News and updates, January 2009

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News and updates, January 2009

Jan 31, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 31, 2009
(41·10¹⁶¹-23)/9 = 4(5)₁₆₀3_<162> = 3 · 7 · 131 · 1123943 · 309453852605561_<15> · C138
C138 = P44 · P94
P44 = 48715522449375037037112608816998451240059843_<44>
P94 = 9773344594347818728692771659151250188561551518867168822085057404744657355124995709625315835227_<94>

Number: 45553_161 N=476113587991429327991160095841723465002630865947020881182067571272286331325153049728211155687436532750693507773602785210557141607007489361 ( 138 digits) SNFS difficulty: 162 digits. Divisors found: r1=48715522449375037037112608816998451240059843 r2=9773344594347818728692771659151250188561551518867168822085057404744657355124995709625315835227 Version: Total time: 19.15 hours. Scaled time: 45.82 units (timescale=2.393). Factorization parameters were as follows: n: 476113587991429327991160095841723465002630865947020881182067571272286331325153049728211155687436532750693507773602785210557141607007489361 m: 100000000000000000000000000000000 deg: 5 c5: 410 c0: -23 skew: 0.56 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 3600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9381225 Max relations in full relation-set: Initial matrix: Pruned matrix : 740977 x 741225 Total sieving time: 17.03 hours. Total relation processing time: 0.72 hours. Matrix solve time: 1.11 hours. Time per square root: 0.28 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 19.15 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047104k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5604.08 BogoMIPS (lpj=2802042) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672376) Calibrating delay using timer specific routine.. 5344.70 BogoMIPS (lpj=2672350)
Jan 31, 2009: By Serge Batalov / Msieve-1.39 / Jan 31, 2009
(41·10¹⁶⁵-23)/9 = 4(5)₁₆₄3_<166> = C166
C166 = P43 · P48 · P76
P43 = 7048830044955730285803652614749917171590703_<43>
P48 = 217664130389283169762486791539612080217356148339_<48>
P76 = 2969186257631440708130691194440226995175932326438344612604677326089467529109_<76>

SNFS difficulty: 166 digits. Divisors found: r1=7048830044955730285803652614749917171590703 (pp43) r2=217664130389283169762486791539612080217356148339 (pp48) r3=2969186257631440708130691194440226995175932326438344612604677326089467529109 (pp76) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.294). Factorization parameters were as follows: n: 4555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 m: 1000000000000000000000000000000000 deg: 5 c5: 41 c0: -23 skew: 0.89 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2100000, 4100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 773789 x 774037 Total sieving time: 0.00 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,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,100000 total time: 37.00 hours.
(41·10¹⁷¹+13)/9 = 4(5)₁₇₀7_<172> = 3 · 7² · 17 · 50513 · 40344357139_<11> · C153
C153 = P62 · P92
P62 = 13545655697291753895167415183155062115257968864458197026561047_<62>
P92 = 66037267802058900270285640006155171253032916972658859255631851488321722456468401221793505867_<92>

SNFS difficulty: 172 digits. Divisors found: r1=13545655697291753895167415183155062115257968864458197026561047 (pp62) r2=66037267802058900270285640006155171253032916972658859255631851488321722456468401221793505867 (pp92) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.302). Factorization parameters were as follows: n: 894518092836540440883213933824080875780792388807894997431695313391332454085486399914701232771571225453111058182290877031803884777922102962656532628162749 m: 10000000000000000000000000000000000 deg: 5 c5: 410 c0: 13 skew: 0.50 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 6600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 982605 x 982853 Total sieving time: 0.00 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,172,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000 total time: 50.00 hours.
Jan 30, 2009 (4th): By Sinkiti Sibata / GGNFS / Jan 30, 2009
(35·10¹⁶⁴+1)/9 = 3(8)₁₆₃9_<165> = 282833 · 347981 · 1195263561592703068137949500679_<31> · C124
C124 = P50 · P74
P50 = 39575882037420828963570411917339240644716762775903_<50>
P74 = 83530607544231245392846006539898621111183905857449706817593594044549213589_<74>

Number: 38889_164 N=3305797470684590126516118944166244859718767479459168848484632525243758609790874378955530593175883268566507494694347289345867 ( 124 digits) SNFS difficulty: 165 digits. Divisors found: r1=39575882037420828963570411917339240644716762775903 (pp50) r2=83530607544231245392846006539898621111183905857449706817593594044549213589 (pp74) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 79.80 hours. Scaled time: 37.75 units (timescale=0.473). Factorization parameters were as follows: name: 38889_164 n: 3305797470684590126516118944166244859718767479459168848484632525243758609790874378955530593175883268566507494694347289345867 m: 1000000000000000000000000000000000 deg: 5 c5: 7 c0: 2 skew: 0.78 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 3650001) Primes: RFBsize:289774, AFBsize:289257, largePrimes:9034055 encountered Relations: rels:9241991, finalFF:676064 Max relations in full relation-set: 28 Initial matrix: 579096 x 676064 with sparse part having weight 68165626. Pruned matrix : 516684 x 519643 with weight 51138428. Total sieving time: 64.49 hours. Total relation processing time: 0.50 hours. Matrix solve time: 14.61 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 79.80 hours. --------- CPU info (if available) ----------
Jan 30, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jan 30, 2009
(43·10²⁰⁶-7)/9 = 4(7)₂₀₆_<207> = 3 · 73 · 1197999487_<10> · 919272050133022870840781_<24> · 227091512033988664050765336907_<30> · 9979120019997928268416395684139_<31> · C111
C111 = P43 · P69
P43 = 2075634083079828998567220764778928732800821_<43>
P69 = 421150384930020461727145617061926763309795192374704172359381305111733_<69>

Number: 47777_206 N=874154093062940053723423566083923324074453222353223316638756093434022663299154755490033595932211400153439132793 ( 111 digits) Divisors found: r1=2075634083079828998567220764778928732800821 r2=421150384930020461727145617061926763309795192374704172359381305111733 Version: Total time: 10.14 hours. Scaled time: 24.15 units (timescale=2.382). Factorization parameters were as follows: name: 47777_206 n: 874154093062940053723423566083923324074453222353223316638756093434022663299154755490033595932211400153439132793 skew: 30687.16 # norm 3.99e+15 c5: 113400 c4: 2920482650 c3: -302366368859399 c2: -2625363309198789138 c1: 137037003928894478826152 c0: 801887937814693936058974480 # alpha -6.60 Y1: 274783993297 Y0: -1504508271055678830873 # Murphy_E 8.66e-10 # M 33913588752037023001154899934271482323043432368019170082195613568306518138961385112480392869526368209010001248 type: gnfs rlim: 2100000 alim: 2100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1050000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8166464 Max relations in full relation-set: Initial matrix: Pruned matrix : 386617 x 386865 Polynomial selection time: 0.76 hours. Total sieving time: 8.40 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.31 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 10.14 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360) Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043) Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)
(43·10²⁰²-7)/9 = 4(7)₂₀₂_<203> = 7331 · 2224447 · 4264331689_<10> · 3282544923857_<13> · 129162515387784254409797833_<27> · 894140490812561508197748839283473_<33> · C112
C112 = P50 · P63
P50 = 12468621839237019750134274632920275340919814102191_<50>
P63 = 145351091738832752462107761351113457049563025712898988930667003_<63>

Number: 47777_202 N=1812327796811753621163200021922067097052888721647496808031500412932013350729735549051173339843739136511233703573 ( 112 digits) Divisors found: r1=12468621839237019750134274632920275340919814102191 r2=145351091738832752462107761351113457049563025712898988930667003 Version: Total time: 11.29 hours. Scaled time: 26.94 units (timescale=2.387). Factorization parameters were as follows: name: 47777_202 n: 1812327796811753621163200021922067097052888721647496808031500412932013350729735549051173339843739136511233703573 skew: 54094.49 # norm 4.44e+15 c5: 7680 c4: 3175216088 c3: -75687149631190 c2: -7247399479012978327 c1: 75161386214624790981960 c0: 3589599881379885118000877349 # alpha -6.21 Y1: 937728520817 Y0: -2982385752308822800816 # Murphy_E 7.94e-10 # M 452990686981099005718217834527867984953168050273452541942955949321535635220026936614575740434782683652135110614 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1200000, 2040001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8532087 Max relations in full relation-set: Initial matrix: Pruned matrix : 384054 x 384302 Polynomial selection time: 0.87 hours. Total sieving time: 9.47 hours. Total relation processing time: 0.57 hours. Matrix solve time: 0.30 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000 total time: 11.29 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360) Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043) Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)
(41·10¹⁸³-23)/9 = 4(5)₁₈₂3_<184> = C184
C184 = P35 · P150
P35 = 14589501503902084137302513137370873_<35>
P150 = 312248883509634249005847902099113991658769635405891185299817342330275330744748507088676770238588018801904100842443828422508631356486325904946577765161_<150>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 4555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 (184 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3268419040 Step 1 took 6263ms Step 2 took 3376ms ********** Factor found in step 2: 14589501503902084137302513137370873 Found probable prime factor of 35 digits: 14589501503902084137302513137370873 Probable prime cofactor 312248883509634249005847902099113991658769635405891185299817342330275330744748507088676770238588018801904100842443828422508631356486325904946577765161 has 150 digits
Jan 30, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Jan 30, 2009
(41·10¹⁵¹-23)/9 = 4(5)₁₅₀3_<152> = 383 · 8447 · 19571 · 9230748389_<10> · C131
C131 = P42 · P90
P42 = 124434346315030176296076825378828222961733_<42>
P90 = 626397301816530774964119179790139452924785821296333787068498699938708732827425248548556339_<90>

Number: 45553_151 N=77945338785038671394181877897307420049103361412246789040632117018754521459012051523341323925873080957218788678619520132547991575487 ( 131 digits) SNFS difficulty: 152 digits. Divisors found: r1=124434346315030176296076825378828222961733 r2=626397301816530774964119179790139452924785821296333787068498699938708732827425248548556339 Version: Total time: 22.11 hours. Scaled time: 43.01 units (timescale=1.945). Factorization parameters were as follows: n: 77945338785038671394181877897307420049103361412246789040632117018754521459012051523341323925873080957218788678619520132547991575487 m: 1000000000000000000000000000000 deg: 5 c5: 410 c0: -23 skew: 0.56 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1200000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 484391 x 484639 Total sieving time: 22.11 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,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 22.11 hours. --------- CPU info (if available) ----------
Jan 30, 2009: By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1 / Jan 30, 2009
(41·10¹⁶³-23)/9 = 4(5)₁₆₂3_<164> = 389 · 45851195581_<11> · C151
C151 = P68 · P83
P68 = 29133329337945510299957110140657349252840116046675345541662393249319_<68>
P83 = 87669991230507932658083828877276980219124823060697439168343320477973842654932855143_<83>

SNFS difficulty: 166 digits. Divisors found: r1=29133329337945510299957110140657349252840116046675345541662393249319 (pp68) r2=87669991230507932658083828877276980219124823060697439168343320477973842654932855143 (pp83) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 2554118727573182363624568773003137949230779989157913559867837585944130801792176347437384308522371049214854200576158632139427275758913382964941710397617 m: 500000000000000000000000000000000 deg: 5 c5: 328 c0: -575 skew: 1.12 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2050000, 4650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 782389 x 782637 Total sieving time: 0.00 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,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,200000 total time: 42.00 hours.
(13·10¹⁶⁹+17)/3 = 4(3)₁₆₈9_<170> = 7² · 113 · 6143 · 165463 · C157
C157 = P35 · C123
P35 = 64817842125068594359353753328875377_<35>
C123 = [118787733468585373018803001626199942041486879025646793084250872377023430370450048163478120248088756637535072725204319132979_<123>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=746734294 Step 1 took 13951ms Step 2 took 13265ms ********** Factor found in step 2: 64817842125068594359353753328875377 Found probable prime factor of 35 digits: 64817842125068594359353753328875377 Composite cofactor has 123 digits
Jan 29, 2009 (9th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 29, 2009
(13·10¹⁶²+17)/3 = 4(3)₁₆₁9_<163> = 71143 · 1199953693995273725407_<22> · C137
C137 = P52 · P85
P52 = 7529261953382445456022978831409101175220907433308991_<52>
P85 = 6741755973701705171652646158601204512690915622307800010016289079913328347215654722829_<85>

Number: 43339_162 N=50760446751781071257905593169998899590553675465934743310278919667953736415005326576711409469460862032185500165163685445643993256418655539 ( 137 digits) SNFS difficulty: 163 digits. Divisors found: r1=7529261953382445456022978831409101175220907433308991 r2=6741755973701705171652646158601204512690915622307800010016289079913328347215654722829 Version: Total time: 23.65 hours. Scaled time: 56.53 units (timescale=2.390). Factorization parameters were as follows: n: 50760446751781071257905593169998899590553675465934743310278919667953736415005326576711409469460862032185500165163685445643993256418655539 m: 100000000000000000000000000000000 deg: 5 c5: 1300 c0: 17 skew: 0.42 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2100000, 4100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9731766 Max relations in full relation-set: Initial matrix: Pruned matrix : 779314 x 779562 Total sieving time: 21.33 hours. Total relation processing time: 0.94 hours. Matrix solve time: 1.28 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 23.65 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360) Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043) Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)
(35·10¹⁶⁴-17)/9 = 3(8)₁₆₃7_<165> = 3² · 227 · 283 · 607 · 721641441052677560056142789_<27> · C130
C130 = P43 · P87
P43 = 2164226505067740336545299545138264786212773_<43>
P87 = 709508928632527276438580379581169517506057775727086708484652773434018533527897889599737_<87>

Number: 38887_164 N=1535538028928731310411299976352496883335984799898135849679037491841562148763146925000134438926258136116973870389355679625086840701 ( 130 digits) SNFS difficulty: 165 digits. Divisors found: r1=2164226505067740336545299545138264786212773 r2=709508928632527276438580379581169517506057775727086708484652773434018533527897889599737 Version: Total time: 20.65 hours. Scaled time: 49.29 units (timescale=2.387). Factorization parameters were as follows: n: 1535538028928731310411299976352496883335984799898135849679037491841562148763146925000134438926258136116973870389355679625086840701 m: 1000000000000000000000000000000000 deg: 5 c5: 7 c0: -34 skew: 1.37 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2200000, 3900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9680389 Max relations in full relation-set: Initial matrix: Pruned matrix : 723944 x 724192 Total sieving time: 18.70 hours. Total relation processing time: 0.80 hours. Matrix solve time: 1.08 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 20.65 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360) Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043) Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)
Jan 29, 2009 (8th): By Serge Batalov / Msieve-1.39, pol51 / Jan 29, 2009
(41·10¹⁵⁸-23)/9 = 4(5)₁₅₇3_<159> = 3² · 89 · C156
C156 = P65 · P92
P65 = 28850941907203007847401689552967354640673245661890210464614317293_<65>
P92 = 19712823566187765936501050571307241754800318770326492415189741533994996509543568798904090021_<92>

SNFS difficulty: 161 digits. Divisors found: r1=28850941907203007847401689552967354640673245661890210464614317293 (pp65) r2=19712823566187765936501050571307241754800318770326492415189741533994996509543568798904090021 (pp92) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 568733527535025662366486336523789707310306561242890830905812179220418920793452628658621167984463864613677347759744763490081842141767235400194201692329033153 m: 50000000000000000000000000000000 c5: 328 c0: -575 skew: 1.12 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1700000, 3500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 613407 x 613655 Total sieving time: 0.00 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,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,200000 total time: 27.00 hours.
(41·10¹⁷⁸-23)/9 = 4(5)₁₇₇3_<179> = 1183943 · 189287933041368939698424948529_<30> · 1208868416299919985898567336255445891869_<40> · C105
C105 = P48 · P57
P48 = 481911941006296666803436041025635734292586173461_<48>
P57 = 348932085078507959564569166156418142784583065154844041511_<57>

Divisors found: r1=481911941006296666803436041025635734292586173461 (pp48) r2=348932085078507959564569166156418142784583065154844041511 (pp57) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.528). Factorization parameters were as follows: name: 45553_178 n: 168154538399558017254478603113207313708895276072507757115220953746111331152469234868619217627939730539571 skew: 9723.82 # norm 1.94e+14 c5: 45840 c4: 436103556 c3: -14526373230872 c2: -44181904912960523 c1: -101954573143161400030 c0: 412019275248612995904320 # alpha -5.43 Y1: 16582549357 Y0: -81826246411099303959 # Murphy_E 1.94e-09 # M 114387187697216149807785384983138201125110014197248308094008292071209457371172444703697085321264377513011 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 275264 x 275512 Total sieving time: 0.00 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: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 6.00 hours.
Jan 29, 2009 (7th): By Erik Branger / GGNFS, Msieve / Jan 29, 2009
(41·10¹³⁹-23)/9 = 4(5)₁₃₈3_<140> = 4007 · 324829275755121868009_<21> · C116
C116 = P45 · P71
P45 = 773862830377449253413698674936532384941341169_<45>
P71 = 45227528252266932279145332153783269490963211018115404781446254785187599_<71>

Number: 45553_139 N=34999903024275338901522874375799121511839485670661437667979695890714240654775511337191106823261682968866354326963231 ( 116 digits) SNFS difficulty: 141 digits. Divisors found: r1=773862830377449253413698674936532384941341169 r2=45227528252266932279145332153783269490963211018115404781446254785187599 Version: Total time: 9.89 hours. Scaled time: 20.66 units (timescale=2.088). Factorization parameters were as follows: n: 34999903024275338901522874375799121511839485670661437667979695890714240654775511337191106823261682968866354326963231 m: 10000000000000000000000000000 deg: 5 c5: 41 c0: -230 skew: 1.41 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 284118 x 284366 Total sieving time: 9.89 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,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 9.89 hours. --------- CPU info (if available) ----------
(41·10¹³¹-23)/9 = 4(5)₁₃₀3_<132> = 3² · 7² · 311 · 43711 · C122
C122 = P40 · P83
P40 = 1801364495446163282257831597361756468273_<40>
P83 = 42184220455933837447552299166930194478197239547739286056819295000322534357624766001_<83>

Number: 45553_131 N=75989156997392977105229538608994471183862080258012139504286349375102219420870458470076856934080344251900169694479805586273 ( 122 digits) SNFS difficulty: 132 digits. Divisors found: r1=1801364495446163282257831597361756468273 r2=42184220455933837447552299166930194478197239547739286056819295000322534357624766001 Version: Total time: 4.54 hours. Scaled time: 3.58 units (timescale=0.789). Factorization parameters were as follows: n: 75989156997392977105229538608994471183862080258012139504286349375102219420870458470076856934080344251900169694479805586273 m: 100000000000000000000000000 deg: 5 c5: 410 c0: -23 skew: 0.56 type: snfs lss: 1 rlim: 1140000 alim: 1140000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1140000/1140000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [570000, 1020001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 180838 x 181086 Total sieving time: 4.54 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,132,5,0,0,0,0,0,0,0,0,1140000,1140000,26,26,47,47,2.3,2.3,50000 total time: 4.54 hours. --------- CPU info (if available) ----------
Jan 29, 2009 (6th): By Tyler Cadigan / GGNFS, Msieve / Jan 29, 2009
(43·10¹⁷⁸-7)/9 = 4(7)₁₇₈_<179> = 383 · 4354027 · 249604739031097_<15> · C156
C156 = P37 · P49 · P70
P37 = 3673652886587821683140672767941328687_<37>
P49 = 6902107741445885438068266121725096751735112138723_<49>
P70 = 4526925785659940824204341239430806891307484383858194682858972240819401_<70>

Number: 47777_178 N=114784494947366634262426183006958123861511699275635538429018736808936826291842714776329045547599116455771782266887863028084494441647275112045251159350246101 ( 156 digits) SNFS difficulty: 181 digits. Divisors found: r1=3673652886587821683140672767941328687 (pp37) r2=6902107741445885438068266121725096751735112138723 (pp49) r3=4526925785659940824204341239430806891307484383858194682858972240819401 (pp70) Version: Msieve-1.39 Total time: 265.08 hours. Scaled time: 678.60 units (timescale=2.560). Factorization parameters were as follows: n: 114784494947366634262426183006958123861511699275635538429018736808936826291842714776329045547599116455771782266887863028084494441647275112045251159350246101 m: 500000000000000000000000000000000000 deg: 5 c5: 344 c0: -175 skew: 0.87 type: snfs lss: 1 rlim: 7300000 alim: 7300000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 7300000/7300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3650000, 7650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1044036 x 1044284 Total sieving time: 265.08 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,181,5,0,0,0,0,0,0,0,0,7300000,7300000,28,28,53,53,2.5,2.5,100000 total time: 265.08 hours. --------- CPU info (if available) ----------
Jan 29, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 29, 2009
(41·10¹⁰³-23)/9 = 4(5)₁₀₂3_<104> = 7990030831_<10> · C94
C94 = P46 · P49
P46 = 1880920131093652155510042425842068306778985389_<46>
P49 = 3031255455185522651922420611150645662026396145867_<49>

Number: 45553_103 N=5701549408145901503037085784626249029245523765558490565924019718661277785944948321258305737263 ( 94 digits) SNFS difficulty: 106 digits. Divisors found: r1=1880920131093652155510042425842068306778985389 (pp46) r2=3031255455185522651922420611150645662026396145867 (pp49) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.47 hours. Scaled time: 1.13 units (timescale=2.392). Factorization parameters were as follows: n: 5701549408145901503037085784626249029245523765558490565924019718661277785944948321258305737263 m: 1000000000000000000000 deg: 5 c5: 41 c0: -2300 skew: 2.24 type: snfs lss: 1 rlim: 240000 alim: 240000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 240000/240000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [120000, 260001) Primes: RFBsize:21221, AFBsize:21090, largePrimes:852509 encountered Relations: rels:745091, finalFF:50700 Max relations in full relation-set: 28 Initial matrix: 42378 x 50700 with sparse part having weight 2823579. Pruned matrix : 40967 x 41242 with weight 1775227. Total sieving time: 0.45 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,240000,240000,25,25,44,44,2.2,2.2,20000 total time: 0.47 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360) Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043) Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)
(41·10¹²⁹-23)/9 = 4(5)₁₂₈3_<130> = 44029 · 1333136341721_<13> · C113
C113 = P33 · P81
P33 = 245833508742300870269048663236781_<33>
P81 = 315708938586453576137949202042096617259121045616596246935483076636501414393941457_<81>

Number: 45553_129 N=77611836114015463765579271944208630546320167838921160599412055952667076355928840955602283169533935707733843129917 ( 113 digits) SNFS difficulty: 131 digits. Divisors found: r1=245833508742300870269048663236781 r2=315708938586453576137949202042096617259121045616596246935483076636501414393941457 Version: Total time: 1.96 hours. Scaled time: 4.67 units (timescale=2.389). Factorization parameters were as follows: n: 77611836114015463765579271944208630546320167838921160599412055952667076355928840955602283169533935707733843129917 m: 100000000000000000000000000 deg: 5 c5: 41 c0: -230 skew: 1.41 type: snfs lss: 1 rlim: 1100000 alim: 1100000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1100000/1100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [550000, 1100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3173600 Max relations in full relation-set: Initial matrix: Pruned matrix : 166118 x 166366 Total sieving time: 1.72 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1100000,1100000,26,26,47,47,2.3,2.3,50000 total time: 1.96 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.72 BogoMIPS (lpj=2672360) Calibrating delay using timer specific routine.. 5344.08 BogoMIPS (lpj=2672043) Calibrating delay using timer specific routine.. 5237.82 BogoMIPS (lpj=2618912)
Jan 29, 2009 (4th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39, pol51 / Jan 29, 2009
(43·10²¹³-7)/9 = 4(7)₂₁₃_<214> = 29 · 3461 · 47701 · 316223 · 600109 · 13162957 · 39284608416614303_<17> · 75505295088633637_<17> · C153
C153 = P37 · P116
P37 = 3526680938895455431728898504444220551_<37>
P116 = 38190540064821716358063950502102091512430090081925348378008427894317449358648344734268599001413164789278233232637447_<116>

Using B1=5000000, B2=11416314010, polynomial Dickson(12), sigma=2511989336 Step 1 took 15349ms Step 2 took 9332ms ********** Factor found in step 2: 3526680938895455431728898504444220551 Found probable prime factor of 37 digits: 3526680938895455431728898504444220551 Probable prime cofactor 38190540064821716358063950502102091512430090081925348378008427894317449358648344734268599001413164789278233232637447 has 116 digits
(43·10²⁰³-7)/9 = 4(7)₂₀₃_<204> = 3 · 67 · 547 · 2838580823343361_<16> · 70019741574365087_<17> · C167
C167 = P43 · C124
P43 = 2334561165143153784276485597559959244336157_<43>
C124 = [9365167244931605937271157091977652941532850887100421862106964322653891953074392906416380032956187565261989128184595620958209_<124>]

Using B1=5000000, B2=23417929090, polynomial Dickson(12), sigma=3473665096 Step 1 took 22798ms Step 2 took 19003ms ********** Factor found in step 2: 2334561165143153784276485597559959244336157 Found probable prime factor of 43 digits: 2334561165143153784276485597559959244336157 Composite cofactor 9365167244931605937271157091977652941532850887100421862106964322653891953074392906416380032956187565261989128184595620958209 has 124 digits
(43·10²³⁴-7)/9 = 4(7)₂₃₄_<235> = 8821 · 576493 · 63521290844627070769256161_<26> · 192264712908627279576854165210309221783217_<42> · C158
C158 = P38 · P121
P38 = 41012255466950321646301229829861542741_<38>
P121 = 1875778410670032148125989730595334818323781272326288536827048138746736685097497248156417793124849522779165277155797324877_<121>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=227219622 Step 1 took 50881ms Step 2 took 33448ms ********** Factor found in step 2: 41012255466950321646301229829861542741 Found probable prime factor of 38 digits: 41012255466950321646301229829861542741 Probable prime cofactor 1875778410670032148125989730595334818323781272326288536827048138746736685097497248156417793124849522779165277155797324877 has 121 digits
(41·10¹⁵⁴-23)/9 = 4(5)₁₅₃3_<155> = 293099 · 105043513 · 152505329 · 27447127457_<11> · 142320476143_<12> · C112
C112 = P32 · P81
P32 = 19133469743565591575826954988903_<32>
P81 = 129811967521642553356376795770261489514163544206752823212917396577776180348802387_<81>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2312512268 Step 1 took 2290ms ********** Factor found in step 1: 19133469743565591575826954988903 Found probable prime factor of 32 digits: 19133469743565591575826954988903 Probable prime cofactor has 81 digits
(41·10¹⁷⁸-23)/9 = 4(5)₁₇₇3_<179> = 1183943 · 189287933041368939698424948529_<30> · C144
C144 = P40 · C105
P40 = 1208868416299919985898567336255445891869_<40>
C105 = [168154538399558017254478603113207313708895276072507757115220953746111331152469234868619217627939730539571_<105>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=744591357 Step 1 took 3877ms Step 2 took 3636ms ********** Factor found in step 2: 1208868416299919985898567336255445891869 Found probable prime factor of 40 digits: 1208868416299919985898567336255445891869
(41·10¹⁹⁶-23)/9 = 4(5)₁₉₅3_<197> = 17188148844872638761949_<23> · C175
C175 = P33 · C142
P33 = 292583499806596595725013018613757_<33>
C142 = [9058627697344100435072959011588414226107521095119906981620337036029788299086931609550622788224999995837661941137272253328636031596381018952121_<142>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3690523421 Step 1 took 4610ms Step 2 took 2451ms ********** Factor found in step 2: 292583499806596595725013018613757 Found probable prime factor of 33 digits: 292583499806596595725013018613757
(43·10²⁴⁹-7)/9 = 4(7)₂₄₉_<250> = 53 · 1103 · 801179 · C240
C240 = P41 · C199
P41 = 25422133258858709804303131627232676780973_<41>
C199 = [4012666034857030268082611148502973012917801084731203623422488400448065571628447168512039491797916152679691062964730175869111228899299131087507442826326840156446022996606392734495211546245324030097309_<199>]

Using B1=5000000, B2=23417929090, polynomial Dickson(12), sigma=907905841 Step 1 took 40103ms Step 2 took 28475ms ********** Factor found in step 2: 25422133258858709804303131627232676780973 Found probable prime factor of 41 digits: 25422133258858709804303131627232676780973 Composite cofactor has 199 digits
(41·10¹²⁸-23)/9 = 4(5)₁₂₇3_<129> = 3 · 967 · 1217 · 1987 · 4421 · 1581473 · 99039401 · C101
C101 = P32 · P70
P32 = 36815704935774161283902098630699_<32>
P70 = 2547309708588572668816893086055764752839607538779524027891261431143921_<70>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3995894486 Step 1 took 8241ms Step 2 took 8956ms ********** Factor found in step 2: 36815704935774161283902098630699 Found probable prime factor of 32 digits: 36815704935774161283902098630699 Probable prime cofactor 2547309708588572668816893086055764752839607538779524027891261431143921 has 70 digits
(41·10¹⁷¹-23)/9 = 4(5)₁₇₀3_<172> = 29 · 1253249 · 5380782097_<10> · C155
C155 = P31 · P125
P31 = 1463794900797595489324207413307_<31>
P125 = 15914036422945819678315903115949927673919089268637693940382042994674920656345122295731706640532780037792152348394058778535167_<125>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1832035179 Step 1 took 4149ms Step 2 took 3431ms ********** Factor found in step 2: 1463794900797595489324207413307 Found probable prime factor of 31 digits: 1463794900797595489324207413307
(41·10¹⁸⁰-23)/9 = 4(5)₁₇₉3_<181> = 283 · 52385059 · 1021842427_<10> · 5329217405573587_<16> · C146
C146 = P31 · P116
P31 = 1236015933287564641565112604157_<31>
P116 = 45653705905749501607668550745050362451412108047028724874923313666054388301773089959197844701598951814422751612491493_<116>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1040011698 Step 1 took 3317ms Step 2 took 3189ms ********** Factor found in step 2: 1236015933287564641565112604157 Found probable prime factor of 31 digits: 1236015933287564641565112604157
(41·10¹²⁴-23)/9 = 4(5)₁₂₃3_<125> = 17 · 105603271 · C116
C116 = P29 · P43 · P45
P29 = 65888693420744699362403856113_<29>
P43 = 2542943309278235960488509909300823318289419_<43>
P45 = 151449373643723932213841050457974953231496357_<45>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2501097197 Step 1 took 8922ms Step 2 took 8826ms ********** Factor found in step 2: 65888693420744699362403856113 Found probable prime factor of 29 digits: 65888693420744699362403856113 Composite cofactor has 87 digits Wed Jan 28 11:15:04 2009 Msieve v. 1.39 Wed Jan 28 11:15:04 2009 random seeds: 275c7966 7c142380 Wed Jan 28 11:15:04 2009 factoring 385127171401687385207501402488493862650469459394203243914566369266391722206958970146583 (87 digits) Wed Jan 28 11:15:04 2009 searching for 15-digit factors Wed Jan 28 11:15:05 2009 commencing quadratic sieve (87-digit input) Wed Jan 28 11:15:05 2009 using multiplier of 3 Wed Jan 28 11:15:05 2009 using 64kb Opteron sieve core Wed Jan 28 11:15:05 2009 sieve interval: 10 blocks of size 65536 Wed Jan 28 11:15:05 2009 processing polynomials in batches of 11 Wed Jan 28 11:15:05 2009 using a sieve bound of 1483927 (56667 primes) Wed Jan 28 11:15:05 2009 using large prime bound of 118714160 (26 bits) Wed Jan 28 11:15:05 2009 using double large prime bound of 342061674768240 (42-49 bits) Wed Jan 28 11:15:05 2009 using trial factoring cutoff of 49 bits Wed Jan 28 11:15:05 2009 polynomial 'A' values have 11 factors Wed Jan 28 11:55:01 2009 56875 relations (15830 full + 41045 combined from 594180 partial), need 56763 Wed Jan 28 11:55:01 2009 begin with 610010 relations Wed Jan 28 11:55:02 2009 reduce to 136243 relations in 9 passes Wed Jan 28 11:55:02 2009 attempting to read 136243 relations Wed Jan 28 11:55:03 2009 recovered 136243 relations Wed Jan 28 11:55:03 2009 recovered 116276 polynomials Wed Jan 28 11:55:03 2009 attempting to build 56875 cycles Wed Jan 28 11:55:03 2009 found 56875 cycles in 5 passes Wed Jan 28 11:55:03 2009 distribution of cycle lengths: Wed Jan 28 11:55:03 2009 length 1 : 15830 Wed Jan 28 11:55:03 2009 length 2 : 11102 Wed Jan 28 11:55:03 2009 length 3 : 10213 Wed Jan 28 11:55:03 2009 length 4 : 7378 Wed Jan 28 11:55:03 2009 length 5 : 5089 Wed Jan 28 11:55:03 2009 length 6 : 3212 Wed Jan 28 11:55:03 2009 length 7 : 1901 Wed Jan 28 11:55:03 2009 length 9+: 2150 Wed Jan 28 11:55:03 2009 largest cycle: 18 relations Wed Jan 28 11:55:03 2009 matrix is 56667 x 56875 (14.0 MB) with weight 3216000 (56.55/col) Wed Jan 28 11:55:03 2009 sparse part has weight 3216000 (56.55/col) Wed Jan 28 11:55:04 2009 filtering completed in 3 passes Wed Jan 28 11:55:04 2009 matrix is 52253 x 52317 (13.0 MB) with weight 2983093 (57.02/col) Wed Jan 28 11:55:04 2009 sparse part has weight 2983093 (57.02/col) Wed Jan 28 11:55:04 2009 saving the first 48 matrix rows for later Wed Jan 28 11:55:04 2009 matrix is 52205 x 52317 (8.6 MB) with weight 2356656 (45.05/col) Wed Jan 28 11:55:04 2009 sparse part has weight 1732285 (33.11/col) Wed Jan 28 11:55:04 2009 matrix includes 64 packed rows Wed Jan 28 11:55:04 2009 using block size 20926 for processor cache size 1024 kB Wed Jan 28 11:55:04 2009 commencing Lanczos iteration Wed Jan 28 11:55:04 2009 memory use: 7.7 MB Wed Jan 28 11:55:18 2009 lanczos halted after 827 iterations (dim = 52203) Wed Jan 28 11:55:18 2009 recovered 16 nontrivial dependencies Wed Jan 28 11:55:19 2009 prp43 factor: 2542943309278235960488509909300823318289419 Wed Jan 28 11:55:19 2009 prp45 factor: 151449373643723932213841050457974953231496357 Wed Jan 28 11:55:19 2009 elapsed time 00:40:15
(41·10¹⁴⁰-23)/9 = 4(5)₁₃₉3_<141> = 3² · 17 · 877 · 19246389499_<11> · 32476760901407_<14> · C112
C112 = P38 · P75
P38 = 23113065209519892999049301512692497833_<38>
P75 = 235001589601884725897441826945509931421660229052691677615339453591200234977_<75>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1100794531 Step 1 took 8421ms Step 2 took 9318ms ********** Factor found in step 2: 23113065209519892999049301512692497833 Found probable prime factor of 38 digits: 23113065209519892999049301512692497833 Probable prime cofactor has 75 digits
(41·10¹⁵⁰-23)/9 = 4(5)₁₄₉3_<151> = 71 · 181 · 461 · 467 · 56663 · C137
C137 = P32 · P49 · P57
P32 = 33408920017609314616108752626191_<32>
P49 = 2321894412504908509073233224243572594876465727407_<49>
P57 = 374612401179637846452271743435694521178321815681110300299_<57>

# I am very grateful to Mr.Erik Branger who kindly released this number # after the factor was found # # When I run ECM, I remove numbers (which are reserved by others) periodically - # but sometimes an overlap happens: a number is cracked and turns out to be reserved. I usually dismiss such factors. This p49 was a quite a bit lucky... # Thank you, Erik! Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4014584566 Step 1 took 11854ms Step 2 took 11645ms ********** Factor found in step 2: 2321894412504908509073233224243572594876465727407 Found probable prime factor of 49 digits: 2321894412504908509073233224243572594876465727407 Composite cofactor has 89 digits Wed Jan 28 15:13:15 2009 Msieve v. 1.39 Wed Jan 28 15:13:15 2009 random seeds: dcc1d19f 8003f6d6 Wed Jan 28 15:13:15 2009 factoring 12515395748615094072564422948254398042726817026678117369398473451436798060732256902531109 (89 digits) Wed Jan 28 15:13:15 2009 searching for 15-digit factors Wed Jan 28 15:13:16 2009 commencing quadratic sieve (89-digit input) Wed Jan 28 15:13:16 2009 using multiplier of 1 Wed Jan 28 15:13:16 2009 using 64kb Opteron sieve core Wed Jan 28 15:13:16 2009 sieve interval: 14 blocks of size 65536 Wed Jan 28 15:13:16 2009 processing polynomials in batches of 8 Wed Jan 28 15:13:16 2009 using a sieve bound of 1537153 (58332 primes) Wed Jan 28 15:13:16 2009 using large prime bound of 122972240 (26 bits) Wed Jan 28 15:13:16 2009 using double large prime bound of 364462296550480 (42-49 bits) Wed Jan 28 15:13:16 2009 using trial factoring cutoff of 49 bits Wed Jan 28 15:13:16 2009 polynomial 'A' values have 11 factors Wed Jan 28 15:51:53 2009 58627 relations (16387 full + 42240 combined from 612438 partial), need 58428 Wed Jan 28 15:51:53 2009 begin with 628825 relations Wed Jan 28 15:51:54 2009 reduce to 140159 relations in 10 passes Wed Jan 28 15:51:54 2009 attempting to read 140159 relations Wed Jan 28 15:51:55 2009 recovered 140159 relations Wed Jan 28 15:51:55 2009 recovered 112789 polynomials Wed Jan 28 15:51:55 2009 attempting to build 58627 cycles Wed Jan 28 15:51:55 2009 found 58627 cycles in 5 passes Wed Jan 28 15:51:55 2009 distribution of cycle lengths: Wed Jan 28 15:51:55 2009 length 1 : 16387 Wed Jan 28 15:51:55 2009 length 2 : 11480 Wed Jan 28 15:51:55 2009 length 3 : 10452 Wed Jan 28 15:51:55 2009 length 4 : 7680 Wed Jan 28 15:51:55 2009 length 5 : 5251 Wed Jan 28 15:51:55 2009 length 6 : 3344 Wed Jan 28 15:51:55 2009 length 7 : 1897 Wed Jan 28 15:51:55 2009 length 9+: 2136 Wed Jan 28 15:51:55 2009 largest cycle: 20 relations Wed Jan 28 15:51:55 2009 matrix is 58332 x 58627 (14.7 MB) with weight 3371755 (57.51/col) Wed Jan 28 15:51:55 2009 sparse part has weight 3371755 (57.51/col) Wed Jan 28 15:51:56 2009 filtering completed in 3 passes Wed Jan 28 15:51:56 2009 matrix is 53667 x 53731 (13.5 MB) with weight 3121580 (58.10/col) Wed Jan 28 15:51:56 2009 sparse part has weight 3121580 (58.10/col) Wed Jan 28 15:51:56 2009 saving the first 48 matrix rows for later Wed Jan 28 15:51:56 2009 matrix is 53619 x 53731 (9.6 MB) with weight 2500423 (46.54/col) Wed Jan 28 15:51:56 2009 sparse part has weight 1968488 (36.64/col) Wed Jan 28 15:51:56 2009 matrix includes 64 packed rows Wed Jan 28 15:51:56 2009 using block size 21492 for processor cache size 1024 kB Wed Jan 28 15:51:57 2009 commencing Lanczos iteration Wed Jan 28 15:51:57 2009 memory use: 8.2 MB Wed Jan 28 15:52:15 2009 lanczos halted after 849 iterations (dim = 53619) Wed Jan 28 15:52:15 2009 recovered 17 nontrivial dependencies Wed Jan 28 15:52:16 2009 prp32 factor: 33408920017609314616108752626191 Wed Jan 28 15:52:16 2009 prp57 factor: 374612401179637846452271743435694521178321815681110300299 Wed Jan 28 15:52:16 2009 elapsed time 00:39:01
(41·10¹⁹⁷-23)/9 = 4(5)₁₉₆3_<198> = 3 · 7 · 107 · 13177 · 23081 · 7187963 · C179
C179 = P34 · P146
P34 = 2099403606495907277667888894462749_<34>
P146 = 44173858540728534572528842326705003005252228743462183058663832241052976873235501629877640848318099432460716303937164016586774713227903561777753721_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2823049403 Step 1 took 15948ms ********** Factor found in step 1: 2099403606495907277667888894462749 Found probable prime factor of 34 digits: 2099403606495907277667888894462749 Probable prime cofactor has 146 digits
(41·10¹⁴⁹-23)/9 = 4(5)₁₄₈3_<150> = 3⁵ · 7 · 6345629 · 325563926267_<12> · 39321173758731261670625114839_<29> · C100
C100 = P40 · P61
P40 = 2906390360860183929041325401980600571603_<40>
P61 = 1134346306261106620176688918771075343769204867780752154765463_<61>

Divisors found: r1=2906390360860183929041325401980600571603 (pp40) r2=1134346306261106620176688918771075343769204867780752154765463 (pp61) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.884). Factorization parameters were as follows: n: 3296853170394634386426903479758021052421717743274532650918450384213305617576039420469949938202947189 skew: 5917.96 # norm 5.93e+13 c5: 57120 c4: -320192048 c3: -593092523794 c2: -5737521223828465 c1: -90444080558235915828 c0: -4032485409702275555140 # alpha -5.83 Y1: 5964523141 Y0: -8959063309188302307 # Murphy_E 3.41e-09 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 [900000, 1400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 183693 x 183941 Total sieving time: 0.00 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: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 4.50 hours.
(41·10¹³⁸-23)/9 = 4(5)₁₃₇3_<139> = 5783 · C135
C135 = P65 · P71
P65 = 31826703588216506921591134020605913404953501401931568298791155907_<65>
P71 = 24751213454811777993464835171415082026382268067334361474439281562727213_<71>

SNFS difficulty: 141 digits. Divisors found: r1=31826703588216506921591134020605913404953501401931568298791155907 (pp65) r2=24751213454811777993464835171415082026382268067334361474439281562727213 (pp71) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.301). Factorization parameters were as follows: n: 787749534074970699560013065114223682440870751436201894441562433953926258958249274694026552923319307548946144830633850173881299594597191 m: 5000000000000000000000000000 deg: 5 c5: 328 c0: -575 skew: 1.12 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [800000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 277212 x 277460 Total sieving time: 0.00 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,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,49,49,2.4,2.4,100000 total time: 10.00 hours.
Jan 29, 2009 (3rd): By Erik Branger / Msieve, GGNFS / Jan 29, 2009
(41·10¹³⁰-23)/9 = 4(5)₁₂₉3_<131> = 313 · 36847 · 9836292279467_<13> · 86954811961293481335701497_<26> · C85
C85 = P42 · P43
P42 = 881390449722686422846375486232579191674737_<42>
P43 = 5239640491095494706973558926511971332248621_<43>

