News and updates, November 2009

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News and updates, November 2009

Nov 30, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 30, 2009
(65·10¹⁶⁵-11)/9 = 7(2)₁₆₄1_<166> = 3 · 1627 · 1117427261_<10> · C154
C154 = P45 · P110
P45 = 113006746106565909443027295307940874726468067_<45>
P110 = 11717592946789296253681058279544472082801984835493741742797532427363964872859069731881552804947725855354637643_<110>

Number: 72221_165 N=1324167051117905466116290415486962399951869164503675847313184589279820521464612022488971168097567147466746257583242944662193031062572818924125189995646081 ( 154 digits) SNFS difficulty: 166 digits. Divisors found: r1=113006746106565909443027295307940874726468067 r2=11717592946789296253681058279544472082801984835493741742797532427363964872859069731881552804947725855354637643 Version: Total time: 24.57 hours. Scaled time: 58.62 units (timescale=2.386). Factorization parameters were as follows: n: 1324167051117905466116290415486962399951869164503675847313184589279820521464612022488971168097567147466746257583242944662193031062572818924125189995646081 m: 1000000000000000000000000000000000 deg: 5 c5: 65 c0: -11 skew: 0.70 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, 4200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9909831 Max relations in full relation-set: Initial matrix: Pruned matrix : 750797 x 751045 Total sieving time: 22.18 hours. Total relation processing time: 0.97 hours. Matrix solve time: 1.26 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 24.57 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 30, 2009: By Sinkiti Sibata / Msieve / Nov 30, 2009
(62·10¹⁶⁴-71)/9 = 6(8)₁₆₃1_<165> = 3 · 8819 · 51539 · 85667 · 791251537184711_<15> · C136
C136 = P39 · P97
P39 = 992475357917463346229619663566535046949_<39>
P97 = 7509737163976481080866171857101385836152469516008259754713441097351260965314523929224542143986219_<97>

Number: 68881_164 N=7453229079683634188103196101922610125639868950413398574507032854609890070168290130051336575627502110007583354854997020130458699173995831 ( 136 digits) SNFS difficulty: 166 digits. Divisors found: r1=992475357917463346229619663566535046949 (pp39) r2=7509737163976481080866171857101385836152469516008259754713441097351260965314523929224542143986219 (pp97) Version: Msieve-1.40 Total time: 43.13 hours. Scaled time: 144.79 units (timescale=3.357). Factorization parameters were as follows: name: 68881_164 n: 7453229079683634188103196101922610125639868950413398574507032854609890070168290130051336575627502110007583354854997020130458699173995831 m: 1000000000000000000000000000000000 deg: 5 c5: 31 c0: -355 skew: 1.63 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, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 801871 x 802119 Total sieving time: 41.78 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.21 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 43.13 hours. --------- CPU info (if available) ----------
Nov 29, 2009 (4th): By Wataru Sakai / GMP-ECM 6.2.1, Msieve / Nov 29, 2009
(5·10¹⁷⁴+31)/9 = (5)₁₇₃9_<174> = 23 · 1259 · 2729 · 92569625550097_<14> · C152
C152 = P36 · P41 · P76
P36 = 319209987870288110798004201214022531_<36>
P41 = 29918625098920000052618788688979657934147_<41>
P76 = 7952135702568029913397518486410342950297753828903848797089446457106865919507_<76>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3191334078 Step 1 took 12315ms Step 2 took 5559ms ********** Factor found in step 2: 319209987870288110798004201214022531 Found probable prime factor of 36 digits: 319209987870288110798004201214022531 Composite cofactor 237916966820869688084184098718279133319024623800428369609709957288403959046532171004082771755032730649929947208705529 has 117 digits ------------------------------ Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1509897548 Step 1 took 10661ms Step 2 took 4556ms ********** Factor found in step 2: 29918625098920000052618788688979657934147 Found probable prime factor of 41 digits: 29918625098920000052618788688979657934147 Probable prime cofactor 7952135702568029913397518486410342950297753828903848797089446457106865919507 has 76 digits
(47·10²⁰⁰+61)/9 = 5(2)₁₉₉9_<201> = 23 · 29 · C198
C198 = P49 · P150
P49 = 1821402884526033038533370786121841309816963740679_<49>
P150 = 429856496359875945099381474633284382898100856895829070340592911058234885519310144276396296060479619834175215447282578435029435921107042424727017527353_<150>

Number: 52229_200 N=782941862402132267199733466600033316674995835415625520573046809928369148758953856405130767949358654006330168249208728968848908878893886390138264201232716974845910378144261202731967349658504081292687 ( 198 digits) SNFS difficulty: 201 digits. Divisors found: r1=1821402884526033038533370786121841309816963740679 r2=429856496359875945099381474633284382898100856895829070340592911058234885519310144276396296060479619834175215447282578435029435921107042424727017527353 Version: Total time: 879.42 hours. Scaled time: 1768.52 units (timescale=2.011). Factorization parameters were as follows: n: 782941862402132267199733466600033316674995835415625520573046809928369148758953856405130767949358654006330168249208728968848908878893886390138264201232716974845910378144261202731967349658504081292687 m: 10000000000000000000000000000000000000000 deg: 5 c5: 47 c0: 61 skew: 1.05 type: snfs lss: 1 rlim: 16100000 alim: 16100000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 16100000/16100000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [8050000, 17750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3153324 x 3153572 Total sieving time: 879.42 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,201,5,0,0,0,0,0,0,0,0,16100000,16100000,29,29,56,56,2.6,2.6,100000 total time: 879.42 hours. --------- CPU info (if available) ----------
Nov 29, 2009 (3rd): By JPascoa / ggnfs, Msieve / Nov 29, 2009
(65·10¹⁶⁵+7)/9 = 7(2)₁₆₄3_<166> = 709 · 67751 · 1829671 · C152
C152 = P75 · P78
P75 = 312974659587106130775379744870042305659798659750210394695905699474058989043_<75>
P78 = 262558886508076207744801887760311254273758547653064352203241793866965567029249_<78>

Number: 72223_165 N=82174278126434783823391208352460875362453913579954847715282054703599326256843388185088845857667117607706749934491923336032382214386373130028033751518707 ( 152 digits) SNFS difficulty: 166 digits. Divisors found: r1=312974659587106130775379744870042305659798659750210394695905699474058989043 (pp75) r2=262558886508076207744801887760311254273758547653064352203241793866965567029249 (pp78) Version: Msieve v. 1.43 Total time: 48.54 hours. Scaled time: 138.34 units (timescale=2.850). Factorization parameters were as follows: n: 82174278126434783823391208352460875362453913579954847715282054703599326256843388185088845857667117607706749934491923336032382214386373130028033751518707 m: 1000000000000000000000000000000000 deg: 5 c5: 65 c0: 7 skew: 0.64 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 4200001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 816606 x 816831 Total sieving time: 47.76 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.67 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 48.54 hours. --------- CPU info (if available) ----------
Nov 29, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 29, 2009
(65·10¹⁶⁴+61)/9 = 7(2)₁₆₃9_<165> = 3⁴ · 319001 · 17439599 · C151
C151 = P76 · P76
P76 = 1097127491350443004053837025887267310248050259027019551554425722997887106267_<76>
P76 = 1460831723951703039628220676876044203673473878553552062390817891003524106873_<76>

Number: 72229_164 N=1602718644584274818803163723477909962133415966700972038765533352034751949940452264830643947910679050139435670063108805415833738405346671012673616073091 ( 151 digits) SNFS difficulty: 166 digits. Divisors found: r1=1097127491350443004053837025887267310248050259027019551554425722997887106267 r2=1460831723951703039628220676876044203673473878553552062390817891003524106873 Version: Total time: 28.82 hours. Scaled time: 68.70 units (timescale=2.384). Factorization parameters were as follows: n: 1602718644584274818803163723477909962133415966700972038765533352034751949940452264830643947910679050139435670063108805415833738405346671012673616073091 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: 122 skew: 1.56 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, 4600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10149598 Max relations in full relation-set: Initial matrix: Pruned matrix : 782891 x 783139 Total sieving time: 26.18 hours. Total relation processing time: 1.18 hours. Matrix solve time: 1.37 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 28.82 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nice split. :-)
Nov 29, 2009: By Dmitry Domanov / GGNFS/msieve / Nov 29, 2009
(59·10¹⁶⁷+31)/9 = 6(5)₁₆₆9_<168> = 1609 · 1613 · 8969 · C158
C158 = P45 · P114
P45 = 180807571184022017815614490573920266850012827_<45>
P114 = 155760902333919403469684574721889190589532983161655736580938118674989762881341704303010429704566137565650015823529_<114>

Number: s158 N=28162750436427633795391345241974761470071604276095120931948649687067221159896234746405373333713070886324764143370807972283060862326022280203040781466618406483 ( 158 digits) SNFS difficulty: 169 digits. Divisors found: r1=180807571184022017815614490573920266850012827 (pp45) r2=155760902333919403469684574721889190589532983161655736580938118674989762881341704303010429704566137565650015823529 (pp114) Version: Msieve-1.40 Total time: 63.41 hours. Scaled time: 119.39 units (timescale=1.883). Factorization parameters were as follows: n: 28162750436427633795391345241974761470071604276095120931948649687067221159896234746405373333713070886324764143370807972283060862326022280203040781466618406483 m: 2000000000000000000000000000000000 deg: 5 c5: 1475 c0: 248 skew: 0.70 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor 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, 5950001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1020495 x 1020720 Total sieving time: 61.85 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.31 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 63.41 hours. --------- CPU info (if available) ----------
Nov 28, 2009 (4th): By Sinkiti Sibata / Msieve / Nov 28, 2009
(26·10¹⁶³-11)/3 = 8(6)₁₆₂3_<164> = 2239 · 8719 · 195407 · 879139434150694749919804433_<27> · C125
C125 = P46 · P79
P46 = 5211438645737500317674537589757818163406227579_<46>
P79 = 4958791117901422260553490157272046951176263951871311374087740608923515632809707_<79>

Number: 86663_163 N=25842435667971333293845691995925430935046775646627219316454740930177241830087326929025122361662134281077043238993181242309353 ( 125 digits) SNFS difficulty: 165 digits. Divisors found: r1=5211438645737500317674537589757818163406227579 (pp46) r2=4958791117901422260553490157272046951176263951871311374087740608923515632809707 (pp79) Version: Msieve-1.40 Total time: 39.13 hours. Scaled time: 131.36 units (timescale=3.357). Factorization parameters were as follows: name: 86663_163 n: 25842435667971333293845691995925430935046775646627219316454740930177241830087326929025122361662134281077043238993181242309353 m: 500000000000000000000000000000000 deg: 5 c5: 208 c0: -275 skew: 1.06 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, 4150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 757161 x 757409 Total sieving time: 37.91 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,165.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 39.13 hours. --------- CPU info (if available) ----------
(65·10¹⁶⁴-11)/9 = 7(2)₁₆₃1_<165> = 7 · 642113 · 1373173 · 4123318093_<10> · 4443565537_<10> · 4462792390541_<13> · C121
C121 = P52 · P69
P52 = 1551622602733807349047209724184123573558714451797777_<52>
P69 = 922284432714733061874653609820085576890214786673481956403908905108631_<69>

Number: 72221_164 N=1431037371949707131839284966982399894566209201602764234918449603635050483060354978307759067701589405764384099117429313287 ( 121 digits) SNFS difficulty: 166 digits. Divisors found: r1=1551622602733807349047209724184123573558714451797777 (pp52) r2=922284432714733061874653609820085576890214786673481956403908905108631 (pp69) Version: Msieve v. 1.42 Total time: 2.07 hours. Scaled time: 1.41 units (timescale=0.681). Factorization parameters were as follows: name: 72221_163 n: 1431037371949707131839284966982399894566209201602764234918449603635050483060354978307759067701589405764384099117429313287 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: -22 skew: 1.11 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, 4050001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 730980 x 731209 Total sieving time: 0.00 hours. Total relation processing time: 0.11 hours. Matrix solve time: 1.74 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 2.07 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 CPU1: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598) Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574) Total of 2 processors activated (7442.34 BogoMIPS). Total time: 38 hours.
Nov 28, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 28, 2009
(43·10¹⁸⁸+11)/9 = 4(7)₁₈₇9_<189> = 8387 · 200015330041_<12> · 73294994688491_<14> · 86021662446856582196340817_<26> · C134
C134 = P38 · P96
P38 = 60652757993607889981105524809786581043_<38>
P96 = 744771959182400709766779466077945682530064054931570187406997451913632109458468682650603381975097_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2151625036 Step 1 took 38024ms Step 2 took 14497ms ********** Factor found in step 2: 60652757993607889981105524809786581043 Found probable prime factor of 38 digits: 60652757993607889981105524809786581043 Probable prime cofactor 744771959182400709766779466077945682530064054931570187406997451913632109458468682650603381975097 has 96 digits
Nov 28, 2009 (2nd): By Dmitry Domanov / GGNFS/msieve 1.42 / Nov 28, 2009
(26·10²⁰⁰-11)/3 = 8(6)₁₉₉3_<201> = C201
C201 = P99 · P103
P99 = 219631702931061976134369747885808367899858190913021959949302323867094375889693220762080723420749513_<99>
P103 = 3945999849296329038851146075899153593764462405886868527184422610760144041919822331667205447984131245551_<103>

Sieving took 39 days on Xeon E5310 1.86GHz (Windows 2003 Server SP2) Postprocessing took 23.5 hours (8 cores) Wed Nov 25 07:01:39 2009 Msieve v. 1.42 Wed Nov 25 07:01:39 2009 random seeds: 0016d1ec c3a03c82 Wed Nov 25 07:01:39 2009 factoring 866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 (201 digits) Wed Nov 25 07:01:42 2009 searching for 15-digit factors Wed Nov 25 07:01:44 2009 commencing number field sieve (201-digit input) Wed Nov 25 07:01:44 2009 R0: -10000000000000000000000000000000000000000 Wed Nov 25 07:01:44 2009 R1: 1 Wed Nov 25 07:01:44 2009 A0: -11 Wed Nov 25 07:01:44 2009 A1: 0 Wed Nov 25 07:01:44 2009 A2: 0 Wed Nov 25 07:01:44 2009 A3: 0 Wed Nov 25 07:01:44 2009 A4: 0 Wed Nov 25 07:01:44 2009 A5: 26 Wed Nov 25 07:01:44 2009 skew 0.84, size 5.578690e-014, alpha 1.471114, combined = 1.386997e-011 Wed Nov 25 07:01:44 2009 Wed Nov 25 07:01:44 2009 commencing relation filtering Wed Nov 25 07:01:44 2009 estimated available RAM is 4095.0 MB Wed Nov 25 07:01:44 2009 commencing duplicate removal, pass 1 Wed Nov 25 07:13:10 2009 found 5943338 hash collisions in 42007041 relations Wed Nov 25 07:14:27 2009 commencing duplicate removal, pass 2 Wed Nov 25 07:18:36 2009 found 5764474 duplicates and 36242567 unique relations Wed Nov 25 07:18:36 2009 memory use: 197.2 MB Wed Nov 25 07:18:36 2009 reading ideals above 18284544 Wed Nov 25 07:18:44 2009 commencing singleton removal, initial pass Wed Nov 25 07:27:59 2009 memory use: 596.8 MB Wed Nov 25 07:27:59 2009 reading all ideals from disk Wed Nov 25 07:28:12 2009 memory use: 661.3 MB Wed Nov 25 07:28:17 2009 commencing in-memory singleton removal Wed Nov 25 07:28:22 2009 begin with 36242567 relations and 36728595 unique ideals Wed Nov 25 07:29:15 2009 reduce to 14764672 relations and 11920362 ideals in 21 passes Wed Nov 25 07:29:15 2009 max relations containing the same ideal: 49 Wed Nov 25 07:29:19 2009 reading ideals above 720000 Wed Nov 25 07:29:20 2009 commencing singleton removal, initial pass Wed Nov 25 07:34:45 2009 memory use: 298.4 MB Wed Nov 25 07:34:45 2009 reading all ideals from disk Wed Nov 25 07:34:54 2009 memory use: 501.5 MB Wed Nov 25 07:34:59 2009 commencing in-memory singleton removal Wed Nov 25 07:35:03 2009 begin with 14764763 relations and 14140030 unique ideals Wed Nov 25 07:35:45 2009 reduce to 14760399 relations and 14135240 ideals in 10 passes Wed Nov 25 07:35:45 2009 max relations containing the same ideal: 189 Wed Nov 25 07:36:05 2009 removing 2180612 relations and 1935203 ideals in 245409 cliques Wed Nov 25 07:36:06 2009 commencing in-memory singleton removal Wed Nov 25 07:36:10 2009 begin with 12579787 relations and 14135240 unique ideals Wed Nov 25 07:36:49 2009 reduce to 12325260 relations and 11939746 ideals in 11 passes Wed Nov 25 07:36:49 2009 max relations containing the same ideal: 164 Wed Nov 25 07:37:05 2009 removing 1622619 relations and 1377210 ideals in 245409 cliques Wed Nov 25 07:37:07 2009 commencing in-memory singleton removal Wed Nov 25 07:37:10 2009 begin with 10702641 relations and 11939746 unique ideals Wed Nov 25 07:37:40 2009 reduce to 10529753 relations and 10386055 ideals in 10 passes Wed Nov 25 07:37:40 2009 max relations containing the same ideal: 149 Wed Nov 25 07:37:54 2009 removing 107501 relations and 98145 ideals in 9356 cliques Wed Nov 25 07:37:55 2009 commencing in-memory singleton removal Wed Nov 25 07:37:57 2009 begin with 10422252 relations and 10386055 unique ideals Wed Nov 25 07:38:15 2009 reduce to 10421333 relations and 10286989 ideals in 6 passes Wed Nov 25 07:38:15 2009 max relations containing the same ideal: 147 Wed Nov 25 07:38:21 2009 relations with 0 large ideals: 2845 Wed Nov 25 07:38:21 2009 relations with 1 large ideals: 240 Wed Nov 25 07:38:21 2009 relations with 2 large ideals: 6154 Wed Nov 25 07:38:21 2009 relations with 3 large ideals: 65255 Wed Nov 25 07:38:21 2009 relations with 4 large ideals: 363951 Wed Nov 25 07:38:21 2009 relations with 5 large ideals: 1202136 Wed Nov 25 07:38:21 2009 relations with 6 large ideals: 2522194 Wed Nov 25 07:38:21 2009 relations with 7+ large ideals: 6258558 Wed Nov 25 07:38:21 2009 commencing 2-way merge Wed Nov 25 07:38:42 2009 reduce to 6106240 relation sets and 5971895 unique ideals Wed Nov 25 07:38:42 2009 commencing full merge Wed Nov 25 07:42:16 2009 memory use: 632.6 MB Wed Nov 25 07:42:18 2009 found 3166995 cycles, need 3150095 Wed Nov 25 07:42:18 2009 weight of 3150095 cycles is about 220790303 (70.09/cycle) Wed Nov 25 07:42:18 2009 distribution of cycle lengths: Wed Nov 25 07:42:18 2009 1 relations: 431731 Wed Nov 25 07:42:18 2009 2 relations: 392606 Wed Nov 25 07:42:18 2009 3 relations: 386090 Wed Nov 25 07:42:18 2009 4 relations: 345382 Wed Nov 25 07:42:18 2009 5 relations: 293444 Wed Nov 25 07:42:18 2009 6 relations: 254531 Wed Nov 25 07:42:18 2009 7 relations: 215315 Wed Nov 25 07:42:18 2009 8 relations: 176756 Wed Nov 25 07:42:18 2009 9 relations: 145428 Wed Nov 25 07:42:18 2009 10+ relations: 508812 Wed Nov 25 07:42:18 2009 heaviest cycle: 24 relations Wed Nov 25 07:42:21 2009 commencing cycle optimization Wed Nov 25 07:42:30 2009 start with 17464318 relations Wed Nov 25 07:43:23 2009 pruned 322260 relations Wed Nov 25 07:43:23 2009 memory use: 477.8 MB Wed Nov 25 07:43:23 2009 distribution of cycle lengths: Wed Nov 25 07:43:23 2009 1 relations: 431731 Wed Nov 25 07:43:23 2009 2 relations: 400095 Wed Nov 25 07:43:23 2009 3 relations: 397367 Wed Nov 25 07:43:23 2009 4 relations: 350474 Wed Nov 25 07:43:23 2009 5 relations: 298352 Wed Nov 25 07:43:23 2009 6 relations: 255742 Wed Nov 25 07:43:23 2009 7 relations: 215378 Wed Nov 25 07:43:23 2009 8 relations: 175429 Wed Nov 25 07:43:23 2009 9 relations: 143520 Wed Nov 25 07:43:23 2009 10+ relations: 482007 Wed Nov 25 07:43:23 2009 heaviest cycle: 24 relations Wed Nov 25 07:43:43 2009 RelProcTime: 2519 Wed Nov 25 07:43:43 2009 Wed Nov 25 07:43:43 2009 commencing linear algebra Wed Nov 25 07:43:48 2009 read 3150095 cycles Wed Nov 25 07:43:57 2009 cycles contain 10285527 unique relations Wed Nov 25 07:55:13 2009 read 10285527 relations Wed Nov 25 07:55:43 2009 using 20 quadratic characters above 536869410 Wed Nov 25 07:57:06 2009 building initial matrix Wed Nov 25 08:00:39 2009 memory use: 1151.5 MB Wed Nov 25 08:00:57 2009 read 3150095 cycles Wed Nov 25 08:06:32 2009 matrix is 3149918 x 3150095 (902.9 MB) with weight 279978388 (88.88/col) Wed Nov 25 08:06:32 2009 sparse part has weight 214627921 (68.13/col) Wed Nov 25 08:08:10 2009 filtering completed in 2 passes Wed Nov 25 08:08:11 2009 matrix is 3146755 x 3146931 (902.7 MB) with weight 279889156 (88.94/col) Wed Nov 25 08:08:11 2009 sparse part has weight 214604908 (68.19/col) Wed Nov 25 08:08:46 2009 read 3146931 cycles Wed Nov 25 08:37:25 2009 matrix is 3146755 x 3146931 (902.7 MB) with weight 279889156 (88.94/col) Wed Nov 25 08:37:25 2009 sparse part has weight 214604908 (68.19/col) Wed Nov 25 08:37:25 2009 saving the first 48 matrix rows for later Wed Nov 25 08:37:28 2009 matrix is 3146707 x 3146931 (855.2 MB) with weight 221919681 (70.52/col) Wed Nov 25 08:37:28 2009 sparse part has weight 205309780 (65.24/col) Wed Nov 25 08:37:28 2009 matrix includes 64 packed rows Wed Nov 25 08:37:28 2009 using block size 65536 for processor cache size 4096 kB Wed Nov 25 08:38:02 2009 commencing Lanczos iteration (8 threads) Wed Nov 25 08:38:02 2009 memory use: 1068.7 MB Thu Nov 26 05:51:48 2009 lanczos halted after 49761 iterations (dim = 3146707) Thu Nov 26 05:51:57 2009 recovered 37 nontrivial dependencies Thu Nov 26 05:51:58 2009 BLanczosTime: 79695 Thu Nov 26 05:51:58 2009 Thu Nov 26 05:51:58 2009 commencing square root phase Thu Nov 26 05:51:58 2009 reading relations for dependency 1 Thu Nov 26 05:52:01 2009 read 1574926 cycles Thu Nov 26 05:52:06 2009 cycles contain 6243919 unique relations Thu Nov 26 06:01:37 2009 read 6243919 relations Thu Nov 26 06:02:38 2009 multiplying 5147940 relations Thu Nov 26 06:13:47 2009 multiply complete, coefficients have about 145.85 million bits Thu Nov 26 06:13:49 2009 initial square root is modulo 171541 Thu Nov 26 06:32:30 2009 sqrtTime: 2432 Thu Nov 26 06:32:30 2009 prp99 factor: 219631702931061976134369747885808367899858190913021959949302323867094375889693220762080723420749513 Thu Nov 26 06:32:30 2009 prp103 factor: 3945999849296329038851146075899153593764462405886868527184422610760144041919822331667205447984131245551 Thu Nov 26 06:32:30 2009 elapsed time 23:30:51
Nov 28, 2009: By Erik Branger / GGNFS, Msieve / Nov 28, 2009
(64·10²⁰⁵-1)/9 = 7(1)₂₀₅_<206> = 431 · 37940267 · 45453581976434362961_<20> · 3413498540067034957579963393050135213037_<40> · C137
C137 = P52 · P85
P52 = 5021904639112661884279481420515331308570490020937987_<52>
P85 = 5581147687333324553148372632272707694103863113163794664870316102823081173696895306077_<85>

Number: 71111_205 N=28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 ( 137 digits) Divisors found: r1=5021904639112661884279481420515331308570490020937987 (pp52) r2=5581147687333324553148372632272707694103863113163794664870316102823081173696895306077 (pp85) Version: Msieve v. 1.43 Total time: 379.42 hours. Scaled time: 380.18 units (timescale=1.002). Factorization parameters were as follows: # Murphy_E = 3.341821e-11, selected by Jeff Gilchrist n: 28027991462592126727645456941213879374870484455341245911407229100340608719858666765731412775742675529856705668542399476690203589001246999 Y0: -200712814366335223924707637 Y1: 1865037990862081 c0: 42756225136356909361925341794202800 c1: 271117863504155830697150367460 c2: -599164415210628480558292 c3: -255405301427474975 c4: 342673420962 c5: 86040 skew: 1286946.34 type: gnfs # selected mechanically rlim: 14600000 alim: 14600000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.6 alambda: 2.6 Factor base limits: 14600000/14600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved algebraic special-q in [7300000, 18600001) Primes: , , Relations: 23161909 relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2131553 x 2131777 Total sieving time: 365.37 hours. Total relation processing time: 0.57 hours. Matrix solve time: 12.50 hours. Time per square root: 0.99 hours. Prototype def-par.txt line would be: gnfs,136,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,14600000,14600000,28,28,55,55,2.6,2.6,100000 total time: 379.42 hours. --------- CPU info (if available) ----------
Nov 27, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 27, 2009
(22·10¹⁶⁴-7)/3 = 7(3)₁₆₃1_<165> = 23 · 53901767 · 139612857686202560949310679923_<30> · C127
C127 = P49 · P78
P49 = 6754321484568289172985434187887056943790139178677_<49>
P78 = 627282892180425272457203747632461341968295653636265909025507998427062127369821_<78>

Number: 73331_164 N=4236870315556380098039369903323088181940804099761376480634290491976797824420141498514838608126730235966130123927245727176506817 ( 127 digits) SNFS difficulty: 166 digits. Divisors found: r1=6754321484568289172985434187887056943790139178677 r2=627282892180425272457203747632461341968295653636265909025507998427062127369821 Version: Total time: 18.55 hours. Scaled time: 44.21 units (timescale=2.383). Factorization parameters were as follows: n: 4236870315556380098039369903323088181940804099761376480634290491976797824420141498514838608126730235966130123927245727176506817 m: 1000000000000000000000000000000000 deg: 5 c5: 11 c0: -35 skew: 1.26 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, 3600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9469802 Max relations in full relation-set: Initial matrix: Pruned matrix : 701714 x 701962 Total sieving time: 16.64 hours. Total relation processing time: 0.71 hours. Matrix solve time: 1.12 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 18.55 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 27, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 27, 2009
(22·10¹⁷²-7)/3 = 7(3)₁₇₁1_<173> = 48214384732603_<14> · 4064286759125334773_<19> · C141
C141 = P34 · P108
P34 = 2528431516575789096617651796309427_<34>
P108 = 148009386868021114014136141181083786229874235422605861967736289169789771857161756134774694674396272086829287_<108>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=897477864 Step 1 took 42495ms Step 2 took 14659ms ********** Factor found in step 2: 2528431516575789096617651796309427 Found probable prime factor of 34 digits: 2528431516575789096617651796309427 Probable prime cofactor 148009386868021114014136141181083786229874235422605861967736289169789771857161756134774694674396272086829287 has 108 digits
Nov 27, 2009 (2nd): By Sinkiti Sibata / Msieve / Nov 27, 2009
(59·10¹⁸⁴+31)/9 = 6(5)₁₈₃9_<185> = 3 · 13 · 41 · C182
C182 = P64 · P118
P64 = 6813977917155969100374090114813988981026000167458606630278080087_<64>
P118 = 6016727141523583670134963894843856668867307701321458618205426905018934714457542819286019955552910616372334350104724943_<118>

Number: 65559_184 N=40997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510041 ( 182 digits) SNFS difficulty: 186 digits. Divisors found: r1=6813977917155969100374090114813988981026000167458606630278080087 (pp64) r2=6016727141523583670134963894843856668867307701321458618205426905018934714457542819286019955552910616372334350104724943 (pp118) Version: Msieve v. 1.42 Total time: 12.43 hours. Scaled time: 9.89 units (timescale=0.796). Factorization parameters were as follows: name: 65559_184 n: 40997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510040997845875894656382461260510041 m: 10000000000000000000000000000000000000 deg: 5 c5: 59 c0: 310 skew: 1.39 type: snfs lss: 1 rlim: 9100000 alim: 9100000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9100000/9100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4550000, 8150001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1832409 x 1832638 Total sieving time: 0.00 hours. Total relation processing time: 0.22 hours. Matrix solve time: 11.85 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,186.000,5,0,0,0,0,0,0,0,0,9100000,9100000,28,28,54,54,2.5,2.5,100000 total time: 12.43 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 CPU1: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598) Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574) Total of 2 processors activated (7442.34 BogoMIPS). Total time: 224 hours.
Nov 27, 2009: By Dmitry Domanov / GGNFS/msieve / Nov 27, 2009
(67·10¹⁶⁶-31)/9 = 7(4)₁₆₅1_<167> = 1361 · C164
C164 = P56 · P109
P56 = 36877280473198598114033606344601705893521134287453029239_<56>
P109 = 1483253158041523948079442997084179518478110622805970858351989516224667268559875468140693529675012634339151679_<109>

N=54698342721854845293493346395624132582251612376520532288350069393419871009878357416931994448526410319209731406645440444117887174463221487468364764470569026042942281 ( 164 digits) SNFS difficulty: 169 digits. Divisors found: r1=36877280473198598114033606344601705893521134287453029239 (pp56) r2=1483253158041523948079442997084179518478110622805970858351989516224667268559875468140693529675012634339151679 (pp109) Version: Msieve-1.40 Total time: 71.53 hours. Scaled time: 66.81 units (timescale=0.934). Factorization parameters were as follows: n: 54698342721854845293493346395624132582251612376520532288350069393419871009878357416931994448526410319209731406645440444117887174463221487468364764470569026042942281 m: 2000000000000000000000000000000000 deg: 5 c5: 335 c0: -496 skew: 1.08 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor 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: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 881679 x 881908 Total sieving time: 69.81 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.42 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,169.000,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,52,52,2.4,2.4,100000 total time: 71.53 hours. --------- CPU info (if available) ----------
Nov 26, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 26, 2009
(64·10¹⁶⁴+17)/9 = 7(1)₁₆₃3_<165> = 17597 · 83719 · 553157761307_<12> · C144
C144 = P45 · P100
P45 = 170993170796291589495847649921540863092737789_<45>
P100 = 5103252092711526530908951977517372031589485749269566130240786228969544705813538735808435514565812117_<100>

Number: 71113_164 N=872621256705554537562497017054806961902356913310789643713475531853359484917297314630534101155105898937701858021584802387719938765947681719989313 ( 144 digits) SNFS difficulty: 166 digits. Divisors found: r1=170993170796291589495847649921540863092737789 r2=5103252092711526530908951977517372031589485749269566130240786228969544705813538735808435514565812117 Version: Total time: 19.82 hours. Scaled time: 47.16 units (timescale=2.379). Factorization parameters were as follows: n: 872621256705554537562497017054806961902356913310789643713475531853359484917297314630534101155105898937701858021584802387719938765947681719989313 m: 2000000000000000000000000000000000 deg: 5 c5: 1 c0: 85 skew: 2.43 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, 3700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9460398 Max relations in full relation-set: Initial matrix: Pruned matrix : 747913 x 748161 Total sieving time: 17.75 hours. Total relation processing time: 0.75 hours. Matrix solve time: 1.25 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 19.82 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 26, 2009: By Sinkiti Sibata / Msieve / Nov 26, 2009
(64·10¹⁶⁸+17)/9 = 7(1)₁₆₇3_<169> = 3 · 20327 · 127507 · 605117 · 67091077 · 28921206504282603801987443_<26> · C120
C120 = P50 · P71
P50 = 27517303792264798529463417344429815937905759318469_<50>
P71 = 28306260058824912668648377802778355092603705182291293454402273353147913_<71>

Number: 71113_168 N=778911957261536368479252748237453420091363555395653283447916728689860273052859142998360002144908357965800974034629705197 ( 120 digits) SNFS difficulty: 170 digits. Divisors found: r1=27517303792264798529463417344429815937905759318469 (pp50) r2=28306260058824912668648377802778355092603705182291293454402273353147913 (pp71) Version: Msieve-1.40 Total time: 53.36 hours. Scaled time: 178.43 units (timescale=3.344). Factorization parameters were as follows: name: 71113_168 n: 778911957261536368479252748237453420091363555395653283447916728689860273052859142998360002144908357965800974034629705197 m: 4000000000000000000000000000000000 deg: 5 c5: 125 c0: 34 skew: 0.77 type: snfs lss: 1 rlim: 4800000 alim: 4800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [2400000, 5100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 963415 x 963663 Total sieving time: 51.24 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.77 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4800000,4800000,27,27,52,52,2.4,2.4,100000 total time: 53.36 hours. --------- CPU info (if available) ----------
Nov 25, 2009 (5th): By Lionel Debroux / GMP-ECM 6.2.3 / Nov 25, 2009
(64·10²⁹⁵-1)/9 = 7(1)₂₉₅_<296> = 138283 · 215123 · C286
C286 = P41 · C245
P41 = 27821253425770631779688809196979341911471_<41>
C245 = [85922149607726026782156764348422317355098680473279943458089419000214805543256458905381333491902976675767807884711080103009541396355333130708765008447187044809202021290263519849408848513151067396999960418817775487954720426652016355985801204889849_<245>]

$ echo 2390461899123524468141610636053234044959304079492194303969631663827271671500068555117428139137024327411407816062631071776594231652495314678420709429643785806299647702800471669183303102305194978145426958761047443438144237490094595452807414027153931517127656700294869702783643631664557879 | ecm -c 10 11e7 GMP-ECM 6.2.3 [powered by GMP 4.2.2] [ECM] Input number is 2390461899123524468141610636053234044959304079492194303969631663827271671500068555117428139137024327411407816062631071776594231652495314678420709429643785806299647702800471669183303102305194978145426958761047443438144237490094595452807414027153931517127656700294869702783643631664557879 (286 digits) Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=3203913405 Step 1 took 1851787ms Step 2 took 612963ms Run 2 out of 10: Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=4242926597 Step 1 took 1853684ms Step 2 took 610135ms Run 3 out of 10: Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=594201858 Step 1 took 1851104ms Step 2 took 615097ms ********** Factor found in step 2: 27821253425770631779688809196979341911471 Found probable prime factor of 41 digits: 27821253425770631779688809196979341911471 Composite cofactor 85922149607726026782156764348422317355098680473279943458089419000214805543256458905381333491902976675767807884711080103009541396355333130708765008447187044809202021290263519849408848513151067396999960418817775487954720426652016355985801204889849 has 245 digits
Nov 25, 2009 (4th): By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 25, 2009
(67·10¹⁹⁰-13)/9 = 7(4)₁₈₉3_<191> = 137 · C189
C189 = P67 · P123
P67 = 1071541119796023713943872177373953979517368086289326500970465961839_<67>
P123 = 507110828875460829568417893845099794914673688551241728438396231258250485605676876586330307290817717364311369996839606707501_<123>

N=543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: r1=1071541119796023713943872177373953979517368086289326500970465961839 (pp67) r2=507110828875460829568417893845099794914673688551241728438396231258250485605676876586330307290817717364311369996839606707501 (pp123) Version: Msieve-1.40 Total time: 365.07 hours. Scaled time: 701.66 units (timescale=1.922). Factorization parameters were as follows: n: 543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339010543390105433901054339 m: 100000000000000000000000000000000000000 deg: 5 c5: 67 c0: -13 skew: 0.72 type: snfs lss: 1 rlim: 11000000 alim: 11000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 11000000/11000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5500000, 11300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1986673 x 1986899 Total sieving time: 359.24 hours. Total relation processing time: 0.24 hours. Matrix solve time: 5.10 hours. Time per square root: 0.49 hours. Prototype def-par.txt line would be: snfs,191.000,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,54,54,2.5,2.5,100000 total time: 365.07 hours. --------- CPU info (if available) ----------
(64·10³³⁷-1)/9 = 7(1)₃₃₇_<338> = 641 · 10305987443_<11> · 128091342428974354289_<21> · 1573635359835609855768700526548279_<34> · C272
C272 = P44 · P229
P44 = 23999825294513644566371981203556549145331093_<44>
P229 = 2225142674642345175756085094630621961303073772087561224909653062753168834580195174703734595980867983796542324738572237891366967450081957758673889677981721953767769280970762737157451510595720274177628529785960348826659378796242959_<229>

Factor=23999825294513644566371981203556549145331093 Method=ECM B1=11000000 Sigma=3143255858
Nov 25, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 25, 2009
2·10¹⁹⁵-1 = 1(9)₁₉₅_<196> = 5899211 · 14379834023187049_<17> · C173
C173 = P61 · P112
P61 = 8005520506168541677107500091857021276142810375469214148691261_<61>
P112 = 2945049630407235486850246768492493463787273516148281573264435077057996480481973645153052764487171176571079917881_<112>

Number: 19999_195 N=23576655207909208424624202624006807544095893996706242465497479933717817335301260997188669857591848828615161079849847110159737109007441407916694060960678075171144655502337941 ( 173 digits) SNFS difficulty: 195 digits. Divisors found: r1=8005520506168541677107500091857021276142810375469214148691261 r2=2945049630407235486850246768492493463787273516148281573264435077057996480481973645153052764487171176571079917881 Version: Total time: 209.06 hours. Scaled time: 499.43 units (timescale=2.389). Factorization parameters were as follows: n: 23576655207909208424624202624006807544095893996706242465497479933717817335301260997188669857591848828615161079849847110159737109007441407916694060960678075171144655502337941 m: 1000000000000000000000000000000000000000 deg: 5 c5: 2 c0: -1 skew: 0.87 type: snfs lss: 1 rlim: 12000000 alim: 12000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6000000, 11100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 22757439 Max relations in full relation-set: Initial matrix: Pruned matrix : 2150669 x 2150917 Total sieving time: 189.52 hours. Total relation processing time: 6.29 hours. Matrix solve time: 12.68 hours. Time per square root: 0.57 hours. Prototype def-par.txt line would be: snfs,195,5,0,0,0,0,0,0,0,0,12000000,12000000,28,28,55,55,2.5,2.5,100000 total time: 209.06 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 25, 2009 (2nd): By juno1369 / GMP-ECM + Alpertron ECM (http://www.alpertron.com.ar/ECM.HTM) / Nov 25, 2009
(59·10¹⁵⁸+13)/9 = 6(5)₁₅₇7_<159> = 3 · 547 · 19577 · 20921 · 20562679 · 40037148484895545334741569_<26> · C115
C115 = P33 · P41 · P41
P33 = 714946817551994226795999183397417_<33>
P41 = 18512159506965237722555703148040570906717_<41>
P41 = 89515591408513589807357573543702422736479_<41>

********** Factor found in step 2: 714946817551994226795999183397417 Found probable prime factor of 33 digits: 714946817551994226795999183397417 Composite cofactor 1657126906514730606466839738594265639188592255458992054267231 172851540589382029443 has 82 digits From Alpertron ECM (http://www.alpertron.com.ar/ECM.HTM) Factors found for 1657126906514730606466839738594265639188592255458992054267231 172851540589382029443 (82 digits): prp41: 18512159506965237722555703148040570906717 prp41: 89515591408513589807357573543702422736479
Nov 25, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 25, 2009
(22·10¹⁶³+17)/3 = 7(3)₁₆₂9_<164> = 41 · 127 · 233861 · 206092781 · 799041773 · C138
C138 = P68 · P70
P68 = 42195990389398706948573405544460493579875597777044234523676722681367_<68>
P70 = 8666676725845304738171565873149213256863607609495312249724267546417367_<70>

Number: 73339_163 N=365699007831793930864297489675417334693538526289939085369313738587375155136237648640690605141401806350384006471083639028582599730736100689 ( 138 digits) SNFS difficulty: 166 digits. Divisors found: r1=42195990389398706948573405544460493579875597777044234523676722681367 r2=8666676725845304738171565873149213256863607609495312249724267546417367 Version: Total time: 23.26 hours. Scaled time: 55.59 units (timescale=2.390). Factorization parameters were as follows: n: 365699007831793930864297489675417334693538526289939085369313738587375155136237648640690605141401806350384006471083639028582599730736100689 m: 1000000000000000000000000000000000 deg: 5 c5: 11 c0: 850 skew: 2.39 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: 9997905 Max relations in full relation-set: Initial matrix: Pruned matrix : 704228 x 704476 Total sieving time: 20.98 hours. Total relation processing time: 0.95 hours. Matrix solve time: 1.17 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4400000,4400000,27,27,51,51,2.4,2.4,100000 total time: 23.26 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 24, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.43 / Nov 24, 2009
(44·10¹⁸⁸+1)/9 = 4(8)₁₈₇9_<189> = 3 · 67 · 12367047777863_<14> · 57831123768707_<14> · 457613923500905847935719079_<27> · C133
C133 = P43 · P44 · P47
P43 = 3845433339200043771803433770523203501433697_<43>
P44 = 39455414314368368652823846825558613685063769_<44>
P47 = 48981864669302978213702667920212673671860980707_<47>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3869374597 Step 1 took 38192ms Step 2 took 14250ms ********** Factor found in step 2: 39455414314368368652823846825558613685063769 Found probable prime factor of 44 digits: 39455414314368368652823846825558613685063769 Composite cofactor 188356495415522399273375625775546911031815645086058261222593402241002941614660946956683779 has 90 digits ------------------------------------- Tue Nov 24 14:30:17 2009 Msieve v. 1.43 Tue Nov 24 14:30:17 2009 random seeds: 05499020 7dd90afa Tue Nov 24 14:30:17 2009 factoring 188356495415522399273375625775546911031815645086058261222593402241002941614660946956683779 (90 digits) Tue Nov 24 14:30:18 2009 searching for 15-digit factors Tue Nov 24 14:30:19 2009 commencing quadratic sieve (90-digit input) Tue Nov 24 14:30:19 2009 using multiplier of 1 Tue Nov 24 14:30:19 2009 using 64kb Pentium 3 sieve core Tue Nov 24 14:30:19 2009 sieve interval: 18 blocks of size 65536 Tue Nov 24 14:30:19 2009 processing polynomials in batches of 6 Tue Nov 24 14:30:19 2009 using a sieve bound of 1571777 (59667 primes) Tue Nov 24 14:30:19 2009 using large prime bound of 125742160 (26 bits) Tue Nov 24 14:30:19 2009 using double large prime bound of 379372269960400 (42-49 bits) Tue Nov 24 14:30:19 2009 using trial factoring cutoff of 49 bits Tue Nov 24 14:30:19 2009 polynomial 'A' values have 11 factors Tue Nov 24 16:15:50 2009 59769 relations (16430 full + 43339 combined from 626554 partial), need 59763 Tue Nov 24 16:15:51 2009 begin with 642984 relations Tue Nov 24 16:15:51 2009 reduce to 143182 relations in 9 passes Tue Nov 24 16:15:51 2009 attempting to read 143182 relations Tue Nov 24 16:15:53 2009 recovered 143182 relations Tue Nov 24 16:15:53 2009 recovered 115145 polynomials Tue Nov 24 16:15:53 2009 attempting to build 59769 cycles Tue Nov 24 16:15:53 2009 found 59769 cycles in 6 passes Tue Nov 24 16:15:53 2009 distribution of cycle lengths: Tue Nov 24 16:15:53 2009 length 1 : 16430 Tue Nov 24 16:15:53 2009 length 2 : 11866 Tue Nov 24 16:15:53 2009 length 3 : 10611 Tue Nov 24 16:15:53 2009 length 4 : 7899 Tue Nov 24 16:15:53 2009 length 5 : 5480 Tue Nov 24 16:15:53 2009 length 6 : 3258 Tue Nov 24 16:15:53 2009 length 7 : 1952 Tue Nov 24 16:15:53 2009 length 9+: 2273 Tue Nov 24 16:15:53 2009 largest cycle: 18 relations Tue Nov 24 16:15:54 2009 matrix is 59667 x 59769 (14.5 MB) with weight 3574237 (59.80/col) Tue Nov 24 16:15:54 2009 sparse part has weight 3574237 (59.80/col) Tue Nov 24 16:15:55 2009 filtering completed in 4 passes Tue Nov 24 16:15:55 2009 matrix is 55137 x 55201 (13.6 MB) with weight 3340434 (60.51/col) Tue Nov 24 16:15:55 2009 sparse part has weight 3340434 (60.51/col) Tue Nov 24 16:15:55 2009 saving the first 48 matrix rows for later Tue Nov 24 16:15:55 2009 matrix is 55089 x 55201 (9.8 MB) with weight 2725857 (49.38/col) Tue Nov 24 16:15:55 2009 sparse part has weight 2231393 (40.42/col) Tue Nov 24 16:15:55 2009 matrix includes 64 packed rows Tue Nov 24 16:15:55 2009 using block size 22080 for processor cache size 1024 kB Tue Nov 24 16:15:56 2009 commencing Lanczos iteration Tue Nov 24 16:15:56 2009 memory use: 9.3 MB Tue Nov 24 16:16:23 2009 lanczos halted after 872 iterations (dim = 55085) Tue Nov 24 16:16:23 2009 recovered 15 nontrivial dependencies Tue Nov 24 16:16:23 2009 prp43 factor: 3845433339200043771803433770523203501433697 Tue Nov 24 16:16:23 2009 prp47 factor: 48981864669302978213702667920212673671860980707 Tue Nov 24 16:16:23 2009 elapsed time 01:46:06
Nov 24, 2009 (2nd): By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.44 SVN / Nov 24, 2009
(2·10¹⁹⁰-17)/3 = (6)₁₈₉1_<190> = 586961 · C185
C185 = P73 · P112
P73 = 3522100398505110525113530527897751734365915827795335855724148825683062971_<73>
P112 = 3224762712419591738492616930735227996266954799592039711609720258477080717575085454686644775301672161668689243631_<112>

