News and updates, December 2008

Since June 16, 2000

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News and updates, December 2008	2008-12-26(Fri) 00:09

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News and updates, December 2008

Dec 29, 2008: Factor tables of this page will be updated in mid-January. Until then, contributions are kept on the web server. You can reserve numbers as usual. If you forgot your reservation keys, tell so by email.
My Pentium 4 processor could not withstand demanding programs and broke down. Take care for your CPU!
Dec 26, 2008: I'm afraid that I can't update this page for several days or a week because my computer crashed yesterday.
Dec 25, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(38·10¹⁴⁵+61)/9 = 4(2)₁₄₄9_<146> = 7 · 89 · 4211 · 240030140333_<12> · 6318701319397581967_<19> · C110
C110 = P42 · P68
P42 = 959520805192593881541714464704553517162347_<42>
P68 = 11059100304528524565462268921955338143239467920276603381903889550329_<68>

Number: n N=10611436828906870090522936495968919633890384936146829850407470739275500463086914188108300526561796213920262163 ( 110 digits) SNFS difficulty: 146 digits. Divisors found: Thu Dec 25 11:57:28 2008 prp42 factor: 959520805192593881541714464704553517162347 Thu Dec 25 11:57:28 2008 prp68 factor: 11059100304528524565462268921955338143239467920276603381903889550329 Thu Dec 25 11:57:28 2008 elapsed time 00:35:41 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.47 hours. Scaled time: 13.66 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_2_144_9 n: 10611436828906870090522936495968919633890384936146829850407470739275500463086914188108300526561796213920262163 type: snfs skew: 1.10 deg: 5 c5: 38 c0: 61 m: 100000000000000000000000000000 rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 1870001) Primes: RFBsize:114155, AFBsize:114048, largePrimes:12063139 encountered Relations: rels:11157151, finalFF:260073 Max relations in full relation-set: 28 Initial matrix: 228269 x 260073 with sparse part having weight 43425032. Pruned matrix : 222316 x 223521 with weight 33941924. Msieve: found 1169180 hash collisions in 12167702 relations Msieve: matrix is 285178 x 285426 (74.7 MB) Total sieving time: 7.09 hours. Total relation processing time: 0.38 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,56,56,2.5,2.5,100000 total time: 7.47 hours. --------- CPU info (if available) ----------
(8·10¹⁸⁸+1)/9 = (8)₁₈₇9_<188> = 10867 · C184
C184 = P72 · P113
P72 = 200566861506992331136426364484679792245665453316940240273757774540395067_<72>
P113 = 40782949523419614037769977548545749947635754809093559084419918633991991426423339650836469118542851487206338102201_<113>

Number: n N=8179708188910360622884778585523961432675889287649663098268969254521844933182008731838491661809964929501140046828829381511814566015357402124679202069466171794321237589848982137562242467 ( 184 digits) SNFS difficulty: 190 digits. Divisors found: Thu Dec 25 21:52:08 2008 prp72 factor: 200566861506992331136426364484679792245665453316940240273757774540395067 Thu Dec 25 21:52:08 2008 prp113 factor: 40782949523419614037769977548545749947635754809093559084419918633991991426423339650836469118542851487206338102201 Thu Dec 25 21:52:08 2008 elapsed time 04:14:57 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20050930-k8 Total time: 69.18 hours. Scaled time: 139.12 units (timescale=2.011). Factorization parameters were as follows: name: KA_8_187_9 n: 8179708188910360622884778585523961432675889287649663098268969254521844933182008731838491661809964929501140046828829381511814566015357402124679202069466171794321237589848982137562242467 type: snfs skew: 1.66 deg: 5 c5: 2 c0: 25 m: 100000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 8600001) Primes: RFBsize:602489, AFBsize:602100, largePrimes:34905775 encountered Relations: rels:31238877, finalFF:727045 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3975978 hash collisions in 36541534 relations Msieve: matrix is 1696807 x 1697055 (460.7 MB) Total sieving time: 68.38 hours. Total relation processing time: 0.80 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,9000000,9000000,29,29,58,58,2.5,2.5,100000 total time: 69.18 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
Dec 25, 2008 (2nd): By Sinkiti Sibata / Msieve
(38·10¹⁴³+61)/9 = 4(2)₁₄₂9_<144> = 3² · 23 · 8898879841_<10> · 576568337208290100918143_<24> · C108
C108 = P51 · P58
P51 = 247067337455777187755752491982412454361833257217269_<51>
P58 = 1609049019393037299239339702182176490310075105569308816401_<58>

Number: 42229_143 N=397543457057266918884845579618051966809384919381927176588582112286687485108113865531283414443127005287628869 ( 108 digits) SNFS difficulty: 145 digits. Divisors found: r1=247067337455777187755752491982412454361833257217269 r2=1609049019393037299239339702182176490310075105569308816401 Version: Total time: 9.34 hours. Scaled time: 18.43 units (timescale=1.972). Factorization parameters were as follows: name: 42229_143 n: 397543457057266918884845579618051966809384919381927176588582112286687485108113865531283414443127005287628869 m: 50000000000000000000000000000 deg: 5 c5: 304 c0: 1525 skew: 1.38 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 262775 x 263023 Total sieving time: 9.34 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 9.34 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁷+61)/9 = 4(2)₁₄₆9_<148> = 167 · 2369773339_<10> · 294392469467_<12> · C125
C125 = P39 · P86
P39 = 390767166238674756702854534057738664529_<39>
P86 = 92741271271455106967496554922563178454113145520981313433082313450604481966509315597931_<86>

Number: 42229_147 N=36240243768118729202943463309695426736944896402283016562377648348010345900851403545823189583259160747606835955616325055489499 ( 125 digits) SNFS difficulty: 149 digits. Divisors found: r1=390767166238674756702854534057738664529 r2=92741271271455106967496554922563178454113145520981313433082313450604481966509315597931 Version: Total time: 11.97 hours. Scaled time: 30.70 units (timescale=2.564). Factorization parameters were as follows: name: 42229_147 n: 36240243768118729202943463309695426736944896402283016562377648348010345900851403545823189583259160747606835955616325055489499 m: 200000000000000000000000000000 deg: 5 c5: 475 c0: 244 skew: 0.88 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 357888 x 358136 Total sieving time: 11.97 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 11.97 hours. --------- CPU info (if available) ----------
(13·10¹⁴⁹-7)/3 = 4(3)₁₄₈1_<150> = 137 · 23119651 · C141
C141 = P57 · P84
P57 = 188970213715321747672299761534754833377917059582227123669_<57>
P84 = 723980555610444002576019194415271366760489277242380215274116190741913804171160915877_<84>

Number: 43331_149 N=136810760319442984511388306121793604504251223416095814639746515650962970987884593570645608634044828921380847408566690807883000354617384592713 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=188970213715321747672299761534754833377917059582227123669 r2=723980555610444002576019194415271366760489277242380215274116190741913804171160915877 Version: Total time: 17.52 hours. Scaled time: 36.01 units (timescale=2.055). Factorization parameters were as follows: name: 43331_149 n: 136810760319442984511388306121793604504251223416095814639746515650962970987884593570645608634044828921380847408566690807883000354617384592713 m: 1000000000000000000000000000000 deg: 5 c5: 13 c0: -70 skew: 1.40 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, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 449125 x 449373 Total sieving time: 17.52 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 17.52 hours. --------- CPU info (if available) ----------
Dec 25, 2008: By Serge Batalov / Msieve-1.39
(13·10¹⁵⁷-7)/3 = 4(3)₁₅₆1_<158> = 17³ · 67 · 137 · 769 · C148
C148 = P45 · P104
P45 = 123302230368263597667057025479304489207485833_<45>
P104 = 10134041800873407971458001266515153364324752965728397706141656301510332896590942027080433617388959869489_<104>

SNFS difficulty: 159 digits. Divisors found: r1=123302230368263597667057025479304489207485833 (pp45) r2=10134041800873407971458001266515153364324752965728397706141656301510332896590942027080433617388959869489 (pp104) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.525). Factorization parameters were as follows: n: 1249549956692905843078530648495289271477668421273383397930121240701021840408969782908108656684854663018608144097023393943249861817083459645496449337 m: 20000000000000000000000000000000 deg: 5 c5: 325 c0: -56 skew: 0.70 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [1550000, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 577511 x 577759 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,52,52,2.4,2.4,100000 total time: 20.00 hours.
(38·10¹⁷³-11)/9 = 4(2)₁₇₂1_<174> = 383 · C172
C172 = P77 · P95
P77 = 21373934917885229960501801036667767687297501292726057634758836826598560231947_<77>
P95 = 51577208181595520712952190859726794005821242274496299179553509825685887968828943498649093422521_<95>

SNFS difficulty: 175 digits. Divisors found: r1=21373934917885229960501801036667767687297501292726057634758836826598560231947 (pp77) r2=51577208181595520712952190859726794005821242274496299179553509825685887968828943498649093422521 (pp95) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 1102407890919640266898752538439222512329561937917029300841311285175514940527995358282564548883086742094574992747316507107629823034522773426167682042355671598491441833478387 m: 50000000000000000000000000000000000 deg: 5 c5: 304 c0: -275 skew: 0.98 type: snfs lss: 1 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 rational special-q in [3000000, 8200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1149407 x 1149655 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.5,2.5,200000 total time: 70.00 hours.
(38·10¹⁶³+43)/9 = 4(2)₁₆₂7_<164> = 1409 · C161
C161 = P52 · P109
P52 = 4810957160735656694134600221951725247720036705800339_<52>
P109 = 6228717072530466781791563604942513648430182164800452761903679474999292240561911205887774266569403833476578177_<109>

SNFS difficulty: 165 digits. Divisors found: r1=4810957160735656694134600221951725247720036705800339 (pp52) r2=6228717072530466781791563604942513648430182164800452761903679474999292240561911205887774266569403833476578177 (pp109) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: n: 29966091002286885892279788660200299660910022868858922797886602002996609100228688589227978866020029966091002286885892279788660200299660910022868858922797886602003 m: 500000000000000000000000000000000 deg: 5 c5: 304 c0: 1075 skew: 1.29 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2050000, 4650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 813692 x 813940 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,100000 total time: 56.00 hours.
(13·10¹⁶⁵-7)/3 = 4(3)₁₆₄1_<166> = 137 · C164
C164 = P79 · P85
P79 = 6085843468199487275442039551130758294656791892404326335166720315393967284370157_<79>
P85 = 5197335501903661657599518956480061122136436218334285817046668712234291023306740922759_<85>

SNFS difficulty: 166 digits. Divisors found: r1=6085843468199487275442039551130758294656791892404326335166720315393967284370157 (pp79) r2=5197335501903661657599518956480061122136436218334285817046668712234291023306740922759 (pp85) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 31630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163017031630170316301703163 m: 1000000000000000000000000000000000 deg: 5 c5: 13 c0: -7 skew: 0.88 type: snfs lss: 1 rlim: 4100000 alim: 4100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4100000/4100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2050000, 4050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 746923 x 747171 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4100000,4100000,27,27,52,52,2.4,2.4,200000 total time: 36.00 hours.
Dec 24, 2008 (5th): By Jo Yeong Uk / GGNFS / Msieve v1.39
(13·10¹²⁹-7)/3 = 4(3)₁₂₈1_<130> = 103993 · 9537211 · 799114214868023969_<18> · C100
C100 = P39 · P62
P39 = 346643489439315219050321521524858945557_<39>
P62 = 15772651068440529298755132621651886781971748870337901617836909_<62>

Number: 43331_129 N=5467486804072968524263441446230274033369319439416686948461744728066650046424741948248473440936163313 ( 100 digits) SNFS difficulty: 131 digits. Divisors found: r1=346643489439315219050321521524858945557 r2=15772651068440529298755132621651886781971748870337901617836909 Version: Total time: 1.74 hours. Scaled time: 4.16 units (timescale=2.391). Factorization parameters were as follows: n: 5467486804072968524263441446230274033369319439416686948461744728066650046424741948248473440936163313 m: 100000000000000000000000000 deg: 5 c5: 13 c0: -70 skew: 1.40 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 1000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2953047 Max relations in full relation-set: Initial matrix: Pruned matrix : 157950 x 158195 Total sieving time: 1.54 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 1.74 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 24, 2008 (4th): By Sinkiti Sibata / Msieve
(13·10¹⁵⁴-7)/3 = 4(3)₁₅₃1_<155> = 4299968837_<10> · 5420661282707945028204253_<25> · 4248099842885959289351740481_<28> · C93
C93 = P43 · P50
P43 = 6196057801656421501364047194416498849394697_<43>
P50 = 70630835377785084555386441008655114290296665265803_<50>

Tue Dec 23 22:52:12 2008 Msieve v. 1.39 Tue Dec 23 22:52:12 2008 random seeds: 4415d7f4 e16d18f3 Tue Dec 23 22:52:12 2008 factoring 437632738580035654262129319099138766292963493690866696448476387894541006903564451451163646691 (93 digits) Tue Dec 23 22:52:13 2008 searching for 15-digit factors Tue Dec 23 22:52:14 2008 commencing quadratic sieve (93-digit input) Tue Dec 23 22:52:14 2008 using multiplier of 19 Tue Dec 23 22:52:14 2008 using 32kb Intel Core sieve core Tue Dec 23 22:52:14 2008 sieve interval: 36 blocks of size 32768 Tue Dec 23 22:52:14 2008 processing polynomials in batches of 6 Tue Dec 23 22:52:14 2008 using a sieve bound of 1923137 (71699 primes) Tue Dec 23 22:52:14 2008 using large prime bound of 232699577 (27 bits) Tue Dec 23 22:52:14 2008 using double large prime bound of 1148767303677169 (42-51 bits) Tue Dec 23 22:52:14 2008 using trial factoring cutoff of 51 bits Tue Dec 23 22:52:14 2008 polynomial 'A' values have 12 factors Wed Dec 24 01:24:11 2008 71822 relations (18303 full + 53519 combined from 959170 partial), need 71795 Wed Dec 24 01:24:12 2008 begin with 977473 relations Wed Dec 24 01:24:13 2008 reduce to 182815 relations in 10 passes Wed Dec 24 01:24:13 2008 attempting to read 182815 relations Wed Dec 24 01:24:15 2008 recovered 182815 relations Wed Dec 24 01:24:15 2008 recovered 165366 polynomials Wed Dec 24 01:24:15 2008 attempting to build 71822 cycles Wed Dec 24 01:24:15 2008 found 71822 cycles in 5 passes Wed Dec 24 01:24:15 2008 distribution of cycle lengths: Wed Dec 24 01:24:15 2008 length 1 : 18303 Wed Dec 24 01:24:15 2008 length 2 : 13016 Wed Dec 24 01:24:15 2008 length 3 : 12483 Wed Dec 24 01:24:15 2008 length 4 : 9444 Wed Dec 24 01:24:15 2008 length 5 : 7095 Wed Dec 24 01:24:15 2008 length 6 : 4692 Wed Dec 24 01:24:15 2008 length 7 : 2928 Wed Dec 24 01:24:15 2008 length 9+: 3861 Wed Dec 24 01:24:15 2008 largest cycle: 22 relations Wed Dec 24 01:24:16 2008 matrix is 71699 x 71822 (18.6 MB) with weight 4599586 (64.04/col) Wed Dec 24 01:24:16 2008 sparse part has weight 4599586 (64.04/col) Wed Dec 24 01:24:17 2008 filtering completed in 3 passes Wed Dec 24 01:24:17 2008 matrix is 67741 x 67805 (17.7 MB) with weight 4379423 (64.59/col) Wed Dec 24 01:24:17 2008 sparse part has weight 4379423 (64.59/col) Wed Dec 24 01:24:17 2008 saving the first 48 matrix rows for later Wed Dec 24 01:24:17 2008 matrix is 67693 x 67805 (11.6 MB) with weight 3510908 (51.78/col) Wed Dec 24 01:24:17 2008 sparse part has weight 2623737 (38.70/col) Wed Dec 24 01:24:17 2008 matrix includes 64 packed rows Wed Dec 24 01:24:17 2008 using block size 27122 for processor cache size 1024 kB Wed Dec 24 01:24:18 2008 commencing Lanczos iteration Wed Dec 24 01:24:18 2008 memory use: 10.9 MB Wed Dec 24 01:24:47 2008 lanczos halted after 1071 iterations (dim = 67691) Wed Dec 24 01:24:47 2008 recovered 16 nontrivial dependencies Wed Dec 24 01:24:48 2008 prp43 factor: 6196057801656421501364047194416498849394697 Wed Dec 24 01:24:48 2008 prp50 factor: 70630835377785084555386441008655114290296665265803 Wed Dec 24 01:24:48 2008 elapsed time 02:32:36
(38·10¹³⁶+61)/9 = 4(2)₁₃₅9_<137> = 11² · 507571 · 990643 · C123
C123 = P32 · P46 · P47
P32 = 12994371931234232563572230204953_<32>
P46 = 2821341889370461231082316680328888029873454389_<46>
P47 = 18929133352137533796090816854860634959299355049_<47>

Number: 42229_136 N=693971668979787672360221564933897224316140193326896041334006376981172056648340109892525747331357177578992585148159179582133 ( 123 digits) SNFS difficulty: 137 digits. Divisors found: r1=12994371931234232563572230204953 r2=2821341889370461231082316680328888029873454389 r3=18929133352137533796090816854860634959299355049 Version: Total time: 6.24 hours. Scaled time: 12.28 units (timescale=1.967). Factorization parameters were as follows: name: 42229_136 n: 693971668979787672360221564933897224316140193326896041334006376981172056648340109892525747331357177578992585148159179582133 m: 1000000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 1370000 alim: 1370000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1370000/1370000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [685000, 1360001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 193020 x 193268 Total sieving time: 6.24 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,137,5,0,0,0,0,0,0,0,0,1370000,1370000,26,26,48,48,2.3,2.3,75000 total time: 6.24 hours. --------- CPU info (if available) ----------
(38·10¹³⁷+61)/9 = 4(2)₁₃₆9_<138> = 3 · 127 · 151 · C133
C133 = P37 · P47 · P50
P37 = 6456539318974069952317840383913635547_<37>
P47 = 84353085074939403498494219218028513808174498829_<47>
P50 = 13475298467557402274192836515690867490289089049393_<50>

Number: 42229_137 N=7339038470080864615984812053018758968594709325793436968281834527858410634653008329808663541781339142761680176291429354995084775550959 ( 133 digits) SNFS difficulty: 139 digits. Divisors found: r1=6456539318974069952317840383913635547 r2=84353085074939403498494219218028513808174498829 r3=13475298467557402274192836515690867490289089049393 Version: Total time: 5.42 hours. Scaled time: 13.96 units (timescale=2.575). Factorization parameters were as follows: name: 42229_137 n: 7339038470080864615984812053018758968594709325793436968281834527858410634653008329808663541781339142761680176291429354995084775550959 m: 2000000000000000000000000000 deg: 5 c5: 475 c0: 244 skew: 0.88 type: snfs lss: 1 rlim: 1460000 alim: 1460000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1460000/1460000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [730000, 1480001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 206320 x 206568 Total sieving time: 5.42 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,139,5,0,0,0,0,0,0,0,0,1460000,1460000,26,26,48,48,2.3,2.3,75000 total time: 5.42 hours. --------- CPU info (if available) ----------
(38·10¹³²+61)/9 = 4(2)₁₃₁9_<133> = 11 · 776001532639_<12> · C120
C120 = P49 · P72
P49 = 2969872220720596372610570814567592219469836109293_<49>
P72 = 166551312272968076499268266318802432077753188457365327152386424859382757_<72>

Number: 42229_132 N=494636115644049218819442914466771717713015102938955522069569580741406160381239875380518653429265348791970272174371660801 ( 120 digits) SNFS difficulty: 134 digits. Divisors found: r1=2969872220720596372610570814567592219469836109293 r2=166551312272968076499268266318802432077753188457365327152386424859382757 Version: Total time: 4.08 hours. Scaled time: 9.61 units (timescale=2.357). Factorization parameters were as follows: name: 42229_132 n: 494636115644049218819442914466771717713015102938955522069569580741406160381239875380518653429265348791970272174371660801 m: 200000000000000000000000000 deg: 5 c5: 475 c0: 244 skew: 0.88 type: snfs lss: 1 rlim: 1210000 alim: 1210000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1210000/1210000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [605000, 1130001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 162582 x 162827 Total sieving time: 4.08 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1210000,1210000,26,26,47,47,2.3,2.3,75000 total time: 4.08 hours. --------- CPU info (if available) ----------
(38·10¹³³+61)/9 = 4(2)₁₃₂9_<134> = 7 · 17 · 31 · 7446191 · 92316751817_<11> · C113
C113 = P52 · P61
P52 = 3454354056951432918786575190491331483927052530924391_<52>
P61 = 4820042812404022801199777592890218362440628066520836743662493_<61>

Number: 42229_133 N=16650134443707430675722745496325348238405457625575494554061037823950827364147409161145258157135657400068205566763 ( 113 digits) SNFS difficulty: 135 digits. Divisors found: r1=3454354056951432918786575190491331483927052530924391 r2=4820042812404022801199777592890218362440628066520836743662493 Version: Total time: 4.36 hours. Scaled time: 8.73 units (timescale=2.003). Factorization parameters were as follows: name: 42229_133 n: 16650134443707430675722745496325348238405457625575494554061037823950827364147409161145258157135657400068205566763 m: 500000000000000000000000000 deg: 5 c5: 304 c0: 1525 skew: 1.38 type: snfs lss: 1 rlim: 1290000 alim: 1290000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1290000/1290000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [645000, 1095001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 149895 x 150143 Total sieving time: 4.36 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1290000,1290000,26,26,47,47,2.3,2.3,75000 total time: 4.36 hours. --------- CPU info (if available) ----------
(13·10¹³⁸-7)/3 = 4(3)₁₃₇1_<139> = 1003753 · 217066632061_<12> · C122
C122 = P57 · P65
P57 = 272710477884165309368820146712980890078113632640440282561_<57>
P65 = 72929015177053713033881917987365982816088025384408340890063152887_<65>

Number: 43331_138 N=19888506580555862802074130987443151078615717105176811792365248436258887922009032248563497555435293494812111456084822903607 ( 122 digits) SNFS difficulty: 140 digits. Divisors found: r1=272710477884165309368820146712980890078113632640440282561 r2=72929015177053713033881917987365982816088025384408340890063152887 Version: Total time: 4.53 hours. Scaled time: 11.65 units (timescale=2.575). Factorization parameters were as follows: name: 43331_138 n: 19888506580555862802074130987443151078615717105176811792365248436258887922009032248563497555435293494812111456084822903607 m: 5000000000000000000000000000 deg: 5 c5: 104 c0: -175 skew: 1.11 type: snfs lss: 1 rlim: 1540000 alim: 1540000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1540000/1540000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [770000, 1370001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 229684 x 229931 Total sieving time: 4.53 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1540000,1540000,26,26,48,48,2.3,2.3,100000 total time: 4.53 hours. --------- CPU info (if available) ----------
(13·10¹²⁶-7)/3 = 4(3)₁₂₅1_<127> = 41 · 113 · 612958849049_<12> · 3602570233447_<13> · C99
C99 = P32 · P68
P32 = 30490364046617984017424864824609_<32>
P68 = 13891636547419071980552984173367140215460386040448597016954924515941_<68>

Wed Dec 24 06:14:06 2008 Msieve v. 1.39 Wed Dec 24 06:14:06 2008 random seeds: 638a2880 0697d978 Wed Dec 24 06:14:06 2008 factoring 423561055534110855772718836647845940152748087470775841943157918715306066768867674318721107189592069 (99 digits) Wed Dec 24 06:14:07 2008 searching for 15-digit factors Wed Dec 24 06:14:09 2008 commencing quadratic sieve (99-digit input) Wed Dec 24 06:14:09 2008 using multiplier of 1 Wed Dec 24 06:14:09 2008 using 32kb Intel Core sieve core Wed Dec 24 06:14:09 2008 sieve interval: 36 blocks of size 32768 Wed Dec 24 06:14:09 2008 processing polynomials in batches of 6 Wed Dec 24 06:14:09 2008 using a sieve bound of 2612251 (95257 primes) Wed Dec 24 06:14:09 2008 using large prime bound of 391837650 (28 bits) Wed Dec 24 06:14:09 2008 using double large prime bound of 2934884765895450 (43-52 bits) Wed Dec 24 06:14:09 2008 using trial factoring cutoff of 52 bits Wed Dec 24 06:14:09 2008 polynomial 'A' values have 13 factors Wed Dec 24 14:57:37 2008 95665 relations (22800 full + 72865 combined from 1444038 partial), need 95353 Wed Dec 24 14:57:39 2008 begin with 1466838 relations Wed Dec 24 14:57:40 2008 reduce to 252523 relations in 11 passes Wed Dec 24 14:57:40 2008 attempting to read 252523 relations Wed Dec 24 14:57:45 2008 recovered 252523 relations Wed Dec 24 14:57:45 2008 recovered 241794 polynomials Wed Dec 24 14:57:45 2008 attempting to build 95665 cycles Wed Dec 24 14:57:45 2008 found 95665 cycles in 6 passes Wed Dec 24 14:57:45 2008 distribution of cycle lengths: Wed Dec 24 14:57:45 2008 length 1 : 22800 Wed Dec 24 14:57:45 2008 length 2 : 16294 Wed Dec 24 14:57:45 2008 length 3 : 15927 Wed Dec 24 14:57:45 2008 length 4 : 13040 Wed Dec 24 14:57:45 2008 length 5 : 10046 Wed Dec 24 14:57:45 2008 length 6 : 6811 Wed Dec 24 14:57:45 2008 length 7 : 4397 Wed Dec 24 14:57:45 2008 length 9+: 6350 Wed Dec 24 14:57:45 2008 largest cycle: 23 relations Wed Dec 24 14:57:45 2008 matrix is 95257 x 95665 (25.5 MB) with weight 6314404 (66.01/col) Wed Dec 24 14:57:45 2008 sparse part has weight 6314404 (66.01/col) Wed Dec 24 14:57:47 2008 filtering completed in 3 passes Wed Dec 24 14:57:47 2008 matrix is 91395 x 91459 (24.5 MB) with weight 6046936 (66.12/col) Wed Dec 24 14:57:47 2008 sparse part has weight 6046936 (66.12/col) Wed Dec 24 14:57:47 2008 saving the first 48 matrix rows for later Wed Dec 24 14:57:47 2008 matrix is 91347 x 91459 (14.3 MB) with weight 4688883 (51.27/col) Wed Dec 24 14:57:47 2008 sparse part has weight 3211621 (35.12/col) Wed Dec 24 14:57:47 2008 matrix includes 64 packed rows Wed Dec 24 14:57:47 2008 using block size 36583 for processor cache size 1024 kB Wed Dec 24 14:57:48 2008 commencing Lanczos iteration Wed Dec 24 14:57:48 2008 memory use: 14.5 MB Wed Dec 24 14:58:43 2008 lanczos halted after 1447 iterations (dim = 91341) Wed Dec 24 14:58:43 2008 recovered 13 nontrivial dependencies Wed Dec 24 14:58:44 2008 prp32 factor: 30490364046617984017424864824609 Wed Dec 24 14:58:44 2008 prp68 factor: 13891636547419071980552984173367140215460386040448597016954924515941 Wed Dec 24 14:58:44 2008 elapsed time 08:44:38
(38·10¹³⁹+61)/9 = 4(2)₁₃₈9_<140> = 7 · 43 · 79 · 118751 · 13963483 · C124
C124 = P41 · P83
P41 = 40995216861330514782493424946046859932427_<41>
P83 = 26120607663077197279728695742834580519372241488994079940765343709210850548980030161_<83>

Number: 42229_139 N=1070819975697581372026915209957136700305843805306366832768537504626396109208627745838362563415637931633490196373116881930747 ( 124 digits) SNFS difficulty: 141 digits. Divisors found: r1=40995216861330514782493424946046859932427 r2=26120607663077197279728695742834580519372241488994079940765343709210850548980030161 Version: Total time: 6.97 hours. Scaled time: 14.00 units (timescale=2.010). Factorization parameters were as follows: name: 42229_139 n: 1070819975697581372026915209957136700305843805306366832768537504626396109208627745838362563415637931633490196373116881930747 m: 10000000000000000000000000000 deg: 5 c5: 19 c0: 305 skew: 1.74 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor 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, 1490001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 208332 x 208580 Total sieving time: 6.97 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 6.97 hours. --------- CPU info (if available) ----------
(13·10¹³⁹-7)/3 = 4(3)₁₃₈1_<140> = 35561357833129779817_<20> · 339685932960896082541_<21> · C100
C100 = P42 · P58
P42 = 580227981425170480885365056415884167587353_<42>
P58 = 6182548491273330202741775652459471890874048806489022017791_<58>

Number: 43331_139 N=3587287631154757617814951158449886668895226167431297560934889849904751035171338016447415764312597223 ( 100 digits) SNFS difficulty: 141 digits. Divisors found: r1=580227981425170480885365056415884167587353 r2=6182548491273330202741775652459471890874048806489022017791 Version: Total time: 7.16 hours. Scaled time: 18.36 units (timescale=2.564). Factorization parameters were as follows: name: 43331_139 n: 3587287631154757617814951158449886668895226167431297560934889849904751035171338016447415764312597223 m: 10000000000000000000000000000 deg: 5 c5: 13 c0: -70 skew: 1.40 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1785001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 267552 x 267800 Total sieving time: 7.16 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 7.16 hours. --------- CPU info (if available) ----------
(13·10¹³⁶-7)/3 = 4(3)₁₃₅1_<137> = 41 · 461 · 1097 · 1144019 · 6912769 · C117
C117 = P39 · P79
P39 = 153868017024233492936781291144992798777_<39>
P79 = 1717501200001193868071551512936241855900994787663081370386972669289649929323709_<79>

Number: 43331_136 N=264268503880925151311871568681403279980594971164576904562485281555967178805595058087289716052263653659523810732303893 ( 117 digits) SNFS difficulty: 138 digits. Divisors found: r1=153868017024233492936781291144992798777 r2=1717501200001193868071551512936241855900994787663081370386972669289649929323709 Version: Total time: 4.87 hours. Scaled time: 12.50 units (timescale=2.564). Factorization parameters were as follows: name: 43331_136 n: 264268503880925151311871568681403279980594971164576904562485281555967178805595058087289716052263653659523810732303893 m: 2000000000000000000000000000 deg: 5 c5: 65 c0: -112 skew: 1.11 type: snfs lss: 1 rlim: 1410000 alim: 1410000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1410000/1410000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [705000, 1380001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 194934 x 195182 Total sieving time: 4.87 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1410000,1410000,26,26,48,48,2.3,2.3,75000 total time: 4.87 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁰+61)/9 = 4(2)₁₃₉9_<141> = 3 · 11 · 13² · 409 · 66376463 · C127
C127 = P61 · P66
P61 = 4363189719756629305373249732984127052389932144242640081636599_<61>
P66 = 639144315774237606362299455808713290546585132219180798704818559069_<66>

Number: 42229_140 N=2788707908027038368820676356991699645995675322839068899344297739110534039864931465687628595805788445793745961473494234473766331 ( 127 digits) SNFS difficulty: 141 digits. Divisors found: r1=4363189719756629305373249732984127052389932144242640081636599 r2=639144315774237606362299455808713290546585132219180798704818559069 Version: Total time: 6.86 hours. Scaled time: 13.78 units (timescale=2.010). Factorization parameters were as follows: name: 42227_140 n: 2788707908027038368820676356991699645995675322839068899344297739110534039864931465687628595805788445793745961473494234473766331 m: 10000000000000000000000000000 deg: 5 c5: 38 c0: 61 skew: 1.10 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 249081 x 249329 Total sieving time: 6.86 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,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 6.86 hours. --------- CPU info (if available) ----------
Dec 24, 2008 (3rd): By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(13·10¹²⁴-7)/3 = 4(3)₁₂₃1_<125> = 67 · 1697 · 60793 · C115
C115 = P43 · P73
P43 = 1498047185326462845874791264840983789868623_<43>
P73 = 4184912521601170246850918800640022065043403650310690001096570127074950871_<73>

Number: n N=6269196423822103232539740936099023112203802212838271361405353100480408276012089605380855071374200647972655269420633 ( 115 digits) SNFS difficulty: 126 digits. Divisors found: r1=1498047185326462845874791264840983789868623 (pp43) r2=4184912521601170246850918800640022065043403650310690001096570127074950871 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.99 hours. Scaled time: 3.64 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_3_123_1 n: 6269196423822103232539740936099023112203802212838271361405353100480408276012089605380855071374200647972655269420633 type: snfs skew: 1.40 deg: 5 c5: 13 c0: -70 m: 10000000000000000000000000 rlim: 650000 alim: 650000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 650000/650000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [325000, 605001) Primes: RFBsize:52831, AFBsize:53207, largePrimes:6633415 encountered Relations: rels:5890129, finalFF:152374 Max relations in full relation-set: 48 Initial matrix: 106103 x 152374 with sparse part having weight 24339461. Pruned matrix : 100481 x 101075 with weight 12235988. Total sieving time: 1.78 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.08 hours. Total square root time: 0.04 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,650000,650000,28,28,56,56,2.5,2.5,50000 total time: 1.99 hours. --------- CPU info (if available) ----------
(13·10¹³⁵-7)/3 = 4(3)₁₃₄1_<136> = 21521 · 376824788300183_<15> · C117
C117 = P46 · P71
P46 = 7462194341926544919338500194924283255312005077_<46>
P71 = 71606695242654519563333342916952318853502485124430637614152778256430721_<71>

Number: n N=534343076083794997371281760082808935626601181033359381519995052241174855210527261550171279430169719357538447850770517 ( 117 digits) SNFS difficulty: 136 digits. Divisors found: r1=7462194341926544919338500194924283255312005077 (pp46) r2=71606695242654519563333342916952318853502485124430637614152778256430721 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.56 hours. Scaled time: 6.51 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_3_134_1 n: 534343076083794997371281760082808935626601181033359381519995052241174855210527261550171279430169719357538447850770517 type: snfs skew: 0.88 deg: 5 c5: 13 c0: -7 m: 1000000000000000000000000000 rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [500000, 1020001) Primes: RFBsize:78498, AFBsize:78306, largePrimes:9031572 encountered Relations: rels:8076284, finalFF:178919 Max relations in full relation-set: 48 Initial matrix: 156869 x 178919 with sparse part having weight 27811347. Pruned matrix : 154011 x 154859 with weight 21176060. Total sieving time: 3.13 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.26 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,56,56,2.5,2.5,75000 total time: 3.56 hours. --------- CPU info (if available) ----------
(34·10¹⁸⁵+11)/9 = 3(7)₁₈₄9_<186> = 1039 · C183
C183 = P36 · P56 · P91
P36 = 553108953256060747840665463564358923_<36>
P56 = 84899358098754026519470500100735842692276241566795948069_<56>
P91 = 7742937698796390773077022171625908268690825320600198553953076059596260413718230752249653803_<91>

GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM] Input number is 363597476205753395358785156667736071008448294300074858303924713934338573414608063308737033472355897764944925676398246176879478130681210565714896802481018072933376109507004598438669661 (183 digits) Using B1=1830000, B2=1986068894, polynomial Dickson(6), sigma=2182743119 Step 1 took 41688ms Step 2 took 20734ms ********** Factor found in step 2: 553108953256060747840665463564358923 Found probable prime factor of 36 digits: 553108953256060747840665463564358923 Composite cofactor 657370440426457224196909528676015642805819843550172264758862997221749950147843630565666366392439605388006719253164554952138526942848104848416356407 has 147 digits Number: n N=657370440426457224196909528676015642805819843550172264758862997221749950147843630565666366392439605388006719253164554952138526942848104848416356407 ( 147 digits) SNFS difficulty: 186 digits. Divisors found: Wed Dec 24 13:32:23 2008 prp56 factor: 84899358098754026519470500100735842692276241566795948069 Wed Dec 24 13:32:23 2008 prp91 factor: 7742937698796390773077022171625908268690825320600198553953076059596260413718230752249653803 Wed Dec 24 13:32:23 2008 elapsed time 20:34:53 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 70.68 hours. Scaled time: 46.58 units (timescale=0.659). Factorization parameters were as follows: name: KA_3_7_184_9 n: 657370440426457224196909528676015642805819843550172264758862997221749950147843630565666366392439605388006719253164554952138526942848104848416356407 type: snfs skew: 0.80 deg: 5 c5: 34 c0: 11 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 3150001) Primes: RFBsize:571119, AFBsize:571308, largePrimes:32711526 encountered Relations: rels:29594547, finalFF:1086092 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 4539192 hash collisions in 33167915 relations Msieve: matrix is 1455727 x 1455975 (395.1 MB) Total sieving time: 68.38 hours. Total relation processing time: 2.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 70.68 hours. --------- CPU info (if available) ----------
Dec 24, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39, Msieve-1.39+pol51 gnfs
(38·10¹⁴⁴+61)/9 = 4(2)₁₄₃9_<145> = 11 · 503 · 919 · 16719328669_<11> · 5872408641739_<13> · C115
C115 = P33 · P39 · P45
P33 = 185958730996919530697610925218379_<33>
P39 = 435936853888932377299397412491753686571_<39>
P45 = 104325299889160694313575763049847352543268633_<45>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1036791296 Step 1 took 8186ms Step 2 took 9254ms ********** Factor found in step 2: 185958730996919530697610925218379 Found probable prime factor of 33 digits: 185958730996919530697610925218379 Composite cofactor has 83 digits Tue Dec 23 05:15:51 2008 Tue Dec 23 05:15:51 2008 Msieve v. 1.39 Tue Dec 23 05:15:51 2008 random seeds: 90094d45 a7ce150a Tue Dec 23 05:15:51 2008 factoring 45479243014700098733299390696402372968311259821857132401813685792934459068137627443 (83 digits) Tue Dec 23 05:15:52 2008 searching for 15-digit factors Tue Dec 23 05:15:52 2008 commencing quadratic sieve (83-digit input) Tue Dec 23 05:15:52 2008 using multiplier of 3 Tue Dec 23 05:15:52 2008 using 64kb Opteron sieve core Tue Dec 23 05:15:52 2008 sieve interval: 6 blocks of size 65536 Tue Dec 23 05:15:52 2008 processing polynomials in batches of 17 Tue Dec 23 05:15:52 2008 using a sieve bound of 1368329 (52647 primes) Tue Dec 23 05:15:52 2008 using large prime bound of 121781281 (26 bits) Tue Dec 23 05:15:52 2008 using trial factoring cutoff of 27 bits Tue Dec 23 05:15:52 2008 polynomial 'A' values have 11 factors Tue Dec 23 05:38:35 2008 52767 relations (26541 full + 26226 combined from 280810 partial), need 52743 Tue Dec 23 05:38:35 2008 begin with 307351 relations Tue Dec 23 05:38:35 2008 reduce to 75673 relations in 2 passes Tue Dec 23 05:38:35 2008 attempting to read 75673 relations Tue Dec 23 05:38:36 2008 recovered 75673 relations Tue Dec 23 05:38:36 2008 recovered 69585 polynomials Tue Dec 23 05:38:36 2008 attempting to build 52767 cycles Tue Dec 23 05:38:36 2008 found 52767 cycles in 1 passes Tue Dec 23 05:38:36 2008 distribution of cycle lengths: Tue Dec 23 05:38:36 2008 length 1 : 26541 Tue Dec 23 05:38:36 2008 length 2 : 26226 Tue Dec 23 05:38:36 2008 largest cycle: 2 relations Tue Dec 23 05:38:36 2008 matrix is 52647 x 52767 (8.0 MB) with weight 1682549 (31.89/col) Tue Dec 23 05:38:36 2008 sparse part has weight 1682549 (31.89/col) Tue Dec 23 05:38:37 2008 filtering completed in 3 passes Tue Dec 23 05:38:37 2008 matrix is 38828 x 38887 (6.4 MB) with weight 1373197 (35.31/col) Tue Dec 23 05:38:37 2008 sparse part has weight 1373197 (35.31/col) Tue Dec 23 05:38:37 2008 saving the first 48 matrix rows for later Tue Dec 23 05:38:37 2008 matrix is 38780 x 38887 (4.3 MB) with weight 1039749 (26.74/col) Tue Dec 23 05:38:37 2008 sparse part has weight 747149 (19.21/col) Tue Dec 23 05:38:37 2008 matrix includes 64 packed rows Tue Dec 23 05:38:37 2008 using block size 15554 for processor cache size 1024 kB Tue Dec 23 05:38:37 2008 commencing Lanczos iteration Tue Dec 23 05:38:37 2008 memory use: 4.3 MB Tue Dec 23 05:38:42 2008 lanczos halted after 615 iterations (dim = 38778) Tue Dec 23 05:38:42 2008 recovered 17 nontrivial dependencies Tue Dec 23 05:38:42 2008 prp39 factor: 435936853888932377299397412491753686571 Tue Dec 23 05:38:42 2008 prp45 factor: 104325299889160694313575763049847352543268633 Tue Dec 23 05:38:42 2008 elapsed time 00:22:51
(38·10¹⁴⁵+43)/9 = 4(2)₁₄₄7_<146> = 1663 · 1723 · C140
C140 = P48 · P93
P48 = 143361658105740544577121897169041849714893542691_<48>
P93 = 102785190506482758977581155294308544825255338892896261035565418692162299061389923861016260253_<93>

SNFS difficulty: 146 digits. Divisors found: r1=143361658105740544577121897169041849714893542691 (pp48) r2=102785190506482758977581155294308544825255338892896261035565418692162299061389923861016260253 (pp93) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.286). Factorization parameters were as follows: n: 14735455339723790094059125859440585500133569147151785776260491207954850254618973891914116647648234899910001267636934356764995196823221960823 m: 100000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 type: snfs lss: 1 rlim: 1940000 alim: 1940000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1940000/1940000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [970000, 2570001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 336574 x 336822 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000 total time: 11.00 hours.
(38·10¹⁵³+43)/9 = 4(2)₁₅₂7_<154> = 3² · C153
C153 = P69 · P85
P69 = 429658841311150490118038632706779529774463197589532158877111287918973_<69>
P85 = 1091879783126345287514741812724212614608670024173592287059530931202710184194869602711_<85>

SNFS difficulty: 155 digits. Divisors found: r1=429658841311150490118038632706779529774463197589532158877111287918973 (pp69) r2=1091879783126345287514741812724212614608670024173592287059530931202710184194869602711 (pp85) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135803 m: 5000000000000000000000000000000 deg: 5 c5: 304 c0: 1075 skew: 1.29 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [1400000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 565118 x 565366 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000 total time: 12.00 hours.
(38·10¹⁴⁶+61)/9 = 4(2)₁₄₅9_<147> = 3 · 11 · 13 · 743 · C142
C142 = P35 · P107
P35 = 29371295975761612541641795908618293_<35>
P107 = 45099515002463330270041583910624200505787042854484125648106218811048271349055997284919050293096397504594099_<107>

SNFS difficulty: 147 digits. Divisors found: r1=29371295975761612541641795908618293 (pp35) r2=45099515002463330270041583910624200505787042854484125648106218811048271349055997284919050293096397504594099 (pp107) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 1324631203500651683693406439032280216667834433648700135914133222343181966331360678601593810207538336744258682347511418843854913841454891253007 m: 100000000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 294682 x 294930 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,49,49,2.3,2.3,200000 total time: 6.00 hours.
(13·10¹⁴⁵-7)/3 = 4(3)₁₄₄1_<146> = 3709 · 3847 · 2170109 · 39052045075867533488696837658421_<32> · C101
C101 = P35 · P66
P35 = 78208945654866767181969270770471203_<35>
P66 = 458206575016335709488301915918886731111651833495759452288453585491_<66>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3061227314 Step 1 took 8259ms Step 2 took 8999ms ********** Factor found in step 2: 78208945654866767181969270770471203 Found probable prime factor of 35 digits: 78208945654866767181969270770471203 Probable prime cofactor 458206575016335709488301915918886731111651833495759452288453585491 has 66 digits
(13·10¹⁶²-7)/3 = 4(3)₁₆₁1_<163> = 97 · 4001 · 239027 · 365699 · 179076571 · 30747058603981_<14> · C125
C125 = P32 · P93
P32 = 35369121000324091221140788630633_<32>
P93 = 655910323226196685402316639620192425902591627772168768126116843748558306589316695535468462797_<93>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3840470679 Step 1 took 9843ms Step 2 took 10386ms ********** Factor found in step 2: 35369121000324091221140788630633 Found probable prime factor of 32 digits: 35369121000324091221140788630633 Probable prime cofactor 655910323226196685402316639620192425902591627772168768126116843748558306589316695535468462797 has 93 digits
(13·10¹⁴⁰-7)/3 = 4(3)₁₃₉1_<141> = 4152577859_<10> · C132
C132 = P46 · P86
P46 = 1618888627972634184177225680705039794519589281_<46>
P86 = 64459560671406830134081826137348849162306203510285790506146547055011181477654430473489_<86>

SNFS difficulty: 141 digits. Divisors found: r1=1618888627972634184177225680705039794519589281 (pp46) r2=64459560671406830134081826137348849162306203510285790506146547055011181477654430473489 (pp86) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.673). Factorization parameters were as follows: n: 104352849735052573600242117298572566832474972586259539976354079321149059118299684921894039635232118915300832492670990117450639071409 m: 10000000000000000000000000000 deg: 5 c5: 13 c0: -7 skew: 0.88 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [785000, 1585001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 261172 x 261420 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,49,49,2.3,2.3,100000 total time: 3.90 hours.
(38·10¹⁵⁴+61)/9 = 4(2)₁₅₃9_<155> = 11 · 3598943 · C148
C148 = P56 · P92
P56 = 15141979967594079491718919468985969669399230154355609013_<56>
P92 = 70435364495469228989127803857011940423160477324626942530227526262722573852534558759089710621_<92>

SNFS difficulty: 156 digits. Divisors found: r1=15141979967594079491718919468985969669399230154355609013 (pp56) r2=70435364495469228989127803857011940423160477324626942530227526262722573852534558759089710621 (pp92) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.307). Factorization parameters were as follows: n: 1066530878200582333156814053010519584177460948501779101207877934822484930669472630820726636637030327622259753443826100714526010508747662406389427073 m: 10000000000000000000000000000000 deg: 5 c5: 19 c0: 305 skew: 1.74 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [1400000, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 470528 x 470776 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,52,52,2.4,2.4,100000 total time: 17.00 hours.
(13·10¹⁹⁴-7)/3 = 4(3)₁₉₃1_<195> = 3881 · 4040009 · 12429749 · 4005775577929_<13> · 66007507859850270736596089399561_<32> · C133
C133 = P31 · P103
P31 = 4448855391179499901841920088701_<31>
P103 = 1890190271245129714956635517993862966113876278013600663354393732491301918077570212567736137795152565619_<103>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1699384495 Step 1 took 9871ms Step 2 took 10861ms ********** Factor found in step 2: 4448855391179499901841920088701 Found probable prime factor of 31 digits: 4448855391179499901841920088701 Probable prime cofactor has 103 digits
(38·10¹⁷⁴+61)/9 = 4(2)₁₇₃9_<175> = 11 · 557 · 23333 · 59218732301_<11> · C156
C156 = P42 · C115
P42 = 262088313569048659823633945899080702035203_<42>
C115 = [1902899549437374369035951375932780225773552267114939321874434723505133347794160411662937567103887497100312817310473_<115>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=113264461 Step 1 took 13984ms Step 2 took 13062ms ********** Factor found in step 2: 262088313569048659823633945899080702035203 Found probable prime factor of 42 digits: 262088313569048659823633945899080702035203 Composite cofactor has 115 digits
(13·10²⁰³-7)/3 = 4(3)₂₀₂1_<204> = 127 · 259042595353901_<15> · C188
C188 = P38 · P150
P38 = 63444856538474819856481993655770160539_<38>
P150 = 207611197901601014143416821146774403219826219131558291970037945989725439970919940184172631734257013957795695677276118342125803124864277075013790561427_<150>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3263277877 Step 1 took 12681ms Step 2 took 11857ms ********** Factor found in step 2: 63444856538474819856481993655770160539 Found probable prime factor of 38 digits: 63444856538474819856481993655770160539 Probable prime cofactor has 150 digits
(13·10¹⁵²-7)/3 = 4(3)₁₅₁1_<153> = 233 · 40277009 · C143
C143 = P41 · P103
P41 = 20031893966274074423596077442708505693053_<41>
P103 = 2305085038050452143230599323022197163476467261349173660893918734016736964140945346920717888247983995591_<103>

SNFS difficulty: 154 digits. Divisors found: r1=20031893966274074423596077442708505693053 (pp41) r2=2305085038050452143230599323022197163476467261349173660893918734016736964140945346920717888247983995591 (pp103) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.689). Factorization parameters were as follows: n: 46175219065471497544696430236163828161418409151702714305658788678833996656676372801075680683544452514045855985835996777599255062948253551329323 m: 2000000000000000000000000000000 deg: 5 c5: 325 c0: -56 skew: 0.70 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1300000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 503364 x 503612 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000 total time: 14.00 hours.
(16·10²²⁰-61)/9 = 1(7)₂₁₉1_<221> = 13 · 353 · 1877 · 16492937 · 1805034167_<10> · 937019983238111_<15> · 55949358235598934650206505967480781_<35> · C148
C148 = P63 · P85
P63 = 502302273034882362079860646223768728379203876736278008316737227_<63>
P85 = 2632707497199637986790781217412309087011431749152792902304523313521897147926180843269_<85>