Wed Jan 28 16:28:26 2009 Msieve v. 1.38 Wed Jan 28 16:28:26 2009 random seeds: 9bceceb0 5c6c8cd8 Wed Jan 28 16:28:26 2009 factoring 4618169088831855625167377731803863520723223439399359351692257045372290483853048787677 (85 digits) Wed Jan 28 16:28:27 2009 searching for 15-digit factors Wed Jan 28 16:28:28 2009 commencing quadratic sieve (85-digit input) Wed Jan 28 16:28:28 2009 using multiplier of 5 Wed Jan 28 16:28:28 2009 using 64kb Pentium 4 sieve core Wed Jan 28 16:28:28 2009 sieve interval: 6 blocks of size 65536 Wed Jan 28 16:28:28 2009 processing polynomials in batches of 17 Wed Jan 28 16:28:28 2009 using a sieve bound of 1429849 (54706 primes) Wed Jan 28 16:28:28 2009 using large prime bound of 115817769 (26 bits) Wed Jan 28 16:28:29 2009 using double large prime bound of 327186471420459 (41-49 bits) Wed Jan 28 16:28:29 2009 using trial factoring cutoff of 49 bits Wed Jan 28 16:28:29 2009 polynomial 'A' values have 11 factors Wed Jan 28 17:11:40 2009 54993 relations (16294 full + 38699 combined from 569218 partial), need 54802 Wed Jan 28 17:11:43 2009 begin with 585512 relations Wed Jan 28 17:11:43 2009 reduce to 127938 relations in 10 passes Wed Jan 28 17:11:43 2009 attempting to read 127938 relations Wed Jan 28 17:11:48 2009 recovered 127938 relations Wed Jan 28 17:11:48 2009 recovered 105631 polynomials Wed Jan 28 17:11:48 2009 attempting to build 54993 cycles Wed Jan 28 17:11:48 2009 found 54993 cycles in 5 passes Wed Jan 28 17:11:48 2009 distribution of cycle lengths: Wed Jan 28 17:11:48 2009 length 1 : 16294 Wed Jan 28 17:11:48 2009 length 2 : 11182 Wed Jan 28 17:11:48 2009 length 3 : 9843 Wed Jan 28 17:11:48 2009 length 4 : 7059 Wed Jan 28 17:11:48 2009 length 5 : 4643 Wed Jan 28 17:11:48 2009 length 6 : 2735 Wed Jan 28 17:11:48 2009 length 7 : 1552 Wed Jan 28 17:11:48 2009 length 9+: 1685 Wed Jan 28 17:11:48 2009 largest cycle: 17 relations Wed Jan 28 17:11:48 2009 matrix is 54706 x 54993 (11.6 MB) with weight 2819163 (51.26/col) Wed Jan 28 17:11:48 2009 sparse part has weight 2819163 (51.26/col) Wed Jan 28 17:11:49 2009 filtering completed in 3 passes Wed Jan 28 17:11:49 2009 matrix is 49283 x 49347 (10.5 MB) with weight 2553042 (51.74/col) Wed Jan 28 17:11:49 2009 sparse part has weight 2553042 (51.74/col) Wed Jan 28 17:11:49 2009 saving the first 48 matrix rows for later Wed Jan 28 17:11:49 2009 matrix is 49235 x 49347 (5.8 MB) with weight 1870616 (37.91/col) Wed Jan 28 17:11:49 2009 sparse part has weight 1212608 (24.57/col) Wed Jan 28 17:11:49 2009 matrix includes 64 packed rows Wed Jan 28 17:11:49 2009 using block size 19738 for processor cache size 512 kB Wed Jan 28 17:11:50 2009 commencing Lanczos iteration Wed Jan 28 17:11:50 2009 memory use: 6.3 MB Wed Jan 28 17:12:10 2009 lanczos halted after 780 iterations (dim = 49234) Wed Jan 28 17:12:10 2009 recovered 17 nontrivial dependencies Wed Jan 28 17:12:11 2009 prp42 factor: 881390449722686422846375486232579191674737 Wed Jan 28 17:12:11 2009 prp43 factor: 5239640491095494706973558926511971332248621 Wed Jan 28 17:12:11 2009 elapsed time 00:43:45
(41·10¹⁴⁸-23)/9 = 4(5)₁₄₇3_<149> = 43 · 251 · 568693575908293016347929797_<27> · 74447260787252610730701827479_<29> · C89
C89 = P42 · P48
P42 = 148975555407778170069581589916437657429373_<42>
P48 = 669201817267739198737277759103990448518471426079_<48>

Wed Jan 28 16:28:55 2009 Msieve v. 1.39 Wed Jan 28 16:28:55 2009 random seeds: b9762c40 a5997af9 Wed Jan 28 16:28:55 2009 factoring 99694712407355923179818470270485392821917098122466030908415422358077625320009088532818467 (89 digits) Wed Jan 28 16:28:56 2009 searching for 15-digit factors Wed Jan 28 16:28:57 2009 commencing quadratic sieve (89-digit input) Wed Jan 28 16:28:57 2009 using multiplier of 3 Wed Jan 28 16:28:57 2009 using 32kb Intel Core sieve core Wed Jan 28 16:28:57 2009 sieve interval: 33 blocks of size 32768 Wed Jan 28 16:28:57 2009 processing polynomials in batches of 7 Wed Jan 28 16:28:57 2009 using a sieve bound of 1558267 (59333 primes) Wed Jan 28 16:28:57 2009 using large prime bound of 124661360 (26 bits) Wed Jan 28 16:28:57 2009 using double large prime bound of 373522957629360 (42-49 bits) Wed Jan 28 16:28:57 2009 using trial factoring cutoff of 49 bits Wed Jan 28 16:28:57 2009 polynomial 'A' values have 11 factors Wed Jan 28 17:37:37 2009 59692 relations (16146 full + 43546 combined from 629922 partial), need 59429 Wed Jan 28 17:37:38 2009 begin with 646068 relations Wed Jan 28 17:37:38 2009 reduce to 145663 relations in 10 passes Wed Jan 28 17:37:38 2009 attempting to read 145663 relations Wed Jan 28 17:37:40 2009 recovered 145663 relations Wed Jan 28 17:37:40 2009 recovered 124755 polynomials Wed Jan 28 17:37:40 2009 attempting to build 59692 cycles Wed Jan 28 17:37:40 2009 found 59692 cycles in 6 passes Wed Jan 28 17:37:40 2009 distribution of cycle lengths: Wed Jan 28 17:37:40 2009 length 1 : 16146 Wed Jan 28 17:37:40 2009 length 2 : 11175 Wed Jan 28 17:37:40 2009 length 3 : 10326 Wed Jan 28 17:37:40 2009 length 4 : 7991 Wed Jan 28 17:37:40 2009 length 5 : 5681 Wed Jan 28 17:37:40 2009 length 6 : 3608 Wed Jan 28 17:37:40 2009 length 7 : 2154 Wed Jan 28 17:37:40 2009 length 9+: 2611 Wed Jan 28 17:37:40 2009 largest cycle: 20 relations Wed Jan 28 17:37:40 2009 matrix is 59333 x 59692 (14.8 MB) with weight 3634461 (60.89/col) Wed Jan 28 17:37:40 2009 sparse part has weight 3634461 (60.89/col) Wed Jan 28 17:37:41 2009 filtering completed in 3 passes Wed Jan 28 17:37:41 2009 matrix is 55373 x 55437 (13.8 MB) with weight 3393295 (61.21/col) Wed Jan 28 17:37:41 2009 sparse part has weight 3393295 (61.21/col) Wed Jan 28 17:37:41 2009 saving the first 48 matrix rows for later Wed Jan 28 17:37:41 2009 matrix is 55325 x 55437 (10.4 MB) with weight 2859681 (51.58/col) Wed Jan 28 17:37:41 2009 sparse part has weight 2396355 (43.23/col) Wed Jan 28 17:37:41 2009 matrix includes 64 packed rows Wed Jan 28 17:37:41 2009 using block size 22174 for processor cache size 2048 kB Wed Jan 28 17:37:42 2009 commencing Lanczos iteration Wed Jan 28 17:37:42 2009 memory use: 9.3 MB Wed Jan 28 17:37:59 2009 lanczos halted after 876 iterations (dim = 55325) Wed Jan 28 17:37:59 2009 recovered 18 nontrivial dependencies Wed Jan 28 17:38:00 2009 prp42 factor: 148975555407778170069581589916437657429373 Wed Jan 28 17:38:00 2009 prp48 factor: 669201817267739198737277759103990448518471426079 Wed Jan 28 17:38:00 2009 elapsed time 01:09:05
(41·10¹¹⁹-23)/9 = 4(5)₁₁₈3_<120> = 3 · 7 · 19 · C118
C118 = P44 · P74
P44 = 13204137097414283580303342290636923082729711_<44>
P74 = 86468599847390874149233253667621779699370576402751798197713344576119700577_<74>

Number: 45553_119 N=1141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247 ( 118 digits) SNFS difficulty: 121 digits. Divisors found: r1=13204137097414283580303342290636923082729711 r2=86468599847390874149233253667621779699370576402751798197713344576119700577 Version: Total time: 2.59 hours. Scaled time: 5.48 units (timescale=2.116). Factorization parameters were as follows: n: 1141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247006404901141743247 m: 1000000000000000000000000 deg: 5 c5: 41 c0: -230 skew: 1.41 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 720001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 88538 x 88786 Total sieving time: 2.59 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,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 2.59 hours. --------- CPU info (if available) ----------
(41·10¹²¹-23)/9 = 4(5)₁₂₀3_<122> = 193 · 3535877 · 746305381 · C104
C104 = P49 · P56
P49 = 6424734750718627625220006148533474581870541453749_<49>
P56 = 13922432274087936529154302972714446189901873148104111717_<56>

Number: 45553_121 N=89447934445859334817066221992763935132167607196659414011628506260431975722429438832612506174321484477033 ( 104 digits) SNFS difficulty: 122 digits. Divisors found: r1=6424734750718627625220006148533474581870541453749 r2=13922432274087936529154302972714446189901873148104111717 Version: Total time: 2.23 hours. Scaled time: 4.46 units (timescale=2.003). Factorization parameters were as follows: n: 89447934445859334817066221992763935132167607196659414011628506260431975722429438832612506174321484477033 m: 1000000000000000000000000 deg: 5 c5: 410 c0: -23 skew: 0.56 type: snfs lss: 1 rlim: 770000 alim: 770000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2Factor base limits: 770000/770000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [385000, 685001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 95980 x 96228 Total sieving time: 2.23 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,122,5,0,0,0,0,0,0,0,0,770000,770000,25,25,46,46,2.2,2.2,50000 total time: 2.23 hours. --------- CPU info (if available) ----------
(41·10¹¹⁸-23)/9 = 4(5)₁₁₇3_<119> = 449153 · 5529329228987_<13> · C101
C101 = P32 · P69
P32 = 21601921391699076224361216972323_<32>
P69 = 849145693764416742375873463293188330565808251248427942826893089602001_<69>

Number: 45553_118 N=18343178526798706907297331767407580668174940804953852814701597268572385811455413189451069954302418323 ( 101 digits) SNFS difficulty: 121 digits. Divisors found: r1=21601921391699076224361216972323 r2=849145693764416742375873463293188330565808251248427942826893089602001 Version: Total time: 2.91 hours. Scaled time: 2.30 units (timescale=0.790). Factorization parameters were as follows: n: 18343178526798706907297331767407580668174940804953852814701597268572385811455413189451069954302418323 m: 500000000000000000000000 deg: 5 c5: 328 c0: -575 skew: 1.12 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 715001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 88452 x 88688 Total sieving time: 2.91 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,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 2.91 hours. --------- CPU info (if available) ----------
(41·10¹²⁵-23)/9 = 4(5)₁₂₄3_<126> = 3 · 7 · C125
C125 = P50 · P76
P50 = 18865962222763737173683333927093976699335628416363_<50>
P76 = 1149855037181548856673552853646671174178134269707019655492195514770948005911_<76>

Number: 45553_125 N=21693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693 ( 125 digits) SNFS difficulty: 126 digits. Divisors found: r1=18865962222763737173683333927093976699335628416363 r2=1149855037181548856673552853646671174178134269707019655492195514770948005911 Version: Total time: 2.71 hours. Scaled time: 5.46 units (timescale=2.016). Factorization parameters were as follows: n: 21693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693121693 m: 10000000000000000000000000 deg: 5 c5: 41 c0: -23 skew: 0.89 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 110535 x 110774 Total sieving time: 2.71 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,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.71 hours. --------- CPU info (if available) ----------
Jan 29, 2009 (2nd): By Ignacio Santos / Msieve 1.39, Yafu 1.06 / Jan 29, 2009
(41·10¹⁰⁵-23)/9 = 4(5)₁₀₄3_<106> = 953 · 9595367 · 702317546407_<12> · C84
C84 = P42 · P43
P42 = 367779635852490880335270511439720960675651_<42>
P43 = 1928704346839101571853571281460612074420179_<43>

Wed Jan 28 16:29:33 2009 Wed Jan 28 16:29:33 2009 Wed Jan 28 16:29:33 2009 Msieve v. 1.39 Wed Jan 28 16:29:33 2009 random seeds: 8259fdd8 6aed4e44 Wed Jan 28 16:29:33 2009 factoring 709338182347601046367561329521658935509574931985120281467871275483245561945908361529 (84 digits) Wed Jan 28 16:29:34 2009 searching for 15-digit factors Wed Jan 28 16:29:35 2009 commencing quadratic sieve (84-digit input) Wed Jan 28 16:29:35 2009 using multiplier of 1 Wed Jan 28 16:29:35 2009 using 32kb Intel Core sieve core Wed Jan 28 16:29:35 2009 sieve interval: 12 blocks of size 32768 Wed Jan 28 16:29:35 2009 processing polynomials in batches of 17 Wed Jan 28 16:29:35 2009 using a sieve bound of 1401437 (53824 primes) Wed Jan 28 16:29:35 2009 using large prime bound of 119122145 (26 bits) Wed Jan 28 16:29:35 2009 using trial factoring cutoff of 27 bits Wed Jan 28 16:29:35 2009 polynomial 'A' values have 11 factors Wed Jan 28 16:52:29 2009 54034 relations (27656 full + 26378 combined from 277915 partial), need 53920 Wed Jan 28 16:52:29 2009 begin with 305571 relations Wed Jan 28 16:52:29 2009 reduce to 77053 relations in 2 passes Wed Jan 28 16:52:29 2009 attempting to read 77053 relations Wed Jan 28 16:52:30 2009 recovered 77053 relations Wed Jan 28 16:52:30 2009 recovered 70831 polynomials Wed Jan 28 16:52:30 2009 attempting to build 54034 cycles Wed Jan 28 16:52:30 2009 found 54034 cycles in 1 passes Wed Jan 28 16:52:30 2009 distribution of cycle lengths: Wed Jan 28 16:52:30 2009 length 1 : 27656 Wed Jan 28 16:52:30 2009 length 2 : 26378 Wed Jan 28 16:52:30 2009 largest cycle: 2 relations Wed Jan 28 16:52:30 2009 matrix is 53824 x 54034 (7.4 MB) with weight 1717018 (31.78/col) Wed Jan 28 16:52:30 2009 sparse part has weight 1717018 (31.78/col) Wed Jan 28 16:52:30 2009 filtering completed in 3 passes Wed Jan 28 16:52:30 2009 matrix is 39180 x 39243 (5.9 MB) with weight 1381772 (35.21/col) Wed Jan 28 16:52:30 2009 sparse part has weight 1381772 (35.21/col) Wed Jan 28 16:52:30 2009 saving the first 48 matrix rows for later Wed Jan 28 16:52:30 2009 matrix is 39132 x 39243 (3.7 MB) with weight 1032357 (26.31/col) Wed Jan 28 16:52:30 2009 sparse part has weight 734730 (18.72/col) Wed Jan 28 16:52:30 2009 matrix includes 64 packed rows Wed Jan 28 16:52:30 2009 using block size 15697 for processor cache size 4096 kB Wed Jan 28 16:52:30 2009 commencing Lanczos iteration Wed Jan 28 16:52:30 2009 memory use: 4.3 MB Wed Jan 28 16:52:35 2009 lanczos halted after 621 iterations (dim = 39131) Wed Jan 28 16:52:35 2009 recovered 16 nontrivial dependencies Wed Jan 28 16:52:35 2009 prp42 factor: 367779635852490880335270511439720960675651 Wed Jan 28 16:52:35 2009 prp43 factor: 1928704346839101571853571281460612074420179 Wed Jan 28 16:52:35 2009 elapsed time 00:23:02
(41·10¹²²-23)/9 = 4(5)₁₂₁3_<123> = 3³ · 409 · 32987 · 467868311 · 2534846137715117_<16> · C91
C91 = P39 · P52
P39 = 458015487802174727396287622703879436789_<39>
P52 = 2302268949633360740904310241142947031318315208517831_<52>

01/28/09 17:21:40 v1.06 @ IGNACIO1, starting SIQS on c91: 1054474836018124158257047066798769193462469896437805554332753148131097644739785979743884659 01/28/09 17:21:40 v1.06 @ IGNACIO1, ==== sieve params ==== 01/28/09 17:21:40 v1.06 @ IGNACIO1, n = 91 digits, 304 bits 01/28/09 17:21:40 v1.06 @ IGNACIO1, factor base: 67412 primes (max prime = 1794517) 01/28/09 17:21:40 v1.06 @ IGNACIO1, single large prime cutoff: 215342040 (120 * pmax) 01/28/09 17:21:40 v1.06 @ IGNACIO1, double large prime range from 43 to 50 bits 01/28/09 17:21:40 v1.06 @ IGNACIO1, double large prime cutoff: 999152734477817 01/28/09 17:21:40 v1.06 @ IGNACIO1, using 10 large prime slices of factor base 01/28/09 17:21:40 v1.06 @ IGNACIO1, buckets hold 1024 elements 01/28/09 17:21:40 v1.06 @ IGNACIO1, sieve interval: 22 blocks of size 32768 01/28/09 17:21:40 v1.06 @ IGNACIO1, polynomial A has ~ 12 factors 01/28/09 17:21:40 v1.06 @ IGNACIO1, using multiplier of 29 01/28/09 17:21:40 v1.06 @ IGNACIO1, using small prime variation correction of 22 bits 01/28/09 17:21:40 v1.06 @ IGNACIO1, trial factoring cutoff at 97 bits 01/28/09 17:21:40 v1.06 @ IGNACIO1, ==== sieving started ==== 01/28/09 18:22:30 v1.06 @ IGNACIO1, sieve time = 1199.1730, relation time = 820.1540, poly_time = 1601.3640 01/28/09 18:22:30 v1.06 @ IGNACIO1, 67481 relations found: 19365 full + 48116 from 818643 partial, using 428968 polys (209 A polys) 01/28/09 18:22:30 v1.06 @ IGNACIO1, trial division touched 28729166 sieve locations out of 618482630656 01/28/09 18:22:30 v1.06 @ IGNACIO1, ==== post processing stage (msieve-1.38) ==== 01/28/09 18:22:31 v1.06 @ IGNACIO1, begin with 838008 relations 01/28/09 18:22:31 v1.06 @ IGNACIO1, reduce to 157869 relations in 10 passes 01/28/09 18:22:33 v1.06 @ IGNACIO1, recovered 157869 relations 01/28/09 18:22:33 v1.06 @ IGNACIO1, recovered 132185 polynomials 01/28/09 18:22:33 v1.06 @ IGNACIO1, attempting to build 67481 cycles 01/28/09 18:22:33 v1.06 @ IGNACIO1, found 67481 cycles in 5 passes 01/28/09 18:22:33 v1.06 @ IGNACIO1, distribution of cycle lengths: 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 1 : 19365 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 2 : 14696 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 3 : 12271 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 4 : 8498 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 5 : 5579 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 6 : 3334 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 7 : 1819 01/28/09 18:22:33 v1.06 @ IGNACIO1, length 9+: 1919 01/28/09 18:22:33 v1.06 @ IGNACIO1, largest cycle: 18 relations 01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix is 67412 x 67481 (16.1 MB) with weight 3938485 (58.36/col) 01/28/09 18:22:34 v1.06 @ IGNACIO1, sparse part has weight 3938485 (58.36/col) 01/28/09 18:22:34 v1.06 @ IGNACIO1, filtering completed in 3 passes 01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix is 62217 x 62281 (15.0 MB) with weight 3685912 (59.18/col) 01/28/09 18:22:34 v1.06 @ IGNACIO1, sparse part has weight 3685912 (59.18/col) 01/28/09 18:22:34 v1.06 @ IGNACIO1, saving the first 48 matrix rows for later 01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix is 62169 x 62281 (10.0 MB) with weight 2926881 (46.99/col) 01/28/09 18:22:34 v1.06 @ IGNACIO1, sparse part has weight 2258498 (36.26/col) 01/28/09 18:22:34 v1.06 @ IGNACIO1, matrix includes 64 packed rows 01/28/09 18:22:34 v1.06 @ IGNACIO1, using block size 24912 for processor cache size 4096 kB 01/28/09 18:22:35 v1.06 @ IGNACIO1, commencing Lanczos iteration 01/28/09 18:22:35 v1.06 @ IGNACIO1, memory use: 9.5 MB 01/28/09 18:22:53 v1.06 @ IGNACIO1, lanczos halted after 985 iterations (dim = 62167) 01/28/09 18:22:53 v1.06 @ IGNACIO1, recovered 18 nontrivial dependencies 01/28/09 18:22:54 v1.06 @ IGNACIO1, prp52 = 2302268949633360740904310241142947031318315208517831 01/28/09 18:22:55 v1.06 @ IGNACIO1, prp39 = 458015487802174727396287622703879436789 01/28/09 18:22:55 v1.06 @ IGNACIO1, Lanczos elapsed time = 23.3690 seconds. 01/28/09 18:22:55 v1.06 @ IGNACIO1, Sqrt elapsed time = 2.2310 seconds. 01/28/09 18:22:55 v1.06 @ IGNACIO1, Total elapsed time = 3675.7900 seconds. 01/28/09 18:22:55 v1.06 @ IGNACIO1, 01/28/09 18:22:55 v1.06 @ IGNACIO1,
Jan 29, 2009: Factorizations of 455...553 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Jan 28, 2009 (3rd): By Robert Backstrom / GGNFS, Msieve / Jan 28, 2009
(64·10²⁶⁷-1)/9 = 7(1)₂₆₇_<268> = 13 · 4391 · 23929 · 36083 · 418460458963_<12> · 41647180748521_<14> · 1015426835807649035390773_<25> · 48287267091784318382365068194688977337835393445648868307_<56> · C150
C150 = P52 · P98
P52 = 2046177675001671248721526888669069941138882384733693_<52>
P98 = 82516129198420259258519024832071643294533917541647385866698598950636164516855352871556074606688239_<98>

Number: n N=168842661393361084737921889601152067797799178106973990993993426212219306097598366298890372513822132593172970190424243529986838118573215023486690136627 ( 150 digits) SNFS difficulty: 180 digits. Divisors found: Wed Jan 28 04:20:25 2009 prp52 factor: 2046177675001671248721526888669069941138882384733693 Wed Jan 28 04:20:25 2009 prp98 factor: 82516129198420259258519024832071643294533917541647385866698598950636164516855352871556074606688239 Wed Jan 28 04:20:25 2009 elapsed time 02:30:29 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 9.30 hours. Scaled time: 16.27 units (timescale=1.750). Factorization parameters were as follows: name: KA_7_1_267 n: 168842661393361084737921889601152067797799178106973990993993426212219306097598366298890372513822132593172970190424243529986838118573215023486690136627 deg: 6 c6: 4 c3: 10 c0: 25 m: 1000000000000000000000000000000 skew: 1.36 type: snfs rlim: 7500000 alim: 7500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 8250001) Primes: RFBsize:508261, AFBsize:507810, largePrimes:37433789 encountered Relations: rels:37525126, finalFF:1242382 Max relations in full relation-set: 28 Initial matrix: 1016137 x 1242382 with sparse part having weight 155967976. Pruned matrix : 849553 x 854697 with weight 135481370. Msieve: found 4171754 hash collisions in 39575190 relations Msieve: matrix is 1148262 x 1148510 (307.2 MB) Total sieving time: 8.33 hours. Total relation processing time: 0.97 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,180,6,0,0,0,0,0,0,0,0,7500000,7500000,29,29,58,58,2.5,2.5,100000 total time: 9.30 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830483) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830446) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22643.68 BogoMIPS).
Jan 28, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1 / Jan 28, 2009
(43·10²⁰²-7)/9 = 4(7)₂₀₂_<203> = 7331 · 2224447 · 4264331689_<10> · 3282544923857_<13> · 129162515387784254409797833_<27> · C145
C145 = P33 · C112
P33 = 894140490812561508197748839283473_<33>
C112 = [1812327796811753621163200021922067097052888721647496808031500412932013350729735549051173339843739136511233703573_<112>]

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=209624069 Step 1 took 3916ms Step 2 took 3799ms ********** Factor found in step 2: 894140490812561508197748839283473 Found probable prime factor of 33 digits: 894140490812561508197748839283473 Composite cofactor has 112 digits
(43·10²³⁸-7)/9 = 4(7)₂₃₈_<239> = 73 · 89 · 109 · 997 · 122701 · C225
C225 = P32 · P194
P32 = 16019823933833801017304935568263_<32>
P194 = 34425922146851837576638249702876396349794779344942534097092159794838474557251330373243197269039118582961540438685946281867896688525526005977130309937227882149560857611922657828168430494238139459_<194>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=1194573843 Step 1 took 7395ms Step 2 took 5997ms ********** Factor found in step 2: 16019823933833801017304935568263 Found probable prime factor of 32 digits: 16019823933833801017304935568263 Probable prime cofactor has 194 digits
(43·10²²⁰-7)/9 = 4(7)₂₂₀_<221> = 523 · 4057 · 656879521 · C206
C206 = P31 · P175
P31 = 3502562889301427433586357821611_<31>
P175 = 9786954860237792671607046950183269287102623628043042827218853752548798081325699178457017851643964035536282843620014130674361843688073589623733707551549094537798547254146976097_<175>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3982886919 Step 1 took 6067ms Step 2 took 5661ms ********** Factor found in step 2: 3502562889301427433586357821611 Found probable prime factor of 31 digits: 3502562889301427433586357821611 Probable prime cofactor has 175 digits
(43·10²⁰⁴-7)/9 = 4(7)₂₀₄_<205> = 1040355723593_<13> · 92650128269537_<14> · 717267726581621_<15> · C164
C164 = P33 · P131
P33 = 707556978655308658653936630923687_<33>
P131 = 97668687460140583325533653402275318211878194887345665390224627878545528890196304695329982444456944390617538106202072842223345362611_<131>

Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=4048053174 Step 1 took 900ms Step 2 took 592ms ********** Factor found in step 2: 707556978655308658653936630923687 Found probable prime factor of 33 digits: 707556978655308658653936630923687 Probable prime cofactor has 131 digits
(43·10²⁰⁶-7)/9 = 4(7)₂₀₆_<207> = 3 · 73 · 1197999487_<10> · 919272050133022870840781_<24> · 227091512033988664050765336907_<30> · C142
C142 = P31 · C111
P31 = 9979120019997928268416395684139_<31>
C111 = [874154093062940053723423566083923324074453222353223316638756093434022663299154755490033595932211400153439132793_<111>]

Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=748490644 Step 1 took 1189ms Step 2 took 740ms ********** Factor found in step 2: 9979120019997928268416395684139 Found probable prime factor of 31 digits: 9979120019997928268416395684139
(43·10²³⁰-7)/9 = 4(7)₂₃₀_<231> = 3 · 73 · C229
C229 = P27 · C202
P27 = 692730088823719508465086751_<27>
C202 = [3149327167508337424894687917653959013981952149120694102773275999128510834233614653207416330576776052801668066525911784723885214992039134786270169083745020741277257567117346186246575033521599505550100733_<202>]

Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=3170109874 Step 1 took 1812ms ********** Factor found in step 1: 692730088823719508465086751 Found probable prime factor of 27 digits: 692730088823719508465086751
(43·10²⁵⁰-7)/9 = 4(7)₂₅₀_<251> = C251
C251 = P42 · C210
P42 = 382055559643912628237678729323622320324517_<42>
C210 = [125054528253189447289899294516188810544311061053758161563935547216828629946964499418093698568954568490304175173591891013243054655738225373622583204023990174911869851275001232783069648585566026456246963123490781_<210>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2259809016 Step 1 took 79929ms Step 2 took 29982ms ********** Factor found in step 2: 382055559643912628237678729323622320324517 Found probable prime factor of 42 digits: 382055559643912628237678729323622320324517 Composite cofactor has 210 digits
(43·10²⁴⁵-7)/9 = 4(7)₂₄₅_<246> = 3² · C245
C245 = P38 · P47 · C161
P38 = 53598747618551486853933977572595599339_<38>
P47 = 27976147881343907065273464547470440058178217281_<47>
C161 = [35403066396506894069278844750214201009889285722256175087036574343440723864063382620752845855264935086210428287407910294761124301971887380413930153470653666732667_<161>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=45451499 Step 1 took 24228ms Step 2 took 20220ms ********** Factor found in step 2: 27976147881343907065273464547470440058178217281 Found probable prime factor of 47 digits: 27976147881343907065273464547470440058178217281 Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2389133407 Step 1 took 24160ms Step 2 took 20492ms ********** Factor found in step 2: 53598747618551486853933977572595599339 Found probable prime factor of 38 digits: 53598747618551486853933977572595599339 Composite cofactor ...
(43·10²³⁴-7)/9 = 4(7)₂₃₄_<235> = 8821 · 576493 · 63521290844627070769256161_<26> · C200
C200 = P42 · C158
P42 = 192264712908627279576854165210309221783217_<42>
C158 = [76929903377789411516700093310652483045899848288680400340995715116837047878585117428117743576767502256527687059432257791095117914169589812646186467347998067857_<158>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3778725536 Step 1 took 14404ms Step 2 took 2805ms ********** Factor found in step 2: 192264712908627279576854165210309221783217 Found probable prime factor of 42 digits: 192264712908627279576854165210309221783217 Composite cofactor has 158 digits
Jan 28, 2009: By Jo Yeong Uk / GMP-ECM / Jan 27, 2009
(8·10¹⁹¹+1)/9 = (8)₁₉₀9_<191> = 2609 · C188
C188 = P38 · P151
P38 = 19309596681702726210004771712508766867_<38>
P151 = 1764412783486459285717951078009843334141086331932434701677798688195359927405853534975872523428117711532280972811375506792046840790602551996700236286963_<151>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 34070099229164004940164388228780716323836293173203866956262510114560708658063966611302755419275158638899535794898002640432690260210382862740087730505515097312720923299689110344533878454921 (188 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3327473856 Step 1 took 19035ms Step 2 took 8027ms ********** Factor found in step 2: 19309596681702726210004771712508766867 Found probable prime factor of 38 digits: 19309596681702726210004771712508766867 Probable prime cofactor 1764412783486459285717951078009843334141086331932434701677798688195359927405853534975872523428117711532280972811375506792046840790602551996700236286963 has 151 digits
By Jo Yeong Uk / GMP-ECM / Jan 28, 2009
(13·10¹⁶³+17)/3 = 4(3)₁₆₂9_<164> = 7 · 241 · 317 · 8795430941251_<13> · 1985156050719971_<16> · C130
C130 = P39 · P92
P39 = 385707927893908191275285558306356222409_<39>
P92 = 12031988618847673970003210390549269057789807769464350948317521072724086706486418168409870769_<92>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 4640833398618822639460743910642182851226314326510127202032591287609238917161096442916131510784187204116371553691206889178711862521 (130 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=615671262 Step 1 took 11700ms Step 2 took 5511ms ********** Factor found in step 2: 385707927893908191275285558306356222409 Found probable prime factor of 39 digits: 385707927893908191275285558306356222409 Probable prime cofactor 12031988618847673970003210390549269057789807769464350948317521072724086706486418168409870769 has 92 digits
Jan 27, 2009 (2nd): Factorizations of 477...77 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Jan 27, 2009: By Erik Branger / GGNFS, Msieve / Jan 27, 2009
(13·10¹⁶⁴+11)/3 = 4(3)₁₆₃7_<165> = 19 · 41 · 796379 · C156
C156 = P72 · P85
P72 = 598661797073473238145780382200311271428592944554907156282580452950134593_<72>
P85 = 1166764738184177016523443436582987050721413715803341695737452720587804424134807603249_<85>

Number: 43337_164 N=698497474923299913146728475612118899596341156962299667492151519836772445023403568936203868454930027765602384708635557541702678174128868592063887794294092657 ( 156 digits) SNFS difficulty: 166 digits. Divisors found: r1=598661797073473238145780382200311271428592944554907156282580452950134593 r2=1166764738184177016523443436582987050721413715803341695737452720587804424134807603249 Version: Total time: 69.52 hours. Scaled time: 54.99 units (timescale=0.791). Factorization parameters were as follows: n: 698497474923299913146728475612118899596341156962299667492151519836772445023403568936203868454930027765602384708635557541702678174128868592063887794294092657 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: 110 skew: 1.53 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2050000, 3950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 707150 x 707398 Total sieving time: 69.52 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,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 69.52 hours. --------- CPU info (if available) ----------
(41·10¹⁷²+13)/9 = 4(5)₁₇₁7_<173> = C173
C173 = P66 · P107
P66 = 846809775727438855533422032738541504094448048857030030647203344013_<66>
P107 = 53796681216181945160186440747727142358218300032577430895455479542146640352712930288135316333731693886056889_<107>

Number: 45557_172 N=45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557 ( 173 digits) SNFS difficulty: 174 digits. Divisors found: r1=846809775727438855533422032738541504094448048857030030647203344013 r2=53796681216181945160186440747727142358218300032577430895455479542146640352712930288135316333731693886056889 Version: Total time: 153.02 hours. Scaled time: 301.75 units (timescale=1.972). Factorization parameters were as follows: n: 45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557 m: 20000000000000000000000000000000000 deg: 5 c5: 1025 c0: 104 skew: 0.63 type: snfs lss: 1 rlim: 5700000 alim: 5700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor base limits: 5700000/5700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2850000, 7850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1140833 x 1141081 Total sieving time: 153.02 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,174,5,0,0,0,0,0,0,0,0,5700000,5700000,27,27,52,52,2.4,2.4,100000 total time: 153.02 hours. --------- CPU info (if available) ----------
Jan 26, 2009 (2nd): By Wataru Sakai / Msieve / Jan 26, 2009
(38·10²⁰³+61)/9 = 4(2)₂₀₂9_<204> = 3 · C204
C204 = P40 · P164
P40 = 6856113896741631556597576234948868923421_<40>
P164 = 20527771688219442244535154146181623000054303924350561860790279591622429058862241151966970921841993193628897638361564188894699065035168720938479822972805057054160883_<164>

Number: 42229_203 N=140740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 ( 204 digits) SNFS difficulty: 205 digits. Divisors found: r1=6856113896741631556597576234948868923421 r2=20527771688219442244535154146181623000054303924350561860790279591622429058862241151966970921841993193628897638361564188894699065035168720938479822972805057054160883 Version: Total time: 1090.97 hours. Scaled time: 2159.02 units (timescale=1.979). Factorization parameters were as follows: n: 140740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 m: 50000000000000000000000000000000000000000 deg: 5 c5: 304 c0: 1525 skew: 1.38 type: snfs lss: 1 rlim: 19000000 alim: 19000000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 19000000/19000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [9500000, 20100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3217971 x 3218219 Total sieving time: 1090.97 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,205,5,0,0,0,0,0,0,0,0,19000000,19000000,29,29,56,56,2.6,2.6,100000 total time: 1090.97 hours. --------- CPU info (if available) ----------
Jan 26, 2009: By Serge Batalov / Msieve-1.39 / Jan 26, 2009
(43·10¹⁷⁹-7)/9 = 4(7)₁₇₉_<180> = 3 · 17² · 16363 · 37418617 · C165
C165 = P68 · P98
P68 = 14145656150669491298815154320590745375349211707577628084877873514139_<68>
P98 = 63625775577778579433341123264082604872882905945721415160648453020214286335148354296475720079558299_<98>

SNFS difficulty: 181 digits. Divisors found: r1=14145656150669491298815154320590745375349211707577628084877873514139 (pp68) r2=63625775577778579433341123264082604872882905945721415160648453020214286335148354296475720079558299 (pp98) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: n: 900028343642920268629193882313065164523095389608686033709901992697050423470050911286995509976226984775059263572750134624657136766028945840031740266801444602051289561 m: 1000000000000000000000000000000000000 deg: 5 c5: 43 c0: -70 skew: 1.10 type: snfs lss: 1 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [4000000, 6700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1586574 x 1586822 Total sieving time: 0.00 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,181,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,55,55,2.5,2.5,100000 total time: 200.00 hours.
Jan 25, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Jan 25, 2009
(38·10¹⁷¹+61)/9 = 4(2)₁₇₀9_<172> = 131 · C170
C170 = P56 · P115
P56 = 19656586353109644988628428880782557935174813548674463961_<56>
P115 = 1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319_<115>

Number: 42229_171 N=32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559 ( 170 digits) SNFS difficulty: 172 digits. Divisors found: r1=19656586353109644988628428880782557935174813548674463961 (pp56) r2=1639689791881402852262937784707669473345717597586097018290930889928565528828480997000727743404647721038578540516319 (pp115) Version: Msieve-1.39 Total time: 69.27 hours. Scaled time: 178.36 units (timescale=2.575). Factorization parameters were as follows: n: 32230703986429177268871925360474978795589482612383375742154368108566581849024597116200169635284139100932994062765055131467345207803223070398642917726887192536047497879559 m: 10000000000000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 5300000 alim: 5300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5300000/5300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2650000, 5950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 984707 x 984955 Total sieving time: 69.27 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,172,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000 total time: 69.27 hours. --------- CPU info (if available) ----------
Jan 25, 2009: By Jo Yeong Uk / GMP-ECM / Jan 25, 2009
(41·10¹⁶¹+13)/9 = 4(5)₁₆₀7_<162> = 19 · 313 · 224473 · 112463872818618759244091017_<27> · C127
C127 = P39 · P88
P39 = 424001769125093094621543918688662607163_<39>
P88 = 7156465706183242170212634190189296953128191851050556387767311790646055779703262249922957_<88>

GMP-ECM 6.1.3 [powered by GMP 4.2.2] [ECM] Input number is 3034354120104753360064970435795476897443162060598250583531604564172670129454802230625243157344730258350741251453786863506340991 (127 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3609433657 Step 1 took 75297ms Step 2 took 31281ms ********** Factor found in step 2: 424001769125093094621543918688662607163 Found probable prime factor of 39 digits: 424001769125093094621543918688662607163 Probable prime cofactor 7156465706183242170212634190189296953128191851050556387767311790646055779703262249922957 has 88 digits
Jan 24, 2009 (6th): By Sinkiti Sibata / GGNFS / Jan 24, 2009
(41·10¹⁴¹+13)/9 = 4(5)₁₄₀7_<142> = 3² · 7 · 293 · 331 · 22391 · 24847 · 178807 · 3914509373_<10> · C112
C112 = P48 · P65
P48 = 152943647887036111477247610987697036703626392511_<48>
P65 = 12518849987703023951410464231756309915231977459305480342194679649_<65>

Number: 45557_141 N=1914678584469877649316146631311483016914465974441251203654318046447997277245008118142822154997288621883177708639 ( 112 digits) SNFS difficulty: 143 digits. Divisors found: r1=152943647887036111477247610987697036703626392511 (pp48) r2=12518849987703023951410464231756309915231977459305480342194679649 (pp65) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 16.53 hours. Scaled time: 7.82 units (timescale=0.473). Factorization parameters were as follows: name: 45557_141 n: 1914678584469877649316146631311483016914465974441251203654318046447997277245008118142822154997288621883177708639 m: 20000000000000000000000000000 deg: 5 c5: 205 c0: 208 skew: 1.00 type: snfs lss: 1 rlim: 1750000 alim: 1750000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1750000/1750000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [875000, 2175001) Primes: RFBsize:131608, AFBsize:131343, largePrimes:3922682 encountered Relations: rels:4027274, finalFF:349003 Max relations in full relation-set: 28 Initial matrix: 263018 x 349003 with sparse part having weight 34653347. Pruned matrix : 235041 x 236420 with weight 20618698. Total sieving time: 14.73 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.50 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1750000,1750000,26,26,48,48,2.3,2.3,100000 total time: 16.53 hours. --------- CPU info (if available) ----------
Jan 24, 2009 (5th): By Serge Batalov / GMP-ECM 6.2.1, polysel+Msieve-1.39/gnfs! / Jan 24, 2009
(64·10²⁸⁵-1)/9 = 7(1)₂₈₅_<286> = 13 · 1009 · 1759 · 5119 · 19009 · 13785887359_<11> · 125860098473209_<15> · 133333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333_<96> · C152
C152 = P42 · P110
P42 = 177742283449499822370246322633403703464107_<42>
P110 = 77026545609119905247041531218744494750493316082997162603430569339652310526470544011921085948181440727270755427_<110>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1333131140 Step 1 took 11737ms Step 2 took 11965ms ********** Factor found in step 2: 177742283449499822370246322633403703464107 Found probable prime factor of 42 digits: 177742283449499822370246322633403703464107 Probable prime cofactor has 110 digits
(64·10²⁷³-1)/9 = 7(1)₂₇₃_<274> = 13 · 163 · 631 · 641 · 18119 · 21757 · 114089 · 119293 · 191360089 · 2202499141477_<13> · 350952042286768401725818393576681_<33> · 13530815674137173613152643233624800312250837_<44> · C150
C150 = P35 · P116
P35 = 65255421091265276492416239359633917_<35>
P116 = 11840544870401401854493322096167872823649699908568717703660676711510644450076098392953725282422610395748825819895357_<116>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1822787502 Step 1 took 11772ms Step 2 took 11985ms ********** Factor found in step 2: 65255421091265276492416239359633917 Found probable prime factor of 35 digits: 65255421091265276492416239359633917 Probable prime cofactor has 116 digits
(64·10²⁷⁹-1)/9 = 7(1)₂₇₉_<280> = 13 · 31 · 1733 · 128599 · 105929849 · 18488064997_<11> · 2021725114081_<13> · 7281843828283_<13> · 2014918111668095329_<19> · 79803629814813067027_<20> · 250196468209067786071679820818025320428585440233101327018900387_<63> · C125
C125 = P33 · P45 · P48
P33 = 420292438080787921643359451399119_<33>
P45 = 730419717857197262419827344582992970030619307_<45>
P48 = 222350289638073289421082995769845047699481936533_<48>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=2662482447 Step 1 took 3322ms Step 2 took 3339ms ********** Factor found in step 2: 420292438080787921643359451399119 Found probable prime factor of 33 digits: 420292438080787921643359451399119 Composite cofactor has 93 digits N=162409035822907584060218661916820012041441209756152258900415577554695186850665254165658442631 ( 93 digits) Divisors found: r1=730419717857197262419827344582992970030619307 (pp45) r2=222350289638073289421082995769845047699481936533 (pp48) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.543). Factorization parameters were as follows: name: t n: 162409035822907584060218661916820012041441209756152258900415577554695186850665254165658442631 Y0: -1489330692417092566815 Y1: 1 c4: 33010008 c3: -38756776794 c2: -162401737450122205 c1: 177686061167819334 c0: 55176205140900388442296 skew: 1635.250 type: gnfs # adj. I(F,S) = 53.898 # E(F1,F2) = 7.827023e-05 # GGNFS version 0.77.1-20060722-k8 polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1232767725. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [600000, 1080001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 171122 x 171358 Total sieving time: 0.00 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: gnfs,92,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,46,46,2.4,2.4,60000 total time: 2.20 hours.
(64·10²⁵³-1)/9 = 7(1)₂₅₃_<254> = 35911 · 4101165361_<10> · 2654271168150479_<16> · C225
C225 = P37 · P189
P37 = 1503012251188960478291218182835329853_<37>
P189 = 121030513207473234467027754682031508099466504424023458323380931963655790995763624722806664691911530138966994414975832462847883393471773674247745852259859301419652934790614763057188332045643_<189>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=358141635 Step 1 took 22129ms Step 2 took 18756ms ********** Factor found in step 2: 1503012251188960478291218182835329853 Found probable prime factor of 37 digits: 1503012251188960478291218182835329853 Probable prime cofactor has 189 digits
Jan 24, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 24, 2009
(41·10¹⁵⁶+13)/9 = 4(5)₁₅₅7_<157> = 3 · 97 · 70406513304649986892243_<23> · C132
C132 = P56 · P77
P56 = 14434671320601927444899804781903476800304653989688760687_<56>
P77 = 15403826606643878294130122774708818300656217739989908114754788714590290120547_<77>