Mon Nov 23 14:28:19 2009 Mon Nov 23 14:28:19 2009 Mon Nov 23 14:28:19 2009 Msieve v. 1.44 Mon Nov 23 14:28:19 2009 random seeds: b070f7b1 fdfdedbf Mon Nov 23 14:28:19 2009 factoring 11357938034497465192179151028205735417969280184998094705894713050214011947415018487883635653248966569613086161885826599495821130648657520119167485857947404796343652587934576005333687701 (185 digits) Mon Nov 23 14:28:24 2009 searching for 15-digit factors Mon Nov 23 14:28:26 2009 commencing number field sieve (185-digit input) Mon Nov 23 14:28:26 2009 R0: -100000000000000000000000000000000000000 Mon Nov 23 14:28:26 2009 R1: 1 Mon Nov 23 14:28:26 2009 A0: -17 Mon Nov 23 14:28:26 2009 A1: 0 Mon Nov 23 14:28:26 2009 A2: 0 Mon Nov 23 14:28:26 2009 A3: 0 Mon Nov 23 14:28:26 2009 A4: 0 Mon Nov 23 14:28:26 2009 A5: 2 Mon Nov 23 14:28:26 2009 skew 1.53, size 3.675878e-13, alpha 1.784858, combined = 4.412690e-11 Mon Nov 23 14:28:26 2009 Mon Nov 23 14:28:26 2009 commencing linear algebra Mon Nov 23 14:28:27 2009 read 1227138 cycles Mon Nov 23 14:28:32 2009 cycles contain 3011522 unique relations Mon Nov 23 14:30:07 2009 read 3011522 relations Mon Nov 23 14:30:19 2009 using 20 quadratic characters above 268432140 Mon Nov 23 14:31:05 2009 building initial matrix Mon Nov 23 14:33:20 2009 memory use: 395.9 MB Mon Nov 23 14:33:21 2009 read 1227138 cycles Mon Nov 23 14:33:28 2009 matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col) Mon Nov 23 14:33:28 2009 sparse part has weight 88420184 (72.05/col) Mon Nov 23 14:33:56 2009 filtering completed in 1 passes Mon Nov 23 14:33:57 2009 matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col) Mon Nov 23 14:33:57 2009 sparse part has weight 88420184 (72.05/col) Mon Nov 23 14:34:18 2009 read 1227138 cycles Mon Nov 23 14:34:25 2009 matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col) Mon Nov 23 14:34:25 2009 sparse part has weight 88420184 (72.05/col) Mon Nov 23 14:34:25 2009 saving the first 48 matrix rows for later Mon Nov 23 14:34:27 2009 matrix is 1226890 x 1227138 (368.4 MB) with weight 91302722 (74.40/col) Mon Nov 23 14:34:27 2009 sparse part has weight 84297943 (68.69/col) Mon Nov 23 14:34:27 2009 matrix includes 64 packed rows Mon Nov 23 14:34:27 2009 using block size 65536 for processor cache size 4096 kB Mon Nov 23 14:34:42 2009 commencing Lanczos iteration Mon Nov 23 14:34:42 2009 memory use: 361.6 MB Mon Nov 23 14:35:04 2009 linear algebra at 0.1%, ETA 9h 0m Mon Nov 23 14:35:44 2009 lanczos halted after 37 iterations (dim = 2338) Mon Nov 23 14:35:44 2009 BLanczosTime: 438 Mon Nov 23 14:35:44 2009 elapsed time 00:07:25 Mon Nov 23 14:35:51 2009 Mon Nov 23 14:35:51 2009 Mon Nov 23 14:35:51 2009 Msieve v. 1.44 Mon Nov 23 14:35:51 2009 random seeds: 6b3576c1 3d110add Mon Nov 23 14:35:51 2009 factoring 11357938034497465192179151028205735417969280184998094705894713050214011947415018487883635653248966569613086161885826599495821130648657520119167485857947404796343652587934576005333687701 (185 digits) Mon Nov 23 14:35:55 2009 searching for 15-digit factors Mon Nov 23 14:35:57 2009 commencing number field sieve (185-digit input) Mon Nov 23 14:35:57 2009 R0: -100000000000000000000000000000000000000 Mon Nov 23 14:35:57 2009 R1: 1 Mon Nov 23 14:35:57 2009 A0: -17 Mon Nov 23 14:35:57 2009 A1: 0 Mon Nov 23 14:35:57 2009 A2: 0 Mon Nov 23 14:35:57 2009 A3: 0 Mon Nov 23 14:35:57 2009 A4: 0 Mon Nov 23 14:35:57 2009 A5: 2 Mon Nov 23 14:35:57 2009 skew 1.53, size 3.675878e-13, alpha 1.784858, combined = 4.412690e-11 Mon Nov 23 14:35:57 2009 Mon Nov 23 14:35:57 2009 commencing linear algebra Mon Nov 23 14:36:01 2009 read 1227138 cycles Mon Nov 23 14:36:09 2009 matrix is 1226938 x 1227138 (388.8 MB) with weight 114097390 (92.98/col) Mon Nov 23 14:36:09 2009 sparse part has weight 88420184 (72.05/col) Mon Nov 23 14:36:09 2009 saving the first 48 matrix rows for later Mon Nov 23 14:36:10 2009 matrix is 1226890 x 1227138 (368.4 MB) with weight 91302722 (74.40/col) Mon Nov 23 14:36:10 2009 sparse part has weight 84297943 (68.69/col) Mon Nov 23 14:36:10 2009 matrix includes 64 packed rows Mon Nov 23 14:36:10 2009 using block size 65536 for processor cache size 4096 kB Mon Nov 23 14:36:25 2009 commencing Lanczos iteration (2 threads) Mon Nov 23 14:36:25 2009 memory use: 371.0 MB Mon Nov 23 14:36:25 2009 restarting at iteration 37 (dim = 2338) Mon Nov 23 14:36:40 2009 linear algebra at 0.3%, ETA 6h44m Mon Nov 23 21:47:28 2009 lanczos halted after 19405 iterations (dim = 1226888) Mon Nov 23 21:47:32 2009 recovered 36 nontrivial dependencies Mon Nov 23 21:47:32 2009 BLanczosTime: 25895 Mon Nov 23 21:47:32 2009 elapsed time 07:11:41 Mon Nov 23 21:49:52 2009 Mon Nov 23 21:49:52 2009 Mon Nov 23 21:49:52 2009 Msieve v. 1.44 Mon Nov 23 21:49:52 2009 random seeds: 2800b6ca f4df187c Mon Nov 23 21:49:52 2009 factoring 11357938034497465192179151028205735417969280184998094705894713050214011947415018487883635653248966569613086161885826599495821130648657520119167485857947404796343652587934576005333687701 (185 digits) Mon Nov 23 21:49:57 2009 searching for 15-digit factors Mon Nov 23 21:49:59 2009 commencing number field sieve (185-digit input) Mon Nov 23 21:49:59 2009 R0: -100000000000000000000000000000000000000 Mon Nov 23 21:49:59 2009 R1: 1 Mon Nov 23 21:49:59 2009 A0: -17 Mon Nov 23 21:49:59 2009 A1: 0 Mon Nov 23 21:49:59 2009 A2: 0 Mon Nov 23 21:49:59 2009 A3: 0 Mon Nov 23 21:49:59 2009 A4: 0 Mon Nov 23 21:49:59 2009 A5: 2 Mon Nov 23 21:49:59 2009 skew 1.53, size 3.675878e-13, alpha 1.784858, combined = 4.412690e-11 Mon Nov 23 21:49:59 2009 Mon Nov 23 21:49:59 2009 commencing square root phase Mon Nov 23 21:49:59 2009 reading relations for dependency 1 Mon Nov 23 21:50:03 2009 read 612889 cycles Mon Nov 23 21:50:05 2009 cycles contain 1503182 unique relations Mon Nov 23 21:51:23 2009 read 1503182 relations Mon Nov 23 21:51:43 2009 multiplying 1503182 relations Mon Nov 23 21:57:34 2009 multiply complete, coefficients have about 37.19 million bits Mon Nov 23 21:57:35 2009 initial square root is modulo 219041 Mon Nov 23 22:05:37 2009 reading relations for dependency 2 Mon Nov 23 22:05:41 2009 read 613137 cycles Mon Nov 23 22:05:42 2009 cycles contain 1505808 unique relations Mon Nov 23 22:06:57 2009 read 1505808 relations Mon Nov 23 22:07:09 2009 multiplying 1505808 relations Mon Nov 23 22:10:11 2009 multiply complete, coefficients have about 37.26 million bits Mon Nov 23 22:10:11 2009 initial square root is modulo 223781 Mon Nov 23 22:16:18 2009 reading relations for dependency 3 Mon Nov 23 22:16:22 2009 read 612903 cycles Mon Nov 23 22:16:24 2009 cycles contain 1504284 unique relations Mon Nov 23 22:17:40 2009 read 1504284 relations Mon Nov 23 22:17:52 2009 multiplying 1504284 relations Mon Nov 23 22:20:53 2009 multiply complete, coefficients have about 37.22 million bits Mon Nov 23 22:20:54 2009 initial square root is modulo 221101 Mon Nov 23 22:26:51 2009 reading relations for dependency 4 Mon Nov 23 22:26:56 2009 read 612973 cycles Mon Nov 23 22:26:58 2009 cycles contain 1504386 unique relations Mon Nov 23 22:28:13 2009 read 1504386 relations Mon Nov 23 22:28:24 2009 multiplying 1504386 relations Mon Nov 23 22:31:25 2009 multiply complete, coefficients have about 37.22 million bits Mon Nov 23 22:31:25 2009 initial square root is modulo 221201 Mon Nov 23 22:37:27 2009 reading relations for dependency 5 Mon Nov 23 22:37:32 2009 read 614430 cycles Mon Nov 23 22:37:33 2009 cycles contain 1508298 unique relations Mon Nov 23 22:38:49 2009 read 1508298 relations Mon Nov 23 22:39:00 2009 multiplying 1508298 relations Mon Nov 23 22:42:00 2009 multiply complete, coefficients have about 37.32 million bits Mon Nov 23 22:42:01 2009 initial square root is modulo 228451 Mon Nov 23 22:48:03 2009 reading relations for dependency 6 Mon Nov 23 22:48:08 2009 read 613942 cycles Mon Nov 23 22:48:09 2009 cycles contain 1506000 unique relations Mon Nov 23 22:49:24 2009 read 1506000 relations Mon Nov 23 22:49:36 2009 multiplying 1506000 relations Mon Nov 23 22:52:36 2009 multiply complete, coefficients have about 37.27 million bits Mon Nov 23 22:52:37 2009 initial square root is modulo 224261 Mon Nov 23 22:58:35 2009 sqrtTime: 4116 Mon Nov 23 22:58:35 2009 prp73 factor: 3522100398505110525113530527897751734365915827795335855724148825683062971 Mon Nov 23 22:58:35 2009 prp112 factor: 3224762712419591738492616930735227996266954799592039711609720258477080717575085454686644775301672161668689243631 Mon Nov 23 22:58:35 2009 elapsed time 01:08:43
Nov 24, 2009: By Erik Branger / GGNFS, Msieve / Nov 24, 2009
(65·10¹⁶⁸+61)/9 = 7(2)₁₆₇9_<169> = 7 · 263 · 55893627458327_<14> · C152
C152 = P71 · P82
P71 = 16686719216640258914430547376206697539119714819396999595221215196753619_<71>
P82 = 4206140780347737673879122417993167985752911241206637624428896147475792512758851313_<82>

Number: 72229_168 N=70186690187322848534813391255912423242710432254098754707341062929635389927685614871669166935399377870972333874531367371664986282656059306612965115651747 ( 152 digits) SNFS difficulty: 170 digits. Divisors found: r1=16686719216640258914430547376206697539119714819396999595221215196753619 (pp71) r2=4206140780347737673879122417993167985752911241206637624428896147475792512758851313 (pp82) Version: Msieve v. 1.43 Total time: 123.43 hours. Scaled time: 97.51 units (timescale=0.790). Factorization parameters were as follows: n: 70186690187322848534813391255912423242710432254098754707341062929635389927685614871669166935399377870972333874531367371664986282656059306612965115651747 m: 5000000000000000000000000000000000 deg: 5 c5: 104 c0: 305 skew: 1.24 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, 5650001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 952088 x 952313 Total sieving time: 116.58 hours. Total relation processing time: 0.39 hours. Matrix solve time: 5.86 hours. Time per square root: 0.60 hours. Prototype def-par.txt line would be: snfs,170.000,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,100000 total time: 123.43 hours. --------- CPU info (if available) ----------
Nov 23, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 23, 2009
(65·10¹⁶³+7)/9 = 7(2)₁₆₂3_<164> = 23291 · 214849 · 16175813 · C147
C147 = P69 · P79
P69 = 813256512052658243117005216012106187806335489002678159581152113487081_<69>
P79 = 1097123981090889200601269157296277423248544642116547145585024451148021609609649_<79>

Number: 72223_163 N=892243222151303127585237134646888700719111322344662705134948669982776787671783703532461989654078209429613406012214041099368896840129135168614444569 ( 147 digits) SNFS difficulty: 166 digits. Divisors found: r1=813256512052658243117005216012106187806335489002678159581152113487081 r2=1097123981090889200601269157296277423248544642116547145585024451148021609609649 Version: Total time: 24.00 hours. Scaled time: 57.32 units (timescale=2.388). Factorization parameters were as follows: n: 892243222151303127585237134646888700719111322344662705134948669982776787671783703532461989654078209429613406012214041099368896840129135168614444569 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: 140 skew: 1.61 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: 9802166 Max relations in full relation-set: Initial matrix: Pruned matrix : 762660 x 762908 Total sieving time: 21.69 hours. Total relation processing time: 0.96 hours. Matrix solve time: 1.27 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 24.00 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 23, 2009 (3rd): By Sinkiti Sibata / Msieve / Nov 23, 2009
(65·10¹⁶¹-11)/9 = 7(2)₁₆₀1_<162> = 20084017 · 191866891 · C147
C147 = P69 · P78
P69 = 311840341079435138195582161480994283224403261766637618030009178235597_<69>
P78 = 601018626647427049816918876130796226415550083819651184343799035882306940635219_<78>

Number: 72221_161 N=187421853528827335653389337039146572529035106115131310350823349232846759604043170270164712568736461349957588460504114904477258557263588332817690743 ( 147 digits) SNFS difficulty: 164 digits. Divisors found: r1=311840341079435138195582161480994283224403261766637618030009178235597 (pp69) r2=601018626647427049816918876130796226415550083819651184343799035882306940635219 (pp78) Version: Msieve-1.40 Total time: 29.98 hours. Scaled time: 100.61 units (timescale=3.356). Factorization parameters were as follows: name: 72221_161 n: 187421853528827335653389337039146572529035106115131310350823349232846759604043170270164712568736461349957588460504114904477258557263588332817690743 m: 200000000000000000000000000000000 deg: 5 c5: 325 c0: -176 skew: 0.88 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, 3500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 661825 x 662073 Total sieving time: 28.97 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.82 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,164.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 29.98 hours. --------- CPU info (if available) ----------
Nov 23, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 23, 2009
(67·10¹⁹⁷+41)/9 = 7(4)₁₉₆9_<198> = 6271 · C195
C195 = P32 · C163
P32 = 14804814301257493957368027068209_<32>
C163 = [8018488822340487237390691124028521224201676513048994685760860292500214647027078234420861913727315979617472630756131310269280591852145065737118488621600044708379791_<163>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2933211590 Step 1 took 75324ms Step 2 took 22413ms ********** Factor found in step 2: 14804814301257493957368027068209 Found probable prime factor of 32 digits: 14804814301257493957368027068209 Composite cofactor 8018488822340487237390691124028521224201676513048994685760860292500214647027078234420861913727315979617472630756131310269280591852145065737118488621600044708379791 has 163 digits
(22·10¹⁹⁵-7)/3 = 7(3)₁₉₄1_<196> = 3137 · C193
C193 = P42 · P151
P42 = 865705014948683820695382200352934286953759_<42>
P151 = 2700330825097480678864281228686638696675856044230083140116407966903315950254431328829179821478217319803331163711026706022488383947812078822791851974157_<151>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2548502624 Step 1 took 70148ms Step 2 took 21764ms ********** Factor found in step 2: 865705014948683820695382200352934286953759 Found probable prime factor of 42 digits: 865705014948683820695382200352934286953759 Probable prime cofactor 2700330825097480678864281228686638696675856044230083140116407966903315950254431328829179821478217319803331163711026706022488383947812078822791851974157 has 151 digits
Nov 23, 2009: By Dmitry Domanov / ECMNET, GMP-ECM / Nov 23, 2009
(65·10¹⁷¹+61)/9 = 7(2)₁₇₀9_<172> = 59 · 103231 · 288734940313_<12> · C154
C154 = P37 · P117
P37 = 5341730797111883898281272847651922239_<37>
P117 = 768824761082780205497364438889436595941143966789197894042997226025202898341403395396514044299198931236559010774835143_<117>

Factor=5341730797111883898281272847651922239 Method=ECM B1=11000000 Sigma=3634509346
(26·10¹⁶⁷-11)/3 = 8(6)₁₆₆3_<168> = 7 · 17 · 691 · 229656809 · C155
C155 = P34 · C122
P34 = 1622000506706154937986411401046767_<34>
C122 = [28294157895160621844921147954393461978100031316274893426210418177756993778953017327769043546792385145405456209408807687549_<122>]

Factor=1622000506706154937986411401046767 Method=ECM B1=11000000 Sigma=420641482
Nov 22, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 22, 2009
(65·10¹⁶²-11)/9 = 7(2)₁₆₁1_<163> = 3 · 59 · 1999 · 4773779 · C151
C151 = P74 · P77
P74 = 70720939585198509430447494622061780717823615546513973846559159308700434243_<74>
P77 = 60460878757510508486907856776275737477095178737018964166774638595681693266091_<77>

Number: 72221_162 N=4275850153877912590311748739884690843676410802291770101508765288141718738539635449718707640413237336721787300567069698882361479787286593316820647154113 ( 151 digits) SNFS difficulty: 165 digits. Divisors found: r1=70720939585198509430447494622061780717823615546513973846559159308700434243 r2=60460878757510508486907856776275737477095178737018964166774638595681693266091 Version: Total time: 24.47 hours. Scaled time: 58.51 units (timescale=2.391). Factorization parameters were as follows: n: 4275850153877912590311748739884690843676410802291770101508765288141718738539635449718707640413237336721787300567069698882361479787286593316820647154113 m: 500000000000000000000000000000000 deg: 5 c5: 52 c0: -275 skew: 1.40 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: 9691817 Max relations in full relation-set: Initial matrix: Pruned matrix : 780277 x 780525 Total sieving time: 21.87 hours. Total relation processing time: 0.95 hours. Matrix solve time: 1.40 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 24.47 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 22, 2009: By Sinkiti Sibata / Msieve / Nov 22, 2009
(64·10¹⁶¹+17)/9 = 7(1)₁₆₀3_<162> = 13 · 47 · 73 · 971 · 3258491 · 17762837059301_<14> · C135
C135 = P61 · P75
P61 = 1045053944364224676875037140958936245274636458765532056637397_<61>
P75 = 271447969722802002620888132932935879664564355019942468315186681947716233563_<75>

Number: 71113_161 N=283677771448474868630729904666453613625367285272102371126053240308003259939380549919808427192636724065025504641791378151488079652355511 ( 135 digits) SNFS difficulty: 162 digits. Divisors found: r1=1045053944364224676875037140958936245274636458765532056637397 (pp61) r2=271447969722802002620888132932935879664564355019942468315186681947716233563 (pp75) Version: Msieve-1.40 Total time: 27.72 hours. Scaled time: 93.03 units (timescale=3.356). Factorization parameters were as follows: name: 71113_161 n: 283677771448474868630729904666453613625367285272102371126053240308003259939380549919808427192636724065025504641791378151488079652355511 m: 200000000000000000000000000000000 deg: 5 c5: 20 c0: 17 skew: 0.97 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, 3300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 613486 x 613734 Total sieving time: 26.85 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.70 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,162.000,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000 total time: 27.72 hours. --------- CPU info (if available) ----------
Nov 21, 2009 (3rd): By Jo Yeong Uk / GMP-ECM / Nov 20, 2009
(59·10¹⁶¹+31)/9 = 6(5)₁₆₀9_<162> = 210347 · 322840801 · C148
C148 = P44 · P105
P44 = 16143737774649079582774376407801783420888231_<44>
P105 = 597971752607197952577929926186380895991725103128877040652814302508296522632908336217817296076502480481187_<105>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 9653499170737935827020930703101546284142908607431751644711794372056984430617103889827634872490523601821211444382589425755902035305126233259825210197 (148 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5772938245 Step 1 took 4633ms Step 2 took 4586ms ********** Factor found in step 2: 16143737774649079582774376407801783420888231 Found probable prime factor of 44 digits: 16143737774649079582774376407801783420888231 Probable prime cofactor 597971752607197952577929926186380895991725103128877040652814302508296522632908336217817296076502480481187 has 105 digits
By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 21, 2009
(59·10¹⁶¹+13)/9 = 6(5)₁₆₀7_<162> = 3 · 7 · 53 · 743 · 196771241 · 2740438472617133_<16> · C133
C133 = P52 · P81
P52 = 5709310195720236828643845210386126013088462671987029_<52>
P81 = 257489903231838133471085108012293074391834736416021232004557239035900683554813379_<81>

Number: 65557_161 N=1470089729816550615327746631666522054342149372565640256703912340728756124298045838952847268330437311459786713438678509201299203660991 ( 133 digits) SNFS difficulty: 162 digits. Divisors found: r1=5709310195720236828643845210386126013088462671987029 r2=257489903231838133471085108012293074391834736416021232004557239035900683554813379 Version: Total time: 23.22 hours. Scaled time: 54.90 units (timescale=2.365). Factorization parameters were as follows: n: 1470089729816550615327746631666522054342149372565640256703912340728756124298045838952847268330437311459786713438678509201299203660991 m: 100000000000000000000000000000000 deg: 5 c5: 590 c0: 13 skew: 0.47 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, 3900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9714777 Max relations in full relation-set: Initial matrix: Pruned matrix : 739625 x 739873 Total sieving time: 20.93 hours. Total relation processing time: 0.95 hours. Matrix solve time: 1.24 hours. Time per square root: 0.10 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: 23.22 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 21, 2009 (2nd): By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 21, 2009
(19·10¹⁸⁸+11)/3 = 6(3)₁₈₇7_<189> = 7 · 13 · 43 · C186
C186 = P73 · P113
P73 = 5821078419106027523809386387218682764306133231192700907154676066616935391_<73>
P113 = 27804753444740559479686096411255814898532711759314529476640305709597762933252999828353482262529345803167942993039_<113>

N=161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743249 ( 186 digits) SNFS difficulty: 190 digits. Divisors found: r1=5821078419106027523809386387218682764306133231192700907154676066616935391 (pp73) r2=27804753444740559479686096411255814898532711759314529476640305709597762933252999828353482262529345803167942993039 (pp113) Version: Msieve-1.40 Total time: 302.13 hours. Scaled time: 570.42 units (timescale=1.888). Factorization parameters were as follows: n: 161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743248999062952551324644347900161853650225743249 m: 50000000000000000000000000000000000000 deg: 5 c5: 152 c0: 275 skew: 1.13 type: snfs lss: 1 rlim: 10500000 alim: 10500000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10500000/10500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5250000, 9950001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1979065 x 1979290 Total sieving time: 295.46 hours. Total relation processing time: 0.24 hours. Matrix solve time: 5.00 hours. Time per square root: 1.43 hours. Prototype def-par.txt line would be: snfs,190.000,5,0,0,0,0,0,0,0,0,10500000,10500000,28,28,54,54,2.5,2.5,100000 total time: 302.13 hours. --------- CPU info (if available) ----------
(22·10¹⁶⁵+17)/3 = 7(3)₁₆₄9_<166> = 862139 · 42698939 · C153
C153 = P39 · P114
P39 = 364142907767587768742722435741327326329_<39>
P114 = 547060294841478817301959720522487529530706748367558955882874997756231160054020556062246281597883447113999513409771_<114>

Factor=364142907767587768742722435741327326329 Method=ECM B1=11000000 Sigma=2604005257
Nov 21, 2009: By Sinkiti Sibata / Msieve / Nov 21, 2009
(67·10¹⁶⁰+41)/9 = 7(4)₁₅₉9_<161> = 109 · 66347 · 90637257619_<11> · 58054843192433_<14> · C130
C130 = P61 · P69
P61 = 6458162601207874684709389465413979594157825818758560151613079_<61>
P69 = 302921652034106781572164003165353167420092868163923517757663653696611_<69>

Number: 74449_160 N=1956317284262773736098062881121294614246555144986523186725985290723465938887825663867140407665727444773244943801461623492925575269 ( 130 digits) SNFS difficulty: 161 digits. Divisors found: r1=6458162601207874684709389465413979594157825818758560151613079 (pp61) r2=302921652034106781572164003165353167420092868163923517757663653696611 (pp69) Version: Msieve-1.40 Total time: 27.61 hours. Scaled time: 91.71 units (timescale=3.322). Factorization parameters were as follows: name: 74449_160 n: 1956317284262773736098062881121294614246555144986523186725985290723465938887825663867140407665727444773244943801461623492925575269 m: 100000000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 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, 3250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 621450 x 621698 Total sieving time: 26.76 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.72 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 27.61 hours. --------- CPU info (if available) ----------
Nov 20, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 20, 2009
(26·10¹⁶¹-11)/3 = 8(6)₁₆₀3_<162> = 7 · 181 · 17387 · 11596073 · 58262188035421_<14> · C134
C134 = P48 · P87
P48 = 456470417364139674264780752174404710974590776491_<48>
P87 = 127567620784121598321005285879102169613744974602163293210674456685787644756891735053249_<87>

Number: 86663_161 N=58230845101478284843358896477726731596932608490207254663143255682978657099665099256090779442717396787440080924159907391956186142369259 ( 134 digits) SNFS difficulty: 162 digits. Divisors found: r1=456470417364139674264780752174404710974590776491 r2=127567620784121598321005285879102169613744974602163293210674456685787644756891735053249 Version: Total time: 16.77 hours. Scaled time: 39.99 units (timescale=2.385). Factorization parameters were as follows: n: 58230845101478284843358896477726731596932608490207254663143255682978657099665099256090779442717396787440080924159907391956186142369259 m: 100000000000000000000000000000000 deg: 5 c5: 260 c0: -11 skew: 0.53 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, 3300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9344646 Max relations in full relation-set: Initial matrix: Pruned matrix : 671327 x 671575 Total sieving time: 15.03 hours. Total relation processing time: 0.64 hours. Matrix solve time: 0.94 hours. Time per square root: 0.16 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: 16.77 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 20, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 20, 2009
(67·10¹⁸¹-13)/9 = 7(4)₁₈₀3_<182> = 127 · 15370583931178846189_<20> · 2253776873153776657897948451534279_<34> · C128
C128 = P41 · P87
P41 = 29200237533398076379310161749061933957963_<41>
P87 = 579483271331262398610183787231750323193470397486915683574230974601792989962677800929853_<87>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4221356910 Step 1 took 38433ms Step 2 took 13993ms ********** Factor found in step 2: 29200237533398076379310161749061933957963 Found probable prime factor of 41 digits: 29200237533398076379310161749061933957963 Probable prime cofactor 579483271331262398610183787231750323193470397486915683574230974601792989962677800929853 has 87 digits
(64·10¹⁹⁸+71)/9 = 7(1)₁₉₇9_<199> = 3 · 2179 · C196
C196 = P36 · P160
P36 = 650785158455981940062100473969000731_<36>
P160 = 1671557573283360183804878381813370410004043685577428419417647214928170607746446482254417566351134107881259634051566957814751822022316355735422517371501836929077_<160>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=68033887 Step 1 took 75578ms Step 2 took 22441ms ********** Factor found in step 2: 650785158455981940062100473969000731 Found probable prime factor of 36 digits: 650785158455981940062100473969000731 Probable prime cofactor 1671557573283360183804878381813370410004043685577428419417647214928170607746446482254417566351134107881259634051566957814751822022316355735422517371501836929077 has 160 digits
Nov 20, 2009: By Markus Tervooren / Msieve / Nov 20, 2009
(67·10¹⁶¹+41)/9 = 7(4)₁₆₀9_<162> = 107 · 3701 · 610339 · 33303780809228167275307_<23> · C128
C128 = P38 · P91
P38 = 75535187214103326538317201830040895523_<38>
P91 = 1224377835729844775852488587301078768602817876340329293496172248138770697175289478200468733_<91>

Sieving took ~50 Core2 2,66Ghz-hours. Msieve v. 1.43 Thu Nov 19 23:37:53 2009 random seeds: 33e3b9eb 433b3587 factoring 92483609042652474194535864343706609135442894008901028868852650839468327428630927857786325232318759223661128228852786657681182359 (128 digits) searching for 15-digit factors commencing number field sieve (128-digit input) R0: -10000000000000000000000000000000000000000 R1: 1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 670 skew 0.49, size 6.343425e-17, alpha -0.256694, combined = 2.982526e-10 commencing relation filtering estimated available RAM is 8010.2 MB commencing duplicate removal, pass 1 found 954666 hash collisions in 4340988 relations added 1374 free relations commencing duplicate removal, pass 2 found 962823 duplicates and 3379539 unique relations memory use: 22.6 MB reading ideals above 100000 commencing singleton removal, initial pass memory use: 94.1 MB reading all ideals from disk memory use: 120.5 MB keeping 3494492 ideals with weight <= 200, target excess is 20944 commencing in-memory singleton removal begin with 3379539 relations and 3494492 unique ideals reduce to 2114129 relations and 1996280 ideals in 11 passes max relations containing the same ideal: 148 removing 238747 relations and 191970 ideals in 46777 cliques commencing in-memory singleton removal begin with 1875382 relations and 1996280 unique ideals reduce to 1859093 relations and 1787574 ideals in 7 passes max relations containing the same ideal: 135 removing 178875 relations and 132098 ideals in 46777 cliques commencing in-memory singleton removal begin with 1680218 relations and 1787574 unique ideals reduce to 1669207 relations and 1644169 ideals in 6 passes max relations containing the same ideal: 128 relations with 0 large ideals: 1163 relations with 1 large ideals: 16 relations with 2 large ideals: 354 relations with 3 large ideals: 4469 relations with 4 large ideals: 29966 relations with 5 large ideals: 168469 relations with 6 large ideals: 284122 relations with 7+ large ideals: 1180648 commencing 2-way merge reduce to 1229772 relation sets and 1204734 unique ideals commencing full merge memory use: 153.3 MB found 628615 cycles, need 624934 weight of 624934 cycles is about 43940256 (70.31/cycle) distribution of cycle lengths: 1 relations: 41923 2 relations: 67759 3 relations: 78031 4 relations: 75883 5 relations: 67754 6 relations: 59751 7 relations: 50497 8 relations: 41772 9 relations: 33672 10+ relations: 107892 heaviest cycle: 24 relations commencing cycle optimization start with 3747573 relations pruned 139208 relations memory use: 109.3 MB distribution of cycle lengths: 1 relations: 41923 2 relations: 69513 3 relations: 82026 4 relations: 78704 5 relations: 70580 6 relations: 61436 7 relations: 51233 8 relations: 41576 9 relations: 33373 10+ relations: 94570 heaviest cycle: 23 relations RelProcTime: 129 commencing linear algebra read 624934 cycles cycles contain 1653741 unique relations read 1653741 relations using 20 quadratic characters above 33554250 building initial matrix memory use: 212.7 MB read 624934 cycles matrix is 624757 x 624934 (186.0 MB) with weight 56594097 (90.56/col) sparse part has weight 41878845 (67.01/col) filtering completed in 2 passes matrix is 624708 x 624885 (186.0 MB) with weight 56592419 (90.56/col) sparse part has weight 41878378 (67.02/col) read 624885 cycles matrix is 624708 x 624885 (186.0 MB) with weight 56592419 (90.56/col) sparse part has weight 41878378 (67.02/col) saving the first 48 matrix rows for later matrix is 624660 x 624885 (177.1 MB) with weight 44687252 (71.51/col) sparse part has weight 40186863 (64.31/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 186.9 MB linear algebra at 0.2%, ETA 0h27m624885 dimensions (0.2%, ETA 0h27m) linear algebra completed 624534 of 624885 dimensions (99.9%, ETA 0h 0m) lanczos halted after 9879 iterations (dim = 624658) recovered 37 nontrivial dependencies BLanczosTime: 1716 commencing square root phase reading relations for dependency 1 read 312907 cycles cycles contain 828596 unique relations read 828596 relations multiplying 828596 relations multiply complete, coefficients have about 25.82 million bits initial square root is modulo 26105269 reading relations for dependency 2 read 312740 cycles cycles contain 828130 unique relations read 828130 relations multiplying 828130 relations multiply complete, coefficients have about 25.81 million bits initial square root is modulo 25855117 reading relations for dependency 3 read 312584 cycles cycles contain 827416 unique relations read 827416 relations multiplying 827416 relations multiply complete, coefficients have about 25.79 million bits initial square root is modulo 25473181 sqrtTime: 243 prp38 factor: 75535187214103326538317201830040895523 prp91 factor: 1224377835729844775852488587301078768602817876340329293496172248138770697175289478200468733 elapsed time 00:34:49
Nov 19, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 19, 2009
(67·10¹⁶⁰-13)/9 = 7(4)₁₅₉3_<161> = 223 · 2790386777_<10> · 1084302893662699352989_<22> · C129
C129 = P51 · P78
P51 = 363065558163129755586591876057933957697079245966993_<51>
P78 = 303897660134854542414694170874725162056604936336714237480477623856561460344929_<78>

Number: 74443_160 N=110334773601330070711761593600846340762094802874387964650626689471684650737015293850889407842085069929569671853321483121928928497 ( 129 digits) SNFS difficulty: 161 digits. Divisors found: r1=363065558163129755586591876057933957697079245966993 r2=303897660134854542414694170874725162056604936336714237480477623856561460344929 Version: Total time: 18.57 hours. Scaled time: 44.30 units (timescale=2.386). Factorization parameters were as follows: n: 110334773601330070711761593600846340762094802874387964650626689471684650737015293850889407842085069929569671853321483121928928497 m: 100000000000000000000000000000000 deg: 5 c5: 67 c0: -13 skew: 0.72 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, 3300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9630508 Max relations in full relation-set: Initial matrix: Pruned matrix : 632716 x 632964 Total sieving time: 16.59 hours. Total relation processing time: 0.74 hours. Matrix solve time: 0.86 hours. Time per square root: 0.38 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: 18.57 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 19, 2009 (4th): By Dmitry Domanov / GGNFS/msieve / Nov 19, 2009
(65·10¹⁶⁷+61)/9 = 7(2)₁₆₆9_<168> = 3 · 3163 · 1283549 · 1810364976295258400527_<22> · 6731034634722746219253576990142331_<34> · C103
C103 = P41 · P63
P41 = 43887433213139645955484994448382146047239_<41>
P63 = 110879128047013805011879885468739184560992940355555347685320723_<63>

N=4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797 ( 103 digits) Divisors found: r1=43887433213139645955484994448382146047239 (pp41) r2=110879128047013805011879885468739184560992940355555347685320723 (pp63) Version: Msieve-1.40 Total time: 6.11 hours. Scaled time: 11.18 units (timescale=1.829). Factorization parameters were as follows: name: gg103 n: 4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797 skew: 3105.38 # norm 1.91e+014 c5: 1392300 c4: 5986291355 c3: -32719573776586 c2: -35617074683990928 c1: 196103299995263016226 c0: -71023059451757055174092 # alpha -6.16 Y1: 84365831159 Y0: -20355880109292170055 # Murphy_E 2.38e-009 # M 1588861051919919182070347774998276303263568046023222671646578452552654468614274410016547985992962233523 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: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 220234 x 220457 Polynomial selection time: 0.56 hours. Total sieving time: 5.26 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.14 hours. Time per square root: 0.11 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: 6.11 hours. --------- CPU info (if available) ----------
Nov 19, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 19, 2009
(59·10¹⁷⁰+13)/9 = 6(5)₁₆₉7_<171> = 3 · 31 · 73 · 229 · 2371 · 136027 · C157
C157 = P33 · C124
P33 = 233155008560892980603136314014073_<33>
C124 = [5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517_<124>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3871599622 Step 1 took 52361ms Step 2 took 17180ms ********** Factor found in step 2: 233155008560892980603136314014073 Found probable prime factor of 33 digits: 233155008560892980603136314014073 Composite cofactor 5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517 has 124 digits
(59·10¹⁷¹+31)/9 = 6(5)₁₇₀9_<172> = 7 · 1319207906438579_<16> · C156
C156 = P37 · P120
P37 = 2356463302077488153069650734241665823_<37>
P120 = 301257269819596050498849046453150412524164514988049351771398639204280300958087733288868202951958003834996085783952664261_<120>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2957564567 Step 1 took 52204ms Step 2 took 17141ms ********** Factor found in step 2: 2356463302077488153069650734241665823 Found probable prime factor of 37 digits: 2356463302077488153069650734241665823 Probable prime cofactor 301257269819596050498849046453150412524164514988049351771398639204280300958087733288868202951958003834996085783952664261 has 120 digits
(22·10¹⁷²+17)/3 = 7(3)₁₇₁9_<173> = 7 · 241 · 3371 · 14678148955213_<14> · C153
C153 = P34 · C120
P34 = 4675036528889963296972072581793651_<34>
C120 = [187919259193893023850805073342750434538681070849906401604520432741490252970095903458623817348949668880171189653291036289_<120>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2243017104 Step 1 took 47067ms ********** Factor found in step 1: 4675036528889963296972072581793651 Found probable prime factor of 34 digits: 4675036528889963296972072581793651 Composite cofactor 187919259193893023850805073342750434538681070849906401604520432741490252970095903458623817348949668880171189653291036289 has 120 digits
Nov 19, 2009 (2nd): By Sinkiti Sibata / Msieve / Nov 19, 2009
(65·10¹⁶⁰+7)/9 = 7(2)₁₅₉3_<161> = 89 · 691 · 1063 · 30689 · 80147 · 345231714617358424861_<21> · C124
C124 = P47 · P77
P47 = 20357986503829909242696372348001111417687352381_<47>
P77 = 63907821471927606482939461715126003027541213468536152840468146898123845327793_<77>

Number: 72223_160 N=1301034567014673497892919265231793046878598035690062464234773174782366433468283011049257436954506807102849869231615244025133 ( 124 digits) SNFS difficulty: 161 digits. Divisors found: r1=20357986503829909242696372348001111417687352381 (pp47) r2=63907821471927606482939461715126003027541213468536152840468146898123845327793 (pp77) Version: Msieve-1.40 Total time: 26.08 hours. Scaled time: 86.65 units (timescale=3.322). Factorization parameters were as follows: name: 72223_160 n: 1301034567014673497892919265231793046878598035690062464234773174782366433468283011049257436954506807102849869231615244025133 m: 100000000000000000000000000000000 deg: 5 c5: 65 c0: 7 skew: 0.64 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, 3150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 611722 x 611970 Total sieving time: 25.21 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.69 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 26.08 hours. --------- CPU info (if available) ----------
Nov 19, 2009: By Robert Backstrom / Msieve / Nov 19, 2009
(10²²⁹-7)/3 = (3)₂₂₈1_<229> = 3814997 · C222
C222 = P101 · P122
P101 = 32956293259679429768656597360038775832848835783382963927693572571464416807016576796602091743934862861_<101>
P122 = 26512225547078900430922693339363341417936176675074791272188321866779709375923927312831198488509643069134973196513414342243_<122>