Number: 17771_220 N=1322414960079354351709834861520621170706984511895469829631709464819715591749118547779968053941698236864151284187903149814300379387206849149544675063 ( 148 digits) Divisors found: r1=502302273034882362079860646223768728379203876736278008316737227 (pp63) r2=2632707497199637986790781217412309087011431749152792902304523313521897147926180843269 (pp85) Version: Msieve-1.39 Total time: 1400.00 hours. Scaled time: 3830.40 units (timescale=2.736). Factorization parameters were as follows: name: 17771_220 n: 1322414960079354351709834861520621170706984511895469829631709464819715591749118547779968053941698236864151284187903149814300379387206849149544675063 skew: 190966.40 c5: 24166860 c4: -17657193107092 c3: -2881381445141050978 c2: 749005469110315625842208 c1: -28000830886921387321901315893 c0: 8308569654994887332138921957235 Y1: 253242919256012579 Y0: -8864032069059734770877792666 # norm 2.53e+20 # alpha -5.85 # Murphy_E 7.15e-12 type: gnfs rlim: 36000000 alim: 36000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 36000000/36000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved algebraic special-q in [18000000, 19000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3086519 x 3086767 Total sieving time: 1280.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 30.00 hours (4 cpu) Time per square root: 1.50 hours. Prototype def-par.txt line would be: gnfs,147,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,36000000,36000000,29,29,58,58,2.6,2.6,100000 total time: 1400.00 hours.
C148 is the largest number which was factored by GNFS in our tables so far. Congratulations!
Dec 24, 2008: By Serge Batalov / GMP-ECM 6.2.1
(38·10²⁰⁵+61)/9 = 4(2)₂₀₄9_<206> = 7 · 996172031694311_<15> · C190
C190 = P39 · C152
P39 = 604708101318908926128095438473785832727_<39>
C152 = [10012970019827499748751154328820037782074317676296066223065340785954584373285105326974194401949500349014357279371189711576864463523554910181915957776451_<152>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3954599440 Step 1 took 16015ms Step 2 took 15053ms ********** Factor found in step 2: 604708101318908926128095438473785832727 Found probable prime factor of 39 digits: 604708101318908926128095438473785832727 Composite cofactor has 152 digits
Dec 23, 2008 (8th): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39
(38·10¹²⁹+61)/9 = 4(2)₁₂₈9_<130> = 113 · 212476189 · 206782920150614243_<18> · C102
C102 = P31 · P72
P31 = 6877800995261078438976596986477_<31>
P72 = 123648287482431227866137204018035742921025020239320352409776567579513327_<72>

Factor found in step 1: 6877800995261078438976596986477
(38·10¹⁵¹+61)/9 = 4(2)₁₅₀9_<152> = 7 · 1117 · 20743 · 192637 · 82137278791_<11> · C128
C128 = P29 · P99
P29 = 56185303161233834414804494597_<29>
P99 = 292829995865447732444269891383468434429946313251210428873631095088198685156325342448697256025078463_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3917450993 Step 1 took 9731ms Step 2 took 10584ms ********** Factor found in step 2: 56185303161233834414804494597 Found probable prime factor of 29 digits: 56185303161233834414804494597 Probable prime cofactor 292829995865447732444269891383468434429946313251210428873631095088198685156325342448697256025078463 has 99 digits
(13·10¹⁴⁵-7)/3 = 4(3)₁₄₄1_<146> = 3709 · 3847 · 2170109 · C133
C133 = P32 · C101
P32 = 39052045075867533488696837658421_<32>
C101 = [35835853124155232087376837262708155018312446867976450226551174108265579054212486580985798592914115673_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2266195174 Step 1 took 9764ms Step 2 took 10698ms ********** Factor found in step 2: 39052045075867533488696837658421 Found probable prime factor of 32 digits: 39052045075867533488696837658421 Composite cofactor has 101 digits
(13·10¹⁸⁶-7)/3 = 4(3)₁₈₅1_<187> = 29 · 41 · 1723 · 2881969280353873_<16> · C165
C165 = P34 · C132
P34 = 2267180036234447141280701752917889_<34>
C132 = [323727512032728409566065549304498685213258027853771402670265835962965506247762803100126933161757433369766377101984695411470824717509_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=980914334 Step 1 took 13664ms Step 2 took 13602ms ********** Factor found in step 2: 2267180036234447141280701752917889 Found probable prime factor of 34 digits: 2267180036234447141280701752917889 Composite cofactor has 132 digits
(13·10¹⁹⁴-7)/3 = 4(3)₁₉₃1_<195> = 3881 · 4040009 · 12429749 · 4005775577929_<13> · C165
C165 = P32 · C133
P32 = 66007507859850270736596089399561_<32>
C133 = [8409183178583936583030174346844415915814492342050749419119294169308338808320971385476178209350780286513505479940764510332776202970919_<133>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=230614363 Step 1 took 13630ms Step 2 took 13457ms ********** Factor found in step 2: 66007507859850270736596089399561 Found probable prime factor of 32 digits: 66007507859850270736596089399561 Composite cofactor 8409183178583936583030174346844415915814492342050749419119294169308338808320971385476178209350780286513505479940764510332776202970919 has 133 digits
(38·10¹⁸⁰+61)/9 = 4(2)₁₇₉9_<181> = 11² · 193 · 2125621 · 9206214079_<10> · 61673945456472526189_<20> · C141
C141 = P32 · P109
P32 = 37615930741760579786512667771617_<32>
P109 = 3982519964961393426250352239850021980260372565021485335616685544317069003492639457212340339450474841652800179_<109>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1328187747 Step 1 took 11835ms Step 2 took 11587ms ********** Factor found in step 2: 37615930741760579786512667771617 Found probable prime factor of 32 digits: 37615930741760579786512667771617 Probable prime cofactor 3982519964961393426250352239850021980260372565021485335616685544317069003492639457212340339450474841652800179 has 109 digits
(38·10¹⁷⁵+61)/9 = 4(2)₁₇₄9_<176> = 7 · 48661 · C171
C171 = P31 · C140
P31 = 1740394642983557583386337035393_<31>
C140 = [71222018811833964655417651567953033432448526235056638873220031832622185237876237006720634532335848847765089902608605674576837157124980845239_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=205899236 Step 1 took 13705ms ********** Factor found in step 1: 1740394642983557583386337035393 Found probable prime factor of 31 digits: 1740394642983557583386337035393 Composite cofactor has 140 digits
(13·10²⁰⁴-7)/3 = 4(3)₂₀₃1_<205> = 119179 · 279991 · 11574691 · 21512664293_<11> · C177
C177 = P32 · P146
P32 = 26308325916731982485427287860457_<32>
P146 = 19823551780928035006602671905281634246612561791914656475871110593336489297213306083897826212562111916418038463405766923512493202714696938292099769_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1594125605 Step 1 took 16110ms Step 2 took 14725ms ********** Factor found in step 2: 26308325916731982485427287860457 Found probable prime factor of 32 digits: 26308325916731982485427287860457 Probable prime cofactor has 146 digits
(13·10¹⁹³-7)/3 = 4(3)₁₉₂1_<194> = 151 · 10209190744703_<14> · C179
C179 = P31 · C148
P31 = 7709568588244219307028066227297_<31>
C148 = [3646059534317701069724515171275791765391252664992167269599666190068435969269326867841860958544963686066522189227458537555849678015726858695874479291_<148>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2528423854 Step 1 took 15951ms Step 2 took 14697ms ********** Factor found in step 2: 7709568588244219307028066227297 Found probable prime factor of 31 digits: 7709568588244219307028066227297 Composite cofactor has 148 digits
(13·10¹²⁵-7)/3 = 4(3)₁₂₄1_<126> = 17 · 19 · 137 · 3943 · 80849611 · C110
C110 = P39 · P71
P39 = 756960282992795240590601586497232434921_<39>
P71 = 40580855963552503455078830310304821124582047703016518551277824518526757_<71>

SNFS difficulty: 126 digits. Divisors found: r1=756960282992795240590601586497232434921 (pp39) r2=40580855963552503455078830310304821124582047703016518551277824518526757 (pp71) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 30718096214260565396870102557694086018037165181434351721059131933001350211212314245444509148935415858799681197 m: 10000000000000000000000000 deg: 5 c5: 13 c0: -7 skew: 0.88 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [445000, 695001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 125763 x 125999 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,49,49,2.3,2.3,50000 total time: 1.30 hours.
Dec 23, 2008 (7th): By Sinkiti Sibata / Msieve
(38·10¹⁵⁵+43)/9 = 4(2)₁₅₄7_<156> = 13 · 648404825447551_<15> · C140
C140 = P62 · P78
P62 = 68502326768501726934975760518634987979255867421670311224348881_<62>
P78 = 731216821236048149998573343592774757206363666972266538567208965878323259710609_<78>

Number: 42227_155 N=50090053626936883206705630949905665484857244831913664200001658149686866574332055065172584204637245327813337676459217261678272501746512978529 ( 140 digits) SNFS difficulty: 156 digits. Divisors found: r1=68502326768501726934975760518634987979255867421670311224348881 r2=731216821236048149998573343592774757206363666972266538567208965878323259710609 Version: Total time: 32.15 hours. Scaled time: 82.43 units (timescale=2.564). Factorization parameters were as follows: name: 42227_155 n: 50090053626936883206705630949905665484857244831913664200001658149686866574332055065172584204637245327813337676459217261678272501746512978529 m: 10000000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 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, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 560105 x 560353 Total sieving time: 32.15 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 32.15 hours. --------- CPU info (if available) ----------
(37·10¹⁵⁶+17)/9 = 4(1)₁₅₅3_<157> = 3³ · 29 · 10189769 · 13778351 · 2556268457_<10> · C131
C131 = P34 · P97
P34 = 3797525954125859456188033584306947_<34>
P97 = 3852375905322761719761070474805539193083531228124173816698883017752530486655049572263981171562611_<97>

Number: 42227_156 N=14629497485512292314226146150939449758591397444048985543210067506643763064342654028641902815319618485210777765254764855395452758617 ( 131 digits) SNFS difficulty: 158 digits. Divisors found: r1=3797525954125859456188033584306947 r2=3852375905322761719761070474805539193083531228124173816698883017752530486655049572263981171562611 Version: Total time: 30.38 hours. Scaled time: 60.50 units (timescale=1.991). Factorization parameters were as follows: name: 42227_156 n: 14629497485512292314226146150939449758591397444048985543210067506643763064342654028641902815319618485210777765254764855395452758617 m: 20000000000000000000000000000000 deg: 5 c5: 185 c0: 272 skew: 1.08 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: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 579590 x 579838 Total sieving time: 30.38 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,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 30.38 hours. --------- CPU info (if available) ----------
(38·10¹¹¹+61)/9 = 4(2)₁₁₀9_<112> = 11339154493_<11> · 7499477233123_<13> · C89
C89 = P37 · P52
P37 = 7397064209141958485367330886373433809_<37>
P52 = 6712279544020820708812321814113647261175372549034179_<52>

Tue Dec 23 17:27:13 2008 Msieve v. 1.39 Tue Dec 23 17:27:13 2008 random seeds: 7cbef738 6f66a5b2 Tue Dec 23 17:27:13 2008 factoring 49651162776832117853392950700141070758766904970016036759288163519498755604332466735157811 (89 digits) Tue Dec 23 17:27:14 2008 searching for 15-digit factors Tue Dec 23 17:27:16 2008 commencing quadratic sieve (89-digit input) Tue Dec 23 17:27:16 2008 using multiplier of 11 Tue Dec 23 17:27:16 2008 using 32kb Intel Core sieve core Tue Dec 23 17:27:16 2008 sieve interval: 32 blocks of size 32768 Tue Dec 23 17:27:16 2008 processing polynomials in batches of 7 Tue Dec 23 17:27:16 2008 using a sieve bound of 1556189 (58842 primes) Tue Dec 23 17:27:16 2008 using large prime bound of 124495120 (26 bits) Tue Dec 23 17:27:16 2008 using double large prime bound of 372626841652480 (42-49 bits) Tue Dec 23 17:27:16 2008 using trial factoring cutoff of 49 bits Tue Dec 23 17:27:16 2008 polynomial 'A' values have 11 factors Tue Dec 23 18:38:03 2008 59083 relations (15371 full + 43712 combined from 629948 partial), need 58938 Tue Dec 23 18:38:04 2008 begin with 645319 relations Tue Dec 23 18:38:04 2008 reduce to 144756 relations in 9 passes Tue Dec 23 18:38:04 2008 attempting to read 144756 relations Tue Dec 23 18:38:06 2008 recovered 144756 relations Tue Dec 23 18:38:06 2008 recovered 124039 polynomials Tue Dec 23 18:38:06 2008 attempting to build 59083 cycles Tue Dec 23 18:38:06 2008 found 59083 cycles in 5 passes Tue Dec 23 18:38:06 2008 distribution of cycle lengths: Tue Dec 23 18:38:06 2008 length 1 : 15371 Tue Dec 23 18:38:06 2008 length 2 : 11272 Tue Dec 23 18:38:06 2008 length 3 : 10572 Tue Dec 23 18:38:06 2008 length 4 : 7903 Tue Dec 23 18:38:06 2008 length 5 : 5658 Tue Dec 23 18:38:06 2008 length 6 : 3490 Tue Dec 23 18:38:06 2008 length 7 : 2178 Tue Dec 23 18:38:06 2008 length 9+: 2639 Tue Dec 23 18:38:06 2008 largest cycle: 20 relations Tue Dec 23 18:38:07 2008 matrix is 58842 x 59083 (14.7 MB) with weight 3621608 (61.30/col) Tue Dec 23 18:38:07 2008 sparse part has weight 3621608 (61.30/col) Tue Dec 23 18:38:07 2008 filtering completed in 3 passes Tue Dec 23 18:38:07 2008 matrix is 55011 x 55075 (13.8 MB) with weight 3403270 (61.79/col) Tue Dec 23 18:38:07 2008 sparse part has weight 3403270 (61.79/col) Tue Dec 23 18:38:08 2008 saving the first 48 matrix rows for later Tue Dec 23 18:38:08 2008 matrix is 54963 x 55075 (10.5 MB) with weight 2875828 (52.22/col) Tue Dec 23 18:38:08 2008 sparse part has weight 2420144 (43.94/col) Tue Dec 23 18:38:08 2008 matrix includes 64 packed rows Tue Dec 23 18:38:08 2008 using block size 22030 for processor cache size 1024 kB Tue Dec 23 18:38:08 2008 commencing Lanczos iteration Tue Dec 23 18:38:08 2008 memory use: 9.3 MB Tue Dec 23 18:38:29 2008 lanczos halted after 871 iterations (dim = 54961) Tue Dec 23 18:38:29 2008 recovered 17 nontrivial dependencies Tue Dec 23 18:38:29 2008 prp37 factor: 7397064209141958485367330886373433809 Tue Dec 23 18:38:29 2008 prp52 factor: 6712279544020820708812321814113647261175372549034179 Tue Dec 23 18:38:29 2008 elapsed time 01:11:16
(38·10¹⁵⁷+43)/9 = 4(2)₁₅₆7_<158> = 3833 · 5659 · C151
C151 = P59 · P92
P59 = 91465142275684836616097261496147067070594607462692509039543_<59>
P92 = 21281731504266448543814676309892699432806272010865082270499088002856980384586766615972344087_<92>

Number: 42227_157 N=1946536599910654994557048257147197041338131628011548883606705701794496211816949357822976664975587383170602105211092084740339931779936681520738685232241 ( 151 digits) SNFS difficulty: 159 digits. Divisors found: r1=91465142275684836616097261496147067070594607462692509039543 r2=21281731504266448543814676309892699432806272010865082270499088002856980384586766615972344087 Version: Total time: 34.06 hours. Scaled time: 85.63 units (timescale=2.514). Factorization parameters were as follows: name:42227_157 n: 1946536599910654994557048257147197041338131628011548883606705701794496211816949357822976664975587383170602105211092084740339931779936681520738685232241 m: 20000000000000000000000000000000 deg: 5 c5: 475 c0: 172 skew: 0.82 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, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 522055 x 522303 Total sieving time: 34.06 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 34.06 hours. --------- CPU info (if available) ----------
(13·10¹¹⁶-7)/3 = 4(3)₁₁₅1_<117> = 41 · 105225587 · C108
C108 = P47 · P61
P47 = 20912340313401736804695249831314117167056127139_<47>
P61 = 4803018351672359716761183080233491333287524164537900935628787_<61>

Number: 43331_116 N=100442354301686248318155650268889154362152020216994424474504576240621884645894815542260238572668695980350393 ( 108 digits) SNFS difficulty: 118 digits. Divisors found: r1=20912340313401736804695249831314117167056127139 r2=4803018351672359716761183080233491333287524164537900935628787 Version: Total time: 1.52 hours. Scaled time: 3.02 units (timescale=1.991). Factorization parameters were as follows: name: 43331_116 n: 100442354301686248318155650268889154362152020216994424474504576240621884645894815542260238572668695980350393 m: 200000000000000000000000 deg: 5 c5: 65 c0: -112 skew: 1.11 type: snfs lss: 1 rlim: 660000 alim: 660000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 660000/660000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [330000, 530001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 68965 x 69199 Total sieving time: 1.52 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000 total time: 1.52 hours. --------- CPU info (if available) ----------
(38·10¹²²+61)/9 = 4(2)₁₂₁9_<123> = 3 · 11 · 13 · 1447 · 8190245732611_<13> · 42734715820119503_<17> · C88
C88 = P38 · P51
P38 = 17894098175364997990374216358774504223_<38>
P51 = 108599467479248166102092723780312641021472824805237_<51>

Tue Dec 23 18:47:15 2008 Msieve v. 1.39 Tue Dec 23 18:47:15 2008 random seeds: 160947d4 cef27f46 Tue Dec 23 18:47:15 2008 factoring 1943289532866025046805189916901455945080339390486360112365850271499631585958241209015851 (88 digits) Tue Dec 23 18:47:16 2008 searching for 15-digit factors Tue Dec 23 18:47:17 2008 commencing quadratic sieve (88-digit input) Tue Dec 23 18:47:17 2008 using multiplier of 19 Tue Dec 23 18:47:17 2008 using 32kb Intel Core sieve core Tue Dec 23 18:47:17 2008 sieve interval: 24 blocks of size 32768 Tue Dec 23 18:47:17 2008 processing polynomials in batches of 9 Tue Dec 23 18:47:17 2008 using a sieve bound of 1506511 (57333 primes) Tue Dec 23 18:47:17 2008 using large prime bound of 120520880 (26 bits) Tue Dec 23 18:47:17 2008 using double large prime bound of 351489263807840 (42-49 bits) Tue Dec 23 18:47:17 2008 using trial factoring cutoff of 49 bits Tue Dec 23 18:47:17 2008 polynomial 'A' values have 11 factors Tue Dec 23 19:37:18 2008 57729 relations (16066 full + 41663 combined from 603363 partial), need 57429 Tue Dec 23 19:37:19 2008 begin with 619429 relations Tue Dec 23 19:37:19 2008 reduce to 138258 relations in 10 passes Tue Dec 23 19:37:19 2008 attempting to read 138258 relations Tue Dec 23 19:37:21 2008 recovered 138258 relations Tue Dec 23 19:37:21 2008 recovered 115980 polynomials Tue Dec 23 19:37:21 2008 attempting to build 57729 cycles Tue Dec 23 19:37:21 2008 found 57729 cycles in 5 passes Tue Dec 23 19:37:21 2008 distribution of cycle lengths: Tue Dec 23 19:37:21 2008 length 1 : 16066 Tue Dec 23 19:37:21 2008 length 2 : 11406 Tue Dec 23 19:37:21 2008 length 3 : 10192 Tue Dec 23 19:37:21 2008 length 4 : 7446 Tue Dec 23 19:37:21 2008 length 5 : 5239 Tue Dec 23 19:37:21 2008 length 6 : 3296 Tue Dec 23 19:37:21 2008 length 7 : 1905 Tue Dec 23 19:37:21 2008 length 9+: 2179 Tue Dec 23 19:37:21 2008 largest cycle: 19 relations Tue Dec 23 19:37:21 2008 matrix is 57333 x 57729 (13.8 MB) with weight 3385288 (58.64/col) Tue Dec 23 19:37:21 2008 sparse part has weight 3385288 (58.64/col) Tue Dec 23 19:37:22 2008 filtering completed in 3 passes Tue Dec 23 19:37:22 2008 matrix is 52973 x 53036 (12.7 MB) with weight 3125748 (58.94/col) Tue Dec 23 19:37:22 2008 sparse part has weight 3125748 (58.94/col) Tue Dec 23 19:37:22 2008 saving the first 48 matrix rows for later Tue Dec 23 19:37:22 2008 matrix is 52925 x 53036 (9.3 MB) with weight 2584488 (48.73/col) Tue Dec 23 19:37:22 2008 sparse part has weight 2112719 (39.84/col) Tue Dec 23 19:37:22 2008 matrix includes 64 packed rows Tue Dec 23 19:37:22 2008 using block size 21214 for processor cache size 1024 kB Tue Dec 23 19:37:23 2008 commencing Lanczos iteration Tue Dec 23 19:37:23 2008 memory use: 8.5 MB Tue Dec 23 19:37:40 2008 lanczos halted after 838 iterations (dim = 52924) Tue Dec 23 19:37:41 2008 recovered 17 nontrivial dependencies Tue Dec 23 19:37:42 2008 prp38 factor: 17894098175364997990374216358774504223 Tue Dec 23 19:37:42 2008 prp51 factor: 108599467479248166102092723780312641021472824805237 Tue Dec 23 19:37:42 2008 elapsed time 00:50:27
(13·10¹¹⁹-7)/3 = 4(3)₁₁₈1_<120> = 23 · 127 · C117
C117 = P48 · P70
P48 = 113514518603811468544415778265029062834435682901_<48>
P70 = 1306890282973394626750519136011642653347252960413338529753654668995311_<70>

Number: 43331_119 N=148351021339723838867967591007645783407508844003195252767317128837156225037087755334930959716991897751911445851877211 ( 117 digits) SNFS difficulty: 121 digits. Divisors found: r1=113514518603811468544415778265029062834435682901 r2=1306890282973394626750519136011642653347252960413338529753654668995311 Version: Total time: 2.19 hours. Scaled time: 4.38 units (timescale=1.997). Factorization parameters were as follows: name: 43331_119 n: 148351021339723838867967591007645783407508844003195252767317128837156225037087755334930959716991897751911445851877211 m: 1000000000000000000000000 deg: 5 c5: 13 c0: -70 skew: 1.40 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, 665001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 87580 x 87818 Total sieving time: 2.19 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 2.19 hours. --------- CPU info (if available) ----------
(38·10¹²⁴+61)/9 = 4(2)₁₂₃9_<125> = 11 · 47² · 383 · 170711 · 1500390189343255882395007_<25> · C89
C89 = P41 · P48
P41 = 63555308651323802072448928885255075100069_<41>
P48 = 278699608001282959114888883431789684547614379749_<48>

Tue Dec 23 20:12:21 2008 Msieve v. 1.39 Tue Dec 23 20:12:21 2008 random seeds: 7df503ec db120c14 Tue Dec 23 20:12:21 2008 factoring 17712839607524491181194896261236888181051603158412905861666362722760429830774699542102681 (89 digits) Tue Dec 23 20:12:22 2008 searching for 15-digit factors Tue Dec 23 20:12:24 2008 commencing quadratic sieve (89-digit input) Tue Dec 23 20:12:24 2008 using multiplier of 1 Tue Dec 23 20:12:24 2008 using 32kb Intel Core sieve core Tue Dec 23 20:12:24 2008 sieve interval: 30 blocks of size 32768 Tue Dec 23 20:12:24 2008 processing polynomials in batches of 7 Tue Dec 23 20:12:24 2008 using a sieve bound of 1546837 (58547 primes) Tue Dec 23 20:12:24 2008 using large prime bound of 123746960 (26 bits) Tue Dec 23 20:12:24 2008 using double large prime bound of 368605688486800 (42-49 bits) Tue Dec 23 20:12:24 2008 using trial factoring cutoff of 49 bits Tue Dec 23 20:12:24 2008 polynomial 'A' values have 11 factors Tue Dec 23 21:02:17 2008 58671 relations (16518 full + 42153 combined from 614508 partial), need 58643 Tue Dec 23 21:02:18 2008 begin with 631026 relations Tue Dec 23 21:02:19 2008 reduce to 139761 relations in 11 passes Tue Dec 23 21:02:19 2008 attempting to read 139761 relations Tue Dec 23 21:02:20 2008 recovered 139761 relations Tue Dec 23 21:02:20 2008 recovered 112916 polynomials Tue Dec 23 21:02:20 2008 attempting to build 58671 cycles Tue Dec 23 21:02:21 2008 found 58671 cycles in 6 passes Tue Dec 23 21:02:21 2008 distribution of cycle lengths: Tue Dec 23 21:02:21 2008 length 1 : 16518 Tue Dec 23 21:02:21 2008 length 2 : 11650 Tue Dec 23 21:02:21 2008 length 3 : 10419 Tue Dec 23 21:02:21 2008 length 4 : 7564 Tue Dec 23 21:02:21 2008 length 5 : 5203 Tue Dec 23 21:02:21 2008 length 6 : 3267 Tue Dec 23 21:02:21 2008 length 7 : 1916 Tue Dec 23 21:02:21 2008 length 9+: 2134 Tue Dec 23 21:02:21 2008 largest cycle: 19 relations Tue Dec 23 21:02:21 2008 matrix is 58547 x 58671 (13.9 MB) with weight 3403013 (58.00/col) Tue Dec 23 21:02:21 2008 sparse part has weight 3403013 (58.00/col) Tue Dec 23 21:02:21 2008 filtering completed in 3 passes Tue Dec 23 21:02:21 2008 matrix is 53864 x 53928 (12.9 MB) with weight 3170121 (58.78/col) Tue Dec 23 21:02:21 2008 sparse part has weight 3170121 (58.78/col) Tue Dec 23 21:02:22 2008 saving the first 48 matrix rows for later Tue Dec 23 21:02:22 2008 matrix is 53816 x 53928 (9.1 MB) with weight 2584186 (47.92/col) Tue Dec 23 21:02:22 2008 sparse part has weight 2066484 (38.32/col) Tue Dec 23 21:02:22 2008 matrix includes 64 packed rows Tue Dec 23 21:02:22 2008 using block size 21571 for processor cache size 1024 kB Tue Dec 23 21:02:22 2008 commencing Lanczos iteration Tue Dec 23 21:02:22 2008 memory use: 8.4 MB Tue Dec 23 21:02:40 2008 lanczos halted after 853 iterations (dim = 53814) Tue Dec 23 21:02:40 2008 recovered 16 nontrivial dependencies Tue Dec 23 21:02:41 2008 prp41 factor: 63555308651323802072448928885255075100069 Tue Dec 23 21:02:41 2008 prp48 factor: 278699608001282959114888883431789684547614379749 Tue Dec 23 21:02:41 2008 elapsed time 00:50:20
(38·10¹²³+61)/9 = 4(2)₁₂₂9_<124> = 59 · 29050033885209937_<17> · C106
C106 = P38 · P68
P38 = 90758930904109184231531507553783048527_<38>
P68 = 27142700885477796848302781645863411898017548539507764956042342567569_<68>

Number: 42229_123 N=2463442514215982536119131591935078249728878201624727560526653267928776465809352361520806512445821303420863 ( 106 digits) SNFS difficulty: 125 digits. Divisors found: r1=90758930904109184231531507553783048527 r2=27142700885477796848302781645863411898017548539507764956042342567569 Version: Total time: 1.88 hours. Scaled time: 4.84 units (timescale=2.575). Factorization parameters were as follows: name: 42229_123 n: 2463442514215982536119131591935078249728878201624727560526653267928776465809352361520806512445821303420863 m: 5000000000000000000000000 deg: 5 c5: 304 c0: 1525 skew: 1.38 type: snfs lss: 1 rlim: 880000 alim: 880000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 880000/880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [440000, 640001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 111021 x 111261 Total sieving time: 1.88 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 1.88 hours. --------- CPU info (if available) ----------
(38·10¹³¹+61)/9 = 4(2)₁₃₀9_<132> = 3 · 661 · C129
C129 = P62 · P68
P62 = 18931593415430636447428825920870807172531523070990639092291417_<62>
P68 = 11246857801195903571673445644347018389968064581167169333729364888739_<68>

Number: 42229_131 N=212920939093405054070712164509441362694010197792346052557852860424721241665265871014736370258306718215946657701574494312769653163 ( 129 digits) SNFS difficulty: 132 digits. Divisors found: r1=18931593415430636447428825920870807172531523070990639092291417 r2=11246857801195903571673445644347018389968064581167169333729364888739 Version: Total time: 3.43 hours. Scaled time: 7.84 units (timescale=2.282). Factorization parameters were as follows: name: 42229_131 n: 212920939093405054070712164509441362694010197792346052557852860424721241665265871014736370258306718215946657701574494312769653163 m: 100000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 1130000 alim: 1130000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1130000/1130000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [565000, 1015001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 159415 x 159663 Total sieving time: 3.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1130000,1130000,26,26,47,47,2.3,2.3,50000 total time: 3.43 hours. --------- CPU info (if available) ----------
(38·10¹²⁵+61)/9 = 4(2)₁₂₄9_<126> = 3⁴ · 23789 · C120
C120 = P48 · P72
P48 = 375555149263134842089555204601763364829365781719_<48>
P72 = 583453381194914039518484879886709379205169265358315351203669660340202799_<72>

Number: 42229_125 N=219118921662736653480897241240879679435937152310888693873048609053267290890344184505974190904823332197951341875626831481 ( 120 digits) SNFS difficulty: 126 digits. Divisors found: r1=375555149263134842089555204601763364829365781719 r2=583453381194914039518484879886709379205169265358315351203669660340202799 Version: Total time: 2.23 hours. Scaled time: 4.43 units (timescale=1.991). Factorization parameters were as follows: name: 42229_125 n: 219118921662736653480897241240879679435937152310888693873048609053267290890344184505974190904823332197951341875626831481 m: 10000000000000000000000000 deg: 5 c5: 38 c0: 61 skew: 1.10 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 123791 x 124029 Total sieving time: 2.23 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.23 hours. --------- CPU info (if available) ----------
(13·10¹⁷⁴-7)/3 = 4(3)₁₇₃1_<175> = 2661733 · 2981915448269_<13> · 57373034177700817_<17> · 210183647146556081_<18> · 1886441303582244311116568671646101_<34> · C89
C89 = P37 · P53
P37 = 1154850117862112282943626662349224241_<37>
P53 = 20781965619296732780146962236360397468436031673870679_<53>

ue Dec 23 21:17:52 2008 Msieve v. 1.39 Tue Dec 23 21:17:52 2008 random seeds: 9d7994a0 f4a4cbfc Tue Dec 23 21:17:52 2008 factoring 24000055444851197132978321002485393490269394924989129370986539182893234062802945405929639 (89 digits) Tue Dec 23 21:17:53 2008 searching for 15-digit factors Tue Dec 23 21:17:54 2008 commencing quadratic sieve (89-digit input) Tue Dec 23 21:17:54 2008 using multiplier of 39 Tue Dec 23 21:17:54 2008 using 32kb Intel Core sieve core Tue Dec 23 21:17:54 2008 sieve interval: 30 blocks of size 32768 Tue Dec 23 21:17:54 2008 processing polynomials in batches of 7 Tue Dec 23 21:17:54 2008 using a sieve bound of 1545007 (58667 primes) Tue Dec 23 21:17:54 2008 using large prime bound of 123600560 (26 bits) Tue Dec 23 21:17:54 2008 using double large prime bound of 367821176096160 (42-49 bits) Tue Dec 23 21:17:54 2008 using trial factoring cutoff of 49 bits Tue Dec 23 21:17:54 2008 polynomial 'A' values have 12 factors Tue Dec 23 22:28:02 2008 58882 relations (15618 full + 43264 combined from 622557 partial), need 58763 Tue Dec 23 22:28:03 2008 begin with 638175 relations Tue Dec 23 22:28:03 2008 reduce to 143131 relations in 9 passes Tue Dec 23 22:28:03 2008 attempting to read 143131 relations Tue Dec 23 22:28:05 2008 recovered 143131 relations Tue Dec 23 22:28:05 2008 recovered 124085 polynomials Tue Dec 23 22:28:05 2008 attempting to build 58882 cycles Tue Dec 23 22:28:05 2008 found 58881 cycles in 5 passes Tue Dec 23 22:28:05 2008 distribution of cycle lengths: Tue Dec 23 22:28:05 2008 length 1 : 15618 Tue Dec 23 22:28:05 2008 length 2 : 11396 Tue Dec 23 22:28:05 2008 length 3 : 10604 Tue Dec 23 22:28:05 2008 length 4 : 7945 Tue Dec 23 22:28:05 2008 length 5 : 5461 Tue Dec 23 22:28:05 2008 length 6 : 3495 Tue Dec 23 22:28:05 2008 length 7 : 2019 Tue Dec 23 22:28:05 2008 length 9+: 2343 Tue Dec 23 22:28:05 2008 largest cycle: 17 relations Tue Dec 23 22:28:06 2008 matrix is 58667 x 58881 (14.2 MB) with weight 3480054 (59.10/col) Tue Dec 23 22:28:06 2008 sparse part has weight 3480054 (59.10/col) Tue Dec 23 22:28:06 2008 filtering completed in 3 passes Tue Dec 23 22:28:06 2008 matrix is 54828 x 54892 (13.3 MB) with weight 3262907 (59.44/col) Tue Dec 23 22:28:06 2008 sparse part has weight 3262907 (59.44/col) Tue Dec 23 22:28:06 2008 saving the first 48 matrix rows for later Tue Dec 23 22:28:06 2008 matrix is 54780 x 54892 (8.1 MB) with weight 2523354 (45.97/col) Tue Dec 23 22:28:06 2008 sparse part has weight 1787841 (32.57/col) Tue Dec 23 22:28:06 2008 matrix includes 64 packed rows Tue Dec 23 22:28:06 2008 using block size 21956 for processor cache size 1024 kB Tue Dec 23 22:28:07 2008 commencing Lanczos iteration Tue Dec 23 22:28:07 2008 memory use: 8.0 MB Tue Dec 23 22:28:24 2008 lanczos halted after 868 iterations (dim = 54778) Tue Dec 23 22:28:24 2008 recovered 17 nontrivial dependencies Tue Dec 23 22:28:24 2008 prp37 factor: 1154850117862112282943626662349224241 Tue Dec 23 22:28:24 2008 prp53 factor: 20781965619296732780146962236360397468436031673870679 Tue Dec 23 22:28:24 2008 elapsed time 01:10:32
Dec 23, 2008 (6th): By Jo Yeong Uk / GGNFS / Msieve v1.39
(38·10¹⁵⁸+7)/9 = 4(2)₁₅₇3_<159> = 3 · 41 · 227 · 457 · 719 · 11692937714243057_<17> · C133
C133 = P60 · P74
P60 = 261684502017364426401172993314582377543873715761538550838501_<60>
P74 = 15040538615515346545319103996178595611693408558594037216409591162891195973_<74>

I've used Greg Childer's x64 binaries that is about 30% faster. Number: 42223_158 N=3935875857674073259892366744726611131660458011927081245662043080032693008432327787653104908465235028172227775906183483719689864556473 ( 133 digits) SNFS difficulty: 161 digits. Divisors found: r1=261684502017364426401172993314582377543873715761538550838501 r2=15040538615515346545319103996178595611693408558594037216409591162891195973 Version: Total time: 16.42 hours. Scaled time: 39.20 units (timescale=2.387). Factorization parameters were as follows: n: 3935875857674073259892366744726611131660458011927081245662043080032693008432327787653104908465235028172227775906183483719689864556473 m: 100000000000000000000000000000000 deg: 5 c5: 19 c0: 350 skew: 1.79 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: rational ideals reading, algebraic ideals reading, Relations: 9164673 Max relations in full relation-set: Initial matrix: Pruned matrix : 657541 x 657789 Total sieving time: 14.77 hours. Total relation processing time: 0.62 hours. Matrix solve time: 0.95 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 16.42 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(13·10¹⁶³-7)/3 = 4(3)₁₆₂1_<164> = 23 · 181 · 201977806379599_<15> · 256380435467453624357_<21> · 3848836599303511776161_<22> · C104
C104 = P40 · P65
P40 = 2484322471920498002597770188046418572961_<40>
P65 = 21022759073577810522071683163551125750312379421937000260369560979_<65>

Number: 43331_163 N=52227312788259904783285448177771151215979194504591185340103120146351292794322523024425734515127250088819 ( 104 digits) Divisors found: r1=2484322471920498002597770188046418572961 r2=21022759073577810522071683163551125750312379421937000260369560979 Version: Total time: 3.98 hours. Scaled time: 9.53 units (timescale=2.391). Factorization parameters were as follows: name: 43331_163 n: 52227312788259904783285448177771151215979194504591185340103120146351292794322523024425734515127250088819 skew: 22078.67 # norm 5.99e+14 c5: 21240 c4: -1497386772 c3: -38425098620186 c2: 845882405351926079 c1: 8026727642520429063354 c0: 1072508182475386490862336 # alpha -6.69 Y1: 84046748929 Y0: -75536254703912113145 # Murphy_E 2.05e-09 # M 14288233827694019863237397998856850064401035115600452898033582468342007884707128037624699464864009909031 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: 5069392 Max relations in full relation-set: Initial matrix: Pruned matrix : 241075 x 241323 Total sieving time: 3.46 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 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: 3.98 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 23, 2008 (5th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(13·10¹⁰⁶-7)/3 = 4(3)₁₀₅1_<107> = 41 · 13774823 · 49522433 · C91
C91 = P32 · P59
P32 = 57847164065344667246749592041001_<32>
P59 = 26783551748975471064496580057189581449979924547068814782949_<59>

Number: n N=1549352512275633183368088459353775952136320751322520942606357553923121412953602781723691949 ( 91 digits) SNFS difficulty: 107 digits. Divisors found: r1=57847164065344667246749592041001 (pp32) r2=26783551748975471064496580057189581449979924547068814782949 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.65 hours. Scaled time: 1.18 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_3_105_1 n: 1549352512275633183368088459353775952136320751322520942606357553923121412953602781723691949 type: snfs skew: 0.56 deg: 5 c5: 130 c0: -7 m: 1000000000000000000000 rlim: 450000 alim: 450000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 2000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [225000, 271001) Primes: RFBsize:37706, AFBsize:37704, largePrimes:4143192 encountered Relations: rels:3498691, finalFF:97136 Max relations in full relation-set: 48 Initial matrix: 75477 x 97136 with sparse part having weight 10956977. Pruned matrix : 70519 x 70960 with weight 5601496. Total sieving time: 0.56 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000 total time: 0.65 hours. --------- CPU info (if available) ----------
(38·10¹¹⁶+61)/9 = 4(2)₁₁₅9_<117> = 3² · 11 · 13 · 6271 · 7643257 · 44775959 · 883573237 · C87
C87 = P40 · P47
P40 = 4242755187407345742527427668930198334521_<40>
P47 = 40776679208206304454293512576431198414080057327_<47>

Tue Dec 23 18:19:00 2008 Tue Dec 23 18:19:00 2008 Tue Dec 23 18:19:00 2008 Msieve v. 1.39 Tue Dec 23 18:19:00 2008 random seeds: 96cc2620 f2dff84d Tue Dec 23 18:19:00 2008 factoring 173005467235862557859424523342614033694193668612191137256544163118007289277935603085367 (87 digits) Tue Dec 23 18:19:01 2008 searching for 15-digit factors Tue Dec 23 18:19:02 2008 commencing quadratic sieve (87-digit input) Tue Dec 23 18:19:02 2008 using multiplier of 7 Tue Dec 23 18:19:02 2008 using 64kb Opteron sieve core Tue Dec 23 18:19:02 2008 sieve interval: 10 blocks of size 65536 Tue Dec 23 18:19:02 2008 processing polynomials in batches of 11 Tue Dec 23 18:19:02 2008 using a sieve bound of 1480243 (56254 primes) Tue Dec 23 18:19:02 2008 using large prime bound of 118419440 (26 bits) Tue Dec 23 18:19:02 2008 using double large prime bound of 340534638927600 (41-49 bits) Tue Dec 23 18:19:02 2008 using trial factoring cutoff of 49 bits Tue Dec 23 18:19:02 2008 polynomial 'A' values have 11 factors Tue Dec 23 18:48:34 2008 56642 relations (16217 full + 40425 combined from 588342 partial), need 56350 Tue Dec 23 18:48:34 2008 begin with 604559 relations Tue Dec 23 18:48:34 2008 reduce to 134247 relations in 11 passes Tue Dec 23 18:48:34 2008 attempting to read 134247 relations Tue Dec 23 18:48:35 2008 recovered 134247 relations Tue Dec 23 18:48:35 2008 recovered 109821 polynomials Tue Dec 23 18:48:35 2008 attempting to build 56642 cycles Tue Dec 23 18:48:36 2008 found 56642 cycles in 5 passes Tue Dec 23 18:48:36 2008 distribution of cycle lengths: Tue Dec 23 18:48:36 2008 length 1 : 16217 Tue Dec 23 18:48:36 2008 length 2 : 11293 Tue Dec 23 18:48:36 2008 length 3 : 10010 Tue Dec 23 18:48:36 2008 length 4 : 7280 Tue Dec 23 18:48:36 2008 length 5 : 5006 Tue Dec 23 18:48:36 2008 length 6 : 3000 Tue Dec 23 18:48:36 2008 length 7 : 1762 Tue Dec 23 18:48:36 2008 length 9+: 2074 Tue Dec 23 18:48:36 2008 largest cycle: 17 relations Tue Dec 23 18:48:36 2008 matrix is 56254 x 56642 (12.9 MB) with weight 3166386 (55.90/col) Tue Dec 23 18:48:36 2008 sparse part has weight 3166386 (55.90/col) Tue Dec 23 18:48:37 2008 filtering completed in 3 passes Tue Dec 23 18:48:37 2008 matrix is 51309 x 51373 (11.8 MB) with weight 2892193 (56.30/col) Tue Dec 23 18:48:37 2008 sparse part has weight 2892193 (56.30/col) Tue Dec 23 18:48:37 2008 saving the first 48 matrix rows for later Tue Dec 23 18:48:37 2008 matrix is 51261 x 51373 (7.7 MB) with weight 2276433 (44.31/col) Tue Dec 23 18:48:37 2008 sparse part has weight 1699820 (33.09/col) Tue Dec 23 18:48:37 2008 matrix includes 64 packed rows Tue Dec 23 18:48:37 2008 using block size 20549 for processor cache size 1024 kB Tue Dec 23 18:48:37 2008 commencing Lanczos iteration Tue Dec 23 18:48:37 2008 memory use: 7.5 MB Tue Dec 23 18:48:51 2008 lanczos halted after 812 iterations (dim = 51259) Tue Dec 23 18:48:51 2008 recovered 16 nontrivial dependencies Tue Dec 23 18:48:52 2008 prp40 factor: 4242755187407345742527427668930198334521 Tue Dec 23 18:48:52 2008 prp47 factor: 40776679208206304454293512576431198414080057327 Tue Dec 23 18:48:52 2008 elapsed time 00:29:52
(13·10¹³⁴-7)/3 = 4(3)₁₃₃1_<135> = 8849 · 48271117 · 8224435209442541_<16> · 423468662193971749903_<21> · C87
C87 = P32 · P55
P32 = 69478828398569728593459721798867_<32>
P55 = 4192380641004827675507764758323249935285647811508989127_<55>

Tue Dec 23 19:41:18 2008 Tue Dec 23 19:41:18 2008 Tue Dec 23 19:41:18 2008 Msieve v. 1.39 Tue Dec 23 19:41:18 2008 random seeds: baed84ac 587f7957 Tue Dec 23 19:41:18 2008 factoring 291281695137860183482012662507685449765126395405237570140944533477572342538205183919109 (87 digits) Tue Dec 23 19:41:18 2008 searching for 15-digit factors Tue Dec 23 19:41:19 2008 commencing quadratic sieve (87-digit input) Tue Dec 23 19:41:19 2008 using multiplier of 29 Tue Dec 23 19:41:19 2008 using 64kb Opteron sieve core Tue Dec 23 19:41:19 2008 sieve interval: 10 blocks of size 65536 Tue Dec 23 19:41:19 2008 processing polynomials in batches of 11 Tue Dec 23 19:41:19 2008 using a sieve bound of 1489667 (56642 primes) Tue Dec 23 19:41:19 2008 using large prime bound of 119173360 (26 bits) Tue Dec 23 19:41:19 2008 using double large prime bound of 344447000754720 (42-49 bits) Tue Dec 23 19:41:19 2008 using trial factoring cutoff of 49 bits Tue Dec 23 19:41:19 2008 polynomial 'A' values have 11 factors Tue Dec 23 20:13:40 2008 56750 relations (16023 full + 40727 combined from 592860 partial), need 56738 Tue Dec 23 20:13:40 2008 begin with 608883 relations Tue Dec 23 20:13:41 2008 reduce to 135001 relations in 8 passes Tue Dec 23 20:13:41 2008 attempting to read 135001 relations Tue Dec 23 20:13:42 2008 recovered 135001 relations Tue Dec 23 20:13:42 2008 recovered 113426 polynomials Tue Dec 23 20:13:42 2008 attempting to build 56750 cycles Tue Dec 23 20:13:42 2008 found 56750 cycles in 6 passes Tue Dec 23 20:13:42 2008 distribution of cycle lengths: Tue Dec 23 20:13:42 2008 length 1 : 16023 Tue Dec 23 20:13:42 2008 length 2 : 11360 Tue Dec 23 20:13:42 2008 length 3 : 9954 Tue Dec 23 20:13:42 2008 length 4 : 7463 Tue Dec 23 20:13:42 2008 length 5 : 5058 Tue Dec 23 20:13:42 2008 length 6 : 3100 Tue Dec 23 20:13:42 2008 length 7 : 1796 Tue Dec 23 20:13:42 2008 length 9+: 1996 Tue Dec 23 20:13:42 2008 largest cycle: 19 relations Tue Dec 23 20:13:42 2008 matrix is 56642 x 56750 (13.3 MB) with weight 3250880 (57.28/col) Tue Dec 23 20:13:42 2008 sparse part has weight 3250880 (57.28/col) Tue Dec 23 20:13:43 2008 filtering completed in 3 passes Tue Dec 23 20:13:43 2008 matrix is 52021 x 52085 (12.3 MB) with weight 3026197 (58.10/col) Tue Dec 23 20:13:43 2008 sparse part has weight 3026197 (58.10/col) Tue Dec 23 20:13:43 2008 saving the first 48 matrix rows for later Tue Dec 23 20:13:43 2008 matrix is 51973 x 52085 (8.6 MB) with weight 2442834 (46.90/col) Tue Dec 23 20:13:43 2008 sparse part has weight 1949032 (37.42/col) Tue Dec 23 20:13:43 2008 matrix includes 64 packed rows Tue Dec 23 20:13:43 2008 using block size 20834 for processor cache size 1024 kB Tue Dec 23 20:13:44 2008 commencing Lanczos iteration Tue Dec 23 20:13:44 2008 memory use: 8.0 MB Tue Dec 23 20:13:59 2008 lanczos halted after 823 iterations (dim = 51967) Tue Dec 23 20:13:59 2008 recovered 13 nontrivial dependencies Tue Dec 23 20:14:00 2008 prp32 factor: 69478828398569728593459721798867 Tue Dec 23 20:14:00 2008 prp55 factor: 4192380641004827675507764758323249935285647811508989127 Tue Dec 23 20:14:00 2008 elapsed time 00:32:42
(13·10¹⁰⁹-7)/3 = 4(3)₁₀₈1_<110> = 17 · 137 · 977 · C104
C104 = P31 · P73
P31 = 3407814690944317539762588740159_<31>
P73 = 5588330392801960092177439750747650769278886747644606354321657148324217573_<73>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 19043994410441148270827281371648092179964575240551285550193450360143908141146468972425614524063478614107 (104 digits) Using B1=714000, B2=696728352, polynomial Dickson(3), sigma=1623556616 Step 1 took 4969ms Step 2 took 2609ms ********** Factor found in step 2: 3407814690944317539762588740159 Found probable prime factor of 31 digits: 3407814690944317539762588740159 Probable prime cofactor 5588330392801960092177439750747650769278886747644606354321657148324217573 has 73 digits
(38·10¹⁰⁹+61)/9 = 4(2)₁₀₈9_<110> = 7 · 199 · 881 · 580373 · C98
C98 = P44 · P55
P44 = 26751738096440014307990911916120465357207011_<44>
P55 = 2215923985067384009560418171449180919028006614390617771_<55>

Number: n N=59279818090142310194468555816137740448324236376809698473858515326593093225915093020485675422392481 ( 98 digits) SNFS difficulty: 111 digits. Divisors found: Wed Dec 24 00:30:23 2008 prp44 factor: 26751738096440014307990911916120465357207011 Wed Dec 24 00:30:23 2008 prp55 factor: 2215923985067384009560418171449180919028006614390617771 Wed Dec 24 00:30:23 2008 elapsed time 00:05:05 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.65 hours. Scaled time: 1.20 units (timescale=1.828). Factorization parameters were as follows: name: KA_4_2_108_9 n: 59279818090142310194468555816137740448324236376809698473858515326593093225915093020485675422392481 type: snfs skew: 1.74 deg: 5 c5: 19 c0: 305 m: 10000000000000000000000 rlim: 450000 alim: 450000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 5000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 275001) Primes: RFBsize:37706, AFBsize:37830, largePrimes:4770991 encountered Relations: rels:3870829, finalFF:81071 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 105623 hash collisions in 3950766 relations Msieve: matrix is 89786 x 90033 (23.6 MB) Total sieving time: 0.60 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,29,29,58,58,2.5,2.5,50000 total time: 0.65 hours. --------- CPU info (if available) ----------
Dec 23, 2008 (4th): By Sinkiti Sibata / Msieve
(38·10¹⁴⁹+43)/9 = 4(2)₁₄₈7_<150> = 13 · 113453640491_<12> · C138
C138 = P39 · P47 · P53
P39 = 123132274553465756860058461410327710779_<39>
P47 = 27267256871151239064440712042018508774862667557_<47>
P53 = 85264047995684401299884905037961478641338880822995323_<53>