Number: 45557_156 N=222349174146447297456867387484271193909218826076840028739075777284927827966982782165223823799367958189327915307092989558940264535789 ( 132 digits) SNFS difficulty: 157 digits. Divisors found: r1=14434671320601927444899804781903476800304653989688760687 r2=15403826606643878294130122774708818300656217739989908114754788714590290120547 Version: Total time: 14.63 hours. Scaled time: 35.00 units (timescale=2.392). Factorization parameters were as follows: n: 222349174146447297456867387484271193909218826076840028739075777284927827966982782165223823799367958189327915307092989558940264535789 m: 10000000000000000000000000000000 deg: 5 c5: 410 c0: 13 skew: 0.5 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1500000, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8452545 Max relations in full relation-set: Initial matrix: Pruned matrix : 548700 x 548948 Total sieving time: 13.28 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.66 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 14.63 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 24, 2009 (3rd): By Serge Batalov / PFGW / Jan 24, 2009
(16·10⁴⁰⁸⁸⁹-1)/3 = 5(3)₄₀₈₈₉_<40890> is PRP.
Jan 24, 2009 (2nd): Factorizations of 711...11 have been experimentally-extended up to n=300.
Jan 24, 2009: By Serge Batalov / PFGW / Jan 23, 2009
(16·10³⁵⁷⁵³-1)/3 = 5(3)₃₅₇₅₃_<35754> is PRP.
Jan 23, 2009 (4th): By Serge Batalov / PFGW / Jan 23, 2009
(16·10¹³⁹⁹³-1)/3 = 5(3)₁₃₉₉₃_<13994> is PRP.
Jan 23, 2009 (3rd): By Tyler Cadigan / GGNFS, Msieve / Jan 23, 2009
(10¹⁸³+53)/9 = (1)₁₈₂7_<183> = 3³ · 13 · 67 · 479 · C175
C175 = P87 · P89
P87 = 814456279501350377438980191700008354472608345334231988740752857383691177765970748860053_<87>
P89 = 12110784655000342767971716456433469345944334541188468092672320809287673550525096267604723_<89>

Number: 11117_183 N=9863704611953624372393435913691282636397008863140279821660669682218168042352617043532681072192976831233010323639294304409923253769436910793454449564989419647929464885048830319 ( 175 digits) SNFS difficulty: 183 digits. Divisors found: r1=814456279501350377438980191700008354472608345334231988740752857383691177765970748860053 (pp87) r2=12110784655000342767971716456433469345944334541188468092672320809287673550525096267604723 (pp89) Version: Msieve-1.39 Total time: 206.87 hours. Scaled time: 516.77 units (timescale=2.498). Factorization parameters were as follows: n: 9863704611953624372393435913691282636397008863140279821660669682218168042352617043532681072192976831233010323639294304409923253769436910793454449564989419647929464885048830319 m: 2000000000000000000000000000000000000 deg: 5 c5: 125 c0: 212 skew: 1.11 type: snfs lss: 1 rlim: 8000000 alim: 8000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [4000000, 7000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1216132 x 1216380 Total sieving time: 206.87 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,183,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,53,53,2.5,2.5,100000 total time: 206.87 hours. --------- CPU info (if available) ----------
Jan 23, 2009 (2nd): By Robert Backstrom / GGNFS, Msieve / Jan 23, 2009
(13·10¹⁴⁸+17)/3 = 4(3)₁₄₇9_<149> = 19 · 23 · 797 · 9203 · 3277258151_<10> · 176436198027869291_<18> · C113
C113 = P48 · P65
P48 = 362219108729606434290438856179997703092034416009_<48>
P65 = 64548063349944856972207822649011628277742635258341188381686224693_<65>

Number: n N=23380541976839200282767325190671790730362187880117941372803799512694979321700372600589803038261427659300210310237 ( 113 digits) Divisors found: Fri Jan 23 18:09:16 2009 prp48 factor: 362219108729606434290438856179997703092034416009 Fri Jan 23 18:09:16 2009 prp65 factor: 64548063349944856972207822649011628277742635258341188381686224693 Fri Jan 23 18:09:16 2009 elapsed time 03:32:35 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-VC8(Wed Total time: 30.15 hours. Scaled time: 27.13 units (timescale=0.900). Factorization parameters were as follows: name: KA_4_3_147_9 n: 23380541976839200282767325190671790730362187880117941372803799512694979321700372600589803038261427659300210310237 skew: 28708.99 # norm 6.29e+014 c5: 2460 c4: -633951779 c3: -20695688236272 c2: 108160939099036276 c1: 5953456783481487169340 c0: -34441072704534910994164809 # alpha -4.20 Y1: 4810509227 Y0: -6245740134592778442020 # Murphy_E 6.93e-010 # M 1477219687526669108968129462520479885433990903110149087199378865914741253162073845052820046771899641015823549705 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2650211) Primes: RFBsize:250150, AFBsize:249326, largePrimes:16923260 encountered Relations: rels:14857181, finalFF:506906 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 988439 hash collisions in 15497920 relations Msieve: matrix is 611376 x 611624 (169.8 MB) Total sieving time: 28.28 hours. Total relation processing time: 1.87 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,56,56,2.6,2.6,100000 total time: 30.15 hours. --------- CPU info (if available) ----------
Jan 23, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 22, 2009
(41·10¹⁶⁹+13)/9 = 4(5)₁₆₈7_<170> = C170
C170 = P76 · P94
P76 = 8672165459367014932964431677102992882630879566220195983511869288408607879899_<76>
P94 = 5253077304509902079900327279449122912774951534438747747863906866303207485311500450868544270143_<94>

Number: 45557_169 N=45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557 ( 170 digits) SNFS difficulty: 171 digits. Divisors found: r1=8672165459367014932964431677102992882630879566220195983511869288408607879899 r2=5253077304509902079900327279449122912774951534438747747863906866303207485311500450868544270143 Version: Total time: 46.93 hours. Scaled time: 112.17 units (timescale=2.390). Factorization parameters were as follows: n: 45555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557 m: 10000000000000000000000000000000000 deg: 5 c5: 41 c0: 130 skew: 1.26 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3100000, 6600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11408430 Max relations in full relation-set: Initial matrix: Pruned matrix : 1056408 x 1056656 Total sieving time: 42.17 hours. Total relation processing time: 1.99 hours. Matrix solve time: 2.65 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000 total time: 46.93 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 23, 2009
(41·10¹⁴⁸+13)/9 = 4(5)₁₄₇7_<149> = 191 · 131310209 · 14599739933_<11> · C129
C129 = P64 · P65
P64 = 1800637357783759974901763552956102654092167352953638442460850199_<64>
P65 = 69093646156740776157080773778646968153929769992325516238093404609_<65>

Number: 45557_148 N=124412600455319753291293023822905556467418502777629884221966937651002000356694604848608553625643657312604663420905456072645167191 ( 129 digits) SNFS difficulty: 151 digits. Divisors found: r1=1800637357783759974901763552956102654092167352953638442460850199 r2=69093646156740776157080773778646968153929769992325516238093404609 Version: Total time: 8.40 hours. Scaled time: 20.02 units (timescale=2.383). Factorization parameters were as follows: n: 124412600455319753291293023822905556467418502777629884221966937651002000356694604848608553625643657312604663420905456072645167191 m: 1000000000000000000000000000000 deg: 5 c5: 41 c0: 1300 skew: 2.00 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7444421 Max relations in full relation-set: Initial matrix: Pruned matrix : 326553 x 326801 Total sieving time: 7.79 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.24 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 8.40 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
(13·10¹⁵⁴+17)/3 = 4(3)₁₅₃9_<155> = 47 · 1289401 · 17252447681025828391281179_<26> · C122
C122 = P45 · P78
P45 = 146931176976577432525516072501443271640471689_<45>
P78 = 282079522909008801832802122354881453999237337536406519426672216146977851866127_<78>

Number: 43339_154 N=41446276302012100498146879584396609173055097640213325449671826370659005132758983843586432026920587622476154011707161578503 ( 122 digits) SNFS difficulty: 156 digits. Divisors found: r1=146931176976577432525516072501443271640471689 r2=282079522909008801832802122354881453999237337536406519426672216146977851866127 Version: Total time: 9.31 hours. Scaled time: 22.19 units (timescale=2.384). Factorization parameters were as follows: n: 41446276302012100498146879584396609173055097640213325449671826370659005132758983843586432026920587622476154011707161578503 m: 10000000000000000000000000000000 deg: 5 c5: 13 c0: 170 skew: 1.67 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1300000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7954348 Max relations in full relation-set: Initial matrix: Pruned matrix : 449296 x 449544 Total sieving time: 8.41 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.45 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 9.31 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 22, 2009 (3rd): By Sinkiti Sibata / Msieve / Jan 22, 2009
(41·10¹⁴⁷+13)/9 = 4(5)₁₄₆7_<148> = 3 · 7 · 484727 · 25526615366041_<14> · 1937528314189504345464269_<25> · C103
C103 = P41 · P63
P41 = 29355415641012754416171952787119471143967_<41>
P63 = 308244485008190237669046414380908430812930699613696887061598997_<63>

Wed Jan 21 17:08:16 2009 Wed Jan 21 17:08:16 2009 Wed Jan 21 17:08:16 2009 Msieve v. 1.39 Wed Jan 21 17:08:16 2009 random seeds: f2c9dc98 27ac341f Wed Jan 21 17:08:16 2009 factoring 9048644976465349194417936214282020920405826876717322267545304616149531433795128952289790672367809801099 (103 digits) Wed Jan 21 17:08:17 2009 searching for 15-digit factors Wed Jan 21 17:08:19 2009 commencing quadratic sieve (103-digit input) Wed Jan 21 17:08:19 2009 using multiplier of 1 Wed Jan 21 17:08:19 2009 using 32kb Intel Core sieve core Wed Jan 21 17:08:19 2009 sieve interval: 36 blocks of size 32768 Wed Jan 21 17:08:19 2009 processing polynomials in batches of 6 Wed Jan 21 17:08:19 2009 using a sieve bound of 3560659 (127500 primes) Wed Jan 21 17:08:19 2009 using large prime bound of 534098850 (28 bits) Wed Jan 21 17:08:19 2009 using double large prime bound of 5125295884020600 (44-53 bits) Wed Jan 21 17:08:19 2009 using trial factoring cutoff of 53 bits Wed Jan 21 17:08:19 2009 polynomial 'A' values have 13 factors Thu Jan 22 09:07:44 2009 127765 relations (31985 full + 95780 combined from 1881547 partial), need 127596 Thu Jan 22 09:07:46 2009 begin with 1913532 relations Thu Jan 22 09:07:48 2009 reduce to 330770 relations in 11 passes Thu Jan 22 09:07:48 2009 attempting to read 330770 relations Thu Jan 22 09:07:54 2009 recovered 330770 relations Thu Jan 22 09:07:54 2009 recovered 319137 polynomials Thu Jan 22 09:07:55 2009 attempting to build 127765 cycles Thu Jan 22 09:07:55 2009 found 127765 cycles in 6 passes Thu Jan 22 09:07:55 2009 distribution of cycle lengths: Thu Jan 22 09:07:55 2009 length 1 : 31985 Thu Jan 22 09:07:55 2009 length 2 : 22531 Thu Jan 22 09:07:55 2009 length 3 : 21549 Thu Jan 22 09:07:55 2009 length 4 : 17313 Thu Jan 22 09:07:55 2009 length 5 : 12810 Thu Jan 22 09:07:55 2009 length 6 : 8530 Thu Jan 22 09:07:55 2009 length 7 : 5448 Thu Jan 22 09:07:55 2009 length 9+: 7599 Thu Jan 22 09:07:55 2009 largest cycle: 19 relations Thu Jan 22 09:07:56 2009 matrix is 127500 x 127765 (37.4 MB) with weight 9284987 (72.67/col) Thu Jan 22 09:07:56 2009 sparse part has weight 9284987 (72.67/col) Thu Jan 22 09:07:59 2009 filtering completed in 4 passes Thu Jan 22 09:07:59 2009 matrix is 121328 x 121392 (35.7 MB) with weight 8883191 (73.18/col) Thu Jan 22 09:07:59 2009 sparse part has weight 8883191 (73.18/col) Thu Jan 22 09:07:59 2009 saving the first 48 matrix rows for later Thu Jan 22 09:07:59 2009 matrix is 121280 x 121392 (26.3 MB) with weight 7483600 (61.65/col) Thu Jan 22 09:07:59 2009 sparse part has weight 6170468 (50.83/col) Thu Jan 22 09:07:59 2009 matrix includes 64 packed rows Thu Jan 22 09:07:59 2009 using block size 43690 for processor cache size 1024 kB Thu Jan 22 09:08:01 2009 commencing Lanczos iteration Thu Jan 22 09:08:01 2009 memory use: 22.9 MB Thu Jan 22 09:10:18 2009 lanczos halted after 1920 iterations (dim = 121278) Thu Jan 22 09:10:18 2009 recovered 16 nontrivial dependencies Thu Jan 22 09:10:19 2009 prp41 factor: 29355415641012754416171952787119471143967 Thu Jan 22 09:10:19 2009 prp63 factor: 308244485008190237669046414380908430812930699613696887061598997 Thu Jan 22 09:10:19 2009 elapsed time 16:02:03
Jan 22, 2009 (2nd): By Serge Batalov / Msieve-1.39 / Jan 22, 2009
(13·10¹⁴³+17)/3 = 4(3)₁₄₂9_<144> = 595261 · 2447584577_<10> · C129
C129 = P51 · P78
P51 = 305898875245419918219285872629868213926480602328937_<51>
P78 = 972297300424393795140250280951268596451060292444954962055583775858618087659551_<78>

SNFS difficulty: 145 digits. Divisors found: r1=305898875245419918219285872629868213926480602328937 (pp51) r2=972297300424393795140250280951268596451060292444954962055583775858618087659551 (pp78) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.733). Factorization parameters were as follows: n: 297424650603980208445370180543684343390316432002990258734180559806241331564648089739012138500185960159673853974878839430171727287 m: 50000000000000000000000000000 deg: 5 c5: 104 c0: 425 skew: 1.33 type: snfs lss: 1 rlim: 1860000 alim: 1860000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 1860000/1860000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [930000, 2230001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 383995 x 384243 Total sieving time: 0.00 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,145,5,0,0,0,0,0,0,0,0,1860000,1860000,26,26,49,49,2.4,2.4,100000 total time: 6.00 hours.
Jan 22, 2009: By Erik Branger / GGNFS, Msieve / Jan 22, 2009
(13·10¹³⁹+17)/3 = 4(3)₁₃₈9_<140> = 7 · 322587019395677_<15> · C125
C125 = P54 · P72
P54 = 190816151611739294445911252917288917593300029648364203_<54>
P72 = 100568514927274055488494266292260629800808063776522036000875666030563667_<72>

Number: 43339_139 N=19190096991730192555558625223758369283698411644425946513238187529045129212903903609655206267406975666951436025446928595212401 ( 125 digits) SNFS difficulty: 141 digits. Divisors found: r1=190816151611739294445911252917288917593300029648364203 r2=100568514927274055488494266292260629800808063776522036000875666030563667 Version: Total time: 7.90 hours. Scaled time: 6.19 units (timescale=0.784). Factorization parameters were as follows: n: 19190096991730192555558625223758369283698411644425946513238187529045129212903903609655206267406975666951436025446928595212401 m: 10000000000000000000000000000 deg: 5 c5: 13 c0: 170 skew: 1.67 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1485001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 208419 x 208667 Total sieving time: 7.90 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,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 7.90 hours. --------- CPU info (if available) ----------
(43·10¹⁶⁸-7)/9 = 4(7)₁₆₈_<169> = 530723676086574731102103897057683_<33> · C136
C136 = P55 · P82
P55 = 1308979129371218843055335143575659161498651650606112393_<55>
P82 = 6877407559410922828407190093693313130619469297610260690908537887846523454630592083_<82>

Number: 47777_168 N=9002382959448748794439199014832033133711285895903932632389666139902386003239170475300347336941766288329532183182089193481662048433984619 ( 136 digits) SNFS difficulty: 171 digits. Divisors found: r1=1308979129371218843055335143575659161498651650606112393 r2=6877407559410922828407190093693313130619469297610260690908537887846523454630592083 Version: Total time: 116.36 hours. Scaled time: 242.96 units (timescale=2.088). Factorization parameters were as follows: n: 9002382959448748794439199014832033133711285895903932632389666139902386003239170475300347336941766288329532183182089193481662048433984619 m: 5000000000000000000000000000000000 deg: 5 c5: 344 c0: -175 skew: 0.87 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 6300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 998810 x 999058 Total sieving time: 116.36 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,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 116.36 hours. --------- CPU info (if available) ----------
Jan 21, 2009 (7th): By Markus Tervooren / Msieve / Jan 21, 2009
(13·10¹⁹⁴+17)/3 = 4(3)₁₉₃9_<195> = 59 · 83 · 157 · 607 · 1361 · 6311 · 164321 · 1786969867_<10> · 19193147198594868597439948288841_<32> · 466809015184227886664481474387139_<33> · C101
C101 = P49 · P52
P49 = 6923543614221823683435637142856143697121804494349_<49>
P52 = 5935033643361588312921134997404606384549571877425379_<52>

Msieve v. 1.38 Tue Jan 20 22:17:21 2009 random seeds: 00f89e0f 4841fd03 factoring 41091464281687809280907055016363623012787750287324348861042488523828133080766450467340391897074683271 (101 digits) searching for 15-digit factors commencing quadratic sieve (101-digit input) using multiplier of 1 using 32kb Intel Core sieve core sieve interval: 36 blocks of size 32768 processing polynomials in batches of 6 using a sieve bound of 2974639 (107321 primes) using large prime bound of 446195850 (28 bits) using double large prime bound of 3708053052160350 (44-52 bits) using trial factoring cutoff of 52 bits polynomial 'A' values have 13 factors sieving in progress (press Ctrl-C to pause) 107596 relations (26016 full + 81580 combined from 1604242 partial), need 107417 107596 relations (26016 full + 81580 combined from 1604242 partial), need 107417 sieving complete, commencing postprocessing begin with 1630258 relations reduce to 281849 relations in 12 passes attempting to read 281849 relations recovered 281849 relations recovered 271135 polynomials attempting to build 107596 cycles found 107596 cycles in 6 passes distribution of cycle lengths: length 1 : 26016 length 2 : 18625 length 3 : 18195 length 4 : 14748 length 5 : 11084 length 6 : 7312 length 7 : 4885 length 9+: 6731 largest cycle: 21 relations matrix is 107321 x 107596 (31.7 MB) with weight 7446349 (69.21/col) sparse part has weight 7446349 (69.21/col) filtering completed in 3 passes matrix is 102535 x 102599 (30.4 MB) with weight 7138488 (69.58/col) sparse part has weight 7138488 (69.58/col) saving the first 48 matrix rows for later matrix is 102487 x 102599 (19.6 MB) with weight 5683979 (55.40/col) sparse part has weight 4114878 (40.11/col) matrix includes 64 packed rows using block size 41039 for processor cache size 4096 kB commencing Lanczos iteration memory use: 17.3 MB linear algebra completed 101083 of 102599 dimensions (98.5%, ETA 0h 0m) lanczos halted after 1624 iterations (dim = 102485) recovered 17 nontrivial dependencies prp49 factor: 6923543614221823683435637142856143697121804494349 prp52 factor: 5935033643361588312921134997404606384549571877425379 elapsed time 08:45:07
Jan 21, 2009 (6th): By Sinkiti Sibata / Msieve / Jan 21, 2009
(41·10¹³¹+13)/9 = 4(5)₁₃₀7_<132> = 2744051 · 403261362516720769854631_<24> · C102
C102 = P35 · P67
P35 = 79005309736995305131116060227523937_<35>
P67 = 5210822446986772338468650809121467546078389156874394153991712631681_<67>

Tue Jan 20 22:13:49 2009 Msieve v. 1.39 Tue Jan 20 22:13:49 2009 random seeds: f46ffff0 52d14748 Tue Jan 20 22:13:49 2009 factoring 411682641408677746814453464337059397301767786709657824132464450814076300835690663029222620192692048097 (102 digits) Tue Jan 20 22:13:50 2009 searching for 15-digit factors Tue Jan 20 22:13:52 2009 commencing quadratic sieve (102-digit input) Tue Jan 20 22:13:52 2009 using multiplier of 2 Tue Jan 20 22:13:52 2009 using 32kb Intel Core sieve core Tue Jan 20 22:13:52 2009 sieve interval: 36 blocks of size 32768 Tue Jan 20 22:13:52 2009 processing polynomials in batches of 6 Tue Jan 20 22:13:52 2009 using a sieve bound of 3198409 (114826 primes) Tue Jan 20 22:13:52 2009 using large prime bound of 479761350 (28 bits) Tue Jan 20 22:13:52 2009 using double large prime bound of 4225182407156700 (44-52 bits) Tue Jan 20 22:13:52 2009 using trial factoring cutoff of 52 bits Tue Jan 20 22:13:52 2009 polynomial 'A' values have 13 factors Wed Jan 21 13:03:10 2009 115071 relations (27861 full + 87210 combined from 1710804 partial), need 114922 Wed Jan 21 13:03:12 2009 begin with 1738665 relations Wed Jan 21 13:03:14 2009 reduce to 301395 relations in 10 passes Wed Jan 21 13:03:14 2009 attempting to read 301395 relations Wed Jan 21 13:03:19 2009 recovered 301395 relations Wed Jan 21 13:03:19 2009 recovered 291722 polynomials Wed Jan 21 13:03:20 2009 attempting to build 115071 cycles Wed Jan 21 13:03:20 2009 found 115071 cycles in 6 passes Wed Jan 21 13:03:20 2009 distribution of cycle lengths: Wed Jan 21 13:03:20 2009 length 1 : 27861 Wed Jan 21 13:03:20 2009 length 2 : 19785 Wed Jan 21 13:03:20 2009 length 3 : 19653 Wed Jan 21 13:03:20 2009 length 4 : 15587 Wed Jan 21 13:03:20 2009 length 5 : 11674 Wed Jan 21 13:03:20 2009 length 6 : 8109 Wed Jan 21 13:03:20 2009 length 7 : 5129 Wed Jan 21 13:03:20 2009 length 9+: 7273 Wed Jan 21 13:03:20 2009 largest cycle: 21 relations Wed Jan 21 13:03:20 2009 matrix is 114826 x 115071 (33.4 MB) with weight 8294028 (72.08/col) Wed Jan 21 13:03:20 2009 sparse part has weight 8294028 (72.08/col) Wed Jan 21 13:03:23 2009 filtering completed in 3 passes Wed Jan 21 13:03:23 2009 matrix is 109772 x 109836 (32.1 MB) with weight 7970453 (72.57/col) Wed Jan 21 13:03:23 2009 sparse part has weight 7970453 (72.57/col) Wed Jan 21 13:03:23 2009 saving the first 48 matrix rows for later Wed Jan 21 13:03:23 2009 matrix is 109724 x 109836 (21.8 MB) with weight 6540242 (59.55/col) Wed Jan 21 13:03:23 2009 sparse part has weight 5054683 (46.02/col) Wed Jan 21 13:03:23 2009 matrix includes 64 packed rows Wed Jan 21 13:03:23 2009 using block size 43690 for processor cache size 1024 kB Wed Jan 21 13:03:24 2009 commencing Lanczos iteration Wed Jan 21 13:03:24 2009 memory use: 19.8 MB Wed Jan 21 13:04:57 2009 lanczos halted after 1737 iterations (dim = 109721) Wed Jan 21 13:04:57 2009 recovered 16 nontrivial dependencies Wed Jan 21 13:04:59 2009 prp35 factor: 79005309736995305131116060227523937 Wed Jan 21 13:04:59 2009 prp67 factor: 5210822446986772338468650809121467546078389156874394153991712631681 Wed Jan 21 13:04:59 2009 elapsed time 14:51:10
(13·10¹⁴⁶+17)/3 = 4(3)₁₄₅9_<147> = 12071 · 29378177 · 84570591056004857773_<20> · 792811709540546005601_<21> · C95
C95 = P41 · P55
P41 = 18207354784516050172954138782410783675017_<41>
P55 = 1000962316970499262148043364808414101538921611237419737_<55>

Wed Jan 21 13:23:17 2009 Msieve v. 1.39 Wed Jan 21 13:23:17 2009 random seeds: 932fa8c0 871e53d0 Wed Jan 21 13:23:17 2009 factoring 18224876031013090904332849103994615678017092717370950399562413140608318359411130578473429610529 (95 digits) Wed Jan 21 13:23:18 2009 searching for 15-digit factors Wed Jan 21 13:23:19 2009 commencing quadratic sieve (95-digit input) Wed Jan 21 13:23:19 2009 using multiplier of 41 Wed Jan 21 13:23:19 2009 using 32kb Intel Core sieve core Wed Jan 21 13:23:19 2009 sieve interval: 36 blocks of size 32768 Wed Jan 21 13:23:19 2009 processing polynomials in batches of 6 Wed Jan 21 13:23:19 2009 using a sieve bound of 2128183 (78718 primes) Wed Jan 21 13:23:19 2009 using large prime bound of 310714718 (28 bits) Wed Jan 21 13:23:19 2009 using double large prime bound of 1933086450144842 (43-51 bits) Wed Jan 21 13:23:19 2009 using trial factoring cutoff of 51 bits Wed Jan 21 13:23:19 2009 polynomial 'A' values have 12 factors Wed Jan 21 16:29:21 2009 79005 relations (20068 full + 58937 combined from 1155124 partial), need 78814 Wed Jan 21 16:29:22 2009 begin with 1175192 relations Wed Jan 21 16:29:23 2009 reduce to 203036 relations in 11 passes Wed Jan 21 16:29:23 2009 attempting to read 203036 relations Wed Jan 21 16:29:26 2009 recovered 203036 relations Wed Jan 21 16:29:26 2009 recovered 184685 polynomials Wed Jan 21 16:29:26 2009 attempting to build 79005 cycles Wed Jan 21 16:29:26 2009 found 79005 cycles in 6 passes Wed Jan 21 16:29:26 2009 distribution of cycle lengths: Wed Jan 21 16:29:26 2009 length 1 : 20068 Wed Jan 21 16:29:26 2009 length 2 : 14388 Wed Jan 21 16:29:26 2009 length 3 : 13331 Wed Jan 21 16:29:26 2009 length 4 : 10426 Wed Jan 21 16:29:26 2009 length 5 : 7737 Wed Jan 21 16:29:26 2009 length 6 : 5229 Wed Jan 21 16:29:26 2009 length 7 : 3324 Wed Jan 21 16:29:26 2009 length 9+: 4502 Wed Jan 21 16:29:26 2009 largest cycle: 21 relations Wed Jan 21 16:29:27 2009 matrix is 78718 x 79005 (21.4 MB) with weight 5297899 (67.06/col) Wed Jan 21 16:29:27 2009 sparse part has weight 5297899 (67.06/col) Wed Jan 21 16:29:28 2009 filtering completed in 3 passes Wed Jan 21 16:29:28 2009 matrix is 74535 x 74599 (20.3 MB) with weight 5026664 (67.38/col) Wed Jan 21 16:29:28 2009 sparse part has weight 5026664 (67.38/col) Wed Jan 21 16:29:28 2009 saving the first 48 matrix rows for later Wed Jan 21 16:29:28 2009 matrix is 74487 x 74599 (14.4 MB) with weight 4141954 (55.52/col) Wed Jan 21 16:29:28 2009 sparse part has weight 3326541 (44.59/col) Wed Jan 21 16:29:28 2009 matrix includes 64 packed rows Wed Jan 21 16:29:28 2009 using block size 29839 for processor cache size 1024 kB Wed Jan 21 16:29:29 2009 commencing Lanczos iteration Wed Jan 21 16:29:29 2009 memory use: 12.9 MB Wed Jan 21 16:30:08 2009 lanczos halted after 1180 iterations (dim = 74485) Wed Jan 21 16:30:08 2009 recovered 17 nontrivial dependencies Wed Jan 21 16:30:09 2009 prp41 factor: 18207354784516050172954138782410783675017 Wed Jan 21 16:30:09 2009 prp55 factor: 1000962316970499262148043364808414101538921611237419737 Wed Jan 21 16:30:09 2009 elapsed time 03:06:52
Jan 21, 2009 (5th): By Erik Branger / GGNFS, Msieve / Jan 21, 2009
(13·10¹³¹+17)/3 = 4(3)₁₃₀9_<132> = 29 · 904733 · 29957120117_<11> · C114
C114 = P56 · P58
P56 = 75290545150991448414835552655069190513078881893534153027_<56>
P58 = 7322563824738082008971167079472877712083747265515945444253_<58>

Number: 43339_131 N=551319822267459194717415093064116246005032550795737682772740698942815633285096006269830717449494717586743599703831 ( 114 digits) SNFS difficulty: 132 digits. Divisors found: r1=75290545150991448414835552655069190513078881893534153027 r2=7322563824738082008971167079472877712083747265515945444253 Version: Total time: 4.98 hours. Scaled time: 3.94 units (timescale=0.792). Factorization parameters were as follows: n: 551319822267459194717415093064116246005032550795737682772740698942815633285096006269830717449494717586743599703831 m: 100000000000000000000000000 deg: 5 c5: 130 c0: 17 skew: 0.67 type: snfs lss: 1 rlim: 1110000 alim: 1110000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1110000/1110000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [555000, 1055001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 167053 x 167297 Total sieving time: 4.98 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,132,5,0,0,0,0,0,0,0,0,1110000,1110000,26,26,47,47,2.3,2.3,50000 total time: 4.98 hours. --------- CPU info (if available) ----------
(13·10¹³⁴+17)/3 = 4(3)₁₃₃9_<135> = 6673369 · C128
C128 = P46 · P83
P46 = 5170562015966718933706945307187386252346192839_<46>
P83 = 12558541543619291989344514474085687960032747195815838307724371092633277051867902229_<83>

Number: 43339_134 N=64934717881377956671260548207859228724401922527187292255730701139609293796481707115751179551637760977001771269254455033631938131 ( 128 digits) SNFS difficulty: 136 digits. Divisors found: r1=5170562015966718933706945307187386252346192839 r2=12558541543619291989344514474085687960032747195815838307724371092633277051867902229 Version: Total time: 4.95 hours. Scaled time: 3.91 units (timescale=0.790). Factorization parameters were as follows: n: 64934717881377956671260548207859228724401922527187292255730701139609293796481707115751179551637760977001771269254455033631938131 m: 1000000000000000000000000000 deg: 5 c5: 13 c0: 170 skew: 1.67 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [650000, 1100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 192101 x 192349 Total sieving time: 4.95 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,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,48,48,2.3,2.3,75000 total time: 4.95 hours. --------- CPU info (if available) ----------
Jan 21, 2009 (4th): By Ignacio Santos / GGNFS, Msieve / Jan 21, 2009
(13·10¹⁵⁶+17)/3 = 4(3)₁₅₅9_<157> = 107 · 347 · C153
C153 = P61 · P92
P61 = 7848665944310548658605692434612903025770055432499188163240129_<61>
P92 = 14870069560900029332823369079022256333783852292742853847835506034728760020780350557624843779_<92>

Number: 43339_156 N=116710208552164974368642660274538321348092685861007119322721682063436487202276746837602233653837521434278686022605869625719338881557093736252884088807491 ( 153 digits) SNFS difficulty: 157 digits. Divisors found: r1=7848665944310548658605692434612903025770055432499188163240129 (pp61) r2=14870069560900029332823369079022256333783852292742853847835506034728760020780350557624843779 (pp92) Version: Msieve-1.39 Total time: 22.70 hours. Scaled time: 58.42 units (timescale=2.574). Factorization parameters were as follows: n: 116710208552164974368642660274538321348092685861007119322721682063436487202276746837602233653837521434278686022605869625719338881557093736252884088807491 m: 10000000000000000000000000000000 deg: 5 c5: 130 c0: 17 skew: 0.67 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1450000, 2650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 536829 x 537077 Total sieving time: 22.70 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,157,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 22.70 hours. --------- CPU info (if available) ----------
Jan 21, 2009 (3rd): By Serge Batalov / Msieve-1.39 / Jan 21, 2009
(41·10¹⁶⁴+13)/9 = 4(5)₁₆₃7_<165> = C165
C165 = P50 · P115
P50 = 59246473337858590252923330703876400107515991544467_<50>
P115 = 7689159031588380373504633593943740054484463334271016968033626444748578728860063210957751627326841633237210040015271_<115>

SNFS difficulty: 166 digits. Divisors found: r1=59246473337858590252923330703876400107515991544467 (pp50) r2=7689159031588380373504633593943740054484463334271016968033626444748578728860063210957751627326841633237210040015271 (pp115) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.277). Factorization parameters were as follows: n: 455555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555557 m: 1000000000000000000000000000000000 deg: 5 c5: 41 c0: 130 skew: 1.26 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2100000, 4500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 873659 x 873907 Total sieving time: 0.00 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,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,100000 total time: 52.00 hours.
(41·10¹⁶⁵+13)/9 = 4(5)₁₆₄7_<166> = 3 · 7 · 35042011 · C157
C157 = P56 · P101
P56 = 66025287958999438614254821967763657340307943048925364047_<56>
P101 = 93761107149891665630911409876334871598782580112338751013349869153898971358258464100313470301176153101_<101>

SNFS difficulty: 166 digits. Divisors found: r1=66025287958999438614254821967763657340307943048925364047 (pp56) r2=93761107149891665630911409876334871598782580112338751013349869153898971358258464100313470301176153101 (pp101) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 6190604098926198362786063189444719117773555202959582748174219137458090838934192930058064624685244717582473540600487139029119396627414360757347265741432959747 m: 1000000000000000000000000000000000 deg: 5 c5: 41 c0: 13 skew: 0.79 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4200000/4200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2100000, 3900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 708729 x 708977 Total sieving time: 0.00 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,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,52,52,2.4,2.4,200000 total time: 33.00 hours.
(13·10¹⁵²+17)/3 = 4(3)₁₅₁9_<153> = C153
C153 = P51 · P102
P51 = 670399596905264032667430020408189520755253035738719_<51>
P102 = 646380659137790069915295704552388520173975520084757105896768093685063584412243426921222988426638350981_<102>

SNFS difficulty: 154 digits. Divisors found: r1=670399596905264032667430020408189520755253035738719 (pp51) r2=646380659137790069915295704552388520173975520084757105896768093685063584412243426921222988426638350981 (pp102) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.733). Factorization parameters were as follows: n: 433333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333339 m: 2000000000000000000000000000000 deg: 5 c5: 325 c0: 136 skew: 0.84 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1300000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 510307 x 510555 Total sieving time: 0.00 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,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000 total time: 13.00 hours.
Jan 21, 2009 (2nd): By Ignacio Santos / GGNFS-Msieve / Jan 20, 2009
(13·10¹³⁰+17)/3 = 4(3)₁₂₉9_<131> = 19 · 640307 · 38351513 · 285733361 · 222209824020355909_<18> · C91
C91 = P43 · P48
P43 = 1570644324244675277406232203685467558728651_<43>
P48 = 931313054549234693627071365157441701143203771309_<48>

Tue Jan 20 13:42:23 2009 Tue Jan 20 13:42:23 2009 Tue Jan 20 13:42:23 2009 Msieve v. 1.39 Tue Jan 20 13:42:23 2009 random seeds: b379af00 0c33bebd Tue Jan 20 13:42:23 2009 factoring 1462761563222727130063118075699260662700284657246345663740202539793096014122267264590074159 (91 digits) Tue Jan 20 13:42:23 2009 searching for 15-digit factors Tue Jan 20 13:42:25 2009 commencing quadratic sieve (91-digit input) Tue Jan 20 13:42:25 2009 using multiplier of 5 Tue Jan 20 13:42:25 2009 using 32kb Intel Core sieve core Tue Jan 20 13:42:25 2009 sieve interval: 36 blocks of size 32768 Tue Jan 20 13:42:25 2009 processing polynomials in batches of 6 Tue Jan 20 13:42:25 2009 using a sieve bound of 1652509 (62283 primes) Tue Jan 20 13:42:25 2009 using large prime bound of 145420792 (27 bits) Tue Jan 20 13:42:25 2009 using double large prime bound of 492864656290952 (42-49 bits) Tue Jan 20 13:42:25 2009 using trial factoring cutoff of 49 bits Tue Jan 20 13:42:25 2009 polynomial 'A' values have 12 factors Tue Jan 20 14:50:04 2009 62440 relations (16596 full + 45844 combined from 698216 partial), need 62379 Tue Jan 20 14:50:05 2009 begin with 714812 relations Tue Jan 20 14:50:05 2009 reduce to 153177 relations in 10 passes Tue Jan 20 14:50:05 2009 attempting to read 153177 relations Tue Jan 20 14:50:07 2009 recovered 153177 relations Tue Jan 20 14:50:07 2009 recovered 132766 polynomials Tue Jan 20 14:50:07 2009 attempting to build 62440 cycles Tue Jan 20 14:50:07 2009 found 62440 cycles in 5 passes Tue Jan 20 14:50:07 2009 distribution of cycle lengths: Tue Jan 20 14:50:07 2009 length 1 : 16596 Tue Jan 20 14:50:07 2009 length 2 : 11960 Tue Jan 20 14:50:07 2009 length 3 : 10999 Tue Jan 20 14:50:07 2009 length 4 : 8205 Tue Jan 20 14:50:07 2009 length 5 : 5901 Tue Jan 20 14:50:07 2009 length 6 : 3759 Tue Jan 20 14:50:07 2009 length 7 : 2267 Tue Jan 20 14:50:07 2009 length 9+: 2753 Tue Jan 20 14:50:07 2009 largest cycle: 20 relations Tue Jan 20 14:50:07 2009 matrix is 62283 x 62440 (15.4 MB) with weight 3790272 (60.70/col) Tue Jan 20 14:50:07 2009 sparse part has weight 3790272 (60.70/col) Tue Jan 20 14:50:08 2009 filtering completed in 3 passes Tue Jan 20 14:50:08 2009 matrix is 58355 x 58418 (14.5 MB) with weight 3572990 (61.16/col) Tue Jan 20 14:50:08 2009 sparse part has weight 3572990 (61.16/col) Tue Jan 20 14:50:08 2009 saving the first 48 matrix rows for later Tue Jan 20 14:50:08 2009 matrix is 58307 x 58418 (9.1 MB) with weight 2792706 (47.81/col) Tue Jan 20 14:50:08 2009 sparse part has weight 2023535 (34.64/col) Tue Jan 20 14:50:08 2009 matrix includes 64 packed rows Tue Jan 20 14:50:08 2009 using block size 23367 for processor cache size 4096 kB Tue Jan 20 14:50:08 2009 commencing Lanczos iteration Tue Jan 20 14:50:08 2009 memory use: 8.8 MB Tue Jan 20 14:50:22 2009 lanczos halted after 924 iterations (dim = 58307) Tue Jan 20 14:50:23 2009 recovered 19 nontrivial dependencies Tue Jan 20 14:50:24 2009 prp43 factor: 1570644324244675277406232203685467558728651 Tue Jan 20 14:50:24 2009 prp48 factor: 931313054549234693627071365157441701143203771309 Tue Jan 20 14:50:24 2009 elapsed time 01:08:01
By Ignacio Santos / GGNFS-Msieve / Jan 21, 2009
(13·10¹⁴⁰+17)/3 = 4(3)₁₃₉9_<141> = 53 · 863 · 929 · 140261005451431_<15> · 2990564816106821799383922547_<28> · C92
C92 = P39 · P53
P39 = 243818690817952710890544697736647626133_<39>
P53 = 99715473523447511465699370816219356662567860601605449_<53>