Sieving ~ 220 CPU days + 161 hrs Lanczos with Msieve 1.42 Thu Nov 12 23:11:10 2009 Thu Nov 12 23:11:10 2009 Thu Nov 12 23:11:10 2009 Msieve v. 1.42 Thu Nov 12 23:11:10 2009 random seeds: a862287b 37faa132 Thu Nov 12 23:11:10 2009 factoring 873744680096297148682773101350625789046055169462343832336783838449501620403196472587877089636855109803057075361614526389754260182467596523230118748018237847456586029643885259499111882219916118763221395281132156416724137223 (222 digits) Thu Nov 12 23:11:12 2009 no P-1/P+1/ECM available, skipping Thu Nov 12 23:11:12 2009 commencing number field sieve (222-digit input) Thu Nov 12 23:11:12 2009 R0: -100000000000000000000000000000000000000 Thu Nov 12 23:11:12 2009 R1: 1 Thu Nov 12 23:11:12 2009 A0: -7 Thu Nov 12 23:11:12 2009 A1: 0 Thu Nov 12 23:11:12 2009 A2: 0 Thu Nov 12 23:11:12 2009 A3: 0 Thu Nov 12 23:11:12 2009 A4: 0 Thu Nov 12 23:11:12 2009 A5: 0 Thu Nov 12 23:11:12 2009 A6: 10 Thu Nov 12 23:11:12 2009 skew 1.00, size 2.833444e-11, alpha 1.102701, combined = 1.358953e-12 Thu Nov 12 23:11:12 2009 Thu Nov 12 23:11:12 2009 commencing relation filtering Thu Nov 12 23:11:12 2009 estimated available RAM is 7923.9 MB Thu Nov 12 23:11:12 2009 commencing duplicate removal, pass 1 Thu Nov 12 23:12:12 2009 error -6 reading relation 9929150 Thu Nov 12 23:13:31 2009 error -11 reading relation 23649746 Thu Nov 12 23:14:21 2009 error -6 reading relation 32916487 Thu Nov 12 23:15:00 2009 error -15 reading relation 40211731 Thu Nov 12 23:15:15 2009 error -11 reading relation 42932952 Thu Nov 12 23:16:49 2009 error -11 reading relation 60575181 Thu Nov 12 23:17:56 2009 error -11 reading relation 69579752 Thu Nov 12 23:18:42 2009 error -6 reading relation 77528636 Thu Nov 12 23:19:27 2009 error -6 reading relation 85390839 Thu Nov 12 23:19:48 2009 found 13696326 hash collisions in 89183073 relations Thu Nov 12 23:20:04 2009 commencing duplicate removal, pass 2 Thu Nov 12 23:21:33 2009 found 12651851 duplicates and 76531222 unique relations Thu Nov 12 23:21:33 2009 memory use: 426.4 MB Thu Nov 12 23:21:33 2009 reading ideals above 91291648 Thu Nov 12 23:21:33 2009 commencing singleton removal, initial pass Thu Nov 12 23:30:15 2009 memory use: 1193.5 MB Thu Nov 12 23:30:22 2009 reading all ideals from disk Thu Nov 12 23:30:27 2009 memory use: 1232.8 MB Thu Nov 12 23:30:34 2009 commencing in-memory singleton removal Thu Nov 12 23:30:42 2009 begin with 76531222 relations and 70805144 unique ideals Thu Nov 12 23:31:54 2009 reduce to 35000016 relations and 23227703 ideals in 19 passes Thu Nov 12 23:31:54 2009 max relations containing the same ideal: 28 Thu Nov 12 23:31:58 2009 reading ideals above 720000 Thu Nov 12 23:31:58 2009 commencing singleton removal, initial pass Thu Nov 12 23:37:32 2009 memory use: 596.8 MB Thu Nov 12 23:37:32 2009 reading all ideals from disk Thu Nov 12 23:37:41 2009 memory use: 1301.4 MB Thu Nov 12 23:37:50 2009 keeping 33583094 ideals with weight <= 200, target excess is 181953 Thu Nov 12 23:37:59 2009 commencing in-memory singleton removal Thu Nov 12 23:38:07 2009 begin with 35000019 relations and 33583094 unique ideals Thu Nov 12 23:40:13 2009 reduce to 34608397 relations and 33189936 ideals in 15 passes Thu Nov 12 23:40:13 2009 max relations containing the same ideal: 200 Thu Nov 12 23:40:50 2009 removing 3807449 relations and 3407449 ideals in 400000 cliques Thu Nov 12 23:40:51 2009 commencing in-memory singleton removal Thu Nov 12 23:40:59 2009 begin with 30800948 relations and 33189936 unique ideals Thu Nov 12 23:42:28 2009 reduce to 30471081 relations and 29447150 ideals in 12 passes Thu Nov 12 23:42:28 2009 max relations containing the same ideal: 190 Thu Nov 12 23:43:00 2009 removing 2782167 relations and 2382167 ideals in 400000 cliques Thu Nov 12 23:43:02 2009 commencing in-memory singleton removal Thu Nov 12 23:43:09 2009 begin with 27688914 relations and 29447150 unique ideals Thu Nov 12 23:44:02 2009 reduce to 27489440 relations and 26862722 ideals in 8 passes Thu Nov 12 23:44:02 2009 max relations containing the same ideal: 181 Thu Nov 12 23:44:31 2009 removing 2450585 relations and 2050585 ideals in 400000 cliques Thu Nov 12 23:44:33 2009 commencing in-memory singleton removal Thu Nov 12 23:44:39 2009 begin with 25038855 relations and 26862722 unique ideals Thu Nov 12 23:45:51 2009 reduce to 24871942 relations and 24642751 ideals in 12 passes Thu Nov 12 23:45:51 2009 max relations containing the same ideal: 166 Thu Nov 12 23:46:17 2009 removing 176554 relations and 158429 ideals in 18125 cliques Thu Nov 12 23:46:18 2009 commencing in-memory singleton removal Thu Nov 12 23:46:24 2009 begin with 24695388 relations and 24642751 unique ideals Thu Nov 12 23:46:53 2009 reduce to 24694507 relations and 24483440 ideals in 5 passes Thu Nov 12 23:46:53 2009 max relations containing the same ideal: 166 Thu Nov 12 23:47:06 2009 relations with 0 large ideals: 6717 Thu Nov 12 23:47:06 2009 relations with 1 large ideals: 1179 Thu Nov 12 23:47:06 2009 relations with 2 large ideals: 8333 Thu Nov 12 23:47:06 2009 relations with 3 large ideals: 89276 Thu Nov 12 23:47:06 2009 relations with 4 large ideals: 546118 Thu Nov 12 23:47:06 2009 relations with 5 large ideals: 2010219 Thu Nov 12 23:47:06 2009 relations with 6 large ideals: 4602823 Thu Nov 12 23:47:06 2009 relations with 7+ large ideals: 17429842 Thu Nov 12 23:47:06 2009 commencing 2-way merge Thu Nov 12 23:47:41 2009 reduce to 15238596 relation sets and 15027528 unique ideals Thu Nov 12 23:47:41 2009 commencing full merge Thu Nov 12 23:54:19 2009 memory use: 1908.0 MB Thu Nov 12 23:54:22 2009 found 8200658 cycles, need 8173728 Thu Nov 12 23:54:26 2009 weight of 8173728 cycles is about 572210818 (70.01/cycle) Thu Nov 12 23:54:26 2009 distribution of cycle lengths: Thu Nov 12 23:54:26 2009 1 relations: 1219496 Thu Nov 12 23:54:26 2009 2 relations: 1113256 Thu Nov 12 23:54:26 2009 3 relations: 1026751 Thu Nov 12 23:54:26 2009 4 relations: 875887 Thu Nov 12 23:54:26 2009 5 relations: 745030 Thu Nov 12 23:54:26 2009 6 relations: 624485 Thu Nov 12 23:54:26 2009 7 relations: 527618 Thu Nov 12 23:54:26 2009 8 relations: 437123 Thu Nov 12 23:54:26 2009 9 relations: 358263 Thu Nov 12 23:54:26 2009 10+ relations: 1245819 Thu Nov 12 23:54:26 2009 heaviest cycle: 24 relations Thu Nov 12 23:54:29 2009 commencing cycle optimization Thu Nov 12 23:54:48 2009 start with 43758680 relations Thu Nov 12 23:56:16 2009 pruned 944312 relations Thu Nov 12 23:56:16 2009 memory use: 1460.4 MB Thu Nov 12 23:56:16 2009 distribution of cycle lengths: Thu Nov 12 23:56:16 2009 1 relations: 1219496 Thu Nov 12 23:56:16 2009 2 relations: 1134660 Thu Nov 12 23:56:16 2009 3 relations: 1058293 Thu Nov 12 23:56:16 2009 4 relations: 890629 Thu Nov 12 23:56:16 2009 5 relations: 757989 Thu Nov 12 23:56:16 2009 6 relations: 628845 Thu Nov 12 23:56:16 2009 7 relations: 528837 Thu Nov 12 23:56:16 2009 8 relations: 434588 Thu Nov 12 23:56:16 2009 9 relations: 353251 Thu Nov 12 23:56:16 2009 10+ relations: 1167140 Thu Nov 12 23:56:16 2009 heaviest cycle: 24 relations Thu Nov 12 23:56:34 2009 RelProcTime: 2722 Thu Nov 12 23:56:34 2009 Thu Nov 12 23:56:34 2009 commencing linear algebra Thu Nov 12 23:56:41 2009 read 8173728 cycles Thu Nov 12 23:56:58 2009 cycles contain 24518900 unique relations Thu Nov 12 23:59:32 2009 read 24518900 relations Fri Nov 13 00:00:18 2009 using 20 quadratic characters above 1073741312 Fri Nov 13 00:02:20 2009 building initial matrix Fri Nov 13 00:07:17 2009 memory use: 3126.0 MB Fri Nov 13 00:07:22 2009 read 8173728 cycles Fri Nov 13 00:07:31 2009 matrix is 8173551 x 8173728 (2459.0 MB) with weight 723523108 (88.52/col) Fri Nov 13 00:07:31 2009 sparse part has weight 554695601 (67.86/col) Fri Nov 13 00:09:44 2009 filtering completed in 2 passes Fri Nov 13 00:09:46 2009 matrix is 8170702 x 8170878 (2458.8 MB) with weight 723445965 (88.54/col) Fri Nov 13 00:09:46 2009 sparse part has weight 554678395 (67.88/col) Fri Nov 13 00:10:31 2009 read 8170878 cycles Fri Nov 13 00:10:36 2009 matrix is 8170702 x 8170878 (2458.8 MB) with weight 723445965 (88.54/col) Fri Nov 13 00:10:36 2009 sparse part has weight 554678395 (67.88/col) Fri Nov 13 00:10:36 2009 saving the first 48 matrix rows for later Fri Nov 13 00:10:39 2009 matrix is 8170654 x 8170878 (2351.5 MB) with weight 572916754 (70.12/col) Fri Nov 13 00:10:39 2009 sparse part has weight 534727936 (65.44/col) Fri Nov 13 00:10:39 2009 matrix includes 64 packed rows Fri Nov 13 00:10:39 2009 using block size 65536 for processor cache size 6144 kB Fri Nov 13 00:11:12 2009 commencing Lanczos iteration (4 threads) Fri Nov 13 00:11:12 2009 memory use: 2546.0 MB Thu Nov 19 17:11:02 2009 lanczos halted after 129209 iterations (dim = 8170651) Thu Nov 19 17:11:17 2009 recovered 34 nontrivial dependencies Thu Nov 19 17:11:17 2009 BLanczosTime: 580483 Thu Nov 19 17:11:17 2009 Thu Nov 19 17:11:17 2009 commencing square root phase Thu Nov 19 17:11:17 2009 reading relations for dependency 1 Thu Nov 19 17:11:19 2009 read 4087359 cycles Thu Nov 19 17:11:28 2009 cycles contain 14942110 unique relations Thu Nov 19 17:13:16 2009 read 14942110 relations Thu Nov 19 17:14:47 2009 multiplying 12262068 relations Thu Nov 19 17:52:42 2009 multiply complete, coefficients have about 340.41 million bits Thu Nov 19 17:52:45 2009 initial square root is modulo 1283017 Thu Nov 19 18:37:22 2009 sqrtTime: 5165 Thu Nov 19 18:37:22 2009 prp101 factor: 32956293259679429768656597360038775832848835783382963927693572571464416807016576796602091743934862861 Thu Nov 19 18:37:22 2009 prp122 factor: 26512225547078900430922693339363341417936176675074791272188321866779709375923927312831198488509643069134973196513414342243 Thu Nov 19 18:37:22 2009 elapsed time 163:26:12
C222 is the fourth largest composite number factored by snfs in our tables so far, and P101 is the third largest prime factor found by nfs in our tables so far. Congratulations!
Nov 18, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 18, 2009
(67·10¹⁶⁰-31)/9 = 7(4)₁₅₉1_<161> = 61982719611999597353_<20> · 143698186760416432999_<21> · C121
C121 = P58 · P64
P58 = 5184273162643458694917399313243984064834873060204015700713_<58>
P64 = 1612213304015942235676505728696547693838364040958693307596122831_<64>

Number: 74441_160 N=8358154164466588821090554087275649937241803372935761744857267124951914706311950912111526869642631543490919504968482278503 ( 121 digits) SNFS difficulty: 161 digits. Divisors found: r1=5184273162643458694917399313243984064834873060204015700713 r2=1612213304015942235676505728696547693838364040958693307596122831 Version: Total time: 17.49 hours. Scaled time: 41.84 units (timescale=2.392). Factorization parameters were as follows: n: 8358154164466588821090554087275649937241803372935761744857267124951914706311950912111526869642631543490919504968482278503 m: 100000000000000000000000000000000 deg: 5 c5: 67 c0: -31 skew: 0.86 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, 3200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9409654 Max relations in full relation-set: Initial matrix: Pruned matrix : 652517 x 652764 Total sieving time: 15.59 hours. Total relation processing time: 0.68 hours. Matrix solve time: 0.91 hours. Time per square root: 0.30 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: 17.49 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
(65·10¹⁶²+61)/9 = 7(2)₁₆₁9_<163> = 7 · 433 · 40118289197111849803_<20> · C140
C140 = P35 · P106
P35 = 13579168028242955813092310115106577_<35>
P106 = 4373904977664475284540946690165627879231370447085692210555464579063477417774709742461792175457447644986089_<106>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 59393990631274162535471601057877005972838099309322799817876122604451444243295438344356023518048699407876740752099950221084230446649917407353 (140 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4563230118 Step 1 took 3998ms ********** Factor found in step 1: 13579168028242955813092310115106577 Found probable prime factor of 35 digits: 13579168028242955813092310115106577 Probable prime cofactor 4373904977664475284540946690165627879231370447085692210555464579063477417774709742461792175457447644986089 has 106 digits
Nov 18, 2009 (3rd): By Sinkiti Sibata / Msieve / Nov 18, 2009
(67·10¹⁵⁸-13)/9 = 7(4)₁₅₇3_<159> = 137 · 367 · 27749 · 723919956530258273_<18> · C132
C132 = P63 · P70
P63 = 323406167861964574204330095340435316519039701961176025430412333_<63>
P70 = 2279079514444156964263123471753688115851723190657786980680661703364237_<70>

Number: 74443_158 N=737068372019091742604361880412597109475278063530233380153041578836135503206432728522468364755483999138828375954292978546680195934921 ( 132 digits) SNFS difficulty: 161 digits. Divisors found: r1=323406167861964574204330095340435316519039701961176025430412333 (pp63) r2=2279079514444156964263123471753688115851723190657786980680661703364237 (pp70) Version: Msieve-1.40 Total time: 27.12 hours. Scaled time: 89.14 units (timescale=3.287). Factorization parameters were as follows: name: 74443_158 n: 737068372019091742604361880412597109475278063530233380153041578836135503206432728522468364755483999138828375954292978546680195934921 m: 50000000000000000000000000000000 deg: 5 c5: 536 c0: -325 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, 3200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 587928 x 588176 Total sieving time: 26.34 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.64 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 27.12 hours. --------- CPU info (if available) ----------
Nov 18, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 18, 2009
(65·10¹⁶⁷+61)/9 = 7(2)₁₆₆9_<168> = 3 · 3163 · 1283549 · 1810364976295258400527_<22> · C137
C137 = P34 · C103
P34 = 6731034634722746219253576990142331_<34>
C103 = [4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797_<103>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2647962607 Step 1 took 42548ms Step 2 took 14762ms ********** Factor found in step 2: 6731034634722746219253576990142331 Found probable prime factor of 34 digits: 6731034634722746219253576990142331 Composite cofactor 4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797 has 103 digits
Nov 18, 2009: By Erik Branger / GGNFS, Msieve / Nov 18, 2009
(59·10¹⁷²-41)/9 = 6(5)₁₇₁1_<173> = 42787 · 31693768213_<11> · 2536830201015107_<16> · 139446318301636885367_<21> · C123
C123 = P58 · P65
P58 = 6709643923662083287600130339490360747447730333693040348921_<58>
P65 = 20366943698391295213823441988462062034872745975969857861877209429_<65>

Number: 65551_172 N=136654940029478911849727109316279734444197648667253976171378912414680437926200903241898447268360383419731066103731951176109 ( 123 digits) Divisors found: r1=6709643923662083287600130339490360747447730333693040348921 (pp58) r2=20366943698391295213823441988462062034872745975969857861877209429 (pp65) Version: Msieve v. 1.43 Total time: 60.19 hours. Scaled time: 58.44 units (timescale=0.971). Factorization parameters were as follows: n: 136654940029478911849727109316279734444197648667253976171378912414680437926200903241898447268360383419731066103731951176109 skew: 772856.50 #skew 772856.50, size 9.317641e-012, alpha -7.085631, combined = 2.065199e-010 c5: 600 c4: -431270722 c3: 325013098061919 c2: -1039884277173083768092 c1: -378596922670397322214778260 c0: -1308313376079945581025641373600 Y1: 9213761994587 Y0: -743867510048013670888093 type: gnfs rlim: 6000000 alim: 6000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [3000000, 5400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 880216 x 880442 Total sieving time: 57.70 hours. Total relation processing time: 0.25 hours. Matrix solve time: 1.86 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,6000000,6000000,27,27,52,52,2.5,2.5,100000 total time: 60.19 hours. --------- CPU info (if available) ----------
Nov 17, 2009 (4th): By Sinkiti Sibata / Msieve / Nov 17, 2009
(67·10¹⁷⁶+41)/9 = 7(4)₁₇₅9_<177> = 7 · C177
C177 = P36 · P42 · P43 · P57
P36 = 381496638149806557062385644326745051_<36>
P42 = 803770627877673149683896774769690484334047_<42>
P43 = 2540492572298568949029546317256747678065197_<43>
P57 = 136519118946285151795581433335283513926057235634807181623_<57>

Number: 74449_176 N=106349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207 ( 177 digits) SNFS difficulty: 177 digits. Divisors found: r1=381496638149806557062385644326745051 (pp36) r2=803770627877673149683896774769690484334047 (pp42) r3=2540492572298568949029546317256747678065197 (pp43) r4=136519118946285151795581433335283513926057235634807181623 (pp57) Version: Msieve-1.40 Total time: 151.29 hours. Scaled time: 507.89 units (timescale=3.357). Factorization parameters were as follows: name: 74449_176 n: 106349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349206349207 m: 100000000000000000000000000000000000 deg: 5 c5: 670 c0: 41 skew: 0.57 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, 8900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1407232 x 1407479 Total sieving time: 146.77 hours. Total relation processing time: 0.17 hours. Matrix solve time: 3.89 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: snfs,177.000,5,0,0,0,0,0,0,0,0,6400000,6400000,28,28,53,53,2.5,2.5,100000 total time: 151.29 hours. --------- CPU info (if available) ----------
(62·10¹⁵⁹-71)/9 = 6(8)₁₅₈1_<160> = 7 · 367 · 397 · 1427 · 1295003 · 27044153094400533691_<20> · C126
C126 = P48 · P78
P48 = 637642494412674002793864923763006295921649455939_<48>
P78 = 211957692852734056509800472053686387750176129582452776229614596712235602760093_<78>

Number: 68881_159 N=135153231980572748044136445861801829429050962561946223951226838695412239454479728772981461313692290146394175213660440191042327 ( 126 digits) SNFS difficulty: 161 digits. Divisors found: r1=637642494412674002793864923763006295921649455939 (pp48) r2=211957692852734056509800472053686387750176129582452776229614596712235602760093 (pp78) Version: Msieve v. 1.42 Total time: 1.59 hours. Scaled time: 1.08 units (timescale=0.681). Factorization parameters were as follows: name: 68881_159 n: 135153231980572748044136445861801829429050962561946223951226838695412239454479728772981461313692290146394175213660440191042327 m: 100000000000000000000000000000000 deg: 5 c5: 31 c0: -355 skew: 1.63 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, 3200001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 652571 x 652797 Total sieving time: 0.00 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.37 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 1.59 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 CPU1: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598) Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574) Total of 2 processors activated (7442.34 BogoMIPS). Total time: 27.7 hours
Nov 17, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 17, 2009
(59·10¹⁵⁹+31)/9 = 6(5)₁₅₈9_<160> = 7 · 41 · 118759055073185934621037_<24> · C135
C135 = P55 · P80
P55 = 2549878433376721403304445956812713905944758972355130839_<55>
P80 = 75429529077254560793474090742639833438562153315193101308443515089992511037341899_<80>

Number: 65559_159 N=192336129433853713462743799811065807296497118520268229199178231611199978210902456189888686092410750956991535069761582060175816921723261 ( 135 digits) SNFS difficulty: 161 digits. Divisors found: r1=2549878433376721403304445956812713905944758972355130839 r2=75429529077254560793474090742639833438562153315193101308443515089992511037341899 Version: Total time: 17.49 hours. Scaled time: 41.79 units (timescale=2.390). Factorization parameters were as follows: n: 192336129433853713462743799811065807296497118520268229199178231611199978210902456189888686092410750956991535069761582060175816921723261 m: 100000000000000000000000000000000 deg: 5 c5: 59 c0: 310 skew: 1.39 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, 3300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9616962 Max relations in full relation-set: Initial matrix: Pruned matrix : 621680 x 621928 Total sieving time: 15.89 hours. Total relation processing time: 0.71 hours. Matrix solve time: 0.80 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3600000,3600000,27,27,51,51,2.4,2.4,100000 total time: 17.49 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672338) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Nov 17, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Nov 17, 2009
(64·10¹⁷⁸+71)/9 = 7(1)₁₇₇9_<179> = 229 · C177
C177 = P38 · P139
P38 = 33350205132654546757222414370710831411_<38>
P139 = 9311153207174220903648886531701264110925845510393319781488890048252156953150920948299831365494816188137632384373019136801433203324125922001_<139>

Number: 71119_178 N=310528869480834546336729742843279961183891314895681707908782144590004852013585638039786511402231926249393498301795245026686074721009218825812712275594371664240659873847646773411 ( 177 digits) SNFS difficulty: 180 digits. Divisors found: r1=33350205132654546757222414370710831411 (pp38) r2=9311153207174220903648886531701264110925845510393319781488890048252156953150920948299831365494816188137632384373019136801433203324125922001 (pp139) Version: Msieve v. 1.43 Total time: 134.74 hours. Scaled time: 234.99 units (timescale=1.744). Factorization parameters were as follows: n: 310528869480834546336729742843279961183891314895681707908782144590004852013585638039786511402231926249393498301795245026686074721009218825812712275594371664240659873847646773411 m: 400000000000000000000000000000000000 deg: 5 c5: 125 c0: 142 skew: 1.03 type: snfs lss: 1 rlim: 7000000 alim: 7000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3500000, 10100001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1578565 x 1578790 Total sieving time: 130.38 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.56 hours. Time per square root: 0.61 hours. Prototype def-par.txt line would be: snfs,180.000,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,53,53,2.5,2.5,100000 total time: 134.74 hours.
Nov 17, 2009: By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 17, 2009
(59·10¹⁶⁴+13)/9 = 6(5)₁₆₃7_<165> = 3² · 89 · 967 · C159
C159 = P48 · P112
P48 = 172494834689383932407753106094143525376103225653_<48>
P112 = 4906529533010920434450031087476390453047270898213110900861533572593100963811674429717024242278907331943447184807_<112>

N=846351000695298864469510778997240465389766870465118647651598319519880856730993646199173932733456957959163707665773981534916353983006706399259916257154714253971 ( 159 digits) SNFS difficulty: 166 digits. Divisors found: r1=172494834689383932407753106094143525376103225653 (pp48) r2=4906529533010920434450031087476390453047270898213110900861533572593100963811674429717024242278907331943447184807 (pp112) Version: Msieve-1.40 Total time: 42.70 hours. Scaled time: 78.56 units (timescale=1.840). Factorization parameters were as follows: n: 846351000695298864469510778997240465389766870465118647651598319519880856730993646199173932733456957959163707665773981534916353983006706399259916257154714253971 m: 1000000000000000000000000000000000 deg: 5 c5: 59 c0: 130 skew: 1.17 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 4500001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 705092 x 705317 Total sieving time: 41.83 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.64 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 42.70 hours. --------- CPU info (if available) ----------
(62·10¹⁹⁰-71)/9 = 6(8)₁₈₉1_<191> = 17 · C190
C190 = P39 · C152
P39 = 159056495352762286480580492048359527989_<39>
C152 = [25477033004606382089474543221740888076315860678491961319226765661507788975891994600263548413995024764740782104709424866797319890147044298005667883592637_<152>]

Factor=159056495352762286480580492048359527989 Method=ECM B1=11000000 Sigma=3757089473
Nov 16, 2009 (3rd): By Wataru Sakai / Msieve / Nov 16, 2009
(55·10¹⁸⁹+17)/9 = 6(1)₁₈₈3_<190> = 19 · C189
C189 = P72 · P117
P72 = 743141132482156367337598193227260139629402238122971076355782741496332829_<72>
P117 = 432807999506483598225778604308585057267632076708114307439969977345662831173299530582744403436363128148721417709214863_<117>

Number: 61113_189 N=321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637427 ( 189 digits) SNFS difficulty: 191 digits. Divisors found: r1=743141132482156367337598193227260139629402238122971076355782741496332829 r2=432807999506483598225778604308585057267632076708114307439969977345662831173299530582744403436363128148721417709214863 Version: Total time: 424.41 hours. Scaled time: 854.34 units (timescale=2.013). Factorization parameters were as follows: n: 321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637426900584795321637427 m: 100000000000000000000000000000000000000 deg: 5 c5: 11 c0: 34 skew: 1.25 type: snfs lss: 1 rlim: 10700000 alim: 10700000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 10700000/10700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5350000, 9650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1681268 x 1681516 Total sieving time: 424.41 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,191,5,0,0,0,0,0,0,0,0,10700000,10700000,28,28,54,54,2.5,2.5,100000 total time: 424.41 hours. --------- CPU info (if available) ----------
Nov 16, 2009 (2nd): By Dmitry Domanov / GGNFS/msieve / Nov 16, 2009
(59·10¹⁶⁰+13)/9 = 6(5)₁₅₉7_<161> = 7039 · 3404279 · C151
C151 = P38 · P113
P38 = 68865197719831614457352449825567313491_<38>
P113 = 39725886046607481763744275688874905087926689678309758721166697739496395380193756474563848842063050364299554448367_<113>

N=2735730997195124102012431130315542645538784010106985048370417728523108614122498641061319159171101423248972776136570302361644318198903522689622662019197 ( 151 digits) SNFS difficulty: 161 digits. Divisors found: r1=68865197719831614457352449825567313491 (pp38) r2=39725886046607481763744275688874905087926689678309758721166697739496395380193756474563848842063050364299554448367 (pp113) Version: Msieve-1.40 Total time: 22.07 hours. Scaled time: 40.59 units (timescale=1.839). Factorization parameters were as follows: n: 2735730997195124102012431130315542645538784010106985048370417728523108614122498641061319159171101423248972776136570302361644318198903522689622662019197 m: 100000000000000000000000000000000 deg: 5 c5: 59 c0: 13 skew: 0.74 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 582651 x 582876 Total sieving time: 21.30 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.43 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,51,51,2.4,2.4,100000 total time: 22.07 hours. --------- CPU info (if available) ----------
(61·10¹⁶⁹-43)/9 = 6(7)₁₆₈3_<170> = 3 · 7 · 41 · 3907 · C164
C164 = P47 · P56 · P61
P47 = 94208236204350919120277255087982042989012675453_<47>
P56 = 27857142756307349104741327554515339623983588929075998349_<56>
P61 = 7677420362824464519085906573888170277526604508620017795302867_<61>

N=20148409218683335808945252907621888875049243868186728718482231563817460300945227936806529326521585568824108780534707732295551531819144047352328923242917512115387099 ( 164 digits) SNFS difficulty: 171 digits. Divisors found: r1=94208236204350919120277255087982042989012675453 (pp47) r2=27857142756307349104741327554515339623983588929075998349 (pp56) r3=7677420362824464519085906573888170277526604508620017795302867 (pp61) Version: Msieve-1.40 Total time: 57.58 hours. Scaled time: 107.10 units (timescale=1.860). Factorization parameters were as follows: n: 20148409218683335808945252907621888875049243868186728718482231563817460300945227936806529326521585568824108780534707732295551531819144047352328923242917512115387099 m: 10000000000000000000000000000000000 deg: 5 c5: 61 c0: -430 skew: 1.48 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor 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, 5650001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 902518 x 902749 Total sieving time: 56.18 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.02 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 57.58 hours. --------- CPU info (if available) ----------
(59·10¹⁷¹-41)/9 = 6(5)₁₇₀1_<172> = 17 · 197 · 2423 · C165
C165 = P42 · P124
P42 = 115282334389384451975024500292983441235287_<42>
P124 = 7007743196898658551854826666555383080225449060710447335296189818414329538606806627654954847443983562896198346607513316876499_<124>

N=807868994539805163632974818874059837322843743225111339751729260698680981338459001942486765633904744550249266608995774612382744832948643918636747635542034840979820213 ( 165 digits) SNFS difficulty: 172 digits. Divisors found: r1=115282334389384451975024500292983441235287 (pp42) r2=7007743196898658551854826666555383080225449060710447335296189818414329538606806627654954847443983562896198346607513316876499 (pp124) Version: Msieve-1.40 Total time: 99.95 hours. Scaled time: 93.55 units (timescale=0.936). Factorization parameters were as follows: n: 807868994539805163632974818874059837322843743225111339751729260698680981338459001942486765633904744550249266608995774612382744832948643918636747635542034840979820213 m: 10000000000000000000000000000000000 deg: 5 c5: 590 c0: -41 skew: 0.59 type: snfs lss: 1 rlim: 5300000 alim: 5300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor 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, 6550001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1033831 x 1034061 Total sieving time: 97.83 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.79 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,172.000,5,0,0,0,0,0,0,0,0,5300000,5300000,27,27,52,52,2.4,2.4,100000 total time: 99.95 hours. --------- CPU info (if available) ----------
Nov 16, 2009: By Sinkiti Sibata / Msieve / Nov 16, 2009
(41·10¹⁹⁸+13)/9 = 4(5)₁₉₇7_<199> = 3 · 31 · C197
C197 = P66 · P132
P66 = 429273887712751328262058289867997079191088552925834213834435798699_<66>
P132 = 114110058266774921221247378607450666721138374033977704640115321152455033337303110382308778010226239545436861604901232470700565846651_<132>

Number: 45557_198 N=48984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307049 ( 197 digits) SNFS difficulty: 201 digits. Divisors found: r1=429273887712751328262058289867997079191088552925834213834435798699 (pp66) r2=114110058266774921221247378607450666721138374033977704640115321152455033337303110382308778010226239545436861604901232470700565846651 (pp132) Version: Msieve v. 1.42 Total time: 51.51 hours. Scaled time: 43.47 units (timescale=0.844). Factorization parameters were as follows: name: 45557_198 n: 48984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307048984468339307049 m: 5000000000000000000000000000000000000000 deg: 5 c5: 328 c0: 325 skew: 1.00 type: snfs rlim: 9500000 alim: 9500000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [4750000, 15250001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3000927 x 3001153 Total sieving time: 0.00 hours. Total relation processing time: 0.42 hours. Matrix solve time: 48.31 hours. Time per square root: 2.78 hours. Prototype def-par.txt line would be: snfs,201.000,5,0,0,0,0,0,0,0,0,9500000,9500000,29,29,56,56,2.6,2.6,100000 total time: 51.51 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 5600+ stepping 02 Memory: 3886124k/4718592k available (3786k kernel code, 656964k absent, 175504k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 5827.16 BogoMIPS (lpj=2913583) Calibrating delay using timer specific routine.. 5826.53 BogoMIPS (lpj=2913268) Total of 2 processors activated (11653.70 BogoMIPS). Total time: 19 days 1 hour.
(26·10¹⁵⁸-11)/3 = 8(6)₁₅₇3_<159> = 61 · 7727 · 429686857 · 106162330928491_<15> · C131
C131 = P61 · P71
P61 = 2841721909924726851632106444328355405349356896512142306774663_<61>
P71 = 14184278665349773058410239428622656980638132940212009488758588338764809_<71>

Number: 86663_158 N=40307775459802312601143666500637781443565300545471354124635599565639079211034939946642064287574656020645475561982776791182117234367 ( 131 digits) SNFS difficulty: 160 digits. Divisors found: r1=2841721909924726851632106444328355405349356896512142306774663 (pp61) r2=14184278665349773058410239428622656980638132940212009488758588338764809 (pp71) Version: Msieve v. 1.42 Total time: 1.48 hours. Scaled time: 0.99 units (timescale=0.668). Factorization parameters were as follows: name: 86663_158 n: 40307775459802312601143666500637781443565300545471354124635599565639079211034939946642064287574656020645475561982776791182117234367 m: 50000000000000000000000000000000 deg: 5 c5: 208 c0: -275 skew: 1.06 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, 3100001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 626336 x 626562 Total sieving time: 0.00 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.27 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,160.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 1.48 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 CPU1: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598) Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574) Total of 2 processors activated (7442.34 BogoMIPS). Total time: 25 hours 51 min.
Nov 15, 2009 (6th): By Dmitry Domanov / GGNFS/msieve / Nov 15, 2009
(62·10¹⁷⁰-71)/9 = 6(8)₁₆₉1_<171> = 3⁵ · 5417 · C165
C165 = P83 · P83
P83 = 15602471926924933938592663806430212082428034579139978305230145191169585707783895579_<83>
P83 = 33542131793373349803791167429073588671109887449475537586566666088049681406989340969_<83>

N=523340169675323979218668320421602840690440997658559198931643248460219267713735290659331800959552642070185150155157698853015608451741156964995042195989374168722676051 ( 165 digits) SNFS difficulty: 171 digits. Divisors found: r1=15602471926924933938592663806430212082428034579139978305230145191169585707783895579 (pp83) r2=33542131793373349803791167429073588671109887449475537586566666088049681406989340969 (pp83) Version: Msieve-1.40 Total time: 69.39 hours. Scaled time: 129.34 units (timescale=1.864). Factorization parameters were as follows: n: 523340169675323979218668320421602840690440997658559198931643248460219267713735290659331800959552642070185150155157698853015608451741156964995042195989374168722676051 m: 10000000000000000000000000000000000 deg: 5 c5: 62 c0: -71 skew: 1.03 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor 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, 6350001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1047650 x 1047883 Total sieving time: 67.68 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.38 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,100000 total time: 69.39 hours. --------- CPU info (if available) ----------
Nice split!
Nov 15, 2009 (5th): By Ignacio Santos / GGNFS, Msieve / Nov 15, 2009
(59·10¹⁷⁹+13)/9 = 6(5)₁₇₈7_<180> = 3 · 7 · 313 · C176
C176 = P47 · P130
P47 = 34227787132453009430793852808645752930870611989_<47>
P130 = 2913849035609246999052003284781673297721777732911788271360592562809210825744751320660074392479293423943525018257580230618885051381_<130>

Number: 65557_179 N=99734604526936795307402336156329766553408725932687594029447064590834558885677096539716348023057288233007082847338438392751491793025339351217945467146745102016667511875179606809 ( 176 digits) SNFS difficulty: 181 digits. Divisors found: r1=34227787132453009430793852808645752930870611989 (pp47) r2=2913849035609246999052003284781673297721777732911788271360592562809210825744751320660074392479293423943525018257580230618885051381 (pp130) Version: Msieve v. 1.43 Total time: 134.63 hours. Scaled time: 234.12 units (timescale=1.739). Factorization parameters were as follows: n: 99734604526936795307402336156329766553408725932687594029447064590834558885677096539716348023057288233007082847338438392751491793025339351217945467146745102016667511875179606809 m: 1000000000000000000000000000000000000 deg: 5 c5: 59 c0: 130 skew: 1.17 type: snfs lss: 1 rlim: 7500000 alim: 7500000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3750000, 10050001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1572029 x 1572254 Total sieving time: 129.41 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.56 hours. Time per square root: 1.46 hours. Prototype def-par.txt line would be: snfs,181.000,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000 total time: 134.63 hours.
Nov 15, 2009 (4th): By Sinkiti Sibata / Msieve / Nov 15, 2009
(22·10¹⁵⁸-7)/3 = 7(3)₁₅₇1_<159> = 4938931 · 116721612901_<12> · 1004920243404713858972261_<25> · C118
C118 = P47 · P72
P47 = 12009077923370648080337714781707462324113111259_<47>
P72 = 105408571886886114038898047458864072059719907211055171359755427498953899_<72>

Number: 73331_158 N=1265859753580831970140805253178104479059768213757511408464260680420987308767554609998630957690867230291891172698848841 ( 118 digits) SNFS difficulty: 160 digits. Divisors found: r1=12009077923370648080337714781707462324113111259 (pp47) r2=105408571886886114038898047458864072059719907211055171359755427498953899 (pp72) Version: Msieve v. 1.42 Total time: 1.74 hours. Scaled time: 1.38 units (timescale=0.796). Factorization parameters were as follows: name: 73331_158 n: 1265859753580831970140805253178104479059768213757511408464260680420987308767554609998630957690867230291891172698848841 m: 50000000000000000000000000000000 deg: 5 c5: 176 c0: -175 skew: 1.00 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1650000, 3050001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 641091 x 641316 Total sieving time: 0.00 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.32 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,160.000,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000 total time: 1.74 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 CPU1: Intel(R) Core(TM)2 CPU 6300 @ 1.86GHz stepping 02 Memory: 4005920k/4980736k available (3786k kernel code, 795360k absent, 179456k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 3721.19 BogoMIPS (lpj=1860598) Calibrating delay using timer specific routine.. 3721.14 BogoMIPS (lpj=1860574) Total of 2 processors activated (7442.34 BogoMIPS). Total time: 25 hours 57 min.
Nov 15, 2009 (3rd): By Markus Tervooren / Msieve / Nov 15, 2009
(59·10¹⁵⁸+31)/9 = 6(5)₁₅₇9_<159> = 6007 · 2562185297819003_<16> · 81019181804777423_<17> · C123
C123 = P58 · P66
P58 = 1812636648515138557638066389371724168451964749993906970903_<58>
P66 = 290029868680170784800973912514904723261070414310744029102462787291_<66>

N=525718769133710523653027683631105261421509093029825731752283277983185064180697266071063641221234058361239671692676215193773 ( 123 digits) SNFS difficulty: 161 digits. Divisors found: r1=1812636648515138557638066389371724168451964749993906970903 (pp58) r2=290029868680170784800973912514904723261070414310744029102462787291 (pp66) Version: Msieve-1.41 Total time: 24.56 hours. Scaled time: 0.00 units (timescale=0.000). Factorization parameters were as follows: n: 525718769133710523653027683631105261421509093029825731752283277983185064180697266071063641221234058361239671692676215193773 m: 50000000000000000000000000000000 deg: 5 c5: 472 c0: 775 skew: 1.10 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [1000000, 5000001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 543990 x 544236 Total sieving time: 23.95 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.34 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,2000000,2000000,29,29,56,56,2.5,2.5,800000 total time: 24.56 hours. --------- CPU info (if available) ---------- [ 0.144009] CPU0: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.236014] CPU1: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.333347] CPU2: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.432500] CPU3: Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b [ 0.004000] Memory: 8197988k/10485760k available (2226k kernel code, 189848k reserved, 1082k data, 392k init) [ 0.083990] Calibrating delay using timer specific routine.. 5337.18 BogoMIPS (lpj=10674366) [ 0.156009] Calibrating delay using timer specific routine.. 5333.33 BogoMIPS (lpj=10666675) [ 0.256016] Calibrating delay using timer specific routine.. 5333.38 BogoMIPS (lpj=10666763) [ 0.352018] Calibrating delay using timer specific routine.. 5333.36 BogoMIPS (lpj=10666735) [ 0.437221] Total of 4 processors activated (21337.26 BogoMIPS).
Nov 15, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 15, 2009
(22·10¹⁵⁷+17)/3 = 7(3)₁₅₆9_<158> = 79² · 89 · 1795517 · 6590261 · 61755013 · C132
C132 = P55 · P77
P55 = 7950796688233200437719771201150520016921625896700384781_<55>
P77 = 22723866813249437260181466059833062612216418676176293743449524658347563807251_<77>

Number: 73339_157 N=180672845002635955973650145697540511621150710038462470711407017816799667146364223424285574886806960321200674321681732470921017847031 ( 132 digits) SNFS difficulty: 158 digits. Divisors found: r1=7950796688233200437719771201150520016921625896700384781 r2=22723866813249437260181466059833062612216418676176293743449524658347563807251 Version: Total time: 13.93 hours. Scaled time: 33.24 units (timescale=2.386). Factorization parameters were as follows: n: 180672845002635955973650145697540511621150710038462470711407017816799667146364223424285574886806960321200674321681732470921017847031 m: 20000000000000000000000000000000 deg: 5 c5: 275 c0: 68 skew: 0.76 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1600000, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8288002 Max relations in full relation-set: Initial matrix: Pruned matrix : 569108 x 569356 Total sieving time: 12.50 hours. Total relation processing time: 0.50 hours. Matrix solve time: 0.78 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000 total time: 13.93 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(26·10¹⁵⁷-11)/3 = 8(6)₁₅₆3_<158> = 13874719638668432738273_<23> · C136
C136 = P46 · P90
P46 = 7990330801087736129609580208900348960160370121_<46>
P90 = 781741409377590402464709803977736132137659344702928238702437054957380692407818254347964111_<90>

Number: 86663_157 N=6246372461835497797590085235144227805300158049988539661664127319813743185508874489362779286942419837673553038815625648251966340584727431 ( 136 digits) SNFS difficulty: 159 digits. Divisors found: r1=7990330801087736129609580208900348960160370121 r2=781741409377590402464709803977736132137659344702928238702437054957380692407818254347964111 Version: Total time: 13.93 hours. Scaled time: 33.31 units (timescale=2.391). Factorization parameters were as follows: n: 6246372461835497797590085235144227805300158049988539661664127319813743185508874489362779286942419837673553038815625648251966340584727431 m: 20000000000000000000000000000000 deg: 5 c5: 325 c0: -44 skew: 0.67 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1600000, 2800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8533070 Max relations in full relation-set: Initial matrix: Pruned matrix : 529316 x 529564 Total sieving time: 12.61 hours. Total relation processing time: 0.52 hours. Matrix solve time: 0.68 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,50,50,2.4,2.4,100000 total time: 13.93 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(65·10¹⁵⁷+7)/9 = 7(2)₁₅₆3_<158> = 9679 · 1876797653_<10> · C145
C145 = P72 · P74
P72 = 340269928723054252687708121264854816897562029160532745490903501797972559_<72>
P74 = 11684209505564680196886999355587721293576873890219180545631517614669025331_<74>

