651846401319_<43>

Number: 79991_115 N=2580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161 ( 115 digits) SNFS difficulty: 115 digits. Divisors found: r1=1952641829846445891880391633628571 (pp34) r2=183792537662905341244235989253778248189 (pp39) r3=7190810275475399982758739592384651846401319 (pp43) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.28 hours. Scaled time: 2.57 units (timescale=2.003). Factorization parameters were as follows: name: 79991_115 n: 2580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161290322580645161 m: 100000000000000000000000 c5: 8 c0: -9 skew: 1.02 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 450001) Primes: RFBsize:49098, AFBsize:64008, largePrimes:2120520 encountered Relations: rels:2265866, finalFF:291540 Max relations in full relation-set: 28 Initial matrix: 113171 x 291540 with sparse part having weight 22877031. Pruned matrix : 73769 x 74398 with weight 3980313. Total sieving time: 1.19 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.03 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.28 hours. --------- CPU info (if available) ----------
8·10¹¹³-9 = 7(9)₁₁₂1_<114> = 60281424871_<11> · C104
C104 = P48 · P56
P48 = 390808792124933992905008532836460473489137122991_<48>
P56 = 33958003771356934218524016876132944905551552683170456031_<56>

Number: 79991_113 N=13271086436857956665003795278321466204613927762908668489758134204339053238368831986794926070452804708721 ( 104 digits) SNFS difficulty: 113 digits. Divisors found: r1=390808792124933992905008532836460473489137122991 (pp48) r2=33958003771356934218524016876132944905551552683170456031 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.88 hours. Scaled time: 1.27 units (timescale=0.675). Factorization parameters were as follows: name:79991_113 n: 13271086436857956665003795278321466204613927762908668489758134204339053238368831986794926070452804708721 m: 20000000000000000000000 c5: 250 c0: -9 skew: 0.51 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:63828, largePrimes:2133195 encountered Relations: rels:2279375, finalFF:293525 Max relations in full relation-set: 28 Initial matrix: 112993 x 293525 with sparse part having weight 23279201. Pruned matrix : 72949 x 73577 with weight 4016180. Total sieving time: 1.70 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.88 hours. --------- CPU info (if available) ----------
8·10¹²¹-9 = 7(9)₁₂₀1_<122> = 19 · 16931 · C117
C117 = P53 · P64
P53 = 66190937999157259563309327452865130078561271454954931_<53>
P64 = 3757121508638448333172650338258137145904700516674921367147594549_<64>

Number: 79991_121 N=248687396833587719816344357438395468915629692031744946205807472434556357227011181607080130187852242383171323856271119 ( 117 digits) SNFS difficulty: 122 digits. Divisors found: r1=66190937999157259563309327452865130078561271454954931 (pp53) r2=3757121508638448333172650338258137145904700516674921367147594549 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.07 hours. Scaled time: 4.17 units (timescale=2.010). Factorization parameters were as follows: name: 79991_121 n: 248687396833587719816344357438395468915629692031744946205807472434556357227011181607080130187852242383171323856271119 m: 2000000000000000000000000 c5: 5 c0: -18 skew: 1.29 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63758, largePrimes:1984467 encountered Relations: rels:1952225, finalFF:141050 Max relations in full relation-set: 28 Initial matrix: 112922 x 141050 with sparse part having weight 10926246. Pruned matrix : 102413 x 103041 with weight 6162277. Total sieving time: 1.93 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.07 hours. --------- CPU info (if available) ----------
Jan 12, 2008 (7th): By Robert Backstrom / GMP-ECM
8·10¹⁰⁸-9 = 7(9)₁₀₇1_<109> = 11897 · 6595030913_<10> · 74285794073_<11> · C85
C85 = P32 · P54
P32 = 10784808302586663079660355798191_<32>
P54 = 127267493166302734542256662357223329760676931011149417_<54>
Jan 12, 2008 (6th): By Jo Yeong Uk / GMP-ECM, Msieve, GGNFS
8·10¹⁹¹-9 = 7(9)₁₉₀1_<192> = C192
C192 = P34 · C159
P34 = 2838215384488977187840273748749501_<34>
C159 = [281867262214153842659280716998882524780880662933308691584296839537167821919759679358142157019600539866645046737600020701546566244595946561032467565638861495491_<159>]
8·10¹²⁶-9 = 7(9)₁₂₅1_<127> = 23 · C126
C126 = P39 · P88
P39 = 217581248286592871920703441696601910487_<39>
P88 = 1598603233024812172766526043763336942138049668499189186436388071437141249364595430510791_<88>

Number: 79991_126 N=347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217 ( 126 digits) SNFS difficulty: 127 digits. Divisors found: r1=217581248286592871920703441696601910487 (pp39) r2=1598603233024812172766526043763336942138049668499189186436388071437141249364595430510791 (pp88) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.48 hours. Scaled time: 3.18 units (timescale=2.151). Factorization parameters were as follows: n: 347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217 m: 20000000000000000000000000 c5: 5 c0: -18 skew: 1.29 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [400000, 720001) Primes: RFBsize:63951, AFBsize:63758, largePrimes:1391980 encountered Relations: rels:1386131, finalFF:169407 Max relations in full relation-set: 28 Initial matrix: 127775 x 169407 with sparse part having weight 8164693. Pruned matrix : 109759 x 110461 with weight 4063548. Total sieving time: 1.42 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000 total time: 1.48 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406451) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405121)
8·10¹³⁷-9 = 7(9)₁₃₆1_<138> = 281 · 45259 · 6783449 · 146011951 · C116
C116 = P31 · P34 · P52
P31 = 9029523373784041010808525557981_<31>
P34 = 1221423363891302373996983840134301_<34>
P52 = 5758491037866755216905701730446521364185825908289891_<52>

Sat Jan 12 21:44:58 2008 Sat Jan 12 21:44:58 2008 Sat Jan 12 21:44:58 2008 Msieve v. 1.28 Sat Jan 12 21:44:58 2008 random seeds: 5b6f6980 09f90c48 Sat Jan 12 21:44:58 2008 factoring 7033555494409129235621750952426445415239612600830862521555814673561206967670680651191 (85 digits) Sat Jan 12 21:44:58 2008 commencing quadratic sieve (85-digit input) Sat Jan 12 21:44:58 2008 using multiplier of 7 Sat Jan 12 21:44:58 2008 using 32kb Intel Core sieve core Sat Jan 12 21:44:58 2008 sieve interval: 12 blocks of size 32768 Sat Jan 12 21:44:58 2008 processing polynomials in batches of 17 Sat Jan 12 21:44:58 2008 using a sieve bound of 1434241 (54480 primes) Sat Jan 12 21:44:58 2008 using large prime bound of 116173521 (26 bits) Sat Jan 12 21:44:58 2008 using double large prime bound of 328997602795950 (41-49 bits) Sat Jan 12 21:44:58 2008 using trial factoring cutoff of 49 bits Sat Jan 12 21:44:58 2008 polynomial 'A' values have 11 factors Sat Jan 12 22:09:30 2008 54635 relations (15866 full + 38769 combined from 573370 partial), need 54576 Sat Jan 12 22:09:30 2008 begin with 589236 relations Sat Jan 12 22:09:31 2008 reduce to 128767 relations in 9 passes Sat Jan 12 22:09:31 2008 attempting to read 128767 relations Sat Jan 12 22:09:32 2008 recovered 128767 relations Sat Jan 12 22:09:32 2008 recovered 108972 polynomials Sat Jan 12 22:09:32 2008 attempting to build 54635 cycles Sat Jan 12 22:09:32 2008 found 54635 cycles in 5 passes Sat Jan 12 22:09:32 2008 distribution of cycle lengths: Sat Jan 12 22:09:32 2008 length 1 : 15866 Sat Jan 12 22:09:32 2008 length 2 : 11089 Sat Jan 12 22:09:32 2008 length 3 : 9652 Sat Jan 12 22:09:32 2008 length 4 : 6995 Sat Jan 12 22:09:32 2008 length 5 : 4741 Sat Jan 12 22:09:32 2008 length 6 : 2779 Sat Jan 12 22:09:32 2008 length 7 : 1683 Sat Jan 12 22:09:32 2008 length 9+: 1830 Sat Jan 12 22:09:32 2008 largest cycle: 17 relations Sat Jan 12 22:09:32 2008 matrix is 54480 x 54635 with weight 2902839 (avg 53.13/col) Sat Jan 12 22:09:32 2008 filtering completed in 3 passes Sat Jan 12 22:09:32 2008 matrix is 49839 x 49903 with weight 2674857 (avg 53.60/col) Sat Jan 12 22:09:33 2008 saving the first 48 matrix rows for later Sat Jan 12 22:09:33 2008 matrix is 49791 x 49903 with weight 2017488 (avg 40.43/col) Sat Jan 12 22:09:33 2008 matrix includes 64 packed rows Sat Jan 12 22:09:33 2008 commencing Lanczos iteration Sat Jan 12 22:10:15 2008 lanczos halted after 789 iterations Sat Jan 12 22:10:15 2008 recovered 15 nontrivial dependencies Sat Jan 12 22:10:16 2008 prp34 factor: 1221423363891302373996983840134301 Sat Jan 12 22:10:16 2008 prp52 factor: 5758491037866755216905701730446521364185825908289891 Sat Jan 12 22:10:16 2008 elapsed time 00:25:18
8·10¹⁴⁶-9 = 7(9)₁₄₅1_<147> = 7² · 74209 · 233102762089_<12> · 458430639997432973730641_<24> · C106
C106 = P34 · P72
P34 = 2237064275354436560413927703682193_<34>
P72 = 920317772467855578861737276438457302528107277025704935144084694913195343_<72>
Jan 12, 2008 (5th): By matsui / GMP-ECM
5·10²⁰⁰-9 = 4(9)₁₉₉1_<201> = 79 · C199
C199 = P34 · C166
P34 = 4565579173849692757873296750073841_<34>
C166 = [1386267477366716881025736493978991704108086368524410882780963548849099077745191410286959757712217661501763612288987394960172120415770934106869087379738850488433099369_<166>]
Jan 12, 2008 (4th): By Sinkiti Sibata / GGNFS
(46·10¹⁸⁶-1)/9 = 5(1)₁₈₆_<187> = 73 · C185
C185 = P40 · P43 · P43 · P61
P40 = 2825392120613905556303145902353338583991_<40>
P43 = 1414261240340299364785702351487807687732347_<43>
P43 = 1940352243663463704570905682634709845035983_<43>
P61 = 9030327814966384090537560378864803219811293177354264381962277_<61>