Tue Jan 20 22:10:54 2009 Tue Jan 20 22:10:54 2009 Tue Jan 20 22:10:54 2009 Msieve v. 1.39 Tue Jan 20 22:10:54 2009 random seeds: a8b04c68 749e672b Tue Jan 20 22:10:54 2009 factoring 24312496208779198415565027300964960051932497256644440241028331720996824305447064254527598717 (92 digits) Tue Jan 20 22:10:55 2009 searching for 15-digit factors Tue Jan 20 22:10:56 2009 commencing quadratic sieve (92-digit input) Tue Jan 20 22:10:56 2009 using multiplier of 53 Tue Jan 20 22:10:56 2009 using 32kb Intel Core sieve core Tue Jan 20 22:10:56 2009 sieve interval: 36 blocks of size 32768 Tue Jan 20 22:10:56 2009 processing polynomials in batches of 6 Tue Jan 20 22:10:56 2009 using a sieve bound of 1779137 (67059 primes) Tue Jan 20 22:10:56 2009 using large prime bound of 186809385 (27 bits) Tue Jan 20 22:10:56 2009 using double large prime bound of 773601948505050 (42-50 bits) Tue Jan 20 22:10:56 2009 using trial factoring cutoff of 50 bits Tue Jan 20 22:10:56 2009 polynomial 'A' values have 12 factors Tue Jan 20 23:37:05 2009 67588 relations (17425 full + 50163 combined from 823918 partial), need 67155 Tue Jan 20 23:37:05 2009 begin with 841343 relations Tue Jan 20 23:37:06 2009 reduce to 168962 relations in 10 passes Tue Jan 20 23:37:06 2009 attempting to read 168962 relations Tue Jan 20 23:37:08 2009 recovered 168962 relations Tue Jan 20 23:37:08 2009 recovered 149354 polynomials Tue Jan 20 23:37:08 2009 attempting to build 67588 cycles Tue Jan 20 23:37:08 2009 found 67588 cycles in 6 passes Tue Jan 20 23:37:08 2009 distribution of cycle lengths: Tue Jan 20 23:37:08 2009 length 1 : 17425 Tue Jan 20 23:37:08 2009 length 2 : 12637 Tue Jan 20 23:37:08 2009 length 3 : 11786 Tue Jan 20 23:37:08 2009 length 4 : 9225 Tue Jan 20 23:37:08 2009 length 5 : 6455 Tue Jan 20 23:37:08 2009 length 6 : 4251 Tue Jan 20 23:37:08 2009 length 7 : 2534 Tue Jan 20 23:37:08 2009 length 9+: 3275 Tue Jan 20 23:37:08 2009 largest cycle: 19 relations Tue Jan 20 23:37:08 2009 matrix is 67059 x 67588 (16.2 MB) with weight 3965480 (58.67/col) Tue Jan 20 23:37:08 2009 sparse part has weight 3965480 (58.67/col) Tue Jan 20 23:37:09 2009 filtering completed in 3 passes Tue Jan 20 23:37:09 2009 matrix is 63057 x 63121 (15.1 MB) with weight 3704002 (58.68/col) Tue Jan 20 23:37:09 2009 sparse part has weight 3704002 (58.68/col) Tue Jan 20 23:37:09 2009 saving the first 48 matrix rows for later Tue Jan 20 23:37:09 2009 matrix is 63009 x 63121 (8.3 MB) with weight 2741154 (43.43/col) Tue Jan 20 23:37:09 2009 sparse part has weight 1801245 (28.54/col) Tue Jan 20 23:37:09 2009 matrix includes 64 packed rows Tue Jan 20 23:37:09 2009 using block size 25248 for processor cache size 4096 kB Tue Jan 20 23:37:09 2009 commencing Lanczos iteration Tue Jan 20 23:37:09 2009 memory use: 8.9 MB Tue Jan 20 23:37:25 2009 lanczos halted after 998 iterations (dim = 63007) Tue Jan 20 23:37:25 2009 recovered 16 nontrivial dependencies Tue Jan 20 23:37:25 2009 prp39 factor: 243818690817952710890544697736647626133 Tue Jan 20 23:37:25 2009 prp53 factor: 99715473523447511465699370816219356662567860601605449 Tue Jan 20 23:37:25 2009 elapsed time 01:26:31
Jan 21, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 20, 2009
(37·10¹⁶³+71)/9 = 4(1)₁₆₂9_<164> = 7 · 83 · 119267 · 880091 · 55050071 · C143
C143 = P68 · P76
P68 = 10612384575172811246762013681618992864158685725196076097302274309919_<68>
P76 = 1153889825563011219897015674381343240915397462487267551725993237549611584283_<76>

Number: 41119_163 N=12245522586253746099968568685920140593209283041694339776310908812238990592165703272639528019191995298183689750221363386742366663616632131403077 ( 143 digits) SNFS difficulty: 166 digits. Divisors found: r1=10612384575172811246762013681618992864158685725196076097302274309919 r2=1153889825563011219897015674381343240915397462487267551725993237549611584283 Version: Total time: 28.05 hours. Scaled time: 66.29 units (timescale=2.363). Factorization parameters were as follows: n: 12245522586253746099968568685920140593209283041694339776310908812238990592165703272639528019191995298183689750221363386742366663616632131403077 m: 1000000000000000000000000000000000 deg: 5 c5: 37 c0: 7100 skew: 2.86 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2400000, 4600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9817186 Max relations in full relation-set: Initial matrix: Pruned matrix : 822349 x 822597 Total sieving time: 24.80 hours. Total relation processing time: 1.08 hours. Matrix solve time: 1.58 hours. Time per square root: 0.60 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000 total time: 28.05 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
(13·10¹¹⁹+17)/3 = 4(3)₁₁₈9_<120> = 61 · 39409 · C114
C114 = P38 · P76
P38 = 53174504914257053921908157404715782721_<38>
P76 = 3389950781078697275386436001539122062289866786416933540275567164715600727591_<76>

Number: 43339_119 N=180258954467558726634106353060457328060342932954623136070413030115586201426624829949942088344358941613708665755111 ( 114 digits) SNFS difficulty: 121 digits. Divisors found: r1=53174504914257053921908157404715782721 r2=3389950781078697275386436001539122062289866786416933540275567164715600727591 Version: Total time: 0.62 hours. Scaled time: 1.48 units (timescale=2.373). Factorization parameters were as follows: n: 180258954467558726634106353060457328060342932954623136070413030115586201426624829949942088344358941613708665755111 m: 1000000000000000000000000 deg: 5 c5: 13 c0: 170 skew: 1.67 type: snfs lss: 1 rlim: 540000 alim: 540000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 540000/540000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [270000, 480001) Primes: rational ideals reading, algebraic ideals reading, Relations: 1248902 Max relations in full relation-set: Initial matrix: Pruned matrix : 65852 x 66093 Total sieving time: 0.57 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,540000,540000,25,25,46,46,2.2,2.2,30000 total time: 0.62 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Jan 21, 2009
(13·10¹²⁷+17)/3 = 4(3)₁₂₆9_<128> = 7² · 53 · C125
C125 = P42 · P83
P42 = 592752898039573593951004187883726962059169_<42>
P83 = 28149874435139797345546297898982553764803447148584606253445998984051523023986318623_<83>

Number: 43339_127 N=16685919650879219612373251187267359774098318572712103709408291618534206135284302400205365164933898087536901553074059812604287 ( 125 digits) SNFS difficulty: 128 digits. Divisors found: r1=592752898039573593951004187883726962059169 r2=28149874435139797345546297898982553764803447148584606253445998984051523023986318623 Version: Total time: 1.46 hours. Scaled time: 3.47 units (timescale=2.379). Factorization parameters were as follows: n: 16685919650879219612373251187267359774098318572712103709408291618534206135284302400205365164933898087536901553074059812604287 m: 10000000000000000000000000 deg: 5 c5: 1300 c0: 17 skew: 0.42 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2874650 Max relations in full relation-set: Initial matrix: Pruned matrix : 141134 x 141381 Total sieving time: 1.29 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 1.46 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
(64·10²²⁷-1)/9 = 7(1)₂₂₇_<228> = 3² · 751 · 997 · 1987 · C218
C218 = P47 · P172
P47 = 12580688216946651173211552347847284253008814449_<47>
P172 = 4221410569361183158650323193996802358668505850306228952322782128251492447111964495002825468261701293097419367623912143526832225354450880609164265860377163061432183372371039_<172>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM] Input number is 53108250208856290879943190686286926212622109904300816889872200157247472868266848651592384100132642859519384361664694008385611426285586037047629303279747426443337256605822525091167881691151711478666627465243279532342511 (218 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=2234649575 Step 1 took 140027ms Step 2 took 75208ms ********** Factor found in step 2: 12580688216946651173211552347847284253008814449 Found probable prime factor of 47 digits: 12580688216946651173211552347847284253008814449 Probable prime cofactor 4221410569361183158650323193996802358668505850306228952322782128251492447111964495002825468261701293097419367623912143526832225354450880609164265860377163061432183372371039 has 172 digits
Jan 20, 2009 (10th): By Ignacio Santos / GGNFS, Msieve / Jan 20, 2009
(41·10¹⁴⁹+13)/9 = 4(5)₁₄₈7_<150> = 2841789641_<10> · 296843519425519604081_<21> · C120
C120 = P45 · P76
P45 = 154871027594058166313738937531850792514615903_<45>
P76 = 3486997760676672775521582454506981045875820749167242223488415063348339937939_<76>

Number: 45557_149 N=540034926414176023335666056013800139388078340991658921250077831465701719953890647536283401844391126584896158401442443917 ( 120 digits) SNFS difficulty: 151 digits. Divisors found: r1=154871027594058166313738937531850792514615903 (pp45) r2=3486997760676672775521582454506981045875820749167242223488415063348339937939 (pp76) Version: Msieve-1.39 Total time: 16.88 hours. Scaled time: 43.46 units (timescale=2.575). Factorization parameters were as follows: n: 540034926414176023335666056013800139388078340991658921250077831465701719953890647536283401844391126584896158401442443917 m: 1000000000000000000000000000000 deg: 5 c5: 41 c0: 130 skew: 1.26 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 383145 x 383393 Total sieving time: 16.88 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,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 16.88 hours. --------- CPU info (if available) ----------
(13·10¹¹⁷+17)/3 = 4(3)₁₁₆9_<118> = 7411 · 17471 · 6436039448261_<13> · C97
C97 = P33 · P65
P33 = 297261112967139716914723682939401_<33>
P65 = 17493258901169028703409497802873699639804029532490523703990738179_<65>

Number: 43339_117 N=5200065610383829033928010205144895632219547651445470984420115504287281256542233743045458514090779 ( 97 digits) SNFS difficulty: 119 digits. Divisors found: r1=297261112967139716914723682939401 (pp33) r2=17493258901169028703409497802873699639804029532490523703990738179 (pp65) Version: Msieve-1.39 Total time: 1.46 hours. Scaled time: 3.77 units (timescale=2.585). Factorization parameters were as follows: n: 5200065610383829033928010205144895632219547651445470984420115504287281256542233743045458514090779 m: 200000000000000000000000 deg: 5 c5: 325 c0: 136 skew: 0.84 type: snfs lss: 1 rlim: 670000 alim: 670000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 670000/670000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [335000, 635001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 79175 x 79416 Total sieving time: 1.46 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,119,5,0,0,0,0,0,0,0,0,670000,670000,25,25,45,45,2.2,2.2,50000 total time: 1.46 hours. --------- CPU info (if available) ----------
Jan 20, 2009 (9th): By Markus Tervooren / ggnfs, msieve / Jan 20, 2009
(11·10¹⁶⁵+1)/3 = 3(6)₁₆₄7_<166> = 19 · 61 · 887 · 10713254678080769_<17> · 12402765290298822972283_<23> · C122
C122 = P47 · P76
P47 = 26797762685568259691978304690654738199883649061_<47>
P76 = 1001672806023220538619289663280526288901729658106205228988334013295716045117_<76>

Msieve v. 1.38 Tue Jan 20 12:57:22 2009 random seeds: 42e45458 9525d86b factoring 26842590144397512873551401406599563534311210783367865165259740185669640725921314367074253535437723207328428322873270685137 (122 digits) searching for 15-digit factors commencing number field sieve (122-digit input) R0: -1000000000000000000000000000000000 R1: 1 A0: 1 A1: 0 A2: 0 A3: 0 A4: 0 A5: 11 size score = 3.209221e-11, Murphy alpha = 0.588883, combined = 2.637243e-11 commencing relation filtering commencing duplicate removal, pass 1 found 634771 hash collisions in 10563124 relations added 10658 free relations commencing duplicate removal, pass 2 found 474889 duplicates and 10098893 unique relations memory use: 50.6 MB reading rational ideals above 7536640 reading algebraic ideals above 7536640 commencing singleton removal, pass 1 relations with 0 large ideals: 363104 relations with 1 large ideals: 1861795 relations with 2 large ideals: 3640577 relations with 3 large ideals: 2962077 relations with 4 large ideals: 896083 relations with 5 large ideals: 32823 relations with 6 large ideals: 342434 relations with 7+ large ideals: 0 10098893 relations and about 9260856 large ideals commencing singleton removal, pass 2 found 3703655 singletons current dataset: 6395238 relations and about 4652025 large ideals commencing singleton removal, pass 3 found 904831 singletons current dataset: 5490407 relations and about 3697823 large ideals commencing singleton removal, pass 4 found 218819 singletons current dataset: 5271588 relations and about 3475326 large ideals commencing singleton removal, final pass memory use: 80.9 MB commencing in-memory singleton removal begin with 5271588 relations and 3675324 unique ideals reduce to 4793006 relations and 3188955 ideals in 11 passes max relations containing the same ideal: 67 reading rational ideals above 720000 reading algebraic ideals above 720000 commencing singleton removal, final pass keeping 3867001 ideals with weight <= 20, new excess is 405067 memory use: 128.4 MB commencing in-memory singleton removal begin with 4803664 relations and 3867001 unique ideals reduce to 4780621 relations and 3791720 ideals in 9 passes max relations containing the same ideal: 20 removing 1185259 relations and 925747 ideals in 259512 cliques commencing in-memory singleton removal begin with 3595362 relations and 3791720 unique ideals reduce to 3415831 relations and 2674760 ideals in 8 passes max relations containing the same ideal: 20 removing 914096 relations and 654584 ideals in 259512 cliques commencing in-memory singleton removal begin with 2501735 relations and 2674760 unique ideals reduce to 2345224 relations and 1852304 ideals in 9 passes max relations containing the same ideal: 19 removing 135512 relations and 112470 ideals in 23042 cliques commencing in-memory singleton removal begin with 2209712 relations and 1852304 unique ideals reduce to 2204720 relations and 1734792 ideals in 5 passes max relations containing the same ideal: 19 relations with 0 large ideals: 47447 relations with 1 large ideals: 256449 relations with 2 large ideals: 603335 relations with 3 large ideals: 695913 relations with 4 large ideals: 423179 relations with 5 large ideals: 141638 relations with 6 large ideals: 34263 relations with 7+ large ideals: 2496 commencing 2-way merge reduce to 1440888 relation sets and 970960 unique ideals commencing full merge memory use: 88.6 MB found 700024 cycles, need 637160 weight of 637160 cycles is about 44625763 (70.04/cycle) distribution of cycle lengths: 1 relations: 71310 2 relations: 62858 3 relations: 65299 4 relations: 63476 5 relations: 60549 6 relations: 55936 7 relations: 50741 8 relations: 44766 9 relations: 39151 10+ relations: 123074 heaviest cycle: 17 relations commencing cycle optimization start with 3795715 relations pruned 140533 relations memory use: 119.7 MB distribution of cycle lengths: 1 relations: 71310 2 relations: 64873 3 relations: 68577 4 relations: 66515 5 relations: 63668 6 relations: 58180 7 relations: 52654 8 relations: 45831 9 relations: 39129 10+ relations: 106423 heaviest cycle: 16 relations commencing linear algebra read 637160 cycles cycles contain 1947546 unique relations read 1947546 relations using 32 quadratic characters above 134205218 building initial matrix memory use: 241.3 MB read 637160 cycles matrix is 636905 x 637160 (187.8 MB) with weight 60278730 (94.61/col) sparse part has weight 42210821 (66.25/col) filtering completed in 3 passes matrix is 634790 x 634990 (187.4 MB) with weight 60136200 (94.70/col) sparse part has weight 42132219 (66.35/col) read 634990 cycles matrix is 634790 x 634990 (187.4 MB) with weight 60136200 (94.70/col) sparse part has weight 42132219 (66.35/col) saving the first 48 matrix rows for later matrix is 634742 x 634990 (179.4 MB) with weight 46027776 (72.49/col) sparse part has weight 40680313 (64.06/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 183.7 MB linear algebra completed 634480 of 634990 dimensions (99.9%, ETA 0h 0m) lanczos halted after 10041 iterations (dim = 634740) recovered 48 nontrivial dependencies commencing square root phase reading relations for dependency 1 read 317703 cycles cycles contain 1209362 unique relations read 1209362 relations multiplying 973474 relations multiply complete, coefficients have about 24.43 million bits initial square root is modulo 10385591 prp47 factor: 26797762685568259691978304690654738199883649061 prp76 factor: 1001672806023220538619289663280526288901729658106205228988334013295716045117 elapsed time 00:40:42
Jan 20, 2009 (8th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39 / Jan 20, 2009
(13·10¹⁰⁸+17)/3 = 4(3)₁₀₇9_<109> = 47 · 67 · C106
C106 = P31 · P75
P31 = 7431209624337076058856861590161_<31>
P75 = 185178228284173749097301724961131305298759518123588151656392167131675512151_<75>

Using B1=1000000, B2=2139490090, polynomial Dickson(6), sigma=3907866496 Step 1 took 2766ms Step 2 took 2914ms ********** Factor found in step 2: 7431209624337076058856861590161 Found probable prime factor of 31 digits: 7431209624337076058856861590161 Probable prime cofactor 185178228284173749097301724961131305298759518123588151656392167131675512151 has 75 digits
(41·10¹⁵⁰+13)/9 = 4(5)₁₄₉7_<151> = 3³ · C150
C150 = P73 · P77
P73 = 8088307089484207164003143469452132928076569867478172561362749573329874913_<73>
P77 = 20860271249437751623432586664881731562191259384907030463575987885758254647007_<77>

SNFS difficulty: 151 digits. Divisors found: r1=8088307089484207164003143469452132928076569867478172561362749573329874913 (pp73) r2=20860271249437751623432586664881731562191259384907030463575987885758254647007 (pp77) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835390946502057613168724279835391 m: 1000000000000000000000000000000 deg: 5 c5: 41 c0: 13 skew: 0.79 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1200000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 378707 x 378955 Total sieving time: 0.00 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,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,52,52,2.5,2.5,100000 total time: 10.00 hours.
(13·10¹⁹⁴+17)/3 = 4(3)₁₉₃9_<195> = 59 · 83 · 157 · 607 · 1361 · 6311 · 164321 · 1786969867_<10> · 19193147198594868597439948288841_<32> · C134
C134 = P33 · C101
P33 = 466809015184227886664481474387139_<33>
C101 = [41091464281687809280907055016363623012787750287324348861042488523828133080766450467340391897074683271_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2675547875 Step 1 took 9760ms Step 2 took 11062ms ********** Factor found in step 2: 466809015184227886664481474387139 Found probable prime factor of 33 digits: 466809015184227886664481474387139 Composite cofactor 41091464281687809280907055016363623012787750287324348861042488523828133080766450467340391897074683271 has 101 digits
(41·10¹⁵¹+13)/9 = 4(5)₁₅₀7_<152> = 23 · 2089 · C147
C147 = P63 · P85
P63 = 412965781222919059431588990535944176008086436258231823868137137_<63>
P85 = 2295942483708757462905739091602534375427222462948952894327050495097814781823941499163_<85>

SNFS difficulty: 153 digits. Divisors found: r1=412965781222919059431588990535944176008086436258231823868137137 (pp63) r2=2295942483708757462905739091602534375427222462948952894327050495097814781823941499163 (pp85) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 948145681427676141185829615908497004090901732794046570140811196444222439601963817835776542875841479292267062575302423784118791091130675287854716331 m: 2000000000000000000000000000000 deg: 5 c5: 205 c0: 208 skew: 1.00 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1300000, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 484451 x 484699 Total sieving time: 0.00 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,153,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.5,2.5,100000 total time: 13.00 hours.
(13·10¹²⁶+17)/3 = 4(3)₁₂₅9_<127> = 23 · 823 · C123
C123 = P55 · P69
P55 = 1235037569989934703742707811318505240683506061828378703_<55>
P69 = 185359247322344949939888900134497341086497558276887388854316050833797_<69>

SNFS difficulty: 127 digits. Divisors found: r1=1235037569989934703742707811318505240683506061828378703 (pp55) r2=185359247322344949939888900134497341086497558276887388854316050833797 (pp69) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.724). Factorization parameters were as follows: n: 228925634388152217937203937520911476218148519907725359677390952154542412876186451124377058129501470406959339285399827425291 m: 10000000000000000000000000 deg: 5 c5: 130 c0: 17 skew: 0.67 type: snfs lss: 1 rlim: 920000 alim: 920000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 920000/920000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [460000, 810001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 129016 x 129264 Total sieving time: 0.00 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,127,5,0,0,0,0,0,0,0,0,920000,920000,26,26,49,49,2.3,2.3,50000 total time: 1.50 hours.
(13·10¹³²+17)/3 = 4(3)₁₃₁9_<133> = 1135151837_<10> · C124
C124 = P34 · P91
P34 = 3063094933197206012414663895563111_<34>
P91 = 1246257211466193660946936592331668212340483802847166733457467467560945277322505374209706577_<91>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1063295750 Step 1 took 12889ms Step 2 took 13509ms ********** Factor found in step 2: 3063094933197206012414663895563111 Found probable prime factor of 34 digits: 3063094933197206012414663895563111 Probable prime cofactor has 91 digits
(13·10¹⁸³+17)/3 = 4(3)₁₈₂9_<184> = 167 · 283 · 7810225216444802043127_<22> · C158
C158 = P35 · P123
P35 = 22638610072965845146515798122211221_<35>
P123 = 518568191759354873354028254138933705605045125722879355590156955694954110429162407309398276854625923840716391560430712626397_<123>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3656209356 Step 1 took 13866ms Step 2 took 13377ms ********** Factor found in step 2: 22638610072965845146515798122211221 Found probable prime factor of 35 digits: 22638610072965845146515798122211221 Probable prime cofactor has 123 digits
(13·10¹⁷⁸+17)/3 = 4(3)₁₇₇9_<179> = 87187 · C174
C174 = P35 · P140
P35 = 46094114770989559758421799869715111_<35>
P140 = 10782634505829926227561117112188195458713080853422097707679005993454827268815418489695411040739292454281066567653882306406788594214781617727_<140>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3477417042 Step 1 took 17027ms Step 2 took 15009ms ********** Factor found in step 2: 46094114770989559758421799869715111 Found probable prime factor of 35 digits: 46094114770989559758421799869715111 Probable prime cofactor has 140 digits
(13·10²⁰¹+17)/3 = 4(3)₂₀₀9_<202> = 28642351 · C195
C195 = P36 · C159
P36 = 173639839240963617425889116964808219_<36>
C159 = [871292669082763675347013625435710106348585444590009214661633110386569980384531612332002172240517268624619132084082982641718821475559431420128713888427596047631_<159>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1427935662 Step 1 took 18469ms Step 2 took 16307ms ********** Factor found in step 2: 173639839240963617425889116964808219 Found probable prime factor of 36 digits: 173639839240963617425889116964808219 Composite cofactor has 159 digits
(13·10¹⁸⁶+17)/3 = 4(3)₁₈₅9_<187> = 11747995868131_<14> · C174
C174 = P35 · P140
P35 = 12190831134079793452119572575592669_<35>
P140 = 30256939506703801770545513093878737710316949009172144340244948068423985584761342197461324879123655207269042321468266519932875399349228090301_<140>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2865496216 Step 1 took 16810ms ********** Factor found in step 1: 12190831134079793452119572575592669 Found probable prime factor of 35 digits: 12190831134079793452119572575592669 Probable prime cofactor has 140 digits
(13·10¹³³+17)/3 = 4(3)₁₃₂9_<134> = 7 · 241 · 75644713537_<11> · 29460856715745037847399_<23> · C98
C98 = P33 · P65
P33 = 698481296045572507449739791354539_<33>
P65 = 16501684500894512039853388964984732166859460649662542459577659921_<65>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1123134991 Step 1 took 8855ms Step 2 took 8967ms ********** Factor found in step 2: 698481296045572507449739791354539 Found probable prime factor of 33 digits: 698481296045572507449739791354539 Probable prime cofactor has 65 digits
(13·10¹⁴⁷+17)/3 = 4(3)₁₄₆9_<148> = 179 · 313 · 242726741 · C135
C135 = P48 · P88
P48 = 317051071730800217076386361855545345075517377299_<48>
P88 = 1005027345848835841745604832051900561300662136688387005636253807451532975144833420805423_<88>

SNFS difficulty: 148 digits. Divisors found: r1=317051071730800217076386361855545345075517377299 (pp48) r2=1005027345848835841745604832051900561300662136688387005636253807451532975144833420805423 (pp88) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: n: 318644997120135010242664186404623364057545817118496018099156617192090829733657448410476343054352884472704599346161173015402965156292477 m: 100000000000000000000000000000 deg: 5 c5: 1300 c0: 17 skew: 0.42 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved rational special-q in [1050000, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 373103 x 373351 Total sieving time: 0.00 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,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,50,50,2.3,2.3,100000 total time: 8.00 hours.
(13·10¹²⁹+17)/3 = 4(3)₁₂₈9_<130> = 11131 · 1176499763_<10> · 616446635683_<12> · C105
C105 = P37 · P69
P37 = 5084951887576689955930793519093430503_<37>
P69 = 105563489060486885995991940896116891423985958592255758808200677488687_<69>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2005348329 Step 1 took 8262ms Step 2 took 9276ms ********** Factor found in step 2: 5084951887576689955930793519093430503 Found probable prime factor of 37 digits: 5084951887576689955930793519093430503 Probable prime cofactor has 69 digits
Jan 20, 2009 (7th): By Sinkiti Sibata / Msieve / Jan 20, 2009
(41·10¹²¹+13)/9 = 4(5)₁₂₀7_<122> = 5399 · 644341 · 8206170209_<10> · C103
C103 = P44 · P60
P44 = 10400541347880596513151322002253490415160669_<44>
P60 = 153431943934224431017641592298558521171642330516337258884163_<60>

Mon Jan 19 20:01:43 2009 Msieve v. 1.39 Mon Jan 19 20:01:43 2009 random seeds: 5b18ff20 202f51b7 Mon Jan 19 20:01:43 2009 factoring 1595775276973598678011037831407391019992414694887644832555308608201214056077442928890564306845304585047 (103 digits) Mon Jan 19 20:01:44 2009 searching for 15-digit factors Mon Jan 19 20:01:46 2009 commencing quadratic sieve (103-digit input) Mon Jan 19 20:01:46 2009 using multiplier of 2 Mon Jan 19 20:01:46 2009 using 32kb Intel Core sieve core Mon Jan 19 20:01:46 2009 sieve interval: 36 blocks of size 32768 Mon Jan 19 20:01:46 2009 processing polynomials in batches of 6 Mon Jan 19 20:01:46 2009 using a sieve bound of 3340487 (120000 primes) Mon Jan 19 20:01:46 2009 using large prime bound of 501073050 (28 bits) Mon Jan 19 20:01:46 2009 using double large prime bound of 4569007548480300 (44-53 bits) Mon Jan 19 20:01:46 2009 using trial factoring cutoff of 53 bits Mon Jan 19 20:01:46 2009 polynomial 'A' values have 13 factors Tue Jan 20 14:14:09 2009 120145 relations (28740 full + 91405 combined from 1795883 partial), need 120096 Tue Jan 20 14:14:11 2009 begin with 1824623 relations Tue Jan 20 14:14:12 2009 reduce to 317252 relations in 11 passes Tue Jan 20 14:14:12 2009 attempting to read 317252 relations Tue Jan 20 14:14:19 2009 recovered 317252 relations Tue Jan 20 14:14:19 2009 recovered 308230 polynomials Tue Jan 20 14:14:19 2009 attempting to build 120145 cycles Tue Jan 20 14:14:19 2009 found 120145 cycles in 6 passes Tue Jan 20 14:14:19 2009 distribution of cycle lengths: Tue Jan 20 14:14:19 2009 length 1 : 28740 Tue Jan 20 14:14:19 2009 length 2 : 20336 Tue Jan 20 14:14:19 2009 length 3 : 20009 Tue Jan 20 14:14:19 2009 length 4 : 16310 Tue Jan 20 14:14:19 2009 length 5 : 12547 Tue Jan 20 14:14:19 2009 length 6 : 8606 Tue Jan 20 14:14:19 2009 length 7 : 5637 Tue Jan 20 14:14:19 2009 length 9+: 7960 Tue Jan 20 14:14:19 2009 largest cycle: 20 relations Tue Jan 20 14:14:20 2009 matrix is 120000 x 120145 (35.6 MB) with weight 8849223 (73.65/col) Tue Jan 20 14:14:20 2009 sparse part has weight 8849223 (73.65/col) Tue Jan 20 14:14:22 2009 filtering completed in 3 passes Tue Jan 20 14:14:22 2009 matrix is 115104 x 115168 (34.3 MB) with weight 8541239 (74.16/col) Tue Jan 20 14:14:22 2009 sparse part has weight 8541239 (74.16/col) Tue Jan 20 14:14:22 2009 saving the first 48 matrix rows for later Tue Jan 20 14:14:23 2009 matrix is 115056 x 115168 (24.4 MB) with weight 7127639 (61.89/col) Tue Jan 20 14:14:23 2009 sparse part has weight 5695827 (49.46/col) Tue Jan 20 14:14:23 2009 matrix includes 64 packed rows Tue Jan 20 14:14:23 2009 using block size 43690 for processor cache size 1024 kB Tue Jan 20 14:14:24 2009 commencing Lanczos iteration Tue Jan 20 14:14:24 2009 memory use: 21.6 MB Tue Jan 20 14:16:15 2009 lanczos halted after 1820 iterations (dim = 115054) Tue Jan 20 14:16:16 2009 recovered 17 nontrivial dependencies Tue Jan 20 14:16:17 2009 prp44 factor: 10400541347880596513151322002253490415160669 Tue Jan 20 14:16:17 2009 prp60 factor: 153431943934224431017641592298558521171642330516337258884163 Tue Jan 20 14:16:17 2009 elapsed time 18:14:34
(41·10¹⁷⁶+13)/9 = 4(5)₁₇₅7_<177> = 15661 · 8878663815812143_<16> · 15515053871634353_<17> · 115993927151348881399_<21> · 1966833408789686089783313_<25> · C96
C96 = P41 · P56
P41 = 19615475179920945071617458596234333359193_<41>
P56 = 47186666258012252043256895418049868713349346463656125033_<56>

Tue Jan 20 16:17:26 2009 Msieve v. 1.39 Tue Jan 20 16:17:26 2009 random seeds: ca946258 b74f2676 Tue Jan 20 16:17:26 2009 factoring 925588880807252467568771876878853373863714814721869609944208374600859523491636368735392507978369 (96 digits) Tue Jan 20 16:17:27 2009 searching for 15-digit factors Tue Jan 20 16:17:28 2009 commencing quadratic sieve (96-digit input) Tue Jan 20 16:17:29 2009 using multiplier of 1 Tue Jan 20 16:17:29 2009 using 32kb Intel Core sieve core Tue Jan 20 16:17:29 2009 sieve interval: 36 blocks of size 32768 Tue Jan 20 16:17:29 2009 processing polynomials in batches of 6 Tue Jan 20 16:17:29 2009 using a sieve bound of 2299939 (84689 primes) Tue Jan 20 16:17:29 2009 using large prime bound of 344990850 (28 bits) Tue Jan 20 16:17:29 2009 using double large prime bound of 2333746148351850 (43-52 bits) Tue Jan 20 16:17:29 2009 using trial factoring cutoff of 52 bits Tue Jan 20 16:17:29 2009 polynomial 'A' values have 12 factors Tue Jan 20 21:50:47 2009 84787 relations (20045 full + 64742 combined from 1295802 partial), need 84785 Tue Jan 20 21:50:48 2009 begin with 1315847 relations Tue Jan 20 21:50:49 2009 reduce to 225957 relations in 11 passes Tue Jan 20 21:50:49 2009 attempting to read 225957 relations Tue Jan 20 21:50:53 2009 recovered 225957 relations Tue Jan 20 21:50:53 2009 recovered 213085 polynomials Tue Jan 20 21:50:53 2009 attempting to build 84787 cycles Tue Jan 20 21:50:54 2009 found 84787 cycles in 6 passes Tue Jan 20 21:50:54 2009 distribution of cycle lengths: Tue Jan 20 21:50:54 2009 length 1 : 20045 Tue Jan 20 21:50:54 2009 length 2 : 14023 Tue Jan 20 21:50:54 2009 length 3 : 14055 Tue Jan 20 21:50:54 2009 length 4 : 11596 Tue Jan 20 21:50:54 2009 length 5 : 8962 Tue Jan 20 21:50:54 2009 length 6 : 6115 Tue Jan 20 21:50:54 2009 length 7 : 4087 Tue Jan 20 21:50:54 2009 length 9+: 5904 Tue Jan 20 21:50:54 2009 largest cycle: 18 relations Tue Jan 20 21:50:54 2009 matrix is 84689 x 84787 (23.6 MB) with weight 5858158 (69.09/col) Tue Jan 20 21:50:54 2009 sparse part has weight 5858158 (69.09/col) Tue Jan 20 21:50:55 2009 filtering completed in 3 passes Tue Jan 20 21:50:55 2009 matrix is 81312 x 81376 (22.9 MB) with weight 5667944 (69.65/col) Tue Jan 20 21:50:55 2009 sparse part has weight 5667944 (69.65/col) Tue Jan 20 21:50:55 2009 saving the first 48 matrix rows for later Tue Jan 20 21:50:56 2009 matrix is 81264 x 81376 (16.5 MB) with weight 4721586 (58.02/col) Tue Jan 20 21:50:56 2009 sparse part has weight 3829854 (47.06/col) Tue Jan 20 21:50:56 2009 matrix includes 64 packed rows Tue Jan 20 21:50:56 2009 using block size 32550 for processor cache size 1024 kB Tue Jan 20 21:50:57 2009 commencing Lanczos iteration Tue Jan 20 21:50:57 2009 memory use: 14.7 MB Tue Jan 20 21:51:46 2009 lanczos halted after 1286 iterations (dim = 81263) Tue Jan 20 21:51:46 2009 recovered 16 nontrivial dependencies Tue Jan 20 21:51:47 2009 prp41 factor: 19615475179920945071617458596234333359193 Tue Jan 20 21:51:47 2009 prp56 factor: 47186666258012252043256895418049868713349346463656125033 Tue Jan 20 21:51:47 2009 elapsed time 05:34:21
Jan 20, 2009 (6th): By Erik Branger / GGNFS, Msieve / Jan 20, 2009
(43·10¹⁷⁰-7)/9 = 4(7)₁₇₀_<171> = 3 · 67 · 823 · 400427303 · 5932620495103062443_<19> · C139
C139 = P56 · P83
P56 = 19724348612725122674663619250491107143649597908233700859_<56>
P83 = 61639219937700802753408962418792264762496168162642674184908540680230576705040487009_<83>

Number: 47777_170 N=1215793462267647551285892538593877354317166737178594605321560408370658353862767905904353311381922334245683040902952768797380928615781640731 ( 139 digits) SNFS difficulty: 171 digits. Divisors found: r1=19724348612725122674663619250491107143649597908233700859 r2=61639219937700802753408962418792264762496168162642674184908540680230576705040487009 Version: Total time: 109.07 hours. Scaled time: 86.17 units (timescale=0.790). Factorization parameters were as follows: n: 1215793462267647551285892538593877354317166737178594605321560408370658353862767905904353311381922334245683040902952768797380928615781640731 m: 10000000000000000000000000000000000 deg: 5 c5: 43 c0: -7 skew: 0.70 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 5450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 915262 x 915510 Total sieving time: 109.07 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,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 109.07 hours. --------- CPU info (if available) ----------
Jan 20, 2009 (5th): By Markus Tervooren / ggnfs,msieve / Jan 20, 2009
(41·10¹⁴⁵+13)/9 = 4(5)₁₄₄7_<146> = 311 · 749129 · 967664057 · C129
C129 = P47 · P83
P47 = 10653204168755044912086128475047056724667021761_<47>
P83 = 18967910352320338815022238253260155162161188295244766291718453109239753146705462339_<83>

Msieve v. 1.38 Tue Jan 20 02:57:00 2009 random seeds: 4f200b6f 822e0064 factoring 202069021637911006139792365982193405950417196982994491279558455816628051731372278017796256873175681136201678990699486273678958979 (129 digits) searching for 15-digit factors commencing number field sieve (129-digit input) R0: -100000000000000000000000000000 R1: 1 A0: 13 A1: 0 A2: 0 A3: 0 A4: 0 A5: 41 size score = 3.775105e-10, Murphy alpha = 0.741107, combined = 2.948783e-10 commencing relation filtering commencing duplicate removal, pass 1 found 843687 hash collisions in 4404710 relations commencing duplicate removal, pass 2 found 995671 duplicates and 3409039 unique relations memory use: 50.6 MB reading rational ideals above 3080192 reading algebraic ideals above 3080192 commencing singleton removal, pass 1 relations with 0 large ideals: 144617 relations with 1 large ideals: 792976 relations with 2 large ideals: 1430566 relations with 3 large ideals: 787622 relations with 4 large ideals: 99293 relations with 5 large ideals: 2793 relations with 6 large ideals: 151172 relations with 7+ large ideals: 0 3409039 relations and about 3584453 large ideals commencing singleton removal, pass 2 found 1701329 singletons current dataset: 1707710 relations and about 1248457 large ideals commencing singleton removal, pass 3 found 371483 singletons current dataset: 1336227 relations and about 845846 large ideals commencing singleton removal, final pass memory use: 22.6 MB commencing in-memory singleton removal begin with 1336227 relations and 865908 unique ideals reduce to 1165662 relations and 690763 ideals in 12 passes max relations containing the same ideal: 28 reading rational ideals above 720000 reading algebraic ideals above 720000 commencing singleton removal, final pass keeping 999380 ideals with weight <= 20, new excess is 134647 memory use: 33.2 MB commencing in-memory singleton removal begin with 1166216 relations and 999380 unique ideals reduce to 1132823 relations and 962999 ideals in 10 passes max relations containing the same ideal: 20 relations with 0 large ideals: 7191 relations with 1 large ideals: 39881 relations with 2 large ideals: 156236 relations with 3 large ideals: 315706 relations with 4 large ideals: 342583 relations with 5 large ideals: 195715 relations with 6 large ideals: 66642 relations with 7+ large ideals: 8869 commencing 2-way merge reduce to 681219 relation sets and 511407 unique ideals ignored 12 oversize relation sets commencing full merge memory use: 51.5 MB found 312399 cycles, need 285607 weight of 285607 cycles is about 20278239 (71.00/cycle) distribution of cycle lengths: 1 relations: 29107 2 relations: 28315 3 relations: 29668 4 relations: 27878 5 relations: 26181 6 relations: 23644 7 relations: 20696 8 relations: 18433 9 relations: 15797 10+ relations: 65888 heaviest cycle: 19 relations commencing cycle optimization start with 1823210 relations pruned 67262 relations memory use: 56.6 MB distribution of cycle lengths: 1 relations: 29107 2 relations: 29151 3 relations: 31160 4 relations: 29052 5 relations: 27443 6 relations: 24372 7 relations: 21373 8 relations: 18600 9 relations: 15958 10+ relations: 59391 heaviest cycle: 19 relations commencing linear algebra read 285607 cycles cycles contain 910667 unique relations read 910667 relations using 32 quadratic characters above 67108748 building initial matrix memory use: 113.4 MB read 285607 cycles matrix is 285292 x 285607 (84.8 MB) with weight 26928793 (94.29/col) sparse part has weight 19096573 (66.86/col) filtering completed in 3 passes matrix is 283618 x 283818 (84.4 MB) with weight 26775760 (94.34/col) sparse part has weight 18996642 (66.93/col) read 283818 cycles matrix is 283618 x 283818 (84.4 MB) with weight 26775760 (94.34/col) sparse part has weight 18996642 (66.93/col) saving the first 48 matrix rows for later matrix is 283570 x 283818 (80.1 MB) with weight 20525132 (72.32/col) sparse part has weight 18169096 (64.02/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 80.8 MB linear algebra completed 283258 of 283818 dimensions (99.8%, ETA 0h 0m) lanczos halted after 4486 iterations (dim = 283568) recovered 47 nontrivial dependencies commencing square root phase reading relations for dependency 1 read 141763 cycles cycles contain 560270 unique relations read 560270 relations multiplying 453468 relations multiply complete, coefficients have about 11.50 million bits initial square root is modulo 4054321 prp47 factor: 10653204168755044912086128475047056724667021761 prp83 factor: 18967910352320338815022238253260155162161188295244766291718453109239753146705462339 elapsed time 00:09:19
Jan 20, 2009 (4th): By Robert Backstrom / GGNFS / Jan 20, 2009
(41·10¹¹²+13)/9 = 4(5)₁₁₁7_<113> = 49448381 · 3789741401_<10> · C96
C96 = P43 · P54
P43 = 1756133435352425513182738620900779191051907_<43>
P54 = 138427438493586209714463563564622332183967287880120571_<54>

Number: n N=243097053108778136984165373438571844484903522635059863349607568848040049721944322939831479478897 ( 96 digits) SNFS difficulty: 113 digits. Divisors found: r1=1756133435352425513182738620900779191051907 (pp43) r2=138427438493586209714463563564622332183967287880120571 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.06 hours. Scaled time: 1.94 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_5_111_7 n: 243097053108778136984165373438571844484903522635059863349607568848040049721944322939831479478897 deg: 5 c5: 4100 c0: 13 m: 10000000000000000000000 skew: 0.32 type: snfs rlim: 480000 alim: 480000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 5000 Factor base limits: 480000/480000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [240000, 345001) Primes: RFBsize:40005, AFBsize:39921, largePrimes:4792058 encountered Relations: rels:4122235, finalFF:101596 Max relations in full relation-set: 48 Initial matrix: 79993 x 101596 with sparse part having weight 13695970. Pruned matrix : 76115 x 76578 with weight 7943284. Total sieving time: 0.95 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.04 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,480000,480000,28,28,56,56,2.5,2.5,50000 total time: 1.06 hours. --------- CPU info (if available) ----------
Jan 20, 2009 (3rd): By Serge Batalov / GMP-ECM 6.2.1 / Jan 20, 2009
(41·10¹⁸⁶+13)/9 = 4(5)₁₈₅7_<187> = 3² · 182687 · 442938256226497_<15> · C166
C166 = P33 · C134
P33 = 475477038574083556369929814369943_<33>
C134 = [13155836064426885594128471441995840999104018528889838729522538451337386795995418446303058262145873857043472284395328315703288515892949_<134>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3142684540 Step 1 took 13757ms Step 2 took 15719ms ********** Factor found in step 2: 475477038574083556369929814369943 Found probable prime factor of 33 digits: 475477038574083556369929814369943 Composite cofactor has 134 digits
(41·10¹⁸¹+13)/9 = 4(5)₁₈₀7_<182> = 12659 · 147554087 · C170
C170 = P32 · P138
P32 = 78477341455780825551529021820629_<32>
P138 = 310775248202494631264165765244128945187442184025682887089121058958659378801935873806320769270522775359779824792305932238101974779883118301_<138>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=2007374422 Step 1 took 9165ms Step 2 took 7552ms ********** Factor found in step 2: 78477341455780825551529021820629 Found probable prime factor of 32 digits: 78477341455780825551529021820629 Probable prime cofactor has 138 digits
(41·10¹⁸⁷+13)/9 = 4(5)₁₈₆7_<188> = 17 · 21997 · C183
C183 = P32 · P151
P32 = 13310078697652045224417963250807_<32>
P151 = 9152681457356347479687513555964152495625936597914799763119468328723604835282886894235884214798391401198686408741531567478099493735823168035935778356799_<151>

Using B1=2000000, B2=5705781910, polynomial Dickson(6), sigma=2991966525 Step 1 took 10725ms Step 2 took 8230ms ********** Factor found in step 2: 13310078697652045224417963250807 Found probable prime factor of 32 digits: 13310078697652045224417963250807 Probable prime cofactor has 151 digits
(41·10¹⁹⁹+13)/9 = 4(5)₁₉₈7_<200> = 83 · 1237 · 3527 · 983947660636931_<15> · C177
C177 = P35 · C142
P35 = 58353764412673836663918994118972963_<35>
C142 = [2191024432013634960794090277665614347010855183558630212912013314951732600038683331878702811507365885655845895638870854178571130009885108643157_<142>]

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2107319941 Step 1 took 16034ms Step 2 took 17177ms ********** Factor found in step 2: 58353764412673836663918994118972963 Found probable prime factor of 35 digits: 58353764412673836663918994118972963 Composite cofactor has 142 digits
Jan 20, 2009 (2nd): Factorizations of 433...339 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Jan 20, 2009: By Robert Backstrom / GGNFS, Msieve / Jan 19, 2009
(41·10¹⁰⁸+13)/9 = 4(5)₁₀₇7_<109> = 3 · 31 · 59 · C105
C105 = P37 · P69
P37 = 6977028609160864473596822556661339871_<37>
P69 = 118996964553052701797392385505489843383257279117694713186886257581941_<69>

Number: n N=830245226089949982787598971305914990988801814389567259988255067533361683170321770649818763542109632869611 ( 105 digits) SNFS difficulty: 111 digits. Divisors found: Tue Jan 20 00:07:32 2009 prp37 factor: 6977028609160864473596822556661339871 Tue Jan 20 00:07:32 2009 prp69 factor: 118996964553052701797392385505489843383257279117694713186886257581941 Tue Jan 20 00:07:32 2009 elapsed time 00:06:34 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.69 hours. Scaled time: 1.27 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_5_107_7 n: 830245226089949982787598971305914990988801814389567259988255067533361683170321770649818763542109632869611 deg: 5 c5: 41 c0: 1300 m: 10000000000000000000000 skew: 1.99 type: snfs rlim: 450000 alim: 450000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 5000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 290141) Primes: RFBsize:37706, AFBsize:37795, largePrimes:4122943 encountered Relations: rels:3438265, finalFF:80821 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 112338 hash collisions in 3530633 relations Msieve: matrix is 89236 x 89484 (23.8 MB) Total sieving time: 0.65 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000 total time: 0.69 hours. --------- CPU info (if available) ----------
By Robert Backstrom / GGNFS, Msieve / Jan 20, 2009
(41·10¹⁰⁹+13)/9 = 4(5)₁₀₈7_<110> = 89 · C108
C108 = P43 · P66
P43 = 2390184965030426407296407175875310828352169_<43>
P66 = 214150863749160623946326406200826672877838975845177529655688925477_<66>

Number: n N=511860174781523096129837702871410736579275905118601747815230961298377028714107365792759051186017478152309613 ( 108 digits) SNFS difficulty: 111 digits. Divisors found: Tue Jan 20 02:34:57 2009 prp43 factor: 2390184965030426407296407175875310828352169 Tue Jan 20 02:34:57 2009 prp66 factor: 214150863749160623946326406200826672877838975845177529655688925477 Tue Jan 20 02:34:57 2009 elapsed time 00:05:39 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.77 hours. Scaled time: 1.41 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_5_108_7 n: 511860174781523096129837702871410736579275905118601747815230961298377028714107365792759051186017478152309613 deg: 5 c5: 41 c0: 130 m: 10000000000000000000000 skew: 1.99 type: snfs rlim: 450000 alim: 450000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 5000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 300191) Primes: RFBsize:37706, AFBsize:37735, largePrimes:4200323 encountered Relations: rels:3518037, finalFF:79232 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 132689 hash collisions in 3630178 relations Msieve: matrix is 94444 x 94692 (24.7 MB) Total sieving time: 0.72 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000 total time: 0.77 hours. --------- CPU info (if available) ----------
Jan 19, 2009 (12th): By Wataru Sakai / Msieve / Jan 19, 2009
(19·10¹⁹⁶+71)/9 = 2(1)₁₉₅9_<197> = 7 · C196
C196 = P88 · P108
P88 = 4024550742728356898279108029508093226251113429243623259829018016784236730049498559965681_<88>
P108 = 749368863424609268346748573675398417191779704699583690103757751394161833140023105513882632166295016315653257_<108>

Number: 21119_196 N=3015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017 ( 196 digits) SNFS difficulty: 197 digits. Divisors found: r1=4024550742728356898279108029508093226251113429243623259829018016784236730049498559965681 r2=749368863424609268346748573675398417191779704699583690103757751394161833140023105513882632166295016315653257 Version: Total time: 966.43 hours. Scaled time: 1823.66 units (timescale=1.887). Factorization parameters were as follows: n: 3015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873015873017 m: 1000000000000000000000000000000000000000 deg: 5 c5: 190 c0: 71 skew: 0.82 type: snfs lss: 1 rlim: 13600000 alim: 13600000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13600000/13600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6800000, 17400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2466460 x 2466708 Total sieving time: 966.43 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,197,5,0,0,0,0,0,0,0,0,13600000,13600000,28,28,55,55,2.5,2.5,100000 total time: 966.43 hours. --------- CPU info (if available) ----------
Jan 19, 2009 (11th): By Markus Tervooren / ggnfs-lasieve4I12e, msieve / Jan 19, 2009
(41·10¹²⁵+13)/9 = 4(5)₁₂₄7_<126> = 19 · 30809 · C120
C120 = P59 · P62
P59 = 20243241615867601351382161917901417424745360191571433538399_<59>
P62 = 38444134271346041617717354848500875864662068641723260690270433_<62>

Number: 125 N=778233898767714074587834989358125967216612294690983249179675036097715048329274179205248561263806296443717839721399856767 ( 120 digits) SNFS difficulty: 126 digits. Divisors found: r1=20243241615867601351382161917901417424745360191571433538399 r2=38444134271346041617717354848500875864662068641723260690270433 Version: Total time: 1.52 hours. Scaled time: 3.09 units (timescale=2.031). Factorization parameters were as follows: n: 778233898767714074587834989358125967216612294690983249179675036097715048329274179205248561263806296443717839721399856767 m: 10000000000000000000000000 deg: 5 c5: 41 c0: 13 skew: 0.79 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 109798 x 110038 Total sieving time: 1.52 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,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 1.52 hours.
Jan 19, 2009 (10th): By Sinkiti Sibata / Msieve / Jan 19, 2009
(41·10¹²⁰+13)/9 = 4(5)₁₁₉7_<121> = 3 · C121
C121 = P35 · P86
P35 = 41942095426732369193715236502410893_<35>
P86 = 36205118105536280255069438315208949195889419727129346127774643983566290888742102900883_<86>

Number: 45557_120 N=1518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519 ( 121 digits) SNFS difficulty: 121 digits. Divisors found: r1=41942095426732369193715236502410893 r2=36205118105536280255069438315208949195889419727129346127774643983566290888742102900883 Version: Total time: 1.59 hours. Scaled time: 3.17 units (timescale=1.991). Factorization parameters were as follows: name: 45557_120 n: 1518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518518519 m: 1000000000000000000000000 deg: 5 c5: 41 c0: 13 skew: 0.79 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 570001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 84577 x 84825 Total sieving time: 1.59 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,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 1.59 hours. --------- CPU info (if available) ----------
(41·10¹⁵⁹+13)/9 = 4(5)₁₅₈7_<160> = 3² · 7 · 23071 · 591164084701_<12> · 964350536796688660109_<21> · 301356908876733753686272429_<27> · C95
C95 = P46 · P50
P46 = 1323084657260748762081931294088186861983105043_<46>
P50 = 13788677845491133788833382578002306992383451342683_<50>

Mon Jan 19 16:58:58 2009 Msieve v. 1.39 Mon Jan 19 16:58:58 2009 random seeds: b244ea38 8f6c6e48 Mon Jan 19 16:58:58 2009 factoring 18243588101280516424498091055426832910648896917003601129649960924737111973905782692799778450369 (95 digits) Mon Jan 19 16:58:59 2009 searching for 15-digit factors Mon Jan 19 16:59:01 2009 commencing quadratic sieve (95-digit input) Mon Jan 19 16:59:01 2009 using multiplier of 1 Mon Jan 19 16:59:01 2009 using 32kb Intel Core sieve core Mon Jan 19 16:59:01 2009 sieve interval: 36 blocks of size 32768 Mon Jan 19 16:59:01 2009 processing polynomials in batches of 6 Mon Jan 19 16:59:01 2009 using a sieve bound of 2128183 (78513 primes) Mon Jan 19 16:59:01 2009 using large prime bound of 310714718 (28 bits) Mon Jan 19 16:59:01 2009 using double large prime bound of 1933086450144842 (43-51 bits) Mon Jan 19 16:59:01 2009 using trial factoring cutoff of 51 bits Mon Jan 19 16:59:01 2009 polynomial 'A' values have 12 factors Mon Jan 19 19:52:38 2009 78710 relations (19906 full + 58804 combined from 1154571 partial), need 78609 Mon Jan 19 19:52:39 2009 begin with 1174477 relations Mon Jan 19 19:52:41 2009 reduce to 201809 relations in 11 passes Mon Jan 19 19:52:41 2009 attempting to read 201809 relations Mon Jan 19 19:52:44 2009 recovered 201809 relations Mon Jan 19 19:52:44 2009 recovered 181459 polynomials Mon Jan 19 19:52:44 2009 attempting to build 78710 cycles Mon Jan 19 19:52:44 2009 found 78710 cycles in 6 passes Mon Jan 19 19:52:44 2009 distribution of cycle lengths: Mon Jan 19 19:52:44 2009 length 1 : 19906 Mon Jan 19 19:52:44 2009 length 2 : 14145 Mon Jan 19 19:52:44 2009 length 3 : 13515 Mon Jan 19 19:52:44 2009 length 4 : 10573 Mon Jan 19 19:52:44 2009 length 5 : 7714 Mon Jan 19 19:52:44 2009 length 6 : 5210 Mon Jan 19 19:52:44 2009 length 7 : 3266 Mon Jan 19 19:52:44 2009 length 9+: 4381 Mon Jan 19 19:52:44 2009 largest cycle: 20 relations Mon Jan 19 19:52:45 2009 matrix is 78513 x 78710 (19.9 MB) with weight 4897447 (62.22/col) Mon Jan 19 19:52:45 2009 sparse part has weight 4897447 (62.22/col) Mon Jan 19 19:52:46 2009 filtering completed in 3 passes Mon Jan 19 19:52:46 2009 matrix is 74338 x 74402 (18.9 MB) with weight 4664277 (62.69/col) Mon Jan 19 19:52:46 2009 sparse part has weight 4664277 (62.69/col) Mon Jan 19 19:52:46 2009 saving the first 48 matrix rows for later Mon Jan 19 19:52:46 2009 matrix is 74290 x 74402 (11.7 MB) with weight 3587319 (48.22/col) Mon Jan 19 19:52:46 2009 sparse part has weight 2609601 (35.07/col) Mon Jan 19 19:52:46 2009 matrix includes 64 packed rows Mon Jan 19 19:52:46 2009 using block size 29760 for processor cache size 1024 kB Mon Jan 19 19:52:47 2009 commencing Lanczos iteration Mon Jan 19 19:52:47 2009 memory use: 11.5 MB Mon Jan 19 19:53:24 2009 lanczos halted after 1176 iterations (dim = 74290) Mon Jan 19 19:53:24 2009 recovered 17 nontrivial dependencies Mon Jan 19 19:53:25 2009 prp46 factor: 1323084657260748762081931294088186861983105043 Mon Jan 19 19:53:25 2009 prp50 factor: 13788677845491133788833382578002306992383451342683 Mon Jan 19 19:53:25 2009 elapsed time 02:54:27
Jan 19, 2009 (9th): By Robert Backstrom / GGNFS, GMP-ECM / Jan 19, 2009
(41·10¹⁰¹+13)/9 = 4(5)₁₀₀7_<102> = 1349637629_<10> · C93
C93 = P45 · P49
P45 = 191496859003974475105682158910488587574696781_<45>
P49 = 1762635505817914536013970629736936246987392363693_<49>

Number: n N=337539162933012410515382537215517688826646930689241738350758117129791107473305010789348372233 ( 93 digits) SNFS difficulty: 102 digits. Divisors found: r1=191496859003974475105682158910488587574696781 (pp45) r2=1762635505817914536013970629736936246987392363693 (pp49) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.53 hours. Scaled time: 0.97 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_5_100_7 n: 337539162933012410515382537215517688826646930689241738350758117129791107473305010789348372233 deg: 5 c5: 410 c0: 13 m: 100000000000000000000 skew: 0.50 type: snfs rlim: 320000 alim: 320000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 5000 Factor base limits: 320000/320000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [160000, 205001) Primes: RFBsize:27608, AFBsize:27356, largePrimes:3421418 encountered Relations: rels:2947643, finalFF:110338 Max relations in full relation-set: 48 Initial matrix: 55031 x 110338 with sparse part having weight 13990398. Pruned matrix : 47933 x 48272 with weight 3369240. Total sieving time: 0.47 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,320000,320000,28,28,56,56,2.5,2.5,20000 total time: 0.53 hours. --------- CPU info (if available) ----------
(41·10¹⁰⁷+13)/9 = 4(5)₁₀₆7_<108> = 17 · 19 · 23 · 29 · 1039 · 824837579 · C91
C91 = P33 · P58
P33 = 541569653892075251734476295882633_<33>
P58 = 4555905249401482963380109946391715265753948941966190484649_<58>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 2467340029083449908401427777071389719828177794433844854548394187576771140822696501492200817 (91 digits) Using B1=998000, B2=1045563762, polynomial Dickson(6), sigma=3539449428 Step 1 took 6203ms Step 2 took 3703ms ********** Factor found in step 2: 541569653892075251734476295882633 Found probable prime factor of 33 digits: 541569653892075251734476295882633 Probable prime cofactor 4555905249401482963380109946391715265753948941966190484649 has 58 digits
Jan 19, 2009 (8th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 19, 2009
(37·10¹⁶³+17)/9 = 4(1)₁₆₂3_<164> = 68483 · 6032309821_<10> · 52051080620258933_<17> · C133
C133 = P39 · P45 · P50
P39 = 201971245076419635985427244193183158857_<39>
P45 = 766865902905323843944912313206274717756086063_<45>
P50 = 12343947829085375388272773864904907879747898874597_<50>

Number: 41113_163 N=1911890646370876376235553188966780688265478666291531097174081860068199318204711570672140611944772184016625969886744063563671797998627 ( 133 digits) SNFS difficulty: 166 digits. Divisors found: r1=201971245076419635985427244193183158857 r2=766865902905323843944912313206274717756086063 r3=12343947829085375388272773864904907879747898874597 Version: Total time: 31.70 hours. Scaled time: 75.68 units (timescale=2.387). Factorization parameters were as follows: n: 1911890646370876376235553188966780688265478666291531097174081860068199318204711570672140611944772184016625969886744063563671797998627 m: 1000000000000000000000000000000000 deg: 5 c5: 37 c0: 1700 skew: 2.15 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4800000/4800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2400000, 4900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9945719 Max relations in full relation-set: Initial matrix: Pruned matrix : 872346 x 872593 Total sieving time: 28.46 hours. Total relation processing time: 1.22 hours. Matrix solve time: 1.80 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,51,51,2.4,2.4,100000 total time: 31.70 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 19, 2009 (7th): By Serge Batalov / GMP-ECM 6.2.1 / Jan 19, 2009
(41·10¹¹⁴+13)/9 = 4(5)₁₁₃7_<115> = 3² · 1463386738819003634121253_<25> · C90
C90 = P34 · P56
P34 = 3930355513162091606821126039498691_<34>
P56 = 88005109415345588123073252123601333380510933225681922451_<56>

Factor found in step 2: 3930355513162091606821126039498691
(41·10¹³⁹+13)/9 = 4(5)₁₃₈7_<140> = 17 · 47 · 607 · 1741 · 2374277 · 429292313655220207781_<21> · C104
C104 = P29 · P76
P29 = 21801657963205126583049668893_<29>
P76 = 2427912805886171394548275652570474227869473125503474032897907815700875098229_<76>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3728230061 Step 1 took 7005ms ********** Factor found in step 1: 21801657963205126583049668893 Found probable prime factor of 29 digits: 21801657963205126583049668893 Probable prime cofactor has 76 digits
(41·10¹³⁴+13)/9 = 4(5)₁₃₃7_<135> = 177797 · 290827 · C124
C124 = P31 · P94
P31 = 1137775100406018011521513383173_<31>
P94 = 7743294372051181915320432604097700365171873233887895228198421676496704674483207801736789446311_<94>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=207593391 Step 1 took 2720ms Step 2 took 2063ms ********** Factor found in step 2: 1137775100406018011521513383173 Found probable prime factor of 31 digits: 1137775100406018011521513383173 Probable prime cofactor has 94 digits
(41·10¹³⁰+13)/9 = 4(5)₁₂₉7_<131> = 547 · 1567 · C125
C125 = P29 · P97
P29 = 30674541940541323556463883511_<29>
P97 = 1732634422343984716886855445721622722403019886436256791707786647044682028108458886668414627731263_<97>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=855165405 Step 1 took 2745ms Step 2 took 2061ms ********** Factor found in step 2: 30674541940541323556463883511 Found probable prime factor of 29 digits: 30674541940541323556463883511 Probable prime cofactor has 97 digits
(41·10¹²⁴+13)/9 = 4(5)₁₂₃7_<125> = 109 · 2459 · C120
C120 = P32 · P88
P32 = 27552660149342947824495408694073_<32>
P88 = 6168687718140127868368841956002554606415386279442679587977932353995948714156451167473139_<88>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4175459408 Step 1 took 9950ms Step 2 took 12236ms ********** Factor found in step 2: 27552660149342947824495408694073 Found probable prime factor of 32 digits: 27552660149342947824495408694073 Probable prime cofactor has 88 digits
(41·10¹⁸⁵+13)/9 = 4(5)₁₈₄7_<186> = 47 · 1051 · 25204917910717160308267_<23> · C159
C159 = P32 · P128
P32 = 28892316820112975460853426075387_<32>
P128 = 12664064608002915777788152889905085475736571681017867784965528678359881731741429305462714381414364105333224200043928341290790089_<128>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1958335583 Step 1 took 11805ms Step 2 took 12660ms ********** Factor found in step 2: 28892316820112975460853426075387 Found probable prime factor of 32 digits: 28892316820112975460853426075387 Probable prime cofactor has 128 digits
Jan 19, 2009 (6th): Factorizations of 455...557 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
433...339 and 455...553 will be extended later.
Jan 19, 2009 (5th): By Serge Batalov / GMP-ECM 6.2.1 / Jan 19, 2009
(38·10¹⁷²+43)/9 = 4(2)₁₇₁7_<173> = 78904708409084059771_<20> · 203557052143526710221580765970953_<33> · C121
C121 = P36 · P85
P36 = 420734513010606963946049354023057901_<36>
P85 = 6248041078509551353101256469453718149726177872481573643816712145739964244757462590629_<85>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3144912507 Step 1 took 9919ms Step 2 took 12237ms ********** Factor found in step 2: 420734513010606963946049354023057901 Found probable prime factor of 36 digits: 420734513010606963946049354023057901 Probable prime cofactor has 85 digits
(31·10¹⁷³+23)/9 = 3(4)₁₇₂7_<174> = 9492103471_<10> · 27069297163_<11> · 92908475405229428506788810564397_<32> · C122
C122 = P37 · P86
P37 = 1271867235151492354244516276979799369_<37>
P86 = 11344428648092218894095486717270656404383494382905349632292223973872748424954682767623_<86>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2246719298 Step 1 took 9904ms Step 2 took 11833ms ********** Factor found in step 2: 1271867235151492354244516276979799369 Found probable prime factor of 37 digits: 1271867235151492354244516276979799369 Probable prime cofactor has 86 digits
(35·10¹⁷⁸+1)/9 = 3(8)₁₇₇9_<179> = 3 · 723328843723621_<15> · 1604042672514887393_<19> · 113924427578431510728409_<24> · C122
C122 = P38 · P85
P38 = 52353651649346759585876888758979954129_<38>
P85 = 1873219822685721131438109990191872553706066300586969533989207471921093745994540622111_<85>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=4024858816 Step 1 took 10025ms Step 2 took 12274ms ********** Factor found in step 2: 52353651649346759585876888758979954129 Found probable prime factor of 38 digits: 52353651649346759585876888758979954129 Probable prime cofactor has 85 digits
Jan 19, 2009 (4th): By Erik Branger / GGNFS, Msieve / Jan 19, 2009
(43·10¹⁷²-7)/9 = 4(7)₁₇₂_<173> = 19 · 223 · 273842461 · C161
C161 = P70 · P91
P70 = 6941291317736286782073303602411662044216942598401706881620737753047439_<70>
P91 = 5932345295064880058048049218132535850826803648773363051774178987910528595746827458377686199_<91>

Number: 47777_172 N=41178136890447562326026403306646311339851781446200174720208011694883423225884632443497443169775352122387018738833041769196401751763481244442735023304349902594361 ( 161 digits) SNFS difficulty: 175 digits. Divisors found: r1=6941291317736286782073303602411662044216942598401706881620737753047439 r2=5932345295064880058048049218132535850826803648773363051774178987910528595746827458377686199 Version: Total time: 126.49 hours. Scaled time: 254.24 units (timescale=2.010). Factorization parameters were as follows: n: 41178136890447562326026403306646311339851781446200174720208011694883423225884632443497443169775352122387018738833041769196401751763481244442735023304349902594361 m: 50000000000000000000000000000000000 deg: 5 c5: 172 c0: -875 skew: 1.38 type: snfs lss: 1 rlim: 5900000 alim: 5900000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5900000/5900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved rational special-q in [2950000, 6850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1176953 x 1177201 Total sieving time: 126.49 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,175,5,0,0,0,0,0,0,0,0,5900000,5900000,28,28,52,52,2.5,2.5,100000 total time: 126.49 hours. --------- CPU info (if available) ----------
Jan 19, 2009 (3rd): By Markus Tervooren / PRIMO / Jan 15, 2009
(13·10²⁷⁴³+11)/3 = 4(3)₂₇₄₂7_<2744> is prime.
Jan 19, 2009 (2nd): List of near-repdigit-related prime numbers is available.
Jan 19, 2009: By Tyler Cadigan / GGNFS msieve / Jan 19, 2009
(43·10¹⁸¹-7)/9 = 4(7)₁₈₁_<182> = 941 · 394782412033130453791_<21> · C159
C159 = P50 · P110
P50 = 11762494900496736764278874195216335838416155314149_<50>
P110 = 10934000222758789623278936927899822714858830939221261071656118922521895869107432990306817336243775060012500783_<110>

Number: 47777_181 N=128611121862230446765269107714484784834155430912953973027917455389262678968963120276135652426748429840669621417121389597978273948148186906111154745216473478667 ( 159 digits) SNFS difficulty: 183 digits. Divisors found: r1=11762494900496736764278874195216335838416155314149 (pp50) r2=10934000222758789623278936927899822714858830939221261071656118922521895869107432990306817336243775060012500783 (pp110) Version: Msieve-1.39 Total time: 208.06 hours. Scaled time: 469.38 units (timescale=2.256). Factorization parameters were as follows: n: 128611121862230446765269107714484784834155430912953973027917455389262678968963120276135652426748429840669621417121389597978273948148186906111154745216473478667 m: 2000000000000000000000000000000000000 deg: 5 c5: 215 c0: -112 skew: 0.88 type: snfs lss: 1 rlim: 8100000 alim: 8100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 8100000/8100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [4050000, 7050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1150786 x 1151034 Total sieving time: 208.06 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,183,5,0,0,0,0,0,0,0,0,8100000,8100000,28,28,53,53,2.5,2.5,100000 total time: 208.06 hours. --------- CPU info (if available) ----------
Jan 18, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 18, 2009
(13·10¹⁷⁶+11)/3 = 4(3)₁₇₅7_<177> = 1627 · 3244693 · 9839424687175087_<16> · 7214678530365912514392376942580747_<34> · C118
C118 = P55 · P63
P55 = 2647921762108576264092059984134504698004998754236125413_<55>
P63 = 436685823521850048650697860974923802737776010762066685670397031_<63>

Number: 43337_176 N=1156309895307811941622908693198246922243653991539782167408598606417694458851169627709353999330698718727763054818848803 ( 118 digits) Divisors found: r1=2647921762108576264092059984134504698004998754236125413 r2=436685823521850048650697860974923802737776010762066685670397031 Version: Total time: 20.45 hours. Scaled time: 48.82 units (timescale=2.387). Factorization parameters were as follows: name: 43337_176 n: 1156309895307811941622908693198246922243653991539782167408598606417694458851169627709353999330698718727763054818848803 skew: 86938.81 # norm 1.35e+16 c5: 6300 c4: 4926644502 c3: -246507659994353 c2: -32087229166127883695 c1: 545959753297972335924309 c0: 16408727250791251967319716217 # alpha -6.33 Y1: 6224387125139 Y0: -44950790497788532043480 # Murphy_E 4.23e-10 # M 491803742154308281868070421448617208199764438528474791943785419864700658290962699773504730358650003601248810959189583 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2000000, 3500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9094056 Max relations in full relation-set: Initial matrix: Pruned matrix : 641503 x 641751 Polynomial selection time: 2.00 hours. Total sieving time: 16.72 hours. Total relation processing time: 0.64 hours. Matrix solve time: 0.95 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000 total time: 20.45 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 18, 2009 (2nd): By Serge Batalov / Msieve-1.39 / Jan 18, 2009
(13·10¹⁶⁹+11)/3 = 4(3)₁₆₈7_<170> = 17 · 41 · 8599 · C163
C163 = P44 · P120
P44 = 22087011810801629543251722041130620916073931_<44>
P120 = 327344016680742970688278759292115174513035620073606621698749651782305565580130278811022668813825639938252180855560809909_<120>

SNFS difficulty: 171 digits. Divisors found: r1=22087011810801629543251722041130620916073931 (pp44) r2=327344016680742970688278759292115174513035620073606621698749651782305565580130278811022668813825639938252180855560809909 (pp120) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.288). Factorization parameters were as follows: n: 7230051162622815627744464853581175037925789531319719591920339963679559905673415585732306020925214074862952989818030179234636794764820061545532442935847922881382279 m: 10000000000000000000000000000000000 deg: 5 c5: 13 c0: 110 skew: 1.53 type: snfs lss: 1 rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2500000, 5200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 901506 x 901754 Total sieving time: 0.00 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,171,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 60.00 hours.
Jan 18, 2009: By Serge Batalov / PFGW / Jan 18, 2009
(7·10¹⁸⁵³⁶+11)/9 = (7)₁₈₅₃₅9_<18536> is PRP.
(25·10⁴³⁷⁵³-1)/3 = 8(3)₄₃₇₅₃_<43754> is PRP.
Jan 17, 2009 (3rd): By Serge Batalov / PFGW / Jan 17, 2009
(25·10¹⁹⁵⁷³-1)/3 = 8(3)₁₉₅₇₃_<19574> is PRP.
Jan 17, 2009 (2nd): By Sinkiti Sibata / Msieve / Jan 17, 2009
(13·10¹⁶²+11)/3 = 4(3)₁₆₁7_<163> = C163
C163 = P32 · P132
P32 = 34524487186108164589266926227963_<32>
P132 = 125514777669947954110061487216222423812216625154435593299309682944607690319606094120290179827989603346109673239467770114779667655099_<132>

Number: 43337_162 N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 ( 163 digits) SNFS difficulty: 164 digits. Divisors found: r1=34524487186108164589266926227963 r2=125514777669947954110061487216222423812216625154435593299309682944607690319606094120290179827989603346109673239467770114779667655099 Version: Total time: 60.01 hours. Scaled time: 118.05 units (timescale=1.967). Factorization parameters were as follows: name: 43337_162 n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 m: 200000000000000000000000000000000 deg: 5 c5: 325 c0: 88 skew: 0.77 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 4000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 721900 x 722148 Total sieving time: 60.01 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,164,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 60.01 hours. --------- CPU info (if available) ----------
Jan 17, 2009: By Serge Batalov / Msieve-1.39 / Jan 17, 2009
(13·10¹⁶⁷+11)/3 = 4(3)₁₆₆7_<168> = 53 · 59 · 463 · 2873041 · C156
C156 = P51 · P105
P51 = 194455719932452560733660170761976392451739776790187_<51>
P105 = 535735812999399153606191070676975358670063586820885715143607054168922311995203320428355887483546091708211_<105>

SNFS difficulty: 169 digits. Divisors found: r1=194455719932452560733660170761976392451739776790187 (pp51) r2=535735812999399153606191070676975358670063586820885715143607054168922311995203320428355887483546091708211 (pp105) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 104176893210395939690502374790242590846413000580702197124951516286550964995388752088010593638802767954770278632816407445627521800813303371615530069372125457 m: 2000000000000000000000000000000000 deg: 5 c5: 325 c0: 88 skew: 0.77 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2300000, 5100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 964562 x 964810 Total sieving time: 0.00 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,169,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.5,2.5,200000 total time: 48.00 hours.
Jan 16, 2009 (2nd): By Sinkiti Sibata / Msieve / Jan 16, 2009
(13·10¹⁶⁸+11)/3 = 4(3)₁₆₇7_<169> = C169
C169 = P31 · P38 · P100
P31 = 5846472133582342637694713367859_<31>
P38 = 74900637750264860219951078932462865953_<38>
P100 = 9895612898452368895553154031861840324724793753937589708723250272302747379331205428168055115630613731_<100>

Number: 43337_168 N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 ( 169 digits) SNFS difficulty: 170 digits. Divisors found: r1=5846472133582342637694713367859 r2=74900637750264860219951078932462865953 r3=9895612898452368895553154031861840324724793753937589708723250272302747379331205428168055115630613731 Version: Total time: 66.86 hours. Scaled time: 172.16 units (timescale=2.575). Factorization parameters were as follows: name: 43337_168 n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 m: 5000000000000000000000000000000000 deg: 5 c5: 104 c0: 275 skew: 1.21 type: snfs lss: 1 rlim: 4900000 alim: 4900000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4900000/4900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2450000, 5250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 912020 x 912268 Total sieving time: 66.86 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,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 66.86 hours. --------- CPU info (if available) ----------
Jan 16, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 16, 2009
(13·10¹⁶¹+11)/3 = 4(3)₁₆₀7_<162> = 109496623 · 14378378550629_<14> · C141
C141 = P49 · P92
P49 = 5715212407053093801499963783289143078633450460831_<49>
P92 = 48159179955016448416285230370078531173553150252889640143095600012242736469510165425171816181_<92>

Number: 43337_161 N=275239942792412661818761527536279723042021475242063102757272718266105632150916056789799483048330444045627931665600434601838675125207672506411 ( 141 digits) SNFS difficulty: 162 digits. Divisors found: r1=5715212407053093801499963783289143078633450460831 r2=48159179955016448416285230370078531173553150252889640143095600012242736469510165425171816181 Version: Total time: 18.32 hours. Scaled time: 43.67 units (timescale=2.384). Factorization parameters were as follows: n: 275239942792412661818761527536279723042021475242063102757272718266105632150916056789799483048330444045627931665600434601838675125207672506411 m: 100000000000000000000000000000000 deg: 5 c5: 130 c0: 11 skew: 0.61 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 3400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9505448 Max relations in full relation-set: Initial matrix: Pruned matrix : 669558 x 669806 Total sieving time: 16.36 hours. Total relation processing time: 0.70 hours. Matrix solve time: 1.01 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 18.32 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 15, 2009 (2nd): By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jan 15, 2009
(13·10¹⁶⁰+11)/3 = 4(3)₁₅₉7_<161> = 7 · 179 · 3764899 · 1327389905836927_<16> · C136
C136 = P62 · P75
P62 = 23089315162879420588279523578469903211678270597405443440485281_<62>
P75 = 299714762079039746128520371602155646310929719488958029620447471553499575433_<75>

Number: 43337_160 N=6920208600610370385069482795491829542945590344404204683796070425699101258300635541173618459414190728743093248609380824846048836985701673 ( 136 digits) SNFS difficulty: 161 digits. Divisors found: r1=23089315162879420588279523578469903211678270597405443440485281 r2=299714762079039746128520371602155646310929719488958029620447471553499575433 Version: Total time: 14.39 hours. Scaled time: 34.33 units (timescale=2.386). Factorization parameters were as follows: n: 6920208600610370385069482795491829542945590344404204683796070425699101258300635541173618459414190728743093248609380824846048836985701673 m: 100000000000000000000000000000000 deg: 5 c5: 13 c0: 11 skew: 0.97 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 2900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9337232 Max relations in full relation-set: Initial matrix: Pruned matrix : 582785 x 583033 Total sieving time: 13.00 hours. Total relation processing time: 0.56 hours. Matrix solve time: 0.77 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 14.39 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 15, 2009: By Serge Batalov / Msieve-1.39 gnfs, GMP-ECM 6.2.1 / Jan 15, 2009
(13·10¹⁵⁷+11)/3 = 4(3)₁₅₆7_<158> = 102880669 · 369766790874394873_<18> · 139134154642600968853_<21> · C112
C112 = P45 · P68
P45 = 216208054409157593062352088920460849768841063_<45>
P68 = 37866467412705690316757476796901761998436087074646294065413033980759_<68>

#borderline gnfs/snfs; found good polynomial => gnfs was faster # N=8187035246648864842469428858836938255001110448154352590335554145448569846238531738387635346650027384212871106817 ( 112 digits) Divisors found: r1=216208054409157593062352088920460849768841063 (pp45) r2=37866467412705690316757476796901761998436087074646294065413033980759 (pp68) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.710). Factorization parameters were as follows: name: 43337_157 n: 8187035246648864842469428858836938255001110448154352590335554145448569846238531738387635346650027384212871106817 skew: 61167.96 # norm 4.07e+15 c5: 6660 c4: 1079689452 c3: 25319299532829 c2: 863041214119956334 c1: -120283268263238551988060 c0: -871283991612239151823826625 # alpha -6.23 Y1: 31108648087 Y0: -4148875289325198945706 # Murphy_E 7.77e-10 # M 3263885175971627639211022329669223352106913257185713554496169784071687074017242523197383252707752474719357954621 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1750000, 3450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 518623 x 518869 Total sieving time: 0.00 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: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,52,52,2.4,2.4,100000 total time: 13.00 hours.
(64·10²²¹+53)/9 = 7(1)₂₂₀7_<222> = 3² · 11 · 128239 · 503398933 · 1004825417137_<13> · 27740572834433626007911111_<26> · 38068287072532520234581880952761336179_<38> · C132
C132 = P42 · P90
P42 = 363210988727484372496492328545443062110799_<42>
P90 = 288696490555827973898065260140780868120540968915440564796920084345573963153343559060691847_<90>

Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=3349363715 Step 1 took 141507ms Step 2 took 59822ms ********** Factor found in step 2: 363210988727484372496492328545443062110799 Found probable prime factor of 42 digits: 363210988727484372496492328545443062110799 Probable prime cofactor has 90 digits
Jan 14, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 14, 2009
(13·10¹⁵⁶+11)/3 = 4(3)₁₅₅7_<157> = 23 · 461 · 142142397253024033_<18> · 315050806155779087190431_<24> · C112
C112 = P50 · P62
P50 = 94337234232523356167988582191740606707889003037461_<50>
P62 = 96739973889631009267195768717081156635720572453826531736908193_<62>

Number: 43337_156 N=9126181576474314099316202688733744758158416274557063351600048441236717182538166050024590943065552750697896817973 ( 112 digits) Divisors found: r1=94337234232523356167988582191740606707889003037461 r2=96739973889631009267195768717081156635720572453826531736908193 Version: Total time: 12.22 hours. Scaled time: 29.16 units (timescale=2.386). Factorization parameters were as follows: name: 43337_156 n: 9126181576474314099316202688733744758158416274557063351600048441236717182538166050024590943065552750697896817973 skew: 18641.35 # norm 1.12e+16 c5: 51300 c4: 9553100985 c3: -245158431981470 c2: -9997132154517714014 c1: -29187811733112763484300 c0: 864894561673356993925839 # alpha -6.16 Y1: 252042445787 Y0: -2818596457005864723910 # Murphy_E 7.05e-10 # M 3166073086433628145140272011787914321793077868154941162459374115294849123320903337401078096742166896587091018999 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8304063 Max relations in full relation-set: Initial matrix: Pruned matrix : 434330 x 434578 Polynomial selection time: 0.87 hours. Total sieving time: 10.15 hours. Total relation processing time: 0.61 hours. Matrix solve time: 0.42 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000 total time: 12.22 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 14, 2009 (3rd): By Sinkiti Sibata / Msieve / Jan 14, 2009
(13·10¹³³+11)/3 = 4(3)₁₃₂7_<134> = 2179 · 10910803 · 921578036018367563267_<21> · C103
C103 = P50 · P53
P50 = 38536635444786366417186177412639724374473793960999_<50>
P53 = 51321842865559002570186158967759114685637664711207997_<53>

Tue Jan 13 14:36:39 2009 Msieve v. 1.39 Tue Jan 13 14:36:39 2009 random seeds: 56a1c8f0 8269d6a3 Tue Jan 13 14:36:39 2009 factoring 1977771148864657359017104644824987705954905186916919276490415161915497019205156970524246398328794909003 (103 digits) Tue Jan 13 14:36:40 2009 searching for 15-digit factors Tue Jan 13 14:36:42 2009 commencing quadratic sieve (103-digit input) Tue Jan 13 14:36:42 2009 using multiplier of 43 Tue Jan 13 14:36:42 2009 using 32kb Intel Core sieve core Tue Jan 13 14:36:42 2009 sieve interval: 36 blocks of size 32768 Tue Jan 13 14:36:42 2009 processing polynomials in batches of 6 Tue Jan 13 14:36:42 2009 using a sieve bound of 3327859 (120000 primes) Tue Jan 13 14:36:42 2009 using large prime bound of 499178850 (28 bits) Tue Jan 13 14:36:42 2009 using double large prime bound of 4537964541132150 (44-53 bits) Tue Jan 13 14:36:42 2009 using trial factoring cutoff of 53 bits Tue Jan 13 14:36:42 2009 polynomial 'A' values have 14 factors Wed Jan 14 07:35:42 2009 120314 relations (29962 full + 90352 combined from 1763406 partial), need 120096 Wed Jan 14 07:35:46 2009 begin with 1793368 relations Wed Jan 14 07:35:47 2009 reduce to 310748 relations in 11 passes Wed Jan 14 07:35:47 2009 attempting to read 310748 relations Wed Jan 14 07:35:54 2009 recovered 310748 relations Wed Jan 14 07:35:54 2009 recovered 301487 polynomials Wed Jan 14 07:35:54 2009 attempting to build 120314 cycles Wed Jan 14 07:35:54 2009 found 120314 cycles in 5 passes Wed Jan 14 07:35:54 2009 distribution of cycle lengths: Wed Jan 14 07:35:54 2009 length 1 : 29962 Wed Jan 14 07:35:54 2009 length 2 : 21154 Wed Jan 14 07:35:54 2009 length 3 : 20471 Wed Jan 14 07:35:54 2009 length 4 : 16386 Wed Jan 14 07:35:54 2009 length 5 : 12141 Wed Jan 14 07:35:54 2009 length 6 : 8168 Wed Jan 14 07:35:54 2009 length 7 : 5007 Wed Jan 14 07:35:54 2009 length 9+: 7025 Wed Jan 14 07:35:54 2009 largest cycle: 18 relations Wed Jan 14 07:35:55 2009 matrix is 120000 x 120314 (34.0 MB) with weight 8436990 (70.12/col) Wed Jan 14 07:35:55 2009 sparse part has weight 8436990 (70.12/col) Wed Jan 14 07:35:57 2009 filtering completed in 3 passes Wed Jan 14 07:35:57 2009 matrix is 114543 x 114607 (32.6 MB) with weight 8076914 (70.47/col) Wed Jan 14 07:35:57 2009 sparse part has weight 8076914 (70.47/col) Wed Jan 14 07:35:57 2009 saving the first 48 matrix rows for later Wed Jan 14 07:35:58 2009 matrix is 114495 x 114607 (20.7 MB) with weight 6465094 (56.41/col) Wed Jan 14 07:35:58 2009 sparse part has weight 4740334 (41.36/col) Wed Jan 14 07:35:58 2009 matrix includes 64 packed rows Wed Jan 14 07:35:58 2009 using block size 43690 for processor cache size 1024 kB Wed Jan 14 07:35:59 2009 commencing Lanczos iteration Wed Jan 14 07:35:59 2009 memory use: 19.6 MB Wed Jan 14 07:37:31 2009 lanczos halted after 1812 iterations (dim = 114493) Wed Jan 14 07:37:32 2009 recovered 16 nontrivial dependencies Wed Jan 14 07:37:33 2009 prp50 factor: 38536635444786366417186177412639724374473793960999 Wed Jan 14 07:37:33 2009 prp53 factor: 51321842865559002570186158967759114685637664711207997 Wed Jan 14 07:37:33 2009 elapsed time 17:00:54
Jan 14, 2009 (2nd): By Erik Branger / Msieve, GGNFS / Jan 14, 2009
(13·10¹⁵²+11)/3 = 4(3)₁₅₁7_<153> = 686270785677248325068309143_<27> · 2641783753842599494853063694281_<31> · C96
C96 = P48 · P49
P48 = 120905449768733457519894583951105281814559946607_<48>
P49 = 1976894276472640254386872707511473139863658297177_<49>