Number: 72223_157 N=3975785135643726702230450539778066801184587100157871451338767600314164799713954972226106445526223512112153625343514325724755468276601912413892029 ( 145 digits) SNFS difficulty: 160 digits. Divisors found: r1=340269928723054252687708121264854816897562029160532745490903501797972559 r2=11684209505564680196886999355587721293576873890219180545631517614669025331 Version: Total time: 16.06 hours. Scaled time: 38.37 units (timescale=2.389). Factorization parameters were as follows: n: 3975785135643726702230450539778066801184587100157871451338767600314164799713954972226106445526223512112153625343514325724755468276601912413892029 m: 50000000000000000000000000000000 deg: 5 c5: 52 c0: 175 skew: 1.27 type: snfs lss: 1 rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1600000, 3000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9396692 Max relations in full relation-set: Initial matrix: Pruned matrix : 601720 x 601968 Total sieving time: 14.61 hours. Total relation processing time: 0.65 hours. Matrix solve time: 0.73 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,51,51,2.4,2.4,100000 total time: 16.06 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(62·10¹⁶²-71)/9 = 6(8)₁₆₁1_<163> = 291727 · 40998522161_<11> · 538331911170192824177_<21> · C127
C127 = P41 · P86
P41 = 13293896052923584707628730999104405807681_<41>
P86 = 80482590851823351939562778795885505113611415145477307256905540960132767325450472770079_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 1069927196854118265491844218314408607974802302696835461705048222248058295906490484465975989906304815245214369775644395405176799 (127 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4381793230 Step 1 took 3319ms Step 2 took 2107ms ********** Factor found in step 2: 13293896052923584707628730999104405807681 Found probable prime factor of 41 digits: 13293896052923584707628730999104405807681 Probable prime cofactor 80482590851823351939562778795885505113611415145477307256905540960132767325450472770079 has 86 digits
Nov 15, 2009: By juno1369 / GGNFS + Msieve / Nov 15, 2009
(61·10¹⁴⁶+11)/9 = 6(7)₁₄₅9_<147> = 7² · 859 · 5557 · 275800236853_<12> · 43877517103969019_<17> · C111
C111 = P41 · P70
P41 = 47018556761287004919324019214769957965617_<41>
P70 = 5092742427046728561746607640479066938348493902951058681904891312864643_<70>

Number: 67779_146 N=239453398876711150609255320785377692625826392338235113766506874627069551944324667803564622358785358784768979731 (111 digits) Divisors found: r1=47018556761287004919324019214769957965617 (pp41) r2=5092742427046728561746607640479066938348493902951058681904891312864643 (pp70) Version: Msieve-1.40 Total time: 213.24 hours. Scaled time: 369.96 units (timescale=1.735). Factorization parameters were as follows: name: 67779_146 n: 239453398876711150609255320785377692625826392338235113766506874627069551944324667803564622358785358784768979731 skew: 62268.21 # norm 6.79e+015 c5: 1740 c4: 571107120 c3: 191509397222949 c2: -1689229856928126946 c1: -167460861686685303277376 c0: 366141206224433326132512000 # alpha -5.54 Y1: 357727841273 Y0: -2677506553543671180733 # Murphy_E 7.08e-010 # M 4169860093312916150953838170334394543046091236561083577223534810475410377208532554651542786886462863183822802 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 2 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 466836 x 467084 Total sieving time: 211.86 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.07 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 213.24 hours. --------- CPU info (if available) ----------
Nov 14, 2009 (6th): By Robert Backstrom / GGNFS, Msieve / Nov 14, 2009
(22·10¹⁷⁸-7)/3 = 7(3)₁₇₇1_<179> = 17 · C178
C178 = P48 · P62 · P69
P48 = 248547605560480925622741006789238584355839363443_<48>
P62 = 52256505242291123397545087983645084835369273482120400731461829_<62>
P69 = 332125758345610575600565424353848439016390715672904492677915743077469_<69>

Number: n N=4313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843 ( 178 digits) SNFS difficulty: 180 digits. Divisors found: Sat Nov 14 06:46:51 2009 prp48 factor: 248547605560480925622741006789238584355839363443 Sat Nov 14 06:46:51 2009 prp62 factor: 52256505242291123397545087983645084835369273482120400731461829 Sat Nov 14 06:46:51 2009 prp69 factor: 332125758345610575600565424353848439016390715672904492677915743077469 Sat Nov 14 06:46:51 2009 elapsed time 05:12:36 (Msieve 1.43 - dependency 5) Version: GGNFS-0.77.1-20051202-athlon Total time: 111.82 hours. Scaled time: 203.84 units (timescale=1.823). Factorization parameters were as follows: name: KA_7_3_177_1 n: 4313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843137254901960784313725490196078431372549019607843 m: 500000000000000000000000000000000000 deg: 5 c5: 176 c0: -175 skew: 1.00 type: snfs lss: 1 rlim: 7200000 alim: 7200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 7200000/7200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [3600000, 5400823) Primes: RFBsize:489319, AFBsize:489694, largePrimes:20744051 encountered Relations: rels:20484312, finalFF:986940 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 1849522 hash collisions in 21701103 relations Msieve: matrix is 1291973 x 1292197 (348.9 MB) Total sieving time: 111.13 hours. Total relation processing time: 0.68 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,7200000,7200000,28,28,56,56,2.5,2.5,100000 total time: 111.82 hours. --------- CPU info (if available) ----------
(67·10¹⁵⁴-31)/9 = 7(4)₁₅₃1_<155> = 131 · 397 · 983 · C148
C148 = P38 · P47 · P64
P38 = 19770670872949815347485142394152319553_<38>
P47 = 70311137559137507052774831616250832259377569867_<47>
P64 = 1047541994464449155489159844448139419478733450739365527434608811_<64>

Number: n N=1456186407891301048633085534526984980452186261655411095560996346126198256401951299349589559407742385341006983633110278828856387112542511922292572761 ( 148 digits) SNFS difficulty: 156 digits. Divisors found: Sat Nov 14 18:58:09 2009 prp38 factor: 19770670872949815347485142394152319553 Sat Nov 14 18:58:09 2009 prp47 factor: 70311137559137507052774831616250832259377569867 Sat Nov 14 18:58:09 2009 prp64 factor: 1047541994464449155489159844448139419478733450739365527434608811 Sat Nov 14 18:58:09 2009 elapsed time 00:55:11 (Msieve 1.43 - dependency 4) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.59 hours. Scaled time: 39.25 units (timescale=1.818). Factorization parameters were as follows: name: KA_7_4_153_1 n: 1456186407891301048633085534526984980452186261655411095560996346126198256401951299349589559407742385341006983633110278828856387112542511922292572761 m: 10000000000000000000000000000000 deg: 5 c5: 67 c0: -310 skew: 1.36 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 50000 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [1450000, 2750249) Primes: RFBsize:210109, AFBsize:210215, largePrimes:7718909 encountered Relations: rels:7439444, finalFF:438767 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 935880 hash collisions in 8065056 relations Msieve: matrix is 535005 x 535232 (143.1 MB) Total sieving time: 21.47 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 21.59 hours. --------- CPU info (if available) ----------
Nov 14, 2009 (5th): By Sinkiti Sibata / Msieve / Nov 14, 2009
(62·10¹⁵⁸-71)/9 = 6(8)₁₅₇1_<159> = 3 · 17 · 67 · 337 · 3559 · C150
C150 = P54 · P97
P54 = 132575299431508438665738676848358063462718878204534843_<54>
P97 = 1267896186810585277293654903308370039889900735456986092170954192488322227543251134228508640175997_<97>

Number: 68881_158 N=168091716614481103463083594268062800883645758833805202718252499935061086452976721473033496538452942958137049236729866564856854058353995213907038763471 ( 150 digits) SNFS difficulty: 161 digits. Divisors found: r1=132575299431508438665738676848358063462718878204534843 (pp54) r2=1267896186810585277293654903308370039889900735456986092170954192488322227543251134228508640175997 (pp97) Version: Msieve-1.40 Total time: 44.43 hours. Scaled time: 89.71 units (timescale=2.019). Factorization parameters were as follows: name: 68881_158 n: 168091716614481103463083594268062800883645758833805202718252499935061086452976721473033496538452942958137049236729866564856854058353995213907038763471 m: 50000000000000000000000000000000 deg: 5 c5: 496 c0: -1775 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, 3500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 631071 x 631319 Total sieving time: 42.50 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.46 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 44.43 hours. --------- CPU info (if available) ----------
Nov 14, 2009 (4th): By Dmitry Domanov / ggnfs/msieve, GGNFS/msieve / Nov 14, 2009
(67·10¹⁶²-13)/9 = 7(4)₁₆₁3_<163> = 3 · 1951 · 57493 · C155
C155 = P72 · P84
P72 = 173168441496788451919618027345869704057432823437379661717120302268074707_<72>
P84 = 127752688946810654048296217810573665123434033505277792306486178869161540657839807481_<84>

Number: s155 N=22122734041943193454188356756799938477403047488699526672317387471683928142875481754603472922346907701289933796334883132221319974580476696915572905405483067 ( 155 digits) SNFS difficulty: 165 digits. Divisors found: r1=173168441496788451919618027345869704057432823437379661717120302268074707 (pp72) r2=127752688946810654048296217810573665123434033505277792306486178869161540657839807481 (pp84) Version: Msieve-1.40 Total time: 42.12 hours. Scaled time: 78.35 units (timescale=1.860). Factorization parameters were as follows: n: 22122734041943193454188356756799938477403047488699526672317387471683928142875481754603472922346907701289933796334883132221319974580476696915572905405483067 m: 500000000000000000000000000000000 deg: 5 c5: 268 c0: -1625 skew: 1.43 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 4450001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 794129 x 794355 Total sieving time: 41.11 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.83 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,165.000,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,51,51,2.4,2.4,100000 total time: 42.12 hours. --------- CPU info (if available) ----------
(22·10¹⁸⁸-7)/3 = 7(3)₁₈₇1_<189> = C189
C189 = P67 · P123
P67 = 1439804239664097685685896347039690976177416861734275651404144103963_<67>
P123 = 509328499758007349074189685847253363748278305932331944594971040870874995118639499429499748714681777407393380275849433840937_<123>

N=733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 ( 189 digits) SNFS difficulty: 190 digits. Divisors found: r1=1439804239664097685685896347039690976177416861734275651404144103963 (pp67) r2=509328499758007349074189685847253363748278305932331944594971040870874995118639499429499748714681777407393380275849433840937 (pp123) Version: Msieve-1.40 Total time: 480.46 hours. Scaled time: 446.35 units (timescale=0.929). Factorization parameters were as follows: n: 733333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333331 m: 50000000000000000000000000000000000000 deg: 5 c5: 176 c0: -175 skew: 1.00 type: snfs lss: 1 rlim: 10600000 alim: 10600000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 10600000/10600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5300000, 10500001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1872355 x 1872580 Total sieving time: 468.26 hours. Total relation processing time: 0.39 hours. Matrix solve time: 11.41 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,190.000,5,0,0,0,0,0,0,0,0,10600000,10600000,28,28,54,54,2.5,2.5,100000 total time: 480.46 hours. --------- CPU info (if available) ----------
Nov 14, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 14, 2009
(62·10¹⁶⁹-71)/9 = 6(8)₁₆₈1_<170> = 3505219 · 1779396887_<10> · 2788933419652123_<16> · 49618119210892708709_<20> · C119
C119 = P38 · P81
P38 = 82660081394313266012448446052941500919_<38>
P81 = 965577024280041750953286497287634496570237721902454230853822326500051858350496669_<81>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1887201488 Step 1 took 126018ms Step 2 took 42743ms ********** Factor found in step 2: 82660081394313266012448446052941500919 Found probable prime factor of 38 digits: 82660081394313266012448446052941500919 Probable prime cofactor 965577024280041750953286497287634496570237721902454230853822326500051858350496669 has 81 digits
(62·10¹⁷¹-71)/9 = 6(8)₁₇₀1_<172> = 7 · 19 · 4349 · 9319 · C163
C163 = P40 · P123
P40 = 1600606687685207079981972189175964607847_<40>
P123 = 798461890260203983777865595532676387857491818084310489921571287545918302724829696269195481540944560007643355765101773720401_<123>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=484386855 Step 1 took 52247ms ********** Factor found in step 1: 1600606687685207079981972189175964607847 Found probable prime factor of 40 digits: 1600606687685207079981972189175964607847 Probable prime cofactor 798461890260203983777865595532676387857491818084310489921571287545918302724829696269195481540944560007643355765101773720401 has 123 digits
Nov 14, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 14, 2009
(83·10¹⁵⁶+7)/9 = 9(2)₁₅₅3_<157> = 528078673 · 2354032321_<10> · 54455392027_<11> · C129
C129 = P38 · P91
P38 = 29549430643279790678513909646388049663_<38>
P91 = 4610356690548903466239224249245927737326743875914578310194061475922915915676673744740852531_<91>

Number: 92223_156 N=136233415268155771401978069668754675273317569461066738883978525382951633384097934807394773511147684886619441567552049872987247053 ( 129 digits) SNFS difficulty: 157 digits. Divisors found: r1=29549430643279790678513909646388049663 r2=4610356690548903466239224249245927737326743875914578310194061475922915915676673744740852531 Version: Total time: 13.30 hours. Scaled time: 31.81 units (timescale=2.392). Factorization parameters were as follows: n: 136233415268155771401978069668754675273317569461066738883978525382951633384097934807394773511147684886619441567552049872987247053 m: 10000000000000000000000000000000 deg: 5 c5: 830 c0: 7 skew: 0.38 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, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8688640 Max relations in full relation-set: Initial matrix: Pruned matrix : 495054 x 495302 Total sieving time: 12.20 hours. Total relation processing time: 0.52 hours. Matrix solve time: 0.52 hours. Time per square root: 0.06 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: 13.30 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵⁶-31)/9 = 7(4)₁₅₅1_<157> = 197 · 100616918774894708640648612559_<30> · C126
C126 = P38 · P44 · P44
P38 = 80153664603958430270698294749615024437_<38>
P44 = 53243536433576582261971256661042578792061799_<44>
P44 = 88004479143123417579377741641004702435368009_<44>

Number: 74441_156 N=375573596903421635313913662354161350696820930953190410603725173618920376118848018490033787713031094858628432879290956933623467 ( 126 digits) SNFS difficulty: 157 digits. Divisors found: r1=80153664603958430270698294749615024437 r2=53243536433576582261971256661042578792061799 r3=88004479143123417579377741641004702435368009 Version: Total time: 14.44 hours. Scaled time: 34.20 units (timescale=2.368). Factorization parameters were as follows: n: 375573596903421635313913662354161350696820930953190410603725173618920376118848018490033787713031094858628432879290956933623467 m: 10000000000000000000000000000000 deg: 5 c5: 670 c0: -31 skew: 0.54 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: 8551031 Max relations in full relation-set: Initial matrix: Pruned matrix : 530012 x 530260 Total sieving time: 13.13 hours. Total relation processing time: 0.55 hours. Matrix solve time: 0.61 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: 14.44 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 14, 2009: By Erik Branger / GGNFS, Msieve / Nov 14, 2009
(59·10¹⁶⁴+31)/9 = 6(5)₁₆₃9_<165> = 41 · 257 · 5763713135701_<13> · 632793202179705926119343697193231_<33> · C116
C116 = P50 · P66
P50 = 34802044557813893139042598653269252013977947167193_<50>
P66 = 490143898602442290601560520700188756718313923047228378482398716229_<66>

Number: 65559_164 N=17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197 ( 116 digits) Divisors found: r1=34802044557813893139042598653269252013977947167193 (pp50) r2=490143898602442290601560520700188756718313923047228378482398716229 (pp66) Version: Msieve v. 1.43 Total time: 32.74 hours. Scaled time: 30.19 units (timescale=0.922). Factorization parameters were as follows: name: 65559_164 n: 17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197 skew: 28874.31 # norm 6.29e+015 c5: 38700 c4: 4290288453 c3: 226518079060538 c2: -3620472774476150580 c1: -58323442579984867482546 c0: 430888104406967566430909160 # alpha -5.57 Y1: 782134821337 Y0: -13453736550076462582111 # Murphy_E 4.89e-010 # M 1490207370408176870324831131388133250549360282891275986372669753761505327303758919313473708023388505821334417351020 type: gnfs rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [1700000, 3000001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 530195 x 530424 Polynomial selection time: 3.13 hours. Total sieving time: 28.46 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.62 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3400000,3400000,27,27,53,53,2.5,2.5,100000 total time: 32.74 hours. --------- CPU info (if available) ----------
Nov 13, 2009 (5th): By Erik Branger / GGNFS, Msieve / Nov 13, 2009
(64·10¹⁵⁷+71)/9 = 7(1)₁₅₆9_<158> = 79 · 270163 · 131876297221_<12> · C140
C140 = P67 · P73
P67 = 9964004601390419339148197840705296103238041512903134110631263792189_<67>
P73 = 2535618074861695477526155884291998519175671403992482425103587424791058763_<73>

Number: 71119_157 N=25264910165290650509851238117231571124114862434002665400453091269791075424520683131999659561821303788450380878240060216801402515711719402207 ( 140 digits) SNFS difficulty: 158 digits. Divisors found: r1=9964004601390419339148197840705296103238041512903134110631263792189 (pp67) r2=2535618074861695477526155884291998519175671403992482425103587424791058763 (pp73) Version: Msieve v. 1.43 Total time: 24.74 hours. Scaled time: 21.77 units (timescale=0.880). Factorization parameters were as follows: n: 25264910165290650509851238117231571124114862434002665400453091269791075424520683131999659561821303788450380878240060216801402515711719402207 m: 20000000000000000000000000000000 deg: 5 c5: 200 c0: 71 skew: 0.81 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3100000/3100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1550000, 2650001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 518813 x 519045 Total sieving time: 23.40 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.62 hours. Time per square root: 0.60 hours. Prototype def-par.txt line would be: snfs,158.000,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 24.74 hours. --------- CPU info (if available) ----------
Nov 13, 2009 (4th): By Dmitry Domanov / GGNFS/msieve / Nov 13, 2009
(62·10¹⁹¹-71)/9 = 6(8)₁₉₀1_<192> = 3 · 67 · 887 · 2539 · 9337 · 39719 · 1602440276322618158898151_<25> · 517452552714882800113775903751182527043_<39> · C112
C112 = P54 · P59
P54 = 231966688952782810983569504127235672501575217898942363_<54>
P59 = 21334532365287813355167771978525860077741292728723571466821_<59>

N=4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023 ( 112 digits) Divisors found: r1=231966688952782810983569504127235672501575217898942363 (pp54) r2=21334532365287813355167771978525860077741292728723571466821 (pp59) Version: Msieve-1.40 Total time: 20.06 hours. Scaled time: 39.49 units (timescale=1.969). Factorization parameters were as follows: name: 112-1 n: 4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023 skew: 35745.19 # norm 5.68e+015 c5: 20520 c4: 7874928393 c3: -125171518425754 c2: -10002823683309029156 c1: 186591281683383709662296 c0: -10471410601966863892978464 # alpha -6.73 Y1: 577849820273 Y0: -2995434647356879034675 # Murphy_E 7.92e-010 # M 1904396237109010344233056436440516679725570088245749401332422872741388847060985884113432289929434595461246543295 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2650001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 392267 x 392493 Polynomial selection time: 1.84 hours. Total sieving time: 17.36 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.50 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 20.06 hours. --------- CPU info (if available) ----------
(65·10¹⁵⁹+7)/9 = 7(2)₁₅₈3_<160> = 23 · 971 · 18793 · C152
C152 = P40 · P112
P40 = 1953853962358201528535638767049885845979_<40>
P112 = 8807153537009589409364235375690005448212234630799533315826453435493873992751942939736651790454264854292839358073_<112>

N=17207891835383235758484443528762219892183657200193172828691880569359507978042076647634841544083820217197423030516824039230894905196218677170418908238467 ( 152 digits) SNFS difficulty: 161 digits. Divisors found: r1=1953853962358201528535638767049885845979 (pp40) r2=8807153537009589409364235375690005448212234630799533315826453435493873992751942939736651790454264854292839358073 (pp112) Version: Msieve-1.40 Total time: 22.98 hours. Scaled time: 43.39 units (timescale=1.888). Factorization parameters were as follows: n: 17207891835383235758484443528762219892183657200193172828691880569359507978042076647634841544083820217197423030516824039230894905196218677170418908238467 m: 100000000000000000000000000000000 deg: 5 c5: 13 c0: 14 skew: 1.01 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 3000001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 645407 x 645633 Total sieving time: 22.28 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.55 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 22.98 hours. --------- CPU info (if available) ----------
(22·10¹⁶⁰-7)/3 = 7(3)₁₅₉1_<161> = 419726063 · C153
C153 = P38 · P48 · P67
P38 = 62892293150312003950256891682691118047_<38>
P48 = 963980414783305788992504638378182452100686241977_<48>
P67 = 2881839886247664950088754545652096672709151792121416684401536364123_<67>

N=174717130523613286633890384198832402107308102364215903679379884811521302486601441601050476899580413554955564752082915883480253008099078501430427810563037 ( 153 digits) SNFS difficulty: 161 digits. Divisors found: r1=62892293150312003950256891682691118047 (pp38) r2=963980414783305788992504638378182452100686241977 (pp48) r3=2881839886247664950088754545652096672709151792121416684401536364123 (pp67) Version: Msieve-1.40 Total time: 19.92 hours. Scaled time: 36.76 units (timescale=1.845). Factorization parameters were as follows: n: 174717130523613286633890384198832402107308102364215903679379884811521302486601441601050476899580413554955564752082915883480253008099078501430427810563037 m: 100000000000000000000000000000000 deg: 5 c5: 22 c0: -7 skew: 0.80 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 2800001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 683391 x 683639 Total sieving time: 19.13 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.58 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 19.92 hours. --------- CPU info (if available) ----------
Nov 13, 2009 (3rd): By Wataru Sakai / Msieve / Nov 13, 2009
(22·10¹⁶⁶+17)/3 = 7(3)₁₆₅9_<167> = 7 · 21629000599603_<14> · C153
C153 = P51 · P102
P51 = 641923119296141775585479279443339644024656140218061_<51>
P102 = 754542863764954247166210709332774211904122796445876029066108488793031852354112276874269887328583596219_<102>

Number: 73339_166 N=484358508750643176663936835681906593235838524767765001810069448234657396117754486652019637082863748781456555081996193969222446620209155086837402235111359 ( 153 digits) SNFS difficulty: 168 digits. Divisors found: r1=641923119296141775585479279443339644024656140218061 r2=754542863764954247166210709332774211904122796445876029066108488793031852354112276874269887328583596219 Version: Total time: 64.38 hours. Scaled time: 129.54 units (timescale=2.012). Factorization parameters were as follows: n: 484358508750643176663936835681906593235838524767765001810069448234657396117754486652019637082863748781456555081996193969222446620209155086837402235111359 m: 2000000000000000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 type: snfs lss: 1 rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2250000, 4450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 744654 x 744902 Total sieving time: 64.38 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,168,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000 total time: 64.38 hours. --------- CPU info (if available) ----------
(25·10¹⁹⁸-43)/9 = 2(7)₁₉₇3_<199> = 5869 · C195
C195 = P58 · P138
P58 = 1451404622524480716557996312602451817462320347463899152439_<58>
P138 = 326095561617768087884395065941298852407265226525174381101383715053134023745318575170785592323285897166994765718293103718772301298550007303_<138>

Number: 27773_198 N=473296605516745233903182446375494594952764998769428825656462391851725639423714053122811003199485053293197781185513337498343461880691391681338861437685768917665322504306999110202381628518960262017 ( 195 digits) SNFS difficulty: 199 digits. Divisors found: r1=1451404622524480716557996312602451817462320347463899152439 r2=326095561617768087884395065941298852407265226525174381101383715053134023745318575170785592323285897166994765718293103718772301298550007303 Version: Total time: 721.86 hours. Scaled time: 1454.54 units (timescale=2.015). Factorization parameters were as follows: n: 473296605516745233903182446375494594952764998769428825656462391851725639423714053122811003199485053293197781185513337498343461880691391681338861437685768917665322504306999110202381628518960262017 m: 5000000000000000000000000000000000000000 deg: 5 c5: 8 c0: -43 skew: 1.40 type: snfs lss: 1 rlim: 14700000 alim: 14700000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 14700000/14700000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [7350000, 15150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2531515 x 2531763 Total sieving time: 721.86 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,199,5,0,0,0,0,0,0,0,0,14700000,14700000,28,28,55,55,2.5,2.5,100000 total time: 721.86 hours. --------- CPU info (if available) ----------
Nov 13, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Nov 13, 2009
(62·10¹⁶⁸-71)/9 = 6(8)₁₆₇1_<169> = 12579647 · C162
C162 = P69 · P94
P69 = 417996494895948005785248123398354871614766916243498866195380490935959_<69>
P94 = 1310110977341236383525940660843416170256038120437603143534793254416808586880932126433244177097_<94>

Number: 68881_168 N=547621796453341567445325682738862933823889405552388623376227400410272950337071373218094982227155411347304808226247436743565927477049943363982223737191424281531023 ( 162 digits) SNFS difficulty: 171 digits. Divisors found: r1=417996494895948005785248123398354871614766916243498866195380490935959 (pp69) r2=1310110977341236383525940660843416170256038120437603143534793254416808586880932126433244177097 (pp94) Version: Msieve v. 1.43 Total time: 71.81 hours. Scaled time: 124.87 units (timescale=1.739). Factorization parameters were as follows: n: 547621796453341567445325682738862933823889405552388623376227400410272950337071373218094982227155411347304808226247436743565927477049943363982223737191424281531023 m: 5000000000000000000000000000000000 deg: 5 c5: 496 c0: -1775 skew: 1.29 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, 6400001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1056436 x 1056661 Total sieving time: 69.24 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.46 hours. Time per square root: 0.98 hours. Prototype def-par.txt line would be: snfs,171.000,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,52,52,2.4,2.4,100000 total time: 71.81 hours.
Nov 13, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 13, 2009
(65·10¹⁵⁶-11)/9 = 7(2)₁₅₅1_<157> = 3 · 149 · 2909 · 484061 · 1869071 · C139
C139 = P48 · P91
P48 = 924547593040272577001488578136091171063098712873_<48>
P91 = 6639944322588482605733024627603148158770302262895769428985277259280354195849327659562685229_<91>

Number: 72221_156 N=6138944541370604791669877501056223782086626050274386084745206959694754003758284585091174261445808018016007420619027077079856127009549252917 ( 139 digits) SNFS difficulty: 157 digits. Divisors found: r1=924547593040272577001488578136091171063098712873 r2=6639944322588482605733024627603148158770302262895769428985277259280354195849327659562685229 Version: Total time: 12.28 hours. Scaled time: 28.83 units (timescale=2.347). Factorization parameters were as follows: n: 6138944541370604791669877501056223782086626050274386084745206959694754003758284585091174261445808018016007420619027077079856127009549252917 m: 10000000000000000000000000000000 deg: 5 c5: 650 c0: -11 skew: 0.44 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, 2500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8015116 Max relations in full relation-set: Initial matrix: Pruned matrix : 554586 x 554834 Total sieving time: 11.01 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.77 hours. Time per square root: 0.08 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: 12.28 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(61·10¹⁶⁰-43)/9 = 6(7)₁₅₉3_<161> = 3 · 258846753455803_<15> · 61739694542088436121217926517233_<32> · C115
C115 = P46 · P69
P46 = 1817926149208691502729521475457905515096473051_<46>
P69 = 777647240937270328992484826480769491945261040621892507628864171690359_<69>

Number: 67773_160 N=1413705254159855371061936185876921103504280730923166822583108539086549753629478508296087325967444560737441760015309 ( 115 digits) Divisors found: r1=1817926149208691502729521475457905515096473051 r2=777647240937270328992484826480769491945261040621892507628864171690359 Version: Total time: 15.79 hours. Scaled time: 37.44 units (timescale=2.371). Factorization parameters were as follows: name: 67773_160 n: 1413705254159855371061936185876921103504280730923166822583108539086549753629478508296087325967444560737441760015309 skew: 50536.77 # norm 4.80e+15 c5: 25380 c4: -614505552 c3: -47647136645839 c2: 5452395569024831359 c1: 140859291886924652868131 c0: -4324536369697488192023050839 # alpha -6.16 Y1: 2826537573989 Y0: -8895576914842352240720 # Murphy_E 5.57e-10 # M 161569964661124522022265799579816433730413328407547361845111517972008345354236704372972149102516328162387493120225 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: 9221835 Max relations in full relation-set: Initial matrix: Pruned matrix : 496281 x 496529 Polynomial selection time: 1.36 hours. Total sieving time: 12.88 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.56 hours. Time per square root: 0.30 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: 15.79 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 12, 2009 (6th): By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Nov 12, 2009
(59·10¹⁵⁶+31)/9 = 6(5)₁₅₅9_<157> = 211 · 1277 · 204371 · 8456385102374933467647900354881_<31> · C116
C116 = P34 · P82
P34 = 3012983645866773188165757444214891_<34>
P82 = 4672349839242065027594979758740290110260235772594442708775254177171296529449693617_<82>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 14077713653404588690555756672692970008608629107471571113503341492890083842753884124196001195304510019047009059050747 (116 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5651182032 Step 1 took 2692ms Step 2 took 1917ms ********** Factor found in step 2: 3012983645866773188165757444214891 Found probable prime factor of 34 digits: 3012983645866773188165757444214891 Probable prime cofactor 4672349839242065027594979758740290110260235772594442708775254177171296529449693617 has 82 digits
(64·10¹⁵⁶+17)/9 = 7(1)₁₅₅3_<157> = 3 · 23 · 1476527597_<10> · 4262940271_<10> · 19870321428695636593969_<23> · C114
C114 = P55 · P60
P55 = 1982357395654855011440038146861915074032606554692317687_<55>
P60 = 415671941297055391986742820832969759498307762414593330759457_<60>

Number: 71113_156 N=824010346996428501902929446579336446349065675339870767096387628080340800443117481808771174671282885478191223615959 ( 114 digits) SNFS difficulty: 157 digits. Divisors found: r1=1982357395654855011440038146861915074032606554692317687 r2=415671941297055391986742820832969759498307762414593330759457 Version: Total time: 12.24 hours. Scaled time: 28.40 units (timescale=2.321). Factorization parameters were as follows: n: 824010346996428501902929446579336446349065675339870767096387628080340800443117481808771174671282885478191223615959 m: 20000000000000000000000000000000 deg: 5 c5: 20 c0: 17 skew: 0.97 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8481172 Max relations in full relation-set: Initial matrix: Pruned matrix : 485933 x 486180 Total sieving time: 11.15 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.51 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 12.24 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(65·10¹⁵⁹+61)/9 = 7(2)₁₅₈9_<160> = 167 · 455921 · 4001016979670712233_<19> · 5379908203555946771_<19> · C115
C115 = P53 · P62
P53 = 96383262843725875562456351579696025282506312998383983_<53>
P62 = 45721228945729185309354981526914135704408442080201681269449463_<62>

Number: 72229_159 N=4406761227014383772744992246241231961679312963933611928862215622302455615422271185419516893972781051599907087151129 ( 115 digits) Divisors found: r1=96383262843725875562456351579696025282506312998383983 r2=45721228945729185309354981526914135704408442080201681269449463 Version: Total time: 15.08 hours. Scaled time: 36.03 units (timescale=2.389). Factorization parameters were as follows: name: 72229_159 n: 4406761227014383772744992246241231961679312963933611928862215622302455615422271185419516893972781051599907087151129 skew: 17359.92 # norm 2.35e+15 c5: 36540 c4: 5231062026 c3: -130362871646254 c2: -1226930863844106788 c1: 8425729364406378361539 c0: 53716536162268136384847162 # alpha -5.10 Y1: 159695469967 Y0: -10381736553568680581705 # Murphy_E 5.72e-10 # M 827678952077618632955342287148713937231119215230854811599520325539777306026637345719092699824163303916063189669290 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: 9155069 Max relations in full relation-set: Initial matrix: Pruned matrix : 523806 x 524054 Polynomial selection time: 1.34 hours. Total sieving time: 12.38 hours. Total relation processing time: 0.67 hours. Matrix solve time: 0.58 hours. Time per square root: 0.12 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: 15.08 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(83·10¹⁶¹+7)/9 = 9(2)₁₆₀3_<162> = 1697 · 2711 · 20543 · 1498481 · 53973738457_<11> · 810578820825230269_<18> · C117
C117 = P32 · P85
P32 = 65656961003311514015883035936551_<32>
P85 = 2266995127807532404937686268783558513717904515654110062784739793001401834333714626621_<85>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 148844010701156356756903072727115500377610663976925506749656983744503128054493059428451193698102694635708042011524171 (117 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6209770295 Step 1 took 3580ms Step 2 took 2050ms ********** Factor found in step 2: 65656961003311514015883035936551 Found probable prime factor of 32 digits: 65656961003311514015883035936551 Probable prime cofactor 2266995127807532404937686268783558513717904515654110062784739793001401834333714626621 has 85 digits
(67·10¹⁶³-31)/9 = 7(4)₁₆₂1_<164> = 1093 · 16633 · 26687 · 14657691415107539107_<20> · C134
C134 = P37 · P38 · P59
P37 = 2379704242579980728400961963262974523_<37>
P38 = 80520601705670054813859962771453621977_<38>
P59 = 54631889004741725520371953058841143590754460348049791924251_<59>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 10468301293755797423881824808300936684163049041001719203135482913387586546663127409790577743604090731829830211783508368815067239088721 (134 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4672242577 Step 1 took 3327ms Step 2 took 2201ms ********** Factor found in step 2: 80520601705670054813859962771453621977 Found probable prime factor of 38 digits: 80520601705670054813859962771453621977 Composite cofactor 130007738044742485114119405003336802697164449362326732828807416813930485046568036276242158857273 has 96 digits Number: 74441_163 N=130007738044742485114119405003336802697164449362326732828807416813930485046568036276242158857273 ( 96 digits) Divisors found: r1=2379704242579980728400961963262974523 r2=54631889004741725520371953058841143590754460348049791924251 Version: Total time: 1.50 hours. Scaled time: 3.46 units (timescale=2.313). Factorization parameters were as follows: name: 74441_163 n: 130007738044742485114119405003336802697164449362326732828807416813930485046568036276242158857273 skew: 1979.38 # norm 1.96e+13 c5: 273300 c4: 304405751 c3: 365710080704 c2: -4895444318937764 c1: -4512394773361583236 c0: 13984228209751842845 # alpha -6.07 Y1: 14191866557 Y0: -861914766383702208 # Murphy_E 6.01e-09 # M 46998393681213226899223521402912408001520722578974367414646002933959646617795624266321907021062 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, 680001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3482298 Max relations in full relation-set: Initial matrix: Pruned matrix : 128893 x 129141 Polynomial selection time: 0.10 hours. Total sieving time: 1.21 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 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: 1.50 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 12, 2009 (5th): By Dmitry Domanov / GGNFS/msieve / Nov 12, 2009
(67·10¹⁷⁵-31)/9 = 7(4)₁₇₄1_<176> = 269 · 3343 · C170
C170 = P57 · P114
P57 = 393007290755296676600975185335423075552050629797117701609_<57>
P114 = 210641059005337681090850353556043252785508344730403422889278293035429519751561094996454076042806528622893752218747_<114>

N=82783471921514349402840807507052348684477963101553203269378776764236255132729705909862637508598052018415492222492812973726873603106134712431841093295366609076552841863923 ( 170 digits) SNFS difficulty: 176 digits. Divisors found: r1=393007290755296676600975185335423075552050629797117701609 (pp57) r2=210641059005337681090850353556043252785508344730403422889278293035429519751561094996454076042806528622893752218747 (pp114) Version: Msieve-1.40 Total time: 82.62 hours. Scaled time: 155.56 units (timescale=1.883). Factorization parameters were as follows: n: 82783471921514349402840807507052348684477963101553203269378776764236255132729705909862637508598052018415492222492812973726873603106134712431841093295366609076552841863923 m: 100000000000000000000000000000000000 deg: 5 c5: 67 c0: -31 skew: 0.86 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3100000, 7200001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1326117 x 1326348 Total sieving time: 79.81 hours. Total relation processing time: 0.16 hours. Matrix solve time: 2.19 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: snfs,176.000,5,0,0,0,0,0,0,0,0,6200000,6200000,28,28,53,53,2.5,2.5,100000 total time: 82.62 hours. --------- CPU info (if available) ----------
(65·10¹⁵⁸-11)/9 = 7(2)₁₅₇1_<159> = 7 · 31 · 3607 · C153
C153 = P41 · P50 · P63
P41 = 83363948032550770439971746177796233984623_<41>
P50 = 63165174686566479174510487178756948267564308740641_<50>
P63 = 175230215598453693379399967411213917661767959640494153861891613_<63>

N=922709455401264339082381061686534020794464197524555073049488031109788087707366529012611450881123650022833510138660518298677075964965999576121471718742259 ( 153 digits) SNFS difficulty: 160 digits. Divisors found: r1=83363948032550770439971746177796233984623 (pp41) r2=63165174686566479174510487178756948267564308740641 (pp50) r3=175230215598453693379399967411213917661767959640494153861891613 (pp63) Version: Msieve-1.40 Total time: 19.63 hours. Scaled time: 36.21 units (timescale=1.845). Factorization parameters were as follows: n: 922709455401264339082381061686534020794464197524555073049488031109788087707366529012611450881123650022833510138660518298677075964965999576121471718742259 m: 50000000000000000000000000000000 deg: 5 c5: 104 c0: -55 skew: 0.88 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1650000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 618184 x 618411 Total sieving time: 18.94 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.47 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,160.000,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,51,51,2.4,2.4,100000 total time: 19.63 hours. --------- CPU info (if available) ----------
Nov 12, 2009 (4th): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 12, 2009
(62·10¹⁹²-71)/9 = 6(8)₁₉₁1_<193> = 807571049183_<12> · C181
C181 = P40 · P142
P40 = 2141731664373514704800209804190966929619_<40>
P142 = 3982936487128283963654011022855118528252029474284443258175563324282085584199674797758328510237897814911957350790362026615847538823628063665653_<142>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2276662570 Step 1 took 63985ms ********** Factor found in step 1: 2141731664373514704800209804190966929619 Found probable prime factor of 40 digits: 2141731664373514704800209804190966929619 Probable prime cofactor 3982936487128283963654011022855118528252029474284443258175563324282085584199674797758328510237897814911957350790362026615847538823628063665653 has 142 digits
Nov 12, 2009 (3rd): By Ignacio Santos / GGNFS, Msieve / Nov 12, 2009
(67·10¹⁶⁴+41)/9 = 7(4)₁₆₃9_<165> = 7 · 97 · 461 · C160
C160 = P44 · P117
P44 = 10965272962460119234911069404341287975741259_<44>
P117 = 216891307273720750758081653250952572647618179283737370490732853103987208380893592346709082214421115917317056152162969_<117>

Number: 74449_164 N=2378272387441159943787579809674315119671471841787381738630704348440332517976367071789394396009329927079328872830225783241414880388872382968587991286293945237971 ( 160 digits) SNFS difficulty: 166 digits. Divisors found: r1=10965272962460119234911069404341287975741259 (pp44) r2=216891307273720750758081653250952572647618179283737370490732853103987208380893592346709082214421115917317056152162969 (pp117) Version: Msieve v. 1.43 Total time: 44.81 hours. Scaled time: 77.93 units (timescale=1.739). Factorization parameters were as follows: n: 2378272387441159943787579809674315119671471841787381738630704348440332517976367071789394396009329927079328872830225783241414880388872382968587991286293945237971 m: 1000000000000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 type: snfs lss: 1 rlim: 4200000 alim: 4200000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 4600001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 794493 x 794718 Total sieving time: 43.79 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.80 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,166.000,5,0,0,0,0,0,0,0,0,4200000,4200000,27,27,51,51,2.4,2.4,100000 total time: 44.81 hours.
Nov 12, 2009 (2nd): By Sinkiti Sibata / Msieve / Nov 12, 2009
(62·10¹⁵⁵-71)/9 = 6(8)₁₅₄1_<156> = 3 · 83 · 1054865761_<10> · 5865205252879032365590891631_<28> · C117
C117 = P57 · P60
P57 = 690204344660474179997645180103744985808246178066443143733_<57>
P60 = 647875762848916317184387762028148718967749699167161314240123_<60>

Number: 68881_155 N=447166666318541071021133120076586888737388050135431182917568426080461179199315021134343779030522598595547672164599159 ( 117 digits) SNFS difficulty: 156 digits. Divisors found: r1=690204344660474179997645180103744985808246178066443143733 (pp57) r2=647875762848916317184387762028148718967749699167161314240123 (pp60) Version: Msieve-1.40 Total time: 35.60 hours. Scaled time: 120.13 units (timescale=3.374). Factorization parameters were as follows: name: 68881_155 n: 447166666318541071021133120076586888737388050135431182917568426080461179199315021134343779030522598595547672164599159 m: 10000000000000000000000000000000 deg: 5 c5: 62 c0: -71 skew: 1.03 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, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 507864 x 508112 Total sieving time: 35.01 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.48 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 35.60 hours. --------- CPU info (if available) ----------
(62·10¹⁵²-71)/9 = 6(8)₁₅₁1_<153> = 3² · 23 · 443 · 1061 · 34279360770581_<14> · C132
C132 = P36 · P96
P36 = 315834675110482422029126787755351387_<36>
P96 = 653984116715282556173259909244692754554281589932741812886644462514507314473058785355215072340543_<96>

Number: 68881_152 N=206550861030187082845434344910136822313692781358486124359562932596625872977417209449469207777000587340003595836995580001075491383141 ( 132 digits) SNFS difficulty: 154 digits. Divisors found: r1=315834675110482422029126787755351387 (pp36) r2=653984116715282556173259909244692754554281589932741812886644462514507314473058785355215072340543 (pp96) Version: Msieve-1.40 Total time: 26.52 hours. Scaled time: 55.30 units (timescale=2.085). Factorization parameters were as follows: name: 68881_152 n: 206550861030187082845434344910136822313692781358486124359562932596625872977417209449469207777000587340003595836995580001075491383141 m: 2000000000000000000000000000000 deg: 5 c5: 775 c0: -284 skew: 0.82 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, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 503235 x 503483 Total sieving time: 25.38 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.88 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,154.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 26.52 hours. --------- CPU info (if available) ----------
Nov 12, 2009: By Erik Branger / GGNFS, Msieve / Nov 12, 2009
(65·10¹⁵⁶+61)/9 = 7(2)₁₅₅9_<157> = 7³ · 23041 · 290912309 · C142
C142 = P54 · P88
P54 = 605691835518887929525069079127539502706299835330479941_<54>
P88 = 5186347188194532049169964537904314800100966481543495236359524310108165939442379395721307_<88>