Number: 51111_186 N=70015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207 ( 185 digits) SNFS difficulty: 187 digits. Divisors found: r1=2825392120613905556303145902353338583991 (pp40) r2=1414261240340299364785702351487807687732347 (pp43) r3=1940352243663463704570905682634709845035983 (pp43) r4=9030327814966384090537560378864803219811293177354264381962277 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 826.01 hours. Scaled time: 1644.60 units (timescale=1.991). Factorization parameters were as follows: name: 51111_186 n: 70015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207001522070015220700152207 m: 10000000000000000000000000000000000000 c5: 460 c0: -1 skew: 0.29 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 13200001) Primes: RFBsize:501962, AFBsize:501266, largePrimes:6770607 encountered Relations: rels:7281007, finalFF:1163691 Max relations in full relation-set: 28 Initial matrix: 1003295 x 1163691 with sparse part having weight 97320435. Pruned matrix : 873987 x 879067 with weight 77783757. Total sieving time: 811.78 hours. Total relation processing time: 0.72 hours. Matrix solve time: 13.15 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 826.01 hours. --------- CPU info (if available) ----------
Jan 12, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(67·10¹⁶⁶+23)/9 = 7(4)₁₆₅7_<167> = 83 · 199 · C163
C163 = P81 · P83
P81 = 367004643653966872365696265950784599299328674117914006464687180669547532610783737_<81>
P83 = 12280882187472171359124427810998046557688853247533252193235475312651380187494652843_<83>

Number: n N=4507140790969573436123051670669276772079944568895346881664009471722736843521489643666794481107007594868586574102103556604979381512650266055848183353178206965214291 ( 163 digits) SNFS difficulty: 167 digits. Divisors found: Sat Jan 12 06:34:13 2008 prp81 factor: 367004643653966872365696265950784599299328674117914006464687180669547532610783737 Sat Jan 12 06:34:13 2008 prp83 factor: 12280882187472171359124427810998046557688853247533252193235475312651380187494652843 Sat Jan 12 06:34:13 2008 elapsed time 01:13:19 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 60.51 hours. Scaled time: 110.67 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_4_165_7 n: 4507140790969573436123051670669276772079944568895346881664009471722736843521489643666794481107007594868586574102103556604979381512650266055848183353178206965214291 skew: 0.51 deg: 5 c5: 670 c0: 23 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4100000) Primes: RFBsize:250150, AFBsize:249316, largePrimes:7893359 encountered Relations: rels:7379758, finalFF:577015 Max relations in full relation-set: 28 Initial matrix: 499533 x 577015 with sparse part having weight 63713644. Pruned matrix : 468271 x 470832 with weight 45026970. Total sieving time: 60.30 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 60.51 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
4·10¹⁶⁴+7 = 4(0)₁₆₃7_<165> = 11 · 37 · 43 · 6449 · 238291 · 18515813 · C144
C144 = P69 · P76
P69 = 196948146026549213753598998945340356169909690257113074987708892318543_<69>
P76 = 4078518408615435716369982093154238241123860446542160172985649100147392724947_<76>

Number: n N=803256639111961948349569451134375723264862953628626206118805410285163427541196501369025854991877728369841645329293165617105583432513049506792221 ( 144 digits) SNFS difficulty: 165 digits. Divisors found: Sat Jan 12 07:34:52 2008 prp69 factor: 196948146026549213753598998945340356169909690257113074987708892318543 Sat Jan 12 07:34:52 2008 prp76 factor: 4078518408615435716369982093154238241123860446542160172985649100147392724947 Sat Jan 12 07:34:52 2008 elapsed time 01:31:42 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.02 hours. Scaled time: 68.52 units (timescale=1.756). Factorization parameters were as follows: name: KA_4_0_163_7 n: 803256639111961948349569451134375723264862953628626206118805410285163427541196501369025854991877728369841645329293165617105583432513049506792221 type: snfs skew: 1.77 deg: 5 c5: 2 c0: 35 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1900000) Primes: RFBsize:230209, AFBsize:229267, largePrimes:7099618 encountered Relations: rels:6578698, finalFF:504591 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 38.81 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 39.02 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 12, 2008 (2nd): By Sinkiti Sibata / PFGW
7·10¹³¹⁴⁵+9 = 7(0)₁₃₁₄₄9_<13146> is PRP.
7·10¹⁶⁶⁴⁶+9 = 7(0)₁₆₆₄₅9_<16647> is PRP.
7·10²⁰⁸⁹¹+9 = 7(0)₂₀₈₉₀9_<20892> is PRP.
Jan 12, 2008: The factor table of 799...991 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jan 11, 2008: By Robert Backstrom / GGNFS, Msieve
(5·10¹⁶³-17)/3 = 1(6)₁₆₂1_<164> = 11 · 47 · 579620986471812630953_<21> · C140
C140 = P59 · P82
P59 = 33002739048257539876683509719350404697818409337940816248091_<59>
P82 = 1685249160148384416019014327429980236270130559391192098286783927630082498099632571_<82>

Number: n N=55617838263672310701551004098935263046156702544564899044762593157589752112781293997694541379125158139575071938101345124582616379953880171961 ( 140 digits) SNFS difficulty: 164 digits. Divisors found: Fri Jan 11 08:30:33 2008 prp59 factor: 33002739048257539876683509719350404697818409337940816248091 Fri Jan 11 08:30:33 2008 prp82 factor: 1685249160148384416019014327429980236270130559391192098286783927630082498099632571 Fri Jan 11 08:30:33 2008 elapsed time 00:50:42 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-k8 Total time: 38.98 hours. Scaled time: 32.67 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_6_162_1 n: 55617838263672310701551004098935263046156702544564899044762593157589752112781293997694541379125158139575071938101345124582616379953880171961 type: snfs deg: 5 c5: 8 c0: -85 skew: 1.60 m: 500000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 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, 3600001) Primes: RFBsize:216816, AFBsize:216871, largePrimes:5732678 encountered Relations: rels:5698376, finalFF:511733 Max relations in full relation-set: 28 Initial matrix: 433752 x 511733 with sparse part having weight 49865175. Pruned matrix : 401349 x 403581 with weight 36480624. Total sieving time: 36.68 hours. Total relation processing time: 0.11 hours. Matrix solve time: 2.19 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 38.98 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
(14·10¹⁶¹-41)/9 = 1(5)₁₆₀1_<162> = 11 · 79 · 2411 · 2528269 · 298614421769978987_<18> · C131
C131 = P49 · P83
P49 = 1237731289012386762849485097499340001383842403737_<49>
P83 = 79452599632851028607355803437954089119988633926215410442037070045079459127725856399_<83>

Number: n N=98340968558953790892585585889392535669496255284578280374020149122636303507627134972206826846954930393394612505752654421559042963063 ( 131 digits) SNFS difficulty: 162 digits. Divisors found: Fri Jan 11 22:44:54 2008 prp49 factor: 1237731289012386762849485097499340001383842403737 Fri Jan 11 22:44:54 2008 prp83 factor: 79452599632851028607355803437954089119988633926215410442037070045079459127725856399 Fri Jan 11 22:44:54 2008 elapsed time 00:58:45 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 40.38 hours. Scaled time: 33.84 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_5_160_1 n: 98340968558953790892585585889392535669496255284578280374020149122636303507627134972206826846954930393394612505752654421559042963063 type: snfs deg: 5 c5: 140 c0: -41 skew: 0.78 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3900001) Primes: RFBsize:216816, AFBsize:216922, largePrimes:5786060 encountered Relations: rels:5738816, finalFF:470992 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 40.25 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 40.38 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 10, 2008 (4th): By matsui / GMP-ECM
(55·10¹⁸³-1)/9 = 6(1)₁₈₃_<184> = 3³ · 7 · 29 · C181
C181 = P31 · C150
P31 = 1814486819606228803034309724019_<31>
C150 = [614478313503825526186774142080138780423238442508754732017910702305971084132729055650327224394349460485381313575366771621956040706591459972940854945749_<150>]
Jan 10, 2008 (3rd): By Jo Yeong Uk / GGNFS
(86·10¹⁷¹+31)/9 = 9(5)₁₇₀9_<172> = 11 · 17 · 1381 · 10267 · 37781 · 215134273 · 6394987531_<10> · 148336234710094457893_<21> · C120
C120 = P43 · P78
P43 = 1096966381258354525082396230206423839135069_<43>
P78 = 426102195310162589018569755129159308229685168412082711285523685052681229610341_<78>

Number: 95559_171 N=467419783235629658103214304014991608228915825261793443002931643083874160506685464483702892779307242690217664321338148529 ( 120 digits) Divisors found: r1=1096966381258354525082396230206423839135069 (pp43) r2=426102195310162589018569755129159308229685168412082711285523685052681229610341 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 48.00 hours. Scaled time: 103.06 units (timescale=2.147). Factorization parameters were as follows: name: 95559_171 n: 467419783235629658103214304014991608228915825261793443002931643083874160506685464483702892779307242690217664321338148529 skew: 34824.01 # norm 1.82e+16 c5: 30660 c4: -7605601439 c3: -528135056994814 c2: 12643616123032503853 c1: -80969674776601688470101 c0: 4409842209862057154181171 # alpha -4.95 Y1: 1049506019249 Y0: -108799574192722567741550 # Murphy_E 2.79e-10 # M 391493396307864520630205026286345938563037358745772478822904461270085767891754310654812573400414010370216518282741011494 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4800001) Primes: RFBsize:315948, AFBsize:316768, largePrimes:7779738 encountered Relations: rels:7883829, finalFF:717826 Max relations in full relation-set: 28 Initial matrix: 632799 x 717826 with sparse part having weight 68095105. Pruned matrix : 566163 x 569390 with weight 50169037. Total sieving time: 45.46 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.17 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 48.00 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Jan 10, 2008 (2nd): By Yousuke Koide
(10¹⁰¹⁹-1)/9 is divisible by 19546240918513258853789109982103832107_<38>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jan 10, 2008: By Kurt Beschorner / Jan 3, 2008
10⁵⁰⁶+1 is divisible by 69691163546816853278309618463969524441_<38>
Reference: Factorizations of numbers of the form 10ⁿ+1 (Alfred Reich)
Jan 9, 2008 (2nd): By Sinkiti Sibata / GGNFS
7·10¹⁶¹+9 = 7(0)₁₆₀9_<162> = 15371116800042997500203_<23> · 57118997757210264206905876447_<29> · C111
C111 = P54 · P58
P54 = 139490464604623382674750512013106688318266001541875221_<54>
P58 = 5715674892138940064628738708170977544099888345108701283569_<58>

Number: 70009_161 N=797282146233441389637438465879864974174079631931857291117873335595617292138291581776356920378174414625935543749 ( 111 digits) SNFS difficulty: 161 digits. Divisors found: r1=139490464604623382674750512013106688318266001541875221 (pp54) r2=5715674892138940064628738708170977544099888345108701283569 (pp58) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 89.61 hours. Scaled time: 60.58 units (timescale=0.676). Factorization parameters were as follows: name: 70009_161 n: 797282146233441389637438465879864974174079631931857291117873335595617292138291581776356920378174414625935543749 m: 100000000000000000000000000000000 c5: 70 c0: 9 skew: 0.66 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4350001) Primes: RFBsize:315948, AFBsize:316621, largePrimes:5728840 encountered Relations: rels:5815604, finalFF:721506 Max relations in full relation-set: 28 Initial matrix: 632637 x 721506 with sparse part having weight 43287861. Pruned matrix : 561950 x 565177 with weight 30874466. Total sieving time: 75.81 hours. Total relation processing time: 0.37 hours. Matrix solve time: 13.19 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 89.61 hours. --------- CPU info (if available) ----------
Jan 9, 2008: By Robert Backstrom / GGNFS, Msieve
4·10¹⁶³+9 = 4(0)₁₆₂9_<164> = 7 · 1303 · 257837 · 959561 · 5915543 · C142
C142 = P66 · P76
P66 = 878200471969328827561876462072079282958405245015115821377184281733_<66>
P76 = 3412018883530127490227807989559980166714774210829016758904628027464337410663_<76>

Number: n N=2996436593884420368599350071793146725644507391872863126806932222472234937356674817826792539332714575692570318811933890006862102836684710318979 ( 142 digits) SNFS difficulty: 165 digits. Divisors found: Wed Jan 09 05:18:19 2008 prp66 factor: 878200471969328827561876462072079282958405245015115821377184281733 Wed Jan 09 05:18:19 2008 prp76 factor: 3412018883530127490227807989559980166714774210829016758904628027464337410663 Wed Jan 09 05:18:19 2008 elapsed time 01:27:31 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 52.44 hours. Scaled time: 68.75 units (timescale=1.311). Factorization parameters were as follows: name: KA_4_0_162_9 n: 2996436593884420368599350071793146725644507391872863126806932222472234937356674817826792539332714575692570318811933890006862102836684710318979 skew: 2.95 deg: 5 c5: 1 c0: 225 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500213) Primes: RFBsize:230209, AFBsize:229862, largePrimes:7327517 encountered Relations: rels:6805231, finalFF:503679 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 52.15 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 52.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
5·10¹⁶⁴+3 = 5(0)₁₆₃3_<165> = 557 · 217837300066202477_<18> · C145
C145 = P64 · P82
P64 = 1196687247426772242533735797290481529635161715296376005028120547_<64>
P82 = 3443514377361480174374528664126918435300112338137700545497427175846407441531435641_<82>

Number: n N=4120809741719225186741054484135263928241671284276174640242932170788013428862000974905621445274870595945310435532020747550508457434928692920215627 ( 145 digits) SNFS difficulty: 165 digits. Divisors found: Wed Jan 9 16:25:56 2008 prp64 factor: 1196687247426772242533735797290481529635161715296376005028120547 Wed Jan 9 16:25:56 2008 prp82 factor: 3443514377361480174374528664126918435300112338137700545497427175846407441531435641 Wed Jan 9 16:25:56 2008 elapsed time 00:57:08 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 38.58 hours. Scaled time: 32.37 units (timescale=0.839). Factorization parameters were as follows: name: KA_5_0_163_3 n: 4120809741719225186741054484135263928241671284276174640242932170788013428862000974905621445274870595945310435532020747550508457434928692920215627 type: snfs deg: 5 c5: 1 c0: 6 skew: 1.43 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3800001) Primes: RFBsize:216816, AFBsize:216821, largePrimes:5658666 encountered Relations: rels:5541692, finalFF:429370 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 38.47 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 38.58 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
(73·10¹⁶⁴-1)/9 = 8(1)₁₆₄_<165> = 61 · 373 · 3620158294151899_<16> · C145
C145 = P67 · P79
P67 = 1043995987473037595727834603195896693955428946648402327832492964027_<67>
P79 = 9432249792339282259291436913130955217924127892296499942188495834211334121986719_<79>

Number: n N=9847230936045602785233094889585613069848563625548151842425600774026787507620946164685576203283969203986063171766643656802199995825880290238757413 ( 145 digits) SNFS difficulty: 166 digits. Divisors found: Wed Jan 09 19:08:01 2008 prp67 factor: 1043995987473037595727834603195896693955428946648402327832492964027 Wed Jan 09 19:08:01 2008 prp79 factor: 9432249792339282259291436913130955217924127892296499942188495834211334121986719 Wed Jan 09 19:08:01 2008 elapsed time 01:57:05 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 74.89 hours. Scaled time: 131.21 units (timescale=1.752). Factorization parameters were as follows: name: KA_8_1_164 n: 9847230936045602785233094889585613069848563625548151842425600774026787507620946164685576203283969203986063171766643656802199995825880290238757413 type: snfs skew: 0.67 deg: 5 c5: 73 c0: -10 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3500269) Primes: RFBsize:230209, AFBsize:230027, largePrimes:7684684 encountered Relations: rels:7147678, finalFF:483126 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 74.61 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 74.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 8, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(52·10¹⁶¹-7)/9 = 5(7)₁₆₁_<162> = 67 · 211 · 399657043 · 41884981582841233_<17> · C133
C133 = P57 · P76
P57 = 303583120466432755281692462570253330795169293513976483517_<57>
P76 = 8042297897793284514496513202115956001841463193178478887769004032896132968527_<76>

Number: n N=2441505891532717595222421523167960460997180306913825571010358957513150181867983231904207917169754437950011734144951653882157895269459 ( 133 digits) SNFS difficulty: 162 digits. Divisors found: Tue Jan 8 23:59:06 2008 prp57 factor: 303583120466432755281692462570253330795169293513976483517 Tue Jan 8 23:59:06 2008 prp76 factor: 8042297897793284514496513202115956001841463193178478887769004032896132968527 Tue Jan 8 23:59:06 2008 elapsed time 00:57:39 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 43.17 hours. Scaled time: 36.18 units (timescale=0.838). Factorization parameters were as follows: name: KA_5_7_161 n: 2441505891532717595222421523167960460997180306913825571010358957513150181867983231904207917169754437950011734144951653882157895269459 type: snfs deg: 5 c5: 520 c0: -7 skew: 0.42 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 4000001) Primes: RFBsize:216816, AFBsize:217161, largePrimes:5742071 encountered Relations: rels:5648051, finalFF:422567 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 43.05 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 43.17 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 8, 2008 (2nd): By matsui / GMP-ECM
(4·10¹⁹²-7)/3 = 1(3)₁₉₁1_<193> = 53 · 113 · C189
C189 = P39 · C151
P39 = 208077415143242929300081213865119997527_<39>
C151 = [1069940136279591667980810496981378274903150054006469796842841376740519957678800554460072994496458619358697351060409992237703368110891340267099632894977_<151>]
Jan 8, 2008: By Robert Backstrom / GGNFS, Msieve
7·10¹⁶⁶+9 = 7(0)₁₆₅9_<167> = 21991 · 972833 · 1082531 · C151
C151 = P68 · P84
P68 = 21801158658206841112555253752829902500472040092585365034962893355053_<68>
P84 = 138642011235137555584320880412798358499970719485097366270743949931671229392787022521_<84>

Number: n N=3022556483630129261598847253569879921858042829617050352190156557137315012023902736896851269624585181616682870685916160325557846898137814787523960148613 ( 151 digits) SNFS difficulty: 166 digits. Divisors found: Tue Jan 08 02:23:48 2008 prp68 factor: 21801158658206841112555253752829902500472040092585365034962893355053 Tue Jan 08 02:23:48 2008 prp84 factor: 138642011235137555584320880412798358499970719485097366270743949931671229392787022521 Tue Jan 08 02:23:48 2008 elapsed time 01:22:44 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.47 hours. Scaled time: 88.50 units (timescale=1.826). Factorization parameters were as follows: name: KA_7_0_165_9 n: 3022556483630129261598847253569879921858042829617050352190156557137315012023902736896851269624585181616682870685916160325557846898137814787523960148613 skew: 0.66 deg: 5 c5: 70 c0: 9 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200001) Primes: RFBsize:250150, AFBsize:250721, largePrimes:7669339 encountered Relations: rels:7156943, finalFF:567239 Max relations in full relation-set: 28 Initial matrix: 500939 x 567239 with sparse part having weight 51971046. Pruned matrix : Total sieving time: 48.24 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 48.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(4·10¹⁶⁷-7)/3 = 1(3)₁₆₆1_<168> = 11 · 1453 · 65789 · 65585573 · C151
C151 = P41 · P110
P41 = 44513060255051568150273475384941022348961_<41>
P110 = 43434155511436613056459493128340863687385119966755835981223737071050592042248993684052667503664574707092147821_<110>

Number: n N=1933387181407858117653716396964261130297665698862132685796900976269788635641054996450601322919821997858497612243316173533210563965043659752396057763981 ( 151 digits) SNFS difficulty: 167 digits. Divisors found: r1=44513060255051568150273475384941022348961 (pp41) r2=43434155511436613056459493128340863687385119966755835981223737071050592042248993684052667503664574707092147821 (pp110) Version: GGNFS-0.77.1-20051202-athlon Total time: 44.09 hours. Scaled time: 80.15 units (timescale=1.818). Factorization parameters were as follows: name: KA_1_3_166_1 n: 1933387181407858117653716396964261130297665698862132685796900976269788635641054996450601322919821997858497612243316173533210563965043659752396057763981 skew: 0.89 deg: 5 c5: 25 c0: -14 m: 2000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2800001) Primes: RFBsize:250150, AFBsize:250081, largePrimes:7547303 encountered Relations: rels:7067753, finalFF:589532 Max relations in full relation-set: 48 Initial matrix: 500295 x 589532 with sparse part having weight 48687984. Pruned matrix : 435661 x 438226 with weight 31937138. Total sieving time: 42.02 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.71 hours. Total square root time: 0.17 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 44.09 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jan 7, 2008 (2nd): By Jo Yeong Uk / GGNFS
7·10¹⁶³+9 = 7(0)₁₆₂9_<164> = 10463 · 17394388742849265431_<20> · 21685605887741051661689_<23> · C119
C119 = P35 · P84
P35 = 18751242705828780547597219322844983_<35>
P84 = 945869076252608429463531219474556440073685963101828788499278956282259958157147275519_<84>

Number: 70009_163 N=17736220616750730441171459656279219097305026284234519209128657392107895275988306959156196633013809260456105154427871177 ( 119 digits) Divisors found: r1=18751242705828780547597219322844983 (pp35) r2=945869076252608429463531219474556440073685963101828788499278956282259958157147275519 (pp84) Version: GGNFS-0.77.1-20050930-nocona Total time: 38.06 hours. Scaled time: 81.90 units (timescale=2.152). Factorization parameters were as follows: name: 70009_163 n: 17736220616750730441171459656279219097305026284234519209128657392107895275988306959156196633013809260456105154427871177 skew: 221395.86 # norm 1.00e+16 c5: 900 c4: -368936484 c3: -64515235009570 c2: -6637800111968368825 c1: 1003631229460161110538300 c0: 64280742149364474007670220864 # alpha -5.48 Y1: 2264490571433 Y0: -114531360207998065534985 # Murphy_E 3.62e-10 # M 13078825261663832417425027932008595424256843732315959701340945098020013622714623701968577018374575816455494749105625740 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4125001) Primes: RFBsize:315948, AFBsize:315634, largePrimes:7634260 encountered Relations: rels:7677465, finalFF:728561 Max relations in full relation-set: 28 Initial matrix: 631658 x 728561 with sparse part having weight 60105103. Pruned matrix : 551454 x 554676 with weight 40275843. Polynomial selection time: 2.27 hours. Total sieving time: 33.75 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.72 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 38.06 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Jan 7, 2008: By Robert Backstrom / GGNFS, Msieve
7·10¹⁵⁹+9 = 7(0)₁₅₈9_<160> = 47 · 71 · 92371871 · 102843119 · C141
C141 = P64 · P77
P64 = 4231538071496958890327182029936342614194854003919814193922731887_<64>
P77 = 52182946885757635675346604057724856979445602984378050368353799424430749322239_<77>

Number: n N=220814126429987102417525345115212994015254781641465598720037588384391899194205728399759788601386125925513113788312586671462061961060563534993 ( 141 digits) SNFS difficulty: 160 digits. Divisors found: Mon Jan 7 10:52:24 2008 prp64 factor: 4231538071496958890327182029936342614194854003919814193922731887 Mon Jan 7 10:52:24 2008 prp77 factor: 52182946885757635675346604057724856979445602984378050368353799424430749322239 Mon Jan 7 10:52:24 2008 elapsed time 00:47:28 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 37.69 hours. Scaled time: 31.55 units (timescale=0.837). Factorization parameters were as follows: name: KA_7_0_158_9 n: 220814126429987102417525345115212994015254781641465598720037588384391899194205728399759788601386125925513113788312586671462061961060563534993 type: snfs deg: 5 c5: 7 c0: 90 skew: 1.66 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3600000) Primes: RFBsize:216816, AFBsize:217356, largePrimes:5850727 encountered Relations: rels:5857858, finalFF:519585 Max relations in full relation-set: 28 Initial matrix: 434238 x 519585 with sparse part having weight 53804158. Pruned matrix : 399638 x 401873 with weight 39322056. Total sieving time: 37.57 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 37.69 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 6, 2008 (5th): By Jo Yeong Uk / GGNFS
7·10¹⁵²+9 = 7(0)₁₅₁9_<153> = 1926832847437_<13> · 6720374834881_<13> · 63639889190749_<14> · C114
C114 = P44 · P71
P44 = 77865850690669784859431617592698851037196011_<44>
P71 = 10908977710449886619312815188508141739609220654946251183378377187561523_<71>

Number: 70009_152 N=849436829589735592329176864706011392830693305217572069249710802758273465640411056591506419610722308940760472684753 ( 114 digits) SNFS difficulty: 152 digits. Divisors found: r1=77865850690669784859431617592698851037196011 (pp44) r2=10908977710449886619312815188508141739609220654946251183378377187561523 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.38 hours. Scaled time: 37.41 units (timescale=2.153). Factorization parameters were as follows: n: 849436829589735592329176864706011392830693305217572069249710802758273465640411056591506419610722308940760472684753 m: 1000000000000000000000000000000 c5: 700 c0: 9 skew: 0.42 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, 2300001) Primes: RFBsize:176302, AFBsize:176233, largePrimes:5591809 encountered Relations: rels:5524453, finalFF:488152 Max relations in full relation-set: 28 Initial matrix: 352603 x 488152 with sparse part having weight 45172811. Pruned matrix : 301081 x 302908 with weight 25623922. Total sieving time: 16.80 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.45 hours. Time per square root: 0.04 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: 17.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Jan 6, 2008 (4th): By Sibata / GGNFS
7·10¹⁷⁸+9 = 7(0)₁₇₇9_<179> = 2521 · 956113 · 1743745060873_<13> · 425228655272117_<15> · 1456142266504809349962840467_<28> · C116
C116 = P47 · P70
P47 = 13724946734647014417463514389532708012499306431_<47>
P70 = 1959728831003640657417517089713455927810208846008120710768293127210569_<70>

Number: 70009_178 N=26897173819877028591110438652440673484340131396511460906841522339126291846561419391159526937917846026688166192869239 ( 116 digits) Divisors found: r1=13724946734647014417463514389532708012499306431 (pp47) r2=1959728831003640657417517089713455927810208846008120710768293127210569 (pp70) Version: GGNFS-0.77.1-20060513-k8 Total time: 46.23 hours. Scaled time: 92.32 units (timescale=1.997). Factorization parameters were as follows: name: 70009_178 n: 26897173819877028591110438652440673484340131396511460906841522339126291846561419391159526937917846026688166192869239 skew: 65128.70 # norm 2.59e+16 c5: 75240 c4: -13181039364 c3: -658562293775890 c2: 51710009653767333541 c1: 1420986165414594796991522 c0: -33687414893484683332845870465 # alpha -6.85 Y1: 2035177406489 Y0: -12901908954921655902182 # Murphy_E 4.88e-10 # M 8982289048165742481213259840673138009408130390316621262097418188889777156561626476495961720222603100592888454691430 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3510001) Primes: RFBsize:315948, AFBsize:315985, largePrimes:7448433 encountered Relations: rels:7438490, finalFF:727459 Max relations in full relation-set: 28 Initial matrix: 632017 x 727459 with sparse part having weight 54906751. Pruned matrix : 548769 x 551993 with weight 34635393. Total sieving time: 42.35 hours. Total relation processing time: 0.31 hours. Matrix solve time: 3.15 hours. Time per square root: 0.41 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 46.23 hours. --------- CPU info (if available) ----------
Jan 6, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
7·10¹⁴⁶+9 = 7(0)₁₄₅9_<147> = 1904249 · C141
C141 = P50 · P92
P50 = 29348460735839486849597048687491482266220440029873_<50>
P92 = 12525324190779213411439080213347337398023495842703998477149462377348409081784748884226366817_<92>

Number: n N=367598985216744238804904190575917330139073198935643395375289681128885980772472507534466343424625666076232677554248420243361031041633735924241 ( 141 digits) SNFS difficulty: 146 digits. Divisors found: r1=29348460735839486849597048687491482266220440029873 (pp50) r2=12525324190779213411439080213347337398023495842703998477149462377348409081784748884226366817 (pp92) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 11.17 hours. Scaled time: 14.57 units (timescale=1.305). Factorization parameters were as follows: name: KA_7_0_145_9 n: 367598985216744238804904190575917330139073198935643395375289681128885980772472507534466343424625666076232677554248420243361031041633735924241 skew: 0.66 deg: 5 c5: 70 c0: 9 m: 100000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:203362, AFBsize:203847, largePrimes:6878552 encountered Relations: rels:6404033, finalFF:539587 Max relations in full relation-set: 28 Initial matrix: 407277 x 539587 with sparse part having weight 31365500. Pruned matrix : 292139 x 294239 with weight 15013733. Total sieving time: 9.38 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.42 hours. Total square root time: 0.17 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 11.17 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁵⁷+9 = 7(0)₁₅₆9_<158> = 79 · 96857225721671_<14> · C142
C142 = P54 · P89
P54 = 643687030404506197051806584898109829074806677658713563_<54>
P89 = 14212293404416947433671925044120391584277610010545822637985641678790000790685720922856627_<89>

Number: n N=9148268936726694531651576219628786925034862262185737873387878910253280521430132640027051308022147551977228490456289749680469055617015909332001 ( 142 digits) SNFS difficulty: 157 digits. Divisors found: Sun Jan 06 15:50:12 2008 prp54 factor: 643687030404506197051806584898109829074806677658713563 Sun Jan 06 15:50:12 2008 prp89 factor: 14212293404416947433671925044120391584277610010545822637985641678790000790685720922856627 Sun Jan 06 15:50:12 2008 elapsed time 00:47:37 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.73 hours. Scaled time: 39.50 units (timescale=1.818). Factorization parameters were as follows: name: KA_7_0_156_9 n: 9148268936726694531651576219628786925034862262185737873387878910253280521430132640027051308022147551977228490456289749680469055617015909332001 skew: 0.42 deg: 5 c5: 700 c0: 9 m: 10000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1599990) Primes: RFBsize:203362, AFBsize:203497, largePrimes:7016855 encountered Relations: rels:6475989, finalFF:479308 Max relations in full relation-set: 28 Initial matrix: 406927 x 479308 with sparse part having weight 42290325. Pruned matrix : Total sieving time: 21.58 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 21.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(5·10¹⁶⁷-17)/3 = 1(6)₁₆₆1_<168> = 11 · 103 · 57165172409_<11> · C154
C154 = P55 · P100
P55 = 1432799642868764623313581007575666255213214630794733651_<55>
P100 = 1795981494721534844168356589654494543435236348703608448307880333492214100092285485025785978171053563_<100>

Number: n N=2573281644235925201154863504962616769184191842715562123978441074187952616988817531559698378059022788805862098468838043405885073260394546721714390639548513 ( 154 digits) SNFS difficulty: 167 digits. Divisors found: Sun Jan 6 18:26:05 2008 prp55 factor: 1432799642868764623313581007575666255213214630794733651 Sun Jan 6 18:26:05 2008 prp100 factor: 1795981494721534844168356589654494543435236348703608448307880333492214100092285485025785978171053563 Sun Jan 6 18:26:05 2008 elapsed time 01:17:38 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 54.16 hours. Scaled time: 45.44 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_6_166_1 n: 2573281644235925201154863504962616769184191842715562123978441074187952616988817531559698378059022788805862098468838043405885073260394546721714390639548513 type: snfs deg: 5 c5: 500 c0: -17 skew: 0.51 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 4700001) Primes: RFBsize:216816, AFBsize:215811, largePrimes:5752099 encountered Relations: rels:5651567, finalFF:380784 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 54.03 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 54.16 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
Jan 6, 2008 (2nd): By Maksym Voznyy / PRIMO
(61·10²¹¹⁶-7)/9 is prime.
(61·10²¹⁸⁰-7)/9 is prime.
(61·10¹⁷⁸⁷⁸-7)/9 is PRP.
(61·10²²⁰⁹³-7)/9 is PRP.
Jan 6, 2008: By Paul Zimmermann
(10³³³-1)/9 is divisible by 378910432397861194405369041242690342635541471617136043289_<57>, cofactor is prime.
Jan 5, 2008 (3rd): By Jo Yeong Uk / GGNFS
7·10¹⁴¹+9 = 7(0)₁₄₀9_<142> = 17627 · 98299 · C133
C133 = P39 · P95
P39 = 101414229444075792057935393801590219007_<39>
P95 = 39835625472292178795478811905988720116944029945084978719281689145836957513895091630614531075119_<95>

Number: 70009_141 N=4039899261695309109005048398359631685685486063939556024524503957895943660252833528639281309585610432411465854402366497268246378586833 ( 133 digits) SNFS difficulty: 141 digits. Divisors found: r1=101414229444075792057935393801590219007 (pp39) r2=39835625472292178795478811905988720116944029945084978719281689145836957513895091630614531075119 (pp95) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.92 hours. Scaled time: 14.86 units (timescale=2.146). Factorization parameters were as follows: n: 4039899261695309109005048398359631685685486063939556024524503957895943660252833528639281309585610432411465854402366497268246378586833 m: 10000000000000000000000000000 c5: 70 c0: 9 skew: 0.66 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1200001) Primes: RFBsize:114155, AFBsize:114417, largePrimes:3355192 encountered Relations: rels:3424431, finalFF:361194 Max relations in full relation-set: 28 Initial matrix: 228640 x 361194 with sparse part having weight 32688347. Pruned matrix : 183772 x 184979 with weight 14082163. Total sieving time: 6.73 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.12 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.92 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
7·10¹⁴²+9 = 7(0)₁₄₁9_<143> = 113 · 337 · 614934441575413662824970403_<27> · C112
C112 = P38 · P75
P38 = 19435116457349819947354128996919945157_<38>
P75 = 153806160331310217740660239181144108766898224889935222716697800849639765959_<75>

Number: 70009_142 N=2989240637896832248093598836643841444086092572084139927456736533426375053444720175992103186377912235052595510563 ( 112 digits) SNFS difficulty: 142 digits. Divisors found: r1=19435116457349819947354128996919945157 (pp38) r2=153806160331310217740660239181144108766898224889935222716697800849639765959 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.54 hours. Scaled time: 16.22 units (timescale=2.152). Factorization parameters were as follows: n: 2989240637896832248093598836643841444086092572084139927456736533426375053444720175992103186377912235052595510563 m: 10000000000000000000000000000 c5: 700 c0: 9 skew: 0.42 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1250001) Primes: RFBsize:114155, AFBsize:114082, largePrimes:3285538 encountered Relations: rels:3277670, finalFF:296280 Max relations in full relation-set: 28 Initial matrix: 228305 x 296280 with sparse part having weight 26224627. Pruned matrix : 203393 x 204598 with weight 14737735. Total sieving time: 7.32 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 7.54 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Jan 5, 2008 (2nd): By Sinkiti Sibata / Msieve, GGNFS
7·10¹⁴⁹+9 = 7(0)₁₄₈9_<150> = 17 · 131 · 449 · 619 · 859 · 907 · 3347 · 43481 · 3089727089_<10> · 1140505032437_<13> · 3687919471679_<13> · C93
C93 = P45 · P49
P45 = 239837507703455294015342234963512005413275037_<45>
P49 = 3200142279977988684517610934831971048558705274893_<49>

Fri Jan 4 14:41:22 2008 Msieve v. 1.30 Fri Jan 4 14:41:22 2008 random seeds: 89fffcd3 bf362a6f Fri Jan 4 14:41:22 2008 factoring 767514148726373849421756982578139971558958367374633360077892901949480634454258309618499746041 (93 digits) Fri Jan 4 14:41:23 2008 commencing quadratic sieve (93-digit input) Fri Jan 4 14:41:23 2008 using multiplier of 1 Fri Jan 4 14:41:23 2008 using 64kb Pentium 4 sieve core Fri Jan 4 14:41:23 2008 sieve interval: 18 blocks of size 65536 Fri Jan 4 14:41:23 2008 processing polynomials in batches of 6 Fri Jan 4 14:41:23 2008 using a sieve bound of 1956883 (72780 primes) Fri Jan 4 14:41:23 2008 using large prime bound of 244610375 (27 bits) Fri Jan 4 14:41:23 2008 using double large prime bound of 1256766767596625 (42-51 bits) Fri Jan 4 14:41:23 2008 using trial factoring cutoff of 51 bits Fri Jan 4 14:41:23 2008 polynomial 'A' values have 12 factors Fri Jan 4 22:12:21 2008 73205 relations (18541 full + 54664 combined from 996755 partial), need 72876 Fri Jan 4 22:12:25 2008 begin with 1015296 relations Fri Jan 4 22:12:27 2008 reduce to 187278 relations in 10 passes Fri Jan 4 22:12:27 2008 attempting to read 187278 relations Fri Jan 4 22:12:34 2008 recovered 187278 relations Fri Jan 4 22:12:34 2008 recovered 167179 polynomials Fri Jan 4 22:12:34 2008 attempting to build 73205 cycles Fri Jan 4 22:12:34 2008 found 73205 cycles in 6 passes Fri Jan 4 22:12:34 2008 distribution of cycle lengths: Fri Jan 4 22:12:34 2008 length 1 : 18541 Fri Jan 4 22:12:34 2008 length 2 : 13029 Fri Jan 4 22:12:34 2008 length 3 : 12466 Fri Jan 4 22:12:34 2008 length 4 : 9874 Fri Jan 4 22:12:34 2008 length 5 : 7323 Fri Jan 4 22:12:34 2008 length 6 : 5045 Fri Jan 4 22:12:34 2008 length 7 : 2957 Fri Jan 4 22:12:34 2008 length 9+: 3970 Fri Jan 4 22:12:34 2008 largest cycle: 21 relations Fri Jan 4 22:12:35 2008 matrix is 72780 x 73205 with weight 4304451 (avg 58.80/col) Fri Jan 4 22:12:37 2008 filtering completed in 4 passes Fri Jan 4 22:12:37 2008 matrix is 68783 x 68847 with weight 4056821 (avg 58.93/col) Fri Jan 4 22:12:37 2008 saving the first 48 matrix rows for later Fri Jan 4 22:12:37 2008 matrix is 68735 x 68847 with weight 3005294 (avg 43.65/col) Fri Jan 4 22:12:37 2008 matrix includes 64 packed rows Fri Jan 4 22:12:37 2008 using block size 21845 for processor cache size 512 kB Fri Jan 4 22:12:38 2008 commencing Lanczos iteration Fri Jan 4 22:13:22 2008 lanczos halted after 1088 iterations (dim = 68733) Fri Jan 4 22:13:22 2008 recovered 15 nontrivial dependencies Fri Jan 4 22:13:23 2008 prp45 factor: 239837507703455294015342234963512005413275037 Fri Jan 4 22:13:23 2008 prp49 factor: 3200142279977988684517610934831971048558705274893 Fri Jan 4 22:13:23 2008 elapsed time 07:32:01
7·10¹¹⁹+9 = 7(0)₁₁₈9_<120> = 31991 · C116
C116 = P44 · P73
P44 = 12429111900259089222404905377487364334851383_<44>
P73 = 1760476070227298881000250830892187832585839053412152708131162759974648953_<73>

Number: 70009_119 N=21881154074583476602794535963239661154699759307305179581757369260104404363727298302647619643024600668938138851551999 ( 116 digits) SNFS difficulty: 120 digits. Divisors found: r1=12429111900259089222404905377487364334851383 (pp44) r2=1760476070227298881000250830892187832585839053412152708131162759974648953 (pp73) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.00 hours. Scaled time: 4.04 units (timescale=2.016). Factorization parameters were as follows: name: 70009_119 n: 21881154074583476602794535963239661154699759307305179581757369260104404363727298302647619643024600668938138851551999 m: 1000000000000000000000000 c5: 7 c0: 90 skew: 1.67 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64083, largePrimes:2159262 encountered Relations: rels:2257962, finalFF:227231 Max relations in full relation-set: 28 Initial matrix: 113247 x 227231 with sparse part having weight 20803966. Pruned matrix : 89761 x 90391 with weight 5658124. Total sieving time: 1.87 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.04 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.00 hours. --------- CPU info (if available) ----------
Jan 5, 2008: By Robert Backstrom / GGNFS, GMP-ECM, Msieve
7·10¹³⁷+9 = 7(0)₁₃₆9_<138> = 260202808401992767_<18> · C121
C121 = P55 · P67
P55 = 1529173935702381764254152743534663932887976167416684647_<55>
P67 = 1759256536718344842192906040610542540050982219751847395727987528241_<67>

Number: n N=2690209242163733079058961856013706690488883800070139975077938579898447635548085461020149959227339603250033223472503615927 ( 121 digits) SNFS difficulty: 137 digits. Divisors found: r1=1529173935702381764254152743534663932887976167416684647 (pp55) r2=1759256536718344842192906040610542540050982219751847395727987528241 (pp67) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.64 hours. Scaled time: 8.43 units (timescale=1.817). Factorization parameters were as follows: name: KA_7_0_136_9 n: 2690209242163733079058961856013706690488883800070139975077938579898447635548085461020149959227339603250033223472503615927 skew: 0.42 deg: 5 c5: 700 c0: 9 m: 1000000000000000000000000000 type: snfs rlim: 2200000 alim: 2200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:162662, AFBsize:162645, largePrimes:6524001 encountered Relations: rels:6138409, finalFF:570651 Max relations in full relation-set: 48 Initial matrix: 325375 x 570651 with sparse part having weight 34157269. Pruned matrix : 163092 x 164782 with weight 16077087. Total sieving time: 4.22 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.20 hours. Total square root time: 0.10 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,75000 total time: 4.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
7·10¹⁶²+9 = 7(0)₁₆₁9_<163> = 23 · 39293 · C157
C157 = P33 · P125
P33 = 296777596371098420029084738265707_<33>
P125 = 26099002118993499083959038032360499646655560409399625783207929493736469419962227821932572864657403345682890557765228381684833_<125>
4·10¹⁶⁷-9 = 3(9)₁₆₆1_<168> = 43 · 443 · 3803 · 8363 · C156
C156 = P50 · P107
P50 = 42090948879771092306041949813824861415659616231911_<50>
P107 = 15685944386992125078642922951658875275870814395996579224833998729276744713659512994944344360612430130357121_<107>

Number: n N=660236283323817840290544661230842159865224455940162022712927557130000768016670936364065296896675298786703649800998664393561639053390956010241141686786288231 ( 156 digits) SNFS difficulty: 167 digits. Divisors found: Sat Jan 5 07:57:07 2008 prp50 factor: 42090948879771092306041949813824861415659616231911 Sat Jan 5 07:57:07 2008 prp107 factor: 15685944386992125078642922951658875275870814395996579224833998729276744713659512994944344360612430130357121 Sat Jan 5 07:57:07 2008 elapsed time 01:13:32 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 108.68 hours. Scaled time: 91.07 units (timescale=0.838). Factorization parameters were as follows: name: KA_3_9_166_1 n: 660236283323817840290544661230842159865224455940162022712927557130000768016670936364065296896675298786703649800998664393561639053390956010241141686786288231 type: snfs deg: 5 c5: 25 c0: -18 skew: 0.94 m: 2000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 8200447) Primes: RFBsize:216816, AFBsize:216551, largePrimes:6419024 encountered Relations: rels:6664364, finalFF:480851 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 108.48 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 108.68 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
5·10¹⁶¹+9 = 5(0)₁₆₀9_<162> = 19 · 499 · 81412523 · 290804753657827_<15> · C136
C136 = P49 · P87
P49 = 2886044097090709483188406135551437413159237776161_<49>
P87 = 771827378327791401197721327141510578461690263003677335551724101499521451664262614805569_<87>

Number: n N=2227527849195920167072818742245789804891947494234442788537785061825357198187109192712412964898187206347293193995545098532526760958240609 ( 136 digits) SNFS difficulty: 161 digits. Divisors found: r1=2886044097090709483188406135551437413159237776161 (pp49) r2=771827378327791401197721327141510578461690263003677335551724101499521451664262614805569 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 26.60 hours. Scaled time: 48.65 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_0_160_9 n: 2227527849195920167072818742245789804891947494234442788537785061825357198187109192712412964898187206347293193995545098532526760958240609 skew: 0.71 deg: 5 c5: 50 c0: 9 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:216816, AFBsize:215821, largePrimes:7227690 encountered Relations: rels:6738236, finalFF:537059 Max relations in full relation-set: 48 Initial matrix: 432702 x 537059 with sparse part having weight 46858226. Pruned matrix : 354338 x 356565 with weight 27479185. Total sieving time: 25.31 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.09 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 26.60 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(55·10¹⁶⁶-1)/9 = 6(1)₁₆₆_<167> = 181 · 201007 · C160
C160 = P48 · P113
P48 = 120497742595657450620499053585177186485899649981_<48>
P113 = 13939638538030391821504360100234375955821869881112474237487787326972602160821849566450875175021582057328890814793_<113>

Number: n N=1679694976432092896000986170298599345420424491720406293294233454751764399703600413660619639537885616394138141834622650400292843519374730307792835204884596968933 ( 160 digits) SNFS difficulty: 167 digits. Divisors found: Sat Jan 05 18:06:27 2008 recovered 43 nontrivial dependencies ... Sat Jan 05 19:46:20 2008 reading relations for dependency 7 ... Sat Jan 05 20:02:44 2008 prp48 factor: 120497742595657450620499053585177186485899649981 Sat Jan 05 20:02:44 2008 prp113 factor: 13939638538030391821504360100234375955821869881112474237487787326972602160821849566450875175021582057328890814793 Sat Jan 05 20:02:44 2008 elapsed time 03:57:05 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 85.32 hours. Scaled time: 149.14 units (timescale=1.748). Factorization parameters were as follows: name: KA_6_1_166 n: 1679694976432092896000986170298599345420424491720406293294233454751764399703600413660619639537885616394138141834622650400292843519374730307792835204884596968933 type: snfs skew: 0.28 deg: 5 c5: 550 c0: -1 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3900307) Primes: RFBsize:230209, AFBsize:229923, largePrimes:7742476 encountered Relations: rels:7182048, finalFF:512843 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 85.01 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.6,2.6,100000 total time: 85.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁵³+9 = 7(0)₁₅₂9_<154> = 229 · 383 · 8814412231_<10> · 659762031526680767195090417_<27> · C113
C113 = P33 · P81
P33 = 104956686158012241596645982785813_<33>
P81 = 130759423488435528873829580092903272449089541268530772072226531544627524905762137_<81>
Jan 4, 2008 (5th): By Robert Backstrom / GGNFS, Msieve
2·10¹⁶⁷-1 = 1(9)₁₆₇_<168> = 4909 · 16729 · 76379 · C155
C155 = P55 · P101
P55 = 2075226395886463745978813668503914095832906194613111381_<55>
P101 = 15364821936988404978129042011260705176086625946572656434503802043499982149928090393044705627002582341_<101>

Number: n N=31885484051733722430122978922374052186415647731414717844225369532026181178111894309739525314658565183166345642115120914615241018237573142523944303656722921 ( 155 digits) SNFS difficulty: 167 digits. Divisors found: Sat Jan 05 01:30:35 2008 prp55 factor: 2075226395886463745978813668503914095832906194613111381 Sat Jan 05 01:30:35 2008 prp101 factor: 15364821936988404978129042011260705176086625946572656434503802043499982149928090393044705627002582341 Sat Jan 05 01:30:35 2008 elapsed time 02:45:45 (Msieve 1.32) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 68.62 hours. Scaled time: 89.89 units (timescale=1.310). Factorization parameters were as follows: name: KA_1_9_167 n: 31885484051733722430122978922374052186415647731414717844225369532026181178111894309739525314658565183166345642115120914615241018237573142523944303656722921 skew: 0.35 deg: 5 c5: 200 c0: -1 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3101069) Primes: RFBsize:230209, AFBsize:229657, largePrimes:7516432 encountered Relations: rels:6973016, finalFF:484541 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 68.25 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 68.62 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jan 4, 2008 (4th): By Jo Yeong Uk / GGNFS
7·10¹⁶⁸-9 = 6(9)₁₆₇1_<169> = 9843923 · 117894475991_<12> · 1261779092388631_<16> · 27635543446430167_<17> · C120
C120 = P52 · P69
P52 = 1537937361615581169410967292004327295366166873569433_<52>
P69 = 112472511207691888590129843674497489028548891319841138462050561658307_<69>

Number: 69991_168 N=172975677141036546015229400354180589109448912005422828633671122239020593886199741604134349538195365917741806140785729931 ( 120 digits) Divisors found: r1=1537937361615581169410967292004327295366166873569433 (pp52) r2=112472511207691888590129843674497489028548891319841138462050561658307 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 45.59 hours. Scaled time: 97.92 units (timescale=2.148). Factorization parameters were as follows: name: 69991_168 n: 172975677141036546015229400354180589109448912005422828633671122239020593886199741604134349538195365917741806140785729931 skew: 67391.34 # norm 5.09e+16 c5: 17280 c4: -30345414866 c3: -366826887495445 c2: 155289263798816555595 c1: 1928173509479924180946865 c0: -5273396086403893411410733594 # alpha -6.54 Y1: 1609298589041 Y0: -100020889963331680840305 # Murphy_E 2.83e-10 # M 2243431063636352947101853464256196889266586342162306354589158668527910371904618647504604110166117078652154422036894215 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4500001) Primes: RFBsize:315948, AFBsize:316323, largePrimes:7733678 encountered Relations: rels:7843528, finalFF:762917 Max relations in full relation-set: 28 Initial matrix: 632354 x 762917 with sparse part having weight 66957880. Pruned matrix : 527399 x 530624 with weight 44323563. Polynomial selection time: 2.69 hours. Total sieving time: 40.77 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.78 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 45.59 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Jan 4, 2008 (3rd): By Robert Backstrom / GMP-ECM
7·10¹²⁷+9 = 7(0)₁₂₆9_<128> = 44879 · C124
C124 = P32 · P37 · P56
P32 = 75697857002716999529892478650803_<32>
P37 = 1098672696747497143987400806595400953_<37>
P56 = 18754390384244538050938832102972339330160248332842058469_<56>
7·10¹³⁴+9 = 7(0)₁₃₃9_<135> = 1373 · 5167 · 3601349599733_<13> · C116
C116 = P31 · P86
P31 = 1439181583139272216526486427199_<31>
P86 = 19037423273913052788182876625430173418517933868978126334120252095713816138227879752697_<86>
Jan 4, 2008 (2nd): By Sinkiti Sibata / Msieve, GGNFS
7·10¹⁴⁸+9 = 7(0)₁₄₇9_<149> = 854417 · 1403083059087052553974969_<25> · 47025413165450464962041376031_<29> · C91
C91 = P40 · P51
P40 = 9370251329536055623552717563916135025857_<40>
P51 = 132513742186678071112443165485840454095701370690399_<51>

Fri Jan 4 08:23:13 2008 Msieve v. 1.30 Fri Jan 4 08:23:13 2008 random seeds: 2a1795f6 2f265fbe Fri Jan 4 08:23:13 2008 factoring 1241687068906518298633710848308113944954223996000579428139069580827675959567636029806646943 (91 digits) Fri Jan 4 08:23:14 2008 commencing quadratic sieve (90-digit input) Fri Jan 4 08:23:14 2008 using multiplier of 2 Fri Jan 4 08:23:14 2008 using 64kb Pentium 4 sieve core Fri Jan 4 08:23:14 2008 sieve interval: 18 blocks of size 65536 Fri Jan 4 08:23:14 2008 processing polynomials in batches of 6 Fri Jan 4 08:23:14 2008 using a sieve bound of 1652503 (62277 primes) Fri Jan 4 08:23:14 2008 using large prime bound of 145420264 (27 bits) Fri Jan 4 08:23:14 2008 using double large prime bound of 492861412574344 (42-49 bits) Fri Jan 4 08:23:14 2008 using trial factoring cutoff of 49 bits Fri Jan 4 08:23:14 2008 polynomial 'A' values have 12 factors Fri Jan 4 12:29:01 2008 62747 relations (16982 full + 45765 combined from 694116 partial), need 62373 Fri Jan 4 12:29:04 2008 begin with 711098 relations Fri Jan 4 12:29:05 2008 reduce to 152534 relations in 10 passes Fri Jan 4 12:29:05 2008 attempting to read 152534 relations Fri Jan 4 12:29:10 2008 recovered 152534 relations Fri Jan 4 12:29:10 2008 recovered 128623 polynomials Fri Jan 4 12:29:10 2008 attempting to build 62747 cycles Fri Jan 4 12:29:10 2008 found 62747 cycles in 5 passes Fri Jan 4 12:29:10 2008 distribution of cycle lengths: Fri Jan 4 12:29:10 2008 length 1 : 16982 Fri Jan 4 12:29:10 2008 length 2 : 12077 Fri Jan 4 12:29:10 2008 length 3 : 10920 Fri Jan 4 12:29:10 2008 length 4 : 8357 Fri Jan 4 12:29:10 2008 length 5 : 5867 Fri Jan 4 12:29:10 2008 length 6 : 3794 Fri Jan 4 12:29:10 2008 length 7 : 2182 Fri Jan 4 12:29:10 2008 length 9+: 2568 Fri Jan 4 12:29:10 2008 largest cycle: 19 relations Fri Jan 4 12:29:11 2008 matrix is 62277 x 62747 with weight 3737470 (avg 59.56/col) Fri Jan 4 12:29:12 2008 filtering completed in 3 passes Fri Jan 4 12:29:12 2008 matrix is 57933 x 57997 with weight 3465014 (avg 59.74/col) Fri Jan 4 12:29:13 2008 saving the first 48 matrix rows for later Fri Jan 4 12:29:13 2008 matrix is 57885 x 57997 with weight 2675909 (avg 46.14/col) Fri Jan 4 12:29:13 2008 matrix includes 64 packed rows Fri Jan 4 12:29:13 2008 using block size 21845 for processor cache size 512 kB Fri Jan 4 12:29:13 2008 commencing Lanczos iteration Fri Jan 4 12:29:46 2008 lanczos halted after 916 iterations (dim = 57883) Fri Jan 4 12:29:46 2008 recovered 17 nontrivial dependencies Fri Jan 4 12:29:47 2008 prp40 factor: 9370251329536055623552717563916135025857 Fri Jan 4 12:29:47 2008 prp51 factor: 132513742186678071112443165485840454095701370690399 Fri Jan 4 12:29:47 2008 elapsed time 04:06:34
7·10¹²⁰+9 = 7(0)₁₁₉9_<121> = 3613 · C118
C118 = P30 · P43 · P45
P30 = 830640561618524856111311045749_<30>
P43 = 5267270292924611350420925089608485692597297_<43>
P45 = 442824191940348923348965981442994565437113881_<45>

Number: 70009_120 N=1937448104068641018544146138942706891779684472737337392748408524771657902020481594243011347910323830611680044284528093 ( 118 digits) SNFS difficulty: 120 digits. Divisors found: r1=830640561618524856111311045749 (pp30) r2=5267270292924611350420925089608485692597297 (pp43) r3=442824191940348923348965981442994565437113881 (pp45) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.11 hours. Scaled time: 4.22 units (timescale=2.003). Factorization parameters were as follows: name: 70009_120 n: 1937448104068641018544146138942706891779684472737337392748408524771657902020481594243011347910323830611680044284528093 m: 1000000000000000000000000 c5: 7 c0: 9 skew: 1.05 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63908, largePrimes:1993457 encountered Relations: rels:1958903, finalFF:135849 Max relations in full relation-set: 28 Initial matrix: 113072 x 135849 with sparse part having weight 10934243. Pruned matrix : 104688 x 105317 with weight 6771158. Total sieving time: 1.96 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.11 hours. --------- CPU info (if available) ----------
Jan 4, 2008: By JMB / GGNFS / Dec 30, 2007
7·10¹⁵⁶-9 = 6(9)₁₅₅1_<157> = 2260571 · 21161214882893_<14> · 625086523594801_<15> · C123
C123 = P35 · P89
P35 = 15854608314307477257889614412447463_<35>
P89 = 14765346313638338741527800132362791570551309344130945927519948485674768514606278097831519_<89>

Number: 7*10^156-9 N=234098782427839665196883000012361900130395680636725922006376080346982807010226027831376517657752445555625517266741812986297 ( 123 digits) SNFS difficulty: 156 digits. Divisors found: r1=15854608314307477257889614412447463 (pp35) r2=14765346313638338741527800132362791570551309344130945927519948485674768514606278097831519 (pp89) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 42.32 hours.
Jan 3, 2008 (2nd): By matsui / GGNFS
3·10¹⁶⁵+1 = 3(0)₁₆₄1_<166> = 116891557 · 518126347 · 1922556849772274468793737_<25> · C125
C125 = P40 · P86
P40 = 1996780824920828139624227695148118615121_<40>
P86 = 12903063841818771390850986103947680780972868837668201185568690923523136035069365410047_<86>

N=25764590462072996269405677531284515063243873374651180669095169968451099335117503157111422341924469479276733945373461939520687 ( 125 digits) SNFS difficulty: 165 digits. Divisors found: r1=1996780824920828139624227695148118615121 (pp40) r2=12903063841818771390850986103947680780972868837668201185568690923523136035069365410047 (pp86) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 71.33 hours. Scaled time: 92.01 units (timescale=1.290). Factorization parameters were as follows: n: 25764590462072996269405677531284515063243873374651180669095169968451099335117503157111422341924469479276733945373461939520687 m: 1000000000000000000000000000000000 c5: 3 c0: 1 skew: 0.8 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 4800001) Primes: RFBsize:348513, AFBsize:348501, largePrimes:5801459 encountered Relations: rels:5977721, finalFF:817358 Max relations in full relation-set: 28 Initial matrix: 697079 x 817358 with sparse part having weight 44467712. Pruned matrix : 598008 x 601557 with weight 30414881. Total sieving time: 59.58 hours. Total relation processing time: 0.11 hours. Matrix solve time: 11.37 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 71.33 hours.
Jan 3, 2008: The factor table of 700...009 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jan 2, 2008 (3rd): By Sinkiti Sibata / PFGW
(19·10¹⁰⁸¹⁹+11)/3 and (19·10¹⁶⁰³⁶+11)/3 are PRPs.
Jan 2, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(2·10¹⁶⁶-17)/3 = (6)₁₆₅1_<166> = 3842906236981734253_<19> · C148
C148 = P64 · P85
P64 = 1100602829068959264051293759364233221830412643879055222397047131_<64>
P85 = 1576225422633670819910453271096401900701665607593218926957327204082110519610002697627_<85>

Number: n N=1734798159401034080171951805732663587453115538866372203257419337379268789106327611243635763708787379629924381790161230793926643180172168189060858137 ( 148 digits) SNFS difficulty: 166 digits. Divisors found: Wed Jan 2 20:49:51 2008 prp64 factor: 1100602829068959264051293759364233221830412643879055222397047131 Wed Jan 2 20:49:51 2008 prp85 factor: 1576225422633670819910453271096401900701665607593218926957327204082110519610002697627 Wed Jan 2 20:49:51 2008 elapsed time 01:07:33 (Msieve 1.32) Version: GGNFS-0.77.1-20050930-k8 Total time: 70.81 hours. Scaled time: 59.62 units (timescale=0.842). Factorization parameters were as follows: name: KA_6_165_1 n: 1734798159401034080171951805732663587453115538866372203257419337379268789106327611243635763708787379629924381790161230793926643180172168189060858137 type: snfs deg: 5 c5: 20 c0: -17 skew: 0.97 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 5600001) Primes: RFBsize:216816, AFBsize:216481, largePrimes:5965439 encountered Relations: rels:5938781, finalFF:342850 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 70.66 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 70.81 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
3·10¹⁶⁷+1 = 3(0)₁₆₆1_<168> = 13² · 23 · 11240783 · C157
C157 = P48 · P110
P48 = 107653808874199343653823320575009810381715666999_<48>
P110 = 63779447095061318423367850224578695523579815789150289866244003646649681085810329261922617536898003393691354119_<110>

Number: n N=6866100407673839710882458256002676877960427288936869306360920082777722078076735615102261401273652713425168105724751281057680269387071669463168216273591018881 ( 157 digits) SNFS difficulty: 167 digits. Divisors found: Wed Jan 02 22:42:17 2008 prp48 factor: 107653808874199343653823320575009810381715666999 Wed Jan 02 22:42:17 2008 prp110 factor: 63779447095061318423367850224578695523579815789150289866244003646649681085810329261922617536898003393691354119 Wed Jan 02 22:42:17 2008 elapsed time 01:12:16 (Msieve 1.32) Version: GGNFS-0.77.1-20051202-athlon Total time: 48.99 hours. Scaled time: 89.01 units (timescale=1.817). Factorization parameters were as follows: name: KA_3_0_166_1 n: 6866100407673839710882458256002676877960427288936869306360920082777722078076735615102261401273652713425168105724751281057680269387071669463168216273591018881 skew: 0.32 deg: 5 c5: 300 c0: 1 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3400000) Primes: RFBsize:250150, AFBsize:250021, largePrimes:7702844 encountered Relations: rels:7199778, finalFF:579094 Max relations in full relation-set: 28 Initial matrix: 500237 x 579094 with sparse part having weight 53234607. Pruned matrix : 463022 x 465587 with weight 36385180. Total sieving time: 48.80 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 48.99 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Jan 2, 2008: By Jo Yeong Uk / GGNFS
(73·10¹⁶⁶-1)/9 = 8(1)₁₆₆_<167> = 3 · 19 · 213287 · 4111361 · 5929768853_<10> · 3669810243913628169910801_<25> · C119
C119 = P55 · P64
P55 = 8223492567479697862048124640209449367402873621875410421_<55>
P64 = 9068131722716584529229143545406928460604605774689721826341970753_<64>

Number: 81111_166 N=74571713822686701323900979192571029758253172648119389362012248244916093237432632041053581859169646820908120119853417013 ( 119 digits) Divisors found: r1=8223492567479697862048124640209449367402873621875410421 (pp55) r2=9068131722716584529229143545406928460604605774689721826341970753 (pp64) Version: GGNFS-0.77.1-20050930-nocona Total time: 38.36 hours. Scaled time: 82.33 units (timescale=2.146). Factorization parameters were as follows: name: 81111_166 n: 74571713822686701323900979192571029758253172648119389362012248244916093237432632041053581859169646820908120119853417013 skew: 63934.65 # norm 5.02e+16 c5: 44700 c4: -8672528716 c3: -1167204485490759 c2: -23508456169732693191 c1: 1360412238556341935907211 c0: -4184003940301627376220420525 # alpha -6.83 Y1: 4470191423393 Y0: -69896334002934700208002 # Murphy_E 3.51e-10 # M 46104542136265429012421759151830318936477223069350986501594276445394325180456204984475629741637253392362953793618722669 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4125001) Primes: RFBsize:315948, AFBsize:316441, largePrimes:7685412 encountered Relations: rels:7784882, finalFF:771369 Max relations in full relation-set: 28 Initial matrix: 632470 x 771369 with sparse part having weight 64136043. Pruned matrix : 516540 x 519766 with weight 40029222. Polynomial selection time: 2.27 hours. Total sieving time: 34.13 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.63 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 38.36 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406450) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117) Calibrating delay using timer specific routine.. 4809.83 BogoMIPS (lpj=2404916) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Jan 1, 2008 (3rd): By Bruce Dodson
10²⁷⁸+1 is divisible by 538978365796508304569088931293097537674917585678041_<51>
(10³³³-1)/9 is divisible by 2391225903192434229494639627847286709185128947978708401_<55>
References: Factoring and Prime Identification (Torbjörn Granlund), The ECMNET Project (Paul Zimmermann)
Jan 1, 2008 (2nd): By Sinkiti Sibata / PFGW
(2·10²⁵⁰⁵+61)/9 is prime.
Jan 1, 2008: By matsui / GGNFS
(5·10¹⁶⁸+7)/3 = 1(6)₁₆₇9_<169> = 331935313 · 683366047897543_<15> · 154074768697553552249_<21> · C125
C125 = P60 · P66
P60 = 389150024577353540408352254416982467679044312048033653164543_<60>
P66 = 122544354335196425279257869050817022387231657467995884738591164013_<66>

N=47688138501357609774618672532490299817298311966335834818528738503217271683915586390382658927785128435204674599608535389191059 ( 125 digits) SNFS difficulty: 169 digits. Divisors found: r1=389150024577353540408352254416982467679044312048033653164543 (pp60) r2=122544354335196425279257869050817022387231657467995884738591164013 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 230.78 hours. Scaled time: 292.87 units (timescale=1.269). Factorization parameters were as follows: n: 47688138501357609774618672532490299817298311966335834818528738503217271683915586390382658927785128435204674599608535389191059 m: 5000000000000000000000000000000000 c5: 8 c0: 35 skew: 1.34 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, 7300001) Primes: RFBsize:412849, AFBsize:413746, largePrimes:6138486 encountered Relations: rels:6454072, finalFF:972179 Max relations in full relation-set: 28 Initial matrix: 826660 x 972179 with sparse part having weight 59419918. Pruned matrix : 704813 x 709010 with weight 42613207. Total sieving time: 211.34 hours. Total relation processing time: 0.28 hours. Matrix solve time: 18.83 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 230.78 hours.

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