Tue Jan 13 16:04:46 2009 Msieve v. 1.38 Tue Jan 13 16:04:46 2009 random seeds: 5ea5d600 8195fe1a Tue Jan 13 16:04:46 2009 factoring 239017291642159478476222200461765008396478220370329255792346259720554607262768237545189658828439 (96 digits) Tue Jan 13 16:04:47 2009 searching for 15-digit factors Tue Jan 13 16:04:49 2009 commencing quadratic sieve (96-digit input) Tue Jan 13 16:04:49 2009 using multiplier of 1 Tue Jan 13 16:04:49 2009 using 64kb Pentium 4 sieve core Tue Jan 13 16:04:49 2009 sieve interval: 18 blocks of size 65536 Tue Jan 13 16:04:49 2009 processing polynomials in batches of 6 Tue Jan 13 16:04:49 2009 using a sieve bound of 2229089 (82353 primes) Tue Jan 13 16:04:49 2009 using large prime bound of 334363350 (28 bits) Tue Jan 13 16:04:49 2009 using double large prime bound of 2205939464917200 (43-51 bits) Tue Jan 13 16:04:49 2009 using trial factoring cutoff of 51 bits Tue Jan 13 16:04:49 2009 polynomial 'A' values have 12 factors Tue Jan 13 22:46:03 2009 82620 relations (19831 full + 62789 combined from 1238445 partial), need 82449 Tue Jan 13 22:46:09 2009 begin with 1258276 relations Tue Jan 13 22:46:10 2009 reduce to 216862 relations in 11 passes Tue Jan 13 22:46:10 2009 attempting to read 216862 relations Tue Jan 13 22:46:19 2009 recovered 216862 relations Tue Jan 13 22:46:19 2009 recovered 202259 polynomials Tue Jan 13 22:46:20 2009 attempting to build 82620 cycles Tue Jan 13 22:46:20 2009 found 82620 cycles in 5 passes Tue Jan 13 22:46:20 2009 distribution of cycle lengths: Tue Jan 13 22:46:20 2009 length 1 : 19831 Tue Jan 13 22:46:20 2009 length 2 : 14384 Tue Jan 13 22:46:20 2009 length 3 : 13780 Tue Jan 13 22:46:20 2009 length 4 : 11180 Tue Jan 13 22:46:20 2009 length 5 : 8539 Tue Jan 13 22:46:20 2009 length 6 : 5941 Tue Jan 13 22:46:20 2009 length 7 : 3722 Tue Jan 13 22:46:20 2009 length 9+: 5243 Tue Jan 13 22:46:20 2009 largest cycle: 21 relations Tue Jan 13 22:46:20 2009 matrix is 82353 x 82620 (22.5 MB) with weight 5571702 (67.44/col) Tue Jan 13 22:46:20 2009 sparse part has weight 5571702 (67.44/col) Tue Jan 13 22:46:22 2009 filtering completed in 3 passes Tue Jan 13 22:46:22 2009 matrix is 78709 x 78773 (21.6 MB) with weight 5338672 (67.77/col) Tue Jan 13 22:46:22 2009 sparse part has weight 5338672 (67.77/col) Tue Jan 13 22:46:23 2009 saving the first 48 matrix rows for later Tue Jan 13 22:46:23 2009 matrix is 78661 x 78773 (14.5 MB) with weight 4301329 (54.60/col) Tue Jan 13 22:46:23 2009 sparse part has weight 3319361 (42.14/col) Tue Jan 13 22:46:23 2009 matrix includes 64 packed rows Tue Jan 13 22:46:23 2009 using block size 21845 for processor cache size 512 kB Tue Jan 13 22:46:24 2009 commencing Lanczos iteration Tue Jan 13 22:46:24 2009 memory use: 13.4 MB Tue Jan 13 22:47:36 2009 lanczos halted after 1245 iterations (dim = 78659) Tue Jan 13 22:47:36 2009 recovered 17 nontrivial dependencies Tue Jan 13 22:47:37 2009 prp48 factor: 120905449768733457519894583951105281814559946607 Tue Jan 13 22:47:37 2009 prp49 factor: 1976894276472640254386872707511473139863658297177 Tue Jan 13 22:47:37 2009 elapsed time 06:42:51
(13·10¹⁵³+11)/3 = 4(3)₁₅₂7_<154> = 17 · 847373 · 12196369 · C140
C140 = P62 · P78
P62 = 65584580921735305097374227398029523494342491423519119650530487_<62>
P78 = 376067887997921142110137083688739434973552935635838676784563793032808788990219_<78>

Number: 43337_153 N=24664254832465748459502657707992646079096609823530663662827043415488430096613894185804502758072751671330661198306629868323758976748404306653 ( 140 digits) SNFS difficulty: 155 digits. Divisors found: r1=65584580921735305097374227398029523494342491423519119650530487 r2=376067887997921142110137083688739434973552935635838676784563793032808788990219 Version: Total time: 26.20 hours. Scaled time: 55.80 units (timescale=2.130). Factorization parameters were as follows: n: 24664254832465748459502657707992646079096609823530663662827043415488430096613894185804502758072751671330661198306629868323758976748404306653 m: 5000000000000000000000000000000 deg: 5 c5: 104 c0: 275 skew: 1.21 type: snfs lss: 1 rlim: 2700000 alim: 2700000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2700000/2700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1350000, 2250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 489813 x 490061 Total sieving time: 26.20 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,155,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,50,50,2.4,2.4,100000 total time: 26.20 hours. --------- CPU info (if available) ----------
Jan 14, 2009: By Serge Batalov / Msieve-1.39 / Jan 14, 2009
(13·10¹⁴⁹+11)/3 = 4(3)₁₄₈7_<150> = 41 · C149
C149 = P37 · P49 · P63
P37 = 5774320557453509533551655639465224157_<37>
P49 = 5039432299373936049812725523191262751395620895863_<49>
P63 = 363208276154368335977320655706641846126561844130682961655421827_<63>

SNFS difficulty: 151 digits. Divisors found: r1=5774320557453509533551655639465224157 (pp37) r2=5039432299373936049812725523191262751395620895863 (pp49) r3=363208276154368335977320655706641846126561844130682961655421827 (pp63) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.558). Factorization parameters were as follows: n: 10569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691056910569105691057 m: 1000000000000000000000000000000 deg: 5 c5: 13 c0: 110 skew: 1.53 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1150000, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 440738 x 440986 Total sieving time: 0.00 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,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,52,52,2.4,2.4,100000 total time: 8.50 hours.
Jan 13, 2009 (5th): By Sinkiti Sibata / Msieve / Jan 13, 2009
(13·10¹¹⁹+11)/3 = 4(3)₁₁₈7_<120> = 29 · 41 · 4236371 · 1843458323135467_<16> · C95
C95 = P34 · P62
P34 = 1878925753271548350891453683398909_<34>
P62 = 24837238859994793450933098574132030571190107627519248166255641_<62>

ue Jan 13 08:53:45 2009 Msieve v. 1.39 Tue Jan 13 08:53:45 2009 random seeds: 4b861124 0f720d93 Tue Jan 13 08:53:45 2009 factoring 46667327734201090114002656028416818839645552235174196745415465210051218566528013255728674495669 (95 digits) Tue Jan 13 08:53:46 2009 searching for 15-digit factors Tue Jan 13 08:53:48 2009 commencing quadratic sieve (95-digit input) Tue Jan 13 08:53:48 2009 using multiplier of 1 Tue Jan 13 08:53:48 2009 using 32kb Intel Core sieve core Tue Jan 13 08:53:48 2009 sieve interval: 36 blocks of size 32768 Tue Jan 13 08:53:48 2009 processing polynomials in batches of 6 Tue Jan 13 08:53:48 2009 using a sieve bound of 2154241 (80000 primes) Tue Jan 13 08:53:48 2009 using large prime bound of 323136150 (28 bits) Tue Jan 13 08:53:48 2009 using double large prime bound of 2074406767356900 (43-51 bits) Tue Jan 13 08:53:48 2009 using trial factoring cutoff of 51 bits Tue Jan 13 08:53:48 2009 polynomial 'A' values have 12 factors Tue Jan 13 12:43:20 2009 80203 relations (19438 full + 60765 combined from 1206755 partial), need 80096 Tue Jan 13 12:43:22 2009 begin with 1226193 relations Tue Jan 13 12:43:23 2009 reduce to 210402 relations in 12 passes Tue Jan 13 12:43:23 2009 attempting to read 210402 relations Tue Jan 13 12:43:26 2009 recovered 210402 relations Tue Jan 13 12:43:26 2009 recovered 194756 polynomials Tue Jan 13 12:43:26 2009 attempting to build 80203 cycles Tue Jan 13 12:43:26 2009 found 80203 cycles in 6 passes Tue Jan 13 12:43:26 2009 distribution of cycle lengths: Tue Jan 13 12:43:26 2009 length 1 : 19438 Tue Jan 13 12:43:26 2009 length 2 : 13891 Tue Jan 13 12:43:26 2009 length 3 : 13446 Tue Jan 13 12:43:26 2009 length 4 : 11032 Tue Jan 13 12:43:26 2009 length 5 : 8138 Tue Jan 13 12:43:26 2009 length 6 : 5435 Tue Jan 13 12:43:26 2009 length 7 : 3618 Tue Jan 13 12:43:26 2009 length 9+: 5205 Tue Jan 13 12:43:26 2009 largest cycle: 19 relations Tue Jan 13 12:43:27 2009 matrix is 80000 x 80203 (21.4 MB) with weight 5300120 (66.08/col) Tue Jan 13 12:43:27 2009 sparse part has weight 5300120 (66.08/col) Tue Jan 13 12:43:28 2009 filtering completed in 3 passes Tue Jan 13 12:43:28 2009 matrix is 76294 x 76358 (20.5 MB) with weight 5073539 (66.44/col) Tue Jan 13 12:43:28 2009 sparse part has weight 5073539 (66.44/col) Tue Jan 13 12:43:28 2009 saving the first 48 matrix rows for later Tue Jan 13 12:43:28 2009 matrix is 76246 x 76358 (13.6 MB) with weight 4108305 (53.80/col) Tue Jan 13 12:43:28 2009 sparse part has weight 3104632 (40.66/col) Tue Jan 13 12:43:28 2009 matrix includes 64 packed rows Tue Jan 13 12:43:28 2009 using block size 30543 for processor cache size 1024 kB Tue Jan 13 12:43:29 2009 commencing Lanczos iteration Tue Jan 13 12:43:29 2009 memory use: 12.7 MB Tue Jan 13 12:44:08 2009 lanczos halted after 1206 iterations (dim = 76244) Tue Jan 13 12:44:08 2009 recovered 16 nontrivial dependencies Tue Jan 13 12:44:09 2009 prp34 factor: 1878925753271548350891453683398909 Tue Jan 13 12:44:09 2009 prp62 factor: 24837238859994793450933098574132030571190107627519248166255641 Tue Jan 13 12:44:09 2009 elapsed time 03:50:24
Jan 13, 2009 (4th): By Tyler Cadigan / GGNFS, msieve / Jan 13, 2009
(43·10¹⁸²-7)/9 = 4(7)₁₈₂_<183> = 3² · 73 · 1181 · 433373007451_<12> · C166
C166 = P52 · P114
P52 = 9186931074291987184692831511277158395546328415501621_<52>
P114 = 154660127199746895179494726776156683293322589732934675735755785599291749630480175689205742714029631751147398445811_<114>

Number: 47777_182 N=1420851928525306131384810224137335708768862208498603709062388536173963432978334067142466657738746292096501148717730968627053157488992019955679761766260696175351159631 ( 166 digits) SNFS difficulty: 185 digits. Divisors found: r1=9186931074291987184692831511277158395546328415501621 r2=154660127199746895179494726776156683293322589732934675735755785599291749630480175689205742714029631751147398445811 Version: Total time: 273.73 hours. Scaled time: 702.12 units (timescale=2.565). Factorization parameters were as follows: n: 1420851928525306131384810224137335708768862208498603709062388536173963432978334067142466657738746292096501148717730968627053157488992019955679761766260696175351159631 m: 5000000000000000000000000000000000000 deg: 5 c5: 172 c0: -875 skew: 1.38 type: snfs lss: 1 rlim: 8700000 alim: 8700000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 8700000/8700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4350000, 8350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1267000 x 1267248 Total sieving time: 273.73 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,185,5,0,0,0,0,0,0,0,0,8700000,8700000,28,28,54,54,2.5,2.5,100000 total time: 273.73 hours. --------- CPU info (if available) ----------
Jan 13, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Jan 13, 2009
(13·10¹⁵⁵+11)/3 = 4(3)₁₅₄7_<156> = 15047321 · 49563511001_<11> · 3135915200879_<13> · 202634515218602715532928720597_<30> · C96
C96 = P42 · P55
P42 = 441057055858236537663291454087634300850011_<42>
P55 = 2073138620268022456807154469119127942872134591485365329_<55>

Number: 43337_155 N=914372416241420607028108988210983881684880008198519659068075381745308228072890313094251568668619 ( 96 digits) Divisors found: r1=441057055858236537663291454087634300850011 r2=2073138620268022456807154469119127942872134591485365329 Version: Total time: 1.74 hours. Scaled time: 4.08 units (timescale=2.344). Factorization parameters were as follows: name: 43337_155 n: 914372416241420607028108988210983881684880008198519659068075381745308228072890313094251568668619 skew: 850.27 # norm 1.28e+13 c5: 1722240 c4: 2528621504 c3: -3201503230244 c2: -1551922914281701 c1: -56054921225939732 c0: 163929427857595464981 # alpha -5.18 Y1: 6580789747 Y0: -881058887475319886 # Murphy_E 5.08e-09 # M 757439245795757934347877784253836113424870900628781300281117679238811095220990558846603867178560 type: gnfs rlim: 800000 alim: 800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 40000 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [400000, 760001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3487001 Max relations in full relation-set: Initial matrix: Pruned matrix : 164098 x 164346 Polynomial selection time: 0.10 hours. Total sieving time: 1.41 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.06 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,95,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,800000,800000,26,26,48,48,2.5,2.5,40000 total time: 1.74 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
(35·10¹⁶²-17)/9 = 3(8)₁₆₁7_<163> = 2589231713141_<13> · 12349029638342801933_<20> · C132
C132 = P59 · P74
P59 = 11781950893253965807469256867841699660786517244589420402301_<59>
P74 = 10322967879635049910907388130429762547909825198231377987413088190570273779_<74>

Number: 38887_162 N=121624700630498173684945589913751429441110900948082268499060929326699912364448415246381069923413339739090111816543268001429891565479 ( 132 digits) SNFS difficulty: 164 digits. Divisors found: r1=11781950893253965807469256867841699660786517244589420402301 r2=10322967879635049910907388130429762547909825198231377987413088190570273779 Version: Total time: 23.59 hours. Scaled time: 56.16 units (timescale=2.381). Factorization parameters were as follows: n: 121624700630498173684945589913751429441110900948082268499060929326699912364448415246381069923413339739090111816543268001429891565479 m: 500000000000000000000000000000000 deg: 5 c5: 28 c0: -425 skew: 1.72 type: snfs lss: 1 rlim: 4400000 alim: 4400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4400000/4400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2200000, 4100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9656646 Max relations in full relation-set: Initial matrix: Pruned matrix : 787435 x 787683 Total sieving time: 21.02 hours. Total relation processing time: 0.90 hours. Matrix solve time: 1.42 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 23.59 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 13, 2009 (2nd): By Erik Branger / Msieve, GGNFS, GMP-ECM / Jan 13, 2009
(13·10¹⁰⁹+11)/3 = 4(3)₁₀₈7_<110> = 41 · 59 · 9733 · 1865681 · 676804619 · C88
C88 = P39 · P49
P39 = 256520167070456431216017369001734033877_<39>
P49 = 5682210117085333630347759668811604515091349537777_<49>

Mon Jan 12 21:26:42 2009 Mon Jan 12 21:26:42 2009 Mon Jan 12 21:26:42 2009 Msieve v. 1.38 Mon Jan 12 21:26:42 2009 random seeds: 69bc3878 fadd585e Mon Jan 12 21:26:42 2009 factoring 1457601488564167582376904387965802781013594372918615550739594838256848206561153609271429 (88 digits) Mon Jan 12 21:26:43 2009 searching for 15-digit factors Mon Jan 12 21:26:45 2009 commencing quadratic sieve (88-digit input) Mon Jan 12 21:26:45 2009 using multiplier of 5 Mon Jan 12 21:26:45 2009 using 64kb Pentium 4 sieve core Mon Jan 12 21:26:45 2009 sieve interval: 12 blocks of size 65536 Mon Jan 12 21:26:45 2009 processing polynomials in batches of 9 Mon Jan 12 21:26:45 2009 using a sieve bound of 1508323 (57218 primes) Mon Jan 12 21:26:45 2009 using large prime bound of 120665840 (26 bits) Mon Jan 12 21:26:45 2009 using double large prime bound of 352250616108160 (42-49 bits) Mon Jan 12 21:26:45 2009 using trial factoring cutoff of 49 bits Mon Jan 12 21:26:45 2009 polynomial 'A' values have 11 factors Mon Jan 12 22:23:31 2009 57690 relations (16809 full + 40881 combined from 591692 partial), need 57314 Mon Jan 12 22:23:33 2009 begin with 608501 relations Mon Jan 12 22:23:34 2009 reduce to 134916 relations in 10 passes Mon Jan 12 22:23:34 2009 attempting to read 134916 relations Mon Jan 12 22:23:36 2009 recovered 134916 relations Mon Jan 12 22:23:36 2009 recovered 105504 polynomials Mon Jan 12 22:23:36 2009 attempting to build 57690 cycles Mon Jan 12 22:23:36 2009 found 57690 cycles in 7 passes Mon Jan 12 22:23:36 2009 distribution of cycle lengths: Mon Jan 12 22:23:36 2009 length 1 : 16809 Mon Jan 12 22:23:36 2009 length 2 : 11829 Mon Jan 12 22:23:36 2009 length 3 : 10374 Mon Jan 12 22:23:36 2009 length 4 : 7297 Mon Jan 12 22:23:36 2009 length 5 : 4893 Mon Jan 12 22:23:36 2009 length 6 : 2942 Mon Jan 12 22:23:36 2009 length 7 : 1710 Mon Jan 12 22:23:36 2009 length 9+: 1836 Mon Jan 12 22:23:36 2009 largest cycle: 19 relations Mon Jan 12 22:23:36 2009 matrix is 57218 x 57690 (13.2 MB) with weight 3227221 (55.94/col) Mon Jan 12 22:23:36 2009 sparse part has weight 3227221 (55.94/col) Mon Jan 12 22:23:37 2009 filtering completed in 3 passes Mon Jan 12 22:23:37 2009 matrix is 51828 x 51892 (11.9 MB) with weight 2919739 (56.27/col) Mon Jan 12 22:23:37 2009 sparse part has weight 2919739 (56.27/col) Mon Jan 12 22:23:38 2009 saving the first 48 matrix rows for later Mon Jan 12 22:23:38 2009 matrix is 51780 x 51892 (7.8 MB) with weight 2281073 (43.96/col) Mon Jan 12 22:23:38 2009 sparse part has weight 1732802 (33.39/col) Mon Jan 12 22:23:38 2009 matrix includes 64 packed rows Mon Jan 12 22:23:38 2009 using block size 20756 for processor cache size 512 kB Mon Jan 12 22:23:38 2009 commencing Lanczos iteration Mon Jan 12 22:23:38 2009 memory use: 7.6 MB Mon Jan 12 22:24:04 2009 lanczos halted after 821 iterations (dim = 51779) Mon Jan 12 22:24:05 2009 recovered 17 nontrivial dependencies Mon Jan 12 22:24:05 2009 prp39 factor: 256520167070456431216017369001734033877 Mon Jan 12 22:24:05 2009 prp49 factor: 5682210117085333630347759668811604515091349537777 Mon Jan 12 22:24:05 2009 elapsed time 00:57:23
(13·10¹¹⁸+11)/3 = 4(3)₁₁₇7_<119> = 7 · 3907 · 46993697 · 260909002660049647_<18> · C90
C90 = P45 · P45
P45 = 168029835493934377112414378163671931047062153_<45>
P45 = 769069462436099182225717832905662638971957219_<45>

Total time: 1h10min Mon Jan 12 21:24:41 2009 Mon Jan 12 21:24:41 2009 Msieve v. 1.39 Mon Jan 12 21:24:41 2009 random seeds: f2f3bb18 d32cd53b Mon Jan 12 21:24:41 2009 factoring 129226615256546289517576317486989013308626224249216040685175451358625604564801902350032507 (90 digits) Mon Jan 12 21:24:43 2009 searching for 15-digit factors Mon Jan 12 21:24:45 2009 commencing quadratic sieve (90-digit input) Mon Jan 12 21:24:45 2009 using multiplier of 3 Mon Jan 12 21:24:45 2009 using 32kb Intel Core sieve core Mon Jan 12 21:24:45 2009 sieve interval: 35 blocks of size 32768 Mon Jan 12 21:24:45 2009 processing polynomials in batches of 6 Mon Jan 12 21:24:45 2009 using a sieve bound of 1575269 (59667 primes) Mon Jan 12 21:24:45 2009 using large prime bound of 126021520 (26 bits) Mon Jan 12 21:24:45 2009 using double large prime bound of 380890718607520 (42-49 bits) Mon Jan 12 21:24:45 2009 using trial factoring cutoff of 49 bits Mon Jan 12 21:24:45 2009 polynomial 'A' values have 11 factors Mon Jan 12 22:26:09 2009 59944 relations (16389 full + 43555 combined from 627938 partial), need 59763 Mon Jan 12 22:32:22 2009 Mon Jan 12 22:32:22 2009 Msieve v. 1.39 Mon Jan 12 22:32:22 2009 random seeds: 22ab1b00 118d0d91 Mon Jan 12 22:32:22 2009 factoring 129226615256546289517576317486989013308626224249216040685175451358625604564801902350032507 (90 digits) Mon Jan 12 22:32:23 2009 searching for 15-digit factors Mon Jan 12 22:32:24 2009 commencing quadratic sieve (90-digit input) Mon Jan 12 22:32:25 2009 using multiplier of 3 Mon Jan 12 22:32:25 2009 using 32kb Intel Core sieve core Mon Jan 12 22:32:25 2009 sieve interval: 35 blocks of size 32768 Mon Jan 12 22:32:25 2009 processing polynomials in batches of 6 Mon Jan 12 22:32:25 2009 using a sieve bound of 1575269 (59667 primes) Mon Jan 12 22:32:25 2009 using large prime bound of 126021520 (26 bits) Mon Jan 12 22:32:25 2009 using double large prime bound of 380890718607520 (42-49 bits) Mon Jan 12 22:32:25 2009 using trial factoring cutoff of 49 bits Mon Jan 12 22:32:25 2009 polynomial 'A' values have 11 factors Mon Jan 12 22:32:25 2009 restarting with 17385 full and 660657 partial relations Mon Jan 12 22:32:25 2009 67663 relations (17385 full + 50278 combined from 660657 partial), need 59763 Mon Jan 12 22:32:26 2009 begin with 678042 relations Mon Jan 12 22:32:26 2009 reduce to 163919 relations in 11 passes Mon Jan 12 22:32:26 2009 attempting to read 163919 relations Mon Jan 12 22:32:33 2009 recovered 162520 relations Mon Jan 12 22:32:33 2009 recovered 132645 polynomials Mon Jan 12 22:32:33 2009 attempting to build 66275 cycles Mon Jan 12 22:32:33 2009 found 66275 cycles in 5 passes Mon Jan 12 22:32:33 2009 distribution of cycle lengths: Mon Jan 12 22:32:33 2009 length 1 : 17235 Mon Jan 12 22:32:33 2009 length 2 : 12652 Mon Jan 12 22:32:33 2009 length 3 : 11758 Mon Jan 12 22:32:33 2009 length 4 : 9057 Mon Jan 12 22:32:33 2009 length 5 : 6448 Mon Jan 12 22:32:33 2009 length 6 : 4039 Mon Jan 12 22:32:33 2009 length 7 : 2302 Mon Jan 12 22:32:33 2009 length 9+: 2784 Mon Jan 12 22:32:33 2009 largest cycle: 19 relations Mon Jan 12 22:32:34 2009 matrix is 59667 x 66275 (16.6 MB) with weight 4087103 (61.67/col) Mon Jan 12 22:32:34 2009 sparse part has weight 4087103 (61.67/col) Mon Jan 12 22:32:34 2009 filtering completed in 4 passes Mon Jan 12 22:32:34 2009 matrix is 54146 x 54210 (12.4 MB) with weight 3023133 (55.77/col) Mon Jan 12 22:32:34 2009 sparse part has weight 3023133 (55.77/col) Mon Jan 12 22:32:34 2009 saving the first 48 matrix rows for later Mon Jan 12 22:32:34 2009 matrix is 54098 x 54210 (9.3 MB) with weight 2525714 (46.59/col) Mon Jan 12 22:32:34 2009 sparse part has weight 2115653 (39.03/col) Mon Jan 12 22:32:34 2009 matrix includes 64 packed rows Mon Jan 12 22:32:35 2009 using block size 21684 for processor cache size 2048 kB Mon Jan 12 22:32:35 2009 commencing Lanczos iteration Mon Jan 12 22:32:35 2009 memory use: 8.5 MB Mon Jan 12 22:32:51 2009 lanczos halted after 857 iterations (dim = 54096) Mon Jan 12 22:32:51 2009 recovered 17 nontrivial dependencies Mon Jan 12 22:32:52 2009 prp45 factor: 168029835493934377112414378163671931047062153 Mon Jan 12 22:32:52 2009 prp45 factor: 769069462436099182225717832905662638971957219 Mon Jan 12 22:32:52 2009 elapsed time 00:00:30
(13·10¹²⁰+11)/3 = 4(3)₁₁₉7_<121> = 409 · 324949958126413_<15> · C104
C104 = P48 · P57
P48 = 227050036432175964827663796653111153454106407169_<48>
P57 = 143602079285817911224220194059875432673371152120802566469_<57>

Number: 43337_120 N=32604857333581178199511028593996626669495904955556867346769957950556347799824542384755536881031900616261 ( 104 digits) SNFS difficulty: 121 digits. Divisors found: r1=227050036432175964827663796653111153454106407169 r2=143602079285817911224220194059875432673371152120802566469 Version: Total time: 2.10 hours. Scaled time: 4.40 units (timescale=2.095). Factorization parameters were as follows: n: 32604857333581178199511028593996626669495904955556867346769957950556347799824542384755536881031900616261 m: 1000000000000000000000000 deg: 5 c5: 13 c0: 11 skew: 0.97 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 615001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 73952 x 74184 Total sieving time: 2.10 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,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 2.10 hours. --------- CPU info (if available) ----------
(13·10¹⁴⁴+11)/3 = 4(3)₁₄₃7_<145> = 41 · 647 · 1109 · 7561082407_<10> · C128
C128 = P38 · P42 · P49
P38 = 24353796243374302911046568308905788143_<38>
P42 = 451509433028751312085588314867466560521161_<42>
P49 = 1771678628451735717484316845181719869224421486619_<49>

Number: 43337_144 N=19481322805051481457546269534110260714900539419098714595161198172145325771983636749495559156356002297169680525224476574968078237 ( 128 digits) SNFS difficulty: 146 digits. Divisors found: r1=24353796243374302911046568308905788143 r2=451509433028751312085588314867466560521161 r3=1771678628451735717484316845181719869224421486619 Version: Total time: 10.80 hours. Scaled time: 23.40 units (timescale=2.166). Factorization parameters were as follows: n: 19481322805051481457546269534110260714900539419098714595161198172145325771983636749495559156356002297169680525224476574968078237 m: 100000000000000000000000000000 deg: 5 c5: 13 c0: 110 skew: 1.53 type: snfs lss: 1 rlim: 1910000 alim: 1910000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1910000/1910000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [955000, 2055001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 304445 x 304693 Total sieving time: 10.80 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,146,5,0,0,0,0,0,0,0,0,1910000,1910000,26,26,49,49,2.3,2.3,100000 total time: 10.80 hours. --------- CPU info (if available) ----------
(13·10¹³⁸+11)/3 = 4(3)₁₃₇7_<139> = 1023833 · 42538632981937_<14> · C119
C119 = P36 · P84
P36 = 447180441827714627908526856724608823_<36>
P84 = 222498272794804930710956102860230693645267326212839296532940428281757809275112947639_<84>

Number: 43337_138 N=99496875934284246500941660778777866839855336465972506147730272280918518895060912149506031717411859566251369164756418897 ( 119 digits) SNFS difficulty: 140 digits. Divisors found: r1=447180441827714627908526856724608823 r2=222498272794804930710956102860230693645267326212839296532940428281757809275112947639 Version: Total time: 8.45 hours. Scaled time: 6.65 units (timescale=0.788). Factorization parameters were as follows: n: 99496875934284246500941660778777866839855336465972506147730272280918518895060912149506031717411859566251369164756418897 m: 5000000000000000000000000000 deg: 5 c5: 104 c0: 275 skew: 1.21 type: snfs lss: 1 rlim: 1540000 alim: 1540000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1540000/1540000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [770000, 1570001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 237133 x 237381 Total sieving time: 8.45 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,140,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000 total time: 8.45 hours. --------- CPU info (if available) ----------
(13·10¹⁴⁶+11)/3 = 4(3)₁₄₅7_<147> = 19 · 83 · 2061038947620030393512130854959_<31> · C114
C114 = P36 · P78
P36 = 163493563027500334028675025536906033_<36>
P78 = 815461660049604937978163799568239320621530827894288671469726321744430193811023_<78>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 133322732313830136091385992077768305157424353549583445582707356592375648731047454889267483803451585005072510601759 (114 digits) Using B1=3000000, B2=3000000-5706890290, polynomial Dickson(6), sigma=303601485 Step 1 took 31122ms Step 2 took 11638ms ********** Factor found in step 2: 163493563027500334028675025536906033 Found probable prime factor of 36 digits: 163493563027500334028675025536906033 Probable prime cofactor 815461660049604937978163799568239320621530827894288671469726321744430193811023 has 78 digits
Jan 13, 2009: By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39
(13·10¹³⁵+11)/3 = 4(3)₁₃₄7_<136> = 383 · 6895616658353_<13> · C121
C121 = P31 · P91
P31 = 1179740285286225325598394472151_<31>
P91 = 1390797187214783276169378207767343950303330104479721308431542522056108887221238741129373313_<91>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=362790999 Step 1 took 3304ms Step 2 took 2472ms ********** Factor found in step 2: 1179740285286225325598394472151 Found probable prime factor of 31 digits: 1179740285286225325598394472151 Probable prime cofactor has 91 digits
(13·10¹⁴¹+11)/3 = 4(3)₁₄₀7_<142> = 53 · 486667 · 402091448583563_<15> · C120
C120 = P33 · P87
P33 = 734205875738359990609171143110293_<33>
P87 = 569077790659862392446982150080883761511884714960641444153678930769424205644134611144393_<87>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3488388741 Step 1 took 3303ms ********** Factor found in step 1: 734205875738359990609171143110293 Found probable prime factor of 33 digits: 734205875738359990609171143110293 Probable prime cofactor has 87 digits
(13·10¹⁰¹+11)/3 = 4(3)₁₀₀7_<102> = 1871 · C99
C99 = P39 · P60
P39 = 287901958827662472078564273285171611759_<39>
P60 = 804458584277280715235351680045826648501228131747829929796633_<60>

SNFS difficulty: 103 digits. Divisors found: r1=287901958827662472078564273285171611759 (pp39) r2=804458584277280715235351680045826648501228131747829929796633 (pp60) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.298). Factorization parameters were as follows: n: 231605202209157313379654373775164796009264208088366292535186174951006591840370568323534651701407447 m: 20000000000000000000000000 deg: 4 c4: 65 c0: 88 skew: 1.08 type: snfs lss: 1 rlim: 360000 alim: 360000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [180000, 220001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 35265 x 35500 Total sieving time: 0.00 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,103,4,0,0,0,0,0,0,0,0,360000,360000,25,25,46,46,2.3,2.3,20000 total time: 0.50 hours.
(13·10¹¹⁶+11)/3 = 4(3)₁₁₅7_<117> = 2243 · C114
C114 = P56 · P58
P56 = 24723085706747411858193701032591750746561027082019126789_<56>
P58 = 7814301247122253025846086919338828487274309830393265849431_<58>

SNFS difficulty: 117 digits. Divisors found: r1=24723085706747411858193701032591750746561027082019126789 (pp56) r2=7814301247122253025846086919338828487274309830393265849431 (pp58) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.297). Factorization parameters were as follows: n: 193193639470946648833407638579283697429038490117402288601575271214147718828949323822261851686729083073264972507059 m: 100000000000000000000000 deg: 5 c5: 130 c0: 11 skew: 0.61 type: snfs lss: 1 rlim: 630000 alim: 630000 lpbr: 25 lpba: 25 mfbr: 48 mfba: 48 rlambda: 2.2 alambda: 2.2 Factor base limits: 630000/630000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 48/48 Sieved rational special-q in [315000, 515001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 65631 x 65861 Total sieving time: 0.00 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,117,5,0,0,0,0,0,0,0,0,630000,630000,25,25,48,48,2.2,2.2,50000 total time: 0.90 hours.
(13·10¹⁹⁸+11)/3 = 4(3)₁₉₇7_<199> = 228521 · C194
C194 = P28 · C166
P28 = 7398690232181262061837908593_<28>
C166 = [2562955921056643657369718794314123503026583369057025549235277178026716563560559650778997176320033555655178458140715495725060185839224317583375229287594620326583476929_<166>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=643488791 Step 1 took 6296ms Step 2 took 3919ms ********** Factor found in step 2: 7398690232181262061837908593 Found probable prime factor of 28 digits: 7398690232181262061837908593 Composite cofactor has 166 digits
(13·10¹⁷¹+11)/3 = 4(3)₁₇₀7_<172> = 197 · 493457 · 218656623667_<12> · 9240619543413967_<16> · 181007105164409904932089_<24> · C114
C114 = P35 · P79
P35 = 42437908770327161353502748258707797_<35>
P79 = 2872058172684506346630550954044468196069561799481335826483411687432830745426269_<79>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1644727183 Step 1 took 8191ms Step 2 took 9318ms ********** Factor found in step 2: 42437908770327161353502748258707797 Found probable prime factor of 35 digits: 42437908770327161353502748258707797 Probable prime cofactor has 79 digits
(13·10¹⁴⁵+11)/3 = 4(3)₁₄₄7_<146> = 1259 · 1072826963357_<13> · 2036616450721_<13> · C119
C119 = P33 · P34 · P53
P33 = 478862024668223181910294165350637_<33>
P34 = 2090097750097179593328371828976553_<34>
P53 = 15739119933263023002620364116075849632754645511358379_<53>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2413085966 Step 1 took 9950ms Step 2 took 2478ms ********** Factor found in step 2: 2090097750097179593328371828976553 Found probable prime factor of 34 digits: 2090097750097179593328371828976553 Composite cofactor has 85 digits Mon Jan 12 14:39:25 2009 Msieve v. 1.39 Mon Jan 12 14:39:25 2009 random seeds: bad1e317 a2e5f3cc Mon Jan 12 14:39:25 2009 factoring 7536866837738320921666098847731440383268647485457604604108798019696763265724702937423 (85 digits) Mon Jan 12 14:39:26 2009 searching for 15-digit factors Mon Jan 12 14:39:26 2009 commencing quadratic sieve (85-digit input) Mon Jan 12 14:39:26 2009 using multiplier of 5 Mon Jan 12 14:39:26 2009 using 64kb Opteron sieve core Mon Jan 12 14:39:26 2009 sieve interval: 6 blocks of size 65536 Mon Jan 12 14:39:26 2009 processing polynomials in batches of 17 Mon Jan 12 14:39:26 2009 using a sieve bound of 1426393 (54706 primes) Mon Jan 12 14:39:26 2009 using large prime bound of 115537833 (26 bits) Mon Jan 12 14:39:26 2009 using double large prime bound of 325764350421651 (41-49 bits) Mon Jan 12 14:39:26 2009 using trial factoring cutoff of 49 bits Mon Jan 12 14:39:26 2009 polynomial 'A' values have 11 factors Mon Jan 12 14:39:26 2009 restarting with 2034 full and 73370 partial relations Mon Jan 12 15:10:08 2009 54908 relations (15814 full + 39094 combined from 574147 partial), need 54802 Mon Jan 12 15:10:08 2009 begin with 589961 relations Mon Jan 12 15:10:09 2009 reduce to 129977 relations in 9 passes Mon Jan 12 15:10:09 2009 attempting to read 129977 relations Mon Jan 12 15:10:10 2009 recovered 129977 relations Mon Jan 12 15:10:10 2009 recovered 112279 polynomials Mon Jan 12 15:10:10 2009 attempting to build 54908 cycles Mon Jan 12 15:10:10 2009 found 54908 cycles in 5 passes Mon Jan 12 15:10:10 2009 distribution of cycle lengths: Mon Jan 12 15:10:10 2009 length 1 : 15814 Mon Jan 12 15:10:10 2009 length 2 : 10905 Mon Jan 12 15:10:10 2009 length 3 : 9701 Mon Jan 12 15:10:10 2009 length 4 : 7053 Mon Jan 12 15:10:10 2009 length 5 : 4821 Mon Jan 12 15:10:10 2009 length 6 : 2985 Mon Jan 12 15:10:10 2009 length 7 : 1681 Mon Jan 12 15:10:10 2009 length 9+: 1948 Mon Jan 12 15:10:10 2009 largest cycle: 19 relations Mon Jan 12 15:10:10 2009 matrix is 54706 x 54908 (13.0 MB) with weight 2967305 (54.04/col) Mon Jan 12 15:10:10 2009 sparse part has weight 2967305 (54.04/col) Mon Jan 12 15:10:11 2009 filtering completed in 3 passes Mon Jan 12 15:10:11 2009 matrix is 50009 x 50073 (12.0 MB) with weight 2733224 (54.58/col) Mon Jan 12 15:10:11 2009 sparse part has weight 2733224 (54.58/col) Mon Jan 12 15:10:11 2009 saving the first 48 matrix rows for later Mon Jan 12 15:10:11 2009 matrix is 49961 x 50073 (7.3 MB) with weight 2067954 (41.30/col) Mon Jan 12 15:10:11 2009 sparse part has weight 1414146 (28.24/col) Mon Jan 12 15:10:11 2009 matrix includes 64 packed rows Mon Jan 12 15:10:11 2009 using block size 20029 for processor cache size 1024 kB Mon Jan 12 15:10:11 2009 commencing Lanczos iteration Mon Jan 12 15:10:11 2009 memory use: 6.8 MB Mon Jan 12 15:10:23 2009 lanczos halted after 791 iterations (dim = 49957) Mon Jan 12 15:10:24 2009 recovered 16 nontrivial dependencies Mon Jan 12 15:10:24 2009 prp33 factor: 478862024668223181910294165350637 Mon Jan 12 15:10:24 2009 prp53 factor: 15739119933263023002620364116075849632754645511358379 Mon Jan 12 15:10:24 2009 elapsed time 00:30:59
(13·10¹⁷⁷+11)/3 = 4(3)₁₇₆7_<178> = 139 · 79801 · 379612468397_<12> · 466858693163647_<15> · C145
C145 = P33 · P112
P33 = 517032018136409059571353874400367_<33>
P112 = 4263395347163435754605167105549384651423460652755404927762370848388609390026405509148863593252815692516229219711_<112>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=593251309 Step 1 took 11725ms Step 2 took 11716ms ********** Factor found in step 2: 517032018136409059571353874400367 Found probable prime factor of 33 digits: 517032018136409059571353874400367 Probable prime cofactor has 112 digits
(13·10¹⁵²+11)/3 = 4(3)₁₅₁7_<153> = 686270785677248325068309143_<27> · C126
C126 = P31 · C96
P31 = 2641783753842599494853063694281_<31>
C96 = [239017291642159478476222200461765008396478220370329255792346259720554607262768237545189658828439_<96>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1460152651 Step 1 took 9733ms Step 2 took 10264ms ********** Factor found in step 2: 2641783753842599494853063694281 Found probable prime factor of 31 digits: 2641783753842599494853063694281 Composite cofactor has 96 digits
(13·10¹⁷⁶+11)/3 = 4(3)₁₇₅7_<177> = 1627 · 3244693 · 9839424687175087_<16> · C151
C151 = P34 · C118
P34 = 7214678530365912514392376942580747_<34>
C118 = [1156309895307811941622908693198246922243653991539782167408598606417694458851169627709353999330698718727763054818848803_<118>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1504423703 Step 1 took 11712ms Step 2 took 12076ms ********** Factor found in step 2: 7214678530365912514392376942580747 Found probable prime factor of 34 digits: 7214678530365912514392376942580747 Composite cofactor has 118 digits
(13·10¹⁷⁰+11)/3 = 4(3)₁₆₉7_<171> = 1499 · 567902254172162219_<18> · C150
C150 = P28 · C123
P28 = 1373651784966490440402937717_<28>
C123 = [370569965767644980357356235399428856137811078710645235253822530344840763763076823444886948979877902193136601912075023451181_<123>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2409739674 Step 1 took 11736ms ********** Factor found in step 1: 1373651784966490440402937717 Found probable prime factor of 28 digits: 1373651784966490440402937717 Composite cofactor has 123 digits
(13·10¹⁹⁴+11)/3 = 4(3)₁₉₃7_<195> = 41 · 135721 · 1536617 · 2790600979_<10> · 1239946990790578721657_<22> · C152
C152 = P31 · P121
P31 = 6080092611502949989510099120823_<31>
P121 = 2408876310650925262480767490286417447634363404060717087626403216670946806218350381194813011157655867258367905899750623429_<121>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3066536428 Step 1 took 11722ms Step 2 took 12009ms ********** Factor found in step 2: 6080092611502949989510099120823 Found probable prime factor of 31 digits: 6080092611502949989510099120823 Probable prime cofactor has 121 digits
(13·10¹⁸⁸+11)/3 = 4(3)₁₈₇7_<189> = 1543 · 142860607 · 255207723123768259319_<21> · C157
C157 = P33 · C125
P33 = 106516169444251311571441538317907_<33>
C125 = [72315988608969549766354716564088708863361398791668800127495140769387943021448338653197888223981621630401019958904218407786589_<125>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2305462360 Step 1 took 13810ms Step 2 took 13184ms ********** Factor found in step 2: 106516169444251311571441538317907 Found probable prime factor of 33 digits: 106516169444251311571441538317907 Composite cofactor has 125 digits
(13·10¹⁹³+11)/3 = 4(3)₁₉₂7_<194> = 53 · 401393 · 411072007 · 274601721738892619_<18> · C161
C161 = P30 · P131
P30 = 528939695216908001586855390299_<30>
P131 = 34115293629840614800212793487061778880381322301987682674528561980984797481451268135182069095737192125952710750608718824379108161659_<131>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2053943442 Step 1 took 14717ms Step 2 took 13078ms ********** Factor found in step 2: 528939695216908001586855390299 Found probable prime factor of 30 digits: 528939695216908001586855390299 Probable prime cofactor has 131 digits
(13·10¹³⁷+11)/3 = 4(3)₁₃₆7_<138> = 17 · C137
C137 = P66 · P71
P66 = 807637985960916768831740876387492333779169190633031900872576802793_<66>
P71 = 31561413060708730150872571599062549070601558958879766962070075808593377_<71>

SNFS difficulty: 139 digits. Divisors found: r1=807637985960916768831740876387492333779169190633031900872576802793 (pp66) r2=31561413060708730150872571599062549070601558958879766962070075808593377 (pp71) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.294). Factorization parameters were as follows: n: 25490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901961 m: 2000000000000000000000000000 deg: 5 c5: 325 c0: 88 skew: 0.77 type: snfs lss: 1 rlim: 1450000 alim: 1450000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1450000/1450000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [725000, 1550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 246638 x 246886 Total sieving time: 0.00 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,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,49,49,2.3,2.3,75000 total time: 5.00 hours.
(13·10¹²⁹+11)/3 = 4(3)₁₂₈7_<130> = 41 · 2389 · 1249529719_<10> · C116
C116 = P31 · P85
P31 = 9281663010039532950468760843457_<31>
P85 = 3814606151552466573303099303750536701596970698329405314826953837863735073362736633211_<85>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=4061892878 Step 1 took 9167ms Step 2 took 8799ms ********** Factor found in step 2: 9281663010039532950468760843457 Found probable prime factor of 31 digits: 9281663010039532950468760843457 Probable prime cofactor has 85 digits
(13·10¹³⁴+11)/3 = 4(3)₁₃₃7_<135> = 23 · 41 · 2545227932836422739_<19> · C114
C114 = P41 · P74
P41 = 11958553032490865212908609128910029714171_<41>
P74 = 15097501805726385936048310070893266742178719854170264340828668499522481111_<74>

SNFS difficulty: 136 digits. Divisors found: r1=11958553032490865212908609128910029714171 (pp41) r2=15097501805726385936048310070893266742178719854170264340828668499522481111 (pp74) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.304). Factorization parameters were as follows: n: 180544276001905585936188669707667634298162509150541346315109038714131653485746682884521027430565136143432076523981 m: 1000000000000000000000000000 deg: 5 c5: 13 c0: 110 skew: 1.53 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [650000, 1175001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 184954 x 185202 Total sieving time: 0.00 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,136,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,49,49,2.3,2.3,75000 total time: 4.00 hours.
(13·10¹⁶³+11)/3 = 4(3)₁₆₂7_<164> = 6481 · 8345621 · 5396446101430979761_<19> · 1657874515633727895602144651126113_<34> · C101
C101 = P48 · P54
P48 = 125111068703916647393850098641471129981479630019_<48>
P54 = 715757956709940897574201232426194262350826823645064711_<54>

Number: 43337_163 N=89549242897312413145121015477987605938666360001715878782232515183403517627085365493127792527593159509 ( 101 digits) Divisors found: r1=125111068703916647393850098641471129981479630019 (pp48) r2=715757956709940897574201232426194262350826823645064711 (pp54) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.530). Factorization parameters were as follows: name: 43337_163 n: 89549242897312413145121015477987605938666360001715878782232515183403517627085365493127792527593159509 skew: 14219.20 # norm 4.72e+13 c5: 6720 c4: 1607219 c3: -3781792674674 c2: -20391760325156031 c1: 389716915741807259611 c0: -741615802863451244838340 # alpha -5.31 Y1: 21711660839 Y0: -26603483783377273221 # Murphy_E 2.92e-09 # M 18256076264919045554073716051401304772283243952469251928239199987692922377652841597411127307286087277 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 [900000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 203363 x 203611 Total sieving time: 0.00 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: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 4.00 hours.
(13·10¹⁷²+11)/3 = 4(3)₁₇₁7_<173> = 7 · 124683707642868001_<18> · 19261998159045934249641919_<26> · 1025177561752975972475736113_<28> · C103
C103 = P46 · P57
P46 = 7484592628038052621285087704880092637265857489_<46>
P57 = 335927650726956320807691331130396826552727400188028875777_<57>

Number: 43337_172 N=2514281618185119047267551628988833847305791628965405631217338056079108891052479407838212838722566143953 ( 103 digits) Divisors found: r1=7484592628038052621285087704880092637265857489 (pp46) r2=335927650726956320807691331130396826552727400188028875777 (pp57) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.724). Factorization parameters were as follows: name: 43337_172 n: 2514281618185119047267551628988833847305791628965405631217338056079108891052479407838212838722566143953 skew: 15171.04 # norm 3.51e+14 c5: 22680 c4: -124055346 c3: -30204415768669 c2: 1652155236686905 c1: 1833485328963513386013 c0: -2986641083616374487288735 # alpha -6.05 Y1: 8174481641 Y0: -40640053367376438856 # Murphy_E 2.35e-09 # M 984034130476818682388074087529638493249314732894513911123846271023921439173263023879179576856922289270 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 289389 x 289636 Total sieving time: 0.00 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: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.00 hours.
(13·10¹⁴⁷+11)/3 = 4(3)₁₄₆7_<148> = 29 · 34632467242938281_<17> · 666707790664577506063621777_<27> · C103
C103 = P46 · P58
P46 = 1632689107448837283748587003497437630804378717_<46>
P58 = 3963707899643478820787903054646032550519819003208303853657_<58>

Number: 43337_147 N=6471502712856816941534410396616323458062704121632605765152696107776979645565714978126919250460773418069 ( 103 digits) Divisors found: r1=1632689107448837283748587003497437630804378717 (pp46) r2=3963707899643478820787903054646032550519819003208303853657 (pp58) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: name: 43337_147 n: 6471502712856816941534410396616323458062704121632605765152696107776979645565714978126919250460773418069 skew: 12803.66 # norm 1.56e+14 c5: 25200 c4: 6526908 c3: -16208983640194 c2: 36664277029938906 c1: 1517588518650563580273 c0: 4101674119551640223937604 # alpha -5.86 Y1: 12176988151 Y0: -48075179412327603905 # Murphy_E 2.43e-09 # M 765771848902745999549250401080960786347242002138049323590434441771344197826450219537382559039935974 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 219161 x 219409 Total sieving time: 0.00 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: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.00 hours.
Jan 12, 2009 (3rd): Factorizations of 433...337 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Jan 12, 2009 (2nd): By Jo Yeong Uk / Msieve / Jan 12, 2009
(37·10¹⁶²+53)/9 = 4(1)₁₆₁7_<163> = 43 · 769 · 6888289 · 49682126487359_<14> · C138
C138 = P50 · P88
P50 = 42028157780136442442379542414682359487864735723991_<50>
P88 = 8643955636962190706372478541886100514006131870100713909201584397138993894515028748366511_<88>

Number: 41117_162 N=363289531354746753320799714164560359754424340577689448833156203649841655419145956572610748257666769704275970426653960602488750448203665401 ( 138 digits) SNFS difficulty: 163 digits. Divisors found: r1=42028157780136442442379542414682359487864735723991 r2=8643955636962190706372478541886100514006131870100713909201584397138993894515028748366511 Version: Total time: 25.85 hours. Scaled time: 61.62 units (timescale=2.384). Factorization parameters were as follows: n: 363289531354746753320799714164560359754424340577689448833156203649841655419145956572610748257666769704275970426653960602488750448203665401 m: 100000000000000000000000000000000 deg: 5 c5: 3700 c0: 53 skew: 0.43 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2300000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9823817 Max relations in full relation-set: Initial matrix: Pruned matrix : 794867 x 795114 Total sieving time: 23.16 hours. Total relation processing time: 1.02 hours. Matrix solve time: 1.41 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000 total time: 25.85 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 12, 2009: By Sinkiti Sibata / Msieve / Jan 12, 2009
(38·10¹⁸⁶+61)/9 = 4(2)₁₈₅9_<187> = 11 · C186
C186 = P83 · P104
P83 = 13933545557012191347373389258569209249638126493880758322318981598763635852951224089_<83>
P104 = 27547789775963625085903934524733271215585771546540325688065243371806745946230760472112031271164240237751_<104>

Number: 42229_186 N=383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383839 ( 186 digits) SNFS difficulty: 187 digits. Divisors found: r1=13933545557012191347373389258569209249638126493880758322318981598763635852951224089 r2=27547789775963625085903934524733271215585771546540325688065243371806745946230760472112031271164240237751 Version: Total time: 289.16 hours. Scaled time: 729.85 units (timescale=2.524). Factorization parameters were as follows: name: 42229_186 n: 383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383838383839 m: 10000000000000000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 9400000 alim: 9400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9400000/9400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4700000, 8500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1786141 x 1786389 Total sieving time: 289.16 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,187,5,0,0,0,0,0,0,0,0,9400000,9400000,28,28,54,54,2.5,2.5,100000 total time: 289.16 hours. --------- CPU info (if available) ----------
Jan 11, 2009: By Jo Yeong Uk / GGNFS,Msieve v1.39 / Jan 11, 2009
(38·10¹⁸⁷+61)/9 = 4(2)₁₈₆9_<188> = 7 · 23 · 4133 · 339381782281_<12> · 14075029066853_<14> · 144197773736360629_<18> · 45994881214842165755089_<23> · C118
C118 = P41 · P77
P41 = 50967802797581625985097478423989003403541_<41>
P77 = 39295969740735967852621112679477369452786973644518223666651441987423587742861_<77>

Number: 42229_187 N=2002829236485565584268140691732974433612639511098407138412154547996959651462215442914520265753338661383557778924870801 ( 118 digits) Divisors found: r1=50967802797581625985097478423989003403541 r2=39295969740735967852621112679477369452786973644518223666651441987423587742861 Version: Total time: 20.95 hours. Scaled time: 50.10 units (timescale=2.392). Factorization parameters were as follows: name: 42229_187 n: 2002829236485565584268140691732974433612639511098407138412154547996959651462215442914520265753338661383557778924870801 skew: 50181.87 # norm 2.28e+16 c5: 50940 c4: 19532943756 c3: -146582757507473 c2: -47355629610985993948 c1: 532654329772897813291676 c0: -41567750101170860235893120 # alpha -6.32 Y1: 7973840395103 Y0: -33030029096995216166631 # Murphy_E 3.85e-10 # M 316121329102452193654767749257544142231626197662659818279564247885496932610354662673936415656052558511673138286534187 type: gnfs rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [2000000, 3500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9431831 Max relations in full relation-set: Initial matrix: Pruned matrix : 581575 x 581823 Polynomial selection time: 1.99 hours. Total sieving time: 17.45 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.69 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,52,52,2.4,2.4,100000 total time: 20.95 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 10, 2009 (4th): The maintenance system is currently running with the new machine. The latest factor table of repunit numbers is available.
Jan 10, 2009 (3rd): By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jan 10, 2009
(38·10¹⁷⁶+43)/9 = 4(2)₁₇₅7_<177> = 7 · 953 · 18013 · 276447312401475563_<18> · 178756426448137413914826142437964919_<36> · C116
C116 = P56 · P61
P56 = 30482242843051625212413261317342328142108260988731555571_<56>
P61 = 2332615422504949792148260086568871957753601757513041367550327_<61>

Number: 42227_176 N=71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717 ( 116 digits) Divisors found: r1=30482242843051625212413261317342328142108260988731555571 r2=2332615422504949792148260086568871957753601757513041367550327 Version: Total time: 17.83 hours. Scaled time: 42.64 units (timescale=2.392). Factorization parameters were as follows: name: 42227_176 n: 71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717 skew: 26032.75 # norm 4.33e+15 c5: 108180 c4: 4459312752 c3: -46190052771889 c2: -6904408880014373882 c1: -13229336043547270296464 c0: 539733616727763783241807616 # alpha -5.62 Y1: 929245002037 Y0: -14572980660116137675005 # Murphy_E 4.64e-10 # M 57258185201645401085393804515614427325718700776340221333725020184573222142112606157960434857721364147424672513767023 type: gnfs rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1650000, 3000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8772174 Max relations in full relation-set: Initial matrix: Pruned matrix : 554186 x 554434 Polynomial selection time: 1.51 hours. Total sieving time: 14.83 hours. Total relation processing time: 0.72 hours. Matrix solve time: 0.64 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000 total time: 17.83 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 10, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1 / Jan 10, 2009
(4·10²⁴⁵-1)/3 = 1(3)₂₄₅_<246> = 293 · 4428013 · 436570924477_<12> · 197820650760877883_<18> · 1940832977077439598289_<22> · 245134337177055685486188936209_<30> · 1675203063576126721567576664071_<31> · C127
C127 = P43 · P84
P43 = 6790775658469834479820078727143989820043129_<43>
P84 = 219865273571187201579781503790690827059370707506151263702320080862487340541571697173_<84>

Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=2724191139 Step 1 took 36312ms Step 2 took 25686ms ********** Factor found in step 2: 6790775658469834479820078727143989820043129 Found probable prime factor of 43 digits: 6790775658469834479820078727143989820043129 Probable prime cofactor has 84 digits
Jan 10, 2009: By Sinkiti Sibata / Msieve / Jan 10, 2009
10²¹³-9 = (9)₂₁₂1_<213> = 2671 · 832477 · 3405841 · 5328359 · 5607750409_<10> · 24831611120690827_<17> · 489257181515888972676839_<24> · 2732757469571315596232602778709665753077_<40> · C102
C102 = P42 · P60
P42 = 582858443410441071978771347365210311353479_<42>
P60 = 228371053847304148819820096048179809718818515793823952998837_<60>

Fri Jan 09 16:34:18 2009 Msieve v. 1.39 Fri Jan 09 16:34:18 2009 random seeds: 70bd276c 631bbe8b Fri Jan 09 16:34:18 2009 factoring 133107996965441716078569858100441760864844458768441551457233330059494248457182487821678740490382903923 (102 digits) Fri Jan 09 16:34:19 2009 searching for 15-digit factors Fri Jan 09 16:34:21 2009 commencing quadratic sieve (102-digit input) Fri Jan 09 16:34:21 2009 using multiplier of 43 Fri Jan 09 16:34:21 2009 using 32kb Intel Core sieve core Fri Jan 09 16:34:21 2009 sieve interval: 36 blocks of size 32768 Fri Jan 09 16:34:21 2009 processing polynomials in batches of 6 Fri Jan 09 16:34:21 2009 using a sieve bound of 3041849 (110000 primes) Fri Jan 09 16:34:21 2009 using large prime bound of 456277350 (28 bits) Fri Jan 09 16:34:21 2009 using double large prime bound of 3860219537782800 (44-52 bits) Fri Jan 09 16:34:21 2009 using trial factoring cutoff of 52 bits Fri Jan 09 16:34:21 2009 polynomial 'A' values have 13 factors Sat Jan 10 09:09:01 2009 110123 relations (26170 full + 83953 combined from 1641709 partial), need 110096 Sat Jan 10 09:09:03 2009 begin with 1667879 relations Sat Jan 10 09:09:04 2009 reduce to 289724 relations in 11 passes Sat Jan 10 09:09:04 2009 attempting to read 289724 relations Sat Jan 10 09:09:10 2009 recovered 289724 relations Sat Jan 10 09:09:10 2009 recovered 281939 polynomials Sat Jan 10 09:09:10 2009 attempting to build 110123 cycles Sat Jan 10 09:09:11 2009 found 110123 cycles in 6 passes Sat Jan 10 09:09:11 2009 distribution of cycle lengths: Sat Jan 10 09:09:11 2009 length 1 : 26170 Sat Jan 10 09:09:11 2009 length 2 : 18921 Sat Jan 10 09:09:11 2009 length 3 : 18607 Sat Jan 10 09:09:11 2009 length 4 : 14860 Sat Jan 10 09:09:11 2009 length 5 : 11537 Sat Jan 10 09:09:11 2009 length 6 : 7928 Sat Jan 10 09:09:11 2009 length 7 : 5001 Sat Jan 10 09:09:11 2009 length 9+: 7099 Sat Jan 10 09:09:11 2009 largest cycle: 20 relations Sat Jan 10 09:09:11 2009 matrix is 110000 x 110123 (32.4 MB) with weight 8061711 (73.21/col) Sat Jan 10 09:09:11 2009 sparse part has weight 8061711 (73.21/col) Sat Jan 10 09:09:13 2009 filtering completed in 3 passes Sat Jan 10 09:09:13 2009 matrix is 105828 x 105892 (31.4 MB) with weight 7802831 (73.69/col) Sat Jan 10 09:09:13 2009 sparse part has weight 7802831 (73.69/col) Sat Jan 10 09:09:13 2009 saving the first 48 matrix rows for later Sat Jan 10 09:09:13 2009 matrix is 105780 x 105892 (22.7 MB) with weight 6525771 (61.63/col) Sat Jan 10 09:09:13 2009 sparse part has weight 5323421 (50.27/col) Sat Jan 10 09:09:13 2009 matrix includes 64 packed rows Sat Jan 10 09:09:13 2009 using block size 42356 for processor cache size 1024 kB Sat Jan 10 09:09:15 2009 commencing Lanczos iteration Sat Jan 10 09:09:15 2009 memory use: 20.0 MB Sat Jan 10 09:10:45 2009 lanczos halted after 1674 iterations (dim = 105780) Sat Jan 10 09:10:45 2009 recovered 18 nontrivial dependencies Sat Jan 10 09:10:46 2009 prp42 factor: 582858443410441071978771347365210311353479 Sat Jan 10 09:10:46 2009 prp60 factor: 228371053847304148819820096048179809718818515793823952998837 Sat Jan 10 09:10:46 2009 elapsed time 16:36:28
Jan 9, 2009 (3rd): By Jo Yeong Uk / GGNFS / Msieve v1.39 / Jan 9, 2009
(38·10¹⁷⁴+61)/9 = 4(2)₁₇₃9_<175> = 11 · 557 · 23333 · 59218732301_<11> · 262088313569048659823633945899080702035203_<42> · C115
C115 = P33 · P40 · P43
P33 = 225417303760371613051787015751701_<33>
P40 = 3509660100567937909308937499352854860151_<40>
P43 = 2405268446283875882037061284565419763257923_<43>

Number: 42229_174 N=1902899549437374369035951375932780225773552267114939321874434723505133347794160411662937567103887497100312817310473 ( 115 digits) Divisors found: r1=225417303760371613051787015751701 r2=3509660100567937909308937499352854860151 r3=2405268446283875882037061284565419763257923 Version: Total time: 15.58 hours. Scaled time: 37.20 units (timescale=2.388). Factorization parameters were as follows: name: 42229_174 n: 1902899549437374369035951375932780225773552267114939321874434723505133347794160411662937567103887497100312817310473 skew: 13305.32 # norm 1.25e+15 c5: 34380 c4: -7761979098 c3: -40170364027258 c2: 1216859679370801634 c1: 2137936139042537055913 c0: -37443904713974567970199586 # alpha -5.26 Y1: 2839122733007 Y0: -8884403306900197748349 # Murphy_E 6.23e-10 # M 1013688461298236633418369179942359190638312815538318044515649165909945628291609200031522087797218085581150778639140 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1400000, 2450001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9217367 Max relations in full relation-set: Initial matrix: Pruned matrix : 514466 x 514714 Polynomial selection time: 1.35 hours. Total sieving time: 12.39 hours. Total relation processing time: 0.66 hours. Matrix solve time: 0.56 hours. Time per square root: 0.61 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000 total time: 15.58 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046968k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.84 BogoMIPS (lpj=2672421) Calibrating delay using timer specific routine.. 5344.41 BogoMIPS (lpj=2672207) Calibrating delay using timer specific routine.. 5291.27 BogoMIPS (lpj=2645639)
Jan 9, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1 / Jan 9, 2009
10²¹³-9 = (9)₂₁₂1_<213> = 2671 · 832477 · 3405841 · 5328359 · 5607750409_<10> · 24831611120690827_<17> · 489257181515888972676839_<24> · C141
C141 = P40 · C102
P40 = 2732757469571315596232602778709665753077_<40>
C102 = [133107996965441716078569858100441760864844458768441551457233330059494248457182487821678740490382903923_<102>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1234666248 Step 1 took 43505ms Step 2 took 20647ms ********** Factor found in step 2: 2732757469571315596232602778709665753077 Found probable prime factor of 40 digits: 2732757469571315596232602778709665753077 Composite cofactor 133107996965441716078569858100441760864844458768441551457233330059494248457182487821678740490382903923 has 102 digits
Jan 9, 2009: By Wataru Sakai / Msieve / Jan 9, 2009
(10¹⁸⁹+53)/9 = (1)₁₈₈7_<189> = 3 · 13 · 281 · 15696287951_<11> · C174
C174 = P43 · P132
P43 = 2966053554214492112333066088061367989981783_<43>
P132 = 217776301578075309920820042799517030257727277508499057170455912299319301245210201540772768640946562600901533506129647135786653246811_<132>

Number: 11117_189 N=645936173319337380411863953498993104769684528176623414613699613686861428843235993970593716471912306280514580984750785536925480164420937113239219942611158442079139517692844013 ( 174 digits) SNFS difficulty: 189 digits. Divisors found: r1=2966053554214492112333066088061367989981783 r2=217776301578075309920820042799517030257727277508499057170455912299319301245210201540772768640946562600901533506129647135786653246811 Version: Total time: 388.16 hours. Scaled time: 780.19 units (timescale=2.010). Factorization parameters were as follows: n: 645936173319337380411863953498993104769684528176623414613699613686861428843235993970593716471912306280514580984750785536925480164420937113239219942611158442079139517692844013 m: 50000000000000000000000000000000000000 deg: 5 c5: 16 c0: 265 skew: 1.75 type: snfs lss: 1 rlim: 10200000 alim: 10200000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 10200000/10200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5100000, 8700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1819800 x 1820048 Total sieving time: 388.16 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,189,5,0,0,0,0,0,0,0,0,10200000,10200000,28,28,54,54,2.5,2.5,100000 total time: 388.16 hours. --------- CPU info (if available) ----------
Jan 8, 2009 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v1.39 / Jan 8, 2009
(38·10¹⁹³+43)/9 = 4(2)₁₉₂7_<194> = C194
C194 = P90 · P105
P90 = 152784569578034018071739097799518165623885883503374346108642124458545616770104505255344901_<90>
P105 = 276351351048296902131663932803456124639908210818778760937627498047154906872033486981422679102588102399927_<105>

Number: 42227_193 N=42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 ( 194 digits) SNFS difficulty: 196 digits. Divisors found: r1=152784569578034018071739097799518165623885883503374346108642124458545616770104505255344901 r2=276351351048296902131663932803456124639908210818778760937627498047154906872033486981422679102588102399927 Version: Total time: 392.71 hours. Scaled time: 938.57 units (timescale=2.390). Factorization parameters were as follows: n: 42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 m: 1000000000000000000000000000000000000000 deg: 5 c5: 19 c0: 2150 skew: 2.57 type: snfs lss: 1 rlim: 16000000 alim: 16000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [8000000, 17100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 24324690 Max relations in full relation-set: Initial matrix: Pruned matrix : 2685234 x 2685482 Total sieving time: 359.53 hours. Total relation processing time: 12.20 hours. Matrix solve time: 20.58 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,55,55,2.5,2.5,100000 total time: 392.71 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047064k/8912896k available (2460k kernel code, 339224k reserved, 1250k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673804) Calibrating delay using timer specific routine.. 5344.80 BogoMIPS (lpj=2672401) Calibrating delay using timer specific routine.. 5344.34 BogoMIPS (lpj=2672172) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Jan 8, 2009: By Robert Backstrom / GGNFS, Msieve / Jan 8, 2009
(29·10¹⁸⁶+43)/9 = 3(2)₁₈₅7_<187> = 4703 · C183
C183 = P69 · P115
P69 = 555923217597268132599534094433976495047551289000224776872217296769257_<69>
P115 = 1232439750546506891785593310267887304617348141319633071530047011017494600720295029123922027255808926803985878794437_<115>

Number: n N=685141871618588607744465707468046400642615824414676211401705767004512486119970704278592860349186098707680676636662177806128475913719375339617738086800387459541191201833345146124223309 ( 183 digits) SNFS difficulty: 187 digits. Divisors found: Thu Jan 08 04:20:59 2009 prp69 factor: 555923217597268132599534094433976495047551289000224776872217296769257 Thu Jan 08 04:20:59 2009 prp115 factor: 1232439750546506891785593310267887304617348141319633071530047011017494600720295029123922027255808926803985878794437 Thu Jan 08 04:20:59 2009 elapsed time 06:18:34 (Msieve 1.39 - dependency 3) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.95 hours. Scaled time: 61.25 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_2_185_7 n: 685141871618588607744465707468046400642615824414676211401705767004512486119970704278592860349186098707680676636662177806128475913719375339617738086800387459541191201833345146124223309 deg: 5 c5: 290 c0: 43 m: 10000000000000000000000000000000000000 skew: 0.68 type: snfs rlim: 8500000 alim: 8500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 10294351) Primes: RFBsize:571119, AFBsize:569357, largePrimes:21303335 encountered Relations: rels:21658760, finalFF:1003877 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2773120 hash collisions in 23837692 relations Msieve: matrix is 1553711 x 1553959 (416.7 MB) Total sieving time: 28.98 hours. Total relation processing time: 0.97 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,8500000,8500000,28,28,56,56,2.5,2.5,100000 total time: 29.95 hours. --------- CPU info (if available) ----------
Jan 6, 2009 (5th): By Wataru Sakai / Msieve / Jan 6, 2009
(38·10¹⁹⁵+61)/9 = 4(2)₁₉₄9_<196> = C196
C196 = P63 · P134
P63 = 115667220018910122248194085154980724584857915458079192026711121_<63>
P134 = 36503187519609639479341262940543033550745399336765316360179329732149272103637012814543123192279806906800310222096607380858092086521349_<134>

Number: 42229_195 N=4222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 ( 196 digits) SNFS difficulty: 196 digits. Divisors found: r1=115667220018910122248194085154980724584857915458079192026711121 r2=36503187519609639479341262940543033550745399336765316360179329732149272103637012814543123192279806906800310222096607380858092086521349 Version: Total time: 671.52 hours. Scaled time: 1286.64 units (timescale=1.916). Factorization parameters were as follows: n: 4222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 m: 1000000000000000000000000000000000000000 deg: 5 c5: 38 c0: 61 skew: 1.10 type: snfs lss: 1 rlim: 13200000 alim: 13200000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 13200000/13200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6600000, 13100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2267319 x 2267567 Total sieving time: 671.52 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,196,5,0,0,0,0,0,0,0,0,13200000,13200000,28,28,55,55,2.5,2.5,100000 total time: 671.52 hours. --------- CPU info (if available) ----------
10¹⁸⁹+3 = 1(0)₁₈₈3_<190> = 149 · 2579 · 7541 · 18804384407_<11> · 89411784830227_<14> · C156
C156 = P69 · P87
P69 = 302326156316901099415054234018340088084227443035320038122354865868161_<69>
P87 = 678896924250950617425559235848387983568344761375171256368612766118378019400194027494837_<87>

Number: 10003_189 N=205248297644156261196720985253614172077029245438613226830452987675960883098054087210769404046438306485121986264348749244919350699056988552234916435950184757 ( 156 digits) SNFS difficulty: 189 digits. Divisors found: r1=302326156316901099415054234018340088084227443035320038122354865868161 r2=678896924250950617425559235848387983568344761375171256368612766118378019400194027494837 Version: Total time: 342.40 hours. Scaled time: 599.54 units (timescale=1.751). Factorization parameters were as follows: n: 205248297644156261196720985253614172077029245438613226830452987675960883098054087210769404046438306485121986264348749244919350699056988552234916435950184757 m: 50000000000000000000000000000000000000 deg: 5 c5: 16 c0: 15 skew: 0.99 type: snfs lss: 1 rlim: 10200000 alim: 10200000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 10200000/10200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5100000, 8700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1273208 x 1273456 Total sieving time: 342.40 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,189,5,0,0,0,0,0,0,0,0,10200000,10200000,28,28,54,54,2.5,2.5,100000 total time: 342.40 hours. --------- CPU info (if available) ----------
Jan 6, 2009 (4th): By Serge Batalov / PFGW / Jan 6, 2009
(5·10³⁸⁶⁹⁰+31)/9 = (5)₃₈₆₈₉9_<38690> is PRP.
(5·10³⁹⁴⁶⁴+31)/9 = (5)₃₉₄₆₃9_<39464> is PRP.
Jan 6, 2009 (3rd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve / Jan 6, 2009
4·10²⁰⁷+1 = 4(0)₂₀₆1_<208> = C208
C208 = P43 · P46 · P55 · P66
P43 = 2137537151086140780378598137246884887064851_<43>
P46 = 2812726946992196303955780250469663669810710081_<46>
P55 = 4510386964277796118081223118223701478503227449062032837_<55>
P66 = 147504388817832250629782059406052001349839987803889705588283463583_<66>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (208 digits) Using B1=3628000, B2=8561127130, polynomial Dickson(6), sigma=3845259699 Step 1 took 70828ms Step 2 took 27344ms ********** Factor found in step 2: 2137537151086140780378598137246884887064851 Found probable prime factor of 43 digits: 2137537151086140780378598137246884887064851 Composite cofactor 1871312504658686833048859441299535119697043458364557065452864462272856482238047511640262600039514668896561348370461632396040769157857079230807910497093290327153082651 has 166 digits Number: n N=1871312504658686833048859441299535119697043458364557065452864462272856482238047511640262600039514668896561348370461632396040769157857079230807910497093290327153082651 ( 166 digits) SNFS difficulty: 207 digits. Divisors found: Tue Jan 6 12:17:23 2009 prp46 factor: 2812726946992196303955780250469663669810710081 Tue Jan 6 12:17:23 2009 prp55 factor: 4510386964277796118081223118223701478503227449062032837 Tue Jan 6 12:17:23 2009 prp66 factor: 147504388817832250629782059406052001349839987803889705588283463583 Tue Jan 6 12:17:23 2009 elapsed time 17:15:12 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20050930-k8 Total time: 101.97 hours. Scaled time: 204.97 units (timescale=2.010). Factorization parameters were as follows: name: KA_4_0_206_1 n: 1871312504658686833048859441299535119697043458364557065452864462272856482238047511640262600039514668896561348370461632396040769157857079230807910497093290327153082651 # n: 4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 deg: 5 c5: 25 c0: 2 m: 200000000000000000000000000000000000000000 skew: 0.60 type: snfs rlim: 10000000 alim: 10000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 30599990) Primes: RFBsize:664579, AFBsize:664295, largePrimes:36509320 encountered Relations: rels:31588687, finalFF:75919 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7840833 hash collisions in 43268992 relations Msieve: matrix is 3150865 x 3151113 (859.6 MB) Total sieving time: 100.96 hours. Total relation processing time: 1.01 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,207,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000 total time: 101.97 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.96 BogoMIPS (lpj=2830481) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830456) Total of 4 processors activated (22643.69 BogoMIPS).
Jan 6, 2009 (2nd): By Justin Card / ggnfs,msieve / Jan 6, 2009
(29·10¹¹²+43)/9 = 3(2)₁₁₁7_<113> = 13 · 37 · 103 · 43239121 · C101
C101 = P29 · P72
P29 = 45090396972221616172354904437_<29>
P72 = 333589422784143321541957121594048625347148135316145689550420073192386257_<72>

Sun Dec 7 00:36:59 2008 Msieve v. 1.39 Sun Dec 7 00:36:59 2008 random seeds: 760852d7 bc69bd5e Sun Dec 7 00:36:59 2008 factoring 15041679499071292646284989557979980982308780587943355373610269065634432656659938885011590841227122309 (101 digits) Sun Dec 7 00:37:00 2008 searching for 15-digit factors Sun Dec 7 00:37:00 2008 commencing number field sieve (101-digit input) Sun Dec 7 00:37:00 2008 R0: -20000000000000000000000 Sun Dec 7 00:37:00 2008 R1: 1 Sun Dec 7 00:37:00 2008 A0: 344 Sun Dec 7 00:37:00 2008 A1: 0 Sun Dec 7 00:37:00 2008 A2: 0 Sun Dec 7 00:37:00 2008 A3: 0 Sun Dec 7 00:37:00 2008 A4: 0 Sun Dec 7 00:37:00 2008 A5: 725 Sun Dec 7 00:37:00 2008 skew 1.00, size 2.348152e-08, alpha 0.523263, combined = 1.972314e-08 Sun Dec 7 00:37:00 2008 Sun Dec 7 00:37:00 2008 commencing relation filtering Sun Dec 7 00:37:00 2008 commencing duplicate removal, pass 1 Sun Dec 7 00:37:00 2008 error -9 reading relation 57 Sun Dec 7 00:37:00 2008 error -9 reading relation 600 Sun Dec 7 00:37:01 2008 error -9 reading relation 6662 Sun Dec 7 00:37:16 2008 found 62189 hash collisions in 1229541 relations Sun Dec 7 00:37:20 2008 added 7524 free relations Sun Dec 7 00:37:20 2008 commencing duplicate removal, pass 2 Sun Dec 7 00:37:21 2008 found 62231 duplicates and 1174834 unique relations Sun Dec 7 00:37:21 2008 memory use: 36.9 MB Sun Dec 7 00:37:21 2008 reading rational ideals above 458752 Sun Dec 7 00:37:21 2008 reading algebraic ideals above 458752 Sun Dec 7 00:37:21 2008 commencing singleton removal, pass 1 Sun Dec 7 00:37:37 2008 relations with 0 large ideals: 17359 Sun Dec 7 00:37:37 2008 relations with 1 large ideals: 170040 Sun Dec 7 00:37:37 2008 relations with 2 large ideals: 503738 Sun Dec 7 00:37:37 2008 relations with 3 large ideals: 322915 Sun Dec 7 00:37:37 2008 relations with 4 large ideals: 78947 Sun Dec 7 00:37:37 2008 relations with 5 large ideals: 9452 Sun Dec 7 00:37:37 2008 relations with 6 large ideals: 72368 Sun Dec 7 00:37:37 2008 relations with 7+ large ideals: 15 Sun Dec 7 00:37:37 2008 1174834 relations and about 1430364 large ideals Sun Dec 7 00:37:37 2008 commencing singleton removal, pass 2 Sun Dec 7 00:37:53 2008 found 678514 singletons Sun Dec 7 00:37:53 2008 current dataset: 496320 relations and about 407268 large ideals Sun Dec 7 00:37:53 2008 commencing singleton removal, pass 3 Sun Dec 7 00:37:59 2008 found 143234 singletons Sun Dec 7 00:37:59 2008 current dataset: 353086 relations and about 251585 large ideals Sun Dec 7 00:37:59 2008 commencing singleton removal, final pass Sun Dec 7 00:38:03 2008 memory use: 11.7 MB Sun Dec 7 00:38:03 2008 commencing in-memory singleton removal Sun Dec 7 00:38:03 2008 begin with 353086 relations and 253896 unique ideals Sun Dec 7 00:38:04 2008 reduce to 310065 relations and 209765 ideals in 10 passes Sun Dec 7 00:38:04 2008 max relations containing the same ideal: 38 Sun Dec 7 00:38:04 2008 reading rational ideals above 229376 Sun Dec 7 00:38:04 2008 reading algebraic ideals above 229376 Sun Dec 7 00:38:04 2008 commencing singleton removal, final pass Sun Dec 7 00:38:08 2008 keeping 280459 ideals with weight <= 20, new excess is 51103 Sun Dec 7 00:38:09 2008 memory use: 11.7 MB Sun Dec 7 00:38:09 2008 commencing in-memory singleton removal Sun Dec 7 00:38:09 2008 begin with 317593 relations and 280459 unique ideals Sun Dec 7 00:38:09 2008 reduce to 309989 relations and 235373 ideals in 4 passes Sun Dec 7 00:38:09 2008 max relations containing the same ideal: 20 Sun Dec 7 00:38:09 2008 relations with 0 large ideals: 5366 Sun Dec 7 00:38:09 2008 relations with 1 large ideals: 31032 Sun Dec 7 00:38:09 2008 relations with 2 large ideals: 79805 Sun Dec 7 00:38:09 2008 relations with 3 large ideals: 98556 Sun Dec 7 00:38:09 2008 relations with 4 large ideals: 62857 Sun Dec 7 00:38:09 2008 relations with 5 large ideals: 23612 Sun Dec 7 00:38:09 2008 relations with 6 large ideals: 8091 Sun Dec 7 00:38:09 2008 relations with 7+ large ideals: 670 Sun Dec 7 00:38:09 2008 commencing 2-way merge Sun Dec 7 00:38:09 2008 reduce to 194123 relation sets and 119507 unique ideals Sun Dec 7 00:38:09 2008 commencing full merge Sun Dec 7 00:38:12 2008 memory use: 9.9 MB Sun Dec 7 00:38:12 2008 found 80647 cycles, need 65707 Sun Dec 7 00:38:12 2008 weight of 65707 cycles is about 5097139 (77.57/cycle) Sun Dec 7 00:38:12 2008 distribution of cycle lengths: Sun Dec 7 00:38:12 2008 1 relations: 6358 Sun Dec 7 00:38:12 2008 2 relations: 5050 Sun Dec 7 00:38:12 2008 3 relations: 5181 Sun Dec 7 00:38:12 2008 4 relations: 5044 Sun Dec 7 00:38:12 2008 5 relations: 4944 Sun Dec 7 00:38:12 2008 6 relations: 4810 Sun Dec 7 00:38:12 2008 7 relations: 4483 Sun Dec 7 00:38:12 2008 8 relations: 4259 Sun Dec 7 00:38:12 2008 9 relations: 3928 Sun Dec 7 00:38:12 2008 10+ relations: 21650 Sun Dec 7 00:38:12 2008 heaviest cycle: 20 relations Sun Dec 7 00:38:12 2008 commencing cycle optimization Sun Dec 7 00:38:13 2008 start with 486593 relations Sun Dec 7 00:38:14 2008 pruned 33805 relations Sun Dec 7 00:38:14 2008 memory use: 13.5 MB Sun Dec 7 00:38:14 2008 distribution of cycle lengths: Sun Dec 7 00:38:14 2008 1 relations: 6358 Sun Dec 7 00:38:14 2008 2 relations: 5301 Sun Dec 7 00:38:14 2008 3 relations: 5583 Sun Dec 7 00:38:14 2008 4 relations: 5487 Sun Dec 7 00:38:14 2008 5 relations: 5416 Sun Dec 7 00:38:14 2008 6 relations: 5327 Sun Dec 7 00:38:14 2008 7 relations: 4957 Sun Dec 7 00:38:14 2008 8 relations: 4627 Sun Dec 7 00:38:14 2008 9 relations: 4289 Sun Dec 7 00:38:14 2008 10+ relations: 18362 Sun Dec 7 00:38:14 2008 heaviest cycle: 19 relations Sun Dec 7 00:38:14 2008 elapsed time 00:01:15 Sun Dec 7 00:38:14 2008 Sun Dec 7 00:38:14 2008 Sun Dec 7 00:38:14 2008 Msieve v. 1.39 Sun Dec 7 00:38:14 2008 random seeds: 1b990db7 ba65cf40 Sun Dec 7 00:38:14 2008 factoring 15041679499071292646284989557979980982308780587943355373610269065634432656659938885011590841227122309 (101 digits) Sun Dec 7 00:38:15 2008 searching for 15-digit factors Sun Dec 7 00:38:16 2008 commencing number field sieve (101-digit input) Sun Dec 7 00:38:16 2008 R0: -20000000000000000000000 Sun Dec 7 00:38:16 2008 R1: 1 Sun Dec 7 00:38:16 2008 A0: 344 Sun Dec 7 00:38:16 2008 A1: 0 Sun Dec 7 00:38:16 2008 A2: 0Sun Dec 7 00:38:16 2008 A3: 0 Sun Dec 7 00:38:16 2008 A4: 0 Sun Dec 7 00:38:16 2008 A5: 725 Sun Dec 7 00:38:16 2008 skew 1.00, size 2.348152e-08, alpha 0.523263, combined = 1.972314e-08 Sun Dec 7 00:38:16 2008 Sun Dec 7 00:38:16 2008 commencing linear algebra Sun Dec 7 00:38:16 2008 read 65707 cycles Sun Dec 7 00:38:16 2008 cycles contain 206245 unique relations Sun Dec 7 00:38:18 2008 read 206245 relations Sun Dec 7 00:38:19 2008 using 20 quadratic characters above 33552150 Sun Dec 7 00:38:21 2008 building initial matrix Sun Dec 7 00:38:23 2008 memory use: 32.0 MB Sun Dec 7 00:38:23 2008 read 65707 cycles Sun Dec 7 00:38:24 2008 matrix is 65498 x 65707 (20.1 MB) with weight 6006938 (91.42/col) Sun Dec 7 00:38:24 2008 sparse part has weight 4541869 (69.12/col) Sun Dec 7 00:38:25 2008 filtering completed in 2 passes Sun Dec 7 00:38:25 2008 matrix is 65276 x 65476 (20.0 MB) with weight 5989908 (91.48/col) Sun Dec 7 00:38:25 2008 sparse part has weight 4530167 (69.19/col) Sun Dec 7 00:38:25 2008 read 65476 cyclesSun Dec 7 00:38:25 2008 matrix is 65276 x 65476 (20.0 MB) with weight 5989908 (91.48/col) Sun Dec 7 00:38:25 2008 sparse part has weight 4530167 (69.19/col) Sun Dec 7 00:38:25 2008 saving the first 48 matrix rows for later Sun Dec 7 00:38:25 2008 matrix is 65228 x 65476 (18.6 MB) with weight 4719058 (72.07/col) Sun Dec 7 00:38:25 2008 sparse part has weight 4224151 (64.51/col) Sun Dec 7 00:38:25 2008 matrix includes 64 packed rows Sun Dec 7 00:38:25 2008 using block size 10922 for processor cache size 256 kB Sun Dec 7 00:38:26 2008 commencing Lanczos iteration Sun Dec 7 00:38:26 2008 memory use: 16.7 MB Sun Dec 7 00:39:09 2008 lanczos halted after 1033 iterations (dim = 65228) Sun Dec 7 00:39:09 2008 recovered 39 nontrivial dependencies Sun Dec 7 00:39:09 2008 elapsed time 00:00:55 Sun Dec 7 00:39:09 2008 Sun Dec 7 00:39:09 2008 Sun Dec 7 00:39:09 2008 Msieve v. 1.39 Sun Dec 7 00:39:09 2008 random seeds: 226198c7 36d1bb1e Sun Dec 7 00:39:09 2008 factoring 15041679499071292646284989557979980982308780587943355373610269065634432656659938885011590841227122309 (101 digits) Sun Dec 7 00:39:10 2008 searching for 15-digit factors Sun Dec 7 00:39:11 2008 commencing number field sieve (101-digit input) Sun Dec 7 00:39:11 2008 R0: -20000000000000000000000 Sun Dec 7 00:39:11 2008 R1: 1 Sun Dec 7 00:39:11 2008 A0: 344 Sun Dec 7 00:39:11 2008 A1: 0 Sun Dec 7 00:39:11 2008 A2: 0 Sun Dec 7 00:39:11 2008 A3: 0 Sun Dec 7 00:39:11 2008 A4: 0 Sun Dec 7 00:39:11 2008 A5: 725 Sun Dec 7 00:39:11 2008 skew 1.00, size 2.348152e-08, alpha 0.523263, combined = 1.972314e-08 Sun Dec 7 00:39:11 2008 Sun Dec 7 00:39:11 2008 commencing square root phase Sun Dec 7 00:39:11 2008 reading relations for dependency 1 Sun Dec 7 00:39:11 2008 read 32712 cycles Sun Dec 7 00:39:11 2008 cycles contain 128877 unique relations Sun Dec 7 00:39:13 2008 read 128877 relations Sun Dec 7 00:39:13 2008 multiplying 102694 relations Sun Dec 7 00:39:22 2008 multiply complete, coefficients have about 2.89 million bits Sun Dec 7 00:39:22 2008 initial square root is modulo 4567151 Sun Dec 7 00:39:38 2008 prp29 factor: 45090396972221616172354904437 Sun Dec 7 00:39:38 2008 prp72 factor: 333589422784143321541957121594048625347148135316145689550420073192386257 Sun Dec 7 00:39:38 2008 elapsed time 00:00:29
Jan 6, 2009: By Tyler Cadigan / ggnfs, msieve / Jan 6, 2009
(43·10¹⁸⁴-7)/9 = 4(7)₁₈₄_<185> = 53 · 26287823 · 4895902625197_<13> · C163
C163 = P81 · P83
P81 = 100986265192381720719980286210366635840357108525083480574351389325029919037606947_<81>
P83 = 69358608608073139344127843528616553111361386937716623546623185659992381518608784037_<83>

Number: 47777_184 N=7004266842269483659952767910075690687168034383305029594855242179827887829067467896729417906148100412760492466019505809155804252673388696948980973408703058013905039 ( 163 digits) SNFS difficulty: 186 digits. Divisors found: r1=100986265192381720719980286210366635840357108525083480574351389325029919037606947 r2=69358608608073139344127843528616553111361386937716623546623185659992381518608784037 Version: Total time: 347.18 hours. Scaled time: 889.14 units (timescale=2.561). Factorization parameters were as follows: n: 7004266842269483659952767910075690687168034383305029594855242179827887829067467896729417906148100412760492466019505809155804252673388696948980973408703058013905039 m: 10000000000000000000000000000000000000 deg: 5 c5: 43 c0: -70 skew: 1.10 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 9500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1331819 x 1332067 Total sieving time: 347.18 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,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000 total time: 347.18 hours. --------- CPU info (if available) ----------
Jan 5, 2009 (8th): By Luigi Morelli / GGNFS 0.77.1, msieve / Jan 4, 2009
(38·10¹⁷⁴-11)/9 = 4(2)₁₇₃1_<175> = 3³ · 7629737812981_<13> · 31668315658185358241_<20> · 64583320974668012969282589628685014327_<38> · C104
C104 = P44 · P60
P44 = 13572177173944141379230865642040566250314827_<44>
P60 = 738367971619864478723854016085408967268073560203846001125847_<60>

Sat Jan 3 17:34:21 2009 Msieve v. 1.39 Sat Jan 3 17:34:21 2009 random seeds: 811586e7 042c0979 Sat Jan 3 17:34:21 2009 factoring 10021260930390560266594511156264428707661578748567959642375971936717369835041789453030241615860197033469 (104 digits) Sat Jan 3 17:34:24 2009 searching for 15-digit factors Sat Jan 3 17:34:26 2009 commencing number field sieve (104-digit input) Sat Jan 3 17:34:26 2009 R0: -41755367312430798657 Sat Jan 3 17:34:26 2009 R1: 129924582887 Sat Jan 3 17:34:26 2009 A0: -12813572907496742341700 Sat Jan 3 17:34:26 2009 A1: 688027892716311984598 Sat Jan 3 17:34:26 2009 A2: 343348771692294918 Sat Jan 3 17:34:26 2009 A3: -3426111865027 Sat Jan 3 17:34:26 2009 A4: -2705875132 Sat Jan 3 17:34:26 2009 A5: 78960 Sat Jan 3 17:34:26 2009 skew 1.00, size 1.020312e-10, alpha -6.266562, combined = 8.239688e-10 Sat Jan 3 17:34:26 2009 Sat Jan 3 17:34:26 2009 commencing relation filtering Sat Jan 3 17:34:26 2009 commencing duplicate removal, pass 1 Sat Jan 3 17:36:04 2009 found 333597 hash collisions in 4633238 relations Sat Jan 3 17:36:40 2009 added 31398 free relations Sat Jan 3 17:36:40 2009 commencing duplicate removal, pass 2 Sat Jan 3 17:36:47 2009 found 311101 duplicates and 4353535 unique relations Sat Jan 3 17:36:47 2009 memory use: 43.3 MB Sat Jan 3 17:36:47 2009 reading rational ideals above 1900544 Sat Jan 3 17:36:47 2009 reading algebraic ideals above 1900544 Sat Jan 3 17:36:47 2009 commencing singleton removal, pass 1 Sat Jan 3 17:38:25 2009 relations with 0 large ideals: 66751 Sat Jan 3 17:38:25 2009 relations with 1 large ideals: 508305 Sat Jan 3 17:38:25 2009 relations with 2 large ideals: 1420633 Sat Jan 3 17:38:25 2009 relations with 3 large ideals: 1653235 Sat Jan 3 17:38:25 2009 relations with 4 large ideals: 658720 Sat Jan 3 17:38:25 2009 relations with 5 large ideals: 15644 Sat Jan 3 17:38:25 2009 relations with 6 large ideals: 30247 Sat Jan 3 17:38:25 2009 relations with 7+ large ideals: 0 Sat Jan 3 17:38:25 2009 4353535 relations and about 4377821 large ideals Sat Jan 3 17:38:25 2009 commencing singleton removal, pass 2 Sat Jan 3 17:40:01 2009 found 1971537 singletons Sat Jan 3 17:40:01 2009 current dataset: 2381998 relations and about 1995952 large ideals Sat Jan 3 17:40:01 2009 commencing singleton removal, pass 3 Sat Jan 3 17:40:56 2009 found 459886 singletons Sat Jan 3 17:40:56 2009 current dataset: 1922112 relations and about 1500649 large ideals Sat Jan 3 17:40:56 2009 commencing singleton removal, final pass Sat Jan 3 17:41:44 2009 memory use: 37.3 MB Sat Jan 3 17:41:44 2009 commencing in-memory singleton removal Sat Jan 3 17:41:45 2009 begin with 1922112 relations and 1542283 unique ideals Sat Jan 3 17:41:51 2009 reduce to 1596578 relations and 1207151 ideals in 15 passes Sat Jan 3 17:41:51 2009 max relations containing the same ideal: 18 Sat Jan 3 17:41:53 2009 reading rational ideals above 720000 Sat Jan 3 17:41:53 2009 reading algebraic ideals above 720000 Sat Jan 3 17:41:53 2009 commencing singleton removal, final pass Sat Jan 3 17:42:38 2009 keeping 1386175 ideals with weight <= 20, new excess is 174884 Sat Jan 3 17:42:39 2009 memory use: 46.5 MB Sat Jan 3 17:42:40 2009 commencing in-memory singleton removal Sat Jan 3 17:42:40 2009 begin with 1608672 relations and 1386175 unique ideals Sat Jan 3 17:42:45 2009 reduce to 1594481 relations and 1314144 ideals in 12 passes Sat Jan 3 17:42:45 2009 max relations containing the same ideal: 20 Sat Jan 3 17:42:48 2009 removing 283569 relations and 244833 ideals in 38736 cliques Sat Jan 3 17:42:48 2009 commencing in-memory singleton removal Sat Jan 3 17:42:49 2009 begin with 1310912 relations and 1314144 unique ideals Sat Jan 3 17:42:52 2009 reduce to 1278048 relations and 1035423 ideals in 10 passes Sat Jan 3 17:42:52 2009 max relations containing the same ideal: 20 Sat Jan 3 17:42:54 2009 removing 211724 relations and 172988 ideals in 38736 cliques Sat Jan 3 17:42:54 2009 commencing in-memory singleton removal Sat Jan 3 17:42:55 2009 begin with 1066324 relations and 1035423 unique ideals Sat Jan 3 17:42:57 2009 reduce to 1040992 relations and 836386 ideals in 8 passes Sat Jan 3 17:42:57 2009 max relations containing the same ideal: 20 Sat Jan 3 17:42:59 2009 relations with 0 large ideals: 23367 Sat Jan 3 17:42:59 2009 relations with 1 large ideals: 137128 Sat Jan 3 17:42:59 2009 relations with 2 large ideals: 316252 Sat Jan 3 17:42:59 2009 relations with 3 large ideals: 342472 Sat Jan 3 17:42:59 2009 relations with 4 large ideals: 175722 Sat Jan 3 17:42:59 2009 relations with 5 large ideals: 40480 Sat Jan 3 17:42:59 2009 relations with 6 large ideals: 5342 Sat Jan 3 17:42:59 2009 relations with 7+ large ideals: 229 Sat Jan 3 17:42:59 2009 commencing 2-way merge Sat Jan 3 17:43:01 2009 reduce to 620654 relation sets and 416048 unique ideals Sat Jan 3 17:43:01 2009 commencing full merge Sat Jan 3 17:43:15 2009 memory use: 35.2 MB Sat Jan 3 17:43:15 2009 found 281974 cycles, need 256248 Sat Jan 3 17:43:15 2009 weight of 256248 cycles is about 18213555 (71.08/cycle) Sat Jan 3 17:43:15 2009 distribution of cycle lengths: Sat Jan 3 17:43:15 2009 1 relations: 31071 Sat Jan 3 17:43:15 2009 2 relations: 24040 Sat Jan 3 17:43:15 2009 3 relations: 23564 Sat Jan 3 17:43:15 2009 4 relations: 22461 Sat Jan 3 17:43:15 2009 5 relations: 21110 Sat Jan 3 17:43:15 2009 6 relations: 19272 Sat Jan 3 17:43:15 2009 7 relations: 17944 Sat Jan 3 17:43:15 2009 8 relations: 16146 Sat Jan 3 17:43:15 2009 9 relations: 14902 Sat Jan 3 17:43:15 2009 10+ relations: 65738 Sat Jan 3 17:43:15 2009 heaviest cycle: 18 relations Sat Jan 3 17:43:15 2009 commencing cycle optimization Sat Jan 3 17:43:17 2009 start with 1677773 relations Sat Jan 3 17:43:25 2009 pruned 57629 relations Sat Jan 3 17:43:25 2009 memory use: 53.4 MB Sat Jan 3 17:43:25 2009 distribution of cycle lengths: Sat Jan 3 17:43:25 2009 1 relations: 31071 Sat Jan 3 17:43:25 2009 2 relations: 24750 Sat Jan 3 17:43:25 2009 3 relations: 24618 Sat Jan 3 17:43:25 2009 4 relations: 23440 Sat Jan 3 17:43:25 2009 5 relations: 21963 Sat Jan 3 17:43:25 2009 6 relations: 19954 Sat Jan 3 17:43:25 2009 7 relations: 18480 Sat Jan 3 17:43:25 2009 8 relations: 16597 Sat Jan 3 17:43:25 2009 9 relations: 15206 Sat Jan 3 17:43:25 2009 10+ relations: 60169 Sat Jan 3 17:43:25 2009 heaviest cycle: 18 relations Sat Jan 3 17:43:27 2009 Sat Jan 3 17:43:27 2009 commencing linear algebra Sat Jan 3 17:43:27 2009 read 256248 cycles Sat Jan 3 17:43:28 2009 cycles contain 881602 unique relations Sat Jan 3 17:43:49 2009 read 881602 relations Sat Jan 3 17:43:52 2009 using 20 quadratic characters above 67108004 Sat Jan 3 17:44:06 2009 building initial matrix Sat Jan 3 17:44:32 2009 memory use: 113.5 MB Sat Jan 3 17:44:32 2009 read 256248 cycles Sat Jan 3 17:44:33 2009 matrix is 255986 x 256248 (76.0 MB) with weight 24294011 (94.81/col) Sat Jan 3 17:44:33 2009 sparse part has weight 17112766 (66.78/col) Sat Jan 3 17:44:47 2009 filtering completed in 3 passes Sat Jan 3 17:44:47 2009 matrix is 254372 x 254572 (75.7 MB) with weight 24167826 (94.94/col) Sat Jan 3 17:44:47 2009 sparse part has weight 17038763 (66.93/col) Sat Jan 3 17:44:49 2009 read 254572 cycles Sat Jan 3 17:44:50 2009 matrix is 254372 x 254572 (75.7 MB) with weight 24167826 (94.94/col) Sat Jan 3 17:44:50 2009 sparse part has weight 17038763 (66.93/col) Sat Jan 3 17:44:50 2009 saving the first 48 matrix rows for later Sat Jan 3 17:44:50 2009 matrix is 254324 x 254572 (73.0 MB) with weight 19149842 (75.22/col) Sat Jan 3 17:44:50 2009 sparse part has weight 16585514 (65.15/col) Sat Jan 3 17:44:50 2009 matrix includes 64 packed rows Sat Jan 3 17:44:50 2009 using block size 65536 for processor cache size 2048 kB Sat Jan 3 17:44:57 2009 commencing Lanczos iteration Sat Jan 3 17:44:57 2009 memory use: 66.9 MB Sat Jan 3 18:15:46 2009 lanczos halted after 4023 iterations (dim = 254323) Sat Jan 3 18:15:48 2009 recovered 28 nontrivial dependencies Sat Jan 3 18:15:48 2009 Sat Jan 3 18:15:48 2009 commencing square root phase Sat Jan 3 18:15:48 2009 reading relations for dependency 1 Sat Jan 3 18:15:48 2009 read 127522 cycles Sat Jan 3 18:15:49 2009 cycles contain 543861 unique relations Sat Jan 3 18:16:02 2009 read 543861 relations Sat Jan 3 18:16:09 2009 multiplying 439974 relations Sat Jan 3 18:18:40 2009 multiply complete, coefficients have about 19.10 million bits Sat Jan 3 18:18:42 2009 initial square root is modulo 306049 Sat Jan 3 18:23:57 2009 prp44 factor: 13572177173944141379230865642040566250314827 Sat Jan 3 18:23:57 2009 prp60 factor: 738367971619864478723854016085408967268073560203846001125847 Sat Jan 3 18:23:57 2009 elapsed time 00:49:36
Jan 5, 2009 (7th): By matsui / GMP-ECM / Jan 3, 2009
(38·10¹⁷⁷+7)/9 = 4(2)₁₇₆3_<178> = 16831 · C174
C174 = P33 · P141
P33 = 808020975537356813887688012648849_<33>
P141 = 310462058233838072707345486814826980908540325495516767238876034746810469799572718449241791002063641759970155278075383181344441444526372947617_<141>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] 250859855161441519946659272902514539969236659867044276764435994428270585361667293816304570270466533314848922953016589758316334277358577756652737343130070834901207428092342833 = 808020975537356813887688012648849* 310462058233838072707345486814826980908540325495516767238876034746810469799572718449241791002063641759970155278075383181344441444526372947617
Jan 5, 2009 (6th): By Wataru Sakai / Msieve / Dec 28, 2008
(37·10¹⁹⁶+53)/9 = 4(1)₁₉₅7_<197> = C197
C197 = P57 · P66 · P74
P57 = 787928319933580324079324593875726511993688471405608499053_<57>
P66 = 706012788310465914244833920240020167224475218813102557627242440651_<66>
P74 = 73902637246869378978147840235120773789941657681890367360187082285806641539_<74>

Number: 41117_196 N=41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117 ( 197 digits) SNFS difficulty: 197 digits. Divisors found: r1=787928319933580324079324593875726511993688471405608499053 r2=706012788310465914244833920240020167224475218813102557627242440651 r3=73902637246869378978147840235120773789941657681890367360187082285806641539 Version: Total time: 1131.63 hours. Scaled time: 2058.43 units (timescale=1.819). Factorization parameters were as follows: n: 41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117 m: 1000000000000000000000000000000000000000 deg: 5 c5: 370 c0: 53 skew: 0.68 type: snfs lss: 1 rlim: 13700000 alim: 13700000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13700000/13700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6850000, 19550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2616836 x 2617084 Total sieving time: 1131.63 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,197,5,0,0,0,0,0,0,0,0,13700000,13700000,28,28,55,55,2.5,2.5,100000 total time: 1131.63 hours. --------- CPU info (if available) ----------
By Wataru Sakai / Msieve / Dec 28, 2008
10¹⁹⁵+3 = 1(0)₁₉₄3_<196> = 17 · 547 · 14549 · 3486070789921_<13> · 5665894963755404087_<19> · C156
C156 = P71 · P86
P71 = 20272161969880531371430224661237837143004245314829323956717291302611671_<71>
P86 = 18459750205074881191572660444812378965121433733944512974732242794281011685914941573309_<86>

Number: 10003_195 N=374219046080813346453326646441267156034345085487650370040062476729896969884729327545583720587165323414765099952683896438559950257399288091712019285405489339 ( 156 digits) SNFS difficulty: 195 digits. Divisors found: r1=20272161969880531371430224661237837143004245314829323956717291302611671 r2=18459750205074881191572660444812378965121433733944512974732242794281011685914941573309 Version: Total time: 436.80 hours. Scaled time: 880.16 units (timescale=2.015). Factorization parameters were as follows: n: 374219046080813346453326646441267156034345085487650370040062476729896969884729327545583720587165323414765099952683896438559950257399288091712019285405489339 m: 1000000000000000000000000000000000000000 deg: 5 c5: 1 c0: 3 skew: 1.25 type: snfs lss: 1 rlim: 12400000 alim: 12400000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12400000/12400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6200000, 10500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2156382 x 2156628 Total sieving time: 436.80 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,195,5,0,0,0,0,0,0,0,0,12400000,12400000,28,28,55,55,2.5,2.5,100000 total time: 436.80 hours. --------- CPU info (if available) ----------
By Wataru Sakai / Msieve / Dec 28, 2008
(28·10¹⁹⁸+53)/9 = 3(1)₁₉₇7_<199> = 3² · C198
C198 = P40 · P158
P40 = 3649332252990078880852899480628274961427_<40>
P158 = 94723907932046213585023172949738787991480229480739179737363021751442282548661569399706013860101034321205826303279398761288808502140485924795670612716211919719_<158>

Number: 31117_198 N=345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013 ( 198 digits) SNFS difficulty: 199 digits. Divisors found: r1=3649332252990078880852899480628274961427 r2=94723907932046213585023172949738787991480229480739179737363021751442282548661569399706013860101034321205826303279398761288808502140485924795670612716211919719 Version: Total time: 1064.77 hours. Scaled time: 2123.15 units (timescale=1.994). Factorization parameters were as follows: n: 345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679012345679013 m: 2000000000000000000000000000000000000000 deg: 5 c5: 875 c0: 53 skew: 0.57 type: snfs lss: 1 rlim: 14800000 alim: 14800000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 14800000/14800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [7400000, 19400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2649513 x 2649761 Total sieving time: 1064.77 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,199,5,0,0,0,0,0,0,0,0,14800000,14800000,28,28,55,55,2.5,2.5,100000 total time: 1064.77 hours. --------- CPU info (if available) ----------
By Wataru Sakai / Msieve / Jan 4, 2009
(10¹⁸⁴+53)/9 = (1)₁₈₃7_<184> = 25931 · C179
C179 = P66 · P113
P66 = 792056942417260752013943287577332059199532709715550910871166602123_<66>
P113 = 54098076096087152994248770015733377320347175047305220233121079901747953425719984522642163758267738475346218307509_<113>

Number: 11117_184 N=42848756743323092480471679114230500602025032243689449350627091554938533458451703023836763376310636346886395091246427484906525437164440673753851032012306162936682392160391466241607 ( 179 digits) SNFS difficulty: 184 digits. Divisors found: r1=792056942417260752013943287577332059199532709715550910871166602123 r2=54098076096087152994248770015733377320347175047305220233121079901747953425719984522642163758267738475346218307509 Version: Total time: 323.64 hours. Scaled time: 626.89 units (timescale=1.937). Factorization parameters were as follows: n: 42848756743323092480471679114230500602025032243689449350627091554938533458451703023836763376310636346886395091246427484906525437164440673753851032012306162936682392160391466241607 m: 5000000000000000000000000000000000000 deg: 5 c5: 16 c0: 265 skew: 1.75 type: snfs lss: 1 rlim: 8400000 alim: 8400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4200000, 7500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1177876 x 1178124 Total sieving time: 323.64 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,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000 total time: 323.64 hours. --------- CPU info (if available) ----------
Jan 5, 2009 (5th): By Jo Yeong Uk / GGNFS / Msieve v1.39 / Dec 27, 2008
(13·10¹⁸⁰-7)/3 = 4(3)₁₇₉1_<181> = C181
C181 = P45 · P137
P45 = 133183810233677421714973688754211562543765317_<45>
P137 = 32536487173105281333067272791516917637471199207130413085188359827144021898760251672172023912689675343132715372285707394906776189397129143_<137>

Number: 43331_180 N=4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 181 digits) SNFS difficulty: 181 digits. Divisors found: r1=133183810233677421714973688754211562543765317 r2=32536487173105281333067272791516917637471199207130413085188359827144021898760251672172023912689675343132715372285707394906776189397129143 Version: Total time: 91.31 hours. Scaled time: 218.15 units (timescale=2.389). Factorization parameters were as follows: n: 4333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 1000000000000000000000000000000000000 deg: 5 c5: 13 c0: -7 skew: 0.88 type: snfs lss: 1 rlim: 6400000 alim: 6400000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6400000/6400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3200000, 5700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 18375208 Max relations in full relation-set: Initial matrix: Pruned matrix : 1307433 x 1307681 Total sieving time: 84.50 hours. Total relation processing time: 2.37 hours. Matrix solve time: 4.11 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,53,53,2.5,2.5,100000 total time: 91.31 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
By Jo Yeong Uk / GMP-ECM / Jan 3, 2008
(64·10²³³-1)/9 = 7(1)₂₃₃_<234> = 3 · 99315959 · 8290079151717433488691043_<25> · C201
C201 = P39 · C163
P39 = 244999355897374262095731654588996987803_<39>
C163 = [1175096545584055105250951509988618729791632937145951352860247520445895686478618432283375088249068144836193263705482510866613839205023692202682641801126636599436267_<163>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 287897896785322994555674978735968899193228526507440203019621524304219703606465390376414637835676262450237955603657481790170414110522262553993340237389283920579700454909980877098926836312194350874851401 (201 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3210162980 Step 1 took 22449ms Step 2 took 8672ms ********** Factor found in step 2: 244999355897374262095731654588996987803 Found probable prime factor of 39 digits: 244999355897374262095731654588996987803 Composite cofactor 1175096545584055105250951509988618729791632937145951352860247520445895686478618432283375088249068144836193263705482510866613839205023692202682641801126636599436267 has 163 digits
By Jo Yeong Uk / GMP-ECM / Jan 3, 2008
(64·10²⁰⁵-1)/9 = 7(1)₂₀₅_<206> = 431 · 37940267 · 45453581976434362961_<20> · C176
C176 = P40 · C137
P40 = 3413498540067034957579963393050135213037_<40>
C137 = [28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999_<137>]

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 95673507938569544419059184259217858706183654907488877608498088047569608854258353672123533863115165791173052496922107368259780351867183146813879315893305406356587115353521925963 (176 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=27677106 Step 1 took 18946ms Step 2 took 7711ms ********** Factor found in step 2: 3413498540067034957579963393050135213037 Found probable prime factor of 40 digits: 3413498540067034957579963393050135213037 Composite cofactor 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 has 137 digits
Jan 5, 2009 (4th): By Sinkiti Sibata / GGNFS, Msieve / Dec 26, 2008
(13·10¹⁵⁶-7)/3 = 4(3)₁₅₅1_<157> = 41 · 373 · 2143 · 11719 · 9094703 · 185189431516811_<15> · C124
C124 = P57 · P68
P57 = 324398260686691813162866343117371269663267936287799013143_<57>
P68 = 20650636734644430907618223992790982393292044921765406119716528349629_<68>

Number: 43331_156 N=6699030638791358287402250465874032297664402985450649877562708199444280779852023252445956714120090595355942969673208670173947 ( 124 digits) SNFS difficulty: 158 digits. Divisors found: r1=324398260686691813162866343117371269663267936287799013143 r2=20650636734644430907618223992790982393292044921765406119716528349629 Version: Total time: 30.15 hours. Scaled time: 76.99 units (timescale=2.554). Factorization parameters were as follows: name: 43331_156 n: 6699030638791358287402250465874032297664402985450649877562708199444280779852023252445956714120090595355942969673208670173947 m: 20000000000000000000000000000000 deg: 5 c5: 65 c0: -112 skew: 1.11 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1500000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 510325 x 510573 Total sieving time: 30.15 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,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 30.15 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 26, 2008
(38·10¹⁵⁶+61)/9 = 4(2)₁₅₅9_<157> = 11 · 139277740661_<12> · 30738460965305809_<17> · C128
C128 = P57 · P72
P57 = 260143260050233689064483536734775966389994188398184680541_<57>
P72 = 344645007197955662990211669087773268820445474115533760904170023354945071_<72>

Number: 42229_156 N=89657075732512441634943806879080168667130713554798202567148299186828703838676016744071926873134410604543640813584660148737563411 ( 128 digits) SNFS difficulty: 157 digits. Divisors found: r1=260143260050233689064483536734775966389994188398184680541 r2=344645007197955662990211669087773268820445474115533760904170023354945071 Version: Total time: 30.26 hours. Scaled time: 64.45 units (timescale=2.130). Factorization parameters were as follows: name: 42229_156 n: 89657075732512441634943806879080168667130713554798202567148299186828703838676016744071926873134410604543640813584660148737563411 m: 10000000000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1500000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 502089 x 502337 Total sieving time: 30.26 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,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 30.26 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 26, 2008
(38·10¹⁵⁸+43)/9 = 4(2)₁₅₇7_<159> = 7 · 23914675839563_<14> · 27158072252539381_<17> · C128
C128 = P46 · P83
P46 = 2144079130668631481647808214278063607290278667_<46>
P83 = 43315047967083261756515628744608261986207073370289699235452899200702857612505217961_<83>

Number: 42227_158 N=92870890390133953204349065543637257872814042586690164133184967513777941557759002933246154398397579798202131837405662527263537987 ( 128 digits) SNFS difficulty: 160 digits. Divisors found: r1=2144079130668631481647808214278063607290278667 (pp46) r2=43315047967083261756515628744608261986207073370289699235452899200702857612505217961 (pp83) Version: GGNFS-0.77.1-20060513-k8 Total time: 68.70 hours. Scaled time: 135.14 units (timescale=1.967). Factorization parameters were as follows: name: 42227_158 n: 92870890390133953204349065543637257872814042586690164133184967513777941557759002933246154398397579798202131837405662527263537987 m: 50000000000000000000000000000000 deg: 5 c5: 304 c0: 1075 skew: 1.29 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3800001) Primes: RFBsize:243539, AFBsize:244049, largePrimes:9512566 encountered Relations: rels:10279905, finalFF:737657 Max relations in full relation-set: 28 Initial matrix: 487655 x 737657 with sparse part having weight 92990337. Pruned matrix : 406380 x 408882 with weight 56550234. Total sieving time: 64.49 hours. Total relation processing time: 0.38 hours. Matrix solve time: 3.58 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 68.70 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 30, 2008
(13·10¹⁵⁹-7)/3 = 4(3)₁₅₈1_<160> = 261962465293_<12> · C149
C149 = P46 · P104
P46 = 1421529768278761348094525780374224513736072633_<46>
P104 = 11636625830464664858325647743978813807681829947015823061574324087054803749479569252497826886832945914199_<104>

Number: 43331_159 N=16541810020327083872025321485770544028139924294453159596961944801609205755724722039495199343773314721281738282611533742164756110685780090298050015967 ( 149 digits) SNFS difficulty: 161 digits. Divisors found: r1=1421529768278761348094525780374224513736072633 r2=11636625830464664858325647743978813807681829947015823061574324087054803749479569252497826886832945914199 Version: Total time: 44.58 hours. Scaled time: 63.93 units (timescale=1.434). Factorization parameters were as follows: namee: 43331_159 n: 16541810020327083872025321485770544028139924294453159596961944801609205755724722039495199343773314721281738282611533742164756110685780090298050015967 m: 100000000000000000000000000000000 deg: 5 c5: 13 c0: -70 skew: 1.40 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 631769 x 632017 Total sieving time: 44.58 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,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 44.58 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 30, 2008
(38·10¹⁶⁰+61)/9 = 4(2)₁₅₉9_<161> = 11 · 43 · 18869 · 569843 · 110972517492503_<15> · C134
C134 = P57 · P78
P57 = 297509719742290474139330475588728831273006432555451274399_<57>
P78 = 251454404374289030062001456994792487277578746400523774726284481964757292298427_<78>

Number: 42229_160 N=74810129373359309205942545336184834206171738221787981982172320932093334776011501165482249537046287347382671874753603894353824973070373 ( 134 digits) SNFS difficulty: 161 digits. Divisors found: r1=297509719742290474139330475588728831273006432555451274399 r2=251454404374289030062001456994792487277578746400523774726284481964757292298427 Version: Total time: 31.41 hours. Scaled time: 80.23 units (timescale=2.554). Factorization parameters were as follows: name: 42229_160 n: 74810129373359309205942545336184834206171738221787981982172320932093334776011501165482249537046287347382671874753603894353824973070373 m: 100000000000000000000000000000000 deg: 5 c5: 38 c0: 61 skew: 1.10 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 678025 x 678273 Total sieving time: 31.41 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,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 31.41 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 30, 2008
(37·10¹⁵⁹+71)/9 = 4(1)₁₅₈9_<160> = 3² · 13670221 · 5103671884417057976104111_<25> · C127
C127 = P63 · P64
P63 = 917687983434563639100375508394927657132123814900083265245269181_<63>
P64 = 7134497314764989439544865488949314528152762596050336212692706881_<64>

Number: 41119_159 N=6547242453605992394048359084317174514160950780412212530466243101929843173758215174684602594958675707590649982800228486375934461 ( 127 digits) SNFS difficulty: 161 digits. Divisors found: r1=917687983434563639100375508394927657132123814900083265245269181 r2=7134497314764989439544865488949314528152762596050336212692706881 Version: Total time: 46.32 hours. Scaled time: 119.27 units (timescale=2.575). Factorization parameters were as follows: name: 41119_159 n: 6547242453605992394048359084317174514160950780412212530466243101929843173758215174684602594958675707590649982800228486375934461 m: 50000000000000000000000000000000 deg: 5 c5: 592 c0: 355 skew: 0.90 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 731975 x 732223 Total sieving time: 46.32 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,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 46.32 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 30, 2008
(37·10¹⁶⁰+53)/9 = 4(1)₁₅₉7_<161> = 15982877657_<11> · 14936450870732756397871099_<26> · C126
C126 = P51 · P76
P51 = 102923831468505464693908978527655484175650802069673_<51>
P76 = 1673173123475487703089313710784677360787957797984518357283275857504571559703_<76>

Number: 41117_160 N=172209388578223980722585214247740618263420413262660881975294049842946008295376192901434462909969745146634753200138846085187119 ( 126 digits) SNFS difficulty: 161 digits. Divisors found: r1=102923831468505464693908978527655484175650802069673 r2=1673173123475487703089313710784677360787957797984518357283275857504571559703 Version: Total time: 38.38 hours. Scaled time: 76.64 units (timescale=1.997). Factorization parameters were as follows: name: 41117_160 n: 172209388578223980722585214247740618263420413262660881975294049842946008295376192901434462909969745146634753200138846085187119 m: 100000000000000000000000000000000 deg: 5 c5: 37 c0: 53 skew: 1.07 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1750000, 3050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 616277 x 616525 Total sieving time: 38.38 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,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 38.38 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 30, 2008
(37·10¹⁶¹+71)/9 = 4(1)₁₆₀9_<162> = 1546639 · 1977323 · 5775877879819762789365782923_<28> · C122
C122 = P37 · P40 · P46
P37 = 3626670489409865161778772779661790717_<37>
P40 = 1094056547819889305859449209860307372049_<40>
P46 = 5865793487276188965814571253468258105175479053_<46>

Number: 41119_161 N=23274193308925800580091780365675474451842556430851579470279177765428849475396951101054084520978737639545301630498743571049 ( 122 digits) SNFS difficulty: 162 digits. Divisors found: r1=3626670489409865161778772779661790717 r2=1094056547819889305859449209860307372049 r3=5865793487276188965814571253468258105175479053 Version: Total time: 64.26 hours. Scaled time: 127.17 units (timescale=1.979). Factorization parameters were as follows: name: 41119_161 n: 23274193308925800580091780365675474451842556430851579470279177765428849475396951101054084520978737639545301630498743571049 m: 100000000000000000000000000000000 deg: 5 c5: 370 c0: 71 skew: 0.72 type: snfs lss: 1 rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1800000, 4100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 715677 x 715925 Total sieving time: 64.26 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,162,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000 total time: 64.26 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Dec 31, 2008
(13·10¹⁶¹-7)/3 = 4(3)₁₆₀1_<162> = 19 · 41 · 127 · 383 · C155
C155 = P73 · P82
P73 = 5999983234384257158361269946239766294623194084668988312408091792411844581_<73>
P82 = 1906040428688038075255133580167729965232323806993136811044332942461242515795310309_<82>

Number: 43331_161 N=11436210616186810746733794056033051070940864173032611313454331432661520178353510635592300745384936999279263615712639063331420759064052429852989183975085529 ( 155 digits) SNFS difficulty: 163 digits. Divisors found: r1=5999983234384257158361269946239766294623194084668988312408091792411844581 r2=1906040428688038075255133580167729965232323806993136811044332942461242515795310309 Version: Total time: 44.13 hours. Scaled time: 86.81 units (timescale=1.967). Factorization parameters were as follows: name: 43331_161 n: 11436210616186810746733794056033051070940864173032611313454331432661520178353510635592300745384936999279263615712639063331420759064052429852989183975085529 m: 200000000000000000000000000000000 deg: 5 c5: 65 c0: -112 skew: 1.11 type: snfs lss: 1 rlim: 3700000 alim: 3700000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3700000/3700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1850000, 3350001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 649756 x 650004 Total sieving time: 44.13 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,163,5,0,0,0,0,0,0,0,0,3700000,3700000,27,27,51,51,2.4,2.4,100000 total time: 44.13 hours. --------- CPU info (if available) ----------
By Sinkiti Sibata / GGNFS, Msieve / Jan 3, 2009
(5·10¹⁷³+1)/3 = 1(6)₁₇₂7_<174> = 455993 · C168
C168 = P58 · P110
P58 = 8500219598995303344027766550865967186625673657927778414937_<58>
P110 = 42999205203292853731733914136598157388065261036006538544990100819846053226208104949425880113589933879959187387_<110>

Number: 16667_173 N=365502686810250742153205568214131942083906258794908401371658483061508985152549856393994352252483408005532248667559955233230919480489101075382005133119733563161422799619 ( 168 digits) SNFS difficulty: 174 digits. Divisors found: r1=8500219598995303344027766550865967186625673657927778414937 r2=42999205203292853731733914136598157388065261036006538544990100819846053226208104949425880113589933879959187387 Version: Total time: 87.96 hours. Scaled time: 173.45 units (timescale=1.972). Factorization parameters were as follows: name: 16667_173 n: 365502686810250742153205568214131942083906258794908401371658483061508985152549856393994352252483408005532248667559955233230919480489101075382005133119733563161422799619 m: 50000000000000000000000000000000000 deg: 5 c5: 8 c0: 5 skew: 0.91 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1014593 x 1014841 Total sieving time: 87.96 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,174,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000 total time: 87.96 hours. --------- CPU info (if available) ----------
Jan 5, 2009 (3rd): By Robert Backstrom / GGNFS, Msieve / Dec 26, 2008
(11·10¹⁶²+1)/3 = 3(6)₁₆₁7_<163> = 23 · 2700321752101367_<16> · C146
C146 = P43 · P45 · P59
P43 = 3601311424601619332921505797693916788527063_<43>
P45 = 219006581842685263283316360850027272068270597_<45>
P59 = 74853176309569178742912503139634782903946826824956002337017_<59>

Number: n N=59037516448183619208320517613893472549936809145932271117752682219909838415162857923435452340460243053973274572185905190972203813950494013678239387 ( 146 digits) SNFS difficulty: 163 digits. Divisors found: Fri Dec 26 18:44:36 2008 prp43 factor: 3601311424601619332921505797693916788527063 Fri Dec 26 18:44:36 2008 prp45 factor: 219006581842685263283316360850027272068270597 Fri Dec 26 18:44:36 2008 prp59 factor: 74853176309569178742912503139634782903946826824956002337017 Fri Dec 26 18:44:36 2008 elapsed time 01:33:44 (Msieve 1.38 - dependency 5) Version: GGNFS-0.77.1-20050930-k8 Total time: 16.79 hours. Scaled time: 14.12 units (timescale=0.841). Factorization parameters were as follows: name: KA_3_6_161_7 n: 59037516448183619208320517613893472549936809145932271117752682219909838415162857923435452340460243053973274572185905190972203813950494013678239387 type: snfs skew: 0.25 deg: 5 c5: 1100 c0: 1 m: 100000000000000000000000000000000 rlim: 5000000 alim: 5000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1600001) Primes: RFBsize:348513, AFBsize:348887, largePrimes:14234355 encountered Relations: rels:12742718, finalFF:710763 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2543311 hash collisions in 15298059 relations Msieve: matrix is 698438 x 698686 (188.0 MB) Total sieving time: 16.44 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,5000000,5000000,28,28,56,56,2.5,2.5,100000 total time: 16.79 hours. --------- CPU info (if available) ----------
By Robert Backstrom / GGNFS, Msieve / Dec 26, 2008
(26·10¹⁸⁸-71)/9 = 2(8)₁₈₇1_<189> = 1063 · C186
C186 = P63 · P123
P63 = 551630183606680962183180226091792336239549492768560137458052747_<63>
P123 = 492662552392220576655684845632298686292166468106550344307131322364753054986270108272824989428881410922859811571673578121621_<123>

Number: n N=271767534232256715793874777882303752482491899236960384655586913347966969791993310337618898296226612313159820215323507891711090205916170168286819274589735549283997073272708268004599142887 ( 186 digits) SNFS difficulty: 189 digits. Divisors found: Fri Dec 26 23:41:20 2008 prp63 factor: 551630183606680962183180226091792336239549492768560137458052747 Fri Dec 26 23:41:20 2008 prp123 factor: 492662552392220576655684845632298686292166468106550344307131322364753054986270108272824989428881410922859811571673578121621 Fri Dec 26 23:41:20 2008 elapsed time 10:55:00 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 92.37 hours. Scaled time: 189.45 units (timescale=2.051). Factorization parameters were as follows: name: KA_2_8_187_1 n: 271767534232256715793874777882303752482491899236960384655586913347966969791993310337618898296226612313159820215323507891711090205916170168286819274589735549283997073272708268004599142887 type: snfs skew: 0.61 deg: 5 c5: 1625 c0: -142 m: 20000000000000000000000000000000000000 rlim: 8800000 alim: 8800000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 9699990) Primes: RFBsize:590006, AFBsize:589311, largePrimes:36356992 encountered Relations: rels:29641144, finalFF:377841 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 4667599 hash collisions in 36683233 relations Msieve: matrix is 2002203 x 2002451 (546.7 MB) Total sieving time: 90.20 hours. Total relation processing time: 2.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,189,5,0,0,0,0,0,0,0,0,8800000,8800000,29,29,58,58,2.5,2.5,100000 total time: 92.37 hours. --------- CPU info (if available) ----------
By Robert Backstrom / GGNFS, Msieve / Dec 26, 2008
(34·10¹⁸⁴-61)/9 = 3(7)₁₈₃1_<185> = 53 · 311 · C181
C181 = P47 · P134
P47 = 23615038763529760781379918751679533732906278799_<47>
P134 = 97053563553730131755939148516339510463922823914532883145382285182480013642372594307251426540528959234992499729986560196434786562183063_<134>

Number: n N=2291923665460036266321529926456214146561777454212083830478540179444141101606368851409196006660060533748575973899034021584528167067753308122173013272934403796504142314977721153781337 ( 181 digits) SNFS difficulty: 186 digits. Divisors found: Mon Dec 29 07:37:41 2008 prp47 factor: 23615038763529760781379918751679533732906278799 Mon Dec 29 07:37:41 2008 prp134 factor: 97053563553730131755939148516339510463922823914532883145382285182480013642372594307251426540528959234992499729986560196434786562183063 Mon Dec 29 07:37:41 2008 elapsed time 32:08:32 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 79.46 hours. Scaled time: 103.62 units (timescale=1.304). Factorization parameters were as follows: name: KA_3_7_183_1 n: 2291923665460036266321529926456214146561777454212083830478540179444141101606368851409196006660060533748575973899034021584528167067753308122173013272934403796504142314977721153781337 type: snfs skew: 1.78 deg: 5 c5: 17 c0: -305 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 7799990) Primes: RFBsize:571119, AFBsize:572228, largePrimes:34514831 encountered Relations: rels:29065709, finalFF:470198 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7201702 hash collisions in 38453133 relations Msieve: matrix is 1922225 x 1922472 (523.8 MB) Total sieving time: 77.83 hours. Total relation processing time: 1.64 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 79.46 hours. --------- CPU info (if available) ----------
Jan 5, 2009 (2nd): By Serge Batalov / Msieve-1.39 / Dec 26, 2008
(37·10¹⁶⁷+71)/9 = 4(1)₁₆₆9_<168> = 192917 · 536917 · C157
C157 = P36 · P121
P36 = 671579014769319852470480752727399003_<36>
P121 = 5909958659554640741535007471124761361498957478297418163309912416636857421100154094569113223106541752187868302557801388357_<121>

SNFS difficulty: 169 digits. Divisors found: r1=671579014769319852470480752727399003 (pp36) r2=5909958659554640741535007471124761361498957478297418163309912416636857421100154094569113223106541752187868302557801388357 (pp121) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=1.593). Factorization parameters were as follows: n: 3969004213911115832399525563866560304543853158222744089491700975143688785806496283323827500714309382345887375134863665890445083117888155800692484226897608071 m: 2000000000000000000000000000000000 deg: 5 c5: 925 c0: 568 skew: 0.91 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 5250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 916149 x 916397 Total sieving time: 0.00 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,169,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 50.00 hours.
By Serge Batalov / GMP-ECM 6.2.1 / Dec 31, 2008
(64·10²³⁰+53)/9 = 7(1)₂₂₉7_<231> = 3⁴ · 17 · C228
C228 = P40 · C189
P40 = 3232206055590841780396196269472673101807_<40>
C189 = [159773402781755490907447637584752460118703047764753337154560922740787663830010334120610537832830875279251407218065664853653746287567720114801810544062706842945696047019376975588206911877603_<189>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=951095515 Step 1 took 81562ms Step 2 took 33204ms ********** Factor found in step 2: 3232206055590841780396196269472673101807 Found probable prime factor of 40 digits: 3232206055590841780396196269472673101807 Composite cofactor 159773402781755490907447637584752460118703047764753337154560922740787663830010334120610537832830875279251407218065664853653746287567720114801810544062706842945696047019376975588206911877603 has 189 digits
By Serge Batalov / GMP-ECM 6.2.1 / Jan 1, 2009
(16·10²⁴³-1)/3 = 5(3)₂₄₃_<244> = 185849 · C239
C239 = P39 · P201
P39 = 142418441176840492033032134216942205277_<39>
P201 = 201498710578279266127850534345602794151552427229210220839574119308833713179199126509670068269959423304410557453149770591553404877715402614939279778740096562086248467773700074883514599656144871992813921_<201>

Run 1107 out of 4410: Using B1=11000000, B2=58553269330, polynomial Dickson(12), sigma=969687583 Step 1 took 88244ms Step 2 took 49818ms ********** Factor found in step 2: 142418441176840492033032134216942205277 Found probable prime factor of 39 digits: 142418441176840492033032134216942205277 Probable prime cofactor 201498710578279266127850534345602794151552427229210220839574119308833713179199126509670068269959423304410557453149770591553404877715402614939279778740096562086248467773700074883514599656144871992813921 has 201 digits
Jan 5, 2009: I'm sorry to have kept you waiting. The maintenance system is currently running with an old unstable machine. Some features of tables were changed.

More: December 2008