Number: 72229_156 N=3141328148055769408108490574107127310905627536310764350258942664672471270571546787474991776204204338886772516964994368059599955681938189802887 ( 142 digits) SNFS difficulty: 157 digits. Divisors found: r1=605691835518887929525069079127539502706299835330479941 (pp54) r2=5186347188194532049169964537904314800100966481543495236359524310108165939442379395721307 (pp88) Version: Msieve v. 1.43 Total time: 29.78 hours. Scaled time: 25.49 units (timescale=0.856). Factorization parameters were as follows: n: 3141328148055769408108490574107127310905627536310764350258942664672471270571546787474991776204204338886772516964994368059599955681938189802887 m: 10000000000000000000000000000000 deg: 5 c5: 650 c0: 61 skew: 0.62 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: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 628739 x 628971 Total sieving time: 28.49 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.91 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,157.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 29.78 hours. --------- CPU info (if available) ----------
Nov 11, 2009 (6th): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 11, 2009
(62·10¹⁹¹-71)/9 = 6(8)₁₉₀1_<192> = 3 · 67 · 887 · 2539 · 9337 · 39719 · 1602440276322618158898151_<25> · C151
C151 = P39 · C112
P39 = 517452552714882800113775903751182527043_<39>
C112 = [4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023_<112>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1659986578 Step 1 took 46926ms Step 2 took 16405ms ********** Factor found in step 2: 517452552714882800113775903751182527043 Found probable prime factor of 39 digits: 517452552714882800113775903751182527043 Composite cofactor 4948900833131795948779300436802723663715157264908054857089072914253472322653488429767164518431236683340445838023 has 112 digits
Nov 11, 2009 (5th): By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Nov 11, 2009
(67·10¹⁹⁷-31)/9 = 7(4)₁₉₆1_<198> = 3² · 62765167725817727_<17> · 569456850647072222011_<21> · 7082290927670325280559_<22> · 143654013588585058279631_<24> · C115
C115 = P39 · P76
P39 = 876417883079711189730801115665794456501_<39>
P76 = 2595419183630539862325486973334714191597155410525075313845472607910755022473_<76>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 2274671786621949951263749654269552518055133473554962856563812879331411196076321546565020576595542670694967075946973 (115 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6695390019 Step 1 took 3447ms Step 2 took 3775ms ********** Factor found in step 2: 876417883079711189730801115665794456501 Found probable prime factor of 39 digits: 876417883079711189730801115665794456501 Probable prime cofactor 2595419183630539862325486973334714191597155410525075313845472607910755022473 has 76 digits
(67·10¹⁵⁵-13)/9 = 7(4)₁₅₄3_<156> = 7 · 709 · 9293712784931_<13> · 1383499142474187967_<19> · C122
C122 = P49 · P73
P49 = 4878885565302112410069827574733270111997783354663_<49>
P73 = 2391108289919426790093946899475837566572606524440706754396837686596322811_<73>

Number: 74443_155 N=11665943720762109867469144547912706865819403378906466080397791627463020253271963189327366442949178885904585225639650117693 ( 122 digits) SNFS difficulty: 156 digits. Divisors found: r1=4878885565302112410069827574733270111997783354663 r2=2391108289919426790093946899475837566572606524440706754396837686596322811 Version: Total time: 11.86 hours. Scaled time: 28.30 units (timescale=2.387). Factorization parameters were as follows: n: 11665943720762109867469144547912706865819403378906466080397791627463020253271963189327366442949178885904585225639650117693 m: 10000000000000000000000000000000 deg: 5 c5: 67 c0: -13 skew: 0.72 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved rational special-q in [1200000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8097644 Max relations in full relation-set: Initial matrix: Pruned matrix : 498919 x 499167 Total sieving time: 10.82 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.54 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 11.86 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(62·10¹⁵⁷-71)/9 = 6(8)₁₅₆1_<158> = 99195219782129_<14> · 862777452673465967877176411389_<30> · C114
C114 = P35 · P80
P35 = 52297659149807374462667474009984713_<35>
P80 = 15391374265113706485561084794199787764149587902549858512746210928097010187565677_<80>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 804932845164033586036914469028264065136979055479450569674957239025392866722070247914821612289988269570817453495701 (114 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8562617314 Step 1 took 2683ms Step 2 took 1934ms ********** Factor found in step 2: 52297659149807374462667474009984713 Found probable prime factor of 35 digits: 52297659149807374462667474009984713 Probable prime cofactor 15391374265113706485561084794199787764149587902549858512746210928097010187565677 has 80 digits
(62·10¹⁹³-71)/9 = 6(8)₁₉₂1_<194> = 75960033942817_<14> · 4397607999596779171_<19> · 369309395407669463317213_<24> · 1171702087614980824891741_<25> · C114
C114 = P37 · P39 · P39
P37 = 2525698696521822456119491163260313393_<37>
P39 = 256813952710105392622923287549523616069_<39>
P39 = 734750347974042448663022462026007717303_<39>

Number: 68881_193 N=476584546263894187249410686004100765778612480514835230007919231006638024959787696980937702139804608084591272660451 ( 114 digits) Divisors found: r1=2525698696521822456119491163260313393 r2=256813952710105392622923287549523616069 r3=734750347974042448663022462026007717303 Version: Total time: 15.21 hours. Scaled time: 36.34 units (timescale=2.389). Factorization parameters were as follows: name: 68881_193 n: 476584546263894187249410686004100765778612480514835230007919231006638024959787696980937702139804608084591272660451 skew: 81967.32 # norm 9.82e+15 c5: 8820 c4: 2345585976 c3: -323570539152345 c2: -15362443811670735002 c1: 597776664594248966729850 c0: 21149383241086351023669060501 # alpha -6.44 Y1: 162832733239 Y0: -8841660780460233148288 # Murphy_E 6.11e-10 # M 113143934203780989554909325109184190545377095444258272813552631118687650210735975240448943877806470142275656860495 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: 9462558 Max relations in full relation-set: Initial matrix: Pruned matrix : 455180 x 455428 Polynomial selection time: 1.15 hours. Total sieving time: 12.32 hours. Total relation processing time: 0.70 hours. Matrix solve time: 0.43 hours. Time per square root: 0.62 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,52,52,2.6,2.6,70000 total time: 15.21 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵⁶+41)/9 = 7(4)₁₅₅9_<157> = 3 · 49722859553004683571304633082687_<32> · C125
C125 = P39 · P86
P39 = 977449831415406822625837597217701697963_<39>
P86 = 51057608111162517212283211587392025819225649128369502205593083124860984531588715088543_<86>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 49906250440729710419014031070881432285557829279347790059994308543147408208496821187368869362262186554536134835916248987737909 (125 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4701809730 Step 1 took 3299ms ********** Factor found in step 1: 977449831415406822625837597217701697963 Found probable prime factor of 39 digits: 977449831415406822625837597217701697963 Probable prime cofactor 51057608111162517212283211587392025819225649128369502205593083124860984531588715088543 has 86 digits
Nov 11, 2009 (4th): By Sinkiti Sibata / Msieve / Nov 11, 2009
(62·10¹⁵¹-71)/9 = 6(8)₁₅₀1_<152> = 331 · 127037 · 11400881 · 134503558337_<12> · C127
C127 = P53 · P74
P53 = 12183800517956357535603106021528312450021649863093099_<53>
P74 = 87687157226222913211851853713756716074490652421247217538196733958337598941_<74>

Number: 68881_151 N=1068362831630975289536719380978717933839318138065193388152189421002793725428131445533649250405126709847471149909608867206808159 ( 127 digits) SNFS difficulty: 153 digits. Divisors found: r1=12183800517956357535603106021528312450021649863093099 (pp53) r2=87687157226222913211851853713756716074490652421247217538196733958337598941 (pp74) Version: Msieve-1.40 Total time: 24.61 hours. Scaled time: 51.14 units (timescale=2.078). Factorization parameters were as follows: name: 68881_151 n: 1068362831630975289536719380978717933839318138065193388152189421002793725428131445533649250405126709847471149909608867206808159 m: 2000000000000000000000000000000 deg: 5 c5: 155 c0: -568 skew: 1.30 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, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 451516 x 451764 Total sieving time: 23.54 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.71 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,153.000,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 24.61 hours. --------- CPU info (if available) ----------
Nov 11, 2009 (3rd): By Erik Branger / GGNFS, Msieve, GMP-ECM / Nov 11, 2009
(62·10¹⁵⁴-71)/9 = 6(8)₁₅₃1_<155> = 43 · 374993 · 2810836267_<10> · 11225367031078217_<17> · C123
C123 = P50 · P73
P50 = 59456498419297853938720187564291652786173012200777_<50>
P73 = 2277309913700930235171299438349941993910174833496615439903369397888974873_<73>

Number: 68881_154 N=135400873284210690693774015755123458723863999599882657194440727495833755486367006735978429661363061336140811098682184076321 ( 123 digits) SNFS difficulty: 156 digits. Divisors found: r1=59456498419297853938720187564291652786173012200777 (pp50) r2=2277309913700930235171299438349941993910174833496615439903369397888974873 (pp73) Version: Msieve v. 1.43 Total time: 23.11 hours. Scaled time: 23.09 units (timescale=0.999). Factorization parameters were as follows: n: 135400873284210690693774015755123458723863999599882657194440727495833755486367006735978429661363061336140811098682184076321 m: 10000000000000000000000000000000 deg: 5 c5: 31 c0: -355 skew: 1.63 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2500001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 506553 x 506780 Total sieving time: 22.27 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.61 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 23.11 hours. --------- CPU info (if available) ----------
(67·10¹⁷⁷+41)/9 = 7(4)₁₇₆9_<178> = 3² · 13 · 29 · 83 · 4273 · 5393 · 5722060324567079183_<19> · 151018584602920158933747156833_<30> · C118
C118 = P32 · P86
P32 = 22758430372083446855719889404943_<32>
P86 = 58328645933672237511735506021370981038299449338001585648578106455857959995279721987707_<86>

GMP-ECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 1327468427179387889781842707701047813219909890609691053184956887763212589049476886379634400599684315962049865391035701 (118 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3389415600 Step 1 took 35225ms Step 2 took 12183ms ********** Factor found in step 2: 22758430372083446855719889404943 Found probable prime factor of 32 digits: 22758430372083446855719889404943 Probable prime cofactor 58328645933672237511735506021370981038299449338001585648578106455857959995279721987707 has 86 digits
Nov 11, 2009 (2nd): By matsui / Msieve / Nov 11, 2009
9·10²²⁹-1 = 8(9)₂₂₉_<230> = 197 · 208440677 · 1189638653569_<13> · 1894742524089853_<16> · 81036479966432843_<17> · 49931612314311537707693_<23> · C153
C153 = P41 · P55 · P57
P41 = 67387210716432592896081650429078156564311_<41>
P55 = 6243050577365052581815882169888181821426803805681795893_<55>
P57 = 571212953652346708852367194795436478812329554530967996239_<57>

N=240310297661166400485936362786332361583251738596432632828490772305058814102347092398830258825622814264893962996338765698926236641973725988355663176866797 ( 153 digits) Divisors found: r1=67387210716432592896081650429078156564311 (pp41) r2=6243050577365052581815882169888181821426803805681795893 (pp55) r3=571212953652346708852367194795436478812329554530967996239 (pp57) Version: Msieve v. 1.43 Total time: 251.99 hours. Scaled time: 435.68 units (timescale=1.729). Factorization parameters were as follows: name: 89999_229 n: 240310297661166400485936362786332361583251738596432632828490772305058814102347092398830258825622814264893962996338765698926236641973725988355663176866797 skew: 767614.43 # norm 1.10e+21 c5: 5687280 c4: -1576344828224 c3: -15992040188510426116 c2: 551458288805369004819659 c1: 3133393285152216531272566657368 c0: 15877934132636447372734593052780585 # alpha -6.25 Y1: 421186069282110373 Y0: -133405467847610273238880604564 # Murphy_E 3.57e-12 # M 94019805174926964203307818923509292211349668657206486672204198932322380976076648921267349291638710915588954585022947785470799284727337408767453363616776 type: gnfs rlim: 24400000 alim: 24400000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 1600000 Factor base limits: 24400000/24400000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved algebraic special-q in [12200000, 45800001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 4602695 x 4602923 Total sieving time: 218.64 hours. Total relation processing time: 0.36 hours. Matrix solve time: 28.28 hours. Time per square root: 4.71 hours. Prototype def-par.txt line would be: gnfs,152,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,24400000,24400000,29,29,58,58,2.6,2.6,100000 total time: 251.99 hours.
c153 is the largest composite number which was factored by gnfs in our tables so far. Congratulations!
Nov 11, 2009: By Dmitry Domanov / GGNFS/msieve / Nov 11, 2009
(65·10¹⁵⁶+7)/9 = 7(2)₁₅₅3_<157> = 103 · 5987 · C152
C152 = P34 · P45 · P73
P34 = 7031297053478820252836704940982133_<34>
P45 = 216618954992476495307119418561129767797475183_<45>
P73 = 7689400150761544910067260025642464616112812856275284452144717121553857737_<73>

Number: s152 N=11711819333835319928165105661331302323679010383699021378394648311182679336332640173810606187552354084695192694563499592518778100483445883917131490757843 ( 152 digits) SNFS difficulty: 159 digits. Divisors found: r1=7031297053478820252836704940982133 (pp34) r2=216618954992476495307119418561129767797475183 (pp45) r3=7689400150761544910067260025642464616112812856275284452144717121553857737 (pp73) Version: Msieve-1.40 Total time: 20.84 hours. Scaled time: 39.70 units (timescale=1.905). Factorization parameters were as follows: n: 11711819333835319928165105661331302323679010383699021378394648311182679336332640173810606187552354084695192694563499592518778100483445883917131490757843 m: 20000000000000000000000000000000 deg: 5 c5: 325 c0: 112 skew: 0.81 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor base limits: 3100000/3100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1550000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 563522 x 563750 Total sieving time: 19.98 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.39 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,159.000,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 20.84 hours. --------- CPU info (if available) ----------
Nov 10, 2009 (7th): By Lionel Debroux, Jeff Gilchrist / ggnfs + msieve / Nov 10, 2009
(16·10²¹⁸-7)/9 = 1(7)₂₁₈_<219> = 3 · 31 · 47803226827_<11> · 4200791891903_<13> · C193
C193 = P84 · P110
P84 = 268323355950355689735829355470693132255531404134917945907444149722706588875965691187_<84>
P110 = 35477063645140320608508880041657003639745603152097560923338385031351604960423622458603280891900739184876928587_<110>

* Sieving with ggnfs-lasieve4I14e on the RSALS grid * Relation filtering and matrix creation by Lionel Debroux * Lanczos iteration and square root phase by Jeff Gilchrist: Msieve v. 1.43 Sat Nov 7 06:20:12 2009 random seeds: 0a61ba43 4d857a70 factoring 9519324776528409561729990009646664138683276667349926474618191233610006802875690133653956702500176615466439936026117646551454778085624851090212971043848299225331138444034552307364883241094262769 (193 digits) no P-1/P+1/ECM available, skipping commencing number field sieve (193-digit input) R0: -2000000000000000000000000000000000000 R1: 1 A0: -7 A1: 0 A2: 0 A3: 0 A4: 0 A5: 0 A6: 25 skew 0.81, size 8.982341e-11, alpha 0.442034, combined = 3.092508e-12 commencing square root phase reading relations for dependency 1 read 2344667 cycles cycles contain 6788734 unique relations read 6788734 relations multiplying 6788734 relations multiply complete, coefficients have about 194.54 million bits initial square root is modulo 9585991 reading relations for dependency 2 read 2347128 cycles cycles contain 6786766 unique relations read 6786766 relations multiplying 6786766 relations multiply complete, coefficients have about 194.49 million bits initial square root is modulo 9541993 reading relations for dependency 3 read 2345872 cycles cycles contain 6789410 unique relations read 6789410 relations multiplying 6789410 relations multiply complete, coefficients have about 194.56 million bits initial square root is modulo 9600571 reading relations for dependency 4 read 2346398 cycles cycles contain 6788602 unique relations read 6788602 relations multiplying 6788602 relations multiply complete, coefficients have about 194.54 million bits initial square root is modulo 9582763 reading relations for dependency 5 read 2346536 cycles cycles contain 6786192 unique relations read 6786192 relations multiplying 6786192 relations multiply complete, coefficients have about 194.48 million bits initial square root is modulo 9533137 sqrtTime: 9409 prp84 factor: 268323355950355689735829355470693132255531404134917945907444149722706588875965691187 prp110 factor: 35477063645140320608508880041657003639745603152097560923338385031351604960423622458603280891900739184876928587 elapsed time 02:36:51
Nov 10, 2009 (6th): By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 10, 2009
(22·10¹⁶⁸+17)/3 = 7(3)₁₆₇9_<169> = 13² · 41 · 8713 · 13669 · 214273369 · 114606497028610906462852186626440387_<36> · C114
C114 = P40 · P74
P40 = 4177882563148851956956378400719707432499_<40>
P74 = 86614926782716481655642989173611606205822555745723844164409561209012769799_<74>

Number: g114 N=361866992313925679835060995464419229628238498308302974917150353218753381622582951726188164535961708450542818297701 ( 114 digits) Divisors found: r1=4177882563148851956956378400719707432499 (pp40) r2=86614926782716481655642989173611606205822555745723844164409561209012769799 (pp74) Version: Msieve-1.40 Total time: 18.28 hours. Scaled time: 34.22 units (timescale=1.872). Factorization parameters were as follows: # Murphy_E = 6.914749e-10, selected by Erik Branger n: 361866992313925679835060995464419229628238498308302974917150353218753381622582951726188164535961708450542818297701 Y0: -9358848905036098722083 Y1: 1217111908793 c0: 250679101103598290355518496 c1: -98749734681377813022512 c2: -1818902650774914967 c3: -83088339013152 c4: 558203372 c5: 5040 skew: 74097.95 type: gnfs # selected mechanically rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 421885 x 422119 Total sieving time: 17.91 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.23 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.5,2.5,100000 total time: 18.28 hours. --------- CPU info (if available) ----------
(65·10¹⁸⁴+61)/9 = 7(2)₁₈₃9_<185> = C185
C185 = P79 · P106
P79 = 7416636363322081411734736677307481195492064107754843900863362332033982448906537_<79>
P106 = 9737867502765395606014252796988801940512562554168295027040851239051448736911790559819965758531428016050317_<106>

Number: s185 N=72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 ( 185 digits) SNFS difficulty: 186 digits. Divisors found: r1=7416636363322081411734736677307481195492064107754843900863362332033982448906537 (pp79) r2=9737867502765395606014252796988801940512562554168295027040851239051448736911790559819965758531428016050317 (pp106) Version: Msieve-1.40 Total time: 356.27 hours. Scaled time: 332.76 units (timescale=0.934). Factorization parameters were as follows: n: 72222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 m: 10000000000000000000000000000000000000 deg: 5 c5: 13 c0: 122 skew: 1.56 type: snfs lss: 1 rlim: 8900000 alim: 8900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5Factor base limits: 8900000/8900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4450000, 8550001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1689410 x 1689637 Total sieving time: 349.66 hours. Total relation processing time: 0.66 hours. Matrix solve time: 5.48 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: snfs,186.000,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000 total time: 356.27 hours. --------- CPU info (if available) ----------
(59·10¹⁶²+31)/9 = 6(5)₁₆₁9_<163> = 11839 · C159
C159 = P64 · P96
P64 = 1603806001192770510753527225209719940802414193940206966754019963_<64>
P96 = 345257123130058654867239834949430629892606823120856523120868703933491053735726127484325472092987_<96>

Number: s159 N=553725446030539366125141950802901896744282080881455828664207750279209017278110951563101237904853075053260879766496794962036958827228275661420352694953590299481 ( 159 digits) SNFS difficulty: 164 digits. Divisors found: r1=1603806001192770510753527225209719940802414193940206966754019963 (pp64) r2=345257123130058654867239834949430629892606823120856523120868703933491053735726127484325472092987 (pp96) Version: Msieve-1.40 Total time: 42.53 hours. Scaled time: 77.11 units (timescale=1.813). Factorization parameters were as follows: n: 553725446030539366125141950802901896744282080881455828664207750279209017278110951563101237904853075053260879766496794962036958827228275661420352694953590299481 m: 200000000000000000000000000000000 deg: 5 c5: 1475 c0: 248 skew: 0.70 type: snfs lss: 1 rlim: 3900000 alim: 3900000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor base limits: 3900000/3900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1950000, 4450001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 832432 x 832658 Total sieving time: 41.20 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.90 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: snfs,164.000,5,0,0,0,0,0,0,0,0,3900000,3900000,27,27,51,51,2.4,2.4,100000 total time: 42.53 hours. --------- CPU info (if available) ----------
(67·10¹⁷⁶-31)/9 = 7(4)₁₇₅1_<177> = 3 · 13 · 71 · C174
C174 = P38 · C137
P38 = 14585106125382471096943606647246369289_<38>
C137 = [18433157929261372543020550729674096547707466849046376880307345015073860397953606708332537812839756446385684607720942028809690211884235201_<137>]

Factor=14585106125382471096943606647246369289 Method=ECM B1=11000000 Sigma=2392920153
(22·10¹⁵⁹-7)/3 = 7(3)₁₅₈1_<160> = 13967 · C156
C156 = P45 · P112
P45 = 324485775047405152706505180736142372790996977_<45>
P112 = 1618089837178662448363775067491171510470582401491581751100635227165937052536156327577009094712259852356951106509_<112>

N=525047134913247893845015632085153098971384931147227989785446648051359156106059521252476074556693157681200925992219756091740053936660222906374549533424023293 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: r1=324485775047405152706505180736142372790996977 (pp45) r2=1618089837178662448363775067491171510470582401491581751100635227165937052536156327577009094712259852356951106509 (pp112) Version: Msieve-1.40 Total time: 18.84 hours. Scaled time: 35.27 units (timescale=1.872). Factorization parameters were as follows: n: 525047134913247893845015632085153098971384931147227989785446648051359156106059521252476074556693157681200925992219756091740053936660222906374549533424023293 m: 100000000000000000000000000000000 deg: 5 c5: 11 c0: -35 skew: 1.26 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4Factor 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, 2700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 637822 x 638049 Total sieving time: 17.98 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.52 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,161.000,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 18.84 hours. --------- CPU info (if available) ----------
(22·10¹⁸⁰-7)/3 = 7(3)₁₇₉1_<181> = 277 · C179
C179 = P38 · C141
P38 = 28341234128475964035151410109192458499_<38>
C141 = [934120491618255487715617124498006305942083239924591056032626276482155278960222427194169266237177630746177989763840285711539332572356417301997_<141>]

Factor=28341234128475964035151410109192458499 Method=ECM B1=11000000 Sigma=413036558
Nov 10, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 10, 2009
(64·10¹⁵⁴+17)/9 = 7(1)₁₅₃3_<155> = 7 · 29944451 · 99126724489936082314891547_<26> · C121
C121 = P36 · P85
P36 = 371458155915584869438887303244455043_<36>
P85 = 9213452798851581780246903010130941751346807705140375743997570945393621607222482291029_<85>

Number: 71113_154 N=3422412186276692664840006343775380636492433642471949424208317432860971893505957363340221351729755835795279923807232709247 ( 121 digits) SNFS difficulty: 156 digits. Divisors found: r1=371458155915584869438887303244455043 r2=9213452798851581780246903010130941751346807705140375743997570945393621607222482291029 Version: Total time: 9.13 hours. Scaled time: 21.70 units (timescale=2.377). Factorization parameters were as follows: n: 3422412186276692664840006343775380636492433642471949424208317432860971893505957363340221351729755835795279923807232709247 m: 20000000000000000000000000000000 deg: 5 c5: 1 c0: 85 skew: 2.43 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: 8251407 Max relations in full relation-set: Initial matrix: Pruned matrix : 418737 x 418985 Total sieving time: 8.36 hours. Total relation processing time: 0.34 hours. Matrix solve time: 0.39 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,50,50,2.4,2.4,100000 total time: 9.13 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(26·10¹⁵⁴-11)/3 = 8(6)₁₅₃3_<155> = 71 · 9070459 · 259328111441557_<15> · C132
C132 = P53 · P79
P53 = 99846047824272537592965345005720564798732938551338279_<53>
P79 = 5197374408355423148064024399326141532315371063525619734573070180253227577341089_<79>

Number: 86663_154 N=518937293737305764742350084321901012525716106131552754160789873608663212996406969680024139053939523745253009213500521776057405245831 ( 132 digits) SNFS difficulty: 156 digits. Divisors found: r1=99846047824272537592965345005720564798732938551338279 r2=5197374408355423148064024399326141532315371063525619734573070180253227577341089 Version: Total time: 10.11 hours. Scaled time: 24.03 units (timescale=2.376). Factorization parameters were as follows: n: 518937293737305764742350084321901012525716106131552754160789873608663212996406969680024139053939523745253009213500521776057405245831 m: 10000000000000000000000000000000 deg: 5 c5: 13 c0: -55 skew: 1.33 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved rational special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7809905 Max relations in full relation-set: Initial matrix: Pruned matrix : 491291 x 491539 Total sieving time: 9.02 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.50 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 10.11 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(61·10¹⁵⁵-43)/9 = 6(7)₁₅₄3_<156> = 19207 · 8129724299_<10> · C142
C142 = P50 · P93
P50 = 10773558329235854559383288960393828305859609444921_<50>
P93 = 402895859408850435228560980284998721882290483647477062554586284734865868390478708391490598441_<93>

Number: 67773_155 N=4340622041948858448170164123031439379962172720964831379039893892595501831032998542728524811238685147412778859492166572369332930590658117968161 ( 142 digits) SNFS difficulty: 156 digits. Divisors found: r1=10773558329235854559383288960393828305859609444921 r2=402895859408850435228560980284998721882290483647477062554586284734865868390478708391490598441 Version: Total time: 12.33 hours. Scaled time: 29.14 units (timescale=2.363). Factorization parameters were as follows: n: 4340622041948858448170164123031439379962172720964831379039893892595501831032998542728524811238685147412778859492166572369332930590658117968161 m: 10000000000000000000000000000000 deg: 5 c5: 61 c0: -43 skew: 0.93 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, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8018085 Max relations in full relation-set: Initial matrix: Pruned matrix : 546740 x 546988 Total sieving time: 11.04 hours. Total relation processing time: 0.43 hours. Matrix solve time: 0.66 hours. Time per square root: 0.20 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: 12.33 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵⁴+41)/9 = 7(4)₁₅₃9_<155> = 11800182871_<11> · 524297866455971_<15> · C131
C131 = P59 · P72
P59 = 13258140745590103120897332331500375538360937115782994093187_<59>
P72 = 907575659674699981238661788307594336802623003262472252087994176094758447_<72>

Number: 74449_154 N=12032765833238956496135533051537246750802755299151411853583075126019010073293713788119609205211450801525502233723112988192573400589 ( 131 digits) SNFS difficulty: 156 digits. Divisors found: r1=13258140745590103120897332331500375538360937115782994093187 r2=907575659674699981238661788307594336802623003262472252087994176094758447 Version: Total time: 14.37 hours. Scaled time: 34.37 units (timescale=2.392). Factorization parameters were as follows: n: 12032765833238956496135533051537246750802755299151411853583075126019010073293713788119609205211450801525502233723112988192573400589 m: 10000000000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8669259 Max relations in full relation-set: Initial matrix: Pruned matrix : 493382 x 493630 Total sieving time: 13.16 hours. Total relation processing time: 0.56 hours. Matrix solve time: 0.53 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 14.37 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 10, 2009 (4th): By Erik Branger / GGNFS, Msieve / Nov 10, 2009
(22·10¹⁶¹-7)/3 = 7(3)₁₆₀1_<162> = 8988583 · 1473843083_<10> · 43685008931_<11> · 792899578558552316971997_<24> · C112
C112 = P47 · P65
P47 = 97195054545007868780229153979999042837726017679_<47>
P65 = 16442360346075195163255521245258464415073491367475255299473133943_<65>

Number: 73331_161 N=1598116110685453051884152389093381063570392044919000755814313712121566721546816342185364254479151650919152978297 ( 112 digits) Divisors found: r1=97195054545007868780229153979999042837726017679 (pp47) r2=16442360346075195163255521245258464415073491367475255299473133943 (pp65) Version: Msieve v. 1.43 Total time: 22.37 hours. Scaled time: 21.93 units (timescale=0.980). Factorization parameters were as follows: name: 73331_161 n: 1598116110685453051884152389093381063570392044919000755814313712121566721546816342185364254479151650919152978297 skew: 18801.73 # norm 1.08e+016 c5: 41040 c4: -11257294188 c3: -442650124089326 c2: 2964052129907482063 c1: -8608213059353517719384 c0: 16835718387366714053310855 # alpha -6.76 Y1: 655947863939 Y0: -2080116740162367855658 # Murphy_E 8.38e-010 # M 1271251820443806534114929805329990668883291174007574987231604085600016271988485379380744146412786916036972965427 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2550001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 439313 x 439538 Polynomial selection time: 1.84 hours. Total sieving time: 19.64 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.46 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 22.37 hours. --------- CPU info (if available) ----------
Nov 10, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 10, 2009
(83·10¹⁸⁹+7)/9 = 9(2)₁₈₈3_<190> = 19 · C189
C189 = P34 · C155
P34 = 5990378735789383269628097762672663_<34>
C155 = [81026615906465431938041626994478818515681338940598425649469860858583139654675179162239812855902595745749467893554470062276252107338980178289378117466811059_<155>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3355232220 Step 1 took 69614ms ********** Factor found in step 1: 5990378735789383269628097762672663 Found probable prime factor of 34 digits: 5990378735789383269628097762672663 Composite cofactor 81026615906465431938041626994478818515681338940598425649469860858583139654675179162239812855902595745749467893554470062276252107338980178289378117466811059 has 155 digits
(22·10¹⁹²+17)/3 = 7(3)₁₉₁9_<193> = 13 · 19 · 47 · C189
C189 = P34 · C156
P34 = 1065586090211622938492027332760513_<34>
C156 = [592813482260539816573285099951893028539801844453071033975475976700379685000061841730286610971791510396786665189169314447668289344543691705287196946935621267_<156>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=485063552 Step 1 took 69609ms Step 2 took 21858ms ********** Factor found in step 2: 1065586090211622938492027332760513 Found probable prime factor of 34 digits: 1065586090211622938492027332760513 Composite cofactor 592813482260539816573285099951893028539801844453071033975475976700379685000061841730286610971791510396786665189169314447668289344543691705287196946935621267 has 156 digits
Nov 10, 2009 (2nd): By Serge Batalov / GMP-ECM / Nov 10, 2009
(62·10¹⁹⁸-71)/9 = 6(8)₁₉₇1_<199> = 18090491 · 96259713961_<11> · 292004497230977_<15> · C167
C167 = P29 · C138
P29 = 20703814083710017434203941181_<29>
C138 = [654356407770923648465491093265011628500438838155395019040655717408451346641013314886383730589549523068829008515207175565727024831982591463_<138>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=4244008742 Step 1 took 7041ms Step 2 took 3980ms ********** Factor found in step 2: 20703814083710017434203941181 Found probable prime factor of 29 digits: 20703814083710017434203941181 Composite cofactor has 138 digits
Nov 10, 2009: Factorizations of 688...881 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Nov 9, 2009 (5th): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 9, 2009
(59·10¹⁶⁸+31)/9 = 6(5)₁₆₇9_<169> = 200353029081433643431_<21> · C149
C149 = P36 · P114
P36 = 163345949950143193676363320218134933_<36>
P114 = 200311193457135555149111399446648559579409439169411343631410357357163826821990473660434904444886971998129104305533_<114>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2903774802 Step 1 took 47356ms Step 2 took 16435ms ********** Factor found in step 2: 163345949950143193676363320218134933 Found probable prime factor of 36 digits: 163345949950143193676363320218134933 Probable prime cofactor 200311193457135555149111399446648559579409439169411343631410357357163826821990473660434904444886971998129104305533 has 114 digits
Nov 9, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 9, 2009
(64·10¹⁵³+71)/9 = 7(1)₁₅₂9_<154> = 3 · 7² · 107 · 5851141 · 28626107 · 28548860107_<11> · C125
C125 = P61 · P65
P61 = 5614634034614379921533744369479856200331498912590870991988599_<61>
P65 = 16839270432055405826800110526516344410089090140539090333981785021_<65>

Number: 71119_153 N=94546340885893875775565511755890916652169251907705803092120211847812361089925446153997345174676984566004539608391284500975579 ( 125 digits) SNFS difficulty: 156 digits. Divisors found: r1=5614634034614379921533744369479856200331498912590870991988599 r2=16839270432055405826800110526516344410089090140539090333981785021 Version: Total time: 12.25 hours. Scaled time: 29.09 units (timescale=2.374). Factorization parameters were as follows: n: 94546340885893875775565511755890916652169251907705803092120211847812361089925446153997345174676984566004539608391284500975579 m: 20000000000000000000000000000000 deg: 5 c5: 1 c0: 3550 skew: 5.13 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8225922 Max relations in full relation-set: Initial matrix: Pruned matrix : 512102 x 512350 Total sieving time: 11.13 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.59 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 12.25 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(59·10¹⁵²+13)/9 = 6(5)₁₅₁7_<153> = 3 · 1489 · 22639 · 11683159 · 1328096507_<10> · 5450109209_<10> · C119
C119 = P56 · P64
P56 = 59178572867084914379468698280517827432559633138291908257_<56>
P64 = 1295318881695982523785877985646207549117537913160065454433420981_<64>

Number: 65557_152 N=76655122826556645524074443634510586228441763475339929480344042662902252605878456624030665388478094256481641219110940117 ( 119 digits) SNFS difficulty: 153 digits. Divisors found: r1=59178572867084914379468698280517827432559633138291908257 r2=1295318881695982523785877985646207549117537913160065454433420981 Version: Total time: 13.11 hours. Scaled time: 30.41 units (timescale=2.319). Factorization parameters were as follows: n: 76655122826556645524074443634510586228441763475339929480344042662902252605878456624030665388478094256481641219110940117 m: 1000000000000000000000000000000 deg: 5 c5: 5900 c0: 13 skew: 0.29 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved rational special-q in [1200000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8453288 Max relations in full relation-set: Initial matrix: Pruned matrix : 459884 x 460132 Total sieving time: 11.78 hours. Total relation processing time: 0.50 hours. Matrix solve time: 0.46 hours. Time per square root: 0.38 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 13.11 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(22·10¹⁶⁷-7)/3 = 7(3)₁₆₆1_<168> = 673 · 554010851 · 558911987 · 5945695037_<10> · 109820016330048359322910570503010931_<36> · C103
C103 = P52 · P52
P52 = 1401391479136958593688939741110720276274288575652677_<52>
P52 = 3845750104092990927871071735575755688207468194738649_<52>

Number: 73331_167 N=5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373 ( 103 digits) Divisors found: r1=1401391479136958593688939741110720276274288575652677 r2=3845750104092990927871071735575755688207468194738649 Version: Total time: 3.55 hours. Scaled time: 8.49 units (timescale=2.390). Factorization parameters were as follows: name: 73331_167 n: 5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373 skew: 4097.75 # norm 1.64e+14 c5: 40320 c4: -1958361504 c3: -17221716378444 c2: 27188414562676651 c1: 33121214055673416898 c0: -33012256189229942644761 # alpha -5.50 Y1: 45693702307 Y0: -42189907306613412250 # Murphy_E 2.46e-09 # M 1997110600840141969487185735223388600956316936391544059751688593970011381357450945414187330994898656216 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1350001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4676874 Max relations in full relation-set: Initial matrix: Pruned matrix : 262876 x 263124 Polynomial selection time: 0.25 hours. Total sieving time: 2.82 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.15 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.55 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(65·10¹⁵³-11)/9 = 7(2)₁₅₂1_<154> = 3 · 19 · 3191 · 30851 · 1993529 · C138
C138 = P46 · P92
P46 = 8594630348195199186618987496491138043989264641_<46>
P92 = 75119066309768402960586373080898748135184106551828886169635340771025166138551902760422135897_<92>

Number: 72221_153 N=645620607034023065579793268856604425328117343665574488428740228244719430439959533731717952309961769144984088201555673934488542847598917977 ( 138 digits) SNFS difficulty: 156 digits. Divisors found: r1=8594630348195199186618987496491138043989264641 r2=75119066309768402960586373080898748135184106551828886169635340771025166138551902760422135897 Version: Total time: 9.93 hours. Scaled time: 23.68 units (timescale=2.385). Factorization parameters were as follows: n: 645620607034023065579793268856604425328117343665574488428740228244719430439959533731717952309961769144984088201555673934488542847598917977 m: 10000000000000000000000000000000 deg: 5 c5: 13 c0: -220 skew: 1.76 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved rational special-q in [1200000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8428433 Max relations in full relation-set: Initial matrix: Pruned matrix : 394554 x 394802 Total sieving time: 9.12 hours. Total relation processing time: 0.39 hours. Matrix solve time: 0.34 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 9.93 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵³-13)/9 = 7(4)₁₅₂3_<154> = 3 · 73 · 599 · 6375191 · C142
C142 = P69 · P74
P69 = 630815937238830387707045431729321900960152842180793375602167922900551_<69>
P74 = 14111250397994772249206335757054905306524045262423288625705324246219742983_<74>

Number: 74443_153 N=8901601645422890581068982807068783308967792576347016429003625587988536935014749786660720721784929209055910888848171892379052067704627089083633 ( 142 digits) SNFS difficulty: 156 digits. Divisors found: r1=630815937238830387707045431729321900960152842180793375602167922900551 r2=14111250397994772249206335757054905306524045262423288625705324246219742983 Version: Total time: 12.11 hours. Scaled time: 28.63 units (timescale=2.364). Factorization parameters were as follows: n: 8901601645422890581068982807068783308967792576347016429003625587988536935014749786660720721784929209055910888848171892379052067704627089083633 m: 10000000000000000000000000000000 deg: 5 c5: 67 c0: -1300 skew: 1.81 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, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8501534 Max relations in full relation-set: Initial matrix: Pruned matrix : 447986 x 448234 Total sieving time: 11.02 hours. Total relation processing time: 0.47 hours. Matrix solve time: 0.42 hours. Time per square root: 0.20 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: 12.11 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(22·10¹⁵⁴-7)/3 = 7(3)₁₅₃1_<155> = 29 · 9311791740963623557_<19> · C135
C135 = P38 · P97
P38 = 65155738369339103941331630969006793233_<38>
P97 = 4167902040813106094398057851557338570627756214904008442532444406520855216370513619157114999436019_<97>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 271562734920253252721963146431377932001653050860753475858443777890484893804596955592971171231575888296804819144102887980271374745659427 (135 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2666678006 Step 1 took 3359ms Step 2 took 2155ms ********** Factor found in step 2: 65155738369339103941331630969006793233 Found probable prime factor of 38 digits: 65155738369339103941331630969006793233 Probable prime cofactor 4167902040813106094398057851557338570627756214904008442532444406520855216370513619157114999436019 has 97 digits
Nov 9, 2009 (3rd): By Erik Branger / GGNFS, Msieve / Nov 9, 2009
(59·10¹⁵⁵+13)/9 = 6(5)₁₅₄7_<156> = 3² · 7² · 31² · C151
C151 = P37 · P114
P37 = 3250014503184800505033627409506459859_<37>
P114 = 475950980723268548624810965719672919720034989274501070593621650713069860521169953430677781461307623085322624985823_<114>

Number: 65557_155 N=1546847590155652194203306635792637477390462871856261678371583728107190770091518320050107374818736991077311180378421843165909366791384530842436793578957 ( 151 digits) SNFS difficulty: 156 digits. Divisors found: r1=3250014503184800505033627409506459859 (pp37) r2=475950980723268548624810965719672919720034989274501070593621650713069860521169953430677781461307623085322624985823 (pp114) Version: Msieve v. 1.43 Total time: 19.02 hours. Scaled time: 19.44 units (timescale=1.022). Factorization parameters were as follows: n: 1546847590155652194203306635792637477390462871856261678371583728107190770091518320050107374818736991077311180378421843165909366791384530842436793578957 m: 10000000000000000000000000000000 deg: 5 c5: 59 c0: 13 skew: 0.74 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, 2250001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 456331 x 456559 Total sieving time: 18.33 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.47 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4,100000 total time: 19.02 hours. --------- CPU info (if available) ----------
Nov 9, 2009 (2nd): By Dmitry Domanov / GGNFS/msieve / Nov 9, 2009
(26·10¹⁸⁸-11)/3 = 8(6)₁₈₇3_<189> = C189
C189 = P62 · P128
P62 = 10259291107232450345127225587209152871731029421866962805442781_<62>
P128 = 84476272055063943325183359642649984717306070885700898533399372021753856257495399877737223250194400158255639618255431995131856723_<128>

N=866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 189 digits) SNFS difficulty: 190 digits. Divisors found: r1=10259291107232450345127225587209152871731029421866962805442781 (pp62) r2=84476272055063943325183359642649984717306070885700898533399372021753856257495399877737223250194400158255639618255431995131856723 (pp128) Version: Msieve-1.40 Total time: 356.05 hours. Scaled time: 660.47 units (timescale=1.855). Factorization parameters were as follows: n: 866666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 50000000000000000000000000000000000000 deg: 5 c5: 208 c0: -275 skew: 1.06 type: snfs lss: 1 rlim: 10600000 alim: 10600000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 10600000/10600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5300000, 10600001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1915479 x 1915705 Total sieving time: 349.52 hours. Total relation processing time: 1.02 hours. Matrix solve time: 4.72 hours. Time per square root: 0.79 hours. Prototype def-par.txt line would be: snfs,190.000,5,0,0,0,0,0,0,0,0,10600000,10600000,28,28,54,54,2.5,2.5,100000 total time: 356.05 hours. --------- CPU info (if available) ----------
Nov 9, 2009: By Robert Backstrom / GGNFS, Msieve / Nov 9, 2009
(59·10¹⁷³+31)/9 = 6(5)₁₇₂9_<174> = 17 · C173
C173 = P64 · P109
P64 = 4177250313399903945138253417266710121030087934303335833373800887_<64>
P109 = 9231453374859386654199536787033338094395429597865246821904001952487028953910042143288170856206510706346989121_<109>

Number: n N=38562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150327 ( 173 digits) SNFS difficulty: 176 digits. Divisors found: Mon Nov 09 17:57:11 2009 prp64 factor: 4177250313399903945138253417266710121030087934303335833373800887 Mon Nov 09 17:57:11 2009 prp109 factor: 9231453374859386654199536787033338094395429597865246821904001952487028953910042143288170856206510706346989121 Mon Nov 09 17:57:11 2009 elapsed time 03:30:32 (Msieve 1.43 - dependency 3) Version: GGNFS-0.77.1-20051202-athlon Total time: 116.60 hours. Scaled time: 212.56 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_5_172_9 n: 38562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150326797385620915032679738562091503267973856209150327 m: 50000000000000000000000000000000000 deg: 5 c5: 472 c0: 775 skew: 1.10 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [3000000, 8200000) Primes: RFBsize:412849, AFBsize:412487, largePrimes:21228147 encountered Relations: rels:21095842, finalFF:563665 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3202566 hash collisions in 24388453 relations Msieve: matrix is 1106425 x 1106655 (295.8 MB) Total sieving time: 115.54 hours. Total relation processing time: 1.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,56,56,2.5,2.5,100000 total time: 116.60 hours. --------- CPU info (if available) ----------
Nov 8, 2009 (5th): By Erik Branger / GGNFS, Msieve / Nov 8, 2009
(67·10¹⁵³-31)/9 = 7(4)₁₅₂1_<154> = 7 · 29 · 107 · 1873 · 9283 · 3851031073116400940153_<22> · C121
C121 = P37 · P84
P37 = 6384161033655476762880992360445318917_<37>
P84 = 801762046385247037048308402141985803146797607769907046767693665075239890836475568119_<84>