Number: 42227_149 N=286272281242565584871308935586551398963328947291933211769489506901789407053841847782020315712273819190869798534111037762948452697250984669 ( 138 digits) SNFS difficulty: 151 digits. Divisors found: r1=123132274553465756860058461410327710779 r2=27267256871151239064440712042018508774862667557 r3=85264047995684401299884905037961478641338880822995323 Version: Total time: 17.03 hours. Scaled time: 33.49 units (timescale=1.967). Factorization parameters were as follows: name: 42227_149 n: 286272281242565584871308935586551398963328947291933211769489506901789407053841847782020315712273819190869798534111037762948452697250984669 m: 1000000000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 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, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 326210 x 326458 Total sieving time: 17.03 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 17.03 hours. --------- CPU info (if available) ----------
Dec 23, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1
(38·10¹⁷⁹+43)/9 = 4(2)₁₇₈7_<180> = 13 · 190548791 · C171
C171 = P32 · C139
P32 = 83693711822605989870189783269927_<32>
C139 = [2036567026754301909068906536670007279613488322697273803941595712633680899678332169392476463478230146670448373216770032371376154711024549247_<139>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=28284232 Step 1 took 50467ms Step 2 took 24270ms ********** Factor found in step 2: 83693711822605989870189783269927 Found probable prime factor of 32 digits: 83693711822605989870189783269927 Composite cofactor has 139 digits
(38·10¹⁹⁵+43)/9 = 4(2)₁₉₄7_<196> = 3 · 1409 · 36583 · 2631581 · C182
C182 = P37 · P145
P37 = 1110098676846052025875562910419707159_<37>
P145 = 9346547020444687949473270005207416033036409081717352834060726263287081343511433873690747964630107753834169432220989123151666306482271859585653093_<145>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3282926492 Step 1 took 58616ms Step 2 took 26203ms ********** Factor found in step 2: 1110098676846052025875562910419707159 Found probable prime factor of 37 digits: 1110098676846052025875562910419707159 Probable prime cofactor has 145 digits
Dec 23, 2008 (2nd): By Robert Backstrom / GMP-ECM
(11·10¹⁶⁶-17)/3 = 3(6)₁₆₅1_<167> = 31 · 9645541 · C159
C159 = P40 · P120
P40 = 1116427148631667120168455525371131408601_<40>
P120 = 109838035390645973298719203114797829250387790912028941879398460215801086922957023513075842014334465944683742916668887991_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 122626164662483025347743472836949508140489448044728201240835654816634849691809178531191224129656978175172463918374192254346624590463586353818380837812123010591 (159 digits) Using B1=2860000, B2=4281671950, polynomial Dickson(6), sigma=2445717877 Step 1 took 37615ms Step 2 took 13651ms ********** Factor found in step 2: 1116427148631667120168455525371131408601 Found probable prime factor of 40 digits: 1116427148631667120168455525371131408601 Probable prime cofactor 109838035390645973298719203114797829250387790912028941879398460215801086922957023513075842014334465944683742916668887991 has 120 digits
Dec 23, 2008: Factorizations of 422...229 and Factorizations of 433...331 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Dec 22, 2008 (5th): By Jo Yeong Uk / GMP-ECM, Msieve
(37·10¹⁹⁰+53)/9 = 4(1)₁₈₉7_<191> = 59 · 33366083669_<11> · 1038688946123696607997710239_<28> · 228822554008790119385212155709949_<33> · C119
C119 = P37 · P41 · P42
P37 = 6700559039122072293901319740648826129_<37>
P41 = 94122795556702802098640504555138641771009_<41>
P42 = 139319457310594504389225773069331905769337_<42>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM] Input number is 87865347299839227077677777536365983116150872999131750437968032584396075641901842890425376739301590272179304048017141257 (119 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2495475907 Step 1 took 13322ms Step 2 took 9282ms ********** Factor found in step 2: 6700559039122072293901319740648826129 Found probable prime factor of 37 digits: 6700559039122072293901319740648826129 Composite cofactor 13113136797515870136423584090069674988260781902340888649157796440990324986327751033 has 83 digits Mon Dec 22 22:59:56 2008 Mon Dec 22 22:59:56 2008 Mon Dec 22 22:59:56 2008 Msieve v. 1.39 Mon Dec 22 22:59:56 2008 random seeds: 5344db90 d0343cf0 Mon Dec 22 22:59:56 2008 factoring 13113136797515870136423584090069674988260781902340888649157796440990324986327751033 (83 digits) Mon Dec 22 22:59:57 2008 searching for 15-digit factors Mon Dec 22 22:59:58 2008 commencing quadratic sieve (83-digit input) Mon Dec 22 22:59:58 2008 using multiplier of 1 Mon Dec 22 22:59:58 2008 using VC8 32kb sieve core Mon Dec 22 22:59:58 2008 sieve interval: 12 blocks of size 32768 Mon Dec 22 22:59:58 2008 processing polynomials in batches of 17 Mon Dec 22 22:59:58 2008 using a sieve bound of 1357919 (52059 primes) Mon Dec 22 22:59:58 2008 using large prime bound of 124928548 (26 bits) Mon Dec 22 22:59:58 2008 using trial factoring cutoff of 27 bits Mon Dec 22 22:59:58 2008 polynomial 'A' values have 10 factors Mon Dec 22 23:15:29 2008 52266 relations (26562 full + 25704 combined from 277983 partial), need 52155 Mon Dec 22 23:15:29 2008 begin with 304545 relations Mon Dec 22 23:15:29 2008 reduce to 74683 relations in 2 passes Mon Dec 22 23:15:29 2008 attempting to read 74683 relations Mon Dec 22 23:15:30 2008 recovered 74683 relations Mon Dec 22 23:15:30 2008 recovered 66029 polynomials Mon Dec 22 23:15:30 2008 attempting to build 52266 cycles Mon Dec 22 23:15:30 2008 found 52266 cycles in 1 passes Mon Dec 22 23:15:30 2008 distribution of cycle lengths: Mon Dec 22 23:15:30 2008 length 1 : 26562 Mon Dec 22 23:15:30 2008 length 2 : 25704 Mon Dec 22 23:15:30 2008 largest cycle: 2 relations Mon Dec 22 23:15:30 2008 matrix is 52059 x 52266 (7.7 MB) with weight 1591401 (30.45/col) Mon Dec 22 23:15:30 2008 sparse part has weight 1591401 (30.45/col) Mon Dec 22 23:15:30 2008 filtering completed in 3 passes Mon Dec 22 23:15:30 2008 matrix is 37218 x 37282 (6.0 MB) with weight 1276780 (34.25/col) Mon Dec 22 23:15:30 2008 sparse part has weight 1276780 (34.25/col) Mon Dec 22 23:15:30 2008 saving the first 48 matrix rows for later Mon Dec 22 23:15:30 2008 matrix is 37170 x 37282 (4.8 MB) with weight 1060890 (28.46/col) Mon Dec 22 23:15:30 2008 sparse part has weight 894883 (24.00/col) Mon Dec 22 23:15:30 2008 matrix includes 64 packed rows Mon Dec 22 23:15:30 2008 using block size 14912 for processor cache size 4096 kB Mon Dec 22 23:15:30 2008 commencing Lanczos iteration Mon Dec 22 23:15:30 2008 memory use: 4.5 MB Mon Dec 22 23:15:35 2008 lanczos halted after 589 iterations (dim = 37168) Mon Dec 22 23:15:35 2008 recovered 15 nontrivial dependencies Mon Dec 22 23:15:35 2008 prp41 factor: 94122795556702802098640504555138641771009 Mon Dec 22 23:15:35 2008 prp42 factor: 139319457310594504389225773069331905769337 Mon Dec 22 23:15:35 2008 elapsed time 00:15:39
Dec 22, 2008 (4th): By Serge Batalov / GMP-ECM 6.2.1
(38·10¹⁷⁶+43)/9 = 4(2)₁₇₅7_<177> = 7 · 953 · 18013 · 276447312401475563_<18> · C152
C152 = P36 · C116
P36 = 178756426448137413914826142437964919_<36>
C116 = [71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717_<116>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1342266695 Step 1 took 43401ms Step 2 took 21416ms ********** Factor found in step 2: 178756426448137413914826142437964919 Found probable prime factor of 36 digits: 178756426448137413914826142437964919 Composite cofactor has 116 digits
Dec 22, 2008 (3rd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v1.39
(38·10¹⁵⁶+7)/9 = 4(2)₁₅₅3_<157> = 1571 · 20627 · 161999 · 31370407 · C137
C137 = P40 · P97
P40 = 3151311867708119352908892784260206809733_<40>
P97 = 8135888003589561713984004929583919997606982433878122227315798705604256568191678963555861658276451_<97>

Number: 42223_156 N=25638720420055904175047718597666401571261026682120717702745767511977789529191792514452212244210202584659272309033290926661594350071497583 ( 137 digits) SNFS difficulty: 157 digits. Divisors found: r1=3151311867708119352908892784260206809733 r2=8135888003589561713984004929583919997606982433878122227315798705604256568191678963555861658276451 Version: Total time: 17.75 hours. Scaled time: 42.36 units (timescale=2.387). Factorization parameters were as follows: n: 25638720420055904175047718597666401571261026682120717702745767511977789529191792514452212244210202584659272309033290926661594350071497583 m: 10000000000000000000000000000000 deg: 5 c5: 380 c0: 7 skew: 0.45 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1500000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8115178 Max relations in full relation-set: Initial matrix: Pruned matrix : 565574 x 565822 Total sieving time: 16.58 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.68 hours. Time per square root: 0.07 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: 17.75 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(35·10¹⁸⁶-17)/9 = 3(8)₁₈₅7_<187> = 157 · 24359 · 61381 · 8547631 · 741825421 · 12281370259_<11> · 1354976246545216979406271187005039_<34> · C117
C117 = P43 · P74
P43 = 5120353883635458429190544130895666258719013_<43>
P74 = 30662425523328166855980476520758336325858134810791000702868819091594477883_<74>

Number: 38887_186 N=157002469610056383002517699709502160585077480848188350871607152214104956824868980051866840757039680270434992140089479 ( 117 digits) Divisors found: r1=5120353883635458429190544130895666258719013 r2=30662425523328166855980476520758336325858134810791000702868819091594477883 Version: Total time: 22.72 hours. Scaled time: 54.15 units (timescale=2.384). Factorization parameters were as follows: name: 38887_186 n: 157002469610056383002517699709502160585077480848188350871607152214104956824868980051866840757039680270434992140089479 skew: 90503.15 # norm 3.19e+16 c5: 7200 c4: -1050000632 c3: 784336535541926 c2: 6556944883925153517 c1: -2168736184919240296891976 c0: 307461253102532191921522760 # alpha -7.15 Y1: 2113994864537 Y0: -29357272872032918557839 # Murphy_E 4.67e-10 # M 22297279247945908317688117096806927032070203219509894621581388695827552723266532914832455914310598281190746054030867 type: gnfs rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1650000, 2925001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9009334 Max relations in full relation-set: Initial matrix: Pruned matrix : 505641 x 505889 Polynomial selection time: 1.73 hours. Total sieving time: 19.51 hours. Total relation processing time: 0.70 hours. Matrix solve time: 0.67 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000 total time: 22.72 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 22, 2008 (2nd): By Sinkiti Sibata / GGNFS, Msieve
(38·10¹⁵⁰+43)/9 = 4(2)₁₄₉7_<151> = 3 · 5404033 · 1315507653822793_<16> · 1793543806775351758201343_<25> · C105
C105 = P46 · P59
P46 = 1474436240860335083889521243713798444857541487_<46>
P59 = 74863559958939232893634955690188665701792653148056199268121_<59>

Number: 42227_150 N=110381545923280664073717632487428289003590698192574383665984937129689496720053069202801052883676794035927 ( 105 digits) Divisors found: r1=1474436240860335083889521243713798444857541487 (pp46) r2=74863559958939232893634955690188665701792653148056199268121 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 15.61 hours. Scaled time: 7.37 units (timescale=0.472). Factorization parameters were as follows: name: 42227_150 n: 110381545923280664073717632487428289003590698192574383665984937129689496720053069202801052883676794035927 skew: 13420.60 # norm 9.52e+14 c5: 107460 c4: -360905256 c3: -62359547385495 c2: -486725426096074673 c1: 4105199284466708023171 c0: -86832314907525862615335 # alpha -6.88 Y1: 67446069691 Y0: -63435188891743035196 # Murphy_E 1.97e-09 # M 69240885770336502168462731026371669070686911436648784413026709589522938575061457362992740606116577231612 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: RFBsize:183072, AFBsize:182694, largePrimes:4397803 encountered Relations: rels:4492136, finalFF:486116 Max relations in full relation-set: 28 Initial matrix: 365843 x 486116 with sparse part having weight 33668090. Pruned matrix : 267920 x 269813 with weight 16505009. Total sieving time: 13.47 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.68 hours. Time per square root: 0.18 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: 15.61 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁰+43)/9 = 4(2)₁₃₉7_<141> = 7 · 2039 · 16902410577105783452297695849_<29> · C109
C109 = P44 · P66
P44 = 12699265945218353733988416402502984096925867_<44>
P66 = 137815655861186307456994950037515633314473360940130795156807220753_<66>

Number: 42227_140 N=1750157665195895484648268135865022403532332639214085226117860426329641105594587945290563927802167775344917851 ( 109 digits) SNFS difficulty: 141 digits. Divisors found: r1=12699265945218353733988416402502984096925867 r2=137815655861186307456994950037515633314473360940130795156807220753 Version: Total time: 10.29 hours. Scaled time: 20.61 units (timescale=2.003). Factorization parameters were as follows: name: 42227_140 n: 1750157665195895484648268135865022403532332639214085226117860426329641105594587945290563927802167775344917851 m: 10000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 255864 x 256112 Total sieving time: 10.29 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 10.29 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁴+43)/9 = 4(2)₁₄₃7_<145> = 3³ · 31 · 1606157397847_<13> · C130
C130 = P59 · P71
P59 = 43754364299985865542408997922500687052406885856436424436163_<59>
P71 = 71780445327028706891060593598257035580865296056623661966850183987404811_<71>

Number: 42227_144 N=3140707754454032100209047495164969064451607130248949747422702757390517541777485585989335253410516591681046770886049171734308580193 ( 130 digits) SNFS difficulty: 146 digits. Divisors found: r1=43754364299985865542408997922500687052406885856436424436163 r2=71780445327028706891060593598257035580865296056623661966850183987404811 Version: Total time: 10.43 hours. Scaled time: 20.90 units (timescale=2.003). Factorization parameters were as follows: name: 42227_144 n: 3140707754454032100209047495164969064451607130248949747422702757390517541777485585989335253410516591681046770886049171734308580193 m: 100000000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 type: snfs lss: 1 rlim: 1920000 alim: 1920000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1920000/1920000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [960000, 1960001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 262590 x 262838 Total sieving time: 10.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000 total time: 10.43 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁶+43)/9 = 4(2)₁₄₅7_<147> = 7² · 9222235349_<10> · 81823735257070026169067_<23> · C113
C113 = P54 · P59
P54 = 324669516616670697087399863175104643086264125364574157_<54>
P59 = 35171265133319275701635037151479684144701079965460533176633_<59>

Number: 42227_146 N=11419037649631533302730167351422803394561213724399974201383070218486899102995497193219122768932079190766508073381 ( 113 digits) SNFS difficulty: 148 digits. Divisors found: r1=324669516616670697087399863175104643086264125364574157 r2=35171265133319275701635037151479684144701079965460533176633 Version: Total time: 13.24 hours. Scaled time: 31.31 units (timescale=2.366). Factorization parameters were as follows: name: 42227_146 n: 11419037649631533302730167351422803394561213724399974201383070218486899102995497193219122768932079190766508073381 m: 200000000000000000000000000000 deg: 5 c5: 95 c0: 344 skew: 1.29 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 362115 x 362360 Total sieving time: 13.24 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 13.24 hours. --------- CPU info (if available) ----------
Dec 22, 2008: By Robert Backstrom / GGNFS, Msieve
(37·10¹⁸⁶+71)/9 = 4(1)₁₈₅9_<187> = 3² · 59² · C183
C183 = P47 · P136
P47 = 55044224415250538928921553264661339723266003429_<47>
P136 = 2383970764021785908203194996945240916853952320935449385966474798602815965953926289351897727903544055041607935420772339895475891591817859_<136>

Number: n N=131223821734211468962019570082387280510425200648316611162536662871815605704334996683938558878710176230045999269402506020336145779026177379141086887902936930994002716687768875837438511 ( 183 digits) SNFS difficulty: 187 digits. Divisors found: Mon Dec 22 05:04:18 2008 prp47 factor: 55044224415250538928921553264661339723266003429 Mon Dec 22 05:04:18 2008 prp136 factor: 2383970764021785908203194996945240916853952320935449385966474798602815965953926289351897727903544055041607935420772339895475891591817859 Mon Dec 22 05:04:19 2008 elapsed time 06:55:19 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 93.76 hours. Scaled time: 192.30 units (timescale=2.051). Factorization parameters were as follows: name: KA_4_1_185_9 n: 131223821734211468962019570082387280510425200648316611162536662871815605704334996683938558878710176230045999269402506020336145779026177379141086887902936930994002716687768875837438511 type: snfs skew: 0.72 deg: 5 c5: 370 c0: 71 m: 10000000000000000000000000000000000000 rlim: 8800000 alim: 8800000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 5700001) Primes: RFBsize:590006, AFBsize:589651, largePrimes:33470457 encountered Relations: rels:31004910, finalFF:1017105 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7398741 hash collisions in 38005293 relations Msieve: matrix is 1645242 x 1645490 (446.2 MB) Total sieving time: 91.92 hours. Total relation processing time: 1.84 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,8800000,8800000,29,29,58,58,2.5,2.5,100000 total time: 93.76 hours. --------- CPU info (if available) ----------
(2·10¹⁸⁶+7)/9 = (2)₁₈₅3_<186> = 61 · 7247 · C180
C180 = P64 · P117
P64 = 1000296869048935293617966311639974939939901074399500816397239041_<64>
P117 = 502539820663756223904404112395960972646821102101410044844975062438931281776309797410654017639319069448362694337047509_<117>

Number: n N=502689009182368786229739433665535365051501745713256638071202379327618261987938982602687425711989861768062809986319318615101833482757641312792455040123379990413720594892227246598869 ( 180 digits) SNFS difficulty: 186 digits. Divisors found: Mon Dec 22 17:13:51 2008 prp64 factor: 1000296869048935293617966311639974939939901074399500816397239041 Mon Dec 22 17:13:51 2008 prp117 factor: 502539820663756223904404112395960972646821102101410044844975062438931281776309797410654017639319069448362694337047509 Mon Dec 22 17:13:51 2008 elapsed time 03:54:27 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 45.86 hours. Scaled time: 92.19 units (timescale=2.010). Factorization parameters were as follows: name: KA_2_185_3 n: 502689009182368786229739433665535365051501745713256638071202379327618261987938982602687425711989861768062809986319318615101833482757641312792455040123379990413720594892227246598869 type: snfs skew: 0.81 deg: 5 c5: 20 c0: 7 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 6750001) Primes: RFBsize:571119, AFBsize:570202, largePrimes:34438043 encountered Relations: rels:31297614, finalFF:904990 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3087212 hash collisions in 32883378 relations Msieve: matrix is 1657566 x 1657814 (456.2 MB) Total sieving time: 45.11 hours. Total relation processing time: 0.76 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 45.86 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
Dec 21, 2008 (5th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(38·10¹⁵⁴-11)/9 = 4(2)₁₅₃1_<155> = 277 · 719 · 6091 · 33053 · 207502704317_<12> · 237956979619_<12> · C119
C119 = P59 · P60
P59 = 51587834613479025493547275460082123019777651055195321608609_<59>
P60 = 413393303095561319836967443404945417817696145003663940983647_<60>

Number: n N=21326065350413624233193962291332887661551544452586939041686174287451002112206135225323163185190177586449359373803417023 ( 119 digits) SNFS difficulty: 156 digits. Divisors found: Sun Dec 21 11:31:14 2008 prp59 factor: 51587834613479025493547275460082123019777651055195321608609 Sun Dec 21 11:31:14 2008 prp60 factor: 413393303095561319836967443404945417817696145003663940983647 Sun Dec 21 11:31:14 2008 elapsed time 01:19:32 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 20.64 hours. Scaled time: 37.54 units (timescale=1.819). Factorization parameters were as follows: name: KA_4_2_153_1 n: 21326065350413624233193962291332887661551544452586939041686174287451002112206135225323163185190177586449359373803417023 type: snfs skew: 1.23 deg: 5 c5: 19 c0: -55 m: 10000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2550001) Primes: RFBsize:216816, AFBsize:216782, largePrimes:16418732 encountered Relations: rels:15539332, finalFF:525467 Max relations in full relation-set: 28 Initial matrix: 433663 x 525467 with sparse part having weight 80415786. Pruned matrix : 404065 x 406297 with weight 54293410. Msieve: found 1223712 hash collisions in 16391218 relations Msieve: matrix is 523190 x 523438 (139.4 MB) Total sieving time: 20.24 hours. Total relation processing time: 0.40 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,56,56,2.5,2.5,100000 total time: 20.64 hours. --------- CPU info (if available) ----------
(38·10¹⁴¹+43)/9 = 4(2)₁₄₀7_<142> = 3 · 173 · 21157 · 180243689 · 173456622431_<12> · C116
C116 = P40 · P76
P40 = 1755675497577629798819125718774504104057_<40>
P76 = 7005262960181509629676894759365346286335418889322710401815129565027157909263_<76>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 12298968533278811763657986664253858669350572760397013486487978589390414885086829887869288821107164783220801116179991 (116 digits) Using B1=2986000, B2=5706890290, polynomial Dickson(6), sigma=3859119621 Step 1 took 23235ms Step 2 took 10750ms ********** Factor found in step 2: 1755675497577629798819125718774504104057 Found probable prime factor of 40 digits: 1755675497577629798819125718774504104057 Probable prime cofactor 7005262960181509629676894759365346286335418889322710401815129565027157909263 has 76 digits
Dec 21, 2008 (4th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39
(38·10¹⁵⁵-11)/9 = 4(2)₁₅₄1_<156> = 103 · 2111 · 58267513 · 7551094801_<10> · C133
C133 = P58 · P75
P58 = 8170250646439144324324539951122523668008977214876413918613_<58>
P75 = 540186647223365813208039585829871641900469751792558202249175396131868628473_<75>

Number: 42221_155 N=4413460303674498541861344363652947120119783104812592625476960256960945509230348423050843447267531724857326155033566161392143756467949 ( 133 digits) SNFS difficulty: 156 digits. Divisors found: r1=8170250646439144324324539951122523668008977214876413918613 r2=540186647223365813208039585829871641900469751792558202249175396131868628473 Version: Total time: 13.44 hours. Scaled time: 32.11 units (timescale=2.389). Factorization parameters were as follows: n: 4413460303674498541861344363652947120119783104812592625476960256960945509230348423050843447267531724857326155033566161392143756467949 m: 10000000000000000000000000000000 deg: 5 c5: 38 c0: -11 skew: 0.78 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: 7818933 Max relations in full relation-set: Initial matrix: Pruned matrix : 471139 x 471387 Total sieving time: 12.38 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.51 hours. Time per square root: 0.25 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: 13.44 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: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(37·10¹⁷³+17)/9 = 4(1)₁₇₂3_<174> = C174
C174 = P82 · P93
P82 = 2309642251320926628434349570227406190719013760451867200648957231633000117723292239_<82>
P93 = 177997744402185728430025384772804913156559791188015710518448917566430790426321615278811044967_<93>

Number: 41113_173 N=411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 ( 174 digits) SNFS difficulty: 176 digits. Divisors found: r1=2309642251320926628434349570227406190719013760451867200648957231633000117723292239 (pp82) r2=177997744402185728430025384772804913156559791188015710518448917566430790426321615278811044967 (pp93) Version: GGNFS-0.77.1-20050930-nocona Total time: 135.17 hours. Scaled time: 322.66 units (timescale=2.387). Factorization parameters were as follows: n: 411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113 m: 100000000000000000000000000000000000 deg: 5 c5: 37 c0: 1700 skew: 2.15 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 5400001) Primes: RFBsize:387202, AFBsize:386654, largePrimes:16029251 encountered Relations: rels:16426603, finalFF:927524 Max relations in full relation-set: 28 Initial matrix: 773923 x 927524 with sparse part having weight 115621215. Pruned matrix : 697149 x 701082 with weight 92001068. Total sieving time: 129.09 hours. Total relation processing time: 0.26 hours. Matrix solve time: 5.71 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,5600000,5600000,28,28,52,52,2.5,2.5,100000 total time: 135.17 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 21, 2008 (3rd): By Sinkiti Sibata / Msieve
(38·10¹¹⁶+43)/9 = 4(2)₁₁₅7_<117> = 7 · C116
C116 = P49 · P68
P49 = 1259410019485966740729222522666084595106750113901_<49>
P68 = 47893425797961438500296126851957768875428420854455429268527512319561_<68>

Number: 42227_116 N=60317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461 ( 116 digits) SNFS difficulty: 118 digits. Divisors found: r1=1259410019485966740729222522666084595106750113901 r2=47893425797961438500296126851957768875428420854455429268527512319561 Version: Total time: 1.82 hours. Scaled time: 3.62 units (timescale=1.985). Factorization parameters were as follows: name: 42227_116 n: 60317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461 m: 200000000000000000000000 deg: 5 c5: 95 c0: 344 skew: 1.29 type: snfs lss: 1 rlim: 660000 alim: 660000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 660000/660000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [330000, 580001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 77068 x 77307 Total sieving time: 1.82 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,118,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000 total time: 1.82 hours. --------- CPU info (if available) ----------
(38·10¹²²+43)/9 = 4(2)₁₂₁7_<123> = 7 · 17 · 61 · 149 · C117
C117 = P57 · P60
P57 = 421173275667591299966378819510053262339263564370298327557_<57>
P60 = 926866564584146824501549658874176921660428292030357582201921_<60>

Number: 42227_122 N=390371427112672185902270102305050820709697309077296521718673900043752418633496601046257062255716090668489495772636997 ( 117 digits) SNFS difficulty: 124 digits. Divisors found: r1=421173275667591299966378819510053262339263564370298327557 r2=926866564584146824501549658874176921660428292030357582201921 Version: Total time: 2.34 hours. Scaled time: 4.65 units (timescale=1.985). Factorization parameters were as follows: name: 42227_122 n: 390371427112672185902270102305050820709697309077296521718673900043752418633496601046257062255716090668489495772636997 m: 2000000000000000000000000 deg: 5 c5: 475 c0: 172 skew: 0.82 type: snfs lss: 1 rlim: 820000 alim: 820000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 820000/820000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [410000, 710001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 91077 x 91317 Total sieving time: 2.34 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,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,46,46,2.2,2.2,50000 total time: 2.34 hours. --------- CPU info (if available) ----------
(38·10¹⁰¹+43)/9 = 4(2)₁₀₀7_<102> = 13 · 115879 · C96
C96 = P36 · P61
P36 = 149610333136568974573076601882886309_<36>
P61 = 1873403840352829086869098148580338599604466026363314354447189_<61>

Sun Dec 21 06:00:54 2008 Msieve v. 1.39 Sun Dec 21 06:00:54 2008 random seeds: 2932d9f0 724ffcd1 Sun Dec 21 06:00:54 2008 factoring 280280572654514438616821274593606077308905258749492821240074840813542390186993609529185431635401 (96 digits) Sun Dec 21 06:00:55 2008 searching for 15-digit factors Sun Dec 21 06:00:56 2008 commencing quadratic sieve (96-digit input) Sun Dec 21 06:00:57 2008 using multiplier of 1 Sun Dec 21 06:00:57 2008 using 32kb Intel Core sieve core Sun Dec 21 06:00:57 2008 sieve interval: 36 blocks of size 32768 Sun Dec 21 06:00:57 2008 processing polynomials in batches of 6 Sun Dec 21 06:00:57 2008 using a sieve bound of 2245951 (83529 primes) Sun Dec 21 06:00:57 2008 using large prime bound of 336892650 (28 bits) Sun Dec 21 06:00:57 2008 using double large prime bound of 2236066681946550 (43-51 bits) Sun Dec 21 06:00:57 2008 using trial factoring cutoff of 51 bits Sun Dec 21 06:00:57 2008 polynomial 'A' values have 12 factors Sun Dec 21 10:26:20 2008 83888 relations (20624 full + 63264 combined from 1250885 partial), need 83625 Sun Dec 21 10:26:21 2008 begin with 1271509 relations Sun Dec 21 10:26:23 2008 reduce to 219257 relations in 14 passes Sun Dec 21 10:26:23 2008 attempting to read 219257 relations Sun Dec 21 10:26:26 2008 recovered 219257 relations Sun Dec 21 10:26:26 2008 recovered 203786 polynomials Sun Dec 21 10:26:26 2008 attempting to build 83888 cycles Sun Dec 21 10:26:26 2008 found 83888 cycles in 5 passes Sun Dec 21 10:26:26 2008 distribution of cycle lengths: Sun Dec 21 10:26:26 2008 length 1 : 20624 Sun Dec 21 10:26:26 2008 length 2 : 14487 Sun Dec 21 10:26:26 2008 length 3 : 14122 Sun Dec 21 10:26:26 2008 length 4 : 11284 Sun Dec 21 10:26:26 2008 length 5 : 8549 Sun Dec 21 10:26:26 2008 length 6 : 5869 Sun Dec 21 10:26:26 2008 length 7 : 3664 Sun Dec 21 10:26:26 2008 length 9+: 5289 Sun Dec 21 10:26:26 2008 largest cycle: 18 relations Sun Dec 21 10:26:27 2008 matrix is 83529 x 83888 (22.8 MB) with weight 5628323 (67.09/col) Sun Dec 21 10:26:27 2008 sparse part has weight 5628323 (67.09/col) Sun Dec 21 10:26:28 2008 filtering completed in 3 passes Sun Dec 21 10:26:28 2008 matrix is 79673 x 79736 (21.7 MB) with weight 5371984 (67.37/col) Sun Dec 21 10:26:28 2008 sparse part has weight 5371984 (67.37/col) Sun Dec 21 10:26:28 2008 saving the first 48 matrix rows for later Sun Dec 21 10:26:28 2008 matrix is 79625 x 79736 (15.2 MB) with weight 4447552 (55.78/col) Sun Dec 21 10:26:28 2008 sparse part has weight 3513534 (44.06/col) Sun Dec 21 10:26:28 2008 matrix includes 64 packed rows Sun Dec 21 10:26:28 2008 using block size 31894 for processor cache size 1024 kB Sun Dec 21 10:26:29 2008 commencing Lanczos iteration Sun Dec 21 10:26:29 2008 memory use: 13.8 MB Sun Dec 21 10:27:14 2008 lanczos halted after 1261 iterations (dim = 79624) Sun Dec 21 10:27:14 2008 recovered 16 nontrivial dependencies Sun Dec 21 10:27:15 2008 prp36 factor: 149610333136568974573076601882886309 Sun Dec 21 10:27:15 2008 prp61 factor: 1873403840352829086869098148580338599604466026363314354447189 Sun Dec 21 10:27:15 2008 elapsed time 04:26:21
(38·10¹²⁹+43)/9 = 4(2)₁₂₈7_<130> = 3 · 31 · 58189 · C123
C123 = P37 · P87
P37 = 1232507627891317146613035330415084249_<37>
P87 = 633034863906915936488414072851613985408624063435282028990273697724896163138531480627299_<87>

Number: 42227_129 N=780220298486415738373901401055962471239385898458475638842840492193351812645781852909460998563306448789737672072710454313451 ( 123 digits) SNFS difficulty: 131 digits. Divisors found: r1=1232507627891317146613035330415084249 r2=633034863906915936488414072851613985408624063435282028990273697724896163138531480627299 Version: Total time: 2.82 hours. Scaled time: 5.67 units (timescale=2.010). Factorization parameters were as follows: name: 42227_129 n: 780220298486415738373901401055962471239385898458475638842840492193351812645781852909460998563306448789737672072710454313451 m: 100000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1080000/1080000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [540000, 840001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 148817 x 149065 Total sieving time: 2.82 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,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,47,47,2.3,2.3,50000 total time: 2.82 hours. --------- CPU info (if available) ----------
(38·10¹³⁴+43)/9 = 4(2)₁₃₃7_<135> = 7 · 179 · 199 · C130
C130 = P36 · P40 · P54
P36 = 976249081765964679035742823768959109_<36>
P40 = 2341296925239378772934166687655885634501_<40>
P54 = 740832125045200102183124573455647869445175399351741849_<54>

Number: 42227_134 N=1693311819361059977550250142260473245004841534978252083330548280998857905738678316651983870759312212387645418722592299976427317041 ( 130 digits) SNFS difficulty: 136 digits. Divisors found: r1=976249081765964679035742823768959109 r2=2341296925239378772934166687655885634501 r3=740832125045200102183124573455647869445175399351741849 Version: Total time: 4.33 hours. Scaled time: 8.49 units (timescale=1.960). Factorization parameters were as follows: name: 42227_134 n: 1693311819361059977550250142260473245004841534978252083330548280998857905738678316651983870759312212387645418722592299976427317041 m: 1000000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 type: snfs lss: 1 rlim: 1310000 alim: 1310000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1310000/1310000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [655000, 1105001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 170006 x 170254 Total sieving time: 4.33 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000 total time: 4.33 hours. --------- CPU info (if available) ----------
(38·10¹⁵⁴+7)/9 = 4(2)₁₅₃3_<155> = 109 · 21407 · 153487 · 1581644833984969930562339_<25> · C119
C119 = P57 · P63
P57 = 321166027817848058882563135857714158627714576218012383011_<57>
P63 = 232085824426105456188431120454237300232428792761128210394472227_<63>

Number: 42223_154 N=74538082343762785448110691159984807842440835697113941110272639034909759506082539134491568195318220352077422549926135497 ( 119 digits) SNFS difficulty: 156 digits. Divisors found: r1=321166027817848058882563135857714158627714576218012383011 r2=232085824426105456188431120454237300232428792761128210394472227 Version: Total time: 21.67 hours. Scaled time: 55.56 units (timescale=2.564). Factorization parameters were as follows: name: 42223_154 n: 74538082343762785448110691159984807842440835697113941110272639034909759506082539134491568195318220352077422549926135497 m: 10000000000000000000000000000000 deg: 5 c5: 19 c0: 35 skew: 1.13 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, 2400001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 460519 x 460767 Total sieving time: 21.67 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,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 21.67 hours. --------- CPU info (if available) ----------
(38·10¹¹⁴+43)/9 = 4(2)₁₁₃7_<115> = 3 · 31 · 270737 · 5986022611_<10> · C98
C98 = P40 · P58
P40 = 8392236225335848609185007290798128808749_<40>
P58 = 3338062573732403028949060455916560045484897247255070478873_<58>

Sun Dec 21 14:24:23 2008 Msieve v. 1.39 Sun Dec 21 14:24:23 2008 random seeds: 4496b508 55cd2144 Sun Dec 21 14:24:23 2008 factoring 28013809653714889828606582246638760452158805911349423981945536736639371761734654695622944462059877 (98 digits) Sun Dec 21 14:24:24 2008 searching for 15-digit factors Sun Dec 21 14:24:26 2008 commencing quadratic sieve (98-digit input) Sun Dec 21 14:24:26 2008 using multiplier of 13 Sun Dec 21 14:24:26 2008 using 32kb Intel Core sieve core Sun Dec 21 14:24:26 2008 sieve interval: 36 blocks of size 32768 Sun Dec 21 14:24:26 2008 processing polynomials in batches of 6 Sun Dec 21 14:24:26 2008 using a sieve bound of 2472797 (90588 primes) Sun Dec 21 14:24:26 2008 using large prime bound of 370919550 (28 bits) Sun Dec 21 14:24:26 2008 using double large prime bound of 2658908975208750 (43-52 bits) Sun Dec 21 14:24:26 2008 using trial factoring cutoff of 52 bits Sun Dec 21 14:24:26 2008 polynomial 'A' values have 13 factors Sun Dec 21 21:45:00 2008 90841 relations (22207 full + 68634 combined from 1358298 partial), need 90684 Sun Dec 21 21:45:01 2008 begin with 1380505 relations Sun Dec 21 21:45:03 2008 reduce to 237264 relations in 13 passes Sun Dec 21 21:45:03 2008 attempting to read 237264 relations Sun Dec 21 21:45:07 2008 recovered 237264 relations Sun Dec 21 21:45:07 2008 recovered 225925 polynomials Sun Dec 21 21:45:07 2008 attempting to build 90841 cycles Sun Dec 21 21:45:07 2008 found 90841 cycles in 6 passes Sun Dec 21 21:45:07 2008 distribution of cycle lengths: Sun Dec 21 21:45:07 2008 length 1 : 22207 Sun Dec 21 21:45:07 2008 length 2 : 16089 Sun Dec 21 21:45:07 2008 length 3 : 15123 Sun Dec 21 21:45:07 2008 length 4 : 12342 Sun Dec 21 21:45:07 2008 length 5 : 9156 Sun Dec 21 21:45:07 2008 length 6 : 6348 Sun Dec 21 21:45:07 2008 length 7 : 4061 Sun Dec 21 21:45:07 2008 length 9+: 5515 Sun Dec 21 21:45:07 2008 largest cycle: 24 relations Sun Dec 21 21:45:08 2008 matrix is 90588 x 90841 (24.3 MB) with weight 6018077 (66.25/col) Sun Dec 21 21:45:08 2008 sparse part has weight 6018077 (66.25/col) Sun Dec 21 21:45:09 2008 filtering completed in 3 passes Sun Dec 21 21:45:09 2008 matrix is 86557 x 86621 (23.3 MB) with weight 5762657 (66.53/col) Sun Dec 21 21:45:09 2008 sparse part has weight 5762657 (66.53/col) Sun Dec 21 21:45:09 2008 saving the first 48 matrix rows for later Sun Dec 21 21:45:09 2008 matrix is 86509 x 86621 (14.0 MB) with weight 4514781 (52.12/col) Sun Dec 21 21:45:09 2008 sparse part has weight 3151662 (36.38/col) Sun Dec 21 21:45:09 2008 matrix includes 64 packed rows Sun Dec 21 21:45:09 2008 using block size 34648 for processor cache size 1024 kB Sun Dec 21 21:45:10 2008 commencing Lanczos iteration Sun Dec 21 21:45:10 2008 memory use: 13.8 MB Sun Dec 21 21:45:59 2008 lanczos halted after 1370 iterations (dim = 86505) Sun Dec 21 21:45:59 2008 recovered 16 nontrivial dependencies Sun Dec 21 21:46:00 2008 prp40 factor: 8392236225335848609185007290798128808749 Sun Dec 21 21:46:00 2008 prp58 factor: 3338062573732403028949060455916560045484897247255070478873 Sun Dec 21 21:46:00 2008 elapsed time 07:21:37
(38·10¹³⁹+43)/9 = 4(2)₁₃₈7_<140> = 23 · 47 · 157 · 1091 · 490913 · 95099288952186151_<17> · C109
C109 = P34 · P76
P34 = 1393980093270082701445581996312139_<34>
P76 = 3503907362859903751937502287009860162839613179165479888499563514926963907713_<76>

Number: 42227_139 N=4884377112489178144273156295792950485073388003515582263988391522853491148860966070259939401017505922337628107 ( 109 digits) SNFS difficulty: 141 digits. Divisors found: r1=1393980093270082701445581996312139 r2=3503907362859903751937502287009860162839613179165479888499563514926963907713 Version: Total time: 6.96 hours. Scaled time: 13.90 units (timescale=1.997). Factorization parameters were as follows: name: 42227_139 n: 4884377112489178144273156295792950485073388003515582263988391522853491148860966070259939401017505922337628107 m: 10000000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor 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, 1490001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 200308 x 200556 Total sieving time: 6.96 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 6.96 hours. --------- CPU info (if available) ----------
Dec 21, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39
(38·10¹²³+43)/9 = 4(2)₁₂₂7_<124> = 3 · 523 · 4981091 · 595375639 · C105
C105 = P37 · P69
P37 = 6625236622908351129130519627635150409_<37>
P69 = 136962354440508632796329576785523794043541101927468396673154669332863_<69>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2291580702 Step 1 took 8167ms Step 2 took 5212ms ********** Factor found in step 2: 6625236622908351129130519627635150409 Found probable prime factor of 37 digits: 6625236622908351129130519627635150409 Probable prime cofactor 136962354440508632796329576785523794043541101927468396673154669332863 has 69 digits
(38·10¹⁰²+43)/9 = 4(2)₁₀₁7_<103> = 3 · 283 · C100
C100 = P46 · P55
P46 = 2339819275170388413017198578896211823485991939_<46>
P55 = 2125450928489942711483795575495927297447161644376716257_<55>

SNFS difficulty: 103 digits. Divisors found: r1=2339819275170388413017198578896211823485991939 (pp46) r2=2125450928489942711483795575495927297447161644376716257 (pp55) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.732). Factorization parameters were as follows: n: 4973171050909566810626881298259390132181651616280591545609213453736421934301792959036775291192252323 m: 20000000000000000000000000 deg: 4 c4: 475 c0: 86 skew: 0.65 type: snfs lss: 1 rlim: 380000 alim: 380000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 380000/380000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [190000, 250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 37602 x 37840 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,103,4,0,0,0,0,0,0,0,0,380000,380000,25,25,44,44,2.2,2.2,20000 total time: 0.30 hours.
(38·10¹⁵²+43)/9 = 4(2)₁₅₁7_<153> = 7 · 113 · 140869 · 549053809 · 611191649 · C128
C128 = P34 · P94
P34 = 3311927853322341988197805383433981_<34>
P94 = 3409384512902395854395804534112932958824831083076127506595975133098149114787081693316069646053_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=965743905 Step 1 took 9800ms Step 2 took 5995ms ********** Factor found in step 2: 3311927853322341988197805383433981 Found probable prime factor of 34 digits: 3311927853322341988197805383433981 Probable prime cofactor 3409384512902395854395804534112932958824831083076127506595975133098149114787081693316069646053 has 94 digits
(38·10¹⁶⁹+43)/9 = 4(2)₁₆₈7_<170> = 59 · 337 · 977 · 39198743 · 227965993 · C147
C147 = P28 · P119
P28 = 2655820141606970410062410591_<28>
P119 = 91584872364486444849043172878832212662987223413797999591678382550522470542734022451786510752287876994744879249741744633_<119>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3830038547 Step 1 took 11702ms Step 2 took 6882ms ********** Factor found in step 2: 2655820141606970410062410591 Found probable prime factor of 28 digits: 2655820141606970410062410591 Probable prime cofactor 91584872364486444849043172878832212662987223413797999591678382550522470542734022451786510752287876994744879249741744633 has 119 digits
(38·10¹¹³+43)/9 = 4(2)₁₁₂7_<114> = 13 · 25237 · 1575809689_<10> · C99
C99 = P41 · P59
P41 = 49735454513288675927478118921779346906991_<41>
P59 = 16420642634281376632440806439033280504579372286731350984533_<59>

SNFS difficulty: 115 digits. Divisors found: r1=49735454513288675927478118921779346906991 (pp41) r2=16420642634281376632440806439033280504579372286731350984533 (pp59) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.727). Factorization parameters were as follows: n: 816688124816270146188018767143009804753821509031817108709323199602796756189812586828039616230570203 m: 50000000000000000000000 deg: 5 c5: 304 c0: 1075 skew: 1.29 type: snfs lss: 1 rlim: 600000 alim: 600000 lpbr: 25 lpba: 25 mfbr: 47 mfba: 47 rlambda: 2.2 alambda: 2.2 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved rational special-q in [300000, 550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 69513 x 69761 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,47,47,2.2,2.2,50000 total time: 0.90 hours.
(38·10²⁰⁵+43)/9 = 4(2)₂₀₄7_<206> = 23 · 39769717773101_<14> · 8283027066071539_<16> · C175
C175 = P37 · P138
P37 = 7446927812275566885066367640755661501_<37>
P138 = 748332346108083517204496076352281303579644183334234639264171266650967495931706368107585190904256579382948621638256477256434360566405057791_<138>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2569832959 Step 1 took 16203ms Step 2 took 8239ms ********** Factor found in step 2: 7446927812275566885066367640755661501 Found probable prime factor of 37 digits: 7446927812275566885066367640755661501 Probable prime cofactor has 138 digits
(38·10¹⁹¹+43)/9 = 4(2)₁₉₀7_<192> = 13 · 717303940796383_<15> · C176
C176 = P35 · C142
P35 = 12195699723660604747700062962777713_<35>
C142 = [3712682365398479438282243464664815196302016944064203440914178876499906302165494535438255401453384930597328776467752153773796030078075034987601_<142>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2348945104 Step 1 took 16054ms Step 2 took 8272ms ********** Factor found in step 2: 12195699723660604747700062962777713 Found probable prime factor of 35 digits: 12195699723660604747700062962777713 Composite cofactor has 142 digits
(38·10¹⁷²+43)/9 = 4(2)₁₇₁7_<173> = 78904708409084059771_<20> · C153
C153 = P33 · C121
P33 = 203557052143526710221580765970953_<33>
C121 = [2628766520436983600848734312946145497452786791325720620424489826049404434795255603834058064887550987569889245091927009729_<121>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1531914312 Step 1 took 11706ms Step 2 took 6748ms ********** Factor found in step 2: 203557052143526710221580765970953 Found probable prime factor of 33 digits: 203557052143526710221580765970953 Composite cofactor has 121 digits
Dec 21, 2008: Factorizations of 422...227 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Dec 20, 2008 (5th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39
(37·10¹⁸⁶+53)/9 = 4(1)₁₈₅7_<187> = 139 · 2017 · 109199 · 4908232860071_<13> · 704264442759638437_<18> · 10378488878367712824242152948117_<32> · C115
C115 = P49 · P67
P49 = 2689929817698759709554943418445374763129549819167_<49>
P67 = 1391502082959891862381969553973756799821963452576981458534155488297_<67>

Number: 41117_186 N=3743042944343746327051073365541314201342334703437542556352179663331113160500440981418270935251237401012936934788599 ( 115 digits) Divisors found: r1=2689929817698759709554943418445374763129549819167 r2=1391502082959891862381969553973756799821963452576981458534155488297 Version: Total time: 23.49 hours. Scaled time: 56.17 units (timescale=2.391). Factorization parameters were as follows: name: 41117_186 n: 3743042944343746327051073365541314201342334703437542556352179663331113160500440981418270935251237401012936934788599 skew: 19576.61 # norm 1.71e+15 c5: 71040 c4: 5792275644 c3: -75240063274582 c2: -1887877505352075585 c1: 13052664014638656996786 c0: 93295585212988908690842265 # alpha -4.74 Y1: 612224461663 Y0: -8797188109558810865144 # Murphy_E 5.31e-10 # M 2485795306113775412739937617463062509924090181073194909416249828870954543475074827476885729509114857968585428779381 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, 2730001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9452756 Max relations in full relation-set: Initial matrix: Pruned matrix : 554579 x 554827 Polynomial selection time: 1.33 hours. Total sieving time: 20.54 hours. Total relation processing time: 0.81 hours. Matrix solve time: 0.69 hours. Time per square root: 0.13 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: 23.49 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: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 20, 2008 (4th): By Erik Branger / GGNFS, Msieve
(37·10¹⁵⁵+53)/9 = 4(1)₁₅₄7_<156> = 3 · 7² · 6133 · 5060729981_<10> · C140
C140 = P66 · P75
P66 = 269367314763042914282201634549081377562001210180121850198455089769_<66>
P75 = 334511345691997716865981461494206580384756565786245263349384660653593436903_<75>

Number: 41117_155 N=90106422946825408363604857144748861894415378687351286417994381988145740514085075549840680353930716088170577060545290073747118283014102345407 ( 140 digits) SNFS difficulty: 156 digits. Divisors found: r1=269367314763042914282201634549081377562001210180121850198455089769 r2=334511345691997716865981461494206580384756565786245263349384660653593436903 Version: Total time: 23.50 hours. Scaled time: 50.72 units (timescale=2.158). Factorization parameters were as follows: n: 90106422946825408363604857144748861894415378687351286417994381988145740514085075549840680353930716088170577060545290073747118283014102345407 m: 10000000000000000000000000000000 deg: 5 c5: 37 c0: 53 skew: 1.07 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4Factor 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, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 464074 x 464322 Total sieving time: 23.50 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,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 23.50 hours. --------- CPU info (if available) ----------
Dec 20, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(29·10¹⁸⁴+43)/9 = 3(2)₁₈₃7_<185> = 13 · 37 · C182
C182 = P84 · P99
P84 = 111279443625051066686752583950724085052587338038048389915997789891205474859639594563_<84>
P99 = 601998579502120043908560040845175574623627224208589111827646965534334972535100226307763607247653009_<99>

Number: n N=66990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990067 ( 182 digits) SNFS difficulty: 186 digits. Divisors found: Sat Dec 20 12:36:23 2008 prp84 factor: 111279443625051066686752583950724085052587338038048389915997789891205474859639594563 Sat Dec 20 12:36:23 2008 prp99 factor: 601998579502120043908560040845175574623627224208589111827646965534334972535100226307763607247653009 Sat Dec 20 12:36:23 2008 elapsed time 02:46:43 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 75.44 hours. Scaled time: 151.78 units (timescale=2.012). Factorization parameters were as follows: name: KA_3_2_183_7 n: 66990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990066990067 type: snfs skew: 1.71 deg: 5 c5: 29 c0: 430 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 5000001) Primes: RFBsize:571119, AFBsize:570987, largePrimes:30886821 encountered Relations: rels:27632037, finalFF:860192 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7185617 hash collisions in 37455763 relations Msieve: matrix is 1392558 x 1392806 (375.4 MB) Total sieving time: 74.58 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 75.44 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
Dec 20, 2008 (2nd): By Sinkiti Sibata / GGNFS, Msieve
(38·10¹⁴⁹+7)/9 = 4(2)₁₄₈3_<150> = 3 · 942700533825610283281_<21> · 20730491537768293860737_<23> · C106
C106 = P52 · P54
P52 = 9200186247536074110725736408181370462425062932285921_<52>
P54 = 782780251568680203916999787491470260852006980070718293_<54>

Number: 42223_149 N=7201724105325000015271685446739135051345465751365130548241989191456787699852270086959653138717414921052853 ( 106 digits) SNFS difficulty: 151 digits. Divisors found: r1=9200186247536074110725736408181370462425062932285921 (pp52) r2=782780251568680203916999787491470260852006980070718293 (pp54) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 32.37 hours. Scaled time: 15.28 units (timescale=0.472). Factorization parameters were as follows: name: 42223_149 n: 7201724105325000015271685446739135051345465751365130548241989191456787699852270086959653138717414921052853 m: 1000000000000000000000000000000 deg: 5 c5: 19 c0: 35 skew: 1.13 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, 1950001) Primes: RFBsize:169511, AFBsize:169171, largePrimes:7064924 encountered Relations: rels:7144749, finalFF:554927 Max relations in full relation-set: 28 Initial matrix: 338747 x 554927 with sparse part having weight 60132314. Pruned matrix : 271443 x 273200 with weight 27469857. Total sieving time: 29.50 hours. Total relation processing time: 0.28 hours. Matrix solve time: 2.48 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 32.37 hours. --------- CPU info (if available) ----------
(38·10¹⁵⁰+7)/9 = 4(2)₁₄₉3_<151> = 863 · 354115717612803949610519013179_<30> · C119
C119 = P44 · P75
P44 = 15431000559815206035395680817815150310335313_<44>
P75 = 895346212652991183542440571902343530844413019287198941007927920963839486323_<75>

Number: 42223_150 N=13816087908676731462588855160525165982813315669594685075162160784517590741668791402353425690447665556919582119807424099 ( 119 digits) SNFS difficulty: 151 digits. Divisors found: r1=15431000559815206035395680817815150310335313 r2=895346212652991183542440571902343530844413019287198941007927920963839486323 Version: Total time: 14.72 hours. Scaled time: 37.91 units (timescale=2.575). Factorization parameters were as follows: name: 42223_150 n: 13816087908676731462588855160525165982813315669594685075162160784517590741668791402353425690447665556919582119807424099 m: 1000000000000000000000000000000 deg: 5 c5: 38 c0: 7 skew: 0.71 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 : 390910 x 391158 Total sieving time: 14.72 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 14.72 hours. --------- CPU info (if available) ----------
Dec 20, 2008: By Serge Batalov / Msieve-1.39
(38·10¹⁷⁰+7)/9 = 4(2)₁₆₉3_<171> = 3 · 157 · 2753 · 196771 · C160
C160 = P42 · P55 · P64
P42 = 153476075151060773153342076445236124223591_<42>
P55 = 1917702948548351014972144075788906674953668710503672193_<55>
P64 = 5622518013204771026946571224850334036846250412736550122129247077_<64>

SNFS difficulty: 171 digits. Divisors found: r1=153476075151060773153342076445236124223591 (pp42) r2=1917702948548351014972144075788906674953668710503672193 (pp55) r3=5622518013204771026946571224850334036846250412736550122129247077 (pp64) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 1654828058268818266826261750512835223969607670110340280285501032823035481764827422126230743258275115337701206453136677726673505147628725557203557147602078050851 m: 10000000000000000000000000000000000 deg: 5 c5: 38 c0: 7 skew: 0.71 type: snfs lss: 1 rlim: 5100000 alim: 5100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5100000/5100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2550000, 5550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 874715 x 874963 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5100000,5100000,27,27,52,52,2.4,2.4,200000 total time: 55.00 hours.
(37·10¹⁶⁶+53)/9 = 4(1)₁₆₅7_<167> = 173898349349_<12> · C156
C156 = P69 · P87
P69 = 538011999070133912246986997440759766268356209654134229710176541138511_<69>
P87 = 439411878873081543610582036653852567797126398884022586714170752552913700796583215412903_<87>

SNFS difficulty: 167 digits. Divisors found: r1=538011999070133912246986997440759766268356209654134229710176541138511 (pp69) r2=439411878873081543610582036653852567797126398884022586714170752552913700796583215412903 (pp87) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.309). Factorization parameters were as follows: n: 236408863367670142721103299844704445499417936577501671655105982078525215703490151195127495684341517913294975327058250115806342823270262708415877058579607433 m: 1000000000000000000000000000000000 deg: 5 c5: 370 c0: 53 skew: 0.68 type: snfs lss: 1 rlim: 4300000 alim: 4300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4300000/4300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2150000, 5650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 954792 x 955039 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,4300000,4300000,27,27,52,52,2.4,2.4,100000 total time: 45.00 hours.
Dec 19, 2008 (4th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39
(37·10¹⁷⁵+71)/9 = 4(1)₁₇₄9_<176> = 7 · 1277 · 131517606982631_<15> · 705741823656784897_<18> · 4900621212089152019167274959_<28> · C113
C113 = P47 · P66
P47 = 27453836811193533274952439583072078790856233791_<47>
P66 = 368286958765672743643689545618535973113755495971514753154648801787_<66>

Number: 41119_175 N=10110890065643541273876685037705613811147665442907802879999742534726910408194518400360771008434790950557690584517 ( 113 digits) Divisors found: r1=27453836811193533274952439583072078790856233791 r2=368286958765672743643689545618535973113755495971514753154648801787 Version: Total time: 17.05 hours. Scaled time: 40.67 units (timescale=2.385). Factorization parameters were as follows: name: 41119_175 n: 10110890065643541273876685037705613811147665442907802879999742534726910408194518400360771008434790950557690584517 skew: 31984.13 # norm 1.63e+15 c5: 30360 c4: 1656856535 c3: -70094780515248 c2: -2243626268782858410 c1: 50520317420498134325496 c0: -50669818649517852164082573 # alpha -5.19 Y1: 1865253410543 Y0: -3195175792034622680434 # Murphy_E 7.24e-10 # M 5786324711396589223504645891167661672681231097769903942441373431869606174401351108406813980815335802242941075202 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1200000, 2160001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8619601 Max relations in full relation-set: Initial matrix: Pruned matrix : 412092 x 412340 Polynomial selection time: 1.04 hours. Total sieving time: 14.87 hours. Total relation processing time: 0.63 hours. Matrix solve time: 0.36 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,51,51,2.6,2.6,60000 total time: 17.05 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: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 19, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(38·10¹⁶⁵-11)/9 = 4(2)₁₆₄1_<166> = 3² · 7 · 29 · 433 · 14103704127121829141_<20> · 512830241895585414353418585991_<30> · C111
C111 = P46 · P66
P46 = 2929181820706174355164874093534364725713662073_<46>
P66 = 251919332497036727931045115049442101193333340434130266632902737037_<66>

Number: n N=737917529034754159507563986949881633271119592299813842582578872003532723125311534918896755506803917146199297701 ( 111 digits) Divisors found: Fri Dec 19 10:35:19 2008 prp46 factor: 2929181820706174355164874093534364725713662073 Fri Dec 19 10:35:19 2008 prp66 factor: 251919332497036727931045115049442101193333340434130266632902737037 Fri Dec 19 10:35:19 2008 elapsed time 01:12:51 (Msieve 1.39 - dependency 5) Version: GGNFS-0.77.1-20051202-athlon Total time: 14.05 hours. Scaled time: 25.30 units (timescale=1.801). Factorization parameters were as follows: n: 737917529034754159507563986949881633271119592299813842582578872003532723125311534918896755506803917146199297701 Y0: -2383114440365214673050 Y1: 666243497711 c0: -312209647156954433244650149 c1: 14556975766321877839966 c2: 843009328727785431 c3: -27567575689852 c4: 956954044 c5: 9600 skew: 23510.92 name: KA_4_2_164_1 type: gnfs rlim: 3400000 alim: 3400000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 2300001) Primes: RFBsize:243539, AFBsize:244085, largePrimes:15000202 encountered Relations: rels:13799352, finalFF:770852 Max relations in full relation-set: 28 Initial matrix: 487700 x 770852 with sparse part having weight 92119394. Pruned matrix : Msieve: found 810713 hash collisions in 14297157 relations Msieve: matrix is 402030 x 402276 (111.7 MB) Total sieving time: 13.69 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3400000,3400000,28,28,56,56,2.5,2.5,100000 total time: 14.05 hours. --------- CPU info (if available) ----------
Dec 19, 2008 (2nd): By Sinkiti Sibata / Msieve
(38·10¹³⁶+7)/9 = 4(2)₁₃₅3_<137> = 409 · 6361 · C131
C131 = P49 · P82
P49 = 8594000668119493432759132571049781552594004445247_<49>
P82 = 1888413082581267978490482365718941523363737007376231943020350468156526437976112641_<82>

Number: 42223_136 N=16229023293389009133139106090876295081397306947333103820777599984556803097659300782781313782997714996228246862748288574754789067327 ( 131 digits) SNFS difficulty: 138 digits. Divisors found: r1=8594000668119493432759132571049781552594004445247 r2=1888413082581267978490482365718941523363737007376231943020350468156526437976112641 Version: Total time: 4.82 hours. Scaled time: 12.40 units (timescale=2.575). Factorization parameters were as follows: name: 42223_136 n: 16229023293389009133139106090876295081397306947333103820777599984556803097659300782781313782997714996228246862748288574754789067327 m: 2000000000000000000000000000 deg: 5 c5: 95 c0: 56 skew: 0.90 type: snfs lss: 1 rlim: 1420000 alim: 1420000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1420000/1420000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [710000, 1385001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 222874 x 223122 Total sieving time: 4.82 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,138,5,0,0,0,0,0,0,0,0,1420000,1420000,26,26,48,48,2.3,2.3,75000 total time: 4.82 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁶+7)/9 = 4(2)₁₄₅3_<147> = 3² · 96157 · 541469 · 22900003348416823_<17> · C119
C119 = P53 · P67
P53 = 13474293956396481663403791718049203306600304054932849_<53>
P67 = 2920132186621567969038207626747820838665582277038474633583932183017_<67>

Number: 42223_146 N=39346719474073836211165386970759767038358231641254866087382141856300037559614084744521490143159896516392312603913225433 ( 119 digits) SNFS difficulty: 148 digits. Divisors found: r1=13474293956396481663403791718049203306600304054932849 r2=2920132186621567969038207626747820838665582277038474633583932183017 Version: Total time: 11.92 hours. Scaled time: 30.69 units (timescale=2.575). Factorization parameters were as follows: 42223_146 n: 39346719474073836211165386970759767038358231641254866087382141856300037559614084744521490143159896516392312603913225433 m: 200000000000000000000000000000 deg: 5 c5: 95 c0: 56 skew: 0.90 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 332704 x 332952 Total sieving time: 11.92 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 11.92 hours. --------- CPU info (if available) ----------
(38·10¹²⁰+7)/9 = 4(2)₁₁₉3_<121> = 29 · 4924903 · 245566854496031743_<18> · C96
C96 = P41 · P55
P41 = 19955093527642430225778981756086814003767_<41>
P55 = 6032841192967150543154636232473256336681085904002749509_<55>

Fri Dec 19 07:35:03 2008 Msieve v. 1.39 Fri Dec 19 07:35:03 2008 random seeds: 6b80e7dc 791eff7b Fri Dec 19 07:35:03 2008 factoring 120385910243073423257026243810404870767812331654226840017936550483511807178296703100252683400403 (96 digits) Fri Dec 19 07:35:04 2008 searching for 15-digit factors Fri Dec 19 07:35:05 2008 commencing quadratic sieve (96-digit input) Fri Dec 19 07:35:05 2008 using multiplier of 37 Fri Dec 19 07:35:05 2008 using 32kb Intel Core sieve core Fri Dec 19 07:35:05 2008 sieve interval: 36 blocks of size 32768 Fri Dec 19 07:35:05 2008 processing polynomials in batches of 6 Fri Dec 19 07:35:06 2008 using a sieve bound of 2192963 (81176 primes) Fri Dec 19 07:35:06 2008 using large prime bound of 328944450 (28 bits) Fri Dec 19 07:35:06 2008 using double large prime bound of 2142005338065300 (43-51 bits) Fri Dec 19 07:35:06 2008 using trial factoring cutoff of 51 bits Fri Dec 19 07:35:06 2008 polynomial 'A' values have 12 factors Fri Dec 19 07:35:06 2008 restarting with 1596 full and 94647 partial relations Fri Dec 19 11:27:17 2008 81338 relations (20175 full + 61163 combined from 1215310 partial), need 81272 Fri Dec 19 11:27:18 2008 begin with 1235485 relations Fri Dec 19 11:27:20 2008 reduce to 211262 relations in 11 passes Fri Dec 19 11:27:20 2008 attempting to read 211262 relations Fri Dec 19 11:27:23 2008 recovered 211262 relations Fri Dec 19 11:27:23 2008 recovered 196167 polynomials Fri Dec 19 11:27:23 2008 attempting to build 81338 cycles Fri Dec 19 11:27:23 2008 found 81338 cycles in 5 passes Fri Dec 19 11:27:23 2008 distribution of cycle lengths: Fri Dec 19 11:27:23 2008 length 1 : 20175 Fri Dec 19 11:27:23 2008 length 2 : 14340 Fri Dec 19 11:27:23 2008 length 3 : 13606 Fri Dec 19 11:27:23 2008 length 4 : 10935 Fri Dec 19 11:27:23 2008 length 5 : 8292 Fri Dec 19 11:27:23 2008 length 6 : 5597 Fri Dec 19 11:27:23 2008 length 7 : 3511 Fri Dec 19 11:27:23 2008 length 9+: 4882 Fri Dec 19 11:27:23 2008 largest cycle: 19 relations Fri Dec 19 11:27:24 2008 matrix is 81176 x 81338 (22.8 MB) with weight 5643868 (69.39/col) Fri Dec 19 11:27:24 2008 sparse part has weight 5643868 (69.39/col) Fri Dec 19 11:27:25 2008 filtering completed in 3 passes Fri Dec 19 11:27:25 2008 matrix is 77244 x 77308 (21.8 MB) with weight 5404103 (69.90/col) Fri Dec 19 11:27:25 2008 sparse part has weight 5404103 (69.90/col) Fri Dec 19 11:27:25 2008 saving the first 48 matrix rows for later Fri Dec 19 11:27:25 2008 matrix is 77196 x 77308 (16.0 MB) with weight 4523024 (58.51/col) Fri Dec 19 11:27:25 2008 sparse part has weight 3722876 (48.16/col) Fri Dec 19 11:27:25 2008 matrix includes 64 packed rows Fri Dec 19 11:27:25 2008 using block size 30923 for processor cache size 1024 kB Fri Dec 19 11:27:26 2008 commencing Lanczos iteration Fri Dec 19 11:27:26 2008 memory use: 14.0 MB Fri Dec 19 11:28:10 2008 lanczos halted after 1222 iterations (dim = 77195) Fri Dec 19 11:28:11 2008 recovered 18 nontrivial dependencies Fri Dec 19 11:28:12 2008 prp41 factor: 19955093527642430225778981756086814003767 Fri Dec 19 11:28:12 2008 prp55 factor: 6032841192967150543154636232473256336681085904002749509 Fri Dec 19 11:28:12 2008 elapsed time 03:53:09
(38·10¹⁵¹+7)/9 = 4(2)₁₅₀3_<152> = 23 · 1176371562578041651_<19> · C133
C133 = P63 · P70
P63 = 485460562826957331754454944330962706119706627186220853762299653_<63>
P70 = 3214509981924084416777889458865269747634632549732810562486889213808567_<70>

Number: 42223_151 N=1560517825037738459854438489255803864062404112623963858125778119538120217593954522496759798220909008287552424483930190183364432527251 ( 133 digits) SNFS difficulty: 153 digits. Divisors found: r1=485460562826957331754454944330962706119706627186220853762299653 r2=3214509981924084416777889458865269747634632549732810562486889213808567 Version: Total time: 22.29 hours. Scaled time: 43.45 units (timescale=1.949). Factorization parameters were as follows: name: 42223_151 n: 1560517825037738459854438489255803864062404112623963858125778119538120217593954522496759798220909008287552424483930190183364432527251 m: 2000000000000000000000000000000 deg: 5 c5: 95 c0: 56 skew: 0.90 type: snfs lss: 1 rlim: 2500000 alim: 2500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1250000, 2050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 438175 x 438423 Total sieving time: 22.29 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 22.29 hours. --------- CPU info (if available) ----------
Dec 19, 2008: By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39
(38·10¹⁶²+7)/9 = 4(2)₁₆₁3_<163> = 22666112659648690795351599407939_<32> · C132
C132 = P34 · P98
P34 = 5160396681170916091071232604105399_<34>
P98 = 36097818491499062140649356899516517790791368456473008648453082759802006328144553713905393610559843_<98>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1554662117 Step 1 took 9808ms Step 2 took 5990ms ********** Factor found in step 2: 5160396681170916091071232604105399 Found probable prime factor of 34 digits: 5160396681170916091071232604105399 Probable prime cofactor 36097818491499062140649356899516517790791368456473008648453082759802006328144553713905393610559843 has 98 digits
(38·10¹⁹¹-11)/9 = 4(2)₁₉₀1_<192> = 41 · 2687 · 774334507 · 375832150285823251963801943606447_<33> · C146
C146 = P39 · P107
P39 = 956276603516830937978406238709621853569_<39>
P107 = 13771571192961589841833862853688482747346196734485423041265570383728431701766189556898870971868907507954463_<107>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2975364834 Step 1 took 11760ms Step 2 took 6495ms ********** Factor found in step 2: 956276603516830937978406238709621853569 Found probable prime factor of 39 digits: 956276603516830937978406238709621853569 Probable prime cofactor 13771571192961589841833862853688482747346196734485423041265570383728431701766189556898870971868907507954463 has 107 digits
(38·10¹⁵⁷+7)/9 = 4(2)₁₅₆3_<158> = 17 · 937 · C154
C154 = P48 · P107
P48 = 174202237292790959315768467382894756765173949951_<48>
P107 = 15215942083033820802184377816467863773879005591771502744651031164528244378458407456255021493967981424428537_<107>

SNFS difficulty: 159 digits. Divisors found: r1=174202237292790959315768467382894756765173949951 (pp48) r2=15215942083033820802184377816467863773879005591771502744651031164528244378458407456255021493967981424428537 (pp107) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.293). Factorization parameters were as follows: n: 2650651153382021609782297835534071330417617064613109562572805714245854869873954562258912814503247047662892976471983314848529237379761580904151059214151687 m: 20000000000000000000000000000000 deg: 5 c5: 475 c0: 28 skew: 0.57 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [1550000, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 616516 x 616764 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,52,52,2.4,2.4,100000 total time: 20.00 hours.
Dec 18, 2008 (9th): By Jo Yeong Uk / GGNFS
(35·10¹⁸⁹+1)/9 = 3(8)₁₈₈9_<190> = C190
C190 = P56 · P135
P56 = 20293470058904574878183102843477356409653799265487560509_<56>
P135 = 191632524038562972599764005358059709580489479276799676408280772785787623231363395916154199246135197563472355670762941811936146063579821_<135>

Number: 38889_189 N=3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 ( 190 digits) SNFS difficulty: 190 digits. Divisors found: r1=20293470058904574878183102843477356409653799265487560509 (pp56) r2=191632524038562972599764005358059709580489479276799676408280772785787623231363395916154199246135197563472355670762941811936146063579821 (pp135) Version: GGNFS-0.77.1-20050930-nocona Total time: 242.97 hours. Scaled time: 568.30 units (timescale=2.339). Factorization parameters were as follows: n: 3888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 m: 100000000000000000000000000000000000000 deg: 5 c5: 7 c0: 2 skew: 0.78 type: snfs lss: 1 rlim: 11000000 alim: 11000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor 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, 9600001) Primes: RFBsize:726517, AFBsize:725838, largePrimes:19522578 encountered Relations: rels:20498731, finalFF:1670579 Max relations in full relation-set: 28 Initial matrix: 1452420 x 1670579 with sparse part having weight 185962661. Pruned matrix : 1271563 x 1278889 with weight 148415716. Total sieving time: 220.23 hours. Total relation processing time: 0.43 hours. Matrix solve time: 22.12 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,11000000,11000000,28,28,54,54,2.5,2.5,100000 total time: 242.97 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 18, 2008 (8th): By Sinkiti Sibata / Msieve
(38·10¹⁰⁴+7)/9 = 4(2)₁₀₃3_<105> = 3 · 61 · 236169149 · C94
C94 = P41 · P54
P41 = 43086254634327649365606923085903856891003_<41>
P54 = 226739972183122477267800170574550311949755005078106823_<54>

Thu Dec 18 13:46:28 2008 Msieve v. 1.39 Thu Dec 18 13:46:28 2008 random seeds: a062d230 7342cb8e Thu Dec 18 13:46:28 2008 factoring 9769376177262383140812846225412865846706679693162836475583025059828022012012145065217901613469 (94 digits) Thu Dec 18 13:46:29 2008 searching for 15-digit factors Thu Dec 18 13:46:31 2008 commencing quadratic sieve (94-digit input) Thu Dec 18 13:46:31 2008 using multiplier of 1 Thu Dec 18 13:46:31 2008 using 32kb Intel Core sieve core Thu Dec 18 13:46:31 2008 sieve interval: 36 blocks of size 32768 Thu Dec 18 13:46:31 2008 processing polynomials in batches of 6 Thu Dec 18 13:46:31 2008 using a sieve bound of 2090227 (77647 primes) Thu Dec 18 13:46:31 2008 using large prime bound of 296812234 (28 bits) Thu Dec 18 13:46:31 2008 using double large prime bound of 1780193407171906 (42-51 bits) Thu Dec 18 13:46:31 2008 using trial factoring cutoff of 51 bits Thu Dec 18 13:46:31 2008 polynomial 'A' values have 12 factors Thu Dec 18 14:13:12 2008 2642 relations (2371 full + 271 combined from 141243 partial), need 77743 Thu Dec 18 14:13:12 2008 elapsed time 00:26:44 Thu Dec 18 14:32:42 2008 Thu Dec 18 14:32:42 2008 Thu Dec 18 14:32:42 2008 Msieve v. 1.39 Thu Dec 18 14:32:42 2008 random seeds: fba8aee8 1a77b463 Thu Dec 18 14:32:42 2008 factoring 9769376177262383140812846225412865846706679693162836475583025059828022012012145065217901613469 (94 digits) Thu Dec 18 14:32:43 2008 searching for 15-digit factors Thu Dec 18 14:32:44 2008 commencing quadratic sieve (94-digit input) Thu Dec 18 14:32:44 2008 using multiplier of 1 Thu Dec 18 14:32:44 2008 using 32kb Intel Core sieve core Thu Dec 18 14:32:44 2008 sieve interval: 36 blocks of size 32768 Thu Dec 18 14:32:44 2008 processing polynomials in batches of 6 Thu Dec 18 14:32:44 2008 using a sieve bound of 2090227 (77647 primes) Thu Dec 18 14:32:44 2008 using large prime bound of 296812234 (28 bits) Thu Dec 18 14:32:44 2008 using double large prime bound of 1780193407171906 (42-51 bits) Thu Dec 18 14:32:44 2008 using trial factoring cutoff of 51 bits Thu Dec 18 14:32:44 2008 polynomial 'A' values have 12 factors Thu Dec 18 14:32:45 2008 restarting with 2371 full and 141243 partial relations Thu Dec 18 17:41:26 2008 77942 relations (18849 full + 59093 combined from 1146357 partial), need 77743 Thu Dec 18 17:41:27 2008 begin with 1165206 relations Thu Dec 18 17:41:29 2008 reduce to 204517 relations in 12 passes Thu Dec 18 17:41:29 2008 attempting to read 204517 relations Thu Dec 18 17:41:32 2008 recovered 204517 relations Thu Dec 18 17:41:32 2008 recovered 188574 polynomials Thu Dec 18 17:41:32 2008 attempting to build 77942 cycles Thu Dec 18 17:41:32 2008 found 77942 cycles in 5 passes Thu Dec 18 17:41:32 2008 distribution of cycle lengths: Thu Dec 18 17:41:32 2008 length 1 : 18849 Thu Dec 18 17:41:32 2008 length 2 : 13493 Thu Dec 18 17:41:32 2008 length 3 : 13130 Thu Dec 18 17:41:32 2008 length 4 : 10465 Thu Dec 18 17:41:32 2008 length 5 : 7976 Thu Dec 18 17:41:32 2008 length 6 : 5543 Thu Dec 18 17:41:32 2008 length 7 : 3515 Thu Dec 18 17:41:32 2008 length 9+: 4971 Thu Dec 18 17:41:32 2008 largest cycle: 19 relations Thu Dec 18 17:41:32 2008 matrix is 77647 x 77942 (20.2 MB) with weight 4982155 (63.92/col) Thu Dec 18 17:41:32 2008 sparse part has weight 4982155 (63.92/col) Thu Dec 18 17:41:34 2008 filtering completed in 3 passes Thu Dec 18 17:41:34 2008 matrix is 74265 x 74329 (19.3 MB) with weight 4766944 (64.13/col) Thu Dec 18 17:41:34 2008 sparse part has weight 4766944 (64.13/col) Thu Dec 18 17:41:34 2008 saving the first 48 matrix rows for later Thu Dec 18 17:41:34 2008 matrix is 74217 x 74329 (12.1 MB) with weight 3736169 (50.27/col) Thu Dec 18 17:41:34 2008 sparse part has weight 2737005 (36.82/col) Thu Dec 18 17:41:34 2008 matrix includes 64 packed rows Thu Dec 18 17:41:34 2008 using block size 29731 for processor cache size 1024 kB Thu Dec 18 17:41:34 2008 commencing Lanczos iteration Thu Dec 18 17:41:34 2008 memory use: 11.8 MB Thu Dec 18 17:42:10 2008 lanczos halted after 1175 iterations (dim = 74213) Thu Dec 18 17:42:10 2008 recovered 15 nontrivial dependencies Thu Dec 18 17:42:11 2008 prp41 factor: 43086254634327649365606923085903856891003 Thu Dec 18 17:42:11 2008 prp54 factor: 226739972183122477267800170574550311949755005078106823 Thu Dec 18 17:42:11 2008 elapsed time 03:09:29
(38·10¹⁷⁶+7)/9 = 4(2)₁₇₅3_<177> = 3 · 29 · 54540943 · 4287368772178003_<16> · 8965485210842005636106031659_<28> · 2471951484413682939511067832881908139_<37> · C87
C87 = P43 · P45
P43 = 4366496618391640554655712516621488728265579_<43>
P45 = 214467496461094603037698726459970575067475919_<45>

Thu Dec 18 17:51:17 2008 Msieve v. 1.39 Thu Dec 18 17:51:17 2008 random seeds: 480a71e4 42ef3d6d Thu Dec 18 17:51:17 2008 factoring 936471598052290722011809167208477610429304981302335238497256676307528852425786219092101 (87 digits) Thu Dec 18 17:51:18 2008 searching for 15-digit factors Thu Dec 18 17:51:20 2008 commencing quadratic sieve (87-digit input) Thu Dec 18 17:51:20 2008 using multiplier of 1 Thu Dec 18 17:51:20 2008 using 32kb Intel Core sieve core Thu Dec 18 17:51:20 2008 sieve interval: 22 blocks of size 32768 Thu Dec 18 17:51:20 2008 processing polynomials in batches of 10 Thu Dec 18 17:51:20 2008 using a sieve bound of 1493299 (57000 primes) Thu Dec 18 17:51:20 2008 using large prime bound of 119463920 (26 bits) Thu Dec 18 17:51:20 2008 using double large prime bound of 345960105556960 (42-49 bits) Thu Dec 18 17:51:20 2008 using trial factoring cutoff of 49 bits Thu Dec 18 17:51:20 2008 polynomial 'A' values have 11 factors Thu Dec 18 18:41:03 2008 57227 relations (15776 full + 41451 combined from 604798 partial), need 57096 Thu Dec 18 18:41:04 2008 begin with 620574 relations Thu Dec 18 18:41:05 2008 reduce to 138470 relations in 12 passes Thu Dec 18 18:41:05 2008 attempting to read 138470 relations Thu Dec 18 18:41:06 2008 recovered 138470 relations Thu Dec 18 18:41:06 2008 recovered 117589 polynomials Thu Dec 18 18:41:07 2008 attempting to build 57227 cycles Thu Dec 18 18:41:07 2008 found 57227 cycles in 5 passes Thu Dec 18 18:41:07 2008 distribution of cycle lengths: Thu Dec 18 18:41:07 2008 length 1 : 15776 Thu Dec 18 18:41:07 2008 length 2 : 11054 Thu Dec 18 18:41:07 2008 length 3 : 9940 Thu Dec 18 18:41:07 2008 length 4 : 7535 Thu Dec 18 18:41:07 2008 length 5 : 5176 Thu Dec 18 18:41:07 2008 length 6 : 3384 Thu Dec 18 18:41:07 2008 length 7 : 2077 Thu Dec 18 18:41:07 2008 length 9+: 2285 Thu Dec 18 18:41:07 2008 largest cycle: 18 relations Thu Dec 18 18:41:07 2008 matrix is 57000 x 57227 (13.2 MB) with weight 3225637 (56.37/col) Thu Dec 18 18:41:07 2008 sparse part has weight 3225637 (56.37/col) Thu Dec 18 18:41:08 2008 filtering completed in 4 passes Thu Dec 18 18:41:08 2008 matrix is 52801 x 52864 (12.3 MB) with weight 3004794 (56.84/col) Thu Dec 18 18:41:08 2008 sparse part has weight 3004794 (56.84/col) Thu Dec 18 18:41:08 2008 saving the first 48 matrix rows for later Thu Dec 18 18:41:08 2008 matrix is 52753 x 52864 (7.8 MB) with weight 2373010 (44.89/col) Thu Dec 18 18:41:08 2008 sparse part has weight 1740382 (32.92/col) Thu Dec 18 18:41:08 2008 matrix includes 64 packed rows Thu Dec 18 18:41:08 2008 using block size 21145 for processor cache size 1024 kB Thu Dec 18 18:41:08 2008 commencing Lanczos iteration Thu Dec 18 18:41:08 2008 memory use: 7.7 MB Thu Dec 18 18:41:24 2008 lanczos halted after 835 iterations (dim = 52753) Thu Dec 18 18:41:24 2008 recovered 17 nontrivial dependencies Thu Dec 18 18:41:25 2008 prp43 factor: 4366496618391640554655712516621488728265579 Thu Dec 18 18:41:25 2008 prp45 factor: 214467496461094603037698726459970575067475919 Thu Dec 18 18:41:25 2008 elapsed time 00:50:08
(38·10¹³⁰+7)/9 = 4(2)₁₂₉3_<131> = C131
C131 = P33 · P98
P33 = 678551793747462240865698141675319_<33>
P98 = 62224022707301452482853572488992317799268371175008642178618762222983732884341974062619005483162217_<98>

Number: 42223_130 N=42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 ( 131 digits) SNFS difficulty: 131 digits. Divisors found: r1=678551793747462240865698141675319 (prp33) r2=62224022707301452482853572488992317799268371175008642178618762222983732884341974062619005483162217 (prp98) Version: Total time: 3.60 hours. Scaled time: 7.17 units (timescale=1.991). Factorization parameters were as follows: name: 42223_130 n: 42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 m: 100000000000000000000000000 deg: 5 c5: 38 c0: 7 skew: 0.71 type: snfs lss: 1 rlim: 1090000 alim: 1090000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1090000/1090000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [545000, 945001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 154826 x 155074 Total sieving time: 3.60 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,131,5,0,0,0,0,0,0,0,0,1090000,1090000,26,26,47,47,2.3,2.3,50000 total time: 3.60 hours. --------- CPU info (if available) ----------
(38·10¹⁵⁵+7)/9 = 4(2)₁₅₄3_<156> = 3⁴ · 21247 · 405706541 · 8153054611907549_<16> · 3631636673976858283592464277485606931_<37> · C89
C89 = P34 · P56
P34 = 1420456107051505106563089043040989_<34>
P56 = 14377913877137253365446313866748979093357534901514687119_<56>

Thu Dec 18 19:12:15 2008 Msieve v. 1.39 Thu Dec 18 19:12:15 2008 random seeds: 766c50d8 0938bf95 Thu Dec 18 19:12:15 2008 factoring 20423195573440195206551390289801512611298882650218935717368875142211566032360322627320691 (89 digits) Thu Dec 18 19:12:16 2008 searching for 15-digit factors Thu Dec 18 19:12:17 2008 commencing quadratic sieve (89-digit input) Thu Dec 18 19:12:17 2008 using multiplier of 1 Thu Dec 18 19:12:17 2008 using 32kb Intel Core sieve core Thu Dec 18 19:12:17 2008 sieve interval: 30 blocks of size 32768 Thu Dec 18 19:12:17 2008 processing polynomials in batches of 7 Thu Dec 18 19:12:17 2008 using a sieve bound of 1546837 (58348 primes) Thu Dec 18 19:12:17 2008 using large prime bound of 123746960 (26 bits) Thu Dec 18 19:12:17 2008 using double large prime bound of 368605688486800 (42-49 bits) Thu Dec 18 19:12:17 2008 using trial factoring cutoff of 49 bits Thu Dec 18 19:12:17 2008 polynomial 'A' values have 11 factors Thu Dec 18 20:18:08 2008 58635 relations (15460 full + 43175 combined from 627841 partial), need 58444 Thu Dec 18 20:18:09 2008 begin with 643301 relations Thu Dec 18 20:18:09 2008 reduce to 144114 relations in 9 passes Thu Dec 18 20:18:09 2008 attempting to read 144114 relations Thu Dec 18 20:18:11 2008 recovered 144114 relations Thu Dec 18 20:18:11 2008 recovered 123018 polynomials Thu Dec 18 20:18:11 2008 attempting to build 58635 cycles Thu Dec 18 20:18:11 2008 found 58635 cycles in 5 passes Thu Dec 18 20:18:11 2008 distribution of cycle lengths: Thu Dec 18 20:18:11 2008 length 1 : 15460 Thu Dec 18 20:18:11 2008 length 2 : 11059 Thu Dec 18 20:18:11 2008 length 3 : 10232 Thu Dec 18 20:18:11 2008 length 4 : 7813 Thu Dec 18 20:18:12 2008 length 5 : 5624 Thu Dec 18 20:18:12 2008 length 6 : 3705 Thu Dec 18 20:18:12 2008 length 7 : 2187 Thu Dec 18 20:18:12 2008 length 9+: 2555 Thu Dec 18 20:18:12 2008 largest cycle: 18 relations Thu Dec 18 20:18:12 2008 matrix is 58348 x 58635 (14.3 MB) with weight 3505595 (59.79/col) Thu Dec 18 20:18:12 2008 sparse part has weight 3505595 (59.79/col) Thu Dec 18 20:18:13 2008 filtering completed in 3 passes Thu Dec 18 20:18:13 2008 matrix is 54671 x 54735 (13.4 MB) with weight 3293020 (60.16/col) Thu Dec 18 20:18:13 2008 sparse part has weight 3293020 (60.16/col) Thu Dec 18 20:18:13 2008 saving the first 48 matrix rows for later Thu Dec 18 20:18:13 2008 matrix is 54623 x 54735 (9.1 MB) with weight 2631716 (48.08/col) Thu Dec 18 20:18:13 2008 sparse part has weight 2059013 (37.62/col) Thu Dec 18 20:18:13 2008 matrix includes 64 packed rows Thu Dec 18 20:18:13 2008 using block size 21894 for processor cache size 1024 kB Thu Dec 18 20:18:13 2008 commencing Lanczos iteration Thu Dec 18 20:18:13 2008 memory use: 8.6 MB Thu Dec 18 20:18:32 2008 lanczos halted after 865 iterations (dim = 54621) Thu Dec 18 20:18:32 2008 recovered 16 nontrivial dependencies Thu Dec 18 20:18:33 2008 prp34 factor: 1420456107051505106563089043040989 Thu Dec 18 20:18:33 2008 prp56 factor: 14377913877137253365446313866748979093357534901514687119 Thu Dec 18 20:18:33 2008 elapsed time 01:06:18
(38·10¹³⁵+7)/9 = 4(2)₁₃₄3_<136> = 509 · C133
C133 = P38 · P46 · P51
P38 = 15913952422398244721190280306070085331_<38>
P46 = 1442361694262586816326270806420410498472186067_<46>
P51 = 361385788135949331769346686225100381937997477289411_<51>

Number: 42223_135 N=8295132067234228334424798079022047587862912027941497489631084915957214581969002401222440515171359965073128137961143855053481772538747 ( 133 digits) SNFS difficulty: 136 digits. Divisors found: r1=15913952422398244721190280306070085331 (prp38) r2=1442361694262586816326270806420410498472186067 (prp46) r3=361385788135949331769346686225100381937997477289411 (prp51) Version: Total time: 5.58 hours. Scaled time: 11.15 units (timescale=1.997). Factorization parameters were as follows: name: 42223_135 n: 8295132067234228334424798079022047587862912027941497489631084915957214581969002401222440515171359965073128137961143855053481772538747 m: 1000000000000000000000000000 deg: 5 c5: 38 c0: 7 skew: 0.71 type: snfs lss: 1 rlim: 1320000 alim: 1320000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1320000/1320000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [660000, 1260001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 183860 x 184108 Total sieving time: 5.58 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000 total time: 5.58 hours. --------- CPU info (if available) ----------
Dec 18, 2008 (7th): By Serge Batalov / GMP-ECM 6.2.1
(38·10¹⁴²+7)/9 = 4(2)₁₄₁3_<143> = 59 · 5563 · 605464278196827737125597251068803_<33> · C105
C105 = P36 · P70
P36 = 108086691733104157882816618677785281_<36>
P70 = 1965709180424130529255869068846906640336734489270747363351530402366733_<70>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=519687493 Step 1 took 8384ms Step 2 took 5062ms ********** Factor found in step 2: 108086691733104157882816618677785281 Found probable prime factor of 36 digits: 108086691733104157882816618677785281 Probable prime cofactor 1965709180424130529255869068846906640336734489270747363351530402366733 has 70 digits
Dec 18, 2008 (6th): By Serge Batalov / PFGW
(8·10⁵³⁴¹¹+1)/9 = (8)₅₃₄₁₀9_<53411> is PRP.
Dec 18, 2008 (5th): By Tyler Cadigan / GGNFS, Msieve
(43·10¹⁸⁵-7)/9 = 4(7)₁₈₅_<186> = 3 · 29 · 47 · 58170373640018484872008409_<26> · C157
C157 = P75 · P82
P75 = 711289181722006572964993391864934683586891620256502264874981119795063837321_<75>
P82 = 2823974552229371081708878262515141661878349230272684194999664683868033689289786137_<82>

Number: 47777_185 N=2008662548458999269449272053889738154785837004738744490237883895960497711975400967535628915609095715969831195102711489927429245865192787596589288254649018977 ( 157 digits) SNFS difficulty: 186 digits. Divisors found: r1=711289181722006572964993391864934683586891620256502264874981119795063837321 r2=2823974552229371081708878262515141661878349230272684194999664683868033689289786137 Version: Total time: 284.19 hours. Scaled time: 728.96 units (timescale=2.565). Factorization parameters were as follows: n: 2008662548458999269449272053889738154785837004738744490237883895960497711975400967535628915609095715969831195102711489927429245865192787596589288254649018977 m: 10000000000000000000000000000000000000 deg: 5 c5: 43 c0: -7 skew: 0.70 type: snfs lss: 1 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Y0: 10000000000000000000000000000000000000 Y1: -1 qintsize: 1000000Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4500000, 8500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1277651 x 1277899 Total sieving time: 284.19 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,54,54,2.5,2.5,100000 total time: 284.19 hours. --------- CPU info (if available) ----------
Dec 18, 2008 (4th): By Robert Backstrom / GGNFS
(38·10¹⁰⁸+7)/9 = 4(2)₁₀₇3_<109> = 41 · 499 · C105
C105 = P47 · P59
P47 = 10295641543941343571168747279625193234146247799_<47>
P59 = 20044871255305051171624283732903041074399663885329714243003_<59>

Number: n N=206374809239074354671402425447100162384389374955873807235066338639338297190587136332285166539040139900397 ( 105 digits) SNFS difficulty: 109 digits. Divisors found: r1=10295641543941343571168747279625193234146247799 (pp47) r2=20044871255305051171624283732903041074399663885329714243003 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.93 hours. Scaled time: 1.70 units (timescale=1.823). Factorization parameters were as follows: name: KA_4_2_107_3 n: 206374809239074354671402425447100162384389374955873807235066338639338297190587136332285166539040139900397 type: snfs skew: 0.36 deg: 5 c5: 2375 c0: 14 m: 2000000000000000000000 rlim: 450000 alim: 450000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [225000, 305001) Primes: RFBsize:37706, AFBsize:38049, largePrimes:4928369 encountered Relations: rels:4458518, finalFF:266912 Max relations in full relation-set: 48 Initial matrix: 75821 x 266912 with sparse part having weight 35358891. Pruned matrix : 56879 x 57322 with weight 4347894. Total sieving time: 0.83 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.01 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000 total time: 0.93 hours. --------- CPU info (if available) ----------
(38·10¹¹⁶+7)/9 = 4(2)₁₁₅3_<117> = 3 · 352637 · C111
C111 = P43 · P68
P43 = 5573083583773648271800694651315923853073163_<43>
P68 = 71613747018533179366658876906680060578395225670235050033207926163611_<68>

Number: n N=399109397881506310287181267821416189284563845372835921190177833695104996755135566434437511494088087015091271593 ( 111 digits) SNFS difficulty: 117 digits. Divisors found: r1=5573083583773648271800694651315923853073163 (pp43) r2=71613747018533179366658876906680060578395225670235050033207926163611 (pp68) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.18 hours. Scaled time: 2.15 units (timescale=1.822). Factorization parameters were as follows: name: KA_4_2_115_3 n: 399109397881506310287181267821416189284563845372835921190177833695104996755135566434437511494088087015091271593 type: snfs skew: 0.45 deg: 5 c5: 380 c0: 7 m: 100000000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [250000, 370001) Primes: RFBsize:41538, AFBsize:41837, largePrimes:5004377 encountered Relations: rels:4345290, finalFF:125163 Max relations in full relation-set: 48 Initial matrix: 83442 x 125163 with sparse part having weight 17533216. Pruned matrix : 76901 x 77382 with weight 7526306. Total sieving time: 1.04 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.03 hours. Total square root time: 0.04 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000 total time: 1.18 hours. --------- CPU info (if available) ----------
Dec 18, 2008 (3rd): By Sinkiti Sibata / GGNFS, Msieve
(37·10¹⁵³+53)/9 = 4(1)₁₅₂7_<154> = 29 · 167 · 2259934847_<10> · 699672253367_<12> · C129
C129 = P34 · P95
P34 = 8719756215598888403735903369151727_<34>
P95 = 61567260829717922876129222772484051350518977065235325715293890266317345837386780159662510836353_<95>

Number: 41117_153 N=536851505297330833256720241859282105348047475598159487710492234018066473949983864532710775744234875425075826135015294154924331631 ( 129 digits) SNFS difficulty: 155 digits. Divisors found: r1=8719756215598888403735903369151727 (pp34) r2=61567260829717922876129222772484051350518977065235325715293890266317345837386780159662510836353 (pp95) Version: GGNFS-0.77.1-20060513-k8 Total time: 38.61 hours. Scaled time: 75.95 units (timescale=1.967). Factorization parameters were as follows: name: 41117_153 n: 536851505297330833256720241859282105348047475598159487710492234018066473949983864532710775744234875425075826135015294154924331631 m: 5000000000000000000000000000000 deg: 5 c5: 296 c0: 1325 skew: 1.35 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: RFBsize:203362, AFBsize:203817, largePrimes:8308051 encountered Relations: rels:8752937, finalFF:805926 Max relations in full relation-set: 28 Initial matrix: 407246 x 805926 with sparse part having weight 93645918. Pruned matrix : 300178 x 302278 with weight 40667714. Total sieving time: 36.68 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.51 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 38.61 hours. --------- CPU info (if available) ----------
(38·10¹⁵¹-11)/9 = 4(2)₁₅₀1_<152> = 41 · 53 · 26021 · 2914313 · C138
C138 = P46 · P92
P46 = 3159193923314794886124358434419958776363525831_<46>
P92 = 81104490278796803941574903528473981354882683238348933245451788515578216046199936350435152579_<92>

Number: 42221_151 N=256224812842318717545533857825918618214117908238051230838133636289935308342853369546321111379845635992526213941974521284389129356892768149 ( 138 digits) SNFS difficulty: 153 digits. Divisors found: r1=3159193923314794886124358434419958776363525831 (prp46) r2=81104490278796803941574903528473981354882683238348933245451788515578216046199936350435152579 (prp92) Version: Total time: 15.14 hours. Scaled time: 38.51 units (timescale=2.544). Factorization parameters were as follows: name: 42221_151 n: 256224812842318717545533857825918618214117908238051230838133636289935308342853369546321111379845635992526213941974521284389129356892768149 m: 2000000000000000000000000000000 deg: 5 c5: 95 c0: -88 skew: 0.98 type: snfs lss: 1 rlim: 2500000 alim: 2500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1250000, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 458616 x 458864 Total sieving time: 15.14 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 15.14 hours. --------- CPU info (if available) ----------
(38·10¹⁴¹+7)/9 = 4(2)₁₄₀3_<142> = 17 · 10799 · 14431 · 10551421125799_<14> · 3918960185104132736939080334753_<31> · C89
C89 = P37 · P53
P37 = 1208319630248751570624525558000988741_<37>
P53 = 31896906018545036923695174984522863360635051803331813_<53>

Thu Dec 18 08:07:13 2008 Msieve v. 1.39 Thu Dec 18 08:07:13 2008 random seeds: ba6ae35c e186a9eb Thu Dec 18 08:07:13 2008 factoring 38541657686407517624151652150298002272942905139355928279567042796973174434731732100117433 (89 digits) Thu Dec 18 08:07:14 2008 searching for 15-digit factors Thu Dec 18 08:07:16 2008 commencing quadratic sieve (89-digit input) Thu Dec 18 08:07:16 2008 using multiplier of 1 Thu Dec 18 08:07:16 2008 using 32kb Intel Core sieve core Thu Dec 18 08:07:16 2008 sieve interval: 32 blocks of size 32768 Thu Dec 18 08:07:16 2008 processing polynomials in batches of 7 Thu Dec 18 08:07:16 2008 using a sieve bound of 1556189 (58802 primes) Thu Dec 18 08:07:16 2008 using large prime bound of 124495120 (26 bits) Thu Dec 18 08:07:16 2008 using double large prime bound of 372626841652480 (42-49 bits) Thu Dec 18 08:07:16 2008 using trial factoring cutoff of 49 bits Thu Dec 18 08:07:16 2008 polynomial 'A' values have 11 factors Thu Dec 18 09:14:07 2008 59134 relations (15874 full + 43260 combined from 629696 partial), need 58898 Thu Dec 18 09:14:08 2008 begin with 645570 relations Thu Dec 18 09:14:08 2008 reduce to 144306 relations in 11 passes Thu Dec 18 09:14:08 2008 attempting to read 144306 relations Thu Dec 18 09:14:10 2008 recovered 144306 relations Thu Dec 18 09:14:10 2008 recovered 122188 polynomials Thu Dec 18 09:14:10 2008 attempting to build 59134 cycles Thu Dec 18 09:14:10 2008 found 59134 cycles in 5 passes Thu Dec 18 09:14:10 2008 distribution of cycle lengths: Thu Dec 18 09:14:10 2008 length 1 : 15874 Thu Dec 18 09:14:10 2008 length 2 : 11011 Thu Dec 18 09:14:10 2008 length 3 : 10357 Thu Dec 18 09:14:10 2008 length 4 : 8156 Thu Dec 18 09:14:10 2008 length 5 : 5506 Thu Dec 18 09:14:10 2008 length 6 : 3538 Thu Dec 18 09:14:10 2008 length 7 : 2140 Thu Dec 18 09:14:10 2008 length 9+: 2552 Thu Dec 18 09:14:10 2008 largest cycle: 17 relations Thu Dec 18 09:14:11 2008 matrix is 58802 x 59134 (14.2 MB) with weight 3496057 (59.12/col) Thu Dec 18 09:14:11 2008 sparse part has weight 3496057 (59.12/col) Thu Dec 18 09:14:12 2008 filtering completed in 3 passes Thu Dec 18 09:14:12 2008 matrix is 54893 x 54957 (13.3 MB) with weight 3263166 (59.38/col) Thu Dec 18 09:14:12 2008 sparse part has weight 3263166 (59.38/col) Thu Dec 18 09:14:12 2008 saving the first 48 matrix rows for later Thu Dec 18 09:14:12 2008 matrix is 54845 x 54957 (9.1 MB) with weight 2632975 (47.91/col) Thu Dec 18 09:14:12 2008 sparse part has weight 2067716 (37.62/col) Thu Dec 18 09:14:12 2008 matrix includes 64 packed rows Thu Dec 18 09:14:12 2008 using block size 21982 for processor cache size 1024 kB Thu Dec 18 09:14:12 2008 commencing Lanczos iteration Thu Dec 18 09:14:12 2008 memory use: 8.6 MB Thu Dec 18 09:14:31 2008 lanczos halted after 869 iterations (dim = 54843) Thu Dec 18 09:14:31 2008 recovered 16 nontrivial dependencies Thu Dec 18 09:14:32 2008 prp37 factor: 1208319630248751570624525558000988741 Thu Dec 18 09:14:32 2008 prp53 factor: 31896906018545036923695174984522863360635051803331813 Thu Dec 18 09:14:32 2008 elapsed time 01:07:19
(38·10¹¹²+7)/9 = 4(2)₁₁₁3_<113> = 11677705261_<11> · C103
C103 = P46 · P58
P46 = 1945013057622469055928792403006550216266423129_<46>
P58 = 1858921524805644843829335015271915581157210985408240421667_<58>

Number: 42223_112 N=3615626638842449735144263478960074279461832207842552622738456544970528368794580610388486685596801536043 ( 103 digits) SNFS difficulty: 114 digits. Divisors found: r1=1945013057622469055928792403006550216266423129 (prp46) r2=1858921524805644843829335015271915581157210985408240421667 (prp58) Version: Total time: 1.45 hours. Scaled time: 2.90 units (timescale=2.003). Factorization parameters were as follows: name: 42223_112 n: 3615626638842449735144263478960074279461832207842552622738456544970528368794580610388486685596801536043 m: 20000000000000000000000 deg: 5 c5: 475 c0: 28 skew: 0.57 type: snfs lss: 1 rlim: 560000 alim: 560000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 560000/560000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [280000, 480001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 60412 x 60652 Total sieving time: 1.45 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,114,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000 total time: 1.45 hours. --------- CPU info (if available) ----------
(38·10¹¹⁵+7)/9 = 4(2)₁₁₄3_<116> = 251 · 15331533874127_<14> · C101
C101 = P34 · P67
P34 = 1634864409020671635063265717434331_<34>
P67 = 6711197497648071834292573110422804102757555587356032161168057878729_<67>

Number: 42223_115 N=10971897930813425274869156495205138122741990801162120520681589565626234907052249695702572980219245299 ( 101 digits) SNFS difficulty: 116 digits. Divisors found: r1=1634864409020671635063265717434331 (prp34) r2=6711197497648071834292573110422804102757555587356032161168057878729 (prp67) Version: Total time: 1.49 hours. Scaled time: 2.96 units (timescale=1.985). Factorization parameters were as follows: name: 42223_115 n: 10971897930813425274869156495205138122741990801162120520681589565626234907052249695702572980219245299 m: 100000000000000000000000 deg: 5 c5: 38 c0: 7 skew: 0.71 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 610000/610000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [305000, 505001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 62313 x 62551 Total sieving time: 1.49 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,610000,610000,25,25,45,45,2.2,2.2,50000 total time: 1.49 hours. --------- CPU info (if available) ----------
(38·10¹²³+7)/9 = 4(2)₁₂₂3_<124> = 41 · 16901347 · C115
C115 = P29 · P34 · P53
P29 = 95138006685886098469807972853_<29>
P34 = 1360440358306411252248900367385263_<34>
P53 = 47076303835257146062311650641289379426604433502131591_<53>

Number: 42223_123 N=6093066417149952780747582444056262558825062765883750556112368024929007747021759924212567087284879117048960830224349 ( 115 digits) SNFS difficulty: 126 digits. Divisors found: r1=95138006685886098469807972853 (prp29) r2=1360440358306411252248900367385263 (prp34) r3=47076303835257146062311650641289379426604433502131591 (prp53) Version: Total time: 1.98 hours. Scaled time: 5.07 units (timescale=2.564). Factorization parameters were as follows: name: 42223_123 n: 6093066417149952780747582444056262558825062765883750556112368024929007747021759924212567087284879117048960830224349 m: 10000000000000000000000000 deg: 5 c5: 19 c0: 350 skew: 1.79 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 745001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 122288 x 122535 Total sieving time: 1.98 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 1.98 hours. --------- CPU info (if available) ----------
(37·10¹⁴⁸+71)/9 = 4(1)₁₄₇9_<149> = 13 · 263 · 54907 · 83365277 · 4787540677386989927_<19> · C114
C114 = P45 · P69
P45 = 624271176245120850697276336102200832129446533_<45>
P69 = 878944475221714294164277298235867536498240189330190166674377210066449_<69>

Number: 42221_148 N=548699701400810060635961055722374030806191032906197312251591427155898046660410692341082608508184132862882522671317 ( 114 digits) SNFS difficulty: 150 digits. Divisors found: r1=624271176245120850697276336102200832129446533 (pp45) r2=878944475221714294164277298235867536498240189330190166674377210066449 (pp69) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 36.14 hours. Scaled time: 17.10 units (timescale=0.473). Factorization parameters were as follows: name: 42221_148 n: 548699701400810060635961055722374030806191032906197312251591427155898046660410692341082608508184132862882522671317 m: 500000000000000000000000000000 deg: 5 c5: 296 c0: 1775 skew: 1.43 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:170002, largePrimes:7101805 encountered Relations: rels:7231912, finalFF:593333 Max relations in full relation-set: 28 Initial matrix: 339580 x 593333 with sparse part having weight 65156158. Pruned matrix : 267308 x 269069 with weight 28342252. Total sieving time: 33.22 hours. Total relation processing time: 0.32 hours. Matrix solve time: 2.48 hours. Time per square root: 0.12 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: 36.14 hours. --------- CPU info (if available) ----------
(38·10¹¹⁷+7)/9 = 4(2)₁₁₆3_<118> = 2657947 · 1142969897_<10> · 95220609140821_<14> · C89
C89 = P41 · P48
P41 = 69563816005530066987621201677220218900731_<41>
P48 = 209819392365296826977778796234537568048688935347_<48>

Thu Dec 18 12:29:54 2008 Msieve v. 1.39 Thu Dec 18 12:29:54 2008 random seeds: 83cedefc 8d8bdba6 Thu Dec 18 12:29:54 2008 factoring 14595837604891628552348108255737179313931799325177429616056819579069705362946879070038657 (89 digits) Thu Dec 18 12:29:55 2008 searching for 15-digit factors Thu Dec 18 12:29:56 2008 commencing quadratic sieve (89-digit input) Thu Dec 18 12:29:56 2008 using multiplier of 73 Thu Dec 18 12:29:56 2008 using 32kb Intel Core sieve core Thu Dec 18 12:29:56 2008 sieve interval: 28 blocks of size 32768 Thu Dec 18 12:29:56 2008 processing polynomials in batches of 8 Thu Dec 18 12:29:56 2008 using a sieve bound of 1537153 (58242 primes) Thu Dec 18 12:29:56 2008 using large prime bound of 122972240 (26 bits) Thu Dec 18 12:29:56 2008 using double large prime bound of 364462296550480 (42-49 bits) Thu Dec 18 12:29:56 2008 using trial factoring cutoff of 49 bits Thu Dec 18 12:29:56 2008 polynomial 'A' values have 12 factors Thu Dec 18 13:23:00 2008 58458 relations (16648 full + 41810 combined from 606551 partial), need 58338 Thu Dec 18 13:23:01 2008 begin with 623199 relations Thu Dec 18 13:23:01 2008 reduce to 137918 relations in 9 passes Thu Dec 18 13:23:01 2008 attempting to read 137918 relations Thu Dec 18 13:23:03 2008 recovered 137918 relations Thu Dec 18 13:23:03 2008 recovered 115182 polynomials Thu Dec 18 13:23:03 2008 attempting to build 58458 cycles Thu Dec 18 13:23:03 2008 found 58458 cycles in 5 passes Thu Dec 18 13:23:03 2008 distribution of cycle lengths: Thu Dec 18 13:23:03 2008 length 1 : 16648 Thu Dec 18 13:23:03 2008 length 2 : 11814 Thu Dec 18 13:23:03 2008 length 3 : 10413 Thu Dec 18 13:23:03 2008 length 4 : 7579 Thu Dec 18 13:23:03 2008 length 5 : 5155 Thu Dec 18 13:23:03 2008 length 6 : 3172 Thu Dec 18 13:23:03 2008 length 7 : 1719 Thu Dec 18 13:23:03 2008 length 9+: 1958 Thu Dec 18 13:23:03 2008 largest cycle: 15 relations Thu Dec 18 13:23:04 2008 matrix is 58242 x 58458 (13.7 MB) with weight 3359561 (57.47/col) Thu Dec 18 13:23:04 2008 sparse part has weight 3359561 (57.47/col) Thu Dec 18 13:23:04 2008 filtering completed in 3 passes Thu Dec 18 13:23:04 2008 matrix is 53596 x 53660 (12.7 MB) with weight 3108809 (57.94/col) Thu Dec 18 13:23:04 2008 sparse part has weight 3108809 (57.94/col) Thu Dec 18 13:23:04 2008 saving the first 48 matrix rows for later Thu Dec 18 13:23:04 2008 matrix is 53548 x 53660 (7.8 MB) with weight 2389963 (44.54/col) Thu Dec 18 13:23:04 2008 sparse part has weight 1717555 (32.01/col) Thu Dec 18 13:23:04 2008 matrix includes 64 packed rows Thu Dec 18 13:23:04 2008 using block size 21464 for processor cache size 1024 kB Thu Dec 18 13:23:05 2008 commencing Lanczos iteration Thu Dec 18 13:23:05 2008 memory use: 7.7 MB Thu Dec 18 13:23:21 2008 lanczos halted after 848 iterations (dim = 53545) Thu Dec 18 13:23:21 2008 recovered 15 nontrivial dependencies Thu Dec 18 13:23:22 2008 prp41 factor: 69563816005530066987621201677220218900731 Thu Dec 18 13:23:22 2008 prp48 factor: 209819392365296826977778796234537568048688935347 Thu Dec 18 13:23:22 2008 elapsed time 00:53:28
(38·10¹¹⁹+7)/9 = 4(2)₁₁₈3_<120> = 3² · C119
C119 = P32 · P88
P32 = 17796655303796507065144186379611_<32>
P88 = 2636089728439345957807003412593302655340134489266022323067968446022844599735148064148277_<88>

Number: 42223_119 N=46913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247 ( 119 digits) SNFS difficulty: 121 digits. Divisors found: r1=17796655303796507065144186379611 (prp32) r2=2636089728439345957807003412593302655340134489266022323067968446022844599735148064148277 (prp88) Version: Total time: 1.91 hours. Scaled time: 3.77 units (timescale=1.978). Factorization parameters were as follows: name: 42223_119 n: 46913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580246913580247 m: 1000000000000000000000000 deg: 5 c5: 19 c0: 35 skew: 1.13 type: snfs lss: 1 rlim: 740000 alim: 740000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [370000, 620001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 81734 x 81967 Total sieving time: 1.91 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,46,46,2.2,2.2,50000 total time: 1.91 hours. --------- CPU info (if available) ----------
(37·10¹⁵³+71)/9 = 4(1)₁₅₂9_<154> = 3 · 47 · 42829 · 3356641 · C141
C141 = P36 · P48 · P58
P36 = 267585967846317503969097730621906439_<36>
P48 = 169083349998879656324913041735201585866792484537_<48>
P58 = 4482632066041583145692570283513003585998276879951383228217_<58>

Number: 41119_153 N=202813692784995100304654547000616001388351317469991900616989696292083774391262123814153905948868605435039400406739699971898527486293769126231 ( 141 digits) SNFS difficulty: 155 digits. Divisors found: r1=267585967846317503969097730621906439 (prp36) r2=169083349998879656324913041735201585866792484537 (prp48) r3=4482632066041583145692570283513003585998276879951383228217 (prp58) Version: Total time: 23.52 hours. Scaled time: 60.31 units (timescale=2.564). Factorization parameters were as follows: name: 41119_152 n: 202813692784995100304654547000616001388351317469991900616989696292083774391262123814153905948868605435039400406739699971898527486293769126231 m: 5000000000000000000000000000000 deg: 5 c5: 296 c0: 1775 skew: 1.43 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: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 481081 x 481329 Total sieving time: 23.52 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 23.52 hours. --------- CPU info (if available) ----------
(38·10¹²⁵+7)/9 = 4(2)₁₂₄3_<126> = 3 · 17 · 1901 · 32672306313541_<14> · C108
C108 = P45 · P64
P45 = 116295998349478982853156680832900513953293021_<45>
P64 = 1146157315974285019595546328596583393702116364957884428638802393_<64>

Number: 42223_125 N=133293509326788711666710854874444178050766096891403697830905172109269902185821542440145829581270460044999253 ( 108 digits) SNFS difficulty: 126 digits. Divisors found: r1=116295998349478982853156680832900513953293021 (prp45) r2=1146157315974285019595546328596583393702116364957884428638802393 (prp64) Version: Total time: 2.03 hours. Scaled time: 5.24 units (timescale=2.575). Factorization parameters were as follows: name: 42223_125 n: 133293509326788711666710854874444178050766096891403697830905172109269902185821542440145829581270460044999253 m: 10000000000000000000000000 deg: 5 c5: 38 c0: 7 skew: 0.71 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 112736 x 112984 Total sieving time: 2.03 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.03 hours. --------- CPU info (if available) ----------
(38·10¹²⁴+7)/9 = 4(2)₁₂₃3_<125> = 7529 · C121
C121 = P49 · P73
P49 = 2711151477562038629795543684920467598635043008193_<49>
P73 = 2068473716730609939247632473759947310004060663074300121852699702217549559_<73>

Number: 42223_124 N=5607945573412434881421466625344962441522409645666386269387996044922595593335399418544590546184383347353197266864420536887 ( 121 digits) SNFS difficulty: 126 digits. Divisors found: r1=2711151477562038629795543684920467598635043008193 (prp49) r2=2068473716730609939247632473759947310004060663074300121852699702217549559 (prp73) Version: Total time: 2.63 hours. Scaled time: 5.29 units (timescale=2.010). Factorization parameters were as follows: name: 42223_124 n: 5607945573412434881421466625344962441522409645666386269387996044922595593335399418544590546184383347353197266864420536887 m: 10000000000000000000000000 deg: 5 c5: 19 c0: 35 skew: 1.13 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [445000, 745001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 113109 x 113351 Total sieving time: 2.63 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,46,46,2.3,2.3,50000 total time: 2.63 hours. --------- CPU info (if available) ----------
Dec 18, 2008 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39
(38·10¹⁰³+7)/9 = 4(2)₁₀₂3_<104> = 41 · 163 · 4120903 · C94
C94 = P35 · P60
P35 = 15228969283328568516002938499690549_<35>
P60 = 100671542589360374820010743674518363883167127317682185376623_<60>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2296685655 Step 1 took 1812ms Step 2 took 1504ms ********** Factor found in step 2: 15228969283328568516002938499690549 Found probable prime factor of 35 digits: 15228969283328568516002938499690549 Probable prime cofactor 100671542589360374820010743674518363883167127317682185376623 has 60 digits
(38·10¹⁴³+7)/9 = 4(2)₁₄₂3_<144> = 3 · 41³ · 54667 · 84584933 · 2220749942527_<13> · C114
C114 = P28 · P86
P28 = 4866734418829920193805385751_<28>
P86 = 40861349391788987053960663317374360811603887138536668614277435169890368201323389007843_<86>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3725277577 Step 1 took 2220ms Step 2 took 1784ms ********** Factor found in step 2: 4866734418829920193805385751 Found probable prime factor of 28 digits: 4866734418829920193805385751 Probable prime cofactor 40861349391788987053960663317374360811603887138536668614277435169890368201323389007843 has 86 digits
(38·10¹³⁴+7)/9 = 4(2)₁₃₃3_<135> = 3 · 274355461 · 7475083489_<10> · C116
C116 = P29 · P88
P29 = 13297128789458489611981711367_<29>
P88 = 5160981478476877174528191139543584005394929170028975707947883782299690148268479826942487_<88>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2193296238 Step 1 took 3614ms Step 2 took 2463ms ********** Factor found in step 2: 13297128789458489611981711367 Found probable prime factor of 29 digits: 13297128789458489611981711367 Probable prime cofactor 5160981478476877174528191139543584005394929170028975707947883782299690148268479826942487 has 88 digits
(38·10¹⁷⁶+7)/9 = 4(2)₁₇₅3_<177> = 3 · 29 · 54540943 · 4287368772178003_<16> · 8965485210842005636106031659_<28> · C124
C124 = P37 · C87
P37 = 2471951484413682939511067832881908139_<37>
C87 = [936471598052290722011809167208477610429304981302335238497256676307528852425786219092101_<87>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1864500341 Step 1 took 3285ms Step 2 took 2524ms ********** Factor found in step 2: 2471951484413682939511067832881908139 Found probable prime factor of 37 digits: 2471951484413682939511067832881908139 Composite cofactor has 87 digits
(38·10¹⁸⁸+7)/9 = 4(2)₁₈₇3_<189> = 3 · 41 · 161837827 · C179
C179 = P34 · C145
P34 = 4517407346651943696614538983948377_<34>
C145 = [4695336080119231002572034438003134103984773018851208689382346363956946707607387905336610628296559396105847033548036718431918869359857064027844119_<145>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2813434907 Step 1 took 5311ms Step 2 took 3484ms ********** Factor found in step 2: 4517407346651943696614538983948377 Found probable prime factor of 34 digits: 4517407346651943696614538983948377
(38·10¹⁶²+7)/9 = 4(2)₁₆₁3_<163> = C163
C163 = P32 · C132
P32 = 22666112659648690795351599407939_<32>
C132 = [186279062741041885017985574573968873226228250750405652759785192197613040280790635024373857044630449303253807700550767095880568892357_<132>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4290004477 Step 1 took 4562ms Step 2 took 2074ms ********** Factor found in step 2: 22666112659648690795351599407939 Found probable prime factor of 32 digits: 22666112659648690795351599407939 Composite cofactor has 132 digits
(38·10¹⁵⁵+7)/9 = 4(2)₁₅₄3_<156> = 3⁴ · 21247 · 405706541 · 8153054611907549_<16> · C125
C125 = P37 · C89
P37 = 3631636673976858283592464277485606931_<37>
C89 = [20423195573440195206551390289801512611298882650218935717368875142211566032360322627320691_<89>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2443936897 Step 1 took 9742ms Step 2 took 5797ms ********** Factor found in step 2: 3631636673976858283592464277485606931 Found probable prime factor of 37 digits: 3631636673976858283592464277485606931 Composite cofactor has 89 digits
(38·10¹⁴²+7)/9 = 4(2)₁₄₁3_<143> = 59 · 5563 · C138
C138 = P33 · C105
P33 = 605464278196827737125597251068803_<33>
C105 = [212467002221435818816699426054912524005576609275217237202725667730873122816617802499885558317173191456973_<105>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=855237390 Step 1 took 11861ms Step 2 took 6523ms ********** Factor found in step 2: 605464278196827737125597251068803 Found probable prime factor of 33 digits: 605464278196827737125597251068803 Composite cofactor has 105 digits
(38·10¹⁵³+7)/9 = 4(2)₁₅₂3_<154> = 41 · C153
C153 = P29 · P45 · P79
P29 = 56625770021249037961199832163_<29>
P45 = 188621649452113576484103965715195827806438457_<45>
P79 = 9641654643505460294402314031716939370932298867900541134767060848222202356644933_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=485009599 Step 1 took 11845ms Step 2 took 6774ms ********** Factor found in step 2: 56625770021249037961199832163 Found probable prime factor of 29 digits: 56625770021249037961199832163 Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1546770427 Step 1 took 11724ms Step 2 took 6721ms ********** Factor found in step 2: 188621649452113576484103965715195827806438457 Found probable prime factor of 45 digits: 188621649452113576484103965715195827806438457
(38·10¹⁷⁸+7)/9 = 4(2)₁₇₇3_<179> = 41 · C178
C178 = P31 · C147
P31 = 3831638300420149104517799143979_<31>
C147 = [268765007905380748598617247784989569226788294214434773423165473690567346198193202300914071893455165689330378310000725717652182828907168758369414757_<147>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1830987632 Step 1 took 15973ms Step 2 took 8310ms ********** Factor found in step 2: 3831638300420149104517799143979 Found probable prime factor of 31 digits: 3831638300420149104517799143979 Composite cofactor has 147 digits
(38·10¹⁹⁵+7)/9 = 4(2)₁₉₄3_<196> = 23 · 18553 · 3149252376494183_<16> · C175
C175 = P32 · P143
P32 = 42889893988079578415478220866263_<32>
P143 = 73254898010487591881808968625718488656302684170273081444857108882017914768115541121202852664845950871593721116081377554264061422226124415883473_<143>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=400399179 Step 1 took 16303ms Step 2 took 8309ms ********** Factor found in step 2: 42889893988079578415478220866263 Found probable prime factor of 32 digits: 42889893988079578415478220866263 Probable prime cofactor has 143 digits
(38·10¹⁹⁷+7)/9 = 4(2)₁₉₆3_<198> = 3 · 181 · C195
C195 = P32 · C164
P32 = 27947028349698781437164987540699_<32>
C164 = [27823106755181784284339819113194093003006848773401981584784546486000626197936927250194729311161601729645412862762131763250467738959280736054302716529829833142273539_<164>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4094683216 Step 1 took 18445ms ********** Factor found in step 1: 27947028349698781437164987540699 Found probable prime factor of 32 digits: 27947028349698781437164987540699 Composite cofactor has 164 digits
(38·10¹²⁸+7)/9 = 4(2)₁₂₇3_<129> = 3³ · 41 · 1567 · 9613 · 22153 · C115
C115 = P57 · P58
P57 = 205996789767280236842224092563294819222483899476019914763_<57>
P58 = 5548460870468833125139443648463825083675241175547040412381_<58>

SNFS difficulty: 131 digits. Divisors found: r1=205996789767280236842224092563294819222483899476019914763 (pp57) r2=5548460870468833125139443648463825083675241175547040412381 (pp58) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.294). Factorization parameters were as follows: n: 1142965127465948919158699701485164461510638059759591797889499511512820592383071296850919410053462850517519989880703 m: 100000000000000000000000000 deg: 5 c5: 19 c0: 350 skew: 1.79 type: snfs lss: 1 rlim: 1080000 alim: 1080000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1080000/1080000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [540000, 940001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 166698 x 166946 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1080000,1080000,26,26,49,49,2.3,2.3,50000 total time: 2.50 hours.
(38·10¹⁶¹+7)/9 = 4(2)₁₆₀3_<162> = 3 · 71 · 199 · 18133 · 3953923 · 102948767865281369_<18> · 223103459630440120241113301_<27> · C103
C103 = P36 · P68
P36 = 515054520953638018081451448555001699_<36>
P68 = 11744374101790571418852539848321630821275916011828441771173016482301_<68>

Number: 42223_161 N=6048992976898055544701500924282843318487253300729386621852067578882185467974673849952876192480058429399 ( 103 digits) Divisors found: r1=515054520953638018081451448555001699 (pp36) r2=11744374101790571418852539848321630821275916011828441771173016482301 (pp68) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.947). Factorization parameters were as follows: name: 42223_161 n: 6048992976898055544701500924282843318487253300729386621852067578882185467974673849952876192480058429399 skew: 9508.02 # norm 1.32e+14 c5: 65640 c4: 494004046 c3: -12223958194410 c2: -80219580147807645 c1: 377628040081781466140 c0: -5661552501923811834276 # alpha -5.67 Y1: 148027261 Y0: -39165430004865054515 # Murphy_E 2.38e-09 # M 1376237156667498328491122275652318259924145043912891828309343895588198824682229544879829222474450612280 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 251057 x 251305 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.00 hours.
(38·10¹⁶⁴+7)/9 = 4(2)₁₆₃3_<165> = 3² · 61 · 7682881 · 40818499 · 4453252165552267529490497_<25> · C123
C123 = P36 · P88
P36 = 425438812577715228012820656931311881_<36>
P88 = 1294414025611891599260150096076852317064818033104359921919372175404128601450000975774169_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1663009270 Step 1 took 10333ms Step 2 took 5828ms ********** Factor found in step 2: 425438812577715228012820656931311881 Found probable prime factor of 36 digits: 425438812577715228012820656931311881 Probable prime cofactor 1294414025611891599260150096076852317064818033104359921919372175404128601450000975774169 has 88 digits
(38·10¹⁸⁶+7)/9 = 4(2)₁₈₅3_<187> = 47 · 2767 · 359878883096258333_<18> · C164
C164 = P32 · C133
P32 = 17220926929820735919650444522083_<32>
C133 = [5238671693611155393110256636771215165291040871189770033614443601009113065979421595887797051522376438298628830110390256780678267308393_<133>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2089980357 Step 1 took 13584ms Step 2 took 7373ms ********** Factor found in step 2: 17220926929820735919650444522083 Found probable prime factor of 32 digits: 17220926929820735919650444522083 Composite cofactor has 133 digits
Dec 18, 2008: Factorizations of 422...223 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Dec 17, 2008 (3rd): By Sinkiti Sibata / Msieve
(37·10¹⁵¹+53)/9 = 4(1)₁₅₀7_<152> = 17 · 19 · 5424157 · 3012826135843_<13> · C130
C130 = P41 · P90
P41 = 30714188652462505796370832052921572228561_<41>
P90 = 253577854611776783427342074390532895866761571131753872950109269776119129811679765690447289_<90>

Number: 41117_151 N=7788438064632821574690358496362360897296483820042841122084535900504402571465752730134408241556280290071228582891922842992630821129 ( 130 digits) SNFS difficulty: 152 digits. Divisors found: r1=30714188652462505796370832052921572228561 (prp41) r2=253577854611776783427342074390532895866761571131753872950109269776119129811679765690447289 (prp90) Version: Total time: 28.65 hours. Scaled time: 56.71 units (timescale=1.979). Factorization parameters were as follows: name: 41117_151 n: 7788438064632821574690358496362360897296483820042841122084535900504402571465752730134408241556280290071228582891922842992630821129 m: 1000000000000000000000000000000 deg: 5 c5: 370 c0: 53 skew: 0.68 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: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 499116 x 499364 Total sieving time: 28.65 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,50,50,2.4,2.4,100000 total time: 28.65 hours. --------- CPU info (if available) ----------
(38·10¹³⁸-11)/9 = 4(2)₁₃₇1_<139> = 3² · 53 · 1021 · C133
C133 = P44 · P90
P44 = 51707817722286821429454583067769802912986421_<44>
P90 = 167664360523445916239872708231359971038766019984240649261322234707681832432375540040788753_<90>

Number: 42221_138 N=8669558192470123675810540950772195266740631686824530195500818702883517869442385424373732790071439440968636048068593544418823618523013 ( 133 digits) SNFS difficulty: 140 digits. Divisors found: r1=51707817722286821429454583067769802912986421 (prp44) r2=167664360523445916239872708231359971038766019984240649261322234707681832432375540040788753 (prp90) Version: Total time: 9.44 hours. Scaled time: 18.50 units (timescale=1.960). Factorization parameters were as follows: name: 42221_138 n: 8669558192470123675810540950772195266740631686824530195500818702883517869442385424373732790071439440968636048068593544418823618523013 m: 5000000000000000000000000000 deg: 5 c5: 304 c0: -275 skew: 0.98 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1785001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 239659 x 239907 Total sieving time: 9.44 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 9.44 hours. --------- CPU info (if available) ----------
(38·10¹⁴²-11)/9 = 4(2)₁₄₁1_<143> = 421 · 2062883 · 364018747 · C126
C126 = P60 · P66
P60 = 226667704464855786266160319294497767450305082964541295658331_<60>
P66 = 589211205531103317422879572675077629800058220084069542829565675771_<66>

Number: 42221_142 N=133555151402705527771020532470635570480603171803939263654479802422770269818472340168044144200161160806498395618241264340998201 ( 126 digits) SNFS difficulty: 144 digits. Divisors found: r1=226667704464855786266160319294497767450305082964541295658331 (prp60) r2=589211205531103317422879572675077629800058220084069542829565675771 (prp66) Version: Total time: 9.54 hours. Scaled time: 24.47 units (timescale=2.564). Factorization parameters were as follows: name: 42221_142 n: 133555151402705527771020532470635570480603171803939263654479802422770269818472340168044144200161160806498395618241264340998201 m: 20000000000000000000000000000 deg: 5 c5: 475 c0: -44 skew: 0.62 type: snfs lss: 1 rlim: 1770000 alim: 1770000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1770000/1770000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [885000, 2185001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 317247 x 317495 Total sieving time: 9.54 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1770000,1770000,26,26,49,49,2.3,2.3,100000 total time: 9.54 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁹-11)/9 = 4(2)₁₄₈1_<150> = C150
C150 = P34 · P53 · P65
P34 = 2156877309792813337917367804096273_<34>
P53 = 10692962417405779727963760437122579230977363713174343_<53>
P65 = 18307017852353217144257078631568701474589782475479036325318027739_<65>

Number: 42221_149 N=422222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 150 digits) SNFS difficulty: 151 digits. Divisors found: r1=2156877309792813337917367804096273 (prp34) r2=10692962417405779727963760437122579230977363713174343 (prp53) r3=18307017852353217144257078631568701474589782475479036325318027739 (prp65) Version: Total time: 16.63 hours. Scaled time: 42.47 units (timescale=2.554). Factorization parameters were as follows: name: 42221_149 n: 422222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 1000000000000000000000000000000 deg: 5 c5: 19 c0: -55 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, 1950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 376776 x 377024 Total sieving time: 16.63 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 16.63 hours. --------- CPU info (if available) ----------
(38·10¹⁴⁰-11)/9 = 4(2)₁₃₉1_<141> = 167 · 569 · 101402387 · C128
C128 = P39 · P89
P39 = 804607420655732570446552759744605618923_<39>
P89 = 54460313579417670846316649744291707051749895931971216643706261352702388356635007215995827_<89>

Number: 42221_140 N=43819172437237618652820907786713083938238055391217746877124393262556917756829365265010678060634024257185753881011836909120234321 ( 128 digits) SNFS difficulty: 141 digits. Divisors found: r1=804607420655732570446552759744605618923 (prp39) r2=54460313579417670846316649744291707051749895931971216643706261352702388356635007215995827 (prp89) Version: Total time: 5.35 hours. Scaled time: 13.57 units (timescale=2.534). Factorization parameters were as follows: name: 42221_140 n: 43819172437237618652820907786713083938238055391217746877124393262556917756829365265010678060634024257185753881011836909120234321 m: 10000000000000000000000000000 deg: 5 c5: 38 c0: -11 skew: 0.78 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 218142 x 218390 Total sieving time: 5.35 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 5.35 hours. --------- CPU info (if available) ----------
Dec 17, 2008 (2nd): By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1
(38·10¹⁵²-11)/9 = 4(2)₁₅₁1_<153> = 47 · 740549 · 1388627 · C139
C139 = P55 · P85
P55 = 2244475534182952124033053975047362318980113940838127137_<55>
P85 = 3892144435855376728741091997536320056326825112992346851623166566331315178926518146493_<85>

SNFS difficulty: 154 digits. Divisors found: r1=2244475534182952124033053975047362318980113940838127137 (pp55) r2=3892144435855376728741091997536320056326825112992346851623166566331315178926518146493 (pp85) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.280). Factorization parameters were as follows: n: 8735822961783701521595509383320306982142781207790003682501701235482336432672547155076594232653301349910915673274832506173076799918724680541 m: 2000000000000000000000000000000 deg: 5 c5: 475 c0: -44 skew: 0.62 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1300000, 2300001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 512153 x 512401 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,27,27,52,52,2.4,2.4,100000 total time: 18.00 hours.
(38·10¹⁶²-11)/9 = 4(2)₁₆₁1_<163> = 3 · 151 · 601 · 673 · 28551353 · 10361935027_<11> · 15788755231694576119999_<23> · C115
C115 = P39 · P77
P39 = 393004019300720895064649178102671858011_<39>
P77 = 12552808589729656412640688337363128700026916814005950670291119358728810118951_<77>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3477203104 Step 1 took 6473ms Step 2 took 4044ms ********** Factor found in step 2: 393004019300720895064649178102671858011 Found probable prime factor of 39 digits: 393004019300720895064649178102671858011 Probable prime cofactor has 77 digits
(38·10¹⁵⁶-11)/9 = 4(2)₁₅₅1_<157> = 3² · 41 · 61 · 205450383023983_<15> · 868117700586089_<15> · C124
C124 = P36 · P88
P36 = 273415711927335176935345351670676383_<36>
P88 = 3846589586178820725082205888583716939157891153434790937819112111477628162272406784535689_<88>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=324217118 Step 1 took 7748ms Step 2 took 4473ms ********** Factor found in step 2: 273415711927335176935345351670676383 Found probable prime factor of 36 digits: 273415711927335176935345351670676383 Probable prime cofactor 3846589586178820725082205888583716939157891153434790937819112111477628162272406784535689 has 88 digits
Dec 17, 2008: By Robert Backstrom / GGNFS, Msieve
(31·10¹⁸⁵+41)/9 = 3(4)₁₈₄9_<186> = 7 · 188753 · C180
C180 = P59 · P122
P59 = 11462491287896624764009877866815918899950651066846725626897_<59>
P122 = 22743026785569236152077669009125297268693301386451793502974838936091495987844715921550687164968936573229303616204234222327_<122>

Number: n N=260691746389986947752917035524464280563521370290004430918747512391057129418903801297723513529355025914021002840783188645209381303642057113525116682682390247303122860067650349129319 ( 180 digits) SNFS difficulty: 186 digits. Divisors found: Wed Dec 17 02:46:14 2008 prp59 factor: 11462491287896624764009877866815918899950651066846725626897 Wed Dec 17 02:46:14 2008 prp122 factor: 22743026785569236152077669009125297268693301386451793502974838936091495987844715921550687164968936573229303616204234222327 Wed Dec 17 02:46:14 2008 elapsed time 03:13:45 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 58.50 hours. Scaled time: 117.71 units (timescale=2.012). Factorization parameters were as follows: name: KA_3_4_184_9 n: 260691746389986947752917035524464280563521370290004430918747512391057129418903801297723513529355025914021002840783188645209381303642057113525116682682390247303122860067650349129319 type: snfs skew: 1.06 deg: 5 c5: 31 c0: 41 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 4100001) Primes: RFBsize:571119, AFBsize:571584, largePrimes:29344877 encountered Relations: rels:26217521, finalFF:1026972 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 5676222 hash collisions in 31554904 relations Msieve: matrix is 1493389 x 1493637 (408.6 MB) Total sieving time: 57.58 hours. Total relation processing time: 0.93 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 58.50 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
(34·10¹⁸⁴+11)/9 = 3(7)₁₈₃9_<185> = 3 · 7 · C184
C184 = P70 · P114
P70 = 3153381182245925815602116031604202495320047121667445799461559645437791_<70>
P114 = 570480286072025881760890891024077848976969633603699632299856594817956338766406814897528070489702511123803391082489_<114>

Number: n N=1798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941799 ( 184 digits) SNFS difficulty: 186 digits. Divisors found: Wed Dec 17 12:43:05 2008 prp70 factor: 3153381182245925815602116031604202495320047121667445799461559645437791 Wed Dec 17 12:43:05 2008 prp114 factor: 570480286072025881760890891024077848976969633603699632299856594817956338766406814897528070489702511123803391082489 Wed Dec 17 12:43:05 2008 elapsed time 04:13:42 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.87 hours. Scaled time: 59.05 units (timescale=2.045). Factorization parameters were as follows: name: KA_3_7_183_9 n: 1798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941798941799 type: snfs skew: 1.26 deg: 5 c5: 17 c0: 55 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 4550001) Primes: RFBsize:571119, AFBsize:571718, largePrimes:31863919 encountered Relations: rels:29900533, finalFF:1289293 Max relations in full relation-set: 28 Initial matrix: 1142902 x 1289291 with sparse part having weight 139239900. Pruned matrix : 1020687 x 1026465 with weight 109219622. Msieve: found 5898080 hash collisions in 35099131 relations Msieve: matrix is 1215906 x 1216154 (330.1 MB) Total sieving time: 27.66 hours. Total relation processing time: 1.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 28.87 hours. --------- CPU info (if available) ----------
Dec 16, 2008 (4th): By Robert Backstrom / GGNFS, Msieve
(11·10²⁰⁴-17)/3 = 3(6)₂₀₃1_<205> = C205
C205 = P48 · P71 · P88
P48 = 221505090182582524572671341559157703350533777731_<48>
P71 = 13194273781235111004047017055681434596445649290434332958327191748518633_<71>
P88 = 1254591174776189824004158294987313249694792007124710608846927570746687005326132416330207_<88>

Number: n N=3666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 ( 205 digits) SNFS difficulty: 206 digits. Divisors found: Tue Dec 16 14:36:52 2008 prp48 factor: 221505090182582524572671341559157703350533777731 Tue Dec 16 14:36:52 2008 prp71 factor: 13194273781235111004047017055681434596445649290434332958327191748518633 Tue Dec 16 14:36:52 2008 prp88 factor: 1254591174776189824004158294987313249694792007124710608846927570746687005326132416330207 Tue Dec 16 14:36:52 2008 elapsed time 17:19:44 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 175.28 hours. Scaled time: 352.66 units (timescale=2.012). Factorization parameters were as follows: name: KA_3_6_203_1 n: 3666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 type: snfs skew: 0.98 deg: 5 c5: 11 c0: -170 m: 100000000000000000000000000000000000000000 rlim: 10000000 alim: 10000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 29800001) Primes: RFBsize:664579, AFBsize:664171, largePrimes:34554940 encountered Relations: rels:27185260, finalFF:103021 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 13574584 hash collisions in 52206683 relations Msieve: matrix is 3208382 x 3208630 (877.7 MB) Total sieving time: 172.35 hours. Total relation processing time: 2.93 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,206,5,0,0,0,0,0,0,0,0,10000000,10000000,29,29,58,58,2.5,2.5,100000 total time: 175.28 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
Dec 16, 2008 (3rd): By Serge Batalov / Msieve-1.39, GMP-ECM 6.2.1
(37·10¹⁶⁸+53)/9 = 4(1)₁₆₇7_<169> = 61 · 48589 · 101917 · C158
C158 = P49 · P52 · P58
P49 = 1155470698301302268611468354403836671616459816573_<49>
P52 = 6382078797307035347345673498114642379600251847737301_<52>
P58 = 1845540960763765864183039787801984859962999384752383870553_<58>

SNFS difficulty: 170 digits. Divisors found: r1=1155470698301302268611468354403836671616459816573 (pp49) r2=6382078797307035347345673498114642379600251847737301 (pp52) r3=1845540960763765864183039787801984859962999384752383870553 (pp58) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.950). Factorization parameters were as follows: n: 13609582016862291049453137524723009045974398678080754559936713443116025299342216519110899671138279626636611560178417519813777040628623124578030888993199988569 m: 5000000000000000000000000000000000 deg: 5 c5: 296 c0: 1325 skew: 1.35 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, 5450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 919522 x 919770 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,4900000,4900000,27,27,52,52,2.4,2.4,200000 total time: 70.00 hours.
10²⁴⁵+3 = 1(0)₂₄₄3_<246> = 397 · C243
C243 = P37 · C207
P37 = 1523139408975506847609408057356772403_<37>
C207 = [165374992782288143099098664420190855135065524201790567845531019468290719579509530782801360420860492125166999904737069490397081057711442662739511913130562317785089919433785439437190546446326948947840039161333_<207>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1013441708 Step 1 took 88160ms Step 2 took 36093ms ********** Factor found in step 2: 1523139408975506847609408057356772403 Found probable prime factor of 37 digits: 1523139408975506847609408057356772403 Composite cofactor has 207 digits
(38·10¹⁶⁰-11)/9 = 4(2)₁₅₉1_<161> = C161
C161 = P58 · P103
P58 = 4232810193853545342342065250180631557044686896193443565813_<58>
P103 = 9974985952248230050213644193474437703849918356907673850080379830337390210326473820200577856401733781817_<103>

SNFS difficulty: 161 digits. Divisors found: r1=4232810193853545342342065250180631557044686896193443565813 (pp58) r2=9974985952248230050213644193474437703849918356907673850080379830337390210326473820200577856401733781817 (pp103) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.883). Factorization parameters were as follows: n: 42222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 100000000000000000000000000000000 deg: 5 c5: 38 c0: -11 skew: 0.78 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [1750000, 2950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 559579 x 559827 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,52,52,2.4,2.4,200000 total time: 20.00 hours.
Dec 16, 2008 (2nd): By Sinkiti Sibata / Msieve, GGNFS
(38·10¹⁵³-11)/9 = 4(2)₁₅₂1_<154> = 3 · 7 · 17 · 78517 · 4943441 · 129735240245090347741_<21> · 3871855789967261077355383_<25> · C95
C95 = P41 · P55
P41 = 15061311339269694752966969737951939626793_<41>
P55 = 4027540334331000455649132757502438402057856590453203831_<55>

Mon Dec 15 21:24:24 2008 Msieve v. 1.39 Mon Dec 15 21:24:24 2008 random seeds: d578aff0 13fce78b Mon Dec 15 21:24:24 2008 factoring 60660038906825554637414355681564907507415461749948153955759950113103673417179000748613297843983 (95 digits) Mon Dec 15 21:24:25 2008 searching for 15-digit factors Mon Dec 15 21:24:27 2008 commencing quadratic sieve (95-digit input) Mon Dec 15 21:24:27 2008 using multiplier of 7 Mon Dec 15 21:24:27 2008 using 64kb Pentium 4 sieve core Mon Dec 15 21:24:27 2008 sieve interval: 18 blocks of size 65536 Mon Dec 15 21:24:27 2008 processing polynomials in batches of 6 Mon Dec 15 21:24:27 2008 using a sieve bound of 2162071 (79904 primes) Mon Dec 15 21:24:27 2008 using large prime bound of 324310650 (28 bits) Mon Dec 15 21:24:27 2008 using double large prime bound of 2087998231332900 (43-51 bits) Mon Dec 15 21:24:27 2008 using trial factoring cutoff of 51 bits Mon Dec 15 21:24:27 2008 polynomial 'A' values have 12 factors Tue Dec 16 03:39:39 2008 80356 relations (19851 full + 60505 combined from 1194222 partial), need 80000 Tue Dec 16 03:39:44 2008 begin with 1214073 relations Tue Dec 16 03:39:45 2008 reduce to 208410 relations in 12 passes Tue Dec 16 03:39:45 2008 attempting to read 208410 relations Tue Dec 16 03:39:52 2008 recovered 208410 relations Tue Dec 16 03:39:52 2008 recovered 191316 polynomials Tue Dec 16 03:39:52 2008 attempting to build 80356 cycles Tue Dec 16 03:39:53 2008 found 80356 cycles in 7 passes Tue Dec 16 03:39:53 2008 distribution of cycle lengths: Tue Dec 16 03:39:53 2008 length 1 : 19851 Tue Dec 16 03:39:53 2008 length 2 : 14166 Tue Dec 16 03:39:53 2008 length 3 : 13601 Tue Dec 16 03:39:53 2008 length 4 : 10899 Tue Dec 16 03:39:53 2008 length 5 : 8038 Tue Dec 16 03:39:53 2008 length 6 : 5507 Tue Dec 16 03:39:53 2008 length 7 : 3514 Tue Dec 16 03:39:53 2008 length 9+: 4780 Tue Dec 16 03:39:53 2008 largest cycle: 22 relations Tue Dec 16 03:39:53 2008 matrix is 79904 x 80356 (21.8 MB) with weight 5402198 (67.23/col) Tue Dec 16 03:39:53 2008 sparse part has weight 5402198 (67.23/col) Tue Dec 16 03:39:56 2008 filtering completed in 4 passes Tue Dec 16 03:39:56 2008 matrix is 75825 x 75889 (20.6 MB) with weight 5108863 (67.32/col) Tue Dec 16 03:39:56 2008 sparse part has weight 5108863 (67.32/col) Tue Dec 16 03:39:56 2008 saving the first 48 matrix rows for later Tue Dec 16 03:39:56 2008 matrix is 75777 x 75889 (14.5 MB) with weight 4195500 (55.28/col) Tue Dec 16 03:39:56 2008 sparse part has weight 3350889 (44.16/col) Tue Dec 16 03:39:56 2008 matrix includes 64 packed rows Tue Dec 16 03:39:56 2008 using block size 21845 for processor cache size 512 kB Tue Dec 16 03:39:57 2008 commencing Lanczos iteration Tue Dec 16 03:39:57 2008 memory use: 13.1 MB Tue Dec 16 03:40:59 2008 lanczos halted after 1200 iterations (dim = 75775) Tue Dec 16 03:40:59 2008 recovered 16 nontrivial dependencies Tue Dec 16 03:41:01 2008 prp41 factor: 15061311339269694752966969737951939626793 Tue Dec 16 03:41:01 2008 prp55 factor: 4027540334331000455649132757502438402057856590453203831 Tue Dec 16 03:41:01 2008 elapsed time 06:16:37
(38·10¹²⁵-11)/9 = 4(2)₁₂₄1_<126> = 53 · 2801 · 349499 · 1447098722403233_<16> · C100
C100 = P47 · P54
P47 = 26028553070102555153152006678575895714988264141_<47>
P54 = 216051847743155505973228004187461561967298916530089431_<54>

Mon Dec 15 19:29:51 2008 Msieve v. 1.39 Mon Dec 15 19:29:51 2008 random seeds: b14ae2d8 9d6205d9 Mon Dec 15 19:29:51 2008 factoring 5623516984876440046820940447597024505155242882926050220394806682266805082143873407184438266180393771 (100 digits) Mon Dec 15 19:29:52 2008 searching for 15-digit factors Mon Dec 15 19:29:53 2008 commencing quadratic sieve (100-digit input) Mon Dec 15 19:29:53 2008 using multiplier of 19 Mon Dec 15 19:29:53 2008 using 32kb Intel Core sieve core Mon Dec 15 19:29:53 2008 sieve interval: 36 blocks of size 32768 Mon Dec 15 19:29:53 2008 processing polynomials in batches of 6 Mon Dec 15 19:29:53 2008 using a sieve bound of 2747231 (100000 primes) Mon Dec 15 19:29:53 2008 using large prime bound of 412084650 (28 bits) Mon Dec 15 19:29:53 2008 using double large prime bound of 3213479781672900 (43-52 bits) Mon Dec 15 19:29:53 2008 using trial factoring cutoff of 52 bits Mon Dec 15 19:29:53 2008 polynomial 'A' values have 13 factors Tue Dec 16 09:38:14 2008 100131 relations (23083 full + 77048 combined from 1514856 partial), need 100096 Tue Dec 16 09:38:16 2008 begin with 1537939 relations Tue Dec 16 09:38:18 2008 reduce to 266334 relations in 11 passes Tue Dec 16 09:38:18 2008 attempting to read 266334 relations Tue Dec 16 09:38:23 2008 recovered 266334 relations Tue Dec 16 09:38:23 2008 recovered 258695 polynomials Tue Dec 16 09:38:23 2008 attempting to build 100131 cycles Tue Dec 16 09:38:23 2008 found 100131 cycles in 7 passes Tue Dec 16 09:38:23 2008 distribution of cycle lengths: Tue Dec 16 09:38:23 2008 length 1 : 23083 Tue Dec 16 09:38:23 2008 length 2 : 16942 Tue Dec 16 09:38:23 2008 length 3 : 16845 Tue Dec 16 09:38:23 2008 length 4 : 13748 Tue Dec 16 09:38:23 2008 length 5 : 10569 Tue Dec 16 09:38:23 2008 length 6 : 7270 Tue Dec 16 09:38:23 2008 length 7 : 4676 Tue Dec 16 09:38:23 2008 length 9+: 6998 Tue Dec 16 09:38:23 2008 largest cycle: 23 relations Tue Dec 16 09:38:24 2008 matrix is 100000 x 100131 (28.5 MB) with weight 7076937 (70.68/col) Tue Dec 16 09:38:24 2008 sparse part has weight 7076937 (70.68/col) Tue Dec 16 09:38:26 2008 filtering completed in 3 passes Tue Dec 16 09:38:26 2008 matrix is 96437 x 96501 (27.6 MB) with weight 6861401 (71.10/col) Tue Dec 16 09:38:26 2008 sparse part has weight 6861401 (71.10/col) Tue Dec 16 09:38:26 2008 saving the first 48 matrix rows for later Tue Dec 16 09:38:26 2008 matrix is 96389 x 96501 (17.9 MB) with weight 5506767 (57.06/col) Tue Dec 16 09:38:26 2008 sparse part has weight 4110435 (42.59/col) Tue Dec 16 09:38:26 2008 matrix includes 64 packed rows Tue Dec 16 09:38:26 2008 using block size 38600 for processor cache size 1024 kB Tue Dec 16 09:38:27 2008 commencing Lanczos iteration Tue Dec 16 09:38:27 2008 memory use: 16.8 MB Tue Dec 16 09:39:35 2008 lanczos halted after 1525 iterations (dim = 96384) Tue Dec 16 09:39:35 2008 recovered 14 nontrivial dependencies Tue Dec 16 09:39:36 2008 prp47 factor: 26028553070102555153152006678575895714988264141 Tue Dec 16 09:39:36 2008 prp54 factor: 216051847743155505973228004187461561967298916530089431 Tue Dec 16 09:39:36 2008 elapsed time 14:09:45
(37·10¹⁵⁰+71)/9 = 4(1)₁₄₉9_<151> = 3³ · 883 · 4889 · 1221948250643_<13> · C131
C131 = P64 · P67
P64 = 3287070246072146574864034007439682346444251917611909212297051483_<64>
P67 = 8781180623418817074662056980380019977887522124119819322642913307399_<67>

Number: 41119_150 N=28864357552625256507880498508537587718402715194719806825118503206248327918753286810133287358446407710796717272680968736991307822717 ( 131 digits) SNFS difficulty: 151 digits. Divisors found: r1=3287070246072146574864034007439682346444251917611909212297051483 (prp64) r2=8781180623418817074662056980380019977887522124119819322642913307399 (prp67) Version: Total time: 16.83 hours. Scaled time: 43.33 units (timescale=2.575). Factorization parameters were as follows: name: 41119_150 n: 28864357552625256507880498508537587718402715194719806825118503206248327918753286810133287358446407710796717272680968736991307822717 m: 1000000000000000000000000000000 deg: 5 c5: 37 c0: 71 skew: 1.14 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, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 389350 x 389598 Total sieving time: 16.83 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 16.83 hours. --------- CPU info (if available) ----------
(37·10¹⁴⁸+53)/9 = 4(1)₁₄₇7_<149> = 22669 · 107310918012420977_<18> · C128
C128 = P39 · P42 · P48
P39 = 244860118170382215335072280041384558599_<39>
P42 = 446917873259314622190911021433246558748781_<42>
P48 = 154431953041875888316954780441581808091078491811_<48>

Number: 41117_148 N=16899853584033955114950120383965912952947644853307839909495057609897055375198928097686899001618067828768496519047079737942880209 ( 128 digits) SNFS difficulty: 150 digits. Divisors found: r1=244860118170382215335072280041384558599 (prp39) r2=446917873259314622190911021433246558748781 (prp42) r3=154431953041875888316954780441581808091078491811 (prp48) Version: Total time: 14.74 hours. Scaled time: 37.79 units (timescale=2.564). Factorization parameters were as follows: name: 41117_148 n: 16899853584033955114950120383965912952947644853307839909495057609897055375198928097686899001618067828768496519047079737942880209 m: 500000000000000000000000000000 deg: 5 c5: 296 c0: 1325 skew: 1.35 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, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 405122 x 405370 Total sieving time: 14.74 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,150,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 14.74 hours. --------- CPU info (if available) ----------
(38·10¹⁰⁸-11)/9 = 4(2)₁₀₇1_<109> = 3 · C109
C109 = P39 · P70
P39 = 247611047803078395531865562134423674323_<39>
P70 = 5683944314660381557602633851722612401459653226858370362546598490499509_<70>

Number: 42221_108 N=1407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407 ( 109 digits) SNFS difficulty: 110 digits. Divisors found: r1=247611047803078395531865562134423674323 (pp39) r2=5683944314660381557602633851722612401459653226858370362546598490499509 (pp70) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 1.47 hours. Scaled time: 0.70 units (timescale=0.474). Factorization parameters were as follows: name: 42221_108 n: 1407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407407 m: 5000000000000000000000 deg: 5 c5: 304 c0: -275 skew: 0.98 type: snfs lss: 1 rlim: 500000 alim: 500000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [250000, 400001) Primes: RFBsize:41538, AFBsize:41548, largePrimes:1113852 encountered Relations: rels:1058520, finalFF:113369 Max relations in full relation-set: 28 Initial matrix: 83153 x 113369 with sparse part having weight 4921853. Pruned matrix : 70547 x 71026 with weight 2259018. Total sieving time: 1.38 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.03 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,500000,500000,25,25,44,44,2.2,2.2,50000 total time: 1.47 hours. --------- CPU info (if available) ----------
(37·10¹⁵⁰+53)/9 = 4(1)₁₄₉7_<151> = 1953649038355327_<16> · C136
C136 = P68 · P69
P68 = 15528730282738141460510651909659560854080390256835141132996522651323_<68>
P69 = 135511677020391780462271499218014916556072164255270934647592478198377_<69>

Number: 41117_150 N=2104324282611188159960451123666380806055558797064658637231912660210061374031014998130279654083126691286869690704509007375842722395502771 ( 136 digits) SNFS difficulty: 151 digits. Divisors found: r1=15528730282738141460510651909659560854080390256835141132996522651323 (prp68) r2=135511677020391780462271499218014916556072164255270934647592478198377 (prp69) Version: Total time: 19.54 hours. Scaled time: 39.28 units (timescale=2.010). Factorization parameters were as follows: name: 41117_150 n: 2104324282611188159960451123666380806055558797064658637231912660210061374031014998130279654083126691286869690704509007375842722395502771 m: 1000000000000000000000000000000 deg: 5 c5: 37 c0: 53 skew: 1.07 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 : 350594 x 350842 Total sieving time: 19.54 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 19.54 hours. --------- CPU info (if available) ----------
(38·10¹³⁴-11)/9 = 4(2)₁₃₃1_<135> = 1491649 · 2946860149_<10> · C119
C119 = P52 · P68
P52 = 4149907820957241490972920909065030923841515609684853_<52>
P68 = 23146027777754951736573466939039243760546766431014482234227004890357_<68>

Number: 42221_134 N=96053881698998834395407603696803899148417871409640815733762490089278910746043202961580105229793209375622816062588662521 ( 119 digits) SNFS difficulty: 136 digits. Divisors found: r1=4149907820957241490972920909065030923841515609684853 (pp52) r2=23146027777754951736573466939039243760546766431014482234227004890357 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 8.31 hours. Scaled time: 3.93 units (timescale=0.473). Factorization parameters were as follows: name: 42221_134 n: 96053881698998834395407603696803899148417871409640815733762490089278910746043202961580105229793209375622816062588662521 m: 1000000000000000000000000000 deg: 5 c5: 19 c0: -55 skew: 1.24 type: snfs lss: 1 rlim: 1310000 alim: 1310000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1310000/1310000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [655000, 1330001) Primes: RFBsize:100730, AFBsize:100660, largePrimes:3230980 encountered Relations: rels:3174985, finalFF:257716 Max relations in full relation-set: 28 Initial matrix: 201455 x 257716 with sparse part having weight 22148514. Pruned matrix : 185025 x 186096 with weight 12827971. Total sieving time: 7.51 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.60 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1310000,1310000,26,26,48,48,2.3,2.3,75000 total time: 8.31 hours. --------- CPU info (if available) ----------
Dec 16, 2008: By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / Msieve v1.39
(38·10¹²⁰-11)/9 = 4(2)₁₁₉1_<121> = 3⁴ · C119
C119 = P42 · P78
P42 = 509139097395824952151373035566844707911509_<42>
P78 = 102381059598382098870388221982891747034455666681264121668445411723287964967049_<78>

Number: 42221_120 N=52126200274348422496570644718792866941015089163237311385459533607681755829903978052126200274348422496570644718792866941 ( 119 digits) SNFS difficulty: 121 digits. Divisors found: r1=509139097395824952151373035566844707911509 r2=102381059598382098870388221982891747034455666681264121668445411723287964967049 Version: Total time: 0.90 hours. Scaled time: 2.14 units (timescale=2.383). Factorization parameters were as follows: n: 52126200274348422496570644718792866941015089163237311385459533607681755829903978052126200274348422496570644718792866941 m: 1000000000000000000000000 deg: 5 c5: 38 c0: -11 skew: 0.78 type: snfs lss: 1 rlim: 600000 alim: 600000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 510001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 69377 x 69607 Total sieving time: 0.84 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.2,2.2,30000 total time: 0.90 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(38·10¹²⁹-11)/9 = 4(2)₁₂₈1_<130> = 3² · 7 · 482513 · 6402719 · 23270251 · C108
C108 = P42 · P67
P42 = 125271917239803673135317586548283560303451_<42>
P67 = 7441702172870640836699293639239075973261209560036712761186574811061_<67>

Number: 42221_129 N=932236298723118086065258271081642050028750773492236275008624201179184424782920531697686204455679770151271511 ( 108 digits) SNFS difficulty: 131 digits. Divisors found: r1=125271917239803673135317586548283560303451 r2=7441702172870640836699293639239075973261209560036712761186574811061 Version: Total time: 2.16 hours. Scaled time: 5.17 units (timescale=2.393). Factorization parameters were as follows: n: 932236298723118086065258271081642050028750773492236275008624201179184424782920531697686204455679770151271511 m: 100000000000000000000000000 deg: 5 c5: 19 c0: -55 skew: 1.24 type: snfs lss: 1 rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [500000, 950001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 147643 x 147891 Total sieving time: 1.98 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.04 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,47,47,2.3,2.3,50000 total time: 2.16 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: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(38·10¹³²-11)/9 = 4(2)₁₃₁1_<133> = 3 · 588953 · 1230907 · C121
C121 = P50 · P71
P50 = 26254955460944566172921225572697038732496864651657_<50>
P71 = 73943953476055737169732831407296594260590759605785391982027707547550781_<71>

Number: 42221_132 N=1941395205120000513014345070903776490531439352431330068809619602452852526039131860535958662912632755808985780565083294117 ( 121 digits) SNFS difficulty: 134 digits. Divisors found: r1=26254955460944566172921225572697038732496864651657 r2=73943953476055737169732831407296594260590759605785391982027707547550781 Version: Total time: 3.02 hours. Scaled time: 7.21 units (timescale=2.390). Factorization parameters were as follows: n: 1941395205120000513014345070903776490531439352431330068809619602452852526039131860535958662912632755808985780565083294117 m: 200000000000000000000000000 deg: 5 c5: 475 c0: -44 skew: 0.62 type: snfs lss: 1 rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [650000, 1250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 208908 x 209156 Total sieving time: 2.72 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,47,47,2.3,2.3,50000 total time: 3.02 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 15, 2008 (10th): By Wataru Sakai / Msieve
(8·10¹⁹⁹-17)/9 = (8)₁₉₈7_<199> = 7 · C199
C199 = P60 · P66 · P74
P60 = 165915290595704680698485074656900719922152047067184299154427_<60>
P66 = 209149051828140486987606736849824369901235273907179420942848736473_<66>
P74 = 36593767584410672419943796220646382293763887819649513105939916736712122971_<74>

Number: 88887_199 N=1269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841 ( 199 digits) SNFS difficulty: 200 digits. Divisors found: r1=165915290595704680698485074656900719922152047067184299154427 r2=209149051828140486987606736849824369901235273907179420942848736473 r3=36593767584410672419943796220646382293763887819649513105939916736712122971 Version: Total time: 755.47 hours. Scaled time: 1492.80 units (timescale=1.976). Factorization parameters were as follows: n: 1269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841269841 m: 10000000000000000000000000000000000000000 deg: 5 c5: 4 c0: -85 skew: 1.84 type: snfs lss: 1 rlim: 15400000 alim: 15400000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 15400000/15400000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7700000, 15500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2674720 x 2674968 Total sieving time: 755.47 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,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000 total time: 755.47 hours. --------- CPU info (if available) ----------
(34·10¹⁹⁴+11)/9 = 3(7)₁₉₃9_<195> = C195
C195 = P49 · P147
P49 = 2691197740780502992199450526686456932840409619277_<49>
P147 = 140375332534358627509741440328961748053188124694231767125239461652617980761194328247328425405232588742773325753465604320143168823613280390506804927_<147>

Number: 37779_194 N=377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 195 digits) SNFS difficulty: 196 digits. Divisors found: r1=2691197740780502992199450526686456932840409619277 r2=140375332534358627509741440328961748053188124694231767125239461652617980761194328247328425405232588742773325753465604320143168823613280390506804927 Version: Total time: 658.53 hours. Scaled time: 1313.11 units (timescale=1.994). Factorization parameters were as follows: n: 377777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 m: 1000000000000000000000000000000000000000 deg: 5 c5: 17 c0: 55 skew: 1.26 type: snfs lss: 1 rlim: 13000000 alim: 13000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 13000000/13000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6500000, 13600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2061273 x 2061521 Total sieving time: 658.53 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,55,55,2.5,2.5,100000 total time: 658.53 hours. --------- CPU info (if available) ----------
Dec 15, 2008 (9th): By Sinkiti Sibata / Msieve
(38·10¹⁰³-11)/9 = 4(2)₁₀₂1_<104> = 733 · 1621 · 6029 · 367134413 · C86
C86 = P41 · P45
P41 = 28306816444502368825148383991347799490833_<41>
P45 = 567143149328791314070560484701937139507375317_<45>

Mon Dec 15 15:27:04 2008 Msieve v. 1.39 Mon Dec 15 15:27:04 2008 random seeds: 651d427f 9761b85e Mon Dec 15 15:27:04 2008 factoring 16054017025807092569396169499940205222006738243601515768240784071360787770700831969061 (86 digits) Mon Dec 15 15:27:06 2008 searching for 15-digit factors Mon Dec 15 15:27:07 2008 commencing quadratic sieve (86-digit input) Mon Dec 15 15:27:07 2008 using multiplier of 29 Mon Dec 15 15:27:07 2008 using 64kb Pentium 4 sieve core Mon Dec 15 15:27:07 2008 sieve interval: 7 blocks of size 65536 Mon Dec 15 15:27:07 2008 processing polynomials in batches of 15 Mon Dec 15 15:27:07 2008 using a sieve bound of 1451119 (55333 primes) Mon Dec 15 15:27:07 2008 using large prime bound of 116089520 (26 bits) Mon Dec 15 15:27:07 2008 using double large prime bound of 328569561530240 (41-49 bits) Mon Dec 15 15:27:07 2008 using trial factoring cutoff of 49 bits Mon Dec 15 15:27:07 2008 polynomial 'A' values have 11 factors Mon Dec 15 16:19:16 2008 55637 relations (16439 full + 39198 combined from 566957 partial), need 55429 Mon Dec 15 16:19:19 2008 begin with 583396 relations Mon Dec 15 16:19:19 2008 reduce to 129329 relations in 9 passes Mon Dec 15 16:19:19 2008 attempting to read 129329 relations Mon Dec 15 16:19:22 2008 recovered 129329 relations Mon Dec 15 16:19:22 2008 recovered 107195 polynomials Mon Dec 15 16:19:23 2008 attempting to build 55637 cycles Mon Dec 15 16:19:23 2008 found 55637 cycles in 5 passes Mon Dec 15 16:19:23 2008 distribution of cycle lengths: Mon Dec 15 16:19:23 2008 length 1 : 16439 Mon Dec 15 16:19:23 2008 length 2 : 11435 Mon Dec 15 16:19:23 2008 length 3 : 9924 Mon Dec 15 16:19:23 2008 length 4 : 7013 Mon Dec 15 16:19:23 2008 length 5 : 4754 Mon Dec 15 16:19:23 2008 length 6 : 2805 Mon Dec 15 16:19:23 2008 length 7 : 1625 Mon Dec 15 16:19:23 2008 length 9+: 1642 Mon Dec 15 16:19:23 2008 largest cycle: 19 relations Mon Dec 15 16:19:23 2008 matrix is 55333 x 55637 (12.3 MB) with weight 2995743 (53.84/col) Mon Dec 15 16:19:23 2008 sparse part has weight 2995743 (53.84/col) Mon Dec 15 16:19:24 2008 filtering completed in 3 passes Mon Dec 15 16:19:24 2008 matrix is 49885 x 49949 (11.1 MB) with weight 2716273 (54.38/col) Mon Dec 15 16:19:24 2008 sparse part has weight 2716273 (54.38/col) Mon Dec 15 16:19:24 2008 saving the first 48 matrix rows for later Mon Dec 15 16:19:24 2008 matrix is 49837 x 49949 (6.8 MB) with weight 2078163 (41.61/col) Mon Dec 15 16:19:24 2008 sparse part has weight 1495961 (29.95/col) Mon Dec 15 16:19:24 2008 matrix includes 64 packed rows Mon Dec 15 16:19:24 2008 using block size 19979 for processor cache size 512 kB Mon Dec 15 16:19:25 2008 commencing Lanczos iteration Mon Dec 15 16:19:25 2008 memory use: 6.9 MB Mon Dec 15 16:19:48 2008 lanczos halted after 789 iterations (dim = 49837) Mon Dec 15 16:19:48 2008 recovered 18 nontrivial dependencies Mon Dec 15 16:19:49 2008 prp41 factor: 28306816444502368825148383991347799490833 Mon Dec 15 16:19:49 2008 prp45 factor: 567143149328791314070560484701937139507375317 Mon Dec 15 16:19:49 2008 elapsed time 00:52:45
(38·10¹⁰⁵-11)/9 = 4(2)₁₀₄1_<106> = 3 · 7² · 17 · 347 · 140986765379_<12> · C89
C89 = P41 · P48
P41 = 43871068211571581561965777755726137512439_<41>
P48 = 787206733759095811393840080371004503026881448697_<48>

Mon Dec 15 15:34:20 2008 Msieve v. 1.39 Mon Dec 15 15:34:20 2008 random seeds: 389128b0 b431d9bf Mon Dec 15 15:34:20 2008 factoring 34535600313353761637815551285629476040788202504999833839791741988242343476339596177841983 (89 digits) Mon Dec 15 15:34:21 2008 searching for 15-digit factors Mon Dec 15 15:34:23 2008 commencing quadratic sieve (89-digit input) Mon Dec 15 15:34:23 2008 using multiplier of 7 Mon Dec 15 15:34:23 2008 using 32kb Intel Core sieve core Mon Dec 15 15:34:23 2008 sieve interval: 32 blocks of size 32768 Mon Dec 15 15:34:23 2008 processing polynomials in batches of 7 Mon Dec 15 15:34:23 2008 using a sieve bound of 1555999 (59000 primes) Mon Dec 15 15:34:23 2008 using large prime bound of 124479920 (26 bits) Mon Dec 15 15:34:23 2008 using double large prime bound of 372544998335040 (42-49 bits) Mon Dec 15 15:34:23 2008 using trial factoring cutoff of 49 bits Mon Dec 15 15:34:23 2008 polynomial 'A' values have 11 factors Mon Dec 15 16:35:25 2008 59266 relations (15945 full + 43321 combined from 625351 partial), need 59096 Mon Dec 15 16:35:26 2008 begin with 641296 relations Mon Dec 15 16:35:27 2008 reduce to 144178 relations in 10 passes Mon Dec 15 16:35:27 2008 attempting to read 144178 relations Mon Dec 15 16:35:29 2008 recovered 144178 relations Mon Dec 15 16:35:29 2008 recovered 120576 polynomials Mon Dec 15 16:35:29 2008 attempting to build 59266 cycles Mon Dec 15 16:35:29 2008 found 59266 cycles in 6 passes Mon Dec 15 16:35:29 2008 distribution of cycle lengths: Mon Dec 15 16:35:29 2008 length 1 : 15945 Mon Dec 15 16:35:29 2008 length 2 : 11323 Mon Dec 15 16:35:29 2008 length 3 : 10530 Mon Dec 15 16:35:29 2008 length 4 : 7966 Mon Dec 15 16:35:29 2008 length 5 : 5549 Mon Dec 15 16:35:29 2008 length 6 : 3419 Mon Dec 15 16:35:29 2008 length 7 : 2034 Mon Dec 15 16:35:29 2008 length 9+: 2500 Mon Dec 15 16:35:29 2008 largest cycle: 21 relations Mon Dec 15 16:35:29 2008 matrix is 59000 x 59266 (14.5 MB) with weight 3552330 (59.94/col) Mon Dec 15 16:35:29 2008 sparse part has weight 3552330 (59.94/col) Mon Dec 15 16:35:30 2008 filtering completed in 4 passes Mon Dec 15 16:35:30 2008 matrix is 54944 x 55008 (13.5 MB) with weight 3325067 (60.45/col) Mon Dec 15 16:35:30 2008 sparse part has weight 3325067 (60.45/col) Mon Dec 15 16:35:30 2008 saving the first 48 matrix rows for later Mon Dec 15 16:35:30 2008 matrix is 54896 x 55008 (9.8 MB) with weight 2725550 (49.55/col) Mon Dec 15 16:35:30 2008 sparse part has weight 2235862 (40.65/col) Mon Dec 15 16:35:30 2008 matrix includes 64 packed rows Mon Dec 15 16:35:30 2008 using block size 22003 for processor cache size 1024 kB Mon Dec 15 16:35:31 2008 commencing Lanczos iteration Mon Dec 15 16:35:31 2008 memory use: 8.9 MB Mon Dec 15 16:35:50 2008 lanczos halted after 870 iterations (dim = 54892) Mon Dec 15 16:35:50 2008 recovered 15 nontrivial dependencies Mon Dec 15 16:35:51 2008 prp41 factor: 43871068211571581561965777755726137512439 Mon Dec 15 16:35:51 2008 prp48 factor: 787206733759095811393840080371004503026881448697 Mon Dec 15 16:35:51 2008 elapsed time 01:01:31
(38·10¹²⁷-11)/9 = 4(2)₁₂₆1_<128> = 499 · 2386393 · 1606241281_<10> · 272625457405895818536527_<24> · C86
C86 = P35 · P52
P35 = 17366429354635051553800208947550843_<35>
P52 = 4662414176865757064462443642505119553194330890299483_<52>

Mon Dec 15 17:43:30 2008 Msieve v. 1.39 Mon Dec 15 17:43:30 2008 random seeds: 68905814 d1f19330 Mon Dec 15 17:43:30 2008 factoring 80969486424588104569192172741595063682559812789268173368043734892383445616679639114169 (86 digits) Mon Dec 15 17:43:31 2008 searching for 15-digit factors Mon Dec 15 17:43:33 2008 commencing quadratic sieve (86-digit input) Mon Dec 15 17:43:33 2008 using multiplier of 1 Mon Dec 15 17:43:33 2008 using 32kb Intel Core sieve core Mon Dec 15 17:43:33 2008 sieve interval: 17 blocks of size 32768 Mon Dec 15 17:43:33 2008 processing polynomials in batches of 12 Mon Dec 15 17:43:33 2008 using a sieve bound of 1469129 (56000 primes) Mon Dec 15 17:43:33 2008 using large prime bound of 117530320 (26 bits) Mon Dec 15 17:43:33 2008 using double large prime bound of 335946198551280 (41-49 bits) Mon Dec 15 17:43:33 2008 using trial factoring cutoff of 49 bits Mon Dec 15 17:43:33 2008 polynomial 'A' values have 11 factors Mon Dec 15 18:13:35 2008 56158 relations (16674 full + 39484 combined from 575315 partial), need 56096 Mon Dec 15 18:13:36 2008 begin with 591989 relations Mon Dec 15 18:13:37 2008 reduce to 130896 relations in 8 passes Mon Dec 15 18:13:37 2008 attempting to read 130896 relations Mon Dec 15 18:13:38 2008 recovered 130896 relations Mon Dec 15 18:13:38 2008 recovered 102453 polynomials Mon Dec 15 18:13:38 2008 attempting to build 56158 cycles Mon Dec 15 18:13:38 2008 found 56158 cycles in 4 passes Mon Dec 15 18:13:38 2008 distribution of cycle lengths: Mon Dec 15 18:13:38 2008 length 1 : 16674 Mon Dec 15 18:13:38 2008 length 2 : 11381 Mon Dec 15 18:13:38 2008 length 3 : 10137 Mon Dec 15 18:13:38 2008 length 4 : 7151 Mon Dec 15 18:13:38 2008 length 5 : 4629 Mon Dec 15 18:13:38 2008 length 6 : 2845 Mon Dec 15 18:13:38 2008 length 7 : 1598 Mon Dec 15 18:13:38 2008 length 9+: 1743 Mon Dec 15 18:13:38 2008 largest cycle: 18 relations Mon Dec 15 18:13:39 2008 matrix is 56000 x 56158 (12.1 MB) with weight 2944603 (52.43/col) Mon Dec 15 18:13:39 2008 sparse part has weight 2944603 (52.43/col) Mon Dec 15 18:13:39 2008 filtering completed in 3 passes Mon Dec 15 18:13:39 2008 matrix is 50465 x 50527 (11.0 MB) with weight 2682817 (53.10/col) Mon Dec 15 18:13:39 2008 sparse part has weight 2682817 (53.10/col) Mon Dec 15 18:13:39 2008 saving the first 48 matrix rows for later Mon Dec 15 18:13:39 2008 matrix is 50417 x 50527 (6.4 MB) with weight 2003995 (39.66/col) Mon Dec 15 18:13:39 2008 sparse part has weight 1381607 (27.34/col) Mon Dec 15 18:13:39 2008 matrix includes 64 packed rows Mon Dec 15 18:13:39 2008 using block size 20210 for processor cache size 1024 kB Mon Dec 15 18:13:40 2008 commencing Lanczos iteration Mon Dec 15 18:13:40 2008 memory use: 6.8 MB Mon Dec 15 18:13:53 2008 lanczos halted after 798 iterations (dim = 50413) Mon Dec 15 18:13:54 2008 recovered 14 nontrivial dependencies Mon Dec 15 18:13:54 2008 prp35 factor: 17366429354635051553800208947550843 Mon Dec 15 18:13:54 2008 prp52 factor: 4662414176865757064462443642505119553194330890299483 Mon Dec 15 18:13:54 2008 elapsed time 00:30:24
(37·10¹⁴³+71)/9 = 4(1)₁₄₂9_<144> = 31 · 151 · 1282121 · C134
C134 = P40 · P95
P40 = 3615287439291684894508158182767387665977_<40>
P95 = 18947360908062300940159800563451894341618031529231267746815252549335160149680738911882646397847_<95>

Number: 41119_143 N=68500155898643929386073770112198146916568725842649511299081359558885873252281044837718846546767740555072432009399126924327815887951519 ( 134 digits) SNFS difficulty: 145 digits. Divisors found: r1=3615287439291684894508158182767387665977 (prp40) r2=18947360908062300940159800563451894341618031529231267746815252549335160149680738911882646397847 (prp95) Version: Total time: 9.91 hours. Scaled time: 25.40 units (timescale=2.564). Factorization parameters were as follows: name: 41119_143 n: 68500155898643929386073770112198146916568725842649511299081359558885873252281044837718846546767740555072432009399126924327815887951519 m: 50000000000000000000000000000 deg: 5 c5: 296 c0: 1775 skew: 1.43 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [950000, 2250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 328954 x 329202 Total sieving time: 9.91 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,49,49,2.3,2.3,100000 total time: 9.91 hours. --------- CPU info (if available) ----------
(37·10¹³⁸+71)/9 = 4(1)₁₃₇9_<139> = 3 · 969010793 · C130
C130 = P61 · P69
P61 = 3476796762562889019061094719588926077162359713038881374966959_<61>
P69 = 406752322152161834672358389592055437109529103077857683960073230597779_<69>

Number: 41119_138 N=1414195156823573553705887742749187696994382569658716247518999894535096649197353543171908066013017432273708813448035939853943784061 ( 130 digits) SNFS difficulty: 140 digits. Divisors found: r1=3476796762562889019061094719588926077162359713038881374966959 (prp61) r2=406752322152161834672358389592055437109529103077857683960073230597779(prp69)Version: Total time: 9.36 hours. Scaled time: 18.63 units (timescale=1.991). Factorization parameters were as follows: name: 41119_138 n: 1414195156823573553705887742749187696994382569658716247518999894535096649197353543171908066013017432273708813448035939853943784061 m: 5000000000000000000000000000 deg: 5 c5: 296 c0: 1775 skew: 1.43 type: snfs lss: 1 rlim: 1570000 alim: 1570000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1570000/1570000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [785000, 1785001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 237971 x 238219 Total sieving time: 9.36 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1570000,1570000,26,26,48,48,2.3,2.3,100000 total time: 9.36 hours. --------- CPU info (if available) ----------
(37·10¹⁴¹+53)/9 = 4(1)₁₄₀7_<142> = 43 · C140
C140 = P43 · P98
P43 = 2344853697342225768244701403474970076911147_<43>
P98 = 40773219775069496196274797925205475166939330156666714576604063888238857689344930254975648637575477_<98>

Number: 41117_141 N=95607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142119 ( 140 digits) SNFS difficulty: 142 digits. Divisors found: r1=2344853697342225768244701403474970076911147 (prp43) r2=40773219775069496196274797925205475166939330156666714576604063888238857689344930254975648637575477 (prp98) Version: Total time: 10.54 hours. Scaled time: 26.09 units (timescale=2.475). Factorization parameters were as follows: name: 41117_141 n: 95607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142118863049095607235142119 m: 10000000000000000000000000000 deg: 5 c5: 370 c0: 53 skew: 0.68 type: snfs lss: 1 rlim: 1660000 alim: 1660000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1660000/1660000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [830000, 2330001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 306636 x 306884 Total sieving time: 10.54 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1660000,1660000,26,26,48,48,2.3,2.3,100000 total time: 10.54 hours. --------- CPU info (if available) ----------
(37·10¹⁴⁵+53)/9 = 4(1)₁₄₄7_<146> = 619 · 4360973 · 23951846117_<11> · C126
C126 = P59 · P68
P59 = 38350460235070243587880442271327734428299906979443252142693_<59>
P68 = 16579659029211224705104833603108275078319308270761472069498739409211_<68>

Number: 41117_145 N=635837554310788391204818689459763367605246338531582846149485015459484002376721164224273149663384689094348905037164216690545223 ( 126 digits) SNFS difficulty: 146 digits. Divisors found: r1=38350460235070243587880442271327734428299906979443252142693 (prp59) r2=16579659029211224705104833603108275078319308270761472069498739409211 (prp68) Version: Total time: 11.28 hours. Scaled time: 22.53 units (timescale=1.997). Factorization parameters were as follows: name: 41117_145 n: 635837554310788391204818689459763367605246338531582846149485015459484002376721164224273149663384689094348905037164216690545223 m: 100000000000000000000000000000 deg: 5 c5: 37 c0: 53 skew: 1.07 type: snfs lss: 1 rlim: 1940000 alim: 1940000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1940000/1940000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [970000, 2070001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 307574 x 307822 Total sieving time: 11.28 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1940000,1940000,26,26,49,49,2.3,2.3,100000 total time: 11.28 hours. --------- CPU info (if available) ----------
Dec 15, 2008 (8th): By Serge Batalov / GMP-ECM 6.2.1, msieve-1.39, GMP-ECM 6.2.1+msieve, Msieve-1.39
(38·10¹⁴⁵-11)/9 = 4(2)₁₄₄1_<146> = 389 · 785143 · 541988574965639_<15> · 11348765752211748977_<20> · C104
C104 = P34 · P35 · P36
P34 = 1325404641036859296643530875431267_<34>
P35 = 36103065167888294499984392024763463_<35>
P36 = 469690089725626719012031234061716021_<36>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2865957120 Step 1 took 8207ms Step 2 took 4973ms ********** Factor found in step 2: 36103065167888294499984392024763463 Found probable prime factor of 35 digits: 36103065167888294499984392024763463 Composite cofactor has 69 digits Sun Dec 14 22:43:05 2008 Sun Dec 14 22:43:05 2008 Msieve v. 1.39 Sun Dec 14 22:43:05 2008 random seeds: ecc3aec6 9d478ede Sun Dec 14 22:43:05 2008 factoring 622529424771364516359872641106451889809872987897208805215742458228607 (69 digits) Sun Dec 14 22:43:05 2008 searching for 15-digit factors Sun Dec 14 22:43:05 2008 commencing quadratic sieve (69-digit input) Sun Dec 14 22:43:05 2008 using multiplier of 7 Sun Dec 14 22:43:05 2008 using 64kb Opteron sieve core Sun Dec 14 22:43:05 2008 sieve interval: 6 blocks of size 65536 Sun Dec 14 22:43:05 2008 processing polynomials in batches of 17 Sun Dec 14 22:43:06 2008 using a sieve bound of 204517 (9095 primes) Sun Dec 14 22:43:06 2008 using large prime bound of 18406530 (24 bits) Sun Dec 14 22:43:06 2008 using trial factoring cutoff of 24 bits Sun Dec 14 22:43:06 2008 polynomial 'A' values have 9 factors Sun Dec 14 22:44:53 2008 9225 relations (4203 full + 5022 combined from 51864 partial), need 9191 Sun Dec 14 22:44:53 2008 begin with 56067 relations Sun Dec 14 22:44:53 2008 reduce to 13607 relations in 2 passes Sun Dec 14 22:44:53 2008 attempting to read 13607 relations Sun Dec 14 22:44:53 2008 recovered 13607 relations Sun Dec 14 22:44:53 2008 recovered 11821 polynomials Sun Dec 14 22:44:53 2008 attempting to build 9225 cycles Sun Dec 14 22:44:53 2008 found 9225 cycles in 1 passes Sun Dec 14 22:44:53 2008 distribution of cycle lengths: Sun Dec 14 22:44:53 2008 length 1 : 4203 Sun Dec 14 22:44:53 2008 length 2 : 5022 Sun Dec 14 22:44:53 2008 largest cycle: 2 relations Sun Dec 14 22:44:53 2008 matrix is 9095 x 9225 (1.3 MB) with weight 267721 (29.02/col) Sun Dec 14 22:44:53 2008 sparse part has weight 267721 (29.02/col) Sun Dec 14 22:44:53 2008 filtering completed in 3 passes Sun Dec 14 22:44:53 2008 matrix is 8379 x 8443 (1.2 MB) with weight 242533 (28.73/col) Sun Dec 14 22:44:53 2008 sparse part has weight 242533 (28.73/col) Sun Dec 14 22:44:53 2008 commencing Lanczos iteration Sun Dec 14 22:44:53 2008 memory use: 1.6 MB Sun Dec 14 22:44:54 2008 lanczos halted after 134 iterations (dim = 8375) Sun Dec 14 22:44:54 2008 recovered 63 nontrivial dependencies Sun Dec 14 22:44:54 2008 prp34 factor: 1325404641036859296643530875431267 Sun Dec 14 22:44:54 2008 prp36 factor: 469690089725626719012031234061716021 Sun Dec 14 22:44:54 2008 elapsed time 00:01:49
(38·10¹⁶³-11)/9 = 4(2)₁₆₂1_<164> = 977 · 1399 · 126913957 · 1065053831_<10> · 1894635371_<10> · 1451688987955948106334132287_<28> · C104
C104 = P32 · P73
P32 = 15325232869025743468160027097037_<32>
P73 = 5421775857181523778303366997185264829240061910861849089673960276292566569_<73>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1701068307 Step 1 took 8199ms Step 2 took 5108ms ********** Factor found in step 2: 15325232869025743468160027097037 Found probable prime factor of 32 digits: 15325232869025743468160027097037 Probable prime cofactor 5421775857181523778303366997185264829240061910861849089673960276292566569 has 73 digits
(38·10¹²⁸-11)/9 = 4(2)₁₂₇1_<129> = 83 · 7143462642221693_<16> · C111
C111 = P28 · P84
P28 = 3980015878546287994687508077_<28>
P84 = 178924335183058703221158270546770884637344930166891465712261296911583661673906338967_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3096623199 Step 1 took 8208ms Step 2 took 5205ms ********** Factor found in step 2: 3980015878546287994687508077 Found probable prime factor of 28 digits: 3980015878546287994687508077 Probable prime cofactor has 84 digits
(38·10¹⁴⁷-11)/9 = 4(2)₁₄₆1_<148> = 3³ · 7² · 47045659 · C137
C137 = P28 · P29 · P36 · P46
P28 = 2551902873964888480833926621_<28>
P29 = 25651567516317837264646215281_<29>
P36 = 140164536628756188314004991027646939_<36>
P46 = 7393421921628468039493253474311183298582706427_<46>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4033410296 Step 1 took 10041ms Step 2 took 5472ms ********** Factor found in step 2: 2551902873964888480833926621 Found probable prime factor of 28 digits: 2551902873964888480833926621 Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3869496862 Step 1 took 6981ms Step 2 took 4380ms ********** Factor found in step 2: 25651567516317837264646215281 Found probable prime factor of 29 digits: 25651567516317837264646215281 Sun Dec 14 23:32:12 2008 Msieve v. 1.39 Sun Dec 14 23:32:12 2008 random seeds: c480db8c b034535a Sun Dec 14 23:32:12 2008 factoring 1036295557745942373186723249313381729835841778863922580350252672039512028042176953 (82 digits) Sun Dec 14 23:32:13 2008 searching for 15-digit factors Sun Dec 14 23:32:14 2008 commencing quadratic sieve (82-digit input) Sun Dec 14 23:32:14 2008 using multiplier of 1 Sun Dec 14 23:32:14 2008 using 64kb Opteron sieve core Sun Dec 14 23:32:14 2008 sieve interval: 6 blocks of size 65536 Sun Dec 14 23:32:14 2008 processing polynomials in batches of 17 Sun Dec 14 23:32:14 2008 using a sieve bound of 1334341 (51025 primes) Sun Dec 14 23:32:14 2008 using large prime bound of 126762395 (26 bits) Sun Dec 14 23:32:14 2008 using trial factoring cutoff of 27 bits Sun Dec 14 23:32:14 2008 polynomial 'A' values have 10 factors Sun Dec 14 23:54:47 2008 51205 relations (26457 full + 24748 combined from 273052 partial), need 51121 Sun Dec 14 23:54:47 2008 begin with 299509 relations Sun Dec 14 23:54:47 2008 reduce to 72932 relations in 2 passes Sun Dec 14 23:54:47 2008 attempting to read 72932 relations Sun Dec 14 23:54:48 2008 recovered 72932 relations Sun Dec 14 23:54:48 2008 recovered 63151 polynomials Sun Dec 14 23:54:48 2008 attempting to build 51205 cycles Sun Dec 14 23:54:48 2008 found 51205 cycles in 1 passes Sun Dec 14 23:54:48 2008 distribution of cycle lengths: Sun Dec 14 23:54:48 2008 length 1 : 26457 Sun Dec 14 23:54:48 2008 length 2 : 24748 Sun Dec 14 23:54:48 2008 largest cycle: 2 relations Sun Dec 14 23:54:49 2008 matrix is 51025 x 51205 (7.5 MB) with weight 1547321 (30.22/col) Sun Dec 14 23:54:49 2008 sparse part has weight 1547321 (30.22/col) Sun Dec 14 23:54:49 2008 filtering completed in 4 passes Sun Dec 14 23:54:49 2008 matrix is 36298 x 36362 (5.8 MB) with weight 1237357 (34.03/col) Sun Dec 14 23:54:49 2008 sparse part has weight 1237357 (34.03/col) Sun Dec 14 23:54:49 2008 saving the first 48 matrix rows for later Sun Dec 14 23:54:49 2008 matrix is 36250 x 36362 (4.4 MB) with weight 984802 (27.08/col) Sun Dec 14 23:54:49 2008 sparse part has weight 795660 (21.88/col) Sun Dec 14 23:54:49 2008 matrix includes 64 packed rows Sun Dec 14 23:54:49 2008 using block size 14544 for processor cache size 1024 kB Sun Dec 14 23:54:50 2008 commencing Lanczos iteration Sun Dec 14 23:54:50 2008 memory use: 4.2 MB Sun Dec 14 23:54:58 2008 lanczos halted after 575 iterations (dim = 36249) Sun Dec 14 23:54:59 2008 recovered 16 nontrivial dependencies Sun Dec 14 23:54:59 2008 prp36 factor: 140164536628756188314004991027646939 Sun Dec 14 23:54:59 2008 prp46 factor: 7393421921628468039493253474311183298582706427 Sun Dec 14 23:54:59 2008 elapsed time 00:22:47
(38·10¹³⁵-11)/9 = 4(2)₁₃₄1_<136> = 3 · 7 · 67 · 10709 · C129
C129 = P30 · P99
P30 = 937437808317976970693932416403_<30>
P99 = 298920435195374668796858613681629028190698771165759803331918105970884920720033436834219559330152989_<99>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4218461253 Step 1 took 8577ms Step 2 took 4940ms ********** Factor found in step 2: 937437808317976970693932416403 Found probable prime factor of 30 digits: 937437808317976970693932416403 Probable prime cofactor 298920435195374668796858613681629028190698771165759803331918105970884920720033436834219559330152989 has 99 digits
(38·10¹³³-11)/9 = 4(2)₁₃₂1_<134> = 1259 · C131
C131 = P36 · P96
P36 = 227346354804397997449555013421517819_<36>
P96 = 147512003565082160996670532501548152339461769615196128904934077918830260161327461047769915156101_<96>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2551179353 Step 1 took 8385ms Step 2 took 4932ms ********** Factor found in step 2: 227346354804397997449555013421517819 Found probable prime factor of 36 digits: 227346354804397997449555013421517819 Probable prime cofactor 147512003565082160996670532501548152339461769615196128904934077918830260161327461047769915156101 has 96 digits
(38·10¹⁹¹-11)/9 = 4(2)₁₉₀1_<192> = 41 · 2687 · 774334507 · C178
C178 = P33 · C146
P33 = 375832150285823251963801943606447_<33>
C146 = [13169431325495540700522931115085114511012173448511242545734463676942758815655542079711578357374161512954053203286078300190494821013860645706028447_<146>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3279824311 Step 1 took 15916ms Step 2 took 8379ms ********** Factor found in step 2: 375832150285823251963801943606447 Found probable prime factor of 33 digits: 375832150285823251963801943606447 Composite cofactor has 146 digits
(38·10¹⁷⁴-11)/9 = 4(2)₁₇₃1_<175> = 3³ · 7629737812981_<13> · 31668315658185358241_<20> · C141
C141 = P38 · C104
P38 = 64583320974668012969282589628685014327_<38>
C104 = [10021260930390560266594511156264428707661578748567959642375971936717369835041789453030241615860197033469_<104>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3366280551 Step 1 took 14481ms Step 2 took 6856ms ********** Factor found in step 2: 64583320974668012969282589628685014327 Found probable prime factor of 38 digits: 64583320974668012969282589628685014327 Composite cofactor has 104 digits
(38·10¹²²-11)/9 = 4(2)₁₂₁1_<123> = 23 · C122
C122 = P41 · P81
P41 = 22983221156969608220878678122685099656223_<41>
P81 = 798734337425041424415227498048707151445996691869167022100770362401392131327274149_<81>

SNFS difficulty: 124 digits. Divisors found: r1=22983221156969608220878678122685099656223 (pp41) r2=798734337425041424415227498048707151445996691869167022100770362401392131327274149 (pp81) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.728). Factorization parameters were as follows: n: 18357487922705314009661835748792270531400966183574879227053140096618357487922705314009661835748792270531400966183574879227 m: 2000000000000000000000000 deg: 5 c5: 475 c0: -44 skew: 0.62 type: snfs lss: 1 rlim: 820000 alim: 820000 lpbr: 25 lpba: 25 mfbr: 48 mfba: 48 rlambda: 2.2 alambda: 2.2 Factor base limits: 820000/820000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 48/48 Sieved rational special-q in [410000, 810001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 101881 x 102120 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,820000,820000,25,25,48,48,2.2,2.2,50000 total time: 1.20 hours.
(38·10¹⁸³-11)/9 = 4(2)₁₈₂1_<184> = 3² · 7 · 6514450079635017199_<19> · C164
C164 = P35 · P129
P35 = 75782147652784397005420137353528113_<35>
P129 = 135755010714898869452949025678199105972122459983334039812159735676716342059338321962469593013630612819204264542435169763895315341_<129>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=821134725 Step 1 took 11704ms Step 2 took 6053ms ********** Factor found in step 2: 75782147652784397005420137353528113 Found probable prime factor of 35 digits: 75782147652784397005420137353528113 Probable prime cofactor 135755010714898869452949025678199105972122459983334039812159735676716342059338321962469593013630612819204264542435169763895315341 has 129 digits
(37·10¹⁶⁰+71)/9 = 4(1)₁₅₉9_<161> = 13 · 1164433 · 1927633 · C148
C148 = P34 · P49 · P67
P34 = 1302813942596384285247378345758543_<34>
P49 = 1023739102807287331415444498937198533190476003389_<49>
P67 = 1056343867181512794323328678468277917562204780290353805173030837321_<67>

SNFS difficulty: 161 digits. Divisors found: r1=1302813942596384285247378345758543 (pp34) r2=1023739102807287331415444498937198533190476003389 (pp49) r3=1056343867181512794323328678468277917562204780290353805173030837321 (pp67) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.174). Factorization parameters were as follows: n: 1408889734971532832959813943795077767526643347374927297662390319135412350788559621130563324497189583241140762438987075704505540800628177844802413867 m: 100000000000000000000000000000000 deg: 5 c5: 37 c0: 71 skew: 1.14 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 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 : 662073 x 662321 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,52,52,2.4,2.4,100000 total time: 35.00 hours.
(38·10¹⁹³-11)/9 = 4(2)₁₉₂1_<194> = 29 · 143251879 · C185
C185 = P32 · C153
P32 = 92238676107852763259816729714369_<32>
C153 = [110186833103092390774649090660008487821406637141568965549388610139834253319507062767249752482557653014855888025715777277839734871796910969834280443874599_<153>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=4093897938 Step 1 took 13765ms Step 2 took 7000ms ********** Factor found in step 2: 92238676107852763259816729714369 Found probable prime factor of 32 digits: 92238676107852763259816729714369 Composite cofactor has 153 digits
Dec 15, 2008 (7th): By Jo Yeong Uk / GGNFS, Msieve
(11·10¹⁹¹-17)/3 = 3(6)₁₉₀1_<192> = C192
C192 = P50 · P142
P50 = 49192191343990162417715955038848218978279791366327_<50>
P142 = 7453757530390289043345066089546327493410373894631714762602742698136076516003603270057275757770990426540518320236664138941399118042301680339843_<142>

Number: 36661_191 N=366666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 ( 192 digits) SNFS difficulty: 192 digits. Divisors found: r1=49192191343990162417715955038848218978279791366327 (pp50) r2=7453757530390289043345066089546327493410373894631714762602742698136076516003603270057275757770990426540518320236664138941399118042301680339843 (pp142) Version: GGNFS-0.77.1-20050930-nocona Total time: 333.93 hours. Scaled time: 792.08 units (timescale=2.372). Factorization parameters were as follows: n: 366666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661 m: 100000000000000000000000000000000000000 deg: 5 c5: 110 c0: -17 skew: 0.69 type: snfs lss: 1 rlim: 13000000 alim: 13000000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13000000/13000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6500000, 11800001) Primes: RFBsize:849252, AFBsize:848849, largePrimes:20997970 encountered Relations: rels:22348036, finalFF:1980622 Max relations in full relation-set: 28 Initial matrix: 1698168 x 1980622 with sparse part having weight 222660520. Pruned matrix : 1459606 x 1468160 with weight 178804439. Total sieving time: 302.57 hours. Total relation processing time: 0.57 hours. Matrix solve time: 30.49 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,55,55,2.5,2.5,100000 total time: 333.93 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: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
(37·10¹⁷⁹+53)/9 = 4(1)₁₇₈7_<180> = 3⁴ · 7 · 23 · 4751018479457_<13> · 13962759095755291_<17> · 49208248701391080839818523_<26> · 2119493083661110697017153309_<28> · C94
C94 = P43 · P52
P43 = 1231767907813054570880909901881618539628959_<43>
P52 = 3699061547272506851328690176815392273739868519354327_<52>

Sun Dec 14 23:07:19 2008 Sun Dec 14 23:07:19 2008 Sun Dec 14 23:07:19 2008 Msieve v. 1.39 Sun Dec 14 23:07:19 2008 random seeds: efc8f9c0 4a2a88b6 Sun Dec 14 23:07:19 2008 factoring 4556385302955576221884023543638349856512194802012137833352589947767890040676035957132831155593 (94 digits) Sun Dec 14 23:07:20 2008 searching for 15-digit factors Sun Dec 14 23:07:21 2008 commencing quadratic sieve (94-digit input) Sun Dec 14 23:07:21 2008 using multiplier of 1 Sun Dec 14 23:07:21 2008 using VC8 32kb sieve core Sun Dec 14 23:07:21 2008 sieve interval: 36 blocks of size 32768 Sun Dec 14 23:07:21 2008 processing polynomials in batches of 6 Sun Dec 14 23:07:21 2008 using a sieve bound of 2059511 (76377 primes) Sun Dec 14 23:07:21 2008 using large prime bound of 284212518 (28 bits) Sun Dec 14 23:07:21 2008 using double large prime bound of 1646484896014146 (42-51 bits) Sun Dec 14 23:07:21 2008 using trial factoring cutoff of 51 bits Sun Dec 14 23:07:21 2008 polynomial 'A' values have 12 factors Mon Dec 15 02:09:04 2008 76723 relations (18644 full + 58079 combined from 1105235 partial), need 76473 Mon Dec 15 02:09:06 2008 begin with 1123879 relations Mon Dec 15 02:09:06 2008 reduce to 199758 relations in 11 passes Mon Dec 15 02:09:06 2008 attempting to read 199758 relations Mon Dec 15 02:09:09 2008 recovered 199758 relations Mon Dec 15 02:09:09 2008 recovered 183205 polynomials Mon Dec 15 02:09:09 2008 attempting to build 76723 cycles Mon Dec 15 02:09:09 2008 found 76723 cycles in 5 passes Mon Dec 15 02:09:09 2008 distribution of cycle lengths: Mon Dec 15 02:09:09 2008 length 1 : 18644 Mon Dec 15 02:09:09 2008 length 2 : 13569 Mon Dec 15 02:09:09 2008 length 3 : 12956 Mon Dec 15 02:09:09 2008 length 4 : 10464 Mon Dec 15 02:09:09 2008 length 5 : 7806 Mon Dec 15 02:09:09 2008 length 6 : 5369 Mon Dec 15 02:09:09 2008 length 7 : 3303 Mon Dec 15 02:09:09 2008 length 9+: 4612 Mon Dec 15 02:09:09 2008 largest cycle: 18 relations Mon Dec 15 02:09:10 2008 matrix is 76377 x 76723 (20.7 MB) with weight 4802821 (62.60/col) Mon Dec 15 02:09:10 2008 sparse part has weight 4802821 (62.60/col) Mon Dec 15 02:09:11 2008 filtering completed in 3 passes Mon Dec 15 02:09:11 2008 matrix is 72800 x 72864 (19.7 MB) with weight 4576855 (62.81/col) Mon Dec 15 02:09:11 2008 sparse part has weight 4576855 (62.81/col) Mon Dec 15 02:09:11 2008 saving the first 48 matrix rows for later Mon Dec 15 02:09:11 2008 matrix is 72752 x 72864 (12.2 MB) with weight 3552283 (48.75/col) Mon Dec 15 02:09:11 2008 sparse part has weight 2460376 (33.77/col) Mon Dec 15 02:09:11 2008 matrix includes 64 packed rows Mon Dec 15 02:09:11 2008 using block size 29145 for processor cache size 4096 kB Mon Dec 15 02:09:11 2008 commencing Lanczos iteration Mon Dec 15 02:09:11 2008 memory use: 11.2 MB Mon Dec 15 02:09:41 2008 lanczos halted after 1151 iterations (dim = 72748) Mon Dec 15 02:09:41 2008 recovered 14 nontrivial dependencies Mon Dec 15 02:09:41 2008 prp43 factor: 1231767907813054570880909901881618539628959 Mon Dec 15 02:09:41 2008 prp52 factor: 3699061547272506851328690176815392273739868519354327 Mon Dec 15 02:09:41 2008 elapsed time 03:02:22
(37·10¹⁸¹+71)/9 = 4(1)₁₈₀9_<182> = 7 · 42323 · 33379705157_<11> · 24127822888595769062376049807_<29> · 47573256735105102134774568941200081_<35> · C103
C103 = P38 · P66
P38 = 10427180460429420252723196144751715523_<38>
P66 = 347339620026515181041293360623135033853462919353750340536712007667_<66>

Number: 41119_181 N=3621772899073458445059701652864566407076358975646712173315673909567467074401737345715255403591778914841 ( 103 digits) Divisors found: r1=10427180460429420252723196144751715523 (pp38) r2=347339620026515181041293360623135033853462919353750340536712007667 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.29 hours. Scaled time: 10.21 units (timescale=2.382). Factorization parameters were as follows: name: 41119_181 n: 3621772899073458445059701652864566407076358975646712173315673909567467074401737345715255403591778914841 skew: 9782.55 # norm 4.14e+14 c5: 73080 c4: -2514835704 c3: 8790142461548 c2: 263294977153601755 c1: 196917554526018178456 c0: -2679866085058324682790127 # alpha -6.43 Y1: 7813826537 Y0: -34595945979182260752 # Murphy_E 2.51e-09 # M 1396009132050224762205095102224607140116956259471065740878701764748997185483488045420616203276518767234 type: gnfs rlim: 1400000 alim: 1400000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [700000, 1350001) Primes: RFBsize:107126, AFBsize:107413, largePrimes:4760133 encountered Relations: rels:4585963, finalFF:244161 Max relations in full relation-set: 28 Initial matrix: 214630 x 244161 with sparse part having weight 22152773. Pruned matrix : 200512 x 201649 with weight 15853660. Polynomial selection time: 0.25 hours. Total sieving time: 3.76 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.14 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1400000,1400000,26,26,50,50,2.6,2.6,50000 total time: 4.29 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: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)
Dec 15, 2008 (6th): By Serge Batalov / Msieve-1.39
(37·10¹⁵⁸+71)/9 = 4(1)₁₅₇9_<159> = 31 · C158
C158 = P38 · P47 · P73
P38 = 56252524761237276570987106972917336289_<38>
P47 = 37279445348853727722204385871231176114193568127_<47>
P73 = 6323915511918555012521989947661747244518565340773117237921653166093351183_<73>

SNFS difficulty: 160 digits. Divisors found: r1=56252524761237276570987106972917336289 (pp38) r2=37279445348853727722204385871231176114193568127 (pp47) r3=6323915511918555012521989947661747244518565340773117237921653166093351183 (pp73) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.559). Factorization parameters were as follows: n: 13261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261648745519713261649 m: 50000000000000000000000000000000 deg: 5 c5: 296 c0: 1775 skew: 1.43 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [1700000, 3200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 646811 x 647059 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,52,52,2.4,2.4,100000 total time: 21.00 hours.
(37·10¹⁵⁹+53)/9 = 4(1)₁₅₈7_<160> = 8473427 · C153
C153 = P42 · P42 · P70
P42 = 443323695339234757494089624823618634934581_<42>
P42 = 452780513252055747543767753370086491619059_<42>
P70 = 2417082367680574707369031567295805948468828136719998084989731464459249_<70>

SNFS difficulty: 161 digits. Divisors found: r1=443323695339234757494089624823618634934581 (pp42) r2=452780513252055747543767753370086491619059 (pp42) r3=2417082367680574707369031567295805948468828136719998084989731464459249 (pp70) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.692). Factorization parameters were as follows: n: 485176907892298017214417627143198508833688082886783719398433610286736536599785554429289484775299428567816907033141503562975300443505456660110615352101471 m: 100000000000000000000000000000000 deg: 5 c5: 37 c0: 530 skew: 1.70 type: snfs lss: 1 rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 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: 52/52 Sieved rational special-q in [1750000, 3650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 723565 x 723813 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,27,27,52,52,2.4,2.4,100000 total time: 26.00 hours.
Dec 15, 2008 (5th): By Robert Backstrom / GGNFS, Msieve
(37·10¹²⁰+71)/9 = 4(1)₁₁₉9_<121> = 3 · 17 · 257 · 169244578693_<12> · C106
C106 = P47 · P60
P47 = 15718212115607084073455098063640139764109946061_<47>
P60 = 117906569540261494882234034595775781192538671358262630919029_<60>

Number: n N=1853280469857407409649560238135051795272682028566957745455654946359544378927120317253367823242200048494769 ( 106 digits) SNFS difficulty: 121 digits. Divisors found: r1=15718212115607084073455098063640139764109946061 (pp47) r2=117906569540261494882234034595775781192538671358262630919029 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.52 hours. Scaled time: 2.79 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_1_119_9 n: 1853280469857407409649560238135051795272682028566957745455654946359544378927120317253367823242200048494769 type: snfs skew: 1.14 deg: 5 c5: 37 c0: 71 m: 1000000000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [250000, 450001) Primes: RFBsize:41538, AFBsize:41148, largePrimes:5521859 encountered Relations: rels:4970497, finalFF:209320 Max relations in full relation-set: 48 Initial matrix: 82751 x 209320 with sparse part having weight 32997515. Pruned matrix : 71450 x 71927 with weight 7104504. Total sieving time: 1.28 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.03 hours. Total square root time: 0.14 hours, sqrts: 10. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,500000,500000,28,28,56,56,2.5,2.5,50000 total time: 1.52 hours. --------- CPU info (if available) ----------
(37·10¹²⁹+71)/9 = 4(1)₁₂₈9_<130> = 3 · 27774323 · 13031386588706799664801_<23> · C100
C100 = P42 · P59
P42 = 128123426410502970074948895719212965675887_<42>
P59 = 29551212498200826094631393040780112047335950040214922506473_<59>

Number: n N=3786202599854369175101763795740950150675265207939197580619648859764781300033378615291421350577516551 ( 100 digits) SNFS difficulty: 131 digits. Divisors found: r1=128123426410502970074948895719212965675887 (pp42) r2=29551212498200826094631393040780112047335950040214922506473 (pp59) Version: GGNFS-0.77.1-20051202-k8 Total time: 3.83 hours. Scaled time: 7.71 units (timescale=2.013). Factorization parameters were as follows: name: KA_4_1_128_9 n: 3786202599854369175101763795740950150675265207939197580619648859764781300033378615291421350577516551 type: snfs skew: 1.81 deg: 5 c5: 37 c0: 710 m: 100000000000000000000000000 rlim: 900000 alim: 900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 650001) Primes: RFBsize:71274, AFBsize:71376, largePrimes:7510334 encountered Relations: rels:6777003, finalFF:229584 Max relations in full relation-set: 28 Initial matrix: 142715 x 229584 with sparse part having weight 24217375. Pruned matrix : 123653 x 124430 with weight 10406862. Total sieving time: 3.63 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.5,2.5,50000 total time: 3.83 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
(37·10¹³¹+53)/9 = 4(1)₁₃₀7_<132> = 3 · 7 · 26317 · 3455435628958223_<16> · C111
C111 = P49 · P62
P49 = 7972700383759441503881272449579513196474094885429_<49>
P62 = 27001959963243168853430820841180310949496723141495794009982343_<62>

Number: n N=215278536561205887322108876493270186092609401846280407032882268561731174025745829832628911912346191386897980147 ( 111 digits) SNFS difficulty: 132 digits. Divisors found: r1=7972700383759441503881272449579513196474094885429 (pp49) r2=27001959963243168853430820841180310949496723141495794009982343 (pp62) Version: GGNFS-0.77.1-20051202-k8 Total time: 4.34 hours. Scaled time: 8.72 units (timescale=2.010). Factorization parameters were as follows: name: KA_4_1_130_7 n: 215278536561205887322108876493270186092609401846280407032882268561731174025745829832628911912346191386897980147 type: snfs skew: 0.68 deg: 5 c5: 370 c0: 53 m: 100000000000000000000000000 rlim: 900000 alim: 900000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [100000, 750001) Primes: RFBsize:71274, AFBsize:70980, largePrimes:7870308 encountered Relations: rels:7124914, finalFF:201480 Max relations in full relation-set: 28 Initial matrix: 142321 x 201480 with sparse part having weight 21993173. Pruned matrix : 129753 x 130528 with weight 11883302. Total sieving time: 4.11 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,900000,900000,28,28,56,56,2.5,2.5,50000 total time: 4.34 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
(37·10¹³⁴+53)/9 = 4(1)₁₃₃7_<135> = 3² · 24986991259982899490059_<23> · C112
C112 = P50 · P62
P50 = 26997291767926798159853751308242719224871556251223_<50>
P62 = 67714634740461212531416188452742326805525020387462321160332809_<62>

Number: n N=1828111751046823473729867845947611785538650552102639379539486366668748152605479610053566238562881946543093275407 ( 112 digits) SNFS difficulty: 136 digits. Divisors found: Mon Dec 15 05:57:05 2008 prp50 factor: 26997291767926798159853751308242719224871556251223 Mon Dec 15 05:57:05 2008 prp62 factor: 67714634740461212531416188452742326805525020387462321160332809 Mon Dec 15 05:57:05 2008 elapsed time 00:12:49 (Msieve 1.39 - dependency 4) Version: GGNFS-0.77.1-20050930-k8 Total time: 4.50 hours. Scaled time: 9.05 units (timescale=2.012). Factorization parameters were as follows: name: KA_4_1_133_7 n: 1828111751046823473729867845947611785538650552102639379539486366668748152605479610053566238562881946543093275407 type: snfs skew: 1.70 deg: 5 c5: 37 c0: 530 m: 1000000000000000000000000000 rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [100000, 800001) Primes: RFBsize:78498, AFBsize:78716, largePrimes:7741734 encountered Relations: rels:6703606, finalFF:108763 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 4.37 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,56,56,2.5,2.5,75000 total time: 4.50 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).
Dec 15, 2008 (4th): By Sinkiti Sibata / Msieve
(37·10¹²⁶+53)/9 = 4(1)₁₂₅7_<127> = 23429971 · C120
C120 = P55 · P65
P55 = 2385657431444900902593170998853579105307250401833124431_<55>
P65 = 73549442015086715345246777178084396489992122857979924708529445617_<65>

Number: 41117_126 N=175463772921917449710505877754228168319589943628658828092920435587014218289519483874355248289087131653347377643408568927 ( 120 digits) SNFS difficulty: 127 digits. Divisors found: r1=2385657431444900902593170998853579105307250401833124431 (prp55) r2=73549442015086715345246777178084396489992122857979924708529445617 (prp65) Version: Total time: 4.07 hours. Scaled time: 7.96 units (timescale=1.955). Factorization parameters were as follows: name: 41117_126 n: 175463772921917449710505877754228168319589943628658828092920435587014218289519483874355248289087131653347377643408568927 m: 10000000000000000000000000 deg: 5 c5: 370 c0: 53 skew: 0.68 type: snfs lss: 1 rlim: 940000 alim: 940000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 940000/940000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [470000, 970001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 156346 x 156594 Total sieving time: 4.07 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,127,5,0,0,0,0,0,0,0,0,940000,940000,26,26,46,46,2.3,2.3,50000 total time: 4.07 hours. --------- CPU info (if available) ----------
(37·10¹²¹+53)/9 = 4(1)₁₂₀7_<122> = 4133 · 12448496033_<11> · 96559317121_<11> · C97
C97 = P42 · P56
P42 = 581119780975231635970058042786794126786889_<42>
P56 = 14240232483206706578295465829097659023799330370860981537_<56>

Sun Dec 14 17:44:52 2008 Msieve v. 1.39 Sun Dec 14 17:44:52 2008 random seeds: 558fa890 5a21134c Sun Dec 14 17:44:52 2008 factoring 8275280781677460242495252428407518810499554171453232349711921873570895749085623666102478562668393 (97 digits) Sun Dec 14 17:44:53 2008 searching for 15-digit factors Sun Dec 14 17:44:55 2008 commencing quadratic sieve (97-digit input) Sun Dec 14 17:44:55 2008 using multiplier of 1 Sun Dec 14 17:44:55 2008 using 32kb Intel Core sieve core Sun Dec 14 17:44:55 2008 sieve interval: 36 blocks of size 32768 Sun Dec 14 17:44:55 2008 processing polynomials in batches of 6 Sun Dec 14 17:44:55 2008 using a sieve bound of 2404009 (88075 primes) Sun Dec 14 17:44:55 2008 using large prime bound of 360601350 (28 bits) Sun Dec 14 17:44:55 2008 using double large prime bound of 2527255810204800 (43-52 bits) Sun Dec 14 17:44:55 2008 using trial factoring cutoff of 52 bits Sun Dec 14 17:44:55 2008 polynomial 'A' values have 13 factors Mon Dec 15 00:37:14 2008 88421 relations (20973 full + 67448 combined from 1337165 partial), need 88171 Mon Dec 15 00:37:16 2008 begin with 1358138 relations Mon Dec 15 00:37:17 2008 reduce to 233452 relations in 11 passes Mon Dec 15 00:37:17 2008 attempting to read 233452 relations Mon Dec 15 00:37:21 2008 recovered 233452 relations Mon Dec 15 00:37:21 2008 recovered 221954 polynomials Mon Dec 15 00:37:21 2008 attempting to build 88421 cycles Mon Dec 15 00:37:21 2008 found 88421 cycles in 7 passes Mon Dec 15 00:37:21 2008 distribution of cycle lengths: Mon Dec 15 00:37:21 2008 length 1 : 20973 Mon Dec 15 00:37:21 2008 length 2 : 15237 Mon Dec 15 00:37:21 2008 length 3 : 14842 Mon Dec 15 00:37:21 2008 length 4 : 12145 Mon Dec 15 00:37:21 2008 length 5 : 9070 Mon Dec 15 00:37:21 2008 length 6 : 6180 Mon Dec 15 00:37:21 2008 length 7 : 4123 Mon Dec 15 00:37:21 2008 length 9+: 5851 Mon Dec 15 00:37:21 2008 largest cycle: 21 relations Mon Dec 15 00:37:22 2008 matrix is 88075 x 88421 (23.7 MB) with weight 5862504 (66.30/col) Mon Dec 15 00:37:22 2008 sparse part has weight 5862504 (66.30/col) Mon Dec 15 00:37:23 2008 filtering completed in 3 passes Mon Dec 15 00:37:23 2008 matrix is 84357 x 84421 (22.7 MB) with weight 5613631 (66.50/col) Mon Dec 15 00:37:23 2008 sparse part has weight 5613631 (66.50/col) Mon Dec 15 00:37:23 2008 saving the first 48 matrix rows for later Mon Dec 15 00:37:23 2008 matrix is 84309 x 84421 (13.9 MB) with weight 4399038 (52.11/col) Mon Dec 15 00:37:23 2008 sparse part has weight 3132727 (37.11/col) Mon Dec 15 00:37:23 2008 matrix includes 64 packed rows Mon Dec 15 00:37:23 2008 using block size 33768 for processor cache size 1024 kB Mon Dec 15 00:37:24 2008 commencing Lanczos iteration Mon Dec 15 00:37:24 2008 memory use: 13.6 MB Mon Dec 15 00:38:11 2008 lanczos halted after 1334 iterations (dim = 84309) Mon Dec 15 00:38:11 2008 recovered 17 nontrivial dependencies Mon Dec 15 00:38:12 2008 prp42 factor: 581119780975231635970058042786794126786889 Mon Dec 15 00:38:12 2008 prp56 factor: 14240232483206706578295465829097659023799330370860981537 Mon Dec 15 00:38:12 2008 elapsed time 06:53:20
(37·10¹³⁵+71)/9 = 4(1)₁₃₄9_<136> = 3 · 157 · 217858747 · C125
C125 = P39 · P86
P39 = 448527358525322314639414749099497098067_<39>
P86 = 89325276139362337612461557618510248967981249045371777169481861806222799110277558174761_<86>

Number: 41119_135 N=40064830156333189911356119025116378434156345249498865836143135288895502259163405215369647868960104691528229503292492741286987 ( 125 digits) SNFS difficulty: 136 digits. Divisors found: r1=448527358525322314639414749099497098067 (prp39) r2=89325276139362337612461557618510248967981249045371777169481861806222799110277558174761 (prp86) Version: Total time: 4.72 hours. Scaled time: 12.09 units (timescale=2.564). Factorization parameters were as follows: name: 41119_135 n: 40064830156333189911356119025116378434156345249498865836143135288895502259163405215369647868960104691528229503292492741286987 m: 1000000000000000000000000000 deg: 5 c5: 37 c0: 71 skew: 1.14 type: snfs lss: 1 rlim: 1320000 alim: 1320000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1320000/1320000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [660000, 1335001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 193544 x 193792 Total sieving time: 4.72 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1320000,1320000,26,26,48,48,2.3,2.3,75000 total time: 4.72 hours. --------- CPU info (if available) ----------
(37·10¹³⁶+71)/9 = 4(1)₁₃₅9_<137> = 13 · 17 · 641 · C132
C132 = P56 · P76
P56 = 97340949537081992813353491071448672787822775697068133607_<56>
P76 = 2981352535792632774733519282793371700345256565006961199069479457120577812397_<76>

Number: 41119_136 N=290207686738842102703715991776925978999944311497950114082994692336713076366191902578063906870000290207686738842102703715991776925979 ( 132 digits) SNFS difficulty: 137 digits. Divisors found: r1=97340949537081992813353491071448672787822775697068133607 (prp56) r2=2981352535792632774733519282793371700345256565006961199069479457120577812397 (prp76) Version: Total time: 6.11 hours. Scaled time: 15.68 units (timescale=2.564). Factorization parameters were as follows: name: 41119_136 n: 290207686738842102703715991776925978999944311497950114082994692336713076366191902578063906870000290207686738842102703715991776925979 m: 1000000000000000000000000000 deg: 5 c5: 370 c0: 71 skew: 0.72 type: snfs lss: 1 rlim: 1370000 alim: 1370000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1370000/1370000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [685000, 1585001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 235989 x 236237 Total sieving time: 6.11 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1370000,1370000,26,26,48,48,2.3,2.3,75000 total time: 6.11 hours. --------- CPU info (if available) ----------
(37·10¹³⁷+53)/9 = 4(1)₁₃₆7_<138> = 3 · 7 · 71 · 349 · 17099 · 19001790168617_<14> · C115
C115 = P41 · P75
P41 = 19452637518709047440619598197258467357591_<41>
P75 = 125000692705880011030652701485196569731361764165251859204813732182028498671_<75>

Number: 41117_137 N=2431593164795021863019909687564068078352019780269255567935109822583356900993305863658209861643608160856750225261561 ( 115 digits) SNFS difficulty: 139 digits. Divisors found: r1=19452637518709047440619598197258467357591 (prp41) r2=125000692705880011030652701485196569731361764165251859204813732182028498671 (prp75) Version: Total time: 8.30 hours. Scaled time: 16.37 units (timescale=1.972). Factorization parameters were as follows: name: 41117_137 n: 2431593164795021863019909687564068078352019780269255567935109822583356900993305863658209861643608160856750225261561 m: 2000000000000000000000000000 deg: 5 c5: 925 c0: 424 skew: 0.86 type: snfs lss: 1 rlim: 1480000 alim: 1480000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1480000/1480000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [740000, 1640001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 247956 x 248204 Total sieving time: 8.30 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1480000,1480000,26,26,48,48,2.3,2.3,75000 total time: 8.30 hours. --------- CPU info (if available) ----------
(37·10¹⁴³+53)/9 = 4(1)₁₄₂7_<144> = 3² · 7 · 1093 · 6362389073_<10> · 224734168564901_<15> · 3210362852397241_<16> · C100
C100 = P42 · P58
P42 = 418741748016711844962144967395757153592003_<42>
P58 = 3106052477718236853520927156215139113532043711670312169297_<58>

Mon Dec 15 00:48:04 2008 Msieve v. 1.39 Mon Dec 15 00:48:04 2008 random seeds: dc2fd100 c9e6d64e Mon Dec 15 00:48:04 2008 factoring 1300633843951373418973286402129012722051843503962648717536449548299399464906466570381194546601331891 (100 digits) Mon Dec 15 00:48:05 2008 searching for 15-digit factors Mon Dec 15 00:48:06 2008 commencing quadratic sieve (100-digit input) Mon Dec 15 00:48:06 2008 using multiplier of 59 Mon Dec 15 00:48:06 2008 using 32kb Intel Core sieve core Mon Dec 15 00:48:06 2008 sieve interval: 36 blocks of size 32768 Mon Dec 15 00:48:06 2008 processing polynomials in batches of 6 Mon Dec 15 00:48:06 2008 using a sieve bound of 2671787 (97647 primes) Mon Dec 15 00:48:06 2008 using large prime bound of 400768050 (28 bits) Mon Dec 15 00:48:06 2008 using double large prime bound of 3056381387395500 (43-52 bits) Mon Dec 15 00:48:06 2008 using trial factoring cutoff of 52 bits Mon Dec 15 00:48:06 2008 polynomial 'A' values have 13 factors Mon Dec 15 12:57:16 2008 97874 relations (23045 full + 74829 combined from 1471490 partial), need 97743 Mon Dec 15 12:57:18 2008 begin with 1494535 relations Mon Dec 15 12:57:20 2008 reduce to 259594 relations in 11 passes Mon Dec 15 12:57:20 2008 attempting to read 259594 relations Mon Dec 15 12:57:25 2008 recovered 259594 relations Mon Dec 15 12:57:25 2008 recovered 251345 polynomials Mon Dec 15 12:57:25 2008 attempting to build 97874 cycles Mon Dec 15 12:57:25 2008 found 97874 cycles in 6 passes Mon Dec 15 12:57:25 2008 distribution of cycle lengths: Mon Dec 15 12:57:25 2008 length 1 : 23045 Mon Dec 15 12:57:25 2008 length 2 : 16691 Mon Dec 15 12:57:25 2008 length 3 : 16220 Mon Dec 15 12:57:25 2008 length 4 : 13422 Mon Dec 15 12:57:25 2008 length 5 : 10290 Mon Dec 15 12:57:25 2008 length 6 : 7121 Mon Dec 15 12:57:25 2008 length 7 : 4546 Mon Dec 15 12:57:25 2008 length 9+: 6539 Mon Dec 15 12:57:25 2008 largest cycle: 23 relations Mon Dec 15 12:57:25 2008 matrix is 97647 x 97874 (27.4 MB) with weight 6794219 (69.42/col) Mon Dec 15 12:57:25 2008 sparse part has weight 6794219 (69.42/col) Mon Dec 15 12:57:27 2008 filtering completed in 3 passes Mon Dec 15 12:57:27 2008 matrix is 93927 x 93990 (26.4 MB) with weight 6556190 (69.75/col) Mon Dec 15 12:57:27 2008 sparse part has weight 6556190 (69.75/col) Mon Dec 15 12:57:27 2008 saving the first 48 matrix rows for later Mon Dec 15 12:57:27 2008 matrix is 93879 x 93990 (16.5 MB) with weight 5222311 (55.56/col) Mon Dec 15 12:57:27 2008 sparse part has weight 3768024 (40.09/col) Mon Dec 15 12:57:27 2008 matrix includes 64 packed rows Mon Dec 15 12:57:27 2008 using block size 37596 for processor cache size 1024 kB Mon Dec 15 12:57:28 2008 commencing Lanczos iteration Mon Dec 15 12:57:28 2008 memory use: 15.9 MB Mon Dec 15 12:58:34 2008 lanczos halted after 1485 iterations (dim = 93877) Mon Dec 15 12:58:34 2008 recovered 16 nontrivial dependencies Mon Dec 15 12:58:35 2008 prp42 factor: 418741748016711844962144967395757153592003 Mon Dec 15 12:58:35 2008 prp58 factor: 3106052477718236853520927156215139113532043711670312169297 Mon Dec 15 12:58:35 2008 elapsed time 12:10:31
Dec 15, 2008 (3rd): Factorizations of 100...003 have been extended up to n=250. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Dec 15, 2008 (2nd): Factorizations of 422...221 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.
Dec 15, 2008: By Serge Batalov / PFGW
(8·10¹²²⁶⁰+1)/9 = (8)₁₂₂₅₉9_<12260> is PRP.
(8·10¹²³⁴¹+1)/9 = (8)₁₂₃₄₀9_<12341> is PRP.
(8·10¹³⁷⁶⁰+1)/9 = (8)₁₃₇₅₉9_<13760> is PRP.
Dec 14, 2008 (5th): By Robert Backstrom / Msieve, GMP-ECM
(37·10¹⁶⁵+71)/9 = 4(1)₁₆₄9_<166> = 3 · 5857 · 24499 · 299407691567021461_<18> · 64864715580932555437_<20> · 214518310799772616827199181657_<30> · C91
C91 = P37 · P54
P37 = 2456479326290440166586254085782156353_<37>
P54 = 933180006098833852846401252904487652104420827030262863_<54>

Sun Dec 14 14:20:07 2008 Sun Dec 14 14:20:07 2008 Sun Dec 14 14:20:07 2008 Msieve v. 1.39 Sun Dec 14 14:20:07 2008 random seeds: a9642068 c7f4fd37 Sun Dec 14 14:20:07 2008 factoring 2292337392689372228652417839233158652643250786585474807666277446662451849304779576555418639 (91 digits) Sun Dec 14 14:20:08 2008 searching for 15-digit factors Sun Dec 14 14:20:09 2008 commencing quadratic sieve (91-digit input) Sun Dec 14 14:20:09 2008 using multiplier of 1 Sun Dec 14 14:20:09 2008 using 64kb Opteron sieve core Sun Dec 14 14:20:09 2008 sieve interval: 18 blocks of size 65536 Sun Dec 14 14:20:09 2008 processing polynomials in batches of 6 Sun Dec 14 14:20:09 2008 using a sieve bound of 1682287 (63529 primes) Sun Dec 14 14:20:09 2008 using large prime bound of 154770404 (27 bits) Sun Dec 14 14:20:09 2008 using double large prime bound of 551363682974648 (42-49 bits) Sun Dec 14 14:20:09 2008 using trial factoring cutoff of 49 bits Sun Dec 14 14:20:09 2008 polynomial 'A' values have 12 factors Sun Dec 14 15:25:56 2008 64164 relations (16520 full + 47644 combined from 732118 partial), need 63625 Sun Dec 14 15:25:57 2008 begin with 748638 relations Sun Dec 14 15:25:57 2008 reduce to 159269 relations in 9 passes Sun Dec 14 15:25:57 2008 attempting to read 159269 relations Sun Dec 14 15:25:59 2008 recovered 159269 relations Sun Dec 14 15:25:59 2008 recovered 138487 polynomials Sun Dec 14 15:25:59 2008 attempting to build 64164 cycles Sun Dec 14 15:25:59 2008 found 64164 cycles in 5 passes Sun Dec 14 15:26:00 2008 distribution of cycle lengths: Sun Dec 14 15:26:00 2008 length 1 : 16520 Sun Dec 14 15:26:00 2008 length 2 : 12059 Sun Dec 14 15:26:00 2008 length 3 : 11161 Sun Dec 14 15:26:00 2008 length 4 : 8627 Sun Dec 14 15:26:00 2008 length 5 : 6320 Sun Dec 14 15:26:00 2008 length 6 : 4020 Sun Dec 14 15:26:00 2008 length 7 : 2506 Sun Dec 14 15:26:00 2008 length 9+: 2951 Sun Dec 14 15:26:00 2008 largest cycle: 18 relations Sun Dec 14 15:26:00 2008 matrix is 63529 x 64164 (16.0 MB) with weight 3927565 (61.21/col) Sun Dec 14 15:26:00 2008 sparse part has weight 3927565 (61.21/col) Sun Dec 14 15:26:01 2008 filtering completed in 4 passes Sun Dec 14 15:26:01 2008 matrix is 59617 x 59681 (14.8 MB) with weight 3649747 (61.15/col) Sun Dec 14 15:26:01 2008 sparse part has weight 3649747 (61.15/col) Sun Dec 14 15:26:01 2008 saving the first 48 matrix rows for later Sun Dec 14 15:26:01 2008 matrix is 59569 x 59681 (9.5 MB) with weight 2881639 (48.28/col) Sun Dec 14 15:26:01 2008 sparse part has weight 2126116 (35.62/col) Sun Dec 14 15:26:01 2008 matrix includes 64 packed rows Sun Dec 14 15:26:01 2008 using block size 23872 for processor cache size 1024 kB Sun Dec 14 15:26:01 2008 commencing Lanczos iteration Sun Dec 14 15:26:01 2008 memory use: 9.2 MB Sun Dec 14 15:26:22 2008 lanczos halted after 944 iterations (dim = 59567) Sun Dec 14 15:26:22 2008 recovered 16 nontrivial dependencies Sun Dec 14 15:26:23 2008 prp37 factor: 2456479326290440166586254085782156353 Sun Dec 14 15:26:23 2008 prp54 factor: 933180006098833852846401252904487652104420827030262863 Sun Dec 14 15:26:23 2008 elapsed time 01:06:16
(37·10¹⁴²+53)/9 = 4(1)₁₄₁7_<143> = 229 · 293 · 311363441 · 4290945583_<10> · 247255819459871080939110673_<27> · C94
C94 = P44 · P51
P44 = 16862793440103708198532263801272697174262183_<44>
P51 = 109991581016708918525866831687260181943473154034893_<51>

Sun Dec 14 18:57:25 2008 Sun Dec 14 18:57:25 2008 Sun Dec 14 18:57:25 2008 Msieve v. 1.39 Sun Dec 14 18:57:25 2008 random seeds: 0a9bc040 124024ef Sun Dec 14 18:57:25 2008 factoring 1854765310835194710428440106540308919972924293904205223172756617211856527940960640436712351419 (94 digits) Sun Dec 14 18:57:26 2008 searching for 15-digit factors Sun Dec 14 18:57:26 2008 commencing quadratic sieve (94-digit input) Sun Dec 14 18:57:27 2008 using multiplier of 11 Sun Dec 14 18:57:27 2008 using 64kb Opteron sieve core Sun Dec 14 18:57:27 2008 sieve interval: 18 blocks of size 65536 Sun Dec 14 18:57:27 2008 processing polynomials in batches of 6 Sun Dec 14 18:57:27 2008 using a sieve bound of 1991609 (73982 primes) Sun Dec 14 18:57:27 2008 using large prime bound of 256917561 (27 bits) Sun Dec 14 18:57:27 2008 using double large prime bound of 1372868018887893 (42-51 bits) Sun Dec 14 18:57:27 2008 using trial factoring cutoff of 51 bits Sun Dec 14 18:57:27 2008 polynomial 'A' values have 12 factors Sun Dec 14 21:16:14 2008 74176 relations (17786 full + 56390 combined from 1040543 partial), need 74078 Sun Dec 14 21:16:16 2008 begin with 1058329 relations Sun Dec 14 21:16:17 2008 reduce to 194080 relations in 12 passes Sun Dec 14 21:16:17 2008 attempting to read 194080 relations Sun Dec 14 21:16:20 2008 recovered 194080 relations Sun Dec 14 21:16:20 2008 recovered 179104 polynomials Sun Dec 14 21:16:20 2008 attempting to build 74176 cycles Sun Dec 14 21:16:20 2008 found 74176 cycles in 5 passes Sun Dec 14 21:16:21 2008 distribution of cycle lengths: Sun Dec 14 21:16:21 2008 length 1 : 17786 Sun Dec 14 21:16:21 2008 length 2 : 12925 Sun Dec 14 21:16:21 2008 length 3 : 12410 Sun Dec 14 21:16:21 2008 length 4 : 10031 Sun Dec 14 21:16:21 2008 length 5 : 7751 Sun Dec 14 21:16:21 2008 length 6 : 5177 Sun Dec 14 21:16:21 2008 length 7 : 3373 Sun Dec 14 21:16:21 2008 length 9+: 4723 Sun Dec 14 21:16:21 2008 largest cycle: 20 relations Sun Dec 14 21:16:21 2008 matrix is 73982 x 74176 (19.3 MB) with weight 4766529 (64.26/col) Sun Dec 14 21:16:21 2008 sparse part has weight 4766529 (64.26/col) Sun Dec 14 21:16:22 2008 filtering completed in 3 passes Sun Dec 14 21:16:22 2008 matrix is 70626 x 70690 (18.5 MB) with weight 4567849 (64.62/col) Sun Dec 14 21:16:22 2008 sparse part has weight 4567849 (64.62/col) Sun Dec 14 21:16:22 2008 saving the first 48 matrix rows for later Sun Dec 14 21:16:22 2008 matrix is 70578 x 70690 (11.4 MB) with weight 3550378 (50.22/col) Sun Dec 14 21:16:22 2008 sparse part has weight 2567736 (36.32/col) Sun Dec 14 21:16:22 2008 matrix includes 64 packed rows Sun Dec 14 21:16:22 2008 using block size 28276 for processor cache size 1024 kB Sun Dec 14 21:16:23 2008 commencing Lanczos iteration Sun Dec 14 21:16:23 2008 memory use: 11.2 MB Sun Dec 14 21:16:55 2008 lanczos halted after 1117 iterations (dim = 70576) Sun Dec 14 21:16:55 2008 recovered 17 nontrivial dependencies Sun Dec 14 21:16:56 2008 prp44 factor: 16862793440103708198532263801272697174262183 Sun Dec 14 21:16:56 2008 prp51 factor: 109991581016708918525866831687260181943473154034893 Sun Dec 14 21:16:56 2008 elapsed time 02:19:31
(37·10¹²⁴+53)/9 = 4(1)₁₂₃7_<125> = 1277 · 47309 · 28722607534355557_<17> · C101
C101 = P36 · P66
P36 = 195169974164679173582454440992292441_<36>
P66 = 121391333009391162020765580291934643735513437889339216293015715737_<66>

GMP-ECM 6.2.1 [powered by GMP 4.2.4] [ECM] Input number is 23691943327258839247481664570054627580787232775552733193324809100671477449073888934217058100029844017 (101 digits) Using B1=1752000, B2=2140281790, polynomial Dickson(6), sigma=1759735969 Step 1 took 16760ms Step 2 took 5941ms ********** Factor found in step 2: 195169974164679173582454440992292441 Found probable prime factor of 36 digits: 195169974164679173582454440992292441 Probable prime cofactor 121391333009391162020765580291934643735513437889339216293015715737 has 66 digits
Dec 14, 2008 (4th): By Justin Card / ggnfs / msieve
(10¹⁸⁵+17)/9 = (1)₁₈₄3_<185> = 107 · 42403 · 4463369 · 97950977 · C163
C163 = P47 · P53 · P64
P47 = 15114737110291755253865525542276220443845732191_<47>
P53 = 62215924351208704620214741244687970502124398308107141_<53>
P64 = 5956668182002404597436168891848003944513400860278422888622352051_<64>

Sieve time, ~ Thu Dec 11 06:25:45 2008 Msieve v. 1.39 Thu Dec 11 06:25:45 2008 random seeds: c119b89d 3c60b76b Thu Dec 11 06:25:45 2008 factoring 5601515784080136495058260409669476551922366725684158384351571184319213658664583664274625015281983236076984038434575826619948188356950956656183633054869264464184481 (163 digits) Thu Dec 11 06:25:47 2008 searching for 15-digit factors Thu Dec 11 06:25:48 2008 commencing number field sieve (163-digit input) Thu Dec 11 06:25:48 2008 R0: -10000000000000000000000000000000000000 Thu Dec 11 06:25:48 2008 R1: 1 Thu Dec 11 06:25:48 2008 A0: 17 Thu Dec 11 06:25:48 2008 A1: 0 Thu Dec 11 06:25:48 2008 A2: 0 Thu Dec 11 06:25:48 2008 A3: 0 Thu Dec 11 06:25:48 2008 A4: 0 Thu Dec 11 06:25:48 2008 A5: 1 Thu Dec 11 06:25:48 2008 skew 0.00, size 1.649244e-12, alpha 1.047729, combined = 1.163083e-12 Thu Dec 11 06:25:48 2008 Thu Dec 11 06:25:48 2008 commencing relation filtering Thu Dec 11 06:25:48 2008 commencing duplicate removal, pass 1 Thu Dec 11 06:28:46 2008 error -9 reading relation 14190429 Thu Dec 11 06:28:55 2008 error -9 reading relation 14949426 Thu Dec 11 06:29:13 2008 error -15 reading relation 16595032 Thu Dec 11 06:29:25 2008 error -9 reading relation 17527780 Thu Dec 11 06:29:35 2008 error -15 reading relation 18356803 Thu Dec 11 06:30:11 2008 found 3465609 hash collisions in 21585522 relations Thu Dec 11 06:31:19 2008 added 24327 free relations Thu Dec 11 06:31:19 2008 commencing duplicate removal, pass 2 Thu Dec 11 06:31:37 2008 found 3270865 duplicates and 18338984 unique relations Thu Dec 11 06:31:37 2008 memory use: 94.6 MB Thu Dec 11 06:31:37 2008 reading rational ideals above 8716288 Thu Dec 11 06:31:37 2008 reading algebraic ideals above 8716288 Thu Dec 11 06:31:37 2008 commencing singleton removal, pass 1 Thu Dec 11 06:35:35 2008 relations with 0 large ideals: 230675 Thu Dec 11 06:35:35 2008 relations with 1 large ideals: 1542279 Thu Dec 11 06:35:35 2008 relations with 2 large ideals: 4605346 Thu Dec 11 06:35:35 2008 relations with 3 large ideals: 6337724 Thu Dec 11 06:35:35 2008 relations with 4 large ideals: 3878423 Thu Dec 11 06:35:35 2008 relations with 5 large ideals: 969234 Thu Dec 11 06:35:35 2008 relations with 6 large ideals: 771397 Thu Dec 11 06:35:35 2008 relations with 7+ large ideals: 3906 Thu Dec 11 06:35:35 2008 18338984 relations and about 18219864 large ideals Thu Dec 11 06:35:35 2008 commencing singleton removal, pass 2 Thu Dec 11 06:39:35 2008 found 6773463 singletons Thu Dec 11 06:39:35 2008 current dataset: 11565521 relations and about 9662777 large ideals Thu Dec 11 06:39:35 2008 commencing singleton removal, pass 3 Thu Dec 11 06:41:58 2008 found 1929828 singletons Thu Dec 11 06:41:58 2008 current dataset: 9635693 relations and about 7596307 large ideals Thu Dec 11 06:41:58 2008 commencing singleton removal, pass 4 Thu Dec 11 06:43:59 2008 found 559893 singletons Thu Dec 11 06:43:59 2008 current dataset: 9075800 relations and about 7022668 large ideals Thu Dec 11 06:43:59 2008 commencing singleton removal, pass 5 Thu Dec 11 06:45:52 2008 found 175568 singletons Thu Dec 11 06:45:52 2008 current dataset: 8900232 relations and about 6845659 large ideals Thu Dec 11 06:45:52 2008 commencing singleton removal, final pass Thu Dec 11 06:47:54 2008 memory use: 157.8 MB Thu Dec 11 06:47:55 2008 commencing in-memory singleton removal Thu Dec 11 06:47:56 2008 begin with 8900232 relations and 7598828 unique ideals Thu Dec 11 06:48:16 2008 reduce to 7009060 relations and 5642900 ideals in 18 passes Thu Dec 11 06:48:16 2008 max relations containing the same ideal: 24 Thu Dec 11 06:48:18 2008 reading rational ideals above 720000 Thu Dec 11 06:48:18 2008 reading algebraic ideals above 720000 Thu Dec 11 06:48:18 2008 commencing singleton removal, final pass Thu Dec 11 06:50:15 2008 keeping 6366128 ideals with weight <= 20, new excess is 589025 Thu Dec 11 06:50:21 2008 memory use: 183.7 MB Thu Dec 11 06:50:21 2008 commencing in-memory singleton removal Thu Dec 11 06:50:22 2008 begin with 7033399 relations and 6366128 unique ideals Thu Dec 11 06:50:37 2008 reduce to 7004721 relations and 6218178 ideals in 11 passes Thu Dec 11 06:50:37 2008 max relations containing the same ideal: 20 Thu Dec 11 06:50:43 2008 removing 599456 relations and 547819 ideals in 51637 cliques Thu Dec 11 06:50:44 2008 commencing in-memory singleton removal Thu Dec 11 06:50:45 2008 begin with 6405265 relations and 6218178 unique idealsThu Dec 11 06:50:57 2008 reduce to 6365591 relations and 5630271 ideals in 10 passes Thu Dec 11 06:50:57 2008 max relations containing the same ideal: 20 Thu Dec 11 06:51:03 2008 removing 432595 relations and 380958 ideals in 51637 cliques Thu Dec 11 06:51:03 2008 commencing in-memory singleton removal Thu Dec 11 06:51:04 2008 begin with 5932996 relations and 5630271 unique ideals Thu Dec 11 06:51:13 2008 reduce to 5909684 relations and 5225798 ideals in 8 passes Thu Dec 11 06:51:13 2008 max relations containing the same ideal: 20 Thu Dec 11 06:51:20 2008 relations with 0 large ideals: 43999 Thu Dec 11 06:51:20 2008 relations with 1 large ideals: 279962 Thu Dec 11 06:51:20 2008 relations with 2 large ideals: 938340 Thu Dec 11 06:51:20 2008 relations with 3 large ideals: 1640855 Thu Dec 11 06:51:20 2008 relations with 4 large ideals: 1630210 Thu Dec 11 06:51:20 2008 relations with 5 large ideals: 952681 Thu Dec 11 06:51:20 2008 relations with 6 large ideals: 358387 Thu Dec 11 06:51:20 2008 relations with 7+ large ideals: 65250 Thu Dec 11 06:51:20 2008 commencing 2-way merge Thu Dec 11 06:51:27 2008 reduce to 3478218 relation sets and 2794332 unique ideals Thu Dec 11 06:51:27 2008 commencing full merge Thu Dec 11 06:52:41 2008 memory use: 269.3 MB Thu Dec 11 06:52:42 2008 found 1701886 cycles, need 1614532 Thu Dec 11 06:52:43 2008 weight of 1614532 cycles is about 113141746 (70.08/cycle) Thu Dec 11 06:52:43 2008 distribution of cycle lengths: Thu Dec 11 06:52:43 2008 1 relations: 209342 Thu Dec 11 06:52:43 2008 2 relations: 191075 Thu Dec 11 06:52:43 2008 3 relations: 185586 Thu Dec 11 06:52:43 2008 4 relations: 165144 Thu Dec 11 06:52:43 2008 5 relations: 146133 Thu Dec 11 06:52:43 2008 6 relations: 126188 Thu Dec 11 06:52:43 2008 7 relations: 106578 Thu Dec 11 06:52:43 2008 8 relations: 93386 Thu Dec 11 06:52:43 2008 9 relations: 78985 Thu Dec 11 06:52:43 2008 10+ relations: 312115 Thu Dec 11 06:52:43 2008 heaviest cycle: 20 relations Thu Dec 11 06:52:44 2008 commencing cycle optimization Thu Dec 11 06:52:48 2008 start with 9412575 relations Thu Dec 11 06:53:15 2008 pruned 235166 relations Thu Dec 11 06:53:15 2008 memory use: 315.3 MB Thu Dec 11 06:53:15 2008 distribution of cycle lengths: Thu Dec 11 06:53:15 2008 1 relations: 209342 Thu Dec 11 06:53:15 2008 2 relations: 195784 Thu Dec 11 06:53:15 2008 3 relations: 192349 Thu Dec 11 06:53:15 2008 4 relations: 169452 Thu Dec 11 06:53:15 2008 5 relations: 149844 Thu Dec 11 06:53:15 2008 6 relations: 127591 Thu Dec 11 06:53:15 2008 7 relations: 107695 Thu Dec 11 06:53:15 2008 8 relations: 93119 Thu Dec 11 06:53:15 2008 9 relations: 78380 Thu Dec 11 06:53:15 2008 10+ relations: 290976 Thu Dec 11 06:53:15 2008 heaviest cycle: 20 relations Thu Dec 11 06:53:21 2008 elapsed time 00:27:36 Fri Dec 12 20:24:42 2008 Msieve v. 1.39 Fri Dec 12 20:24:42 2008 random seeds: 8a67411e b53fa8c3 Fri Dec 12 20:24:42 2008 factoring 5601515784080136495058260409669476551922366725684158384351571184319213658664583664274625015281983236076984038434575826619948188356950956656183633054869264464184481 (163 digits) Fri Dec 12 20:24:45 2008 searching for 15-digit factors Fri Dec 12 20:24:46 2008 commencing number field sieve (163-digit input) Fri Dec 12 20:24:46 2008 R0: -10000000000000000000000000000000000000 Fri Dec 12 20:24:46 2008 R1: 1 Fri Dec 12 20:24:46 2008 A0: 17 Fri Dec 12 20:24:46 2008 A1: 0 Fri Dec 12 20:24:46 2008 A2: 0 Fri Dec 12 20:24:46 2008 A3: 0 Fri Dec 12 20:24:46 2008 A4: 0 Fri Dec 12 20:24:46 2008 A5: 1 Fri Dec 12 20:24:46 2008 skew 0.00, size 1.649244e-12, alpha 1.047729, combined = 1.163083e-12 Fri Dec 12 20:24:46 2008 Fri Dec 12 20:24:46 2008 commencing linear algebra Fri Dec 12 20:24:47 2008 read 1599998 cycles Fri Dec 12 20:24:54 2008 cycles contain 5294098 unique relations Fri Dec 12 20:26:00 2008 read 5294098 relations Fri Dec 12 20:26:14 2008 using 20 quadratic characters above 268434548 Fri Dec 12 20:27:04 2008 building initial matrix Fri Dec 12 20:28:25 2008 memory use: 643.5 MB Fri Dec 12 20:28:27 2008 read 1599998 cycles Fri Dec 12 20:28:29 2008 matrix is 1599798 x 1599998 (480.2 MB) with weight 141340528 (88.34/col) Fri Dec 12 20:28:29 2008 sparse part has weight 108280053 (67.68/col) Fri Dec 12 20:28:55 2008 filtering completed in 1 passes Fri Dec 12 20:28:55 2008 matrix is 1599798 x 1599998 (480.2 MB) with weight 141340528 (88.34/col) Fri Dec 12 20:28:55 2008 sparse part has weight 108280053 (67.68/col) Fri Dec 12 20:29:10 2008 read 1599998 cycles Fri Dec 12 20:29:12 2008 matrix is 1599798 x 1599998 (480.2 MB) with weight 141340528 (88.34/col) Fri Dec 12 20:29:12 2008 sparse part has weight 108280053 (67.68/col) Fri Dec 12 20:29:12 2008 saving the first 48 matrix rows for later Fri Dec 12 20:29:13 2008 matrix is 1599750 x 1599998 (452.7 MB) with weight 111950279 (69.97/col) Fri Dec 12 20:29:13 2008 sparse part has weight 102665798 (64.17/col) Fri Dec 12 20:29:13 2008 matrix includes 64 packed rows Fri Dec 12 20:29:13 2008 using block size 10922 for processor cache size 256 kB Fri Dec 12 20:29:23 2008 commencing Lanczos iteration (2 threads) Fri Dec 12 20:29:23 2008 memory use: 448.0 MB Sat Dec 13 00:51:35 2008 lanczos error: submatrix is not invertible Sat Dec 13 00:51:35 2008 lanczos halted after 7210 iterations (dim = 455967) Sat Dec 13 00:51:35 2008 linear algebra failed; retrying... Sat Dec 13 00:51:35 2008 commencing Lanczos iteration (2 threads) Sat Dec 13 00:51:35 2008 memory use: 448.0 MB Sat Dec 13 16:07:31 2008 lanczos halted after 25302 iterations (dim = 1599744) Sat Dec 13 16:07:38 2008 recovered 31 nontrivial dependencies Sat Dec 13 16:07:38 2008 elapsed time 19:42:56 Sat Dec 13 18:12:48 2008 Sat Dec 13 18:12:48 2008 Sat Dec 13 18:12:48 2008 Msieve v. 1.39 Sat Dec 13 18:12:48 2008 random seeds: 595748d8 c5a6942b Sat Dec 13 18:12:48 2008 factoring 5601515784080136495058260409669476551922366725684158384351571184319213658664583664274625015281983236076984038434575826619948188356950956656183633054869264464184481 (163 digits) Sat Dec 13 18:12:49 2008 searching for 15-digit factors Sat Dec 13 18:12:51 2008 commencing number field sieve (163-digit input) Sat Dec 13 18:12:51 2008 R0: -10000000000000000000000000000000000000 Sat Dec 13 18:12:51 2008 R1: 1 Sat Dec 13 18:12:51 2008 A0: 17 Sat Dec 13 18:12:51 2008 A1: 0 Sat Dec 13 18:12:51 2008 A2: 0 Sat Dec 13 18:12:51 2008 A3: 0 Sat Dec 13 18:12:51 2008 A4: 0 Sat Dec 13 18:12:51 2008 A5: 1 Sat Dec 13 18:12:51 2008 skew 0.00, size 1.649244e-12, alpha 1.047729, combined = 1.163083e-12 Sat Dec 13 18:12:51 2008 Sat Dec 13 18:12:51 2008 commencing square root phase Sat Dec 13 18:12:51 2008 reading relations for dependency 1 Sat Dec 13 18:12:51 2008 read 800041 cycles Sat Dec 13 18:12:54 2008 cycles contain 3218627 unique relations Sat Dec 13 18:13:39 2008 read 3218627 relations Sat Dec 13 18:14:03 2008 multiplying 2646900 relations Sat Dec 13 18:18:29 2008 multiply complete, coefficients have about 59.07 million bits Sat Dec 13 18:18:31 2008 initial square root is modulo 301859771 Sat Dec 13 18:27:26 2008 reading relations for dependency 2 Sat Dec 13 18:27:27 2008 read 799909 cycles Sat Dec 13 18:27:30 2008 cycles contain 3215839 unique relations Sat Dec 13 18:28:13 2008 read 3215839 relations Sat Dec 13 18:28:37 2008 multiplying 2645928 relations Sat Dec 13 18:33:02 2008 multiply complete, coefficients have about 59.05 million bits Sat Dec 13 18:33:04 2008 initial square root is modulo 299845591 Sat Dec 13 18:41:52 2008 Newton iteration failed to converge Sat Dec 13 18:41:52 2008 algebraic square root failed Sat Dec 13 18:41:52 2008 reading relations for dependency 3 Sat Dec 13 18:41:53 2008 read 800016 cycles Sat Dec 13 18:41:56 2008 cycles contain 3214264 unique relations Sat Dec 13 18:42:37 2008 read 3214264 relations Sat Dec 13 18:43:02 2008 multiplying 2644520 relations Sat Dec 13 18:47:26 2008 multiply complete, coefficients have about 59.01 million bits Sat Dec 13 18:47:28 2008 initial square root is modulo 296690551 Sat Dec 13 18:56:23 2008 prp47 factor: 15114737110291755253865525542276220443845732191 Sat Dec 13 18:56:23 2008 prp53 factor: 62215924351208704620214741244687970502124398308107141 Sat Dec 13 18:56:23 2008 prp64 factor: 5956668182002404597436168891848003944513400860278422888622352051 Sat Dec 13 18:56:23 2008 elapsed time 00:43:35
Dec 14, 2008 (3rd): By Serge Batalov / GMP-ECM 6.2.1, GMP-ECM 6.2.1; msieve/QS, Msieve-1.39
(37·10¹⁹¹+71)/9 = 4(1)₁₉₀9_<192> = 19 · 163 · 227 · 8221 · 220274727766969_<15> · 47092463385596851290407_<23> · 256080813541464866622802649_<27> · 16242434872628753856635344333_<29> · C91
C91 = P31 · P60
P31 = 4636700600036784458682270386851_<31>
P60 = 355561060921631143485837742682771800699261664861095825932721_<60>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2648465071 Step 1 took 5340ms Step 2 took 3444ms ********** Factor found in step 2: 4636700600036784458682270386851 Found probable prime factor of 31 digits: 4636700600036784458682270386851 Probable prime cofactor 355561060921631143485837742682771800699261664861095825932721 has 60 digits
(37·10¹⁴⁴+71)/9 = 4(1)₁₄₃9_<145> = 3 · 23 · 7400711 · 408887911 · 20186612443_<11> · 29905721311256110223_<20> · C98
C98 = P36 · P62
P36 = 618775808407328473965636674049547033_<36>
P62 = 52708584683780887941137184058447905146401641743810396364826463_<62>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3429082305 Step 1 took 6624ms Step 2 took 3648ms ********** Factor found in step 2: 618775808407328473965636674049547033 Found probable prime factor of 36 digits: 618775808407328473965636674049547033 Probable prime cofactor 52708584683780887941137184058447905146401641743810396364826463 has 62 digits
(37·10¹⁷⁶+53)/9 = 4(1)₁₇₅7_<177> = 3 · 45963274037027449_<17> · 218721874752653920697929367_<27> · 167559923470916489335366527497_<30> · C104
C104 = P32 · P32 · P41
P32 = 15102382275566300653137564378239_<32>
P32 = 91977583043394794293256969720219_<32>
P41 = 58564869249345584602048726485816313603829_<41>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3150125923 Step 1 took 6465ms ********** Factor found in step 1: 91977583043394794293256969720219 Found probable prime factor of 32 digits: 91977583043394794293256969720219 Composite cofactor has 72 digits Sat Dec 13 15:36:47 2008 Msieve v. 1.39 Sat Dec 13 15:36:47 2008 random seeds: ff568006 9809a85b Sat Dec 13 15:36:47 2008 factoring 884469043322174635950314079773456828426465440667479238633610773754677131 (72 digits) Sat Dec 13 15:36:47 2008 searching for 15-digit factors Sat Dec 13 15:36:48 2008 commencing quadratic sieve (72-digit input) Sat Dec 13 15:36:48 2008 using multiplier of 1 Sat Dec 13 15:36:48 2008 using 64kb Opteron sieve core Sat Dec 13 15:36:48 2008 sieve interval: 6 blocks of size 65536 Sat Dec 13 15:36:48 2008 processing polynomials in batches of 17 Sat Dec 13 15:36:48 2008 using a sieve bound of 414311 (17438 primes) Sat Dec 13 15:36:48 2008 using large prime bound of 41431100 (25 bits) Sat Dec 13 15:36:48 2008 using trial factoring cutoff of 25 bits Sat Dec 13 15:36:48 2008 polynomial 'A' values have 9 factors Sat Dec 13 15:39:26 2008 17777 relations (8871 full + 8906 combined from 97264 partial), need 17534 Sat Dec 13 15:39:27 2008 begin with 106135 relations Sat Dec 13 15:39:27 2008 reduce to 25588 relations in 2 passes Sat Dec 13 15:39:27 2008 attempting to read 25588 relations Sat Dec 13 15:39:27 2008 recovered 25588 relations Sat Dec 13 15:39:27 2008 recovered 19369 polynomials Sat Dec 13 15:39:27 2008 attempting to build 17777 cycles Sat Dec 13 15:39:27 2008 found 17777 cycles in 1 passes Sat Dec 13 15:39:27 2008 distribution of cycle lengths: Sat Dec 13 15:39:27 2008 length 1 : 8871 Sat Dec 13 15:39:27 2008 length 2 : 8906 Sat Dec 13 15:39:27 2008 largest cycle: 2 relations Sat Dec 13 15:39:27 2008 matrix is 17438 x 17777 (2.5 MB) with weight 515169 (28.98/col) Sat Dec 13 15:39:27 2008 sparse part has weight 515169 (28.98/col) Sat Dec 13 15:39:27 2008 filtering completed in 3 passes Sat Dec 13 15:39:27 2008 matrix is 12817 x 12880 (2.0 MB) with weight 411137 (31.92/col) Sat Dec 13 15:39:27 2008 sparse part has weight 411137 (31.92/col) Sat Dec 13 15:39:27 2008 saving the first 48 matrix rows for later Sat Dec 13 15:39:27 2008 matrix is 12769 x 12880 (1.4 MB) with weight 303997 (23.60/col) Sat Dec 13 15:39:27 2008 sparse part has weight 226977 (17.62/col) Sat Dec 13 15:39:27 2008 matrix includes 64 packed rows Sat Dec 13 15:39:27 2008 commencing Lanczos iteration Sat Dec 13 15:39:27 2008 memory use: 1.8 MB Sat Dec 13 15:39:31 2008 lanczos halted after 203 iterations (dim = 12764) Sat Dec 13 15:39:31 2008 recovered 15 nontrivial dependencies Sat Dec 13 15:39:31 2008 prp32 factor: 15102382275566300653137564378239 Sat Dec 13 15:39:31 2008 prp41 factor: 58564869249345584602048726485816313603829 Sat Dec 13 15:39:31 2008 elapsed time 00:02:44
(37·10¹³³+53)/9 = 4(1)₁₃₂7_<134> = 19² · 15163783 · 1587776027_<10> · C115
C115 = P32 · P84
P32 = 13869327544356415887390661584931_<32>
P84 = 341035670790310249149005077592957449976141974679492733387937361436382697840615082307_<84>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3785622199 Step 1 took 6436ms Step 2 took 4048ms ********** Factor found in step 2: 13869327544356415887390661584931 Found probable prime factor of 32 digits: 13869327544356415887390661584931 Probable prime cofactor 341035670790310249149005077592957449976141974679492733387937361436382697840615082307 has 84 digits
(37·10¹⁷⁹+53)/9 = 4(1)₁₇₈7_<180> = 3⁴ · 7 · 23 · 4751018479457_<13> · 13962759095755291_<17> · 49208248701391080839818523_<26> · C121
C121 = P28 · C94
P28 = 2119493083661110697017153309_<28>
C94 = [4556385302955576221884023543638349856512194802012137833352589947767890040676035957132831155593_<94>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1915012220 Step 1 took 7824ms Step 2 took 4376ms ********** Factor found in step 2: 2119493083661110697017153309 Found probable prime factor of 28 digits: 2119493083661110697017153309 Composite cofactor has 94 digits
(37·10¹⁸¹+71)/9 = 4(1)₁₈₀9_<182> = 7 · 42323 · 33379705157_<11> · 24127822888595769062376049807_<29> · C138
C138 = P35 · C103
P35 = 47573256735105102134774568941200081_<35>
C103 = [3621772899073458445059701652864566407076358975646712173315673909567467074401737345715255403591778914841_<103>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=721560188 Step 1 took 9244ms Step 2 took 4985ms ********** Factor found in step 2: 47573256735105102134774568941200081 Found probable prime factor of 35 digits: 47573256735105102134774568941200081 Composite cofactor has 103 digits
(37·10¹⁰⁴+53)/9 = 4(1)₁₀₃7_<105> = 3 · 1289213 · C99
C99 = P35 · P64
P35 = 22837832423823428406549535979434663_<35>
P64 = 4654343177283332444580397105529579718882636552190002130060404781_<64>

SNFS difficulty: 105 digits. Divisors found: r1=22837832423823428406549535979434663 (pp35) r2=4654343177283332444580397105529579718882636552190002130060404781 (pp64) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 106295109525762645146331162528641145440696794895053832870935242692275859021773001852321561322323803 m: 100000000000000000000000000 deg: 4 c4: 37 c0: 53 skew: 1.09 type: snfs lss: 1 rlim: 400000 alim: 400000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 400000/400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [200000, 250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 42219 x 42456 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,105,4,0,0,0,0,0,0,0,0,400000,400000,25,25,45,45,2.2,2.2,50000 total time: 0.50 hours.
(37·10¹⁰⁹+53)/9 = 4(1)₁₀₈7_<110> = 151 · C108
C108 = P39 · P69
P39 = 345934149021961984853714355585332061497_<39>
P69 = 787025550240151752957429692905459301021394747512814523416460876641811_<69>

SNFS difficulty: 111 digits. Divisors found: r1=345934149021961984853714355585332061497 (pp39) r2=787025550240151752957429692905459301021394747512814523416460876641811 (pp69) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.314). Factorization parameters were as follows: n: 272259013980868285504047093451066961000735835172921265636497424576894775570272259013980868285504047093451067 m: 10000000000000000000000 deg: 5 c5: 37 c0: 530 skew: 1.70 type: snfs lss: 1 rlim: 510000 alim: 510000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 510000/510000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [255000, 405001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 63238 x 63485 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,510000,510000,25,25,44,44,2.2,2.2,50000 total time: 0.50 hours.
(37·10¹⁹⁴+71)/9 = 4(1)₁₉₃9_<195> = 116269 · 575551 · 474471463 · 16349135082988589810249_<23> · C153
C153 = P31 · C123
P31 = 7590690876337436335686621759791_<31>
C123 = [104333861145851641332524267483514811395721107982807617312384858364100696592011759800416745004248697924636939449966193271653_<123>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3439223145 Step 1 took 9237ms Step 2 took 5184ms ********** Factor found in step 2: 7590690876337436335686621759791 Found probable prime factor of 31 digits: 7590690876337436335686621759791 Composite cofactor has 123 digits
(37·10¹⁸⁶+53)/9 = 4(1)₁₈₅7_<187> = 139 · 2017 · 109199 · 4908232860071_<13> · 704264442759638437_<18> · C146
C146 = P32 · C115
P32 = 10378488878367712824242152948117_<32>
C115 = [3743042944343746327051073365541314201342334703437542556352179663331113160500440981418270935251237401012936934788599_<115>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1287780505 Step 1 took 11689ms Step 2 took 6736ms ********** Factor found in step 2: 10378488878367712824242152948117 Found probable prime factor of 32 digits: 10378488878367712824242152948117 Composite cofactor has 115 digits
(37·10¹⁸²+71)/9 = 4(1)₁₈₁9_<183> = 6554489 · 1825044564102727319125284089_<28> · C149
C149 = P37 · P112
P37 = 8755789092289348926356821244998051583_<37>
P112 = 3925107994217788084008788634318649563433570976255456089438348678247691568468116466972296949254207197157811247233_<112>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3972661220 Step 1 took 11736ms Step 2 took 6719ms ********** Factor found in step 2: 8755789092289348926356821244998051583 Found probable prime factor of 37 digits: 8755789092289348926356821244998051583 Probable prime cofactor has 112 digits
(37·10¹⁶⁹+53)/9 = 4(1)₁₆₈7_<170> = 19 · C169
C169 = P33 · C136
P33 = 291511918341504324969778930777933_<33>
C136 = [7422484481487542405434963871001284300917097043855519001904556196162796366335291956314614258679614931018465138599301201369883800196508571_<136>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=104395819 Step 1 took 10737ms Step 2 took 2968ms ********** Factor found in step 2: 291511918341504324969778930777933 Found probable prime factor of 33 digits: 291511918341504324969778930777933 Composite cofactor has 136 digits
(37·10¹⁹⁵+71)/9 = 4(1)₁₉₄9_<196> = 3² · 251 · 2291104455149_<13> · C180
C180 = P31 · C150
P31 = 2450016983244960343376200468679_<31>
C150 = [324211935613233135510755071528084489947422054060634139633546393659957487226795682741016274539652285925049436071103008421381656621387039362598589743471_<150>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=45812530 Step 1 took 12433ms Step 2 took 6316ms ********** Factor found in step 2: 2450016983244960343376200468679 Found probable prime factor of 31 digits: 2450016983244960343376200468679 Composite cofactor has 150 digits
(37·10¹⁴¹+71)/9 = 4(1)₁₄₀9_<142> = 3² · 3816740789_<10> · C132
C132 = P39 · P94
P39 = 116328262062925150698065808106966699829_<39>
P94 = 1028818580921946643296788098261946277585679831371276345580742344707061170637149919562915568911_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1887761298 Step 1 took 7593ms Step 2 took 4548ms ********** Factor found in step 2: 116328262062925150698065808106966699829 Found probable prime factor of 39 digits: 116328262062925150698065808106966699829 Probable prime cofactor 1028818580921946643296788098261946277585679831371276345580742344707061170637149919562915568911 has 94 digits
(37·10¹⁹⁰+53)/9 = 4(1)₁₈₉7_<191> = 59 · 33366083669_<11> · 1038688946123696607997710239_<28> · C152
C152 = P33 · C119
P33 = 228822554008790119385212155709949_<33>
C119 = [87865347299839227077677777536365983116150872999131750437968032584396075641901842890425376739301590272179304048017141257_<119>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1937590972 Step 1 took 9284ms Step 2 took 5233ms ********** Factor found in step 2: 228822554008790119385212155709949 Found probable prime factor of 33 digits: 228822554008790119385212155709949 Composite cofactor has 119 digits
(37·10¹⁵¹+71)/9 = 4(1)₁₅₀9_<152> = 7 · 29 · 719 · C147
C147 = P36 · P111
P36 = 493619702531188780719146460090685151_<36>
P111 = 570613182110476873637098969632150989726981775506952535058010084196523573240634138994101843197569157770130203517_<111>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1976020518 Step 1 took 9117ms Step 2 took 5172ms ********** Factor found in step 2: 493619702531188780719146460090685151 Found probable prime factor of 36 digits: 493619702531188780719146460090685151 Probable prime cofactor 570613182110476873637098969632150989726981775506952535058010084196523573240634138994101843197569157770130203517 has 111 digits
(37·10²⁰⁵+71)/9 = 4(1)₂₀₄9_<206> = 7 · 2136133 · 64219024439_<11> · C188
C188 = P33 · P155
P33 = 811192614843691594162179215721103_<33>
P155 = 52777059952387829531805686963212177397005658748073113430271392340308625968747192771664150630058513871014711473629321309366475928080999258279957374370363597_<155>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2220468459 Step 1 took 15901ms Step 2 took 8896ms ********** Factor found in step 2: 811192614843691594162179215721103 Found probable prime factor of 33 digits: 811192614843691594162179215721103 Probable prime cofactor has 155 digits
(37·10²⁰²+71)/9 = 4(1)₂₀₁9_<203> = 13 · 331 · 617 · 385329041 · 13678610652367342939958859931_<29> · C160
C160 = P33 · P128
P33 = 240415440947317746742029988668383_<33>
P128 = 12219870898197088877898626768426211369986433162099804061070145673200443592688273807744355365435476148474134453244176088463782133_<128>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=939060094 Step 1 took 10797ms Step 2 took 5572ms ********** Factor found in step 2: 240415440947317746742029988668383 Found probable prime factor of 33 digits: 240415440947317746742029988668383 Probable prime cofactor 12219870898197088877898626768426211369986433162099804061070145673200443592688273807744355365435476148474134453244176088463782133 has 128 digits
(37·10¹¹²+53)/9 = 4(1)₁₁₁7_<113> = 67619 · 1002388368083_<13> · C96
C96 = P37 · P60
P37 = 1809172218365498113906379744251961009_<37>
P60 = 335254443186106734337422576507034330357097141008436045500069_<60>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1919125461 Step 1 took 6853ms Step 2 took 4585ms ********** Factor found in step 2: 1809172218365498113906379744251961009 Found probable prime factor of 37 digits: 1809172218365498113906379744251961009 Probable prime cofactor 335254443186106734337422576507034330357097141008436045500069 has 60 digits
(37·10²⁰²+53)/9 = 4(1)₂₀₁7_<203> = 83 · 103969 · C196
C196 = P35 · C161
P35 = 83073232889032830958318021005925831_<35>
C161 = [57347718339390154926339184530294156960878348876030304573157521297170923496818684614574091715773458560271341921644399653208512139175830624309009733603768798562441_<161>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2223104446 Step 1 took 14353ms Step 2 took 7001ms ********** Factor found in step 2: 83073232889032830958318021005925831 Found probable prime factor of 35 digits: 83073232889032830958318021005925831 Composite cofactor has 161 digits
(37·10¹⁶⁹+71)/9 = 4(1)₁₆₈9_<170> = 7² · 253366636945487563_<18> · C151
C151 = P32 · P119
P32 = 37501399965585490651118726058947_<32>
P119 = 88301123028773088784112825094403290394334942803635440323854002374944693073141336324975710529936256947568638512598023071_<119>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1399304808 Step 1 took 11746ms Step 2 took 6891ms ********** Factor found in step 2: 37501399965585490651118726058947 Found probable prime factor of 32 digits: 37501399965585490651118726058947 Probable prime cofactor 88301123028773088784112825094403290394334942803635440323854002374944693073141336324975710529936256947568638512598023071 has 119 digits
Dec 14, 2008 (2nd): By Sinkiti Sibata / GGNFS, Msieve
(37·10¹⁶²+17)/9 = 4(1)₁₆₁3_<163> = 3 · 19290329 · 66993539 · 288466127633_<12> · 2388806425599695184089_<22> · C115
C115 = P57 · P59
P57 = 130111273985304522814275954174641281081665867559899941167_<57>
P59 = 11827002600902938664289039732901650255844924476182741339279_<59>

Number: 41113_162 N=1538826375830991453057437176484248990299753945815650506175461641309026854092360282091108310398235858496090886198593 ( 115 digits) Divisors found: r1=130111273985304522814275954174641281081665867559899941167 (pp57) r2=11827002600902938664289039732901650255844924476182741339279 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 57.40 hours. Scaled time: 27.15 units (timescale=0.473). Factorization parameters were as follows: name: 41113_162 n: 1538826375830991453057437176484248990299753945815650506175461641309026854092360282091108310398235858496090886198593 skew: 68560.79 # norm 5.34e+15 c5: 16380 c4: -491501907 c3: -284502307743748 c2: 2095670281966397398 c1: 491009361245004074554604 c0: -4355927952840396465531407136 # alpha -5.95 Y1: 2733249033247 Y0: -9875881410257126254633 # Murphy_E 5.70e-10 # M 1019663148516304371654520437573394188902720054438743156392681884195776859271800520987608419626613033809430724205437 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, 2950001) Primes: RFBsize:250150, AFBsize:250583, largePrimes:7640929 encountered Relations: rels:7618928, finalFF:654352 Max relations in full relation-set: 28 Initial matrix: 500815 x 654352 with sparse part having weight 58437435. Pruned matrix : 379734 x 382302 with weight 34243244. Total sieving time: 50.65 hours. Total relation processing time: 0.58 hours. Matrix solve time: 5.82 hours. Time per square root: 0.35 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 57.40 hours. --------- CPU info (if available) ----------
(37·10¹⁰³+53)/9 = 4(1)₁₀₂7_<104> = 17 · 113 · 89983 · 4032812257_<10> · C86
C86 = P38 · P49
P38 = 35314393767842084307850317582733171637_<38>
P49 = 1669981352997280313025282068382464491328210820391_<49>

Sun Dec 14 06:13:22 2008 Msieve v. 1.39 Sun Dec 14 06:13:22 2008 random seeds: 1925d00c b04ad9d7 Sun Dec 14 06:13:22 2008 factoring 58974379084699647746013481661671328339377519785913665155065638330419588046029182450067 (86 digits) Sun Dec 14 06:13:22 2008 searching for 15-digit factors Sun Dec 14 06:13:24 2008 commencing quadratic sieve (86-digit input) Sun Dec 14 06:13:24 2008 using multiplier of 23 Sun Dec 14 06:13:24 2008 using 32kb Intel Core sieve core Sun Dec 14 06:13:24 2008 sieve interval: 16 blocks of size 32768 Sun Dec 14 06:13:24 2008 processing polynomials in batches of 13 Sun Dec 14 06:13:24 2008 using a sieve bound of 1452827 (55667 primes) Sun Dec 14 06:13:24 2008 using large prime bound of 116226160 (26 bits) Sun Dec 14 06:13:24 2008 using double large prime bound of 329266038078320 (41-49 bits) Sun Dec 14 06:13:24 2008 using trial factoring cutoff of 49 bits Sun Dec 14 06:13:24 2008 polynomial 'A' values have 11 factors Sun Dec 14 06:55:41 2008 55968 relations (15882 full + 40086 combined from 584002 partial), need 55763 Sun Dec 14 06:55:41 2008 begin with 599884 relations Sun Dec 14 06:55:42 2008 reduce to 133031 relations in 9 passes Sun Dec 14 06:55:42 2008 attempting to read 133031 relations Sun Dec 14 06:55:43 2008 recovered 133031 relations Sun Dec 14 06:55:43 2008 recovered 113790 polynomials Sun Dec 14 06:55:44 2008 attempting to build 55968 cycles Sun Dec 14 06:55:44 2008 found 55968 cycles in 5 passes Sun Dec 14 06:55:44 2008 distribution of cycle lengths: Sun Dec 14 06:55:44 2008 length 1 : 15882 Sun Dec 14 06:55:44 2008 length 2 : 10993 Sun Dec 14 06:55:44 2008 length 3 : 9934 Sun Dec 14 06:55:44 2008 length 4 : 7402 Sun Dec 14 06:55:44 2008 length 5 : 4990 Sun Dec 14 06:55:44 2008 length 6 : 3014 Sun Dec 14 06:55:44 2008 length 7 : 1771 Sun Dec 14 06:55:44 2008 length 9+: 1982 Sun Dec 14 06:55:44 2008 largest cycle: 18 relations Sun Dec 14 06:55:44 2008 matrix is 55667 x 55968 (12.8 MB) with weight 3143787 (56.17/col) Sun Dec 14 06:55:44 2008 sparse part has weight 3143787 (56.17/col) Sun Dec 14 06:55:44 2008 filtering completed in 3 passes Sun Dec 14 06:55:44 2008 matrix is 51132 x 51196 (11.9 MB) with weight 2902891 (56.70/col) Sun Dec 14 06:55:44 2008 sparse part has weight 2902891 (56.70/col) Sun Dec 14 06:55:44 2008 saving the first 48 matrix rows for later Sun Dec 14 06:55:45 2008 matrix is 51084 x 51196 (7.8 MB) with weight 2292166 (44.77/col) Sun Dec 14 06:55:45 2008 sparse part has weight 1727978 (33.75/col) Sun Dec 14 06:55:45 2008 matrix includes 64 packed rows Sun Dec 14 06:55:45 2008 using block size 20478 for processor cache size 1024 kB Sun Dec 14 06:55:45 2008 commencing Lanczos iteration Sun Dec 14 06:55:45 2008 memory use: 7.5 MB Sun Dec 14 06:56:00 2008 lanczos halted after 809 iterations (dim = 51081) Sun Dec 14 06:56:00 2008 recovered 15 nontrivial dependencies Sun Dec 14 06:56:01 2008 prp38 factor: 35314393767842084307850317582733171637 Sun Dec 14 06:56:01 2008 prp49 factor: 1669981352997280313025282068382464491328210820391 Sun Dec 14 06:56:01 2008 elapsed time 00:42:39
(37·10¹⁰²+71)/9 = 4(1)₁₀₁9_<103> = 3 · 1244232153403207_<16> · C88
C88 = P34 · P54
P34 = 2649665594353355667701413432585159_<34>
P54 = 415666929362892300678012893291131874171779345720654421_<54>

Sun Dec 14 06:32:50 2008 Msieve v. 1.39 Sun Dec 14 06:32:50 2008 random seeds: 62e79a6d 45d19e2c Sun Dec 14 06:32:50 2008 factoring 1101378361443362334800454697333708457237190352894806247424401857396076767882135292337939 (88 digits) Sun Dec 14 06:32:51 2008 searching for 15-digit factors Sun Dec 14 06:32:52 2008 commencing quadratic sieve (88-digit input) Sun Dec 14 06:32:53 2008 using multiplier of 11 Sun Dec 14 06:32:53 2008 using 32kb Intel Core sieve core Sun Dec 14 06:32:53 2008 sieve interval: 24 blocks of size 32768 Sun Dec 14 06:32:53 2008 processing polynomials in batches of 9 Sun Dec 14 06:32:53 2008 using a sieve bound of 1508383 (57226 primes) Sun Dec 14 06:32:53 2008 using large prime bound of 120670640 (26 bits) Sun Dec 14 06:32:53 2008 using double large prime bound of 352275850752880 (42-49 bits) Sun Dec 14 06:32:53 2008 using trial factoring cutoff of 49 bits Sun Dec 14 06:32:53 2008 polynomial 'A' values have 11 factors Sun Dec 14 07:22:11 2008 57405 relations (15925 full + 41480 combined from 602836 partial), need 57322 Sun Dec 14 07:22:13 2008 begin with 618761 relations Sun Dec 14 07:22:13 2008 reduce to 137376 relations in 9 passes Sun Dec 14 07:22:13 2008 attempting to read 137376 relations Sun Dec 14 07:22:16 2008 recovered 137376 relations Sun Dec 14 07:22:16 2008 recovered 114537 polynomials Sun Dec 14 07:22:16 2008 attempting to build 57405 cycles Sun Dec 14 07:22:16 2008 found 57405 cycles in 6 passes Sun Dec 14 07:22:16 2008 distribution of cycle lengths: Sun Dec 14 07:22:16 2008 length 1 : 15925 Sun Dec 14 07:22:16 2008 length 2 : 11211 Sun Dec 14 07:22:16 2008 length 3 : 10151 Sun Dec 14 07:22:16 2008 length 4 : 7733 Sun Dec 14 07:22:16 2008 length 5 : 5182 Sun Dec 14 07:22:16 2008 length 6 : 3216 Sun Dec 14 07:22:16 2008 length 7 : 1838 Sun Dec 14 07:22:16 2008 length 9+: 2149 Sun Dec 14 07:22:16 2008 largest cycle: 20 relations Sun Dec 14 07:22:16 2008 matrix is 57226 x 57405 (13.5 MB) with weight 3317254 (57.79/col) Sun Dec 14 07:22:16 2008 sparse part has weight 3317254 (57.79/col) Sun Dec 14 07:22:17 2008 filtering completed in 3 passes Sun Dec 14 07:22:17 2008 matrix is 52706 x 52770 (12.6 MB) with weight 3079370 (58.35/col) Sun Dec 14 07:22:17 2008 sparse part has weight 3079370 (58.35/col) Sun Dec 14 07:22:17 2008 saving the first 48 matrix rows for later Sun Dec 14 07:22:17 2008 matrix is 52658 x 52770 (8.6 MB) with weight 2474966 (46.90/col) Sun Dec 14 07:22:17 2008 sparse part has weight 1945695 (36.87/col) Sun Dec 14 07:22:17 2008 matrix includes 64 packed rows Sun Dec 14 07:22:17 2008 using block size 21108 for processor cache size 2048 kB Sun Dec 14 07:22:17 2008 commencing Lanczos iteration Sun Dec 14 07:22:17 2008 memory use: 8.1 MB Sun Dec 14 07:22:33 2008 lanczos halted after 834 iterations (dim = 52656) Sun Dec 14 07:22:33 2008 recovered 17 nontrivial dependencies Sun Dec 14 07:22:33 2008 prp34 factor: 2649665594353355667701413432585159 Sun Dec 14 07:22:33 2008 prp54 factor: 415666929362892300678012893291131874171779345720654421 Sun Dec 14 07:22:33 2008 elapsed time 00:49:43
(37·10¹¹⁰+71)/9 = 4(1)₁₀₉9_<111> = 163 · 3253 · 4993 · 115781 · 322350781 · C88
C88 = P38 · P50
P38 = 43729720990949949880600834845372658547_<38>
P50 = 95144404324151060163204535145958036377440540232891_<50>

Sun Dec 14 06:38:51 2008 Msieve v. 1.39 Sun Dec 14 06:38:51 2008 random seeds: 706bda11 1a3ccd2d Sun Dec 14 06:38:51 2008 factoring 4160638254945257795077203040399477793071467096507626461078106980750015463188979201669377 (88 digits) Sun Dec 14 06:38:52 2008 searching for 15-digit factors Sun Dec 14 06:38:54 2008 commencing quadratic sieve (88-digit input) Sun Dec 14 06:38:54 2008 using multiplier of 1 Sun Dec 14 06:38:54 2008 using 64kb Pentium 4 sieve core Sun Dec 14 06:38:54 2008 sieve interval: 14 blocks of size 65536 Sun Dec 14 06:38:54 2008 processing polynomials in batches of 8 Sun Dec 14 06:38:54 2008 using a sieve bound of 1518589 (58000 primes) Sun Dec 14 06:38:54 2008 using large prime bound of 121487120 (26 bits) Sun Dec 14 06:38:54 2008 using double large prime bound of 356577817808960 (42-49 bits) Sun Dec 14 06:38:54 2008 using trial factoring cutoff of 49 bits Sun Dec 14 06:38:54 2008 polynomial 'A' values have 11 factors Sun Dec 14 08:02:47 2008 58224 relations (16052 full + 42172 combined from 612983 partial), need 58096 Sun Dec 14 08:02:50 2008 begin with 629035 relations Sun Dec 14 08:02:50 2008 reduce to 140474 relations in 9 passes Sun Dec 14 08:02:50 2008 attempting to read 140474 relations Sun Dec 14 08:02:54 2008 recovered 140474 relations Sun Dec 14 08:02:54 2008 recovered 114957 polynomials Sun Dec 14 08:02:54 2008 attempting to build 58224 cycles Sun Dec 14 08:02:54 2008 found 58224 cycles in 6 passes Sun Dec 14 08:02:54 2008 distribution of cycle lengths: Sun Dec 14 08:02:54 2008 length 1 : 16052 Sun Dec 14 08:02:54 2008 length 2 : 11306 Sun Dec 14 08:02:54 2008 length 3 : 10232 Sun Dec 14 08:02:54 2008 length 4 : 7703 Sun Dec 14 08:02:54 2008 length 5 : 5269 Sun Dec 14 08:02:54 2008 length 6 : 3373 Sun Dec 14 08:02:54 2008 length 7 : 1952 Sun Dec 14 08:02:54 2008 length 9+: 2337 Sun Dec 14 08:02:54 2008 largest cycle: 17 relations Sun Dec 14 08:02:54 2008 matrix is 58000 x 58224 (13.7 MB) with weight 3353101 (57.59/col) Sun Dec 14 08:02:54 2008 sparse part has weight 3353101 (57.59/col) Sun Dec 14 08:02:56 2008 filtering completed in 3 passes Sun Dec 14 08:02:56 2008 matrix is 53684 x 53747 (12.7 MB) with weight 3122843 (58.10/col) Sun Dec 14 08:02:56 2008 sparse part has weight 3122843 (58.10/col) Sun Dec 14 08:02:56 2008 saving the first 48 matrix rows for later Sun Dec 14 08:02:56 2008 matrix is 53636 x 53747 (8.7 MB) with weight 2504409 (46.60/col) Sun Dec 14 08:02:56 2008 sparse part has weight 1952885 (36.33/col) Sun Dec 14 08:02:56 2008 matrix includes 64 packed rows Sun Dec 14 08:02:56 2008 using block size 21498 for processor cache size 512 kB Sun Dec 14 08:02:57 2008 commencing Lanczos iteration Sun Dec 14 08:02:57 2008 memory use: 8.2 MB Sun Dec 14 08:03:27 2008 lanczos halted after 849 iterations (dim = 53632) Sun Dec 14 08:03:27 2008 recovered 14 nontrivial dependencies Sun Dec 14 08:03:28 2008 prp38 factor: 43729720990949949880600834845372658547 Sun Dec 14 08:03:28 2008 prp50 factor: 95144404324151060163204535145958036377440540232891 Sun Dec 14 08:03:28 2008 elapsed time 01:24:37
(37·10¹³⁴+71)/9 = 4(1)₁₃₃9_<135> = 22541 · 25579 · 9712652137_<10> · 44720537897489_<14> · 275014982787607_<15> · C88
C88 = P44 · P44
P44 = 76781171389640257460964238610947216532089199_<44>
P44 = 77740357280063944340382379702634468726758129_<44>

Sun Dec 14 08:13:01 2008 Msieve v. 1.39 Sun Dec 14 08:13:01 2008 random seeds: 9c481be0 3d650de5 Sun Dec 14 08:13:01 2008 factoring 5968995696212457427044842553502875786013425970251737697198124448731278272530146726348671 (88 digits) Sun Dec 14 08:13:03 2008 searching for 15-digit factors Sun Dec 14 08:13:05 2008 commencing quadratic sieve (88-digit input) Sun Dec 14 08:13:05 2008 using multiplier of 1 Sun Dec 14 08:13:05 2008 using 64kb Pentium 4 sieve core Sun Dec 14 08:13:05 2008 sieve interval: 14 blocks of size 65536 Sun Dec 14 08:13:05 2008 processing polynomials in batches of 8 Sun Dec 14 08:13:05 2008 using a sieve bound of 1527443 (57997 primes) Sun Dec 14 08:13:05 2008 using large prime bound of 122195440 (26 bits) Sun Dec 14 08:13:05 2008 using double large prime bound of 360328813713040 (42-49 bits) Sun Dec 14 08:13:05 2008 using trial factoring cutoff of 49 bits Sun Dec 14 08:13:05 2008 polynomial 'A' values have 11 factors Sun Dec 14 09:46:40 2008 58202 relations (15835 full + 42367 combined from 613321 partial), need 58093 Sun Dec 14 09:46:42 2008 begin with 629156 relations Sun Dec 14 09:46:43 2008 reduce to 141005 relations in 9 passes Sun Dec 14 09:46:43 2008 attempting to read 141005 relations Sun Dec 14 09:46:46 2008 recovered 141005 relations Sun Dec 14 09:46:46 2008 recovered 118767 polynomials Sun Dec 14 09:46:46 2008 attempting to build 58202 cycles Sun Dec 14 09:46:46 2008 found 58202 cycles in 6 passes Sun Dec 14 09:46:46 2008 distribution of cycle lengths: Sun Dec 14 09:46:46 2008 length 1 : 15835 Sun Dec 14 09:46:46 2008 length 2 : 11324 Sun Dec 14 09:46:46 2008 length 3 : 10272 Sun Dec 14 09:46:46 2008 length 4 : 7605 Sun Dec 14 09:46:46 2008 length 5 : 5453 Sun Dec 14 09:46:46 2008 length 6 : 3261 Sun Dec 14 09:46:47 2008 length 7 : 2085 Sun Dec 14 09:46:47 2008 length 9+: 2367 Sun Dec 14 09:46:47 2008 largest cycle: 17 relations Sun Dec 14 09:46:47 2008 matrix is 57997 x 58202 (13.9 MB) with weight 3398010 (58.38/col) Sun Dec 14 09:46:47 2008 sparse part has weight 3398010 (58.38/col) Sun Dec 14 09:46:48 2008 filtering completed in 4 passes Sun Dec 14 09:46:48 2008 matrix is 53933 x 53997 (12.9 MB) with weight 3176190 (58.82/col) Sun Dec 14 09:46:48 2008 sparse part has weight 3176190 (58.82/col) Sun Dec 14 09:46:48 2008 saving the first 48 matrix rows for later Sun Dec 14 09:46:48 2008 matrix is 53885 x 53997 (8.5 MB) with weight 2513844 (46.56/col) Sun Dec 14 09:46:48 2008 sparse part has weight 1912992 (35.43/col) Sun Dec 14 09:46:48 2008 matrix includes 64 packed rows Sun Dec 14 09:46:48 2008 using block size 21598 for processor cache size 512 kB Sun Dec 14 09:46:49 2008 commencing Lanczos iteration Sun Dec 14 09:46:49 2008 memory use: 8.2 MB Sun Dec 14 09:47:17 2008 lanczos halted after 853 iterations (dim = 53880) Sun Dec 14 09:47:17 2008 recovered 14 nontrivial dependencies Sun Dec 14 09:47:18 2008 prp44 factor: 76781171389640257460964238610947216532089199 Sun Dec 14 09:47:18 2008 prp44 factor: 77740357280063944340382379702634468726758129 Sun Dec 14 09:47:18 2008 elapsed time 01:34:17
(37·10¹⁰²+53)/9 = 4(1)₁₀₁7_<103> = 71 · 11839 · 7469039 · C90
C90 = P34 · P56
P34 = 7516248271660755869850274614285353_<34>
P56 = 87120428179153067595948563227353363024319865790575626979_<56>

un Dec 14 09:26:56 2008 Msieve v. 1.39 Sun Dec 14 09:26:56 2008 random seeds: 2832f164 98fb12c3 Sun Dec 14 09:26:56 2008 factoring 654818767727904256865639176292309801451437776014272230779785284420421232481315337991338587 (90 digits) Sun Dec 14 09:26:57 2008 searching for 15-digit factors Sun Dec 14 09:26:59 2008 commencing quadratic sieve (90-digit input) Sun Dec 14 09:26:59 2008 using multiplier of 3 Sun Dec 14 09:26:59 2008 using 32kb Intel Core sieve core Sun Dec 14 09:26:59 2008 sieve interval: 36 blocks of size 32768 Sun Dec 14 09:26:59 2008 processing polynomials in batches of 6 Sun Dec 14 09:26:59 2008 using a sieve bound of 1613867 (61176 primes) Sun Dec 14 09:26:59 2008 using large prime bound of 135564828 (27 bits) Sun Dec 14 09:26:59 2008 using double large prime bound of 434374788405180 (42-49 bits) Sun Dec 14 09:26:59 2008 using trial factoring cutoff of 49 bits Sun Dec 14 09:26:59 2008 polynomial 'A' values have 12 factors Sun Dec 14 10:29:25 2008 61573 relations (17144 full + 44429 combined from 653984 partial), need 61272 Sun Dec 14 10:29:26 2008 begin with 671128 relations Sun Dec 14 10:29:26 2008 reduce to 146946 relations in 11 passes Sun Dec 14 10:29:26 2008 attempting to read 146946 relations Sun Dec 14 10:29:28 2008 recovered 146946 relations Sun Dec 14 10:29:28 2008 recovered 120493 polynomials Sun Dec 14 10:29:28 2008 attempting to build 61573 cycles Sun Dec 14 10:29:29 2008 found 61573 cycles in 5 passes Sun Dec 14 10:29:29 2008 distribution of cycle lengths: Sun Dec 14 10:29:29 2008 length 1 : 17144 Sun Dec 14 10:29:29 2008 length 2 : 12393 Sun Dec 14 10:29:29 2008 length 3 : 10791 Sun Dec 14 10:29:29 2008 length 4 : 8064 Sun Dec 14 10:29:29 2008 length 5 : 5463 Sun Dec 14 10:29:29 2008 length 6 : 3441 Sun Dec 14 10:29:29 2008 length 7 : 1974 Sun Dec 14 10:29:29 2008 length 9+: 2303 Sun Dec 14 10:29:29 2008 largest cycle: 18 relations Sun Dec 14 10:29:29 2008 matrix is 61176 x 61573 (14.7 MB) with weight 3596232 (58.41/col) Sun Dec 14 10:29:29 2008 sparse part has weight 3596232 (58.41/col) Sun Dec 14 10:29:30 2008 filtering completed in 3 passes Sun Dec 14 10:29:30 2008 matrix is 56580 x 56644 (13.5 MB) with weight 3322339 (58.65/col) Sun Dec 14 10:29:30 2008 sparse part has weight 3322339 (58.65/col) Sun Dec 14 10:29:30 2008 saving the first 48 matrix rows for later Sun Dec 14 10:29:30 2008 matrix is 56532 x 56644 (8.3 MB) with weight 2561002 (45.21/col) Sun Dec 14 10:29:30 2008 sparse part has weight 1840625 (32.49/col) Sun Dec 14 10:29:30 2008 matrix includes 64 packed rows Sun Dec 14 10:29:30 2008 using block size 22657 for processor cache size 1024 kB Sun Dec 14 10:29:30 2008 commencing Lanczos iteration Sun Dec 14 10:29:30 2008 memory use: 8.3 MB Sun Dec 14 10:29:48 2008 lanczos halted after 895 iterations (dim = 56529) Sun Dec 14 10:29:48 2008 recovered 16 nontrivial dependencies Sun Dec 14 10:29:49 2008 prp34 factor: 7516248271660755869850274614285353 Sun Dec 14 10:29:49 2008 prp56 factor: 87120428179153067595948563227353363024319865790575626979 Sun Dec 14 10:29:49 2008 elapsed time 01:02:53
(37·10¹⁰⁵+53)/9 = 4(1)₁₀₄7_<106> = 111733 · 546863 · C95
C95 = P45 · P51
P45 = 204636041354677447482853109425426041565256449_<45>
P51 = 328788855581546082125121238993357453012048109411927_<51>

Sun Dec 14 08:15:04 2008 Msieve v. 1.39 Sun Dec 14 08:15:04 2008 random seeds: 868f8b33 3eb24c1e Sun Dec 14 08:15:04 2008 factoring 67282049847742334963616862975582700215581962408551703345462075578114834596968610334356334267223 (95 digits) Sun Dec 14 08:15:05 2008 searching for 15-digit factors Sun Dec 14 08:15:06 2008 commencing quadratic sieve (95-digit input) Sun Dec 14 08:15:06 2008 using multiplier of 3 Sun Dec 14 08:15:06 2008 using 32kb Intel Core sieve core Sun Dec 14 08:15:06 2008 sieve interval: 36 blocks of size 32768 Sun Dec 14 08:15:06 2008 processing polynomials in batches of 6 Sun Dec 14 08:15:06 2008 using a sieve bound of 2196599 (80826 primes) Sun Dec 14 08:15:06 2008 using large prime bound of 329489850 (28 bits) Sun Dec 14 08:15:06 2008 using double large prime bound of 2148402323041500 (43-51 bits) Sun Dec 14 08:15:06 2008 using trial factoring cutoff of 51 bits Sun Dec 14 08:15:06 2008 polynomial 'A' values have 12 factors Sun Dec 14 13:22:18 2008 81008 relations (19048 full + 61960 combined from 1237185 partial), need 80922 Sun Dec 14 13:22:23 2008 begin with 1256233 relations Sun Dec 14 13:22:23 2008 reduce to 215120 relations in 13 passes Sun Dec 14 13:22:23 2008 attempting to read 215120 relations Sun Dec 14 13:22:29 2008 recovered 215120 relations Sun Dec 14 13:22:29 2008 recovered 202169 polynomials Sun Dec 14 13:22:29 2008 attempting to build 81008 cycles Sun Dec 14 13:22:29 2008 found 81008 cycles in 6 passes Sun Dec 14 13:22:29 2008 distribution of cycle lengths: Sun Dec 14 13:22:29 2008 length 1 : 19048 Sun Dec 14 13:22:29 2008 length 2 : 13883 Sun Dec 14 13:22:29 2008 length 3 : 13540 Sun Dec 14 13:22:29 2008 length 4 : 11060 Sun Dec 14 13:22:29 2008 length 5 : 8465 Sun Dec 14 13:22:29 2008 length 6 : 5764 Sun Dec 14 13:22:29 2008 length 7 : 3725 Sun Dec 14 13:22:29 2008 length 9+: 5523 Sun Dec 14 13:22:29 2008 largest cycle: 20 relations Sun Dec 14 13:22:30 2008 matrix is 80826 x 81008 (22.2 MB) with weight 5506807 (67.98/col) Sun Dec 14 13:22:30 2008 sparse part has weight 5506807 (67.98/col) Sun Dec 14 13:22:30 2008 filtering completed in 3 passes Sun Dec 14 13:22:30 2008 matrix is 77469 x 77533 (21.4 MB) with weight 5302804 (68.39/col) Sun Dec 14 13:22:30 2008 sparse part has weight 5302804 (68.39/col) Sun Dec 14 13:22:31 2008 saving the first 48 matrix rows for later Sun Dec 14 13:22:31 2008 matrix is 77421 x 77533 (14.7 MB) with weight 4320453 (55.72/col) Sun Dec 14 13:22:31 2008 sparse part has weight 3383624 (43.64/col) Sun Dec 14 13:22:31 2008 matrix includes 64 packed rows Sun Dec 14 13:22:31 2008 using block size 31013 for processor cache size 2048 kB Sun Dec 14 13:22:31 2008 commencing Lanczos iteration Sun Dec 14 13:22:31 2008 memory use: 13.5 MB Sun Dec 14 13:23:10 2008 lanczos halted after 1226 iterations (dim = 77418) Sun Dec 14 13:23:10 2008 recovered 15 nontrivial dependencies Sun Dec 14 13:23:11 2008 prp45 factor: 204636041354677447482853109425426041565256449 Sun Dec 14 13:23:11 2008 prp51 factor: 328788855581546082125121238993357453012048109411927 Sun Dec 14 13:23:11 2008 elapsed time 05:08:07
(37·10¹¹⁴+53)/9 = 4(1)₁₁₃7_<115> = C115
C115 = P54 · P62
P54 = 337537008280418766192929438347918809616735002757194727_<54>
P62 = 12179734400251853325768968702888321780028003904068045443286571_<62>

Number: 41117_114 N=4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117 ( 115 digits) SNFS difficulty: 116 digits. Divisors found: r1=337537008280418766192929438347918809616735002757194727 (prp54) r2=12179734400251853325768968702888321780028003904068045443286571 (prp62) Version: Total time: 1.79 hours. Scaled time: 3.50 units (timescale=1.960). Factorization parameters were as follows: name: 41117_114 n: 4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111117 m: 100000000000000000000000 deg: 5 c5: 37 c0: 530 skew: 1.70 type: snfs lss: 1 rlim: 610000 alim: 610000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Fa