Number: 74441_153 N=5118578014796569030767959609696286789242595413285599606741445460908841782819618432069526246322988087219996094931712807123 ( 121 digits) SNFS difficulty: 156 digits. Divisors found: r1=6384161033655476762880992360445318917 (pp37) r2=801762046385247037048308402141985803146797607769907046767693665075239890836475568119 (pp84) Version: Msieve-1.40 Total time: 26.48 hours. Scaled time: 26.27 units (timescale=0.992). Factorization parameters were as follows: n: 5118578014796569030767959609696286789242595413285599606741445460908841782819618432069526246322988087219996094931712807123 m: 5000000000000000000000000000000 deg: 5 c5: 536 c0: -775 skew: 1.08 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 517516 x 517745 Total sieving time: 25.51 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.63 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,156.000,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 26.48 hours. --------- CPU info (if available) ----------
Nov 8, 2009 (4th): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 8, 2009
(22·10¹⁶⁷-7)/3 = 7(3)₁₆₆1_<168> = 673 · 554010851 · 558911987 · 5945695037_<10> · C138
C138 = P36 · C103
P36 = 109820016330048359322910570503010931_<36>
C103 = [5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373_<103>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4116852324 Step 1 took 42504ms Step 2 took 14782ms ********** Factor found in step 2: 109820016330048359322910570503010931 Found probable prime factor of 36 digits: 109820016330048359322910570503010931 Composite cofactor 5389401426765989035878493200566942374516146102706060431089988040720698547959542215951996250572612213373 has 103 digits
Nov 8, 2009 (3rd): By shyguy7129 / GGNFS and Msieve v1.40 / Nov 8, 2009
(65·10¹⁷⁰+61)/9 = 7(2)₁₆₉9_<171> = 3 · 79 · 2293 · 140130990851_<12> · 3757774694852316444096913_<25> · 10144116873340791964390133_<26> · C105
C105 = P38 · P68
P38 = 21971222154598869664832900623562106017_<38>
P68 = 11323613996205652033225521245915447835096235974204481742262021487883_<68>

Yes! My first submitted factors! :D Number: 72229_170 N=248793638703559462811024537742910133006111369698373954144678461344908746356065631383501263120031326892011 ( 105 digits) Divisors found: r1=21971222154598869664832900623562106017 (pp38) r2=11323613996205652033225521245915447835096235974204481742262021487883 (pp68) Version: Msieve-1.40 Total time: 21.65 hours. Scaled time: 38.56 units (timescale=1.781). Factorization parameters were as follows: name: 72229_170 n: 248793638703559462811024537742910133006111369698373954144678461344908746356065631383501263120031326892011 skew: 60992.32 # norm 3.41e+014 c5: 960 c4: 182155542 c3: -5698389781438 c2: -468425103552598334 c1: 10463967835739232401989 c0: -997954568530928284717567 # alpha -5.04 Y1: 30184793243 Y0: -191739245141787164928 # Murphy_E 1.68e-009 # M 14245238078513029591920117460774843530496924943504703352168798349066508904664795693381848673546224366040 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: 2 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 282011 x 282259 Total sieving time: 21.07 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.41 hours. Time per square root: 0.07 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: 21.65 hours. --------- CPU info (if available) ----------
Nov 8, 2009 (2nd): By Sinkiti Sibata / Msieve / Nov 8, 2009
(67·10¹⁸¹+41)/9 = 7(4)₁₈₀9_<182> = 53 · 911 · 42131 · 4676297 · 8281979 · 141991566527749086929197_<24> · 165108482396811425155660189_<27> · C110
C110 = P48 · P63
P48 = 121710843248256603777008924948983385611121242357_<48>
P63 = 331160752353019654210539187583083132861767802689536904567422471_<63>

Number: 74449_181 N=40305854419613099392933000322931607765920560992330095901788930477410295183773700750837580338887703146798804147 ( 110 digits) Divisors found: r1=121710843248256603777008924948983385611121242357 (pp48) r2=331160752353019654210539187583083132861767802689536904567422471 (pp63) Version: Msieve-1.40 Total time: 21.25 hours. Scaled time: 44.16 units (timescale=2.078). Factorization parameters were as follows: name: 74449_181 n: 40305854419613099392933000322931607765920560992330095901788930477410295183773700750837580338887703146798804147 skew: 33186.82 # norm 1.64e+15 c5: 30600 c4: 1047455254 c3: -78351538124717 c2: 129431081918751312 c1: 48327712299484053859320 c0: -514868110317796072713683808 # alpha -6.04 Y1: 654077347 Y0: -1056645576467103752827 # Murphy_E 9.67e-10 # M 15796330503120420793036355885019577620524107447618867199386924482341371764583299519964820756277157127611672118 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 394960 x 395208 Polynomial selection time: 1.51 hours. Total sieving time: 18.66 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.54 hours. Time per square root: 0.41 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 21.25 hours. --------- CPU info (if available) ----------
Nov 8, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 8, 2009
(65·10¹⁵¹-11)/9 = 7(2)₁₅₀1_<152> = 2632819547_<10> · 359828389017095641457_<21> · C122
C122 = P46 · P77
P46 = 4707966628617424628297466037653799757180336867_<46>
P77 = 16192762768567533085113383462849628534669727951104188819800098462441995657197_<77>

Number: 72221_151 N=76234986739534643662491549126650708645656218262843499744778693818048201701410833734282766803893429828567760567175512981799 ( 122 digits) SNFS difficulty: 152 digits. Divisors found: r1=4707966628617424628297466037653799757180336867 r2=16192762768567533085113383462849628534669727951104188819800098462441995657197 Version: Total time: 7.84 hours. Scaled time: 18.42 units (timescale=2.350). Factorization parameters were as follows: n: 76234986739534643662491549126650708645656218262843499744778693818048201701410833734282766803893429828567760567175512981799 m: 1000000000000000000000000000000 deg: 5 c5: 650 c0: -11 skew: 0.44 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1100000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7347944 Max relations in full relation-set: Initial matrix: Pruned matrix : 453651 x 453899 Total sieving time: 7.07 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.44 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000 total time: 7.84 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵¹-31)/9 = 7(4)₁₅₀1_<152> = 1193 · 6254113478800077538215938702699113_<34> · C115
C115 = P55 · P61
P55 = 8228829892112628636884835633777315487804386047416617137_<55>
P61 = 1212517479021868655624024510948004899355487100786836051889177_<61>

Number: 74441_151 N=9977600076084199905958097161900099571496695646133438177125099495316432470281666399300303712370663052339771363026249 ( 115 digits) SNFS difficulty: 152 digits. Divisors found: r1=8228829892112628636884835633777315487804386047416617137 r2=1212517479021868655624024510948004899355487100786836051889177 Version: Total time: 9.71 hours. Scaled time: 23.17 units (timescale=2.387). Factorization parameters were as follows: n: 9977600076084199905958097161900099571496695646133438177125099495316432470281666399300303712370663052339771363026249 m: 1000000000000000000000000000000 deg: 5 c5: 670 c0: -31 skew: 0.54 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1100000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7894010 Max relations in full relation-set: Initial matrix: Pruned matrix : 428637 x 428885 Total sieving time: 8.86 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.38 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2200000,2200000,27,27,50,50,2.4,2.4,100000 total time: 9.71 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(59·10¹⁵⁵+31)/9 = 6(5)₁₅₄9_<156> = 23 · 31674983 · C147
C147 = P35 · P113
P35 = 82384832793625986764249254072567903_<35>
P113 = 10922398337410720857723866317273548007359511055401276844847935368467831986721558208027076999570364927664168943417_<113>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 899839960732960711222255438670508322602943884295822813523593072688578946213134106435594072781082341661234885691494267087353195443745889379497344551 (147 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3405593309 Step 1 took 4664ms Step 2 took 4649ms ********** Factor found in step 2: 82384832793625986764249254072567903 Found probable prime factor of 35 digits: 82384832793625986764249254072567903 Probable prime cofactor 10922398337410720857723866317273548007359511055401276844847935368467831986721558208027076999570364927664168943417 has 113 digits
(65·10¹⁵²+7)/9 = 7(2)₁₅₁3_<153> = 3 · 241 · 27347519063_<11> · 1725333177913_<13> · C128
C128 = P38 · P91
P38 = 10514619222825497091683354104111810879_<38>
P91 = 2013483581578352610412684711209758302904144260026256812619717594875763736046702067763469301_<91>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 21171013171707276297284205554612886487286809273598944016623603709651069407896630669000876694960644238838461982364112370634325579 (128 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6792566349 Step 1 took 4196ms Step 2 took 5756ms ********** Factor found in step 2: 10514619222825497091683354104111810879 Found probable prime factor of 38 digits: 10514619222825497091683354104111810879 Probable prime cofactor 2013483581578352610412684711209758302904144260026256812619717594875763736046702067763469301 has 91 digits
Nov 7, 2009 (6th): By Dmitry Domanov / GGNFS/msieve / Nov 7, 2009
(65·10¹⁵⁵+7)/9 = 7(2)₁₅₄3_<156> = 3 · 9007 · 1081789 · 8911250809018619_<16> · 142782376236086436331_<21> · C110
C110 = P52 · P58
P52 = 7392507812931635296203627398671630725771305605141003_<52>
P58 = 2626768526217301127090637292882797495139799918052500317901_<58>

N=19418406852824315665554762157458974239206989197334760372678432542908053342430535858752210495531479837429994703 ( 110 digits) Divisors found: r1=7392507812931635296203627398671630725771305605141003 (pp52) r2=2626768526217301127090637292882797495139799918052500317901 (pp58) Version: Msieve-1.40 Total time: 15.75 hours. Scaled time: 31.01 units (timescale=1.969). Factorization parameters were as follows: name: g110 n: 19418406852824315665554762157458974239206989197334760372678432542908053342430535858752210495531479837429994703 skew: 29767.14 # norm 3.00e+015 c5: 16560 c4: 3825657986 c3: 19567041570883 c2: -2418931829640980736 c1: 30620557498708644779402 c0: -74115411399096749338291340 # alpha -6.43 Y1: 203416736417 Y0: -1032349374499642407141 # Murphy_E 1.04e-009 # M 4165853837495179387505368821618801681724638475605636957434987794044042429718757847059943296685210951731399213 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 391563 x 391788 Polynomial selection time: 1.42 hours. Total sieving time: 13.33 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.44 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 15.75 hours. --------- CPU info (if available) ----------
Nov 7, 2009 (5th): By Sinkiti Sibata / Msieve / Nov 7, 2009
(62·10¹⁵⁰-17)/9 = 6(8)₁₄₉7_<151> = 19 · 96457 · 54014052471186550121_<20> · C125
C125 = P61 · P64
P61 = 7152115416516333263116824921083071837423457619295848531485227_<61>
P64 = 9730172787565460411900025374086137070224048862984493336589028567_<64>

Number: 68887_150 N=69591318799314634387182087997398280009882822525775350033620638088104875270633081216732421635499310384553331373497069641479709 ( 125 digits) SNFS difficulty: 151 digits. Divisors found: r1=7152115416516333263116824921083071837423457619295848531485227 (pp61) r2=9730172787565460411900025374086137070224048862984493336589028567 (pp64) Version: Msieve-1.40 Total time: 17.64 hours. Scaled time: 36.65 units (timescale=2.078). Factorization parameters were as follows: name: 68887_150 n: 69591318799314634387182087997398280009882822525775350033620638088104875270633081216732421635499310384553331373497069641479709 m: 1000000000000000000000000000000 deg: 5 c5: 62 c0: -17 skew: 0.77 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, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 407535 x 407783 Total sieving time: 16.87 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.57 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 17.64 hours. --------- CPU info (if available) ----------
(83·10¹⁹⁰+7)/9 = 9(2)₁₈₉3_<191> = 3 · C191
C191 = P86 · P105
P86 = 31409756452905266401572874729021762403039657905422482493898473135389505774302363727127_<86>
P105 = 978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683_<105>

Number: 92223_190 N=30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741 ( 191 digits) SNFS difficulty: 191 digits. Divisors found: r1=31409756452905266401572874729021762403039657905422482493898473135389505774302363727127 (pp86) r2=978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683 (pp105) Version: Msieve v. 1.42 Total time: 12.72 hours. Scaled time: 13.02 units (timescale=1.024). Factorization parameters were as follows: name: 92223_190 n: 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741 m: 100000000000000000000000000000000000000 deg: 5 c5: 83 c0: 7 skew: 0.61 type: snfs lss: 1 rlim: 11100000 alim: 11100000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 11100000/11100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5550000, 10550001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2084496 x 2084721 Total sieving time: 0.00 hours. Total relation processing time: 0.21 hours. Matrix solve time: 11.53 hours. Time per square root: 0.98 hours. Prototype def-par.txt line would be: snfs,191.000,5,0,0,0,0,0,0,0,0,11100000,11100000,28,28,54,54,2.5,2.5,100000 total time: 12.72 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU1: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU2: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU3: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941) Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880) Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886) Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891) Total of 4 processors activated (19151.19 BogoMIPS). total time: 9 days 1 hour.
Nov 7, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 7, 2009
(67·10¹⁴⁹+41)/9 = 7(4)₁₄₈9_<150> = 29 · 967 · 10301 · 164117 · 63136961 · 75921228000284137_<17> · C112
C112 = P54 · P58
P54 = 658356174664422161569086775878853672793637262114046597_<54>
P58 = 4975847405368765597872979135265543799568390928601303262351_<58>

Number: 74449_149 N=3275879863512470866831524279102943957767823250262292240603618506109442210271627224143756567808563929798129769547 ( 112 digits) SNFS difficulty: 151 digits. Divisors found: r1=658356174664422161569086775878853672793637262114046597 r2=4975847405368765597872979135265543799568390928601303262351 Version: Total time: 9.16 hours. Scaled time: 21.88 units (timescale=2.390). Factorization parameters were as follows: n: 3275879863512470866831524279102943957767823250262292240603618506109442210271627224143756567808563929798129769547 m: 1000000000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 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, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7095270 Max relations in full relation-set: Initial matrix: Pruned matrix : 381891 x 382139 Total sieving time: 8.45 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.31 hours. Time per square root: 0.08 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: 9.16 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(26·10¹⁵⁵-11)/3 = 8(6)₁₅₄3_<156> = 7 · 1279 · 83773 · 865854809489_<12> · 1961948617039_<13> · 67938871020299_<14> · C110
C110 = P53 · P57
P53 = 50356743151076883375850389237566626845654858552124607_<53>
P57 = 198824902404933934450436748117874509387381569435016167809_<57>

Number: 86663_155 N=10012174542443186661944529159441458449529896878553572027502711511349648695308726206045539833575579812190176063 ( 110 digits) Divisors found: r1=50356743151076883375850389237566626845654858552124607 r2=198824902404933934450436748117874509387381569435016167809 Version: Total time: 9.20 hours. Scaled time: 21.96 units (timescale=2.387). Factorization parameters were as follows: name: 86663_155 n: 10012174542443186661944529159441458449529896878553572027502711511349648695308726206045539833575579812190176063 skew: 19361.44 # norm 7.28e+14 c5: 36960 c4: -373375372 c3: 24010419126067 c2: 188419687096119335 c1: -10703912390072075189035 c0: -9921381275227903704194995 # alpha -5.79 Y1: 308100795223 Y0: -770122196696138062932 # Murphy_E 1.05e-09 # M 6923705748279385336736257457255098262017080868569703732932894391890534226799406036569569582345272734642801167 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, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7841955 Max relations in full relation-set: Initial matrix: Pruned matrix : 402815 x 403063 Polynomial selection time: 0.80 hours. Total sieving time: 7.42 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.34 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 9.20 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(26·10¹⁵⁶-11)/3 = 8(6)₁₅₅3_<157> = 19 · 439 · 4201 · 22108555559_<11> · 18897188991137_<14> · 19562245823564779_<17> · C110
C110 = P54 · P56
P54 = 694703188931333880775047897831384327876136440996742187_<54>
P56 = 43561789316255219047093334112623127241673869427391777277_<56>

Number: 86663_156 N=30262513953557411191067054802305039488066876688632568417434093173819283820734068340557697961554591668893884799 ( 110 digits) Divisors found: r1=694703188931333880775047897831384327876136440996742187 r2=43561789316255219047093334112623127241673869427391777277 Version: Total time: 8.76 hours. Scaled time: 20.90 units (timescale=2.387). Factorization parameters were as follows: name: 86663_156 n: 30262513953557411191067054802305039488066876688632568417434093173819283820734068340557697961554591668893884799 skew: 46936.13 # norm 2.00e+15 c5: 4800 c4: -1514434876 c3: -32339594241746 c2: 4238527376382421943 c1: -26343690099191295496866 c0: -124555876330930538048212671 # alpha -6.41 Y1: 329728317391 Y0: -1445236780624805468530 # Murphy_E 1.08e-09 # M 26147608521632649352970030633720039196717174907616904289542536532064184713838448536232324936389216869986608630 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, 1650001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7866072 Max relations in full relation-set: Initial matrix: Pruned matrix : 385170 x 385418 Polynomial selection time: 0.66 hours. Total sieving time: 7.20 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.36 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 8.76 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(64·10¹⁵¹+17)/9 = 7(1)₁₅₀3_<152> = 29 · 283 · 134839 · 172147 · 757057201 · C129
C129 = P56 · P74
P56 = 13630504369805610897121892199912194495690789284130587631_<56>
P74 = 36174074472493502044830834515488572039115437822520724375951219171660917333_<74>

Number: 71113_151 N=493070880170996278534516753255530271753988214548501769867880630567332323531819123807127232541599603419990823093435241101803308123 ( 129 digits) SNFS difficulty: 152 digits. Divisors found: r1=13630504369805610897121892199912194495690789284130587631 r2=36174074472493502044830834515488572039115437822520724375951219171660917333 Version: Total time: 8.48 hours. Scaled time: 20.14 units (timescale=2.374). Factorization parameters were as follows: n: 493070880170996278534516753255530271753988214548501769867880630567332323531819123807127232541599603419990823093435241101803308123 m: 2000000000000000000000000000000 deg: 5 c5: 20 c0: 17 skew: 0.97 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved rational special-q in [1000000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7995257 Max relations in full relation-set: Initial matrix: Pruned matrix : 358493 x 358741 Total sieving time: 7.81 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.31 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,50,50,2.4,2.4,100000 total time: 8.48 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 7, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 7, 2009
(26·10¹⁶⁵-11)/3 = 8(6)₁₆₄3_<166> = 83 · 173 · 6255630651772921_<16> · 166231483601086409378491_<24> · C123
C123 = P41 · P83
P41 = 24162374121281115547743488148094071736559_<41>
P83 = 24021709649431187683343098336454103859214433857791311652928195887896967260267801493_<83>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=522846101 Step 1 took 34052ms Step 2 took 13550ms ********** Factor found in step 2: 24162374121281115547743488148094071736559 Found probable prime factor of 41 digits: 24162374121281115547743488148094071736559 Probable prime cofactor 24021709649431187683343098336454103859214433857791311652928195887896967260267801493 has 83 digits
Nov 7, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Nov 6, 2009
(67·10¹⁸⁴-31)/9 = 7(4)₁₈₃1_<185> = 317 · 809 · 3547 · 33564732315787_<14> · 114897340823411617_<18> · 60403131124295658838209997353451_<32> · C114
C114 = P48 · P67
P48 = 339804285505812771909306394351621065329986786223_<48>
P67 = 1033907895700441246559141545237427637530368994032326666507566286553_<67>

Number: 74441_184 N=351326333777306830594696036569012983844843250127802988338902578492097989153379793913822350569995529157766770559319 ( 114 digits) Divisors found: r1=339804285505812771909306394351621065329986786223 (pp48) r2=1033907895700441246559141545237427637530368994032326666507566286553 (pp67) Version: Msieve-1.40 Total time: 23.21 hours. Scaled time: 22.44 units (timescale=0.967). Factorization parameters were as follows: n: 351326333777306830594696036569012983844843250127802988338902578492097989153379793913822350569995529157766770559319 c5: 10800 c4: 1941725750 c3: 81144728246589 c2: -2951244695963751041 c1: 4701141700422248571895 c0: 240834821565109408055254255 Y1: 1235140464791 Y0:-7988311196055664378158 skew: 35675.38 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 525895 x 526143 Total sieving time: 22.16 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.61 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 23.21 hours. --------- CPU info (if available) ----------
Nov 7, 2009: By Erik Branger / PFGW / Nov 7, 2009
7·10¹⁴⁴³⁶+3 = 7(0)₁₄₄₃₅3_<14437> is PRP.
7·10²⁸³³⁸+3 = 7(0)₂₈₃₃₇3_<28339> is PRP.
7·10³²⁷⁹⁶+3 = 7(0)₃₂₇₉₅3_<32797> is PRP.
7·10³⁸⁰⁷⁹+3 = 7(0)₃₈₀₇₈3_<38080> is PRP.
7·10⁵⁶⁷⁷⁹+3 = 7(0)₅₆₇₇₈3_<56780> is PRP.
7·10⁹¹²¹⁵+3 = 7(0)₉₁₂₁₄3_<91216> is PRP.
PRP91216 is the second largest unprovable quasi-repdigit PRP in our tables so far. Congratulations!
Nov 6, 2009 (8th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 6, 2009
(64·10¹⁷⁶+17)/9 = 7(1)₁₇₅3_<177> = 18122431 · 827630411 · 618217711189847_<15> · 51198705749027445793243239875789577253_<38> · C109
C109 = P53 · P56
P53 = 27199328739913350726751375837743051073898498013179701_<53>
P56 = 55071379802039998793236341692499167334341927807025765323_<56>

Number: 71113_176 N=1497904563396310154769792820729281585688689422098966010957032096218297475296578253879252017930370140253308423 ( 109 digits) Divisors found: r1=27199328739913350726751375837743051073898498013179701 r2=55071379802039998793236341692499167334341927807025765323 Version: Total time: 7.39 hours. Scaled time: 17.62 units (timescale=2.385). Factorization parameters were as follows: name: 71113_176 n: 1497904563396310154769792820729281585688689422098966010957032096218297475296578253879252017930370140253308423 skew: 37228.70 # norm 1.29e+15 c5: 6720 c4: 1929577034 c3: -28048451333417 c2: -2581066827369582849 c1: 23728062558893855083337 c0: 189889730972645309855811835 # alpha -6.65 Y1: 294450677543 Y0: -740650055075990989806 # Murphy_E 1.28e-09 # M 406037342834116125047075340806279652058520344301271931613697935723559786272925786257733844006528099117428762 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, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8123905 Max relations in full relation-set: Initial matrix: Pruned matrix : 371166 x 371414 Polynomial selection time: 0.58 hours. Total sieving time: 5.59 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.30 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 7.39 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁴⁷-31)/9 = 7(4)₁₄₆1_<148> = 7² · 173 · 1007857 · C138
C138 = P49 · P90
P49 = 3543243945117669927050599146096106098149924350703_<49>
P90 = 245917899090014024113532245535836223215750238360235398952104060053448988922276779413690323_<90>

Number: 74441_147 N=871347106946750342151715673907223653960159603609685187432378536350270402789209264962140023280103965088548237737624848609941132704889347069 ( 138 digits) SNFS difficulty: 148 digits. Divisors found: r1=3543243945117669927050599146096106098149924350703 r2=245917899090014024113532245535836223215750238360235398952104060053448988922276779413690323 Version: Total time: 8.99 hours. Scaled time: 21.45 units (timescale=2.385). Factorization parameters were as follows: n: 871347106946750342151715673907223653960159603609685187432378536350270402789209264962140023280103965088548237737624848609941132704889347069 m: 100000000000000000000000000000 deg: 5 c5: 6700 c0: -31 skew: 0.34 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1650000, 3375001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7066652 Max relations in full relation-set: Initial matrix: Pruned matrix : 456862 x 457110 Total sieving time: 7.75 hours. Total relation processing time: 0.74 hours. Matrix solve time: 0.44 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,49,49,2.3,2.3,75000 total time: 8.99 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁴⁷-13)/9 = 7(4)₁₄₆3_<148> = 3⁴ · 23 · 15032488729_<11> · 8212675315501962911_<19> · C116
C116 = P50 · P66
P50 = 35712120107599973268429717906238004919995676811669_<50>
P66 = 906333983462578850099373864796225485410057952884119428606963987551_<66>

Number: 74443_147 N=32367108075015143797053757675227277037681912296576239310580627885454876717201364888999929590596992736623682287532619 ( 116 digits) SNFS difficulty: 148 digits. Divisors found: r1=35712120107599973268429717906238004919995676811669 r2=906333983462578850099373864796225485410057952884119428606963987551 Version: Total time: 8.34 hours. Scaled time: 19.90 units (timescale=2.385). Factorization parameters were as follows: n: 32367108075015143797053757675227277037681912296576239310580627885454876717201364888999929590596992736623682287532619 m: 100000000000000000000000000000 deg: 5 c5: 6700 c0: -13 skew: 0.29 type: snfs lss: 1 rlim: 3150000 alim: 3150000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 3150000/3150000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1575000, 3150001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7259667 Max relations in full relation-set: Initial matrix: Pruned matrix : 442603 x 442851 Total sieving time: 7.15 hours. Total relation processing time: 0.71 hours. Matrix solve time: 0.43 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,3150000,3150000,27,27,49,49,2.4,2.4,75000 total time: 8.34 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁴⁹-31)/9 = 7(4)₁₄₈1_<150> = 3 · 127 · 1753489837597_<13> · C136
C136 = P44 · P92
P44 = 20881086487350036134625000283626100896654287_<44>
P92 = 53364319064384742665900100125286466593148958555660756921564191235935418790516441550676542399_<92>

Number: 74441_149 N=1114304961721960173022091383380176976662874322011077839586378960447874153953371814034523514291547521078222901018637342512063392400614513 ( 136 digits) SNFS difficulty: 151 digits. Divisors found: r1=20881086487350036134625000283626100896654287 r2=53364319064384742665900100125286466593148958555660756921564191235935418790516441550676542399 Version: Total time: 10.05 hours. Scaled time: 23.97 units (timescale=2.386). Factorization parameters were as follows: n: 1114304961721960173022091383380176976662874322011077839586378960447874153953371814034523514291547521078222901018637342512063392400614513 m: 1000000000000000000000000000000 deg: 5 c5: 67 c0: -310 skew: 1.36 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, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7412479 Max relations in full relation-set: Initial matrix: Pruned matrix : 371929 x 372177 Total sieving time: 9.35 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.30 hours. Time per square root: 0.04 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: 10.05 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 6, 2009 (7th): By Ignacio Santos / GGNFS, Msieve / Nov 6, 2009
5·10¹⁷⁴-7 = 4(9)₁₇₃3_<175> = 876443 · 26652181993_<11> · C159
C159 = P68 · P91
P68 = 46574391450747667692326738358784174396260537130314435096266571242987_<68>
P91 = 4595855531487340412820083355763538183249547281424390205839848914976852602041592456013124361_<91>

Number: 49993_174 N=214049174574575365805581376060199503058514198958035247503679069080324429338324460035489376300752092001338476663839616038201832417706699020583274339297180106307 ( 159 digits) SNFS difficulty: 175 digits. Divisors found: r1=46574391450747667692326738358784174396260537130314435096266571242987 (pp68) r2=4595855531487340412820083355763538183249547281424390205839848914976852602041592456013124361 (pp91) Version: Msieve v. 1.43 Total time: 56.13 hours. Scaled time: 97.62 units (timescale=1.739). Factorization parameters were as follows: n: 214049174574575365805581376060199503058514198958035247503679069080324429338324460035489376300752092001338476663839616038201832417706699020583274339297180106307 m: 100000000000000000000000000000000000 deg: 5 c5: 1 c0: -14 skew: 1.70 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 5500001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 995237 x 995463 Total sieving time: 54.41 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.30 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000 total time: 56.13 hours.
Nov 6, 2009 (6th): By Wataru Sakai / GMP-ECM 6.2.1 / Nov 6, 2009
(22·10¹⁵⁷-7)/3 = 7(3)₁₅₆1_<158> = 367 · 316304551 · 8534437607_<10> · 2443395325355902608359_<22> · C116
C116 = P38 · P79
P38 = 23693488595112602719126859782566256591_<38>
P79 = 1278592829499304611645554337323796642663523431026589589200118777890584774879621_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=236403890 Step 1 took 31182ms Step 2 took 13038ms ********** Factor found in step 2: 23693488595112602719126859782566256591 Found probable prime factor of 38 digits: 23693488595112602719126859782566256591 Probable prime cofactor 1278592829499304611645554337323796642663523431026589589200118777890584774879621 has 79 digits
(59·10¹⁶⁴+31)/9 = 6(5)₁₆₃9_<165> = 41 · 257 · 5763713135701_<13> · C149
C149 = P33 · C116
P33 = 632793202179705926119343697193231_<33>
C116 = [17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197_<116>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3331270017 Step 1 took 47229ms Step 2 took 16627ms ********** Factor found in step 2: 632793202179705926119343697193231 Found probable prime factor of 33 digits: 632793202179705926119343697193231 Composite cofactor 17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197 has 116 digits
(35·10¹⁹⁸+1)/9 = 3(8)₁₉₇9_<199> = 47 · C197
C197 = P82 · P116
P82 = 6326374989656440646106970407770659705730121493408302755378873328843303115001775919_<82>
P116 = 13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673_<116>

Number: 38889_198 N=82742316784869976359338061465721040189125295508274231678486997635933806146572104018912529550827423167848699763593380614657210401891252955082742316784869976359338061465721040189125295508274231678487 ( 197 digits) SNFS difficulty: 200 digits. Divisors found: r1=6326374989656440646106970407770659705730121493408302755378873328843303115001775919 r2=13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673 Version: Total time: 569.79 hours. Scaled time: 1133.32 units (timescale=1.989). Factorization parameters were as follows: n: 82742316784869976359338061465721040189125295508274231678486997635933806146572104018912529550827423167848699763593380614657210401891252955082742316784869976359338061465721040189125295508274231678487 m: 10000000000000000000000000000000000000000 deg: 5 c5: 7 c0: 20 skew: 1.23 type: snfs lss: 1 rlim: 15600000 alim: 15600000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 15600000/15600000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7800000, 13500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2705232 x 2705480 Total sieving time: 569.79 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,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000 total time: 569.79 hours. --------- CPU info (if available) ----------
(44·10¹⁹³-71)/9 = 4(8)₁₉₂1_<194> = 6203 · C190
C190 = P43 · P71 · P78
P43 = 1618166115802996840565371152078318243943573_<43>
P71 = 18615892194719893987578001772834971645694757182039038565591672722464263_<71>
P78 = 261638365738076548906793103513491078188631394698342571980380378304781956600273_<78>

Number: 48881_193 N=7881491034803947910509251795726082361581313701255664821681265337560678524728178121697386569222777509090583409461371737689648378024969996596628871334658856825550360936464434771705447185053827 ( 190 digits) SNFS difficulty: 194 digits. Divisors found: r1=1618166115802996840565371152078318243943573 r2=18615892194719893987578001772834971645694757182039038565591672722464263 r3=261638365738076548906793103513491078188631394698342571980380378304781956600273 Version: Total time: 653.71 hours. Scaled time: 1316.58 units (timescale=2.014). Factorization parameters were as follows: n: 7881491034803947910509251795726082361581313701255664821681265337560678524728178121697386569222777509090583409461371737689648378024969996596628871334658856825550360936464434771705447185053827 m: 200000000000000000000000000000000000000 deg: 5 c5: 1375 c0: -71 skew: 0.55 type: snfs lss: 1 rlim: 12300000 alim: 12300000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12300000/12300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6150000, 13250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2399210 x 2399457 Total sieving time: 653.71 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,194,5,0,0,0,0,0,0,0,0,12300000,12300000,28,28,55,55,2.5,2.5,100000 total time: 653.71 hours. --------- CPU info (if available) ----------
Nov 6, 2009 (5th): By Sinkiti Sibata / Msieve / Nov 6, 2009
(67·10¹⁴⁰+41)/9 = 7(4)₁₃₉9_<141> = 7 · 3371 · C137
C137 = P30 · P108
P30 = 191509589725032360358047867623_<30>
P108 = 164734656570897235288033852810835623477513274568840397755400314955254385028426104714427625363827448134452979_<108>

Number: 74449_140 N=31548266493386635777617682097065069476816732823852372947596916745537332900133256110710871909329340358708498726297599035658958530509998917 ( 137 digits) SNFS difficulty: 141 digits. Divisors found: r1=191509589725032360358047867623 (pp30) r2=164734656570897235288033852810835623477513274568840397755400314955254385028426104714427625363827448134452979 (pp108) Version: Msieve-1.40 Total time: 7.22 hours. Scaled time: 14.81 units (timescale=2.051). Factorization parameters were as follows: name: 74449_140 n: 31548266493386635777617682097065069476816732823852372947596916745537332900133256110710871909329340358708498726297599035658958530509998917 m: 10000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 1620000 alim: 1620000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1620000/1620000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [810000, 1710001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 239634 x 239869 Total sieving time: 6.92 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.19 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000 total time: 7.22 hours. --------- CPU info (if available) ----------
(67·10¹³¹-31)/9 = 7(4)₁₃₀1_<132> = 3 · 143834439524998271722493_<24> · C109
C109 = P42 · P67
P42 = 323849544307374500128746883591241254838333_<42>
P67 = 5327271893239009943943442287524260619878365564348217121263894689563_<67>

Number: 74441_131 N=1725234575026937588591813062917426515403728981243743236270453675510075150479189227318557947230693458787418479 ( 109 digits) SNFS difficulty: 134 digits. Divisors found: r1=323849544307374500128746883591241254838333 (pp42) r2=5327271893239009943943442287524260619878365564348217121263894689563 (pp67) Version: Msieve-1.40 Total time: 4.53 hours. Scaled time: 9.44 units (timescale=2.085). Factorization parameters were as follows: name: 74441_131 n: 1725234575026937588591813062917426515403728981243743236270453675510075150479189227318557947230693458787418479 m: 200000000000000000000000000 deg: 5 c5: 335 c0: -496 skew: 1.08 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [600000, 1200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 166901 x 167149 Total sieving time: 4.35 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,134.000,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000 total time: 4.53 hours. --------- CPU info (if available) ----------
(67·10¹⁴⁴+41)/9 = 7(4)₁₄₃9_<145> = 3 · 79 · 25803630551_<11> · 2084763626306649558391910071_<28> · C105
C105 = P42 · P64
P42 = 423626916383930124653960797887297047400541_<42>
P64 = 1378360327126022364048330167071772464929240931307881983759154457_<64>

Number: 74449_144 N=583910535046342049640391332785757616154332420151820936864626808268428880468476996626812295569863964361237 ( 105 digits) SNFS difficulty: 146 digits. Divisors found: r1=423626916383930124653960797887297047400541 (pp42) r2=1378360327126022364048330167071772464929240931307881983759154457 (pp64) Version: Msieve-1.40 Total time: 15.07 hours. Scaled time: 29.55 units (timescale=1.961). Factorization parameters were as follows: name: 74449_144 n: 583910535046342049640391332785757616154332420151820936864626808268428880468476996626812295569863964361237 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2480001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 353335 x 353583 Total sieving time: 15.07 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,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 15.07 hours. --------- CPU info (if available) ----------
(67·10¹³⁵+41)/9 = 7(4)₁₃₄9_<136> = 3 · 13 · 163 · 251 · 189043 · C125
C125 = P56 · P69
P56 = 71240130359442359976794234666514935013351341284492389997_<56>
P69 = 346434435442088830363099162339575704342482076530326806769161585968817_<69>

Number: 74449_135 N=24680034341894226799147907831007002424011323440141068996191301321234332937934131467895911287545293909501468601748729044723549 ( 125 digits) SNFS difficulty: 136 digits. Divisors found: r1=71240130359442359976794234666514935013351341284492389997 (pp56) r2=346434435442088830363099162339575704342482076530326806769161585968817 (pp69) Version: Msieve-1.40 Total time: 4.73 hours. Scaled time: 9.85 units (timescale=2.085). Factorization parameters were as follows: name: 74449_135 n: 24680034341894226799147907831007002424011323440141068996191301321234332937934131467895911287545293909501468601748729044723549 m: 1000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 1340000 alim: 1340000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1340000/1340000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [670000, 1270001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 189985 x 190228 Total sieving time: 4.52 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000 total time: 4.73 hours. --------- CPU info (if available) ----------
Nov 6, 2009 (4th): By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.44 SVN. / Nov 6, 2009
(49·10²⁰¹+41)/9 = 5(4)₂₀₀9_<202> = 1653191 · C196
C196 = P44 · P152
P44 = 37275012028726822642622072954781884705885423_<44>
P152 = 88351259701921852832633429667747775669808345171415609203853358189987067824413888270327700386840290722262317778160874561417235000119736451519483267715993_<152>

Msieve v. 1.44 Thu Nov 5 21:18:46 2009 random seeds: 0f697e6c 28abe295 factoring 3293294268142304455107996864515016380106378781667964829499098679126879135226628045062212681078256804231600852197020455860480999741980475604116187690620408920956165648400241983197612643937962670039 (196 digits) searching for 15-digit factors commencing number field sieve (196-digit input) R0: -10000000000000000000000000000000000000000 R1: 1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 0 A5: 490 skew 0.61, size 2.833956e-14, alpha 1.214899, combined = 9.459428e-12 commencing relation filtering estimated available RAM is 1148.0 MB commencing duplicate removal, pass 1 error -9 reading relation 8945276 error -9 reading relation 11307712 error -9 reading relation 11518069 error -15 reading relation 11544804 error -9 reading relation 12509643 error -15 reading relation 12756522 error -15 reading relation 12795024 error -1 reading relation 23489632 error -9 reading relation 23643833 error -15 reading relation 24407655 error -15 reading relation 25776837 error -1 reading relation 26227026 error -15 reading relation 26416665 error -9 reading relation 31485538 found 8862011 hash collisions in 44999986 relations added 730520 free relations commencing duplicate removal, pass 2 found 9014662 duplicates and 36715844 unique relations memory use: 213.2 MB reading ideals above 19202048 commencing singleton removal, initial pass memory use: 753.0 MB removing singletons from LP file start with 36715844 relations and 36580329 ideals pass 1: found 14595173 singletons pruned dataset has 22120671 relations and 19124588 large ideals reading all ideals from disk memory use: 382.0 MB commencing in-memory singleton removal begin with 22120671 relations and 19124588 unique ideals reduce to 15684674 relations and 12316705 ideals in 18 passes max relations containing the same ideal: 30 reading ideals above 720000 commencing singleton removal, initial pass memory use: 376.5 MB reading all ideals from disk memory use: 531.7 MB keeping 14648359 ideals with weight <= 200, target excess is 116482 commencing in-memory singleton removal begin with 15684983 relations and 14648359 unique ideals reduce to 15682203 relations and 14644226 ideals in 9 passes max relations containing the same ideal: 200 removing 2846610 relations and 2446610 ideals in 400000 cliques commencing in-memory singleton removal begin with 12835593 relations and 14644226 unique ideals reduce to 12465195 relations and 11815179 ideals in 11 passes max relations containing the same ideal: 175 removing 2135745 relations and 1735745 ideals in 400000 cliques commencing in-memory singleton removal begin with 10329450 relations and 11815179 unique ideals reduce to 10053854 relations and 9795074 ideals in 9 passes max relations containing the same ideal: 147 removing 792609 relations and 668949 ideals in 123660 cliques commencing in-memory singleton removal begin with 9261245 relations and 9795074 unique ideals reduce to 9216708 relations and 9081049 ideals in 7 passes max relations containing the same ideal: 139 relations with 0 large ideals: 2906 relations with 1 large ideals: 272 relations with 2 large ideals: 7222 relations with 3 large ideals: 70678 relations with 4 large ideals: 374670 relations with 5 large ideals: 1150194 relations with 6 large ideals: 2257720 relations with 7+ large ideals: 5353046 commencing 2-way merge reduce to 5570453 relation sets and 5434794 unique ideals commencing full merge memory use: 661.0 MB found 2928967 cycles, need 2910994 weight of 2910994 cycles is about 203790381 (70.01/cycle) distribution of cycle lengths: 1 relations: 364884 2 relations: 359563 3 relations: 360513 4 relations: 323963 5 relations: 286525 6 relations: 247293 7 relations: 211854 8 relations: 175678 9 relations: 142574 10+ relations: 438147 heaviest cycle: 23 relations commencing cycle optimization start with 15939067 relations pruned 326649 relations memory use: 540.6 MB distribution of cycle lengths: 1 relations: 364884 2 relations: 366593 3 relations: 371489 4 relations: 329960 5 relations: 291790 6 relations: 249668 7 relations: 212738 8 relations: 175029 9 relations: 140569 10+ relations: 408274 heaviest cycle: 23 relations RelProcTime: 1858 elapsed time 00:31:01 Msieve v. 1.44 Thu Nov 5 21:54:39 2009 random seeds: 239a98bf cd32137d factoring 3293294268142304455107996864515016380106378781667964829499098679126879135226628045062212681078256804231600852197020455860480999741980475604116187690620408920956165648400241983197612643937962670039 (196 digits) searching for 15-digit factors commencing number field sieve (196-digit input) R0: -10000000000000000000000000000000000000000 R1: 1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 0 A5: 490 skew 0.61, size 2.833956e-14, alpha 1.214899, combined = 9.459428e-12 commencing linear algebra read 2910994 cycles cycles contain 9097602 unique relations read 9097602 relations using 20 quadratic characters above 536868404 building initial matrix memory use: 1163.2 MB read 2910994 cycles matrix is 2910816 x 2910994 (876.2 MB) with weight 256607789 (88.15/col) sparse part has weight 197667834 (67.90/col) filtering completed in 2 passes matrix is 2908807 x 2908984 (876.0 MB) with weight 256551143 (88.19/col) sparse part has weight 197651271 (67.95/col) read 2908984 cycles matrix is 2908807 x 2908984 (876.0 MB) with weight 256551143 (88.19/col) sparse part has weight 197651271 (67.95/col) saving the first 48 matrix rows for later matrix is 2908759 x 2908984 (831.7 MB) with weight 204497989 (70.30/col) sparse part has weight 188932378 (64.95/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (2 threads) memory use: 849.9 MB restarting at iteration 45547 (dim = 2880023) linear algebra completed 2908597 of 2908984 dimensions (100.0%, ETA 0h 0m) lanczos halted after 46003 iterations (dim = 2908755) recovered 35 nontrivial dependencies BLanczosTime: 102677 commencing square root phase reading relations for dependency 1 read 1454148 cycles cycles contain 4549318 unique relations read 4549318 relations multiplying 4549318 relations multiply complete, coefficients have about 146.17 million bits initial square root is modulo 176051 reading relations for dependency 2 read 1453033 cycles cycles contain 4546544 unique relations read 4546544 relations multiplying 4546544 relations multiply complete, coefficients have about 146.07 million bits initial square root is modulo 174721 sqrtTime: 6024 prp44 factor: 37275012028726822642622072954781884705885423 prp152 factor: 88351259701921852832633429667747775669808345171415609203853358189987067824413888270327700386840290722262317778160874561417235000119736451519483267715993 elapsed time 01:57:43
Nov 6, 2009 (3rd): By Dmitry Domanov / GGNFS/msieve / Nov 6, 2009
(67·10¹⁷³-31)/9 = 7(4)₁₇₂1_<174> = 3 · C174
C174 = P84 · P90
P84 = 430710479242399035363062350740645865987466720557004828022753286974516590870289028663_<84>
P90 = 576136778897578548828836762015811405604962956451806450404338507568484460587741229848480869_<90>

N=248148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 ( 174 digits) SNFS difficulty: 176 digits. Divisors found: r1=430710479242399035363062350740645865987466720557004828022753286974516590870289028663 (pp84) r2=576136778897578548828836762015811405604962956451806450404338507568484460587741229848480869 (pp90) Version: Msieve-1.40 Total time: 104.00 hours. Scaled time: 197.49 units (timescale=1.899). Factorization parameters were as follows: n: 248148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 m: 50000000000000000000000000000000000 deg: 5 c5: 536 c0: -775 skew: 1.08 type: snfs lss: 1 rlim: 6100000 alim: 6100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 6100000/6100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3050000, 8350001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1467553 x 1467786 Total sieving time: 100.25 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.82 hours. Time per square root: 0.75 hours. Prototype def-par.txt line would be: snfs,176.000,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000 total time: 104.00 hours. --------- CPU info (if available) ----------
Nov 6, 2009 (2nd): By Erik Branger / GGNFS, Msieve / Nov 6, 2009
(22·10¹⁵⁶+17)/3 = 7(3)₁₅₅9_<157> = 13 · 19 · 6971 · 470900400663529_<15> · C136
C136 = P32 · P51 · P54
P32 = 22374456972596767383679482063529_<32>
P51 = 828191017353098997423669770686587010084194267524507_<51>
P54 = 488087078674160901172508648961369204695734529976060181_<54>

Number: 73339_156 N=9044411846105054274209815905986355691082748507066852603612928749817550676873652715990888627685568833319637972505812247201723505291521743 ( 136 digits) SNFS difficulty: 158 digits. Divisors found: r1=22374456972596767383679482063529 (pp32) r2=828191017353098997423669770686587010084194267524507 (pp51) r3=488087078674160901172508648961369204695734529976060181 (pp54) Version: Msieve-1.40 Total time: 26.33 hours. Scaled time: 23.30 units (timescale=0.885). Factorization parameters were as follows: n: 9044411846105054274209815905986355691082748507066852603612928749817550676873652715990888627685568833319637972505812247201723505291521743 m: 20000000000000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 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, 2700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 560422 x 560649 Total sieving time: 24.67 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.80 hours. Time per square root: 0.74 hours. Prototype def-par.txt line would be: snfs,158.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 26.33 hours. --------- CPU info (if available) ----------
Nov 6, 2009: By Markus Tervooren / Msieve / Nov 6, 2009
(67·10¹⁴⁶+41)/9 = 7(4)₁₄₅9_<147> = 7³ · 2579 · 137933 · C136
C136 = P42 · P95
P42 = 552752232810877924907944618081429138807679_<42>
P95 = 11037942908547355150244790836990039717387364320115120207780436833145912926736258397877527823631_<95>

Sieving time: ~5 hours Msieve v. 1.43 Thu Nov 5 15:55:15 2009 random seeds: 22e75df5 c52ae233 factoring 6101247588338546677929745539946244193317898526731142823774618663407511729661540242208206561765864438885995914092862234746612155140462449 (136 digits) searching for 15-digit factors commencing number field sieve (136-digit input) R0: 100000000000000000000000000000 R1: -1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 0 A5: 670 skew 0.57, size 1.339951e-10, alpha 0.971714, combined = 1.477459e-09 commencing relation filtering estimated available RAM is 8010.2 MB commencing duplicate removal, pass 1 found 2463214 hash collisions in 18330753 relations added 379270 free relations commencing duplicate removal, pass 2 found 2223391 duplicates and 16486632 unique relations memory use: 98.6 MB reading ideals above 720000 commencing singleton removal, initial pass memory use: 344.5 MB reading all ideals from disk memory use: 435.9 MB keeping 12885881 ideals with weight <= 200, target excess is 116169 commencing in-memory singleton removal begin with 16486632 relations and 12885881 unique ideals reduce to 11845160 relations and 7680342 ideals in 12 passes max relations containing the same ideal: 166 removing 1545647 relations and 1145647 ideals in 400000 cliques commencing in-memory singleton removal begin with 10299513 relations and 7680342 unique ideals reduce to 10195507 relations and 6426531 ideals in 7 passes max relations containing the same ideal: 147 removing 1178313 relations and 778313 ideals in 400000 cliques commencing in-memory singleton removal begin with 9017194 relations and 6426531 unique ideals reduce to 8952428 relations and 5581283 ideals in 6 passes max relations containing the same ideal: 136 removing 1045750 relations and 645750 ideals in 400000 cliques commencing in-memory singleton removal begin with 7906678 relations and 5581283 unique ideals reduce to 7837859 relations and 4863952 ideals in 5 passes max relations containing the same ideal: 122 removing 954446 relations and 554446 ideals in 400000 cliques commencing in-memory singleton removal begin with 6883413 relations and 4863952 unique ideals reduce to 6814170 relations and 4236837 ideals in 5 passes max relations containing the same ideal: 110 removing 927971 relations and 527971 ideals in 400000 cliques commencing in-memory singleton removal begin with 5886199 relations and 4236837 unique ideals reduce to 5819767 relations and 3638595 ideals in 5 passes max relations containing the same ideal: 98 removing 899906 relations and 499906 ideals in 400000 cliques commencing in-memory singleton removal begin with 4919861 relations and 3638595 unique ideals reduce to 4851525 relations and 3065913 ideals in 7 passes max relations containing the same ideal: 92 removing 875905 relations and 475905 ideals in 400000 cliques commencing in-memory singleton removal begin with 3975620 relations and 3065913 unique ideals reduce to 3901513 relations and 2509651 ideals in 5 passes max relations containing the same ideal: 77 removing 854371 relations and 454371 ideals in 400000 cliques commencing in-memory singleton removal begin with 3047142 relations and 2509651 unique ideals reduce to 2976954 relations and 1979149 ideals in 8 passes max relations containing the same ideal: 60 removing 853727 relations and 453727 ideals in 400000 cliques commencing in-memory singleton removal begin with 2123227 relations and 1979149 unique ideals reduce to 2056703 relations and 1453401 ideals in 6 passes max relations containing the same ideal: 45 removing 649792 relations and 350445 ideals in 299347 cliques commencing in-memory singleton removal begin with 1406911 relations and 1453401 unique ideals reduce to 1352520 relations and 1044337 ideals in 6 passes max relations containing the same ideal: 35 removing 361208 relations and 202857 ideals in 158351 cliques commencing in-memory singleton removal begin with 991312 relations and 1044337 unique ideals reduce to 943024 relations and 789269 ideals in 7 passes max relations containing the same ideal: 28 removing 67885 relations and 48887 ideals in 18998 cliques commencing in-memory singleton removal begin with 875139 relations and 789269 unique ideals reduce to 870935 relations and 736093 ideals in 5 passes max relations containing the same ideal: 27 relations with 0 large ideals: 2892 relations with 1 large ideals: 12725 relations with 2 large ideals: 78477 relations with 3 large ideals: 199963 relations with 4 large ideals: 264046 relations with 5 large ideals: 196441 relations with 6 large ideals: 93686 relations with 7+ large ideals: 22705 commencing 2-way merge reduce to 716617 relation sets and 581775 unique ideals commencing full merge memory use: 59.6 MB found 334086 cycles, need 315975 weight of 315975 cycles is about 22212740 (70.30/cycle) distribution of cycle lengths: 1 relations: 17641 2 relations: 28997 3 relations: 35315 4 relations: 35873 5 relations: 34500 6 relations: 30819 7 relations: 27240 8 relations: 23611 9 relations: 20033 10+ relations: 61946 heaviest cycle: 18 relations commencing cycle optimization start with 1977808 relations pruned 109779 relations memory use: 55.2 MB distribution of cycle lengths: 1 relations: 17641 2 relations: 30199 3 relations: 38011 4 relations: 38567 5 relations: 37162 6 relations: 32764 7 relations: 28595 8 relations: 23952 9 relations: 19883 10+ relations: 49201 heaviest cycle: 17 relations RelProcTime: 483 commencing linear algebra read 315975 cycles cycles contain 820073 unique relations read 820073 relations using 20 quadratic characters above 134195000 building initial matrix memory use: 99.5 MB read 315975 cycles matrix is 315792 x 315975 (91.9 MB) with weight 27669770 (87.57/col) sparse part has weight 20606850 (65.22/col) filtering completed in 2 passes matrix is 315546 x 315729 (91.8 MB) with weight 27657347 (87.60/col) sparse part has weight 20599994 (65.25/col) read 315729 cycles matrix is 315546 x 315729 (91.8 MB) with weight 27657347 (87.60/col) sparse part has weight 20599994 (65.25/col) saving the first 48 matrix rows for later matrix is 315498 x 315729 (86.7 MB) with weight 21774880 (68.97/col) sparse part has weight 19583486 (62.03/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 90.9 MB linear algebra at 1.9%, ETA 0h 6m315729 dimensions (1.9%, ETA 0h 6m) linear algebra completed 313716 of 315729 dimensions (99.4%, ETA 0h 0m) lanczos halted after 4990 iterations (dim = 315494) recovered 34 nontrivial dependencies BLanczosTime: 435 commencing square root phase reading relations for dependency 1 read 157809 cycles cycles contain 410208 unique relations read 410208 relations multiplying 410208 relations multiply complete, coefficients have about 12.09 million bits initial square root is modulo 8837471 sqrtTime: 48 prp42 factor: 552752232810877924907944618081429138807679 prp95 factor: 11037942908547355150244790836990039717387364320115120207780436833145912926736258397877527823631 elapsed time 00:16:07
Nov 5, 2009 (7th): By Ignacio Santos / GGNFS, Msieve / Nov 5, 2009
(65·10¹⁷⁴+7)/9 = 7(2)₁₇₃3_<175> = 17 · 3919 · C171
C171 = P35 · P136
P35 = 28045218294644002661656500892213117_<35>
P136 = 3865341215601827188809187731591195001845176710932875113565226610209954285454175288779980587070108534688701518416552656964627055137706053_<136>

Number: 72223_174 N=108404338174837852126476175228107743905591495763058136412683641118265797430650409351458538676166222208880149831472948114348231424916653741534038128307374663738081776897201 ( 171 digits) SNFS difficulty: 176 digits. Divisors found: r1=28045218294644002661656500892213117 (pp35) r2=3865341215601827188809187731591195001845176710932875113565226610209954285454175288779980587070108534688701518416552656964627055137706053 (pp136) Version: Msieve-1.40 Total time: 77.49 hours. Scaled time: 134.75 units (timescale=1.739). Factorization parameters were as follows: n: 108404338174837852126476175228107743905591495763058136412683641118265797430650409351458538676166222208880149831472948114348231424916653741534038128307374663738081776897201 m: 100000000000000000000000000000000000 deg: 5 c5: 13 c0: 14 skew: 1.01 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3000000, 6700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1284651 x 1284877 Total sieving time: 74.58 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.34 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,176.000,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000 total time: 77.49 hours.
Nov 5, 2009 (6th): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM v6.2.3, YAFU v1.10 / Nov 5, 2009
(67·10¹⁶⁸-31)/9 = 7(4)₁₆₇1_<169> = 7606561 · 163572667 · 590259537485086986353_<21> · 151964056301483322443154779593_<30> · C104
C104 = P47 · P57
P47 = 97126863769841467874236485364535089605312141371_<47>
P57 = 686767840130450661304870889966446488159378580482101462377_<57>

Number: 74441_168 N=66703606449858545643662707449559166574748186359301268429300565428305734048800989227920948282512461698867 ( 104 digits) Divisors found: r1=97126863769841467874236485364535089605312141371 r2=686767840130450661304870889966446488159378580482101462377 Version: Total time: 4.22 hours. Scaled time: 10.06 units (timescale=2.384). Factorization parameters were as follows: name: 74441_168 n: 66703606449858545643662707449559166574748186359301268429300565428305734048800989227920948282512461698867 skew: 22384.96 # norm 2.87e+14 c5: 15660 c4: -501824996 c3: -18525148742447 c2: 266426610854246285 c1: 4333073707957086227643 c0: 14764715322523703194493871 # alpha -6.14 Y1: 7300412317 Y0: -84308575724840796752 # Murphy_E 2.08e-09 # M 5388142146302891828223044752647144935689243276179164408869092559758099099626333652594346077847048977290 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4950394 Max relations in full relation-set: Initial matrix: Pruned matrix : 255278 x 255526 Polynomial selection time: 0.29 hours. Total sieving time: 3.36 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.14 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 4.22 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁴⁴-31)/9 = 7(4)₁₄₃1_<145> = 1086632116511402147705630873_<28> · C118
C118 = P47 · P72
P47 = 34655482245468834228541408388489501901665410519_<47>
P72 = 197686862953873716181311104410965221646157892429803380406605260036919143_<72>

Number: 74441_144 N=6850933569260401192979346688968304304118740526220941882187274314238921954387217432618656883866956371791087169104665217 ( 118 digits) SNFS difficulty: 146 digits. Divisors found: r1=34655482245468834228541408388489501901665410519 r2=197686862953873716181311104410965221646157892429803380406605260036919143 Version: Total time: 7.05 hours. Scaled time: 16.85 units (timescale=2.389). Factorization parameters were as follows: n: 6850933569260401192979346688968304304118740526220941882187274314238921954387217432618656883866956371791087169104665217 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: -310 skew: 1.36 type: snfs lss: 1 rlim: 2550000 alim: 2550000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2550000/2550000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1275000, 2775001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4934852 Max relations in full relation-set: Initial matrix: Pruned matrix : 407050 x 407298 Total sieving time: 6.06 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.33 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2550000,2550000,26,26,49,49,2.3,2.3,75000 total time: 7.05 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵⁵+41)/9 = 7(4)₁₅₄9_<156> = 47 · 53 · 241 · 302983 · 14851037 · 252442321 · 79435952371_<11> · 96107273394271_<14> · C105
C105 = P36 · P69
P36 = 513981777262743485425131597124856197_<36>
P69 = 278216723864481525034470316274854133774845275372355082172887637024697_<69>

Number: 74449_155 N=142998326196084153152602303181725148518916237710184541230536160066661148293488886572640010918329062497309 ( 105 digits) Divisors found: r1=513981777262743485425131597124856197 r2=278216723864481525034470316274854133774845275372355082172887637024697 Version: Total time: 4.48 hours. Scaled time: 10.70 units (timescale=2.388). Factorization parameters were as follows: name: 74449_155 n: 142998326196084153152602303181725148518916237710184541230536160066661148293488886572640010918329062497309 skew: 16634.07 # norm 6.75e+14 c5: 36000 c4: 2507890170 c3: -33754989641093 c2: -411802020026744711 c1: 5598836560479622272525 c0: 714646846507642901515845 # alpha -6.87 Y1: 30603097547 Y0: -83138744797431074138 # Murphy_E 2.01e-09 # M 23638809882836740827105361457170598519475955087418326994978122984763654287971205979734490448061304881821 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6901969 Max relations in full relation-set: Initial matrix: Pruned matrix : 284502 x 284750 Polynomial selection time: 0.34 hours. Total sieving time: 3.45 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 4.48 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁵⁷+41)/9 = 7(4)₁₅₆9_<158> = 19 · 79 · 569 · 13280256271_<11> · 679103402368889_<15> · 396291799469414089_<18> · C110
C110 = P33 · P38 · P40
P33 = 896016956955767255596724244933401_<33>
P38 = 13950563607253532674032704293646041067_<38>
P40 = 1951074733192853860565440794148429905793_<40>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 24388320126912700619412278763299846909289095649545527020097226863181940482234364839456257636794737384518876531 (110 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5977138773 Step 1 took 3494ms Step 2 took 3760ms ********** Factor found in step 2: 896016956955767255596724244933401 Found probable prime factor of 33 digits: 896016956955767255596724244933401 Composite cofactor 27218592167912123174017720102720354477066164208529016911587995682062219201131 has 77 digits 11/05/09 08:01:26 v1.10 @ 조영욱-PC, starting SIQS on c77: 27218592167912123174017720102720354477066164208529016911587995682062219201131 11/05/09 08:01:26 v1.10 @ 조영욱-PC, random seeds: 1415046673, 1328948052 11/05/09 08:01:27 v1.10 @ 조영욱-PC, ==== sieve params ==== 11/05/09 08:01:27 v1.10 @ 조영욱-PC, n = 77 digits, 258 bits 11/05/09 08:01:27 v1.10 @ 조영욱-PC, factor base: 32200 primes (max prime = 805451) 11/05/09 08:01:27 v1.10 @ 조영욱-PC, single large prime cutoff: 68463335 (85 * pmax) 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using 12 large prime slices of factor base 11/05/09 08:01:27 v1.10 @ 조영욱-PC, buckets hold 1024 elements 11/05/09 08:01:27 v1.10 @ 조영욱-PC, sieve interval: 5 blocks of size 65536 11/05/09 08:01:27 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using multiplier of 11 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning 11/05/09 08:01:27 v1.10 @ 조영욱-PC, trial factoring cutoff at 94 bits 11/05/09 08:01:27 v1.10 @ 조영욱-PC, ==== sieving started ==== 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sieve time = 101.5450, relation time = 27.2180, poly_time = 69.2010 11/05/09 08:04:45 v1.10 @ 조영욱-PC, 32279 relations found: 16966 full + 15313 from 161385 partial, using 73331 polys (143 A polys) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, on average, sieving found 2.43 rels/poly and 899.51 rels/sec 11/05/09 08:04:45 v1.10 @ 조영욱-PC, trial division touched 1264882 sieve locations out of 48058204160 11/05/09 08:04:45 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 11/05/09 08:04:45 v1.10 @ 조영욱-PC, begin with 178351 relations 11/05/09 08:04:45 v1.10 @ 조영욱-PC, reduce to 45610 relations in 2 passes 11/05/09 08:04:45 v1.10 @ 조영욱-PC, recovered 45610 relations 11/05/09 08:04:45 v1.10 @ 조영욱-PC, recovered 33913 polynomials 11/05/09 08:04:45 v1.10 @ 조영욱-PC, attempting to build 32279 cycles 11/05/09 08:04:45 v1.10 @ 조영욱-PC, found 32279 cycles in 1 passes 11/05/09 08:04:45 v1.10 @ 조영욱-PC, distribution of cycle lengths: 11/05/09 08:04:45 v1.10 @ 조영욱-PC, length 1 : 16966 11/05/09 08:04:45 v1.10 @ 조영욱-PC, length 2 : 15313 11/05/09 08:04:45 v1.10 @ 조영욱-PC, largest cycle: 2 relations 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 32200 x 32279 (4.7 MB) with weight 967198 (29.96/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 967198 (29.96/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, filtering completed in 4 passes 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 27821 x 27885 (4.0 MB) with weight 819515 (29.39/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 819515 (29.39/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 27773 x 27885 (2.8 MB) with weight 596633 (21.40/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 452964 (16.24/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 11/05/09 08:04:45 v1.10 @ 조영욱-PC, commencing Lanczos iteration 11/05/09 08:04:45 v1.10 @ 조영욱-PC, memory use: 3.9 MB 11/05/09 08:04:52 v1.10 @ 조영욱-PC, lanczos halted after 441 iterations (dim = 27773) 11/05/09 08:04:52 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies 11/05/09 08:04:52 v1.10 @ 조영욱-PC, prp38 = 13950563607253532674032704293646041067 11/05/09 08:04:52 v1.10 @ 조영욱-PC, prp40 = 1951074733192853860565440794148429905793 11/05/09 08:04:52 v1.10 @ 조영욱-PC, Lanczos elapsed time = 7.2070 seconds. 11/05/09 08:04:52 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.2030 seconds. 11/05/09 08:04:52 v1.10 @ 조영욱-PC, SIQS elapsed time = 205.6860 seconds. 11/05/09 08:04:52 v1.10 @ 조영욱-PC, 11/05/09 08:04:52 v1.10 @ 조영욱-PC,
(67·10¹⁴⁵-31)/9 = 7(4)₁₄₄1_<146> = 709 · 322066412869815736192367293_<27> · C117
C117 = P55 · P62
P55 = 9260894445086141962651210313544909342955325247050444087_<55>
P62 = 35203649447637528618873300517503888994181400098044701486542239_<62>

Number: 74441_145 N=326017281616386218615956963496149396800689269848098363793483088850308834552548967331260168013696545100284199033290793 ( 117 digits) SNFS difficulty: 146 digits. Divisors found: r1=9260894445086141962651210313544909342955325247050444087 r2=35203649447637528618873300517503888994181400098044701486542239 Version: Total time: 6.29 hours. Scaled time: 15.05 units (timescale=2.391). Factorization parameters were as follows: n: 326017281616386218615956963496149396800689269848098363793483088850308834552548967331260168013696545100284199033290793 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: -31 skew: 0.86 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4800623 Max relations in full relation-set: Initial matrix: Pruned matrix : 307282 x 307530 Total sieving time: 5.82 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.20 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,75000 total time: 6.29 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(64·10¹⁹⁹+17)/9 = 7(1)₁₉₈3_<200> = 89 · 179 · 16258282818944805107865067621_<29> · 490563121353478979588912991233_<30> · 5075327543140798696604465814559_<31> · C108
C108 = P52 · P56
P52 = 1407294183161809776961599301547364443542425110383681_<52>
P56 = 78356655111566972388515530318074663443442995516794711409_<56>

Number: 71113_199 N=110270864950524289144339133459841021143400357504267999886887205650991511373184710031303560333324391658116529 ( 108 digits) Divisors found: r1=1407294183161809776961599301547364443542425110383681 r2=78356655111566972388515530318074663443442995516794711409 Version: Total time: 7.36 hours. Scaled time: 17.58 units (timescale=2.389). Factorization parameters were as follows: name: 71113_199 n: 110270864950524289144339133459841021143400357504267999886887205650991511373184710031303560333324391658116529 skew: 16176.26 # norm 1.23e+15 c5: 35700 c4: -1151299406 c3: -81809870864120 c2: 211043661978170827 c1: 3912276685296992122992 c0: -12446168675693330275146900 # alpha -5.86 Y1: 307474834733 Y0: -314746746576521188279 # Murphy_E 1.37e-09 # M 20791178240142767970955924393944064521478715602414181529369486113938951120512110021307848257334770395712637 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1550001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7458099 Max relations in full relation-set: Initial matrix: Pruned matrix : 288207 x 288455 Polynomial selection time: 0.50 hours. Total sieving time: 6.22 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 7.36 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 5, 2009 (5th): By Dmitry Domanov / GGNFS, msieve 1.43 / Nov 5, 2009
(67·10¹³⁸-31)/9 = 7(4)₁₃₇1_<139> = 43 · 1487 · 128826294607_<12> · C123
C123 = P52 · P72
P52 = 2155169564333464472349918628266493657340772283669081_<52>
P72 = 419340596308113045083191970050775890985316605601219929324602580966516003_<72>

Number: 123-1 N=903750090252691191717440333954198932390180191786769441344692739715470950187355528108887414276522629304579395374002342803243 ( 123 digits) SNFS difficulty: 141 digits. Divisors found: r1=2155169564333464472349918628266493657340772283669081 (pp52) r2=419340596308113045083191970050775890985316605601219929324602580966516003 (pp72) Version: Msieve-1.40 Total time: 6.21 hours. Scaled time: 12.23 units (timescale=1.969). Factorization parameters were as follows: n: 903750090252691191717440333954198932390180191786769441344692739715470950187355528108887414276522629304579395374002342803243 m: 5000000000000000000000000000 deg: 5 c5: 536 c0: -775 skew: 1.08 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1990001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 264792 x 265017 Total sieving time: 5.97 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.18 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 6.21 hours. --------- CPU info (if available) ----------
(67·10¹⁴¹+41)/9 = 7(4)₁₄₀9_<142> = 3² · 13 · C140
C140 = P30 · P45 · P67
P30 = 104293407448198211674022417719_<30>
P45 = 266908416852904564619693685732080119715284043_<45>
P67 = 2285742510120211041888511644779295382229835659384985236947755209441_<67>

Number: 140-1 N=63627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294397 ( 140 digits) SNFS difficulty: 142 digits. Divisors found: r1=104293407448198211674022417719 (pp30) r2=266908416852904564619693685732080119715284043 (pp45) r3=2285742510120211041888511644779295382229835659384985236947755209441 (pp67) Version: Msieve-1.40 Total time: 6.69 hours. Scaled time: 12.74 units (timescale=1.905). Factorization parameters were as follows: n: 63627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294397 m: 10000000000000000000000000000 deg: 5 c5: 670 c0: 41 skew: 0.57 type: snfs lss: 1 rlim: 1680000 alim: 1680000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1680000/1680000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [840000, 2040001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 294207 x 294432 Total sieving time: 6.17 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.32 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000 total time: 6.69 hours. --------- CPU info (if available) ----------
(67·10¹³³+41)/9 = 7(4)₁₃₂9_<134> = 353081 · 7404732168439_<13> · 949521322502583250865947_<24> · C92
C92 = P36 · P57
P36 = 206990362108995995540706786083800799_<36>
P57 = 144875098665335013194730379024627109574296907971431258387_<57>

Thu Nov 05 13:28:38 2009 Msieve v. 1.43 Thu Nov 05 13:28:38 2009 random seeds: b092c728 739803fc Thu Nov 05 13:28:38 2009 factoring 29987749133314216840538328401109372365462907275873647359634749454350166358605722808406051213 (92 digits) Thu Nov 05 13:28:39 2009 searching for 15-digit factors Thu Nov 05 13:28:40 2009 commencing quadratic sieve (92-digit input) Thu Nov 05 13:28:40 2009 using multiplier of 53 Thu Nov 05 13:28:40 2009 using VC8 32kb sieve core Thu Nov 05 13:28:40 2009 sieve interval: 36 blocks of size 32768 Thu Nov 05 13:28:40 2009 processing polynomials in batches of 6 Thu Nov 05 13:28:40 2009 using a sieve bound of 1787717 (66930 primes) Thu Nov 05 13:28:40 2009 using large prime bound of 187710285 (27 bits) Thu Nov 05 13:28:40 2009 using double large prime bound of 780330238063215 (42-50 bits) Thu Nov 05 13:28:40 2009 using trial factoring cutoff of 50 bits Thu Nov 05 13:28:40 2009 polynomial 'A' values have 12 factors Thu Nov 05 15:11:33 2009 67077 relations (17712 full + 49365 combined from 818509 partial), need 67026 Thu Nov 05 15:11:37 2009 begin with 836221 relations Thu Nov 05 15:11:37 2009 reduce to 166378 relations in 11 passes Thu Nov 05 15:11:37 2009 attempting to read 166378 relations Thu Nov 05 15:11:39 2009 recovered 166378 relations Thu Nov 05 15:11:39 2009 recovered 145981 polynomials Thu Nov 05 15:11:40 2009 attempting to build 67077 cycles Thu Nov 05 15:11:40 2009 found 67077 cycles in 6 passes Thu Nov 05 15:11:40 2009 distribution of cycle lengths: Thu Nov 05 15:11:40 2009 length 1 : 17712 Thu Nov 05 15:11:40 2009 length 2 : 12595 Thu Nov 05 15:11:40 2009 length 3 : 11833 Thu Nov 05 15:11:40 2009 length 4 : 8937 Thu Nov 05 15:11:40 2009 length 5 : 6400 Thu Nov 05 15:11:40 2009 length 6 : 4055 Thu Nov 05 15:11:40 2009 length 7 : 2510 Thu Nov 05 15:11:40 2009 length 9+: 3035 Thu Nov 05 15:11:40 2009 largest cycle: 23 relations Thu Nov 05 15:11:40 2009 matrix is 66930 x 67077 (16.4 MB) with weight 4018873 (59.91/col) Thu Nov 05 15:11:40 2009 sparse part has weight 4018873 (59.91/col) Thu Nov 05 15:11:40 2009 filtering completed in 3 passes Thu Nov 05 15:11:40 2009 matrix is 62762 x 62826 (15.4 MB) with weight 3798024 (60.45/col) Thu Nov 05 15:11:40 2009 sparse part has weight 3798024 (60.45/col) Thu Nov 05 15:11:40 2009 saving the first 48 matrix rows for later Thu Nov 05 15:11:41 2009 matrix is 62714 x 62826 (9.0 MB) with weight 2879392 (45.83/col) Thu Nov 05 15:11:41 2009 sparse part has weight 1970064 (31.36/col) Thu Nov 05 15:11:41 2009 matrix includes 64 packed rows Thu Nov 05 15:11:41 2009 using block size 25130 for processor cache size 6144 kB Thu Nov 05 15:11:41 2009 commencing Lanczos iteration Thu Nov 05 15:11:41 2009 memory use: 9.6 MB Thu Nov 05 15:11:48 2009 linear algebra at 38.3%, ETA 0h 0m Thu Nov 05 15:11:59 2009 lanczos halted after 993 iterations (dim = 62714) Thu Nov 05 15:11:59 2009 recovered 18 nontrivial dependencies Thu Nov 05 15:12:00 2009 prp36 factor: 206990362108995995540706786083800799 Thu Nov 05 15:12:00 2009 prp57 factor: 144875098665335013194730379024627109574296907971431258387 Thu Nov 05 15:12:00 2009 elapsed time 01:43:22
Nov 5, 2009 (4th): By Sinkiti Sibata / Msieve, GGNFS / Nov 5, 2009
(67·10¹⁵⁰+41)/9 = 7(4)₁₄₉9_<151> = 3² · 23 · 198148463 · C141
C141 = P35 · P106
P35 = 20717939788962621561499247182422137_<35>
P106 = 8760414861837486390460724581872136579955758254687113253234500957057212238208046927618976198274194583616297_<106>

Number: 74449_150 N=181497747633882346312517962380201339855560835063081505846794519711730643938420467789908245811486286339700685380221257507780590325469086766689 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=20717939788962621561499247182422137 (pp35) r2=8760414861837486390460724581872136579955758254687113253234500957057212238208046927618976198274194583616297 (pp106) Version: Msieve-1.40 Total time: 17.61 hours. Scaled time: 36.48 units (timescale=2.071). Factorization parameters were as follows: name: 74449_150 n: 181497747633882346312517962380201339855560835063081505846794519711730643938420467789908245811486286339700685380221257507780590325469086766689 m: 1000000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 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, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 448148 x 448396 Total sieving time: 16.69 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.69 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 17.61 hours. --------- CPU info (if available) ----------
(62·10¹⁵⁰-71)/9 = 6(8)₁₄₉1_<151> = 985483 · 41851752012515441_<17> · C129
C129 = P42 · P87
P42 = 487000537391850390878280007869998072687387_<42>
P87 = 342970652274908800371221025897560617960050601182101051487751425298682261487633167922521_<87>

Number: 68881_150 N=167026891967514041560512106776883305292659958797087512558130233271448139287140102811153939235403213386239930950692215778269942627 ( 129 digits) SNFS difficulty: 151 digits. Divisors found: r1=487000537391850390878280007869998072687387 (pp42) r2=342970652274908800371221025897560617960050601182101051487751425298682261487633167922521 (pp87) Version: GGNFS-0.77.1-20060513-k8 Total time: 28.87 hours. Scaled time: 56.06 units (timescale=1.942). Factorization parameters were as follows: name: 68881_150 n: 167026891967514041560512106776883305292659958797087512558130233271448139287140102811153939235403213386239930950692215778269942627 m: 1000000000000000000000000000000 deg: 5 c5: 62 c0: -71 skew: 1.03 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: RFBsize:176302, AFBsize:176285, largePrimes:6922539 encountered Relations: rels:6824198, finalFF:406801 Max relations in full relation-set: 28 Initial matrix: 352653 x 406801 with sparse part having weight 42278766. Pruned matrix : 332656 x 334483 with weight 31669257. Total sieving time: 26.80 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.72 hours. Time per square root: 0.19 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: 28.87 hours. --------- CPU info (if available) ----------
Nov 5, 2009 (3rd): By Serge Batalov / Msieve / Nov 5, 2009
(67·10¹²⁰-31)/9 = 7(4)₁₁₉1_<121> = 72126317 · 10506700696103_<14> · C100
C100 = P48 · P53
P48 = 248173394390078679300038958119545859112216157363_<48>
P53 = 39583751858057050006460477944893403895270269829507257_<53>

SNFS difficulty: 121 digits. Divisors found: r1=248173394390078679300038958119545859112216157363 (pp48) r2=39583751858057050006460477944893403895270269829507257 (pp53) Version: Msieve v. 1.44 SVN130 Total time: 0.86 hours. Scaled time: 2.06 units (timescale=2.400). Factorization parameters were as follows: n: 9823634061308601992262375977557460526603204910482843794627402711296077541420800355402220532262483291 m: 1000000000000000000000000 deg: 5 c5: 67 c0: -31 skew: 0.86 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 675001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 80715 x 80940 Total sieving time: 0.79 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 0.86 hours.
(67·10¹²⁰+41)/9 = 7(4)₁₁₉9_<121> = 3 · 10878293325400967777_<20> · C102
C102 = P44 · P58
P44 = 38149372465301295430054963118277813058918169_<44>
P58 = 5979472529270312373079165688301574540864076057469555901091_<58>

SNFS difficulty: 121 digits. Divisors found: r1=38149372465301295430054963118277813058918169 (pp44) r2=5979472529270312373079165688301574540864076057469555901091 (pp58) Version: Msieve v. 1.44 SVN130 Total time: 0.92 hours. Scaled time: 2.20 units (timescale=2.400). Factorization parameters were as follows: n: 228113124665170349134703467583011286242415225834237151834456021181025487623010089878132800918426822379 m: 1000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 675001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 78053 x 78278 Total sieving time: 0.86 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 0.92 hours.
Nov 5, 2009 (2nd): By Robert Backstrom / Msieve / Nov 5, 2009
(8·10²²⁰+7)/3 = 2(6)₂₁₉9_<221> = 23432840917_<11> · C211
C211 = P63 · P72 · P76
P63 = 609079768500831052828490055657690521244152789163817285070668259_<63>
P72 = 796566640808664328548424906689815506613506880016762451255084828876058099_<72>
P76 = 2345565144724188907165081244897249978800113689094388155072548075040871134977_<76>

Sieving ~ 220 CPU days + 117 hrs Lanczos with Msieve 1.42 Sat Oct 31 15:34:27 2009 Sat Oct 31 15:34:27 2009 Sat Oct 31 15:34:27 2009 Msieve v. 1.42 Sat Oct 31 15:34:27 2009 random seeds: b45cd8a4 5e8cbb4f Sat Oct 31 15:34:27 2009 factoring 1138003998794725682926321155405412538979627242039312593634276438708887713594111225991671194456334842477805341329483266540910587391526508465762511226229679040784257745433430779376748272005804726927838540861403257 (211 digits) Sat Oct 31 15:34:29 2009 no P-1/P+1/ECM available, skipping Sat Oct 31 15:34:29 2009 commencing number field sieve (211-digit input) Sat Oct 31 15:34:29 2009 R0: -10000000000000000000000000000000000000 Sat Oct 31 15:34:29 2009 R1: 1 Sat Oct 31 15:34:29 2009 A0: 175 Sat Oct 31 15:34:29 2009 A1: 0 Sat Oct 31 15:34:29 2009 A2: 0 Sat Oct 31 15:34:29 2009 A3: 0 Sat Oct 31 15:34:29 2009 A4: 0 Sat Oct 31 15:34:29 2009 A5: 0 Sat Oct 31 15:34:29 2009 A6: 2 Sat Oct 31 15:34:29 2009 skew 1.00, size 3.489374e-11, alpha 1.918928, combined = 1.519785e-12 Sat Oct 31 15:34:29 2009 Sat Oct 31 15:34:29 2009 commencing relation filtering Sat Oct 31 15:34:29 2009 estimated available RAM is 7923.2 MB Sat Oct 31 15:34:29 2009 commencing duplicate removal, pass 1 Sat Oct 31 15:36:03 2009 error -11 reading relation 17254458 Sat Oct 31 15:36:54 2009 error -11 reading relation 26696095 Sat Oct 31 15:36:58 2009 error -11 reading relation 27363947 Sat Oct 31 15:36:58 2009 error -15 reading relation 27363955 Sat Oct 31 15:38:59 2009 error -11 reading relation 45804540 Sat Oct 31 15:39:03 2009 error -9 reading relation 46551733 Sat Oct 31 15:39:43 2009 found 10149236 hash collisions in 53207787 relations Sat Oct 31 15:39:58 2009 added 11 free relations Sat Oct 31 15:39:58 2009 commencing duplicate removal, pass 2 Sat Oct 31 15:40:36 2009 found 10095437 duplicates and 43112361 unique relations Sat Oct 31 15:40:36 2009 memory use: 330.4 MB Sat Oct 31 15:40:36 2009 reading ideals above 42532864 Sat Oct 31 15:40:36 2009 commencing singleton removal, initial pass Sat Oct 31 15:45:48 2009 memory use: 596.8 MB Sat Oct 31 15:45:52 2009 reading all ideals from disk Sat Oct 31 15:45:55 2009 memory use: 817.8 MB Sat Oct 31 15:46:00 2009 commencing in-memory singleton removal Sat Oct 31 15:46:04 2009 begin with 43112361 relations and 40663350 unique ideals Sat Oct 31 15:46:48 2009 reduce to 22314083 relations and 17056552 ideals in 16 passes Sat Oct 31 15:46:48 2009 max relations containing the same ideal: 27 Sat Oct 31 15:46:51 2009 reading ideals above 720000 Sat Oct 31 15:46:51 2009 commencing singleton removal, initial pass Sat Oct 31 15:50:17 2009 memory use: 532.8 MB Sat Oct 31 15:50:17 2009 reading all ideals from disk Sat Oct 31 15:50:18 2009 memory use: 816.4 MB Sat Oct 31 15:50:24 2009 keeping 22080764 ideals with weight <= 200, target excess is 125696 Sat Oct 31 15:50:29 2009 commencing in-memory singleton removal Sat Oct 31 15:50:34 2009 begin with 22314094 relations and 22080764 unique ideals Sat Oct 31 15:51:34 2009 reduce to 22292479 relations and 22059060 ideals in 11 passes Sat Oct 31 15:51:34 2009 max relations containing the same ideal: 200 Sat Oct 31 15:51:56 2009 removing 650811 relations and 607005 ideals in 43806 cliques Sat Oct 31 15:51:57 2009 commencing in-memory singleton removal Sat Oct 31 15:52:02 2009 begin with 21641668 relations and 22059060 unique ideals Sat Oct 31 15:52:44 2009 reduce to 21625957 relations and 21436291 ideals in 8 passes Sat Oct 31 15:52:44 2009 max relations containing the same ideal: 200 Sat Oct 31 15:53:06 2009 removing 467462 relations and 423656 ideals in 43806 cliques Sat Oct 31 15:53:06 2009 commencing in-memory singleton removal Sat Oct 31 15:53:12 2009 begin with 21158495 relations and 21436291 unique ideals Sat Oct 31 15:53:52 2009 reduce to 21150366 relations and 21004483 ideals in 8 passes Sat Oct 31 15:53:52 2009 max relations containing the same ideal: 198 Sat Oct 31 15:54:03 2009 relations with 0 large ideals: 4811 Sat Oct 31 15:54:03 2009 relations with 1 large ideals: 417 Sat Oct 31 15:54:03 2009 relations with 2 large ideals: 3897 Sat Oct 31 15:54:03 2009 relations with 3 large ideals: 44781 Sat Oct 31 15:54:03 2009 relations with 4 large ideals: 304685 Sat Oct 31 15:54:03 2009 relations with 5 large ideals: 1255957 Sat Oct 31 15:54:03 2009 relations with 6 large ideals: 3252807 Sat Oct 31 15:54:03 2009 relations with 7+ large ideals: 16283011 Sat Oct 31 15:54:03 2009 commencing 2-way merge Sat Oct 31 15:54:34 2009 reduce to 13461304 relation sets and 13315421 unique ideals Sat Oct 31 15:54:34 2009 commencing full merge Sat Oct 31 16:00:41 2009 memory use: 1639.9 MB Sat Oct 31 16:00:43 2009 found 7160180 cycles, need 7153621 Sat Oct 31 16:00:47 2009 weight of 7153621 cycles is about 500859937 (70.01/cycle) Sat Oct 31 16:00:47 2009 distribution of cycle lengths: Sat Oct 31 16:00:47 2009 1 relations: 1050682 Sat Oct 31 16:00:47 2009 2 relations: 1061471 Sat Oct 31 16:00:47 2009 3 relations: 984923 Sat Oct 31 16:00:47 2009 4 relations: 812616 Sat Oct 31 16:00:47 2009 5 relations: 657769 Sat Oct 31 16:00:47 2009 6 relations: 527246 Sat Oct 31 16:00:47 2009 7 relations: 421690 Sat Oct 31 16:00:47 2009 8 relations: 331726 Sat Oct 31 16:00:47 2009 9 relations: 261587 Sat Oct 31 16:00:47 2009 10+ relations: 1043911 Sat Oct 31 16:00:47 2009 heaviest cycle: 28 relations Sat Oct 31 16:00:50 2009 commencing cycle optimization Sat Oct 31 16:01:06 2009 start with 38264635 relations Sat Oct 31 16:02:27 2009 pruned 895565 relations Sat Oct 31 16:02:27 2009 memory use: 1259.8 MB Sat Oct 31 16:02:27 2009 distribution of cycle lengths: Sat Oct 31 16:02:27 2009 1 relations: 1050682 Sat Oct 31 16:02:27 2009 2 relations: 1084140 Sat Oct 31 16:02:27 2009 3 relations: 1019860 Sat Oct 31 16:02:27 2009 4 relations: 826893 Sat Oct 31 16:02:27 2009 5 relations: 666675 Sat Oct 31 16:02:27 2009 6 relations: 526965 Sat Oct 31 16:02:27 2009 7 relations: 417613 Sat Oct 31 16:02:27 2009 8 relations: 325306 Sat Oct 31 16:02:27 2009 9 relations: 253971 Sat Oct 31 16:02:27 2009 10+ relations: 981516 Sat Oct 31 16:02:27 2009 heaviest cycle: 28 relations Sat Oct 31 16:02:43 2009 RelProcTime: 1694 Sat Oct 31 16:02:43 2009 Sat Oct 31 16:02:43 2009 commencing linear algebra Sat Oct 31 16:02:48 2009 read 7153621 cycles Sat Oct 31 16:03:02 2009 cycles contain 20976846 unique relations Sat Oct 31 16:05:09 2009 read 20976846 relations Sat Oct 31 16:05:47 2009 using 20 quadratic characters above 536870702 Sat Oct 31 16:07:28 2009 building initial matrix Sat Oct 31 16:11:42 2009 memory use: 2662.3 MB Sat Oct 31 16:11:46 2009 read 7153621 cycles Sat Oct 31 16:11:50 2009 matrix is 7153443 x 7153621 (2122.1 MB) with weight 619248046 (86.56/col) Sat Oct 31 16:11:50 2009 sparse part has weight 484755663 (67.76/col) Sat Oct 31 16:13:28 2009 filtering completed in 2 passes Sat Oct 31 16:13:29 2009 matrix is 7151802 x 7151980 (2122.0 MB) with weight 619201053 (86.58/col) Sat Oct 31 16:13:29 2009 sparse part has weight 484741960 (67.78/col) Sat Oct 31 16:14:11 2009 read 7151980 cycles Sat Oct 31 16:14:15 2009 matrix is 7151802 x 7151980 (2122.0 MB) with weight 619201053 (86.58/col) Sat Oct 31 16:14:15 2009 sparse part has weight 484741960 (67.78/col) Sat Oct 31 16:14:15 2009 saving the first 48 matrix rows for later Sat Oct 31 16:14:18 2009 matrix is 7151754 x 7151980 (2042.1 MB) with weight 494163750 (69.09/col) Sat Oct 31 16:14:18 2009 sparse part has weight 463811895 (64.85/col) Sat Oct 31 16:14:18 2009 matrix includes 64 packed rows Sat Oct 31 16:14:18 2009 using block size 65536 for processor cache size 6144 kB Sat Oct 31 16:14:46 2009 commencing Lanczos iteration (4 threads) Sat Oct 31 16:14:46 2009 memory use: 2218.4 MB Thu Nov 5 10:26:49 2009 lanczos halted after 113099 iterations (dim = 7151754) Thu Nov 5 10:27:00 2009 recovered 40 nontrivial dependencies Thu Nov 5 10:27:00 2009 BLanczosTime: 411857 Thu Nov 5 10:27:00 2009 Thu Nov 5 10:27:00 2009 commencing square root phase Thu Nov 5 10:27:00 2009 reading relations for dependency 1 Thu Nov 5 10:27:02 2009 read 3576106 cycles Thu Nov 5 10:27:10 2009 cycles contain 12847903 unique relations Thu Nov 5 10:28:35 2009 read 12847903 relations Thu Nov 5 10:29:52 2009 multiplying 10490752 relations Thu Nov 5 10:49:26 2009 multiply complete, coefficients have about 272.47 million bits Thu Nov 5 10:49:29 2009 initial square root is modulo 77557 Thu Nov 5 11:21:08 2009 reading relations for dependency 2 Thu Nov 5 11:21:09 2009 read 3577523 cycles Thu Nov 5 11:21:17 2009 cycles contain 12847085 unique relations Thu Nov 5 11:22:42 2009 read 12847085 relations Thu Nov 5 11:24:00 2009 multiplying 10490164 relations Thu Nov 5 11:43:34 2009 multiply complete, coefficients have about 272.46 million bits Thu Nov 5 11:43:36 2009 initial square root is modulo 77557 Thu Nov 5 12:15:13 2009 reading relations for dependency 3 Thu Nov 5 12:15:14 2009 read 3574396 cycles Thu Nov 5 12:15:22 2009 cycles contain 12841056 unique relations Thu Nov 5 12:16:47 2009 read 12841056 relations Thu Nov 5 12:18:05 2009 multiplying 10485418 relations Thu Nov 5 12:37:39 2009 multiply complete, coefficients have about 272.32 million bits Thu Nov 5 12:37:41 2009 initial square root is modulo 77017 Thu Nov 5 13:09:16 2009 sqrtTime: 9736 Thu Nov 5 13:09:16 2009 prp63 factor: 609079768500831052828490055657690521244152789163817285070668259 Thu Nov 5 13:09:16 2009 prp72 factor: 796566640808664328548424906689815506613506880016762451255084828876058099 Thu Nov 5 13:09:16 2009 prp76 factor: 2345565144724188907165081244897249978800113689094388155072548075040871134977 Thu Nov 5 13:09:16 2009 elapsed time 117:34:49
Nov 5, 2009: By Erik Branger / GGNFS, Msieve / Nov 5, 2009
(67·10¹⁴⁵+41)/9 = 7(4)₁₄₄9_<146> = 563 · C144
C144 = P37 · P38 · P69
P37 = 6082655084179705302299740326973200613_<37>
P38 = 75145263081390269628363377895509391047_<38>
P69 = 289287120475685604509159180322914778804255865863282240870880979061193_<69>

Number: 74449_145 N=132228142885336491020327610025656206828498125123347148213933293862245904874679297414643773435958160647325833826721926189066508782316952832050523 ( 144 digits) SNFS difficulty: 146 digits. Divisors found: r1=6082655084179705302299740326973200613 (pp37) r2=75145263081390269628363377895509391047 (pp38) r3=289287120475685604509159180322914778804255865863282240870880979061193 (pp69) Version: Msieve-1.40 Total time: 9.60 hours. Scaled time: 9.62 units (timescale=1.002). Factorization parameters were as follows: n: 132228142885336491020327610025656206828498125123347148213933293862245904874679297414643773435958160647325833826721926189066508782316952832050523 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2280001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 317816 x 318042 Total sieving time: 9.11 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.24 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 9.60 hours. --------- CPU info (if available) ----------
Nov 4, 2009 (8th): By Jo Yeong Uk / GMP-ECM, YAFU v1.10, Msieve, GGNFS / Nov 4, 2009
(67·10¹¹⁴-31)/9 = 7(4)₁₁₃1_<115> = 2179 · C112
C112 = P35 · P78
P35 = 13079519603592591828724136575259833_<35>
P78 = 261206072937066617575379951763202353709110249235984400041972053868280867577163_<78>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 3416449951557799194329712916220488501351282443526592218652796899699148437101626638111264086482076385701901993779 (112 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2024510530 Step 1 took 3463ms Step 2 took 3791ms ********** Factor found in step 2: 13079519603592591828724136575259833 Found probable prime factor of 35 digits: 13079519603592591828724136575259833 Probable prime cofactor 261206072937066617575379951763202353709110249235984400041972053868280867577163 has 78 digits
(67·10¹²⁸+41)/9 = 7(4)₁₂₇9_<129> = 7 · 23² · 850211 · 156528760163174468436985270573_<30> · C91
C91 = P34 · P57
P34 = 9280978564452803005420807952719117_<34>
P57 = 162766095942852035592368755877316356049781939213380763333_<57>

11/03/09 23:20:43 v1.10 @ 조영욱-PC, starting SIQS on c91: 1510628647465278088780074442873108582826769882337327979799715993558798504460665158401736961 11/03/09 23:20:43 v1.10 @ 조영욱-PC, random seeds: 3179975179, 4127114576 11/03/09 23:20:43 v1.10 @ 조영욱-PC, ==== sieve params ==== 11/03/09 23:20:43 v1.10 @ 조영욱-PC, n = 91 digits, 300 bits 11/03/09 23:20:43 v1.10 @ 조영욱-PC, factor base: 67412 primes (max prime = 1795439) 11/03/09 23:20:43 v1.10 @ 조영욱-PC, single large prime cutoff: 215452680 (120 * pmax) 11/03/09 23:20:43 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 11/03/09 23:20:43 v1.10 @ 조영욱-PC, double large prime cutoff: 1000076957903973 11/03/09 23:20:43 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base 11/03/09 23:20:43 v1.10 @ 조영욱-PC, buckets hold 1024 elements 11/03/09 23:20:43 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536 11/03/09 23:20:43 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors 11/03/09 23:20:43 v1.10 @ 조영욱-PC, using multiplier of 1 11/03/09 23:20:43 v1.10 @ 조영욱-PC, using small prime variation correction of 20 bits 11/03/09 23:20:43 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 11/03/09 23:20:43 v1.10 @ 조영욱-PC, trial factoring cutoff at 96 bits 11/03/09 23:20:43 v1.10 @ 조영욱-PC, ==== sieving started ==== 11/04/09 00:02:57 v1.10 @ 조영욱-PC, sieve time = 1131.6620, relation time = 624.9660, poly_time = 777.0980 11/04/09 00:02:57 v1.10 @ 조영욱-PC, 67543 relations found: 20169 full + 47374 from 802231 partial, using 353318 polys (191 A polys) 11/04/09 00:02:57 v1.10 @ 조영욱-PC, on average, sieving found 2.33 rels/poly and 324.47 rels/sec 11/04/09 00:02:57 v1.10 @ 조영욱-PC, trial division touched 22403114 sieve locations out of 509411065856 11/04/09 00:02:57 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 11/04/09 00:02:58 v1.10 @ 조영욱-PC, begin with 822400 relations 11/04/09 00:02:58 v1.10 @ 조영욱-PC, reduce to 153642 relations in 9 passes 11/04/09 00:02:59 v1.10 @ 조영욱-PC, failed to read relation 81905 11/04/09 00:02:59 v1.10 @ 조영욱-PC, recovered 153641 relations 11/04/09 00:02:59 v1.10 @ 조영욱-PC, recovered 124453 polynomials 11/04/09 00:03:00 v1.10 @ 조영욱-PC, attempting to build 67542 cycles 11/04/09 00:03:00 v1.10 @ 조영욱-PC, found 67542 cycles in 5 passes 11/04/09 00:03:00 v1.10 @ 조영욱-PC, distribution of cycle lengths: 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 1 : 20169 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 2 : 15486 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 3 : 12345 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 4 : 8239 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 5 : 5235 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 6 : 2848 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 7 : 1600 11/04/09 00:03:00 v1.10 @ 조영욱-PC, length 9+: 1620 11/04/09 00:03:00 v1.10 @ 조영욱-PC, largest cycle: 17 relations 11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix is 67412 x 67542 (16.1 MB) with weight 3671773 (54.36/col) 11/04/09 00:03:00 v1.10 @ 조영욱-PC, sparse part has weight 3671773 (54.36/col) 11/04/09 00:03:00 v1.10 @ 조영욱-PC, filtering completed in 3 passes 11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix is 61730 x 61793 (14.9 MB) with weight 3405157 (55.11/col) 11/04/09 00:03:00 v1.10 @ 조영욱-PC, sparse part has weight 3405157 (55.11/col) 11/04/09 00:03:00 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix is 61682 x 61793 (10.0 MB) with weight 2620105 (42.40/col) 11/04/09 00:03:00 v1.10 @ 조영욱-PC, sparse part has weight 1998266 (32.34/col) 11/04/09 00:03:00 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 11/04/09 00:03:00 v1.10 @ 조영욱-PC, using block size 24717 for processor cache size 4096 kB 11/04/09 00:03:01 v1.10 @ 조영욱-PC, commencing Lanczos iteration 11/04/09 00:03:01 v1.10 @ 조영욱-PC, memory use: 8.9 MB 11/04/09 00:03:17 v1.10 @ 조영욱-PC, lanczos halted after 977 iterations (dim = 61681) 11/04/09 00:03:17 v1.10 @ 조영욱-PC, recovered 16 nontrivial dependencies 11/04/09 00:03:19 v1.10 @ 조영욱-PC, prp34 = 9280978564452803005420807952719117 11/04/09 00:03:20 v1.10 @ 조영욱-PC, prp57 = 162766095942852035592368755877316356049781939213380763333 11/04/09 00:03:20 v1.10 @ 조영욱-PC, Lanczos elapsed time = 19.4370 seconds. 11/04/09 00:03:20 v1.10 @ 조영욱-PC, Sqrt elapsed time = 2.8390 seconds. 11/04/09 00:03:20 v1.10 @ 조영욱-PC, SIQS elapsed time = 2556.8360 seconds. 11/04/09 00:03:20 v1.10 @ 조영욱-PC, 11/04/09 00:03:20 v1.10 @ 조영욱-PC,
(67·10¹³⁹+41)/9 = 7(4)₁₃₈9_<140> = 19 · 61 · 786547 · 1674291299_<10> · C122
C122 = P36 · P86
P36 = 534377673459567913254367877976611999_<36>
P86 = 91273531275261258156042651910406956385468817913185449840182337837085448090326006202513_<86>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 48774537291313219904007442623079158405753926520188764791281515395495425389421219582074322630262240994295077354023619753487 (122 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4575964169 Step 1 took 4212ms Step 2 took 4056ms ********** Factor found in step 2: 534377673459567913254367877976611999 Found probable prime factor of 36 digits: 534377673459567913254367877976611999 Probable prime cofactor 91273531275261258156042651910406956385468817913185449840182337837085448090326006202513 has 86 digits
(65·10¹⁷⁹+61)/9 = 7(2)₁₇₈9_<180> = 3 · 87323 · 1020080559737_<13> · 54796149540726227_<17> · 83447890470698339_<17> · 27708832797767384789479_<23> · C107
C107 = P53 · P55
P53 = 21317743601667445804930194324444375759367676750060383_<53>
P55 = 1000602544242060901983833714061031406596803672213547933_<55>

Number: 72229_179 N=21330588485328361158875002080392748528233289527820690150638446324869293334374003458821833553113928414838339 ( 107 digits) Divisors found: r1=21317743601667445804930194324444375759367676750060383 r2=1000602544242060901983833714061031406596803672213547933 Version: Total time: 5.92 hours. Scaled time: 14.12 units (timescale=2.384). Factorization parameters were as follows: name: 72229_179 n: 21330588485328361158875002080392748528233289527820690150638446324869293334374003458821833553113928414838339 skew: 9489.31 # norm 3.74e+14 c5: 83520 c4: -436405264 c3: -43730910773101 c2: 49262942741116958 c1: 1251380323824997943208 c0: 1910004788418672326199040 # alpha -5.50 Y1: 141394237039 Y0: -191180153518733060139 # Murphy_E 1.54e-09 # M 1630275644399714633370982263982210328654134408964574373092281722022933840800618587339707463745250196639887 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7190161 Max relations in full relation-set: Initial matrix: Pruned matrix : 325405 x 325653 Polynomial selection time: 0.48 hours. Total sieving time: 4.47 hours. Total relation processing time: 0.62 hours. Matrix solve time: 0.23 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 5.92 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(62·10¹⁴⁶+1)/9 = 6(8)₁₄₅9_<147> = 13² · 6211201993_<10> · C135
C135 = P44 · P92
P44 = 37581034560382870644756808555485568620305131_<44>
P92 = 17462969313698974114395124223099743671734245518631937018327064999870014820154330993298790107_<92>

Number: 68889_146 N=656276453305026685950132845745911740356925604415194223087379708869983185964276540678527362642992488434795315111654799315241895464139017 ( 135 digits) SNFS difficulty: 147 digits. Divisors found: r1=37581034560382870644756808555485568620305131 r2=17462969313698974114395124223099743671734245518631937018327064999870014820154330993298790107 Version: Total time: 5.79 hours. Scaled time: 13.84 units (timescale=2.390). Factorization parameters were as follows: n: 656276453305026685950132845745911740356925604415194223087379708869983185964276540678527362642992488434795315111654799315241895464139017 m: 100000000000000000000000000000 deg: 5 c5: 620 c0: 1 skew: 0.28 type: snfs lss: 1 rlim: 2550000 alim: 2550000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2550000/2550000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1275000, 2475001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6418793 Max relations in full relation-set: Initial matrix: Pruned matrix : 368564 x 368812 Total sieving time: 4.91 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.27 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2550000,2550000,27,27,49,49,2.3,2.3,75000 total time: 5.79 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁷¹-13)/9 = 7(4)₁₇₀3_<172> = 3 · 61 · 83 · 41231 · 19326177205969_<14> · 168398177444718134299_<21> · 2407940199983494858529_<22> · C109
C109 = P46 · P64
P46 = 1214668126324414697566041461258645928187122911_<46>
P64 = 1248799068463420195167977322133851867633591392772046781046404093_<64>

Number: 74443_171 N=1516876424646137080131556036817394582794742250003026910441101316886042947544731337541309623794566063964474723 ( 109 digits) Divisors found: r1=1214668126324414697566041461258645928187122911 r2=1248799068463420195167977322133851867633591392772046781046404093 Version: Total time: 6.92 hours. Scaled time: 16.50 units (timescale=2.385). Factorization parameters were as follows: name: 74443_171 n: 1516876424646137080131556036817394582794742250003026910441101316886042947544731337541309623794566063964474723 skew: 36638.54 # norm 1.70e+14 c5: 3060 c4: -1398829 c3: -9178005934770 c2: 64214779489920807 c1: 6712137520935301876937 c0: -90999322526528824438261920 # alpha -4.43 Y1: 258078464281 Y0: -869052006919087136947 # Murphy_E 1.27e-09 # M 110391089666132681615043182607453260645570670579022439977078871060208071876625052537906603026807031519173360 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, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7879005 Max relations in full relation-set: Initial matrix: Pruned matrix : 383485 x 383733 Polynomial selection time: 0.59 hours. Total sieving time: 5.13 hours. Total relation processing time: 0.74 hours. Matrix solve time: 0.32 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 6.92 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(62·10¹⁴⁶-53)/9 = 6(8)₁₄₅3_<147> = 109 · 3546785903202467_<16> · 185105741159841547_<18> · C112
C112 = P43 · P70
P43 = 7988310259462790706409802227377510746398133_<43>
P70 = 1205071721783088836806307130889214158089504203258137865788043317649411_<70>

Number: 68883_146 N=9626486798508338321166672386969836655287169461778109422543113922006059190158733271959627346684232163256318949663 ( 112 digits) SNFS difficulty: 147 digits. Divisors found: r1=7988310259462790706409802227377510746398133 r2=1205071721783088836806307130889214158089504203258137865788043317649411 Version: Total time: 6.61 hours. Scaled time: 15.77 units (timescale=2.387). Factorization parameters were as follows: n: 9626486798508338321166672386969836655287169461778109422543113922006059190158733271959627346684232163256318949663 m: 100000000000000000000000000000 deg: 5 c5: 620 c0: -53 skew: 0.61 type: snfs lss: 1 rlim: 2700000 alim: 2700000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2700000/2700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1350000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6538304 Max relations in full relation-set: Initial matrix: Pruned matrix : 327576 x 327824 Total sieving time: 6.03 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.23 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2700000,2700000,27,27,49,49,2.3,2.3,75000 total time: 6.61 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
(67·10¹⁴²+41)/9 = 7(4)₁₄₁9_<143> = 53 · 179 · 78816360949_<11> · C128
C128 = P31 · P32 · P66
P31 = 5118133093176327142512580486229_<31>
P32 = 27674980031210292772854978064813_<32>
P66 = 702891226094754909284926680011670954449302856594259786842594019299_<66>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 99560487302786486582644809814735788246936425457152388359549310276129385428030351314778327957138435828264320333796516810153455923 (128 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1716764280 Step 1 took 3338ms Step 2 took 2186ms ********** Factor found in step 2: 5118133093176327142512580486229 Found probable prime factor of 31 digits: 5118133093176327142512580486229 Composite cofactor 19452500646285261173250463683416786680393536413987397222165417022651024930736875120889266594826087 has 98 digits Number: 74449_142 N=19452500646285261173250463683416786680393536413987397222165417022651024930736875120889266594826087 ( 98 digits) Divisors found: r1=27674980031210292772854978064813 r2=702891226094754909284926680011670954449302856594259786842594019299 Version: Total time: 1.87 hours. Scaled time: 4.47 units (timescale=2.388). Factorization parameters were as follows: name: 74449_142 n: 19452500646285261173250463683416786680393536413987397222165417022651024930736875120889266594826087 skew: 5805.73 # norm 4.06e+13 c5: 35280 c4: 259186874 c3: -2930668561767 c2: 524670497488280 c1: -23868613045324035750 c0: -31419060311344238082400 # alpha -6.08 Y1: 13298192977 Y0: -3534166219473880023 # Murphy_E 4.66e-09 # M 8517735180229158762591976824665689918174103680536278391078828022506025160905842757400524632744508 type: gnfs rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [500000, 850001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4177363 Max relations in full relation-set: Initial matrix: Pruned matrix : 140601 x 140849 Polynomial selection time: 0.13 hours. Total sieving time: 1.54 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000 total time: 1.87 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)
Nov 4, 2009 (7th): By Erik Branger / GGNFS, Msieve / Nov 4, 2009
(65·10¹⁹⁴+7)/9 = 7(2)₁₉₃3_<195> = 3⁴ · 7884797231020992193_<19> · 2877176822753658311521667_<25> · 7624190601160779016659090250310483321_<37> · C113
C113 = P54 · P60
P54 = 273052063919366325763016102592425759636306414864987143_<54>
P60 = 188794586580741684905644457692277873007482836138123024351931_<60>

Number: 72223_194 N=51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133 ( 113 digits) Divisors found: r1=273052063919366325763016102592425759636306414864987143 (pp54) r2=188794586580741684905644457692277873007482836138123024351931 (pp60) Version: Msieve-1.40 Total time: 26.12 hours. Scaled time: 26.30 units (timescale=1.007). Factorization parameters were as follows: name: 72223_194 n: 51550751522675018522266287786788814275048077732851829746459474778039978537603238494488272159493076802130222223133 skew: 28101.07 # norm 2.49e+015 c5: 87480 c4: 1004856129 c3: -222070576128524 c2: -740136820656606496 c1: 74425772279683296958096 c0: 159258230282416511732846400 # alpha -5.86 Y1: 1063974041153 Y0: -3581499945924918201797 # Murphy_E 7.00e-010 # M 40610620651381900874736357795463379534833466793705614090822895704528946406243335529977265381704063465118931453860 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 432800 x 433031 Polynomial selection time: 2.11 hours. Total sieving time: 23.07 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.42 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 26.12 hours. --------- CPU info (if available) ----------
(67·10¹¹⁸-31)/9 = 7(4)₁₁₇1_<119> = 431 · 3539 · 123923 · 1288218067_<10> · C99
C99 = P48 · P51
P48 = 479267594069721891682480549097268372227422319287_<48>
P51 = 637903656034309727455345127696823887454307086504547_<51>

Number: 74441_118 N=305726550475843054138201474310211542232754706418797583515046928519829271317105437137867816611297989 ( 99 digits) SNFS difficulty: 121 digits. Divisors found: r1=479267594069721891682480549097268372227422319287 (pp48) r2=637903656034309727455345127696823887454307086504547 (pp51) Version: Msieve-1.40 Total time: 1.99 hours. Scaled time: 2.01 units (timescale=1.010). Factorization parameters were as follows: n: 305726550475843054138201474310211542232754706418797583515046928519829271317105437137867816611297989 m: 500000000000000000000000 deg: 5 c5: 536 c0: -775 skew: 1.08 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: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 95723 x 95968 Total sieving time: 1.93 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 1.99 hours. --------- CPU info (if available) ----------
(67·10¹¹⁹+41)/9 = 7(4)₁₁₈9_<120> = 811 · 853 · 1039 · 333881591 · C103
C103 = P45 · P58
P45 = 727595767725356441642506603221253749877381111_<45>
P58 = 4263479919140776269933631073169481493401714827270904579177_<58>

Number: 74449_119 N=3102089944948873714259994593663261709240030517685023487311603560248802223498469606951297942226303725647 ( 103 digits) SNFS difficulty: 121 digits. Divisors found: r1=727595767725356441642506603221253749877381111 (pp45) r2=4263479919140776269933631073169481493401714827270904579177 (pp58) Version: Msieve-1.40 Total time: 1.69 hours. Scaled time: 1.67 units (timescale=0.987). Factorization parameters were as follows: n: 3102089944948873714259994593663261709240030517685023487311603560248802223498469606951297942226303725647 m: 1000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 675001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 95333 x 95575 Total sieving time: 1.63 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.03 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 1.69 hours. --------- CPU info (if available) ----------
(59·10¹⁷⁸+31)/9 = 6(5)₁₇₇9_<179> = 3² · 13² · 10671276340193789_<17> · 290179339919672299_<18> · 169217453948985191765727316229_<30> · C113
C113 = P46 · P67
P46 = 9637005396204158450469257031873149606840099171_<46>
P67 = 8535130676803352925904743730167548657372518054588374638333334952871_<67>

Number: 65559_178 N=82253100389661563231365197085823719682424676832690472227216104481816562001877507221746140576667601734398251169941 ( 113 digits) Divisors found: r1=9637005396204158450469257031873149606840099171 (pp46) r2=8535130676803352925904743730167548657372518054588374638333334952871 (pp67) Version: Msieve-1.40 Total time: 25.72 hours. Scaled time: 26.06 units (timescale=1.013). Factorization parameters were as follows: name: 65559_178 n: 82253100389661563231365197085823719682424676832690472227216104481816562001877507221746140576667601734398251169941 skew: 12858.02 # norm 8.46e+014 c5: 162060 c4: -2600632228 c3: -43692937574329 c2: 145313605466800506 c1: 4516704750475308887274 c0: 19446884015649887308035447 # alpha -4.68 Y1: 926005928683 Y0: -3476127198522949132180 # Murphy_E 6.68e-010 # M 50982245736449504221446289649068838682897607864980664373131986764254935603578078285367076831133484162907276979025 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 464548 x 464773 Polynomial selection time: 2.10 hours. Total sieving time: 22.63 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.51 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 25.72 hours. --------- CPU info (if available) ----------
Nov 4, 2009 (6th): By Sinkiti Sibata / Msieve, GGNFS / Nov 4, 2009
(62·10¹⁴⁷-17)/9 = 6(8)₁₄₆7_<148> = 433 · 21503 · 127314740505811_<15> · C127
C127 = P43 · P84
P43 = 7380239265137471589931683785983880322126223_<43>
P84 = 787432068869086227477331279235335612534521397355267720469263971274835068264710154221_<84>

Number: 68887_147 N=5811437073296063859169550612223697098994871055649316965880296678454586156059632707044651861383469849288953521078203648958237283 ( 127 digits) SNFS difficulty: 149 digits. Divisors found: r1=7380239265137471589931683785983880322126223 (pp43) r2=787432068869086227477331279235335612534521397355267720469263971274835068264710154221 (pp84) Version: Msieve-1.40 Total time: 16.55 hours. Scaled time: 34.61 units (timescale=2.092). Factorization parameters were as follows: name: 68887_147 n: 5811437073296063859169550612223697098994871055649316965880296678454586156059632707044651861383469849288953521078203648958237283 m: 200000000000000000000000000000 deg: 5 c5: 775 c0: -68 skew: 0.61 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 403004 x 403252 Total sieving time: 15.72 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.54 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 16.55 hours. --------- CPU info (if available) ----------
(65·10¹⁴⁸+61)/9 = 7(2)₁₄₇9_<149> = 107 · 311 · 928044632639367136695800189501_<30> · C115
C115 = P56 · P59
P56 = 50242177561928748451743732864142031671748151278840517047_<56>
P59 = 46546750019341659505338843132529449656489198973335043828091_<59>

Number: 72229_148 N=2338610079402474063205803718148611082030518374643004494619329802098483811535795841671290368340696296730300622967277 ( 115 digits) SNFS difficulty: 150 digits. Divisors found: r1=50242177561928748451743732864142031671748151278840517047 (pp56) r2=46546750019341659505338843132529449656489198973335043828091 (pp59) Version: GGNFS-0.77.1-20060513-k8 Total time: 28.48 hours. Scaled time: 56.48 units (timescale=1.983). Factorization parameters were as follows: name: 72229_148 n: 2338610079402474063205803718148611082030518374643004494619329802098483811535795841671290368340696296730300622967277 m: 500000000000000000000000000000 deg: 5 c5: 104 c0: 305 skew: 1.24 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 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: 49/49 Sieved rational special-q in [1150000, 2050001) Primes: RFBsize:169511, AFBsize:169717, largePrimes:7420057 encountered Relations: rels:7854988, finalFF:832362 Max relations in full relation-set: 28 Initial matrix: 339294 x 832362 with sparse part having weight 97295036. Pruned matrix : 241666 x 243426 with weight 37932161. Total sieving time: 26.92 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.22 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 28.48 hours. --------- CPU info (if available) ----------
(67·10¹⁵⁰-31)/9 = 7(4)₁₄₉1_<151> = 691 · 877 · 32363 · 30693713 · 88802717 · 44229582577_<11> · 5862187185226627723561_<22> · C93
C93 = P41 · P53
P41 = 52149321682005352760460016522007528725573_<41>
P53 = 10299330898577574176970919887050802682776591407979701_<53>

Wed Nov 04 11:38:20 2009 Msieve v. 1.42 Wed Nov 04 11:38:20 2009 random seeds: 089ec948 20f939fa Wed Nov 04 11:38:20 2009 factoring 537103120139339161837271430024183269497567761442391196882272189956546662230998950851183593673 (93 digits) Wed Nov 04 11:38:21 2009 searching for 15-digit factors Wed Nov 04 11:38:21 2009 commencing quadratic sieve (93-digit input) Wed Nov 04 11:38:21 2009 using multiplier of 5 Wed Nov 04 11:38:21 2009 using 32kb Intel Core sieve core Wed Nov 04 11:38:21 2009 sieve interval: 36 blocks of size 32768 Wed Nov 04 11:38:21 2009 processing polynomials in batches of 6 Wed Nov 04 11:38:21 2009 using a sieve bound of 1954487 (72941 primes) Wed Nov 04 11:38:21 2009 using large prime bound of 244310875 (27 bits) Wed Nov 04 11:38:21 2009 using double large prime bound of 1253998370578250 (42-51 bits) Wed Nov 04 11:38:21 2009 using trial factoring cutoff of 51 bits Wed Nov 04 11:38:21 2009 polynomial 'A' values have 12 factors Wed Nov 04 14:26:40 2009 73249 relations (18003 full + 55246 combined from 1003555 partial), need 73037 Wed Nov 04 14:26:42 2009 begin with 1021558 relations Wed Nov 04 14:26:43 2009 reduce to 190009 relations in 11 passes Wed Nov 04 14:26:43 2009 attempting to read 190009 relations Wed Nov 04 14:26:45 2009 recovered 190009 relations Wed Nov 04 14:26:45 2009 recovered 173099 polynomials Wed Nov 04 14:26:46 2009 attempting to build 73249 cycles Wed Nov 04 14:26:46 2009 found 73249 cycles in 6 passes Wed Nov 04 14:26:46 2009 distribution of cycle lengths: Wed Nov 04 14:26:46 2009 length 1 : 18003 Wed Nov 04 14:26:46 2009 length 2 : 12924 Wed Nov 04 14:26:46 2009 length 3 : 12314 Wed Nov 04 14:26:46 2009 length 4 : 9925 Wed Nov 04 14:26:46 2009 length 5 : 7590 Wed Nov 04 14:26:46 2009 length 6 : 5002 Wed Nov 04 14:26:46 2009 length 7 : 3092 Wed Nov 04 14:26:46 2009 length 9+: 4399 Wed Nov 04 14:26:46 2009 largest cycle: 22 relations Wed Nov 04 14:26:46 2009 matrix is 72941 x 73249 (18.7 MB) with weight 4614755 (63.00/col) Wed Nov 04 14:26:46 2009 sparse part has weight 4614755 (63.00/col) Wed Nov 04 14:26:47 2009 filtering completed in 3 passes Wed Nov 04 14:26:47 2009 matrix is 69394 x 69458 (17.8 MB) with weight 4391238 (63.22/col) Wed Nov 04 14:26:47 2009 sparse part has weight 4391238 (63.22/col) Wed Nov 04 14:26:47 2009 saving the first 48 matrix rows for later Wed Nov 04 14:26:47 2009 matrix is 69346 x 69458 (10.7 MB) with weight 3426212 (49.33/col) Wed Nov 04 14:26:47 2009 sparse part has weight 2392857 (34.45/col) Wed Nov 04 14:26:47 2009 matrix includes 64 packed rows Wed Nov 04 14:26:47 2009 using block size 27783 for processor cache size 1024 kB Wed Nov 04 14:26:48 2009 commencing Lanczos iteration Wed Nov 04 14:26:48 2009 memory use: 11.2 MB Wed Nov 04 14:27:19 2009 lanczos halted after 1098 iterations (dim = 69346) Wed Nov 04 14:27:19 2009 recovered 18 nontrivial dependencies Wed Nov 04 14:27:19 2009 prp41 factor: 52149321682005352760460016522007528725573 Wed Nov 04 14:27:19 2009 prp53 factor: 10299330898577574176970919887050802682776591407979701 Wed Nov 04 14:27:19 2009 elapsed time 02:48:59
(67·10¹³⁶-31)/9 = 7(4)₁₃₅1_<137> = 1229 · 2243 · 973091086236793_<15> · 31185773135760457_<17> · C99
C99 = P43 · P57
P43 = 4810783287458379447319665714720974617182731_<43>
P57 = 184980237899848999666716380766074086221876478826386870813_<57>

Number: 74441_136 N=889899836998668686633900800566801256698255608757109609947713814087374076702236000012655652911530303 ( 99 digits) SNFS difficulty: 139 digits. Divisors found: r1=4810783287458379447319665714720974617182731 (pp43) r2=184980237899848999666716380766074086221876478826386870813 (pp57) Version: GGNFS-0.77.1-20060513-k8 Total time: 9.69 hours. Scaled time: 18.94 units (timescale=1.956). Factorization parameters were as follows: name: 74441_136 n: 889899836998668686633900800566801256698255608757109609947713814087374076702236000012655652911530303 m: 2000000000000000000000000000 deg: 5 c5: 335 c0: -496 skew: 1.08 type: snfs lss: 1 rlim: 1450000 alim: 1450000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 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: 48/48 Sieved rational special-q in [725000, 1550001) Primes: RFBsize:110630, AFBsize:110790, largePrimes:3539552 encountered Relations: rels:3573888, finalFF:316292 Max relations in full relation-set: 28 Initial matrix: 221487 x 316292 with sparse part having weight 29442668. Pruned matrix : 194165 x 195336 with weight 14866622. Total sieving time: 9.16 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.34 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1450000,1450000,26,26,48,48,2.3,2.3,75000 total time: 9.69 hours. --------- CPU info (if available) ----------
(67·10¹⁵⁸-31)/9 = 7(4)₁₅₇1_<159> = 3 · 13 · 47 · 7057 · 8995960241_<10> · 311380275064099_<15> · 693785995312617674467398121_<27> · C101
C101 = P50 · P51
P50 = 93224551460111137035240108268625574954487489831903_<50>
P51 = 317654677042421270612800208132930793843765449092733_<51>

Number: 74441_158 N=29613214786486185544278227521549428503432789847535163482886575624753396192189049354232057714028860899 ( 101 digits) Divisors found: r1=93224551460111137035240108268625574954487489831903 (pp50) r2=317654677042421270612800208132930793843765449092733 (pp51) Version: Msieve-1.40 Total time: 5.22 hours. Scaled time: 17.25 units (timescale=3.305). Factorization parameters were as follows: name: 74441_158 n: 29613214786486185544278227521549428503432789847535163482886575624753396192189049354232057714028860899 skew: 2475.53 # norm 7.83e+13 c5: 286800 c4: -2941514404 c3: 3174525952836 c2: 18842763152668317 c1: 16056592382406591394 c0: 4443972655071256500177 # alpha -4.91 Y1: 60202425107 Y0: -10064370379691956090 # Murphy_E 3.01e-09 # M 5135300505416392765969601109169315018788510709089396459401407529503863629792793102008601301469075470 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 : 214611 x 214859 Polynomial selection time: 0.55 hours. Total sieving time: 4.53 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 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: 5.22 hours. --------- CPU info (if available) ----------
(67·10¹⁶⁷-31)/9 = 7(4)₁₆₆1_<168> = 3 · 97 · 1789 · 13892257 · 96862933 · 31292114101_<11> · 51882071872753_<14> · 186886300862329234750824700241_<30> · C94
C94 = P38 · P56
P38 = 84574198791351340668356637482340533647_<38>
P56 = 41412453686437193224539957363738958943723854038718898569_<56>

Wed Nov 04 14:47:54 2009 Msieve v. 1.42 Wed Nov 04 14:47:54 2009 random seeds: b7fa92a0 b09111fb Wed Nov 04 14:47:54 2009 factoring 3502425090514369839464801792831352863378564620939980353829959014019250494360162188995524651143 (94 digits) Wed Nov 04 14:47:55 2009 searching for 15-digit factors Wed Nov 04 14:47:55 2009 commencing quadratic sieve (94-digit input) Wed Nov 04 14:47:55 2009 using multiplier of 7 Wed Nov 04 14:47:55 2009 using 32kb Intel Core sieve core Wed Nov 04 14:47:55 2009 sieve interval: 36 blocks of size 32768 Wed Nov 04 14:47:55 2009 processing polynomials in batches of 6 Wed Nov 04 14:47:55 2009 using a sieve bound of 2025253 (75248 primes) Wed Nov 04 14:47:55 2009 using large prime bound of 271383902 (28 bits) Wed Nov 04 14:47:55 2009 using double large prime bound of 1515134967946490 (42-51 bits) Wed Nov 04 14:47:55 2009 using trial factoring cutoff of 51 bits Wed Nov 04 14:47:55 2009 polynomial 'A' values have 12 factors Wed Nov 04 17:50:50 2009 75673 relations (18625 full + 57048 combined from 1070859 partial), need 75344 Wed Nov 04 17:50:51 2009 begin with 1089484 relations Wed Nov 04 17:50:52 2009 reduce to 195943 relations in 11 passes Wed Nov 04 17:50:52 2009 attempting to read 195943 relations Wed Nov 04 17:50:55 2009 recovered 195943 relations Wed Nov 04 17:50:55 2009 recovered 179427 polynomials Wed Nov 04 17:50:56 2009 attempting to build 75673 cycles Wed Nov 04 17:50:56 2009 found 75673 cycles in 6 passes Wed Nov 04 17:50:56 2009 distribution of cycle lengths: Wed Nov 04 17:50:56 2009 length 1 : 18625 Wed Nov 04 17:50:56 2009 length 2 : 13525 Wed Nov 04 17:50:56 2009 length 3 : 12818 Wed Nov 04 17:50:56 2009 length 4 : 10120 Wed Nov 04 17:50:56 2009 length 5 : 7691 Wed Nov 04 17:50:56 2009 length 6 : 5105 Wed Nov 04 17:50:56 2009 length 7 : 3291 Wed Nov 04 17:50:56 2009 length 9+: 4498 Wed Nov 04 17:50:56 2009 largest cycle: 20 relations Wed Nov 04 17:50:56 2009 matrix is 75248 x 75673 (19.9 MB) with weight 4909489 (64.88/col) Wed Nov 04 17:50:56 2009 sparse part has weight 4909489 (64.88/col) Wed Nov 04 17:50:57 2009 filtering completed in 3 passes Wed Nov 04 17:50:57 2009 matrix is 71566 x 71630 (18.9 MB) with weight 4655436 (64.99/col) Wed Nov 04 17:50:57 2009 sparse part has weight 4655436 (64.99/col) Wed Nov 04 17:50:57 2009 saving the first 48 matrix rows for later Wed Nov 04 17:50:57 2009 matrix is 71518 x 71630 (12.2 MB) with weight 3691149 (51.53/col) Wed Nov 04 17:50:57 2009 sparse part has weight 2758033 (38.50/col) Wed Nov 04 17:50:57 2009 matrix includes 64 packed rows Wed Nov 04 17:50:57 2009 using block size 28652 for processor cache size 1024 kB Wed Nov 04 17:50:58 2009 commencing Lanczos iteration Wed Nov 04 17:50:58 2009 memory use: 12.2 MB Wed Nov 04 17:51:32 2009 lanczos halted after 1132 iterations (dim = 71517) Wed Nov 04 17:51:32 2009 recovered 17 nontrivial dependencies Wed Nov 04 17:51:33 2009 prp38 factor: 84574198791351340668356637482340533647 Wed Nov 04 17:51:33 2009 prp56 factor: 41412453686437193224539957363738958943723854038718898569 Wed Nov 04 17:51:33 2009 elapsed time 03:03:39
(67·10¹³¹+41)/9 = 7(4)₁₃₀9_<132> = 79 · 18493896401067727171723339878571_<32> · C99
C99 = P37 · P63
P37 = 4525308800973640811158291449529412591_<37>
P63 = 112597451591228804139139623565260342727756344221799002605550371_<63>

Number: 74449_131 N=509538238652991184285965430122845534851877702982919855855689867384284811642128713318697751892121261 ( 99 digits) SNFS difficulty: 132 digits. Divisors found: r1=4525308800973640811158291449529412591 (pp37) r2=112597451591228804139139623565260342727756344221799002605550371 (pp63) Version: Msieve-1.40 Total time: 3.42 hours. Scaled time: 11.42 units (timescale=3.339). Factorization parameters were as follows: name: 74449_131 n: 509538238652991184285965430122845534851877702982919855855689867384284811642128713318697751892121261 m: 100000000000000000000000000 deg: 5 c5: 670 c0: 41 skew: 0.57 type: snfs lss: 1 rlim: 1150000 alim: 1150000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1150000/1150000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [575000, 1175001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 178722 x 178970 Total sieving time: 3.32 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.06 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,132.000,5,0,0,0,0,0,0,0,0,1150000,1150000,26,26,47,47,2.3,2.3,50000 total time: 3.42 hours. --------- CPU info (if available) ----------
Nov 4, 2009 (5th): By Dmitry Domanov / GGNFS/msieve / Nov 4, 2009
(65·10¹⁴⁹-11)/9 = 7(2)₁₄₈1_<150> = 229 · 10309737107_<11> · C138
C138 = P61 · P78
P61 = 1760809446734728886340349673660727500140667053250604025945597_<61>
P78 = 173730237829917538457626291929595253008299451778851719371130464180604004301231_<78>

Number: 138-1 N=305905843954389967281676045820831821698738895584262287043064623509243937335538029868173413204853119730514843003514032989035405710006129907 ( 138 digits) SNFS difficulty: 151 digits. Divisors found: r1=1760809446734728886340349673660727500140667053250604025945597 (pp61) r2=173730237829917538457626291929595253008299451778851719371130464180604004301231 (pp78) Version: Msieve-1.40 Total time: 11.49 hours. Scaled time: 21.02 units (timescale=1.829). Factorization parameters were as follows: n: 305905843954389967281676045820831821698738895584262287043064623509243937335538029868173413204853119730514843003514032989035405710006129907 m: 1000000000000000000000000000000 deg: 5 c5: 13 c0: -22 skew: 1.11 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1850001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 379854 x 380082 Total sieving time: 11.15 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.18 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 11.49 hours. --------- CPU info (if available) ----------
(62·10¹⁴⁹+1)/9 = 6(8)₁₄₈9_<150> = 20483 · 1451521 · C140
C140 = P46 · P95
P46 = 2159958576333471630827291022074668095705599543_<46>
P95 = 10727212141443721091591595069382603712040863221467467516173427204992746524141860104161935808261_<95>

Number: 140-1 N=23170333865059911320172901781817463495296432410996862069873982088491668836825268806120304124323254449187510933228247007723728437099297224723 ( 140 digits) SNFS difficulty: 151 digits. Divisors found: r1=2159958576333471630827291022074668095705599543 (pp46) r2=10727212141443721091591595069382603712040863221467467516173427204992746524141860104161935808261 (pp95) Version: Msieve-1.40 Total time: 11.72 hours. Scaled time: 21.56 units (timescale=1.839). Factorization parameters were as follows: n: 23170333865059911320172901781817463495296432410996862069873982088491668836825268806120304124323254449187510933228247007723728437099297224723 m: 1000000000000000000000000000000 deg: 5 c5: 31 c0: 5 skew: 0.69 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1850001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 347406 x 347631 Total sieving time: 11.26 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.15 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 11.72 hours. --------- CPU info (if available) ----------
(62·10¹⁵⁰-53)/9 = 6(8)₁₄₉3_<151> = 29 · 9210591331619_<13> · C137
C137 = P63 · P74
P63 = 661875852763457366391885680418340090691973432419556589889316841_<63>
P74 = 38966117144008027984903360062825590816642015961644316334865082860882091613_<74>

Number: 137-1 N=25790732013571089390629829637694401439543992384512237925102922325233751728027886870816186678957658224553701159626991355378692243745754533 ( 137 digits) SNFS difficulty: 151 digits. Divisors found: r1=661875852763457366391885680418340090691973432419556589889316841 (pp63) r2=38966117144008027984903360062825590816642015961644316334865082860882091613 (pp74) Version: Msieve-1.40 Total time: 14.57 hours. Scaled time: 27.09 units (timescale=1.860). Factorization parameters were as follows: n: 25790732013571089390629829637694401439543992384512237925102922325233751728027886870816186678957658224553701159626991355378692243745754533 m: 1000000000000000000000000000000 deg: 5 c5: 62 c0: -53 skew: 0.97 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4Factor 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: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 416838 x 417064 Total sieving time: 14.21 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.23 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 14.57 hours. --------- CPU info (if available) ----------
(67·10¹¹⁵+41)/9 = 7(4)₁₁₄9_<116> = C116
C116 = P44 · P72
P44 = 75238973175295618288828136185615790213603981_<44>
P72 = 989439931230852392677882277821169072176642871144176663604322784136109029_<72>

Number: s116 N=74444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 ( 116 digits) SNFS difficulty: 116 digits. Divisors found: r1=75238973175295618288828136185615790213603981 (pp44) r2=989439931230852392677882277821169072176642871144176663604322784136109029 (pp72) Version: Msieve-1.40 Total time: 0.85 hours. Scaled time: 1.52 units (timescale=1.793). Factorization parameters were as follows: n: 74444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444449 m: 100000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 620000 alim: 620000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2Factor base limits: 620000/620000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [310000, 510001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 64899 x 65124 Total sieving time: 0.82 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours.