News and updates, April 2008

Since June 16, 2000

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News and updates, April 2008	2008-05-05(Mon) 00:07

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News and updates, April 2008

Apr 30, 2008 (2nd): By Jo Yeong Uk / GGNFS
(16·10¹⁵⁸+11)/9 = 1(7)₁₅₇9_<159> = 23 · 71483 · 882289667416631_<15> · 1223089082743541046463_<22> · C117
C117 = P34 · P41 · P43
P34 = 2134129586476034361751373376668327_<34>
P41 = 28096861999607415883106912277348090679271_<41>
P43 = 1671086683923658132629175023545298008290231_<43>

Number: 17779_158 N=100202275398200758288755959759199695048283608989076012457803031165111105417145614149076922956946071387503593890491527 ( 117 digits) SNFS difficulty: 160 digits. Divisors found: r1=2134129586476034361751373376668327 (pp34) r2=28096861999607415883106912277348090679271 (pp41) r3=1671086683923658132629175023545298008290231 (pp43) Version: GGNFS-0.77.1-20050930-nocona Total time: 22.59 hours. Scaled time: 53.61 units (timescale=2.373). Factorization parameters were as follows: n: 100202275398200758288755959759199695048283608989076012457803031165111105417145614149076922956946071387503593890491527 m: 100000000000000000000000000000000 c5: 4 c0: 275 skew: 2.33 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:282328, largePrimes:5697960 encountered Relations: rels:5807108, finalFF:723224 Max relations in full relation-set: 28 Initial matrix: 565538 x 723224 with sparse part having weight 44336124. Pruned matrix : 436240 x 439131 with weight 27143298. Total sieving time: 21.63 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.85 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 22.59 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047208k/8912896k available (2434k kernel code, 339080k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673792) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.03 BogoMIPS (lpj=2672015) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346)
Apr 30, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(28·10¹⁸⁴+17)/9 = 3(1)₁₈₃3_<185> = 3³ · C184
C184 = P42 · P60 · P82
P42 = 397173737675450362503394621695281766949091_<42>
P60 = 382277231274590218916165085392883779524628449879451093458519_<60>
P82 = 7589144149261590771957712617331762006980147309781393383050491171157371995675701711_<82>

Number: n N=1152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707819 ( 184 digits) SNFS difficulty: 186 digits. Divisors found: Wed Apr 30 04:16:48 2008 prp42 factor: 397173737675450362503394621695281766949091 Wed Apr 30 04:16:48 2008 prp60 factor: 382277231274590218916165085392883779524628449879451093458519 Wed Apr 30 04:16:48 2008 prp82 factor: 7589144149261590771957712617331762006980147309781393383050491171157371995675701711 Wed Apr 30 04:16:48 2008 elapsed time 04:15:04 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 83.28 hours. Scaled time: 108.02 units (timescale=1.297). Factorization parameters were as follows: name: KA_3_1_183_3 n: 1152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707818930041152263374485596707819 skew: 1.43 deg: 5 c5: 14 c0: 85 m: 10000000000000000000000000000000000000 type: snfs rlim: 7000000 alim: 7000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 6100319) Primes: RFBsize:476648, AFBsize:477009, largePrimes:9217175 encountered Relations: rels:8915077, finalFF:1033124 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 82.91 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.5,2.5,100000 total time: 83.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
6·10¹⁹⁷-1 = 5(9)₁₉₇_<198> = 1887671 · 21510659 · 29874643 · 51335819857675817_<17> · 193601769040977856894563633949553_<33> · C128
C128 = P40 · P89
P40 = 1977341005678468116703941828020617788403_<40>
P89 = 25168487085362731602320955256733472748105735580583285164870970125177601063461429215617779_<89>
(55·10¹⁸¹-1)/9 = 6(1)₁₈₁_<182> = 61 · 67 · 577 · 877 · 111781 · 143711 · 1586030472739_<13> · 20195363842211281211_<20> · C131
C131 = P38 · P94
P38 = 40766640584137816710957234478076320681_<38>
P94 = 1408685357301870566274220078616240034649709444750645317100034544822179685039407926776633883623_<94>
(16·10¹⁶²+11)/9 = 1(7)₁₆₁9_<163> = 3 · 53 · 7253 · 70321 · C152
C152 = P40 · P56 · P57
P40 = 8738921168068223070819335162356745813567_<40>
P56 = 13556939193433310268348957012659665344973696429079407199_<56>
P57 = 185036823188116760892677166163881313320229342307235722089_<57>

Number: n N=2508532960507369683116226125792753818248735064626633650889410151638428241599905078493703429185525506304829918711 ( 112 digits) Divisors found: Wed Apr 30 16:29:28 2008 prp56 factor: 13556939193433310268348957012659665344973696429079407199 Wed Apr 30 16:29:28 2008 prp57 factor: 185036823188116760892677166163881313320229342307235722089 Wed Apr 30 16:29:28 2008 elapsed time 00:49:00 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 20.01 hours. Scaled time: 16.71 units (timescale=0.835). Factorization parameters were as follows: name: KA_1_7_161_9 n: 2508532960507369683116226125792753818248735064626633650889410151638428241599905078493703429185525506304829918711 skew: 43366.64 # norm 5.45e+15 c5: 43920 c4: -4846848468 c3: -236249798478376 c2: 8406881964709630013 c1: 187479335648406438045156 c0: -3098499176790197889764617485 # alpha -6.91 Y1: 499363817177 Y0: -2245709765640471211154 # Murphy_E 8.54e-10 # M 1428327081851271319039963154859251667243927909391619659471900613331547899535708849353768931258657004078679706063 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 special-q in [100000, 1199990) Primes: RFBsize:250150, AFBsize:249777, largePrimes:6866749 encountered Relations: rels:6624270, finalFF:602658 Max relations in full relation-set: 28 Initial matrix: 500007 x 602658 with sparse part having weight 37395817. Pruned matrix : Total sieving time: 19.82 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 20.01 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Apr 29, 2008 (4th): By Wataru Sakai / GGNFS
(10¹⁷³+17)/9 = (1)₁₇₂3_<173> = 31 · 53 · 10668971 · C162
C162 = P48 · P115
P48 = 614269433286889380330990067993202633882411638463_<48>
P115 = 1031902079348278117543760295595941783929099708583219958186262256627756188911338017448835857763642355585371803328367_<115>

Number: 11113_173 N=633865905488829556896400642079141824365163309702470659600118424221394547036781255642529888084966541508328054517246866001820594204902217663114060440336321276179921 ( 162 digits) SNFS difficulty: 173 digits. Divisors found: r1=614269433286889380330990067993202633882411638463 (pp48) r2=1031902079348278117543760295595941783929099708583219958186262256627756188911338017448835857763642355585371803328367 (pp115) Version: GGNFS-0.77.1-20060722-nocona Total time: 188.18 hours. Scaled time: 379.19 units (timescale=2.015). Factorization parameters were as follows: n: 633865905488829556896400642079141824365163309702470659600118424221394547036781255642529888084966541508328054517246866001820594204902217663114060440336321276179921 m: 10000000000000000000000000000000000 c5: 1000 c0: 17 skew: 0.44 type: snfsFactor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10100001) Primes: RFBsize:501962, AFBsize:502426, largePrimes:6671675 encountered Relations: rels:7329088, finalFF:1319979 Max relations in full relation-set: 32 Initial matrix: 1004454 x 1319979 with sparse part having weight 79827464. Pruned matrix : 724483 x 729569 with weight 58377937. Total sieving time: 184.22 hours. Total relation processing time: 0.11 hours. Matrix solve time: 3.67 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 188.18 hours. --------- CPU info (if available) ----------
Apr 29, 2008 (3rd): By Justin Card / GGNFS
(16·10¹⁰⁸+11)/9 = 1(7)₁₀₇9_<109> = 3 · 65998337 · 365057178973_<12> · C89
C89 = P39 · P50
P39 = 263637240968512413080732461825073633921_<39>
P50 = 93294399702451015285120102344332879893080173318533_<50>

Number: 17779_108 N=24595878135367791087706078241140290995475829227525763189262553146307598541431528166757893 ( 89 digits) SNFS difficulty: 109 digits. Divisors found: r1=263637240968512413080732461825073633921 (pp39) r2=93294399702451015285120102344332879893080173318533 (pp50) Version: GGNFS-0.77.1-20060722-k8 Total time: 1.32 hours. Scaled time: 2.66 units (timescale=2.016). Factorization parameters were as follows: n: 24595878135367791087706078241140290995475829227525763189262553146307598541431528166757893 m: 2000000000000000000000 c5: 500 c0: 11 skew: 0.47 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:63914, largePrimes:2364436 encountered Relations: rels:2857998, finalFF:623070 Max relations in full relation-set: 32 Initial matrix: 113078 x 623070 with sparse part having weight 46023530. Pruned matrix : 55805 x 56434 with weight 4401643. Total sieving time: 1.22 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.32 hours. --------- CPU info (if available) ---------- Memory: 2783488k/2936036k available (1999k kernel code, 143628k reserved, 892k data, 148k init) Calibrating delay using timer specific routine.. 4975.48 BogoMIPS (lpj=9950968)
Apr 29, 2008 (2nd): By matsui / GGNFS
2·10¹⁸⁶-3 = 1(9)₁₈₅7_<187> = 19 · C186
C186 = P48 · P138
P48 = 536702269647034089326974744111747439562722018687_<48>
P138 = 196129518818625224605331844109132005572907239230106882174824783188659356706656419547350123734666037979415918599396117880712943463613520849_<138>

N=105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263 ( 186 digits) SNFS difficulty: 186 digits. Divisors found: r1=536702269647034089326974744111747439562722018687 (pp48) r2=196129518818625224605331844109132005572907239230106882174824783188659356706656419547350123734666037979415918599396117880712943463613520849 (pp138) Version: GGNFS-0.77.1-20060513-prescott Total time: 867.04 hours. Scaled time: 1474.84 units (timescale=1.701). Factorization parameters were as follows: n: 105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263 m: 10000000000000000000000000000000000000 c5: 20 c0: -3 skew: 0.68 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 15800001) Primes: RFBsize:501962, AFBsize:502546, largePrimes:6966429 encountered Relations: rels:7485469, finalFF:1145980 Max relations in full relation-set: 28 Initial matrix: 1004574 x 1145980 with sparse part having weight 110867418. Pruned matrix : 897006 x 902092 with weight 92492864. Total sieving time: 843.59 hours. Total relation processing time: 0.23 hours. Matrix solve time: 22.90 hours. Time per square root: 0.32 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 867.04 hours.
Apr 29, 2008: By Jo Yeong Uk / GGNFS
(16·10¹⁵⁴+11)/9 = 1(7)₁₅₃9_<155> = 67 · 44257 · 434857 · 118980623 · 5586083449_<10> · 5904045757_<10> · C115
C115 = P39 · P76
P39 = 424574177680638046809321367987093479461_<39>
P76 = 8275367395159157100758043906017743682611898325580244458730518452024285252847_<76>

Number: 17779_154 N=3513507306804862810538722776440328397675041984180199354540267312541637491202827793705688552751190010953335386275467 ( 115 digits) SNFS difficulty: 156 digits. Divisors found: r1=424574177680638046809321367987093479461 (pp39) r2=8275367395159157100758043906017743682611898325580244458730518452024285252847 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 18.84 hours. Scaled time: 40.37 units (timescale=2.143). Factorization parameters were as follows: n: 3513507306804862810538722776440328397675041984180199354540267312541637491202827793705688552751190010953335386275467 m: 20000000000000000000000000000000 c5: 1 c0: 220 skew: 2.94 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216842, largePrimes:5504362 encountered Relations: rels:5391098, finalFF:491424 Max relations in full relation-set: 28 Initial matrix: 433721 x 491424 with sparse part having weight 37285454. Pruned matrix : 399502 x 401734 with weight 26928509. Total sieving time: 17.98 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.74 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 18.84 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671) Total of 4 processors activated (19393.17 BogoMIPS).
(16·10¹⁵⁷+11)/9 = 1(7)₁₅₆9_<158> = 17 · 78300281 · 419383201693_<12> · 6455324213993_<13> · C124
C124 = P46 · P79
P46 = 4914350290219746139126636107283086748016976763_<46>
P79 = 1003852793048281716132218328272508392055966130363433679564450662607859607459021_<79>

Number: 17779_157 N=4933284264854726011199914777590554288912649583309790986348928487950729049522496039958276785689365379111664392646812831729023 ( 124 digits) SNFS difficulty: 158 digits. Divisors found: r1=4914350290219746139126636107283086748016976763 (pp46) r2=1003852793048281716132218328272508392055966130363433679564450662607859607459021 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 26.38 hours. Scaled time: 56.41 units (timescale=2.138). Factorization parameters were as follows: n: 4933284264854726011199914777590554288912649583309790986348928487950729049522496039958276785689365379111664392646812831729023 m: 20000000000000000000000000000000 c5: 50 c0: 11 skew: 0.74 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:283028, largePrimes:5726623 encountered Relations: rels:5800542, finalFF:692066 Max relations in full relation-set: 28 Initial matrix: 566239 x 692066 with sparse part having weight 44440711. Pruned matrix : 466921 x 469816 with weight 28684118. Total sieving time: 25.29 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.96 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 26.38 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671) Total of 4 processors activated (19393.17 BogoMIPS).
Apr 28, 2008 (4th): By Justin Card / GGNFS
(16·10¹⁶⁵+11)/9 = 1(7)₁₆₄9_<166> = 3 · 139 · 155609 · 92488378321_<11> · 1521710760532564759_<19> · 281473921296763649761469_<24> · C105
C105 = P41 · P65
P41 = 29020234627925602195812824299370283577151_<41>
P65 = 23831333665399274683827843453947996114011483468521275295280977823_<65>

Number: 17779_165 N=691590894466269197730146910797393517066082048486545304291390199393830336725204059012699605334945540522273 ( 105 digits) Divisors found: r1=29020234627925602195812824299370283577151 (pp41) r2=23831333665399274683827843453947996114011483468521275295280977823 (pp65) Version: GGNFS-0.77.1-20060722-k8 Total time: 16.44 hours. Scaled time: 33.17 units (timescale=2.018). Factorization parameters were as follows: name: 17779_165 n: 691590894466269197730146910797393517066082048486545304291390199393830336725204059012699605334945540522273 skew: 15009.73 # norm 3.47e+14 c5: 16800 c4: 1595716796 c3: -4454616847204 c2: -293960595689521449 c1: -1548469487062960190204 c0: 36690328126755034441600 # alpha -5.82 Y1: 97184239787 Y0: -132709482478364848917 # Murphy_E 1.77e-09 # M 278220095968292048864566809319835243296760349851295271958673057244600229804999456623869010072640694735745 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, 2300001) Primes: RFBsize:183072, AFBsize:183403, largePrimes:4536354 encountered Relations: rels:4756460, finalFF:577861 Max relations in full relation-set: 32 Initial matrix: 366556 x 577861 with sparse part having weight 45965216. Pruned matrix : 226843 x 228739 with weight 22348975. Total sieving time: 15.10 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.14 hours. Time per square root: 0.08 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: 16.44 hours. --------- CPU info (if available) ----------
Apr 28, 2008 (3rd): By Jo Yeong Uk / GGNFS, GMP-ECM
(16·10¹⁴⁴+11)/9 = 1(7)₁₄₃9_<145> = 3 · 89 · 313 · 119918389149593_<15> · 9474242254151046271_<19> · C107
C107 = P39 · P69
P39 = 119839803340528054651439296435684615981_<39>
P69 = 156239383006847491926868354100145305520439669088317032907096506743443_<69>

Number: 17779_144 N=18723696933586044238822912804459035527501235116307888482182981914368803208101426662639442126351540344762583 ( 107 digits) SNFS difficulty: 146 digits. Divisors found: r1=119839803340528054651439296435684615981 (pp39) r2=156239383006847491926868354100145305520439669088317032907096506743443 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.90 hours. Scaled time: 19.00 units (timescale=2.135). Factorization parameters were as follows: n: 18723696933586044238822912804459035527501235116307888482182981914368803208101426662639442126351540344762583 m: 200000000000000000000000000000 c5: 1 c0: 220 skew: 2.94 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: RFBsize:135072, AFBsize:135239, largePrimes:3797650 encountered Relations: rels:3966868, finalFF:457655 Max relations in full relation-set: 28 Initial matrix: 270375 x 457655 with sparse part having weight 41124222. Pruned matrix : 204905 x 206320 with weight 17448813. Total sieving time: 8.66 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.17 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 8.90 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671) Total of 4 processors activated (19393.17 BogoMIPS).
(16·10¹⁴⁵+11)/9 = 1(7)₁₄₄9_<146> = 19² · 30519143 · C136
C136 = P33 · P48 · P56
P33 = 219688159837927926313717321649179_<33>
P48 = 181683550514854037041455877867851313467232812473_<48>
P56 = 40427387536757891148686148058262026542402816481494289519_<56>

Number: 17779_145 N=1613607623978796108975503488209942683714546869329096238203971838817228567752709581275427586264502413452233709831637068300797031823380173 ( 136 digits) SNFS difficulty: 146 digits. Divisors found: r1=219688159837927926313717321649179 (pp33) r2=181683550514854037041455877867851313467232812473 (pp48) r3=40427387536757891148686148058262026542402816481494289519 (pp56) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.81 hours. Scaled time: 16.64 units (timescale=2.130). Factorization parameters were as follows: n: 1613607623978796108975503488209942683714546869329096238203971838817228567752709581275427586264502413452233709831637068300797031823380173 m: 200000000000000000000000000000 c5: 1 c0: 22 skew: 1.86 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1425001) Primes: RFBsize:135072, AFBsize:134864, largePrimes:3695013 encountered Relations: rels:3765759, finalFF:378118 Max relations in full relation-set: 28 Initial matrix: 270000 x 378118 with sparse part having weight 32616641. Pruned matrix : 226218 x 227632 with weight 16299176. Total sieving time: 7.54 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.20 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 7.81 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671) Total of 4 processors activated (19393.17 BogoMIPS).
(16·10¹⁶³+11)/9 = 1(7)₁₆₂9_<164> = 19 · 31 · 659 · 128339 · 42696731346006600727_<20> · 33367508415177134907584971_<26> · C108
C108 = P32 · P76
P32 = 59088108152824243798798734618151_<32>
P76 = 4239353385152396199790986646873480940040953204280123465501575552424783987733_<76>
Apr 28, 2008 (2nd): By Sinkiti Sibata / Msieve
(16·10¹⁰³+11)/9 = 1(7)₁₀₂9_<104> = 31 · 457 · 24203 · C95
C95 = P30 · P66
P30 = 331329502808201944657710910493_<30>
P66 = 156484119198691203682352050843360865193448277522438180479674417403_<66>

Sun Apr 27 17:53:55 2008 Msieve v. 1.33 Sun Apr 27 17:53:55 2008 random seeds: cc72b41b e55fc60c Sun Apr 27 17:53:55 2008 factoring 51847805411481765012285536782252654602695323913086773291749786111357201858764951982326454509679 (95 digits) Sun Apr 27 17:53:56 2008 searching for 15-digit factors Sun Apr 27 17:53:58 2008 commencing quadratic sieve (95-digit input) Sun Apr 27 17:53:59 2008 using multiplier of 1 Sun Apr 27 17:53:59 2008 using 64kb Pentium 4 sieve core Sun Apr 27 17:53:59 2008 sieve interval: 18 blocks of size 65536 Sun Apr 27 17:53:59 2008 processing polynomials in batches of 6 Sun Apr 27 17:53:59 2008 using a sieve bound of 2160127 (80000 primes) Sun Apr 27 17:53:59 2008 using large prime bound of 324019050 (28 bits) Sun Apr 27 17:53:59 2008 using double large prime bound of 2084620300746750 (43-51 bits) Sun Apr 27 17:53:59 2008 using trial factoring cutoff of 51 bits Sun Apr 27 17:53:59 2008 polynomial 'A' values have 12 factors Sun Apr 27 23:42:43 2008 80276 relations (20458 full + 59818 combined from 1185745 partial), need 80096 Sun Apr 27 23:42:47 2008 begin with 1206203 relations Sun Apr 27 23:42:49 2008 reduce to 206482 relations in 12 passes Sun Apr 27 23:42:49 2008 attempting to read 206482 relations Sun Apr 27 23:42:55 2008 recovered 206482 relations Sun Apr 27 23:42:55 2008 recovered 188456 polynomials Sun Apr 27 23:42:56 2008 attempting to build 80276 cycles Sun Apr 27 23:42:56 2008 found 80276 cycles in 7 passes Sun Apr 27 23:42:56 2008 distribution of cycle lengths: Sun Apr 27 23:42:56 2008 length 1 : 20458 Sun Apr 27 23:42:56 2008 length 2 : 14410 Sun Apr 27 23:42:56 2008 length 3 : 13520 Sun Apr 27 23:42:56 2008 length 4 : 10770 Sun Apr 27 23:42:56 2008 length 5 : 7925 Sun Apr 27 23:42:56 2008 length 6 : 5271 Sun Apr 27 23:42:56 2008 length 7 : 3408 Sun Apr 27 23:42:56 2008 length 9+: 4514 Sun Apr 27 23:42:56 2008 largest cycle: 24 relations Sun Apr 27 23:42:56 2008 matrix is 80000 x 80276 (21.4 MB) with weight 5291532 (65.92/col) Sun Apr 27 23:42:56 2008 sparse part has weight 5291532 (65.92/col) Sun Apr 27 23:42:58 2008 filtering completed in 3 passes Sun Apr 27 23:42:58 2008 matrix is 75601 x 75665 (20.3 MB) with weight 5013453 (66.26/col) Sun Apr 27 23:42:58 2008 sparse part has weight 5013453 (66.26/col) Sun Apr 27 23:42:58 2008 saving the first 48 matrix rows for later Sun Apr 27 23:42:59 2008 matrix is 75553 x 75665 (13.5 MB) with weight 4044903 (53.46/col) Sun Apr 27 23:42:59 2008 sparse part has weight 3073075 (40.61/col) Sun Apr 27 23:42:59 2008 matrix includes 64 packed rows Sun Apr 27 23:42:59 2008 using block size 21845 for processor cache size 512 kB Sun Apr 27 23:43:00 2008 commencing Lanczos iteration Sun Apr 27 23:43:00 2008 memory use: 12.5 MB Sun Apr 27 23:43:59 2008 lanczos halted after 1196 iterations (dim = 75553) Sun Apr 27 23:43:59 2008 recovered 18 nontrivial dependencies Sun Apr 27 23:44:00 2008 prp30 factor: 331329502808201944657710910493 Sun Apr 27 23:44:00 2008 prp66 factor: 156484119198691203682352050843360865193448277522438180479674417403 Sun Apr 27 23:44:00 2008 elapsed time 05:50:05
(16·10¹¹¹+11)/9 = 1(7)₁₁₀9_<112> = 3 · 3067 · 16644371 · C101
C101 = P30 · P71
P30 = 311891772685877294689988053111_<30>
P71 = 37219551555730460553756515602487763210155431764457159024923543299294359_<71>

Mon Apr 28 01:26:31 2008 Msieve v. 1.33 Mon Apr 28 01:26:31 2008 random seeds: 780f0fe4 d2f66e36 Mon Apr 28 01:26:31 2008 factoring 11608471913290175427106165301392768225200713865227417729953035601937285096499113827092370346514700849 (101 digits) Mon Apr 28 01:26:33 2008 searching for 15-digit factors Mon Apr 28 01:26:35 2008 commencing quadratic sieve (101-digit input) Mon Apr 28 01:26:35 2008 using multiplier of 1 Mon Apr 28 01:26:35 2008 using 64kb Pentium 4 sieve core Mon Apr 28 01:26:35 2008 sieve interval: 18 blocks of size 65536 Mon Apr 28 01:26:35 2008 processing polynomials in batches of 6 Mon Apr 28 01:26:35 2008 using a sieve bound of 2825047 (102495 primes) Mon Apr 28 01:26:35 2008 using large prime bound of 423757050 (28 bits) Mon Apr 28 01:26:35 2008 using double large prime bound of 3379173047684850 (43-52 bits) Mon Apr 28 01:26:35 2008 using trial factoring cutoff of 52 bits Mon Apr 28 01:26:35 2008 polynomial 'A' values have 13 factors Mon Apr 28 19:30:31 2008 102795 relations (24275 full + 78520 combined from 1544216 partial), need 102591 Mon Apr 28 19:30:38 2008 begin with 1568491 relations Mon Apr 28 19:30:40 2008 reduce to 271830 relations in 12 passes Mon Apr 28 19:30:40 2008 attempting to read 271830 relations Mon Apr 28 19:30:50 2008 recovered 271830 relations Mon Apr 28 19:30:50 2008 recovered 261688 polynomials Mon Apr 28 19:30:50 2008 attempting to build 102795 cycles Mon Apr 28 19:30:51 2008 found 102795 cycles in 6 passes Mon Apr 28 19:30:51 2008 distribution of cycle lengths: Mon Apr 28 19:30:51 2008 length 1 : 24275 Mon Apr 28 19:30:51 2008 length 2 : 17638 Mon Apr 28 19:30:51 2008 length 3 : 16976 Mon Apr 28 19:30:51 2008 length 4 : 14225 Mon Apr 28 19:30:51 2008 length 5 : 10704 Mon Apr 28 19:30:51 2008 length 6 : 7374 Mon Apr 28 19:30:51 2008 length 7 : 4841 Mon Apr 28 19:30:51 2008 length 9+: 6762 Mon Apr 28 19:30:51 2008 largest cycle: 19 relations Mon Apr 28 19:30:51 2008 matrix is 102495 x 102795 (27.4 MB) with weight 6780827 (65.96/col) Mon Apr 28 19:30:51 2008 sparse part has weight 6780827 (65.96/col) Mon Apr 28 19:30:53 2008 filtering completed in 3 passes Mon Apr 28 19:30:53 2008 matrix is 98309 x 98373 (26.4 MB) with weight 6514221 (66.22/col) Mon Apr 28 19:30:53 2008 sparse part has weight 6514221 (66.22/col) Mon Apr 28 19:30:54 2008 saving the first 48 matrix rows for later Mon Apr 28 19:30:54 2008 matrix is 98261 x 98373 (15.4 MB) with weight 4981754 (50.64/col) Mon Apr 28 19:30:54 2008 sparse part has weight 3455551 (35.13/col) Mon Apr 28 19:30:54 2008 matrix includes 64 packed rows Mon Apr 28 19:30:54 2008 using block size 21845 for processor cache size 512 kB Mon Apr 28 19:30:55 2008 commencing Lanczos iteration Mon Apr 28 19:30:55 2008 memory use: 15.7 MB Mon Apr 28 19:32:32 2008 lanczos halted after 1556 iterations (dim = 98261) Mon Apr 28 19:32:33 2008 recovered 17 nontrivial dependencies Mon Apr 28 19:32:34 2008 prp30 factor: 311891772685877294689988053111 Mon Apr 28 19:32:34 2008 prp71 factor: 37219551555730460553756515602487763210155431764457159024923543299294359 Mon Apr 28 19:32:34 2008 elapsed time 18:06:03
Apr 28, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(16·10¹³⁰+11)/9 = 1(7)₁₂₉9_<131> = C131
C131 = P51 · P80
P51 = 740649800611949626773509486419719295510999559861201_<51>
P80 = 24002946821951728642362452236161911211145684438969667380651086125420098239262979_<80>

Number: n N=17777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 131 digits) SNFS difficulty: 131 digits. Divisors found: Mon Apr 28 01:29:04 2008 prp51 factor: 740649800611949626773509486419719295510999559861201 Mon Apr 28 01:29:04 2008 prp80 factor: 24002946821951728642362452236161911211145684438969667380651086125420098239262979 Mon Apr 28 01:29:04 2008 elapsed time 00:03:59 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 2.04 hours. Scaled time: 1.70 units (timescale=0.835). Factorization parameters were as follows: name: KA_1_7_129_9 n: 17777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 type: snfs deg: 5 c5: 1 c0: 22 skew: 1.86 m: 200000000000000000000000000 rlim: 1000000 alim: 1000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved special-q in [100000, 439990) Primes: RFBsize:78498, AFBsize:78572, largePrimes:1538766 encountered Relations: rels:1564015, finalFF:194448 Max relations in full relation-set: 28 Initial matrix: 157134 x 194448 with sparse part having weight 10069071. Pruned matrix : Total sieving time: 1.99 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.5,2.5,50000 total time: 2.04 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(16·10¹³⁵+11)/9 = 1(7)₁₃₄9_<136> = 3 · 31543 · C131
C131 = P42 · P90
P42 = 116913662942380963981152305353982462461229_<42>
P90 = 160689668656667462774664759034224831860341321263111183165054495696018746338066716792796019_<90>

Number: n N=18786817759648498639716976590450895367992663747664857261281190520641428925358798864806536873239469695101689522004647389043293047351 ( 131 digits) SNFS difficulty: 136 digits. Divisors found: Mon Apr 28 03:16:59 2008 prp42 factor: 116913662942380963981152305353982462461229 Mon Apr 28 03:16:59 2008 prp90 factor: 160689668656667462774664759034224831860341321263111183165054495696018746338066716792796019 Mon Apr 28 03:16:59 2008 elapsed time 00:05:27 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 3.72 hours. Scaled time: 3.10 units (timescale=0.833). Factorization parameters were as follows: name: KA_1_7_134_9 n: 18786817759648498639716976590450895367992663747664857261281190520641428925358798864806536873239469695101689522004647389043293047351 type: snfs deg: 5 c5: 1 c0: 22 skew: 1.86 m: 2000000000000000000000000000 rlim: 1200000 alim: 1200000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved special-q in [100000, 760000) Primes: RFBsize:92938, AFBsize:93010, largePrimes:1459042 encountered Relations: rels:1486909, finalFF:209935 Max relations in full relation-set: 28 Initial matrix: 186012 x 209935 with sparse part having weight 8026945. Pruned matrix : 165211 x 166205 with weight 5314324. Total sieving time: 3.68 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,43,43,2.5,2.5,75000 total time: 3.72 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(16·10¹³⁷+11)/9 = 1(7)₁₃₆9_<138> = 7 · 28319 · 94698649 · C124
C124 = P44 · P81
P44 = 25057095028301441065470887673091378935372641_<44>
P81 = 377943618185876629077139501895581334015847645792582347898293700223261113504154307_<81>

Number: n N=9470169156223587389224065451365074531135004558489529786850901405282576799155265960697494003782555977979977594246624610114787 ( 124 digits) SNFS difficulty: 138 digits. Divisors found: r1=25057095028301441065470887673091378935372641 (pp44) r2=377943618185876629077139501895581334015847645792582347898293700223261113504154307 (pp81) Version: GGNFS-0.77.1-20051202-k8 Total time: 6.04 hours. Scaled time: 5.06 units (timescale=0.837). Factorization parameters were as follows: name: KA_1_7_136_9 n: 9470169156223587389224065451365074531135004558489529786850901405282576799155265960697494003782555977979977594246624610114787 type: snfs deg: 5 c5: 50 c0: 11 skew: 0.74 m: 2000000000000000000000000000 rlim: 1000000 alim: 1000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [100000, 1240001) Primes: RFBsize:78498, AFBsize:78657, largePrimes:1532234 encountered Relations: rels:1527221, finalFF:178475 Max relations in full relation-set: 28 Initial matrix: 157220 x 178475 with sparse part having weight 11121586. Pruned matrix : 150304 x 151154 with weight 7874976. Total sieving time: 5.86 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,43,43,2.5,2.5,75000 total time: 6.04 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(16·10¹⁴²+11)/9 = 1(7)₁₄₁9_<143> = 326017631 · C134
C134 = P38 · P46 · P51
P38 = 27671075944796408029522595003337759929_<38>
P46 = 6590894924445613177053144476952932493083835323_<46>
P51 = 298996394724726338639789823356192339064617460410927_<51>

Number: n N=54530111525710024491828105387888600962742956002210131321940002004915426729721184244105429309673677672290606202760174580183296214976109 ( 134 digits) SNFS difficulty: 143 digits. Divisors found: Mon Apr 28 17:53:49 2008 prp38 factor: 27671075944796408029522595003337759929 Mon Apr 28 17:53:49 2008 prp46 factor: 6590894924445613177053144476952932493083835323 Mon Apr 28 17:53:49 2008 prp51 factor: 298996394724726338639789823356192339064617460410927 Mon Apr 28 17:53:49 2008 elapsed time 00:12:27 Version: GGNFS-0.77.1-20050930-k8 Total time: 7.73 hours. Scaled time: 6.48 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_7_141_9 n: 54530111525710024491828105387888600962742956002210131321940002004915426729721184244105429309673677672290606202760174580183296214976109 type: snfs deg: 5 c5: 50 c0: 11 skew: 0.74 m: 20000000000000000000000000000 rlim: 1000000 alim: 1000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved special-q in [100000, 1600897) Primes: RFBsize:78498, AFBsize:78657, largePrimes:2604383 encountered Relations: rels:2484203, finalFF:121506 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 7.63 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1000000,1000000,26,26,45,45,2.5,2.5,100000 total time: 7.73 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(16·10¹⁶⁸+11)/9 = 1(7)₁₆₇9_<169> = 3² · 71 · C166
C166 = P34 · P133
P34 = 1920233553146556380827007015720641_<34>
P133 = 1448847117213251607625355567575003378529401722538088872843295916219662258839658830543803065160753377230243618938669969296230845983821_<133>
Apr 27, 2008 (3rd): By Jo Yeong Uk / GGNFS, GMP-ECM
(16·10¹³⁶+11)/9 = 1(7)₁₃₅9_<137> = 23 · 53 · 441405097643_<12> · 808610497337_<12> · 2616087389059_<13> · C98
C98 = P30 · P68
P30 = 878422995771064242156524199679_<30>
P68 = 17780382705310184963084137750438109941582309771712168927829813727591_<68>

Number: 17779_136 N=15618697041954592395199300036107685358583358819631114262492224881317156816884962005048828995643289 ( 98 digits) Divisors found: r1=878422995771064242156524199679 (pp30) r2=17780382705310184963084137750438109941582309771712168927829813727591 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.55 hours. Scaled time: 5.43 units (timescale=2.131). Factorization parameters were as follows: name: 17779_136 n: 15618697041954592395199300036107685358583358819631114262492224881317156816884962005048828995643289 skew: 2515.38 # norm 1.60e+13 c5: 227880 c4: -100766386 c3: -2631617626383 c2: 3483269386581489 c1: 8847300392404231453 c0: -10566367372676025532153 # alpha -5.45 Y1: 27021702347 Y0: -2329100152203075420 # Murphy_E 4.63e-09 # M 5611294509854701452427197899181609930823487150004322445320319899280321733814839177639706302297392 type: gnfs rlim: 1300000 alim: 1300000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [650000, 1000001) Primes: RFBsize:100021, AFBsize:100521, largePrimes:3729833 encountered Relations: rels:3572357, finalFF:257700 Max relations in full relation-set: 28 Initial matrix: 200626 x 257700 with sparse part having weight 19363794. Pruned matrix : 163294 x 164361 with weight 9665215. Polynomial selection time: 0.20 hours. Total sieving time: 2.17 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,97,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1300000,1300000,26,26,48,48,2.5,2.5,50000 total time: 2.55 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671) Total of 4 processors activated (19393.17 BogoMIPS).
(16·10¹⁶⁹+11)/9 = 1(7)₁₆₈9_<170> = C170
C170 = P43 · P127
P43 = 2775860259573482934248483330570378457853049_<43>
P127 = 6404421013797493046865420439571729954912032159024481277804152948807882071405358296499945494751597025942489791947474746224573771_<127>
(16·10¹⁴¹+11)/9 = 1(7)₁₄₀9_<142> = 3² · 17 · 4799 · 4244407045105529_<16> · C120
C120 = P37 · P83
P37 = 6522369570081283852203348349906721407_<37>
P83 = 87460682613272569632304161894821897127960481192555515075521999576953130373280138819_<83>

Number: 17779_141 N=570450894855346227484587960803916244029526110944038813634612710061479771528045222860658881615959667876449462506118998333 ( 120 digits) SNFS difficulty: 142 digits. Divisors found: r1=6522369570081283852203348349906721407 (pp37) r2=87460682613272569632304161894821897127960481192555515075521999576953130373280138819 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.91 hours. Scaled time: 12.68 units (timescale=2.144). Factorization parameters were as follows: n: 570450894855346227484587960803916244029526110944038813634612710061479771528045222860658881615959667876449462506118998333 m: 20000000000000000000000000000 c5: 5 c0: 11 skew: 1.17 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114558, largePrimes:3326212 encountered Relations: rels:3407379, finalFF:377949 Max relations in full relation-set: 28 Initial matrix: 228778 x 377949 with sparse part having weight 32131042. Pruned matrix : 176386 x 177593 with weight 12842783. Total sieving time: 5.74 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 5.91 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167428k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4957.34 BogoMIPS (lpj=2478671) Total of 4 processors activated (19393.17 BogoMIPS).
Apr 27, 2008 (2nd): By Sinkiti Sibata / Msieve, GGNFS
(16·10¹²²+11)/9 = 1(7)₁₂₁9_<123> = 2957 · 484877128152342319_<18> · 8773066214071332211_<19> · C83
C83 = P29 · P54
P29 = 64143200499177888756970894601_<29>
P54 = 220339529129826668084568653822613720420620993023058483_<54>

Sun Apr 27 06:13:50 2008 Msieve v. 1.33 Sun Apr 27 06:13:50 2008 random seeds: 34d55870 5576daea Sun Apr 27 06:13:50 2008 factoring 14133282594868918897014068537774654409902449086370890143333043941049463297651950283 (83 digits) Sun Apr 27 06:13:52 2008 searching for 15-digit factors Sun Apr 27 06:13:53 2008 commencing quadratic sieve (83-digit input) Sun Apr 27 06:13:53 2008 using multiplier of 1 Sun Apr 27 06:13:53 2008 using 64kb Pentium 4 sieve core Sun Apr 27 06:13:53 2008 sieve interval: 6 blocks of size 65536 Sun Apr 27 06:13:53 2008 processing polynomials in batches of 17 Sun Apr 27 06:13:53 2008 using a sieve bound of 1359077 (52059 primes) Sun Apr 27 06:13:53 2008 using large prime bound of 125035084 (26 bits) Sun Apr 27 06:13:53 2008 using trial factoring cutoff of 27 bits Sun Apr 27 06:13:53 2008 polynomial 'A' values have 10 factors Sun Apr 27 06:51:31 2008 52222 relations (26417 full + 25805 combined from 282787 partial), need 52155 Sun Apr 27 06:51:32 2008 begin with 309204 relations Sun Apr 27 06:51:32 2008 reduce to 74824 relations in 2 passes Sun Apr 27 06:51:32 2008 attempting to read 74824 relations Sun Apr 27 06:51:34 2008 recovered 74824 relations Sun Apr 27 06:51:34 2008 recovered 67842 polynomials Sun Apr 27 06:51:34 2008 attempting to build 52222 cycles Sun Apr 27 06:51:34 2008 found 52222 cycles in 1 passes Sun Apr 27 06:51:34 2008 distribution of cycle lengths: Sun Apr 27 06:51:34 2008 length 1 : 26417 Sun Apr 27 06:51:34 2008 length 2 : 25805 Sun Apr 27 06:51:34 2008 largest cycle: 2 relations Sun Apr 27 06:51:34 2008 matrix is 52059 x 52222 (7.0 MB) with weight 1615986 (30.94/col) Sun Apr 27 06:51:34 2008 sparse part has weight 1615986 (30.94/col) Sun Apr 27 06:51:35 2008 filtering completed in 4 passes Sun Apr 27 06:51:35 2008 matrix is 45234 x 45298 (5.9 MB) with weight 1376746 (30.39/col) Sun Apr 27 06:51:35 2008 sparse part has weight 1376746 (30.39/col) Sun Apr 27 06:51:35 2008 saving the first 48 matrix rows for later Sun Apr 27 06:51:35 2008 matrix is 45186 x 45298 (4.6 MB) with weight 1113733 (24.59/col) Sun Apr 27 06:51:35 2008 sparse part has weight 928738 (20.50/col) Sun Apr 27 06:51:35 2008 matrix includes 64 packed rows Sun Apr 27 06:51:35 2008 commencing Lanczos iteration Sun Apr 27 06:51:35 2008 memory use: 6.3 MB Sun Apr 27 06:52:36 2008 lanczos halted after 716 iterations (dim = 45172) Sun Apr 27 06:52:36 2008 recovered 10 nontrivial dependencies Sun Apr 27 06:52:37 2008 prp29 factor: 64143200499177888756970894601 Sun Apr 27 06:52:37 2008 prp54 factor: 220339529129826668084568653822613720420620993023058483 Sun Apr 27 06:52:37 2008 elapsed time 00:38:47
(16·10¹²³+11)/9 = 1(7)₁₂₂9_<124> = 3⁵ · 53 · C120
C120 = P46 · P74
P46 = 3127936728760055563783574813204076500296280377_<46>
P74 = 44130349846097590297953030403378448580759948085469636863079649654491796613_<74>

Number: 17779_123 N=138036942136639318097505845001768598321125691263124293639085160165989422919308780012250778614626739481153643743906963101 ( 120 digits) SNFS difficulty: 124 digits. Divisors found: r1=3127936728760055563783574813204076500296280377 (pp46) r2=44130349846097590297953030403378448580759948085469636863079649654491796613 (pp74) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.64 hours. Scaled time: 1.78 units (timescale=0.677). Factorization parameters were as follows: name: 17779_123 n: 138036942136639318097505845001768598321125691263124293639085160165989422919308780012250778614626739481153643743906963101 m: 2000000000000000000000000 c5: 500 c0: 11 skew: 0.47 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:49098, AFBsize:63914, largePrimes:2151100 encountered Relations: rels:2241438, finalFF:227478 Max relations in full relation-set: 28 Initial matrix: 113078 x 227478 with sparse part having weight 20178265. Pruned matrix : 88548 x 89177 with weight 5335089. Total sieving time: 2.40 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.64 hours. --------- CPU info (if available) ----------
(16·10¹²⁴+11)/9 = 1(7)₁₂₃9_<125> = 12300377951_<11> · 595919247296270033_<18> · C97
C97 = P32 · P65
P32 = 51816470851532967590612913006763_<32>
P65 = 46806242024873304391156980530608793867173799266257699394339756951_<65>

Number: 17779_124 N=2425334275551645003990077583460898220356269581536513355431225872560438064950944002546028039259613 ( 97 digits) SNFS difficulty: 125 digits. Divisors found: r1=51816470851532967590612913006763 (pp32) r2=46806242024873304391156980530608793867173799266257699394339756951 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 3.05 hours. Scaled time: 2.07 units (timescale=0.677). Factorization parameters were as follows: name: 17779_124 n: 2425334275551645003990077583460898220356269581536513355431225872560438064950944002546028039259613 m: 10000000000000000000000000 c5: 8 c0: 55 skew: 1.47 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:64019, largePrimes:2066221 encountered Relations: rels:2056554, finalFF:139191 Max relations in full relation-set: 28 Initial matrix: 113182 x 139191 with sparse part having weight 12160681. Pruned matrix : 105923 x 106552 with weight 7525402. Total sieving time: 2.72 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.21 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.05 hours. --------- CPU info (if available) ----------
Apr 27, 2008: By Robert Backstrom / GMP-ECM, GGNFS
(16·10¹²⁸+11)/9 = 1(7)₁₂₇9_<129> = C129
C129 = P29 · P100
P29 = 32710453956769251258301493239_<29>
P100 = 5434891793697886900299526331565538939027676011247994752035924882091324105223592214028104168618741861_<100>
(16·10¹⁴⁰+11)/9 = 1(7)₁₃₉9_<141> = C141
C141 = P33 · P108
P33 = 325913857692204415401309983425939_<33>
P108 = 545474743039838751488576360288698540556507517839459352048194572123867434191137681771453058583347982000134561_<108>
(16·10¹¹⁵+11)/9 = 1(7)₁₁₄9_<116> = 4106117 · 31044253863947_<14> · C96
C96 = P33 · P63
P33 = 376009549465429802217359002735787_<33>
P63 = 370907873250938245237270331446578676378971815606577371756099183_<63>
(16·10¹³²+11)/9 = 1(7)₁₃₁9_<133> = 3² · 10258433 · 1163149133_<10> · 4572945031709856547_<19> · C97
C97 = P39 · P58
P39 = 393755777432321520680320952896244231087_<39>
P58 = 9193811940508378094496295181426517692653384859674800617411_<58>
(16·10¹¹⁷+11)/9 = 1(7)₁₁₆9_<118> = 3 · 54319 · C113
C113 = P45 · P68
P45 = 385663420156498117850474192254799661294286001_<45>
P68 = 28287593603832924128934670018553127378252757220332340058030657206447_<68>

Number: n N=10909490097251285785684430725760647150952568946272806800430652121588994506389892902899401546283852659154119048447 ( 113 digits) SNFS difficulty: 118 digits. Divisors found: r1=385663420156498117850474192254799661294286001 (pp45) r2=28287593603832924128934670018553127378252757220332340058030657206447 (pp68) Version: GGNFS-0.77.1-20051202-k8 Total time: 1.04 hours. Scaled time: 0.87 units (timescale=0.837). Factorization parameters were as follows: name: KA_1_7_116_9 n: 10909490097251285785684430725760647150952568946272806800430652121588994506389892902899401546283852659154119048447 type: snfs deg: 5 c5: 50 c0: 11 skew: 0.74 m: 200000000000000000000000 rlim: 600000 alim: 600000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [100000, 220001) Primes: RFBsize:49098, AFBsize:49122, largePrimes:1775672 encountered Relations: rels:1748487, finalFF:152025 Max relations in full relation-set: 28 Initial matrix: 98285 x 152025 with sparse part having weight 11114209. Pruned matrix : 80390 x 80945 with weight 3947440. Total sieving time: 0.96 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.5,2.5,50000 total time: 1.04 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Apr 26, 2008 (2nd): The factor table of 177...779 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Apr 26, 2008: By Robert Backstrom / GGNFS
(85·10¹⁶⁷+41)/9 = 9(4)₁₆₆9_<168> = 11 · 2179 · 466717 · C158
C158 = P75 · P84
P75 = 478777639625485469663091713680607336457292333499171590319017223759486984099_<75>
P84 = 176335202682166386931839569414134269241546576483219882902726853160083292707756562887_<84>

Number: n N=84425352123049197208177915165707899447036189177692463379021379908918745208076669939396868139201725618297748923996932993146192178295917212487074132321862533813 ( 158 digits) SNFS difficulty: 168 digits. Divisors found: Sat Apr 26 04:46:51 2008 prp75 factor: 478777639625485469663091713680607336457292333499171590319017223759486984099 Sat Apr 26 04:46:51 2008 prp84 factor: 176335202682166386931839569414134269241546576483219882902726853160083292707756562887 Sat Apr 26 04:46:51 2008 elapsed time 01:20:35 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 70.44 hours. Scaled time: 128.83 units (timescale=1.829). Factorization parameters were as follows: name: KA_9_4_166_9 n: 84425352123049197208177915165707899447036189177692463379021379908918745208076669939396868139201725618297748923996932993146192178295917212487074132321862533813 skew: 0.34 deg: 5 c5: 8500 c0: 41 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 5000001) Primes: RFBsize:230209, AFBsize:229823, largePrimes:7938150 encountered Relations: rels:7368085, finalFF:505504 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 70.15 hours. Total relation processing time: 0.28 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,168,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 70.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(16·10¹⁶⁴-43)/9 = 1(7)₁₆₃3_<165> = 11063693333597774647989287_<26> · C140
C140 = P53 · P87
P53 = 37825696522622096171083659643078327824572061489197777_<53>
P87 = 424805772907959277493320907232824775148202682469380305573348520991402189391592516027227_<87>

Number: n N=16068574247074387113577017620238159213093751526506479937667554421487231709771454916780284266738393304073675357872389785275140835203319874379 ( 140 digits) SNFS difficulty: 165 digits. Divisors found: Sat Apr 26 11:25:38 2008 prp53 factor: 37825696522622096171083659643078327824572061489197777 Sat Apr 26 11:25:38 2008 prp87 factor: 424805772907959277493320907232824775148202682469380305573348520991402189391592516027227 Sat Apr 26 11:25:38 2008 elapsed time 01:38:39 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 76.73 hours. Scaled time: 100.59 units (timescale=1.311). Factorization parameters were as follows: name: KA_1_7_163_3 n: 16068574247074387113577017620238159213093751526506479937667554421487231709771454916780284266738393304073675357872389785275140835203319874379 skew: 1.93 deg: 5 c5: 8 c0: -215 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3500001) Primes: RFBsize:216816, AFBsize:216381, largePrimes:7668818 encountered Relations: rels:7112633, finalFF:424994 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 76.41 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 76.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Apr 25, 2008: By Robert Backstrom / GGNFS
(5·10¹⁶⁶-11)/3 = 1(6)₁₆₅3_<167> = 17 · 19 · 73 · 756571 · 10397899 · C149
C149 = P70 · P80
P70 = 2332212323169386388539679035029940177328309787579459539882098944585367_<70>
P80 = 38526539008572372320474777732088353752020424841256198151210841483240600452254379_<80>

Number: n N=89852069044858560668750522416608538221723838872348015749209852062494094029896856524204751899820732855080213308886948940351550969450891700210565072093 ( 149 digits) SNFS difficulty: 166 digits. Divisors found: Fri Apr 25 04:39:41 2008 prp70 factor: 2332212323169386388539679035029940177328309787579459539882098944585367 Fri Apr 25 04:39:41 2008 prp80 factor: 38526539008572372320474777732088353752020424841256198151210841483240600452254379 Fri Apr 25 04:39:41 2008 elapsed time 01:01:06 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 49.93 hours. Scaled time: 91.03 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_6_165_3 n: 89852069044858560668750522416608538221723838872348015749209852062494094029896856524204751899820732855080213308886948940351550969450891700210565072093 skew: 0.74 deg: 5 c5: 50 c0: -11 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3400247) Primes: RFBsize:230209, AFBsize:229978, largePrimes:7618075 encountered Relations: rels:7060809, finalFF:508891 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 49.69 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 49.93 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(16·10¹⁶²-43)/9 = 1(7)₁₆₁3_<163> = 3 · 6173 · 25301 · 172688383333_<12> · C143
C143 = P66 · P77
P66 = 326773001141993809558562853170105920525309244037613952095021260743_<66>
P77 = 67237717844254366899445055496166348279678953568775065861539166002421097389093_<77>

Number: n N=21971470849905589781816163859762807759659618505769802309846316269757328765929790453755702044661205491733330322156227744695485489829202477276099 ( 143 digits) SNFS difficulty: 163 digits. Divisors found: Fri Apr 25 07:05:56 2008 prp66 factor: 326773001141993809558562853170105920525309244037613952095021260743 Fri Apr 25 07:05:56 2008 prp77 factor: 67237717844254366899445055496166348279678953568775065861539166002421097389093 Fri Apr 25 07:05:56 2008 elapsed time 01:24:53 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 49.89 hours. Scaled time: 72.29 units (timescale=1.449). Factorization parameters were as follows: name: KA_1_7_161_3 n: 21971470849905589781816163859762807759659618505769802309846316269757328765929790453755702044661205491733330322156227744695485489829202477276099 skew: 0.97 deg: 5 c5: 50 c0: -43 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500001) Primes: RFBsize:216816, AFBsize:217591, largePrimes:7367926 encountered Relations: rels:6812297, finalFF:451630 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 49.66 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 49.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Apr 24, 2008 (3rd): By Jo Yeong Uk / GGNFS
8·10¹⁸⁷-1 = 7(9)₁₈₇_<188> = 50221 · 718693111 · 5015358357341_<13> · 153590809952823656448053791352618581_<36> · C127
C127 = P39 · P89
P39 = 102746196181289754298239251281338562669_<39>
P89 = 28004524047110445703490411149385111933719827225584358402128727994530576296739317131430321_<89>

Number: 79999_187 N=2877358321708056371637969064791902153383448514723182208423678494914578167998439620341180341926287474457161806866745674265286749 ( 127 digits) Divisors found: r1=102746196181289754298239251281338562669 (pp39) r2=28004524047110445703490411149385111933719827225584358402128727994530576296739317131430321 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 105.29 hours. Scaled time: 225.52 units (timescale=2.142). Factorization parameters were as follows: name: 79999_187 n: 2877358321708056371637969064791902153383448514723182208423678494914578167998439620341180341926287474457161806866745674265286749 skew: 118531.10 # norm 1.27e+18 c5: 211680 c4: 27888457668 c3: -30707314002614800 c2: -457033680365705694301 c1: 74995606544574695438010410 c0: 1800229401639660547285944025875 # alpha -6.47 Y1: 79155702651047 Y0: -1685242049280354239419882 # Murphy_E 1.10e-10 # M 1590663983762522431907323915639751824626006268440442543393364548175785465778167857020397429970250589216784389782494022134624971 type: gnfs rlim: 10000000 alim: 10000000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved algebraic special-q in [5000000, 9400001) Primes: RFBsize:664579, AFBsize:664026, largePrimes:14317582 encountered Relations: rels:14420782, finalFF:1501288 Max relations in full relation-set: 28 Initial matrix: 1328687 x 1501288 with sparse part having weight 116492666. Pruned matrix : 1169118 x 1175825 with weight 77386664. Total sieving time: 94.61 hours. Total relation processing time: 0.38 hours. Matrix solve time: 9.80 hours. Time per square root: 0.50 hours. Prototype def-par.txt line would be: gnfs,126,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,10000000,10000000,28,28,52,52,2.5,2.5,100000 total time: 105.29 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407673) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.06 BogoMIPS).
Apr 24, 2008 (2nd): By Sinkiti Sibata / GGNFS
(16·10¹⁵⁷-43)/9 = 1(7)₁₅₆3_<158> = · 457 · 467333 · 4456892921623_<13> · C136
C136 = P58 · P78
P58 = 2901114003506502307610374028265030500707093188178486117273_<58>
P78 = 495215781372945896967601620398746944009945389531259589750405256931914950509179_<78>

Number: 17773_157 N=1436677438098467843084575873801589371763127357660342525685576450844456202363206072561849265365343365545478507747923070405695314056948867 ( 136 digits) SNFS difficulty: 158 digits. Divisors found: r1=2901114003506502307610374028265030500707093188178486117273 (pp58) r2=495215781372945896967601620398746944009945389531259589750405256931914950509179 (pp78) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 66.41 hours. Scaled time: 44.96 units (timescale=0.677). Factorization parameters were as follows: name: 17773_157 n: 1436677438098467843084575873801589371763127357660342525685576450844456202363206072561849265365343365545478507747923070405695314056948867 m: 20000000000000000000000000000000 c5: 50 c0: -43 skew: 0.97 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:283917, largePrimes:5731714 encountered Relations: rels:5820203, finalFF:703323 Max relations in full relation-set: 28 Initial matrix: 567128 x 703323 with sparse part having weight 45486140. Pruned matrix : 458529 x 461428 with weight 29111704. Total sieving time: 57.29 hours. Total relation processing time: 0.29 hours. Matrix solve time: 8.63 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 66.41 hours. --------- CPU info (if available) ----------
Apr 24, 2008: By Robert Backstrom / GMP-ECM
8·10¹⁷²+3 = 8(0)₁₇₁3_<173> = 7 · 11² · 53 · 261587 · 13420331 · 14742878852145643127878371424312249_<35> · C122
C122 = P41 · P82
P41 = 14102707670245966200868549502313038790457_<41>
P82 = 2441555056445183184204788723617272663411410204503080174188931011979879367292787673_<82>
Apr 23, 2008: By Robert Backstrom / GGNFS, Msieve
10¹⁸⁴+3 = 1(0)₁₈₃3_<185> = 7 · C184
C184 = P67 · P117
P67 = 9818100172727968626557779746645595165748218531909597522519996742899_<67>
P117 = 145503855474974097626225854491524811807124225128548763972026441569570512183910306970186124416727300719805279405934471_<117>

Number: n N=1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 ( 184 digits) SNFS difficulty: 185 digits. Divisors found: Wed Apr 23 01:45:47 2008 prp67 factor: 9818100172727968626557779746645595165748218531909597522519996742899 Wed Apr 23 01:45:47 2008 prp117 factor: 145503855474974097626225854491524811807124225128548763972026441569570512183910306970186124416727300719805279405934471 Wed Apr 23 01:45:47 2008 elapsed time 03:35:36 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 75.46 hours. Scaled time: 97.80 units (timescale=1.296). Factorization parameters were as follows: name: KA_1_0_183_3 n: 1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571429 skew: 1.97 deg: 5 c5: 1 c0: 30 m: 10000000000000000000000000000000000000 type: snfs rlim: 7000000 alim: 7000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4699990) Primes: RFBsize:476648, AFBsize:475219, largePrimes:9263849 encountered Relations: rels:9010978, finalFF:1072839 Max relations in full relation-set: 28 Initial matrix: 951931 x 1072839 with sparse part having weight 55004411. Pruned matrix : Total sieving time: 75.09 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,7000000,7000000,28,28,48,48,2.5,2.5,100000 total time: 75.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Apr 22, 2008 (2nd): By Wataru Sakai / GGNFS
(16·10¹⁸²-7)/9 = 1(7)₁₈₂_<183> = 3 · 227 · 30853 · 1396054142825212027_<19> · 30844830282414589468929329921501_<32> · C126
C126 = P50 · P76
P50 = 77353780133776529862472058000124963556450822141289_<50>
P76 = 2540193343944179996047245110605127443108044311279781450571038782918768697763_<76>

Number: template N=196493557424740682427240818584015055922748541801083874106162700859906957590919852245108331779080425865538457466900821724236507 ( 126 digits) Divisors found: r1=77353780133776529862472058000124963556450822141289 (pp50) r2=2540193343944179996047245110605127443108044311279781450571038782918768697763 (pp76) Version: GGNFS-0.77.1-20060722-nocona Total time: 175.25 hours. Scaled time: 353.13 units (timescale=2.015). Factorization parameters were as follows: name: template n: 196493557424740682427240818584015055922748541801083874106162700859906957590919852245108331779080425865538457466900821724236507 skew: 532555.37 # norm 4.26e+17 c5: 360 c4: -1530324443 c3: 3607202194095335 c2: 98272719477410458842 c1: -109507700429145984560920665 c0: 91593504604744425816368538465 # alpha -5.05 Y1: 33768739669423 Y0: -3527058784468384430641268 # Murphy_E 1.08e-10 # M 167783583878167419122603057044635014571958614459810334116778788696171969889816762212443121528709944125342409454564030436877113 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 60000 Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2700000, 9480001) Primes: RFBsize:374362, AFBsize:374330, largePrimes:9514076 encountered Relations: rels:10472238, finalFF:937321 Max relations in full relation-set: 32 Initial matrix: 748767 x 937321 with sparse part having weight 138147417. Pruned matrix : 617364 x 621171 with weight 115795060. Total sieving time: 169.06 hours. Total relation processing time: 0.25 hours. Matrix solve time: 5.52 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: gnfs,125,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5,60000 total time: 175.25 hours. --------- CPU info (if available) ----------
Apr 22, 2008: By Jo Yeong Uk / GGNFS
(5·10¹⁶¹-11)/3 = 1(6)₁₆₀3_<162> = 7 · 1259 · 29803 · 148639 · 6067219597_<10> · 88884873097_<11> · 405666641269_<12> · C116
C116 = P33 · P84
P33 = 121384631786385382186720547431793_<33>
P84 = 160761351830866943488566918884895797008739383646571499046004747235276493743031507551_<84>

Number: 16663_161 N=19513957497471335445827696533813670496727362690069642235708411907732675763782069629125383015431683072942154136968943 ( 116 digits) Divisors found: r1=121384631786385382186720547431793 (pp33) r2=160761351830866943488566918884895797008739383646571499046004747235276493743031507551 (pp84) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.38 hours. Scaled time: 54.26 units (timescale=2.138). Factorization parameters were as follows: name: 16663_161 n: 19513957497471335445827696533813670496727362690069642235708411907732675763782069629125383015431683072942154136968943 skew: 24827.25 # norm 1.19e+16 c5: 39600 c4: 13149981748 c3: -456242557359933 c2: -6241594165039819254 c1: 13965529947566801370158 c0: -32658529279555611788809464 # alpha -6.00 Y1: 4007171096653 Y0: -13756933333544773509065 # Murphy_E 4.99e-10 # M 9725444623948773597185089542966777252611422691702276753671161477699391779206570499114792041792732623559418709227838 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 70000 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, 3080001) Primes: RFBsize:250150, AFBsize:251683, largePrimes:7620277 encountered Relations: rels:7585076, finalFF:636556 Max relations in full relation-set: 28 Initial matrix: 501916 x 636556 with sparse part having weight 57705817. Pruned matrix : 397719 x 400292 with weight 35269443. Polynomial selection time: 1.51 hours. Total sieving time: 22.62 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.96 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000 total time: 25.38 hours. --------- CPU info (if available) ----------
Apr 21, 2008: By Sinkiti Sibata / GGNFS
(16·10¹⁵¹-43)/9 = 1(7)₁₅₀3_<152> = 13 · 71 · 660625704667_<12> · C137
C137 = P40 · P98
P40 = 2059807738909432649830264775862735198581_<40>
P98 = 14154470212110609361234331264093140155481663019204352112608445144751444243122493047528117504605313_<98>

Number: 17773_151 N=29155487283068471826109014159539684461899607166052702691944454477590659352794774953445901173552777684030303570065790988266341893082660853 ( 137 digits) SNFS difficulty: 152 digits. Divisors found: r1=2059807738909432649830264775862735198581 (pp40) r2=14154470212110609361234331264093140155481663019204352112608445144751444243122493047528117504605313 (pp98) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 34.51 hours. Scaled time: 23.33 units (timescale=0.676). Factorization parameters were as follows: name: 17773_151 n: 29155487283068471826109014159539684461899607166052702691944454477590659352794774953445901173552777684030303570065790988266341893082660853 m: 2000000000000000000000000000000 c5: 5 c0: -43 skew: 1.54 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175898, largePrimes:5380793 encountered Relations: rels:5213423, finalFF:415029 Max relations in full relation-set: 28 Initial matrix: 352265 x 415029 with sparse part having weight 35736426. Pruned matrix : 322290 x 324115 with weight 24241194. Total sieving time: 30.40 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.76 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 34.51 hours. --------- CPU info (if available) ----------
Apr 20, 2008 (3rd): By Wataru Sakai / GMP-ECM
(16·10¹⁹¹-43)/9 = 1(7)₁₉₀3_<192> = 678961553437_<12> · 1221328889923_<13> · C168
C168 = P38 · P130
P38 = 64024419926416439664546147244965522487_<38>
P130 = 3348528562739821307034868195960668802228141828168170031835393402661109187594911879893998700809150934886296138950389462224621424829_<130>
Apr 20, 2008 (2nd): By Jo Yeong Uk / GGNFS
10¹⁷⁵+3 = 1(0)₁₇₄3_<176> = 13 · 1550513 · C168
C168 = P41 · P127
P41 = 84605989629414611161564159889389410528733_<41>
P127 = 5863813190635906011331311978267233281067998931182925784006119151460092105536944514992383719950101352924989857277216412589708939_<127>

Number: 10003_175 N=496113717995766066307880533236915285953249517566617777967182970559272467092653056911337880281707260262099853899471187426851132992261767060817439627549571806730566444287 ( 168 digits) SNFS difficulty: 175 digits. Divisors found: r1=84605989629414611161564159889389410528733 (pp41) r2=5863813190635906011331311978267233281067998931182925784006119151460092105536944514992383719950101352924989857277216412589708939 (pp127) Version: GGNFS-0.77.1-20050930-nocona Total time: 105.85 hours. Scaled time: 226.62 units (timescale=2.141). Factorization parameters were as follows: n: 496113717995766066307880533236915285953249517566617777967182970559272467092653056911337880281707260262099853899471187426851132992261767060817439627549571806730566444287 m: 100000000000000000000000000000000000 c5: 1 c0: 3 skew: 1.25 type: snfs Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [4200000, 6000001) Primes: RFBsize:564877, AFBsize:564406, largePrimes:10850911 encountered Relations: rels:11119170, finalFF:1442537 Max relations in full relation-set: 28 Initial matrix: 1129347 x 1442537 with sparse part having weight 89062627. Pruned matrix : 837022 x 842732 with weight 50559156. Total sieving time: 100.83 hours. Total relation processing time: 0.17 hours. Matrix solve time: 4.76 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,50,50,2.6,2.6,100000 total time: 105.85 hours. --------- CPU info (if available) ----------
(16·10¹⁵⁹-43)/9 = 1(7)₁₅₈3_<160> = 3 · 225493 · 10664310082475575481_<20> · C135
C135 = P50 · P85
P50 = 50742578999008560483591754078912162960258196529877_<50>
P85 = 4856438048175192886765210965298149844959246658051867441833610068768177210758899421951_<85>

Number: 17773_159 N=246428191313320666306972352915263184365357951694412511444685487421882568203843254315116845466116984910218199201031653835403409401130027 ( 135 digits) SNFS difficulty: 161 digits. Divisors found: r1=50742578999008560483591754078912162960258196529877 (pp50) r2=4856438048175192886765210965298149844959246658051867441833610068768177210758899421951 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 36.12 hours. Scaled time: 77.31 units (timescale=2.140). Factorization parameters were as follows: n: 246428191313320666306972352915263184365357951694412511444685487421882568203843254315116845466116984910218199201031653835403409401130027 m: 200000000000000000000000000000000 c5: 1 c0: -860 skew: 3.86 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 4200001) Primes: RFBsize:283146, AFBsize:282747, largePrimes:5782527 encountered Relations: rels:5844803, finalFF:676274 Max relations in full relation-set: 28 Initial matrix: 565957 x 676274 with sparse part having weight 47468304. Pruned matrix : 489177 x 492070 with weight 33466786. Total sieving time: 34.67 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.32 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 36.12 hours. --------- CPU info (if available) ----------
Apr 20, 2008: By Sinkiti Sibata / GGNFS
(16·10¹⁴⁹-43)/9 = 1(7)₁₄₈3_<150> = 74257 · 1756286687473_<13> · 40000271800450469_<17> · C116
C116 = P34 · P82
P34 = 8451328395281915175077609691314123_<34>
P82 = 4032336289143467545190727664762401688975731101155506963337129845941832951058267739_<82>

Number: 17773_149 N=34078598179763894284357022031702951463430782892473350643743951375598986101203012608356279387739075999304334885977897 ( 116 digits) SNFS difficulty: 150 digits. Divisors found: r1=8451328395281915175077609691314123 (pp34) r2=4032336289143467545190727664762401688975731101155506963337129845941832951058267739 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 33.88 hours. Scaled time: 22.94 units (timescale=0.677). Factorization parameters were as follows: name: 17773_149 n: 34078598179763894284357022031702951463430782892473350643743951375598986101203012608356279387739075999304334885977897 m: 1000000000000000000000000000000 c5: 8 c0: -215 skew: 1.93 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175813, largePrimes:5492730 encountered Relations: rels:5379374, finalFF:457983 Max relations in full relation-set: 28 Initial matrix: 352180 x 457983 with sparse part having weight 40625337. Pruned matrix : 304476 x 306300 with weight 23877941. Total sieving time: 30.09 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.43 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 33.88 hours. --------- CPU info (if available) ----------
Apr 19, 2008 (3rd): By Wataru Sakai / Msieve
(16·10¹⁶³-43)/9 = 1(7)₁₆₂3_<164> = 13 · 1193 · 6396333453947_<13> · 6011603269643265989_<19> · 37780493521163729849057_<23> · C105
C105 = P38 · P68
P38 = 13909049981855630404289973234462069073_<38>
P68 = 56729267307243269741500070065132179405855567563697922136760577391119_<68>

Thu Apr 17 23:17:26 2008 Msieve v. 1.35 Thu Apr 17 23:17:26 2008 random seeds: 610e60e2 1e46c7c2 Thu Apr 17 23:17:26 2008 factoring 789050214410495208081559944595870731751665549451986335130440150439214112960298838225645198526905114762687 (105 digits) Thu Apr 17 23:17:27 2008 searching for 15-digit factors Thu Apr 17 23:17:28 2008 commencing quadratic sieve (105-digit input) Thu Apr 17 23:17:28 2008 using multiplier of 7 Thu Apr 17 23:17:28 2008 using 32kb Intel Core sieve core Thu Apr 17 23:17:28 2008 sieve interval: 38 blocks of size 32768 Thu Apr 17 23:17:28 2008 processing polynomials in batches of 6 Thu Apr 17 23:17:28 2008 using a sieve bound of 4083571 (144667 primes) Thu Apr 17 23:17:28 2008 using large prime bound of 612535650 (29 bits) Thu Apr 17 23:17:28 2008 using double large prime bound of 6558982124812350 (44-53 bits) Thu Apr 17 23:17:28 2008 using trial factoring cutoff of 53 bits Thu Apr 17 23:17:28 2008 polynomial 'A' values have 14 factors Sat Apr 19 06:43:23 2008 144798 relations (34124 full + 110674 combined from 2149152 partial), need 144763 Sat Apr 19 06:43:26 2008 begin with 2183276 relations Sat Apr 19 06:43:27 2008 reduce to 381872 relations in 15 passes Sat Apr 19 06:43:27 2008 attempting to read 381872 relations Sat Apr 19 06:43:32 2008 recovered 381872 relations Sat Apr 19 06:43:32 2008 recovered 374155 polynomials Sat Apr 19 06:43:32 2008 attempting to build 144798 cycles Sat Apr 19 06:43:32 2008 found 144798 cycles in 6 passes Sat Apr 19 06:43:32 2008 distribution of cycle lengths: Sat Apr 19 06:43:32 2008 length 1 : 34124 Sat Apr 19 06:43:32 2008 length 2 : 24668 Sat Apr 19 06:43:32 2008 length 3 : 24516 Sat Apr 19 06:43:32 2008 length 4 : 19930 Sat Apr 19 06:43:32 2008 length 5 : 15205 Sat Apr 19 06:43:32 2008 length 6 : 10259 Sat Apr 19 06:43:32 2008 length 7 : 6779 Sat Apr 19 06:43:32 2008 length 9+: 9317 Sat Apr 19 06:43:32 2008 largest cycle: 21 relations Sat Apr 19 06:43:33 2008 matrix is 144667 x 144798 (40.5 MB) with weight 10044000 (69.37/col) Sat Apr 19 06:43:33 2008 sparse part has weight 10044000 (69.37/col) Sat Apr 19 06:43:33 2008 filtering completed in 3 passes Sat Apr 19 06:43:33 2008 matrix is 139120 x 139183 (39.2 MB) with weight 9715429 (69.80/col) Sat Apr 19 06:43:33 2008 sparse part has weight 9715429 (69.80/col) Sat Apr 19 06:43:34 2008 saving the first 48 matrix rows for later Sat Apr 19 06:43:34 2008 matrix is 139072 x 139183 (22.9 MB) with weight 7554305 (54.28/col) Sat Apr 19 06:43:34 2008 sparse part has weight 5178932 (37.21/col) Sat Apr 19 06:43:34 2008 matrix includes 64 packed rows Sat Apr 19 06:43:34 2008 using block size 55673 for processor cache size 6144 kB Sat Apr 19 06:43:35 2008 commencing Lanczos iteration Sat Apr 19 06:43:35 2008 memory use: 23.1 MB Sat Apr 19 06:45:04 2008 lanczos halted after 2201 iterations (dim = 139068) Sat Apr 19 06:45:04 2008 recovered 15 nontrivial dependencies Sat Apr 19 06:45:05 2008 prp38 factor: 13909049981855630404289973234462069073 Sat Apr 19 06:45:05 2008 prp68 factor: 56729267307243269741500070065132179405855567563697922136760577391119 Sat Apr 19 06:45:05 2008 elapsed time 31:27:39
Apr 19, 2008 (2nd): By Robert Backstrom / GGNFS
(16·10¹⁴⁵-43)/9 = 1(7)₁₄₄3_<146> = 13 · 59 · 113 · 6113 · 97900993 · C129
C129 = P65 · P65
P65 = 16622796863443524019743377225276094967799622716440295866198684081_<65>
P65 = 20618547874697345788229642446357994038980128189862291645786008147_<65>

Number: n N=342737932940279177877666996901874480937332396368251728885802533313270128140969346250666588135979889005893165891963390853345207907 ( 129 digits) SNFS difficulty: 146 digits. Divisors found: r1=16622796863443524019743377225276094967799622716440295866198684081 (pp65) r2=20618547874697345788229642446357994038980128189862291645786008147 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.98 hours. Scaled time: 10.86 units (timescale=1.818). Factorization parameters were as follows: name: KA_1_7_144_3 n: 342737932940279177877666996901874480937332396368251728885802533313270128140969346250666588135979889005893165891963390853345207907 skew: 1.22 deg: 5 c5: 16 c0: -43 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:114155, AFBsize:114182, largePrimes:6568235 encountered Relations: rels:5836571, finalFF:264019 Max relations in full relation-set: 48 Initial matrix: 228401 x 264019 with sparse part having weight 31268000. Pruned matrix : 216769 x 217975 with weight 21023686. Total sieving time: 5.41 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.41 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 5.98 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Apr 19, 2008: By Jo Yeong Uk / GGNFS, GMP-ECM
(16·10¹⁵⁵-43)/9 = 1(7)₁₅₄3_<156> = 29 · 3673 · 234391757431997529389_<21> · C130
C130 = P35 · P95
P35 = 88308179609882380758786014994362513_<35>
P95 = 80633456936717508249547250917177803523254243013044383853109355147287095866161662111291070396717_<95>

Number: 17773_155 N=7120593797733366076311318086086978160341727352661331057070689454547745192982183077839045352871475585630105847818565550177423069821 ( 130 digits) SNFS difficulty: 156 digits. Divisors found: r1=88308179609882380758786014994362513 (pp35) r2=80633456936717508249547250917177803523254243013044383853109355147287095866161662111291070396717 (pp95) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.46 hours. Scaled time: 43.68 units (timescale=2.135). Factorization parameters were as follows: n: 7120593797733366076311318086086978160341727352661331057070689454547745192982183077839045352871475585630105847818565550177423069821 m: 20000000000000000000000000000000 c5: 1 c0: -86 skew: 2.44 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:217561, largePrimes:5624338 encountered Relations: rels:5571441, finalFF:535073 Max relations in full relation-set: 28 Initial matrix: 434441 x 535073 with sparse part having weight 42701966. Pruned matrix : 379229 x 381465 with weight 27894484. Total sieving time: 19.62 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.72 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 20.46 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
Apr 18, 2008 (4th): By Wataru Sakai / GMP-ECM
(16·10¹⁷⁷-43)/9 = 1(7)₁₇₆3_<178> = 3 · 39341 · 55469 · C168
C168 = P28 · P140
P28 = 3540849013711996267182661087_<28>
P140 = 76692532456878501730549593664595518204648519628890706699390350654932773905434667749384344629111220283370888580298809813332301394964563882217_<140>
Apr 18, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(16·10¹⁵⁸-43)/9 = 1(7)₁₅₇3_<159> = 17 · 112897531 · C149
C149 = P39 · P111
P39 = 515585271951048556898212277218261286633_<39>
P111 = 179656777145804708129547858060856269933397255736927677551557880399873254058579628363977016884753579212620803503_<111>

Number: n N=92628388302568645595550127548210992985873169297302502712303507160362538255924552544689072063877202571563233471253199962663372400097705975507053475399 ( 149 digits) SNFS difficulty: 160 digits. Divisors found: Fri Apr 18 17:59:12 2008 prp39 factor: 515585271951048556898212277218261286633 Fri Apr 18 17:59:12 2008 prp111 factor: 179656777145804708129547858060856269933397255736927677551557880399873254058579628363977016884753579212620803503 Fri Apr 18 17:59:12 2008 elapsed time 00:35:03 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 29.43 hours. Scaled time: 24.66 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_7_157_3 n: 92628388302568645595550127548210992985873169297302502712303507160362538255924552544689072063877202571563233471253199962663372400097705975507053475399 type: snfs deg: 5 c5: 4 c0: -1075 skew: 2.44 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 1899990) Primes: RFBsize:216816, AFBsize:216841, largePrimes:5530400 encountered Relations: rels:5435017, finalFF:515675 Max relations in full relation-set: 28 Initial matrix: 433721 x 515675 with sparse part having weight 39258233. Pruned matrix : Total sieving time: 29.27 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 29.43 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Apr 18, 2008 (2nd): By Sinkiti Sibata / GGNFS
(16·10¹¹⁸-43)/9 = 1(7)₁₁₇3_<119> = 7 · 1319 · 649573 · 3859171 · C102
C102 = P47 · P56
P47 = 47350955974127276757526684432655467293045031819_<47>
P56 = 16221234355104901470997952766497166240721117007085516953_<56>

Number: 17773_118 N=768090953794573057816630109157861769746161838397065624797169366829056643479552845083229414945948927507 ( 102 digits) SNFS difficulty: 119 digits. Divisors found: r1=47350955974127276757526684432655467293045031819 (pp47) r2=16221234355104901470997952766497166240721117007085516953 (pp56) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.26 hours. Scaled time: 1.53 units (timescale=0.677). Factorization parameters were as follows: name: 17773_118 n: 768090953794573057816630109157861769746161838397065624797169366829056643479552845083229414945948927507 m: 200000000000000000000000 c5: 500 c0: -43 skew: 0.61 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64058, largePrimes:2018699 encountered Relations: rels:2002457, finalFF:151962 Max relations in full relation-set: 28 Initial matrix: 113222 x 151962 with sparse part having weight 11986315. Pruned matrix : 100073 x 100703 with weight 5851889. Total sieving time: 1.99 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.16 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,119,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.26 hours. --------- CPU info (if available) ----------
Apr 18, 2008: By Jo Yeong Uk / GGNFS, GMP-ECM
(16·10¹³⁸-43)/9 = 1(7)₁₃₇3_<139> = 3² · 14639 · 51266269 · C126
C126 = P59 · P68
P59 = 11632544748654663205292509039845800240928717050619027960643_<59>
P68 = 22626485891727523197151601650522464210578871505272726012964428807469_<68>

Number: 17773_138 N=263203609640323824392458107325806099995043923027122226226760883014902997330558765169460769491743099274902294390038895556442567 ( 126 digits) SNFS difficulty: 140 digits. Divisors found: r1=11632544748654663205292509039845800240928717050619027960643 (pp59) r2=22626485891727523197151601650522464210578871505272726012964428807469 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.90 hours. Scaled time: 12.67 units (timescale=2.145). Factorization parameters were as follows: n: 263203609640323824392458107325806099995043923027122226226760883014902997330558765169460769491743099274902294390038895556442567 m: 10000000000000000000000000000 c5: 4 c0: -1075 skew: 3.06 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114037, largePrimes:3315183 encountered Relations: rels:3373564, finalFF:357868 Max relations in full relation-set: 28 Initial matrix: 228256 x 357868 with sparse part having weight 30397126. Pruned matrix : 180827 x 182032 with weight 12710286. Total sieving time: 5.73 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 5.90 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
8·10¹⁸⁷-1 = 7(9)₁₈₇_<188> = 50221 · 718693111 · 5015358357341_<13> · C162
C162 = P36 · C127
P36 = 153590809952823656448053791352618581_<36>
C127 = [2877358321708056371637969064791902153383448514723182208423678494914578167998439620341180341926287474457161806866745674265286749_<127>]
(16·10¹⁴⁶-43)/9 = 1(7)₁₄₅3_<147> = 1759223 · 66378044054429_<14> · C127
C127 = P55 · P73
P55 = 1056295968541772519047500174110259791732144028688415153_<55>
P73 = 1441273845342654536010084697268847716723542480648916997795263989062923623_<73>

Number: 17773_146 N=1522411752400144126632930397778883985122615881675977475582863474157301360548134270400340874386530077118346961505716336554859319 ( 127 digits) SNFS difficulty: 147 digits. Divisors found: r1=1056295968541772519047500174110259791732144028688415153 (pp55) r2=1441273845342654536010084697268847716723542480648916997795263989062923623 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.88 hours. Scaled time: 21.20 units (timescale=2.146). Factorization parameters were as follows: n: 1522411752400144126632930397778883985122615881675977475582863474157301360548134270400340874386530077118346961505716336554859319 m: 200000000000000000000000000000 c5: 5 c0: -43 skew: 1.54 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1575001) Primes: RFBsize:135072, AFBsize:134733, largePrimes:3762790 encountered Relations: rels:3832797, finalFF:363069 Max relations in full relation-set: 28 Initial matrix: 269870 x 363069 with sparse part having weight 33914108. Pruned matrix : 236804 x 238217 with weight 18742821. Total sieving time: 9.56 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.24 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 9.88 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
8·10¹⁸⁴-1 = 7(9)₁₈₄_<185> = 1999080062901581503437318550484654902159553_<43> · C143
C143 = P35 · P109
P35 = 15637703450006173973828739274219217_<35>
P109 = 2559097461890393718243754256765145837067277294067140964364353690368762236330319581826659779608172818332729999_<109>
Apr 17, 2008 (3th): By Sinkiti Sibata / Msieve, GGNFS
(16·10¹²⁶-43)/9 = 1(7)₁₂₅3_<127> = 3 · 17 · 109 · 2289551683_<10> · C114
C114 = P34 · P80
P34 = 3874799090028982983788638177832431_<34>
P80 = 36047998691929861569706472795198049716524625691428470311891766732822101755440039_<80>

Number: 17773_126 N=139678752528855796515825665771919737666695102874942258747881123820068740828534251491647142474744904176151610104809 ( 114 digits) SNFS difficulty: 127 digits. Divisors found: r1=3874799090028982983788638177832431 (pp34) r2=36047998691929861569706472795198049716524625691428470311891766732822101755440039 (pp80) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.68 hours. Scaled time: 5.34 units (timescale=1.992). Factorization parameters were as follows: name: 17773_126 n: 139678752528855796515825665771919737666695102874942258747881123820068740828534251491647142474744904176151610104809 m: 20000000000000000000000000 c5: 5 c0: -43 skew: 1.54 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63728, largePrimes:2127400 encountered Relations: rels:2149094, finalFF:154047 Max relations in full relation-set: 28 Initial matrix: 112891 x 154047 with sparse part having weight 14322637. Pruned matrix : 103876 x 104504 with weight 7465249. Total sieving time: 2.51 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.68 hours. --------- CPU info (if available) ----------
(16·10¹²⁵-43)/9 = 1(7)₁₂₄3_<126> = 139 · 467649979411443427_<18> · C106
C106 = P31 · P32 · P44
P31 = 1103899759447808710603942658389_<31>
P32 = 85253848617475439469702760423117_<32>
P44 = 29060168036435085334340301632974120249835357_<44>

Number: 17773_125 N=2734901902818018639322144720567010346065153400121065763221178022074487392487751189852112831885124154884141 ( 106 digits) SNFS difficulty: 126 digits. Divisors found: r1=1103899759447808710603942658389 (pp31) r2=85253848617475439469702760423117 (pp32) r3=29060168036435085334340301632974120249835357 (pp44) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.14 hours. Scaled time: 6.28 units (timescale=2.000). Factorization parameters were as follows: name: 17773_125 n: 2734901902818018639322144720567010346065153400121065763221178022074487392487751189852112831885124154884141 m: 20000000000000000000000000 c5: 1 c0: -86 skew: 2.44 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63853, largePrimes:2190075 encountered Relations: rels:2273813, finalFF:198568 Max relations in full relation-set: 28 Initial matrix: 113015 x 198568 with sparse part having weight 19369229. Pruned matrix : 97297 x 97926 with weight 6884251. Total sieving time: 2.99 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.05 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.14 hours. --------- CPU info (if available) ----------
(16·10¹¹⁹-43)/9 = 1(7)₁₁₈3_<120> = 96881956739185113311_<20> · C100
C100 = P34 · P67
P34 = 1468279725698321121821741190940259_<34>
P67 = 1249757551140585021286231031388970942154095925690579253003177838577_<67>

Wed Apr 16 18:47:15 2008 Msieve v. 1.33 Wed Apr 16 18:47:15 2008 random seeds: b6b676bf 3e282a6a Wed Apr 16 18:47:15 2008 factoring 1834993674378103706510951864175520316649357398636129200483879762498449964268488473520406877952571443 (100 digits) Wed Apr 16 18:47:16 2008 searching for 15-digit factors Wed Apr 16 18:47:18 2008 commencing quadratic sieve (100-digit input) Wed Apr 16 18:47:18 2008 using multiplier of 7 Wed Apr 16 18:47:18 2008 using 64kb Pentium 4 sieve core Wed Apr 16 18:47:18 2008 sieve interval: 18 blocks of size 65536 Wed Apr 16 18:47:18 2008 processing polynomials in batches of 6 Wed Apr 16 18:47:18 2008 using a sieve bound of 2676997 (97647 primes) Wed Apr 16 18:47:18 2008 using large prime bound of 401549550 (28 bits) Wed Apr 16 18:47:18 2008 using double large prime bound of 3067117780557750 (43-52 bits) Wed Apr 16 18:47:18 2008 using trial factoring cutoff of 52 bits Wed Apr 16 18:47:18 2008 polynomial 'A' values have 13 factors Thu Apr 17 12:45:34 2008 97796 relations (22955 full + 74841 combined from 1478103 partial), need 97743 Thu Apr 17 12:45:40 2008 begin with 1501058 relations Thu Apr 17 12:45:42 2008 reduce to 259398 relations in 12 passes Thu Apr 17 12:45:42 2008 attempting to read 259398 relations Thu Apr 17 12:45:51 2008 recovered 259398 relations Thu Apr 17 12:45:51 2008 recovered 250343 polynomials Thu Apr 17 12:45:51 2008 attempting to build 97796 cycles Thu Apr 17 12:45:51 2008 found 97796 cycles in 6 passes Thu Apr 17 12:45:51 2008 distribution of cycle lengths: Thu Apr 17 12:45:51 2008 length 1 : 22955 Thu Apr 17 12:45:51 2008 length 2 : 16414 Thu Apr 17 12:45:51 2008 length 3 : 16469 Thu Apr 17 12:45:51 2008 length 4 : 13428 Thu Apr 17 12:45:51 2008 length 5 : 10245 Thu Apr 17 12:45:51 2008 length 6 : 7142 Thu Apr 17 12:45:51 2008 length 7 : 4639 Thu Apr 17 12:45:51 2008 length 9+: 6504 Thu Apr 17 12:45:51 2008 largest cycle: 22 relations Thu Apr 17 12:45:52 2008 matrix is 97647 x 97796 (26.6 MB) with weight 6573420 (67.22/col) Thu Apr 17 12:45:52 2008 sparse part has weight 6573420 (67.22/col) Thu Apr 17 12:45:54 2008 filtering completed in 3 passes Thu Apr 17 12:45:54 2008 matrix is 93857 x 93921 (25.6 MB) with weight 6345777 (67.57/col) Thu Apr 17 12:45:54 2008 sparse part has weight 6345777 (67.57/col) Thu Apr 17 12:45:55 2008 saving the first 48 matrix rows for later Thu Apr 17 12:45:55 2008 matrix is 93809 x 93921 (15.0 MB) with weight 4909957 (52.28/col) Thu Apr 17 12:45:55 2008 sparse part has weight 3371549 (35.90/col) Thu Apr 17 12:45:55 2008 matrix includes 64 packed rows Thu Apr 17 12:45:55 2008 using block size 21845 for processor cache size 512 kB Thu Apr 17 12:45:56 2008 commencing Lanczos iteration Thu Apr 17 12:45:56 2008 memory use: 15.1 MB Thu Apr 17 12:47:24 2008 lanczos halted after 1485 iterations (dim = 93807) Thu Apr 17 12:47:25 2008 recovered 17 nontrivial dependencies Thu Apr 17 12:47:26 2008 prp34 factor: 1468279725698321121821741190940259 Thu Apr 17 12:47:26 2008 prp67 factor: 1249757551140585021286231031388970942154095925690579253003177838577 Thu Apr 17 12:47:26 2008 elapsed time 18:00:11
(16·10¹²⁰-43)/9 = 1(7)₁₁₉3_<121> = 3⁴ · C119
C119 = P50 · P69
P50 = 85510357558761421141383126907634041186486316417099_<50>
P69 = 256669185187810792308602187020497433738883870719060728193378032088567_<69>

Number: 17773_120 N=21947873799725651577503429355281207133058984910836762688614540466392318244170096021947873799725651577503429355281207133 ( 119 digits) SNFS difficulty: 121 digits. Divisors found: r1=85510357558761421141383126907634041186486316417099 (pp50) r2=256669185187810792308602187020497433738883870719060728193378032088567 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.59 hours. Scaled time: 1.75 units (timescale=0.677). Factorization parameters were as follows: name: 17773_120 n: 21947873799725651577503429355281207133058984910836762688614540466392318244170096021947873799725651577503429355281207133 m: 2000000000000000000000000 c5: 1 c0: -86 skew: 2.44 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:49098, AFBsize:63853, largePrimes:2194643 encountered Relations: rels:2335783, finalFF:263665 Max relations in full relation-set: 28 Initial matrix: 113015 x 263665 with sparse part having weight 24306850. Pruned matrix : 84489 x 85118 with weight 5577315. Total sieving time: 2.36 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.59 hours. --------- CPU info (if available) ----------
Apr 17, 2008 (2nd): By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(16·10¹⁴⁴-43)/9 = 1(7)₁₄₃3_<145> = 3 · 227 · C142
C142 = P39 · P52 · P52
P39 = 122929344325063661695898389182280845929_<39>
P52 = 3221391447437790783926804430055858823974940817522169_<52>
P52 = 6592213962798872415463349088189519733800364363571333_<52>

Number: n N=2610540055473976178821993799967368249306575297764725077500407896883667808777940936531244901288954152390275738293359438733888073095121553271333 ( 142 digits) SNFS difficulty: 145 digits. Divisors found: r1=122929344325063661695898389182280845929 (pp39) r2=3221391447437790783926804430055858823974940817522169 (pp52) r3=6592213962798872415463349088189519733800364363571333 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.63 hours. Scaled time: 12.12 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_7_143_3 n: 2610540055473976178821993799967368249306575297764725077500407896883667808777940936531244901288954152390275738293359438733888073095121553271333 skew: 1.93 deg: 5 c5: 8 c0: -215 m: 100000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:114155, AFBsize:114062, largePrimes:6704802 encountered Relations: rels:5987168, finalFF:270894 Max relations in full relation-set: 48 Initial matrix: 228282 x 270894 with sparse part having weight 34317305. Pruned matrix : 216547 x 217752 with weight 22303479. Total sieving time: 5.95 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.43 hours. Total square root time: 0.11 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 6.63 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(16·10¹⁶¹-43)/9 = 1(7)₁₆₀3_<162> = 103 · 1021849 · 334680190961971_<15> · 24695725106873857_<17> · 218931718291791250301_<21> · C102
C102 = P35 · P68
P35 = 36407080834751143443498565731037777_<35>
P68 = 25639360582377136928119325942391403410234951772381760032053460807861_<68>

Number: n N=933454273273936577612474901491001066341309617815789327012871967840898500121908855872904953600329564997 ( 102 digits) Divisors found: r1=36407080834751143443498565731037777 (pp35) r2=25639360582377136928119325942391403410234951772381760032053460807861 (pp68) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.34 hours. Scaled time: 9.74 units (timescale=1.823). Factorization parameters were as follows: name: KA_1_7_160_3 n: 933454273273936577612474901491001066341309617815789327012871967840898500121908855872904953600329564997 skew: 11093.37 # norm 3.99e+13 c5: 1800 c4: 372271082 c3: -473746083165 c2: -47756910272386885 c1: 76919695839272232985 c0: 206237387055222311017528 # alpha -5.02 Y1: 13814165629 Y0: -55329866672127928995 # Murphy_E 2.56e-09 # M 833706548574107714639820363179423211715410901127672776498804591771767671390163419824815462115955586024 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 [100000, 900001) Primes: RFBsize:169511, AFBsize:169583, largePrimes:4051501 encountered Relations: rels:4057067, finalFF:469111 Max relations in full relation-set: 48 Initial matrix: 339174 x 469111 with sparse part having weight 27040198. Pruned matrix : 217394 x 219153 with weight 8801689. Total sieving time: 4.95 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.19 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.34 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(14·10¹⁶⁶-23)/9 = 1(5)₁₆₅3_<167> = 107 · 127 · 507742003 · C154
C154 = P40 · P42 · P73
P40 = 3383246862790582749480921165155169175417_<40>
P42 = 432508300655604026409962871945358873577669_<42>
P73 = 1540730929988680743737736570091962036281428096254323888738391539667343483_<73>

Number: n N=666378916296932729031689796754642939121851670277389480145678840927507410551912991473639321490092225320869301481127 ( 114 digits) Divisors found: Thu Apr 17 22:20:15 2008 prp42 factor: 432508300655604026409962871945358873577669 Thu Apr 17 22:20:15 2008 prp73 factor: 1540730929988680743737736570091962036281428096254323888738391539667343483 Thu Apr 17 22:20:15 2008 elapsed time 00:44:24 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 26.74 hours. Scaled time: 22.39 units (timescale=0.837). Factorization parameters were as follows: name: KA_1_5_165_3 n: 666378916296932729031689796754642939121851670277389480145678840927507410551912991473639321490092225320869301481127 skew: 21772.53 # norm 1.15e+16 c5: 127920 c4: -23604014380 c3: -521830973354640 c2: 13654652291457606849 c1: 43808656190295530955502 c0: -112301076362569465313946696 # alpha -6.55 Y1: 1193146480793 Y0: -5538090041817291334015 # Murphy_E 5.94e-10 # M 424840657608522257635537657543679823340115623023876770799204026916388698189137461913456436848462018965001840737620 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 special-q in [100000, 1500151) Primes: RFBsize:250150, AFBsize:250624, largePrimes:6967090 encountered Relations: rels:6656946, finalFF:539540 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 26.53 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 26.74 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Apr 17, 2008: By Jo Yeong Uk / GMP-ECM, GGNFS
(5·10¹⁷²-11)/3 = 1(6)₁₇₁3_<173> = 449 · 613 · 14983621 · 640773929 · 765796020212228084429127317516663_<33> · C118
C118 = P48 · P71
P48 = 320495677550936751308035792497362918849303147407_<48>
P71 = 25697154737133609560344670840251726771651958436082806086312019002604671_<71>

Number: 16663_172 N=8235827018608900184232630962747782531914857076776112095668712602895011246947560520007279169172594208954918011259738097 ( 118 digits) Divisors found: r1=320495677550936751308035792497362918849303147407 (pp48) r2=25697154737133609560344670840251726771651958436082806086312019002604671 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 36.65 hours. Scaled time: 78.44 units (timescale=2.140). Factorization parameters were as follows: name: 16663_172 n: 8235827018608900184232630962747782531914857076776112095668712602895011246947560520007279169172594208954918011259738097 skew: 23994.76 # norm 3.56e+15 c5: 81780 c4: -8722177613 c3: -172048388133462 c2: 5431487071876079458 c1: 32188035299275822248228 c0: -42858347921993434993922144 # alpha -4.89 Y1: 2047839378167 Y0: -39866902854599812345335 # Murphy_E 3.69e-10 # M 4397100284139661905595764503103251667391894199048783655171359813332510445129267787214586724263171904117759984428094451 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 4125001) Primes: RFBsize:315948, AFBsize:315538, largePrimes:7637241 encountered Relations: rels:7680602, finalFF:728503 Max relations in full relation-set: 28 Initial matrix: 631569 x 728503 with sparse part having weight 61666293. Pruned matrix : 551228 x 554449 with weight 41570758. Polynomial selection time: 1.98 hours. Total sieving time: 32.52 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.82 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,75000 total time: 36.65 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
(16·10¹³³-43)/9 = 1(7)₁₃₂3_<134> = 13 · 233 · 25933 · 97813 · 71667448168957_<14> · C107
C107 = P49 · P58
P49 = 3342143748489434590572597197368580584310674477981_<49>
P58 = 9660103826638798656998936740469404831436423757669777126209_<58>

Number: 17773_133 N=32285455613959725746999532746011021932043083571604268600338314952656034453773659817804519379721595428504029 ( 107 digits) SNFS difficulty: 135 digits. Divisors found: r1=3342143748489434590572597197368580584310674477981 (pp49) r2=9660103826638798656998936740469404831436423757669777126209 (pp58) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.97 hours. Scaled time: 6.35 units (timescale=2.135). Factorization parameters were as follows: n: 32285455613959725746999532746011021932043083571604268600338314952656034453773659817804519379721595428504029 m: 1000000000000000000000000000 c5: 4 c0: -1075 skew: 3.06 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1250001) Primes: RFBsize:107126, AFBsize:107108, largePrimes:2273625 encountered Relations: rels:2404790, finalFF:294421 Max relations in full relation-set: 28 Initial matrix: 214298 x 294421 with sparse part having weight 21471334. Pruned matrix : 181853 x 182988 with weight 10321115. Total sieving time: 2.83 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.97 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
8·10¹⁹⁴-1 = 7(9)₁₉₄_<195> = 17 · 50287 · 3097537 · 119605714808559453334057_<24> · C160
C160 = P28 · P132
P28 = 5565233219278259235319671553_<28>
P132 = 453872150920361109687290122732532032688530998219435391743981449214557842553014055993102429286314732251554440782531327487375989287353_<132>
(16·10¹³⁴-43)/9 = 1(7)₁₃₃3_<135> = 263 · 197047159 · C124
C124 = P58 · P67
P58 = 2863834785747777662736218202774989738378574194792058607181_<58>
P67 = 1197853171614762586665272443737488891329168220783862099262703556449_<67>

Number: 17773_134 N=3430453581088659560179837616813547764407849068970136086958872262619484904091371908295926398270918423889605423047490150260269 ( 124 digits) SNFS difficulty: 136 digits. Divisors found: r1=2863834785747777662736218202774989738378574194792058607181 (pp58) r2=1197853171614762586665272443737488891329168220783862099262703556449 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.41 hours. Scaled time: 7.33 units (timescale=2.147). Factorization parameters were as follows: n: 3430453581088659560179837616813547764407849068970136086958872262619484904091371908295926398270918423889605423047490150260269 m: 2000000000000000000000000000 c5: 1 c0: -860 skew: 3.86 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1350001) Primes: RFBsize:107126, AFBsize:106968, largePrimes:2335679 encountered Relations: rels:2477311, finalFF:295035 Max relations in full relation-set: 28 Initial matrix: 214158 x 295035 with sparse part having weight 23189974. Pruned matrix : 186064 x 187198 with weight 11633275. Total sieving time: 3.25 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.41 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
8·10¹⁷⁸-1 = 7(9)₁₇₈_<179> = 17 · 54799 · C173
C173 = P40 · P134
P40 = 5885133257828395389165904720779636286561_<40>
P134 = 14591909625581121136482174824446665198803833208568420920881318532185496567756234695562377208236552712810015744424723901294952789939873_<134>
8·10¹⁸⁵-1 = 7(9)₁₈₅_<186> = 1949 · 88692237787921626581_<20> · C163
C163 = P34 · P129
P34 = 9213214841645127155231659857590189_<34>
P129 = 502321002341718432286600942522787211853191175238165401879857931010912161900095448258817976719920746592180033543258552863249190139_<129>
8·10¹⁸²-1 = 7(9)₁₈₂_<183> = 6689 · 45833 · C175
C175 = P38 · C137
P38 = 64965178089572382042423526852742694223_<38>
C137 = [40167044071217756780187592392246187076622588646967716036404892251010744662016892972703963262216033825927684995558723281578766771102057449_<137>]
Apr 16, 2008 (4th): By Sinkiti Sibata / Msieve, GGNFS
(16·10¹¹²-43)/9 = 1(7)₁₁₁3_<113> = 7² · 193 · 20145617 · 175080692421274249_<18> · C84
C84 = P37 · P48
P37 = 2746131666830462403852624787266510433_<37>
P48 = 194081392436622661770145240283408879646755217701_<48>

Wed Apr 16 12:58:21 2008 Msieve v. 1.33 Wed Apr 16 12:58:21 2008 random seeds: b6b6c24f 7a2fe73c Wed Apr 16 12:58:21 2008 factoring 532973057712759689286185744598002512654979895804101219214304241467155374801502774533 (84 digits) Wed Apr 16 12:58:22 2008 searching for 15-digit factors Wed Apr 16 12:58:24 2008 commencing quadratic sieve (84-digit input) Wed Apr 16 12:58:24 2008 using multiplier of 17 Wed Apr 16 12:58:24 2008 using 64kb Pentium 4 sieve core Wed Apr 16 12:58:24 2008 sieve interval: 6 blocks of size 65536 Wed Apr 16 12:58:24 2008 processing polynomials in batches of 17 Wed Apr 16 12:58:24 2008 using a sieve bound of 1409171 (53610 primes) Wed Apr 16 12:58:24 2008 using large prime bound of 119779535 (26 bits) Wed Apr 16 12:58:24 2008 using double large prime bound of 347607157783030 (41-49 bits) Wed Apr 16 12:58:24 2008 using trial factoring cutoff of 49 bits Wed Apr 16 12:58:24 2008 polynomial 'A' values have 11 factors Wed Apr 16 13:43:34 2008 54072 relations (15871 full + 38201 combined from 574707 partial), need 53706 Wed Apr 16 13:43:36 2008 begin with 590578 relations Wed Apr 16 13:43:37 2008 reduce to 126745 relations in 10 passes Wed Apr 16 13:43:37 2008 attempting to read 126745 relations Wed Apr 16 13:43:40 2008 recovered 126745 relations Wed Apr 16 13:43:40 2008 recovered 103500 polynomials Wed Apr 16 13:43:40 2008 attempting to build 54072 cycles Wed Apr 16 13:43:40 2008 found 54072 cycles in 6 passes Wed Apr 16 13:43:40 2008 distribution of cycle lengths: Wed Apr 16 13:43:40 2008 length 1 : 15871 Wed Apr 16 13:43:40 2008 length 2 : 11043 Wed Apr 16 13:43:40 2008 length 3 : 9527 Wed Apr 16 13:43:40 2008 length 4 : 6881 Wed Apr 16 13:43:40 2008 length 5 : 4611 Wed Apr 16 13:43:40 2008 length 6 : 2779 Wed Apr 16 13:43:40 2008 length 7 : 1614 Wed Apr 16 13:43:40 2008 length 9+: 1746 Wed Apr 16 13:43:40 2008 largest cycle: 23 relations Wed Apr 16 13:43:41 2008 matrix is 53610 x 54072 (11.5 MB) with weight 2792115 (51.64/col) Wed Apr 16 13:43:41 2008 sparse part has weight 2792115 (51.64/col) Wed Apr 16 13:43:41 2008 filtering completed in 3 passes Wed Apr 16 13:43:41 2008 matrix is 48794 x 48858 (10.4 MB) with weight 2519161 (51.56/col) Wed Apr 16 13:43:41 2008 sparse part has weight 2519161 (51.56/col) Wed Apr 16 13:43:41 2008 saving the first 48 matrix rows for later Wed Apr 16 13:43:41 2008 matrix is 48746 x 48858 (5.8 MB) with weight 1866562 (38.20/col) Wed Apr 16 13:43:41 2008 sparse part has weight 1221018 (24.99/col) Wed Apr 16 13:43:41 2008 matrix includes 64 packed rows Wed Apr 16 13:43:41 2008 commencing Lanczos iteration Wed Apr 16 13:43:41 2008 memory use: 7.6 MB Wed Apr 16 13:45:18 2008 lanczos halted after 773 iterations (dim = 48746) Wed Apr 16 13:45:18 2008 recovered 18 nontrivial dependencies Wed Apr 16 13:45:19 2008 prp37 factor: 2746131666830462403852624787266510433 Wed Apr 16 13:45:19 2008 prp48 factor: 194081392436622661770145240283408879646755217701 Wed Apr 16 13:45:19 2008 elapsed time 00:46:58
(16·10¹⁴⁷-43)/9 = 1(7)₁₄₆3_<148> = 3³ · 47 · 2309 · 4518779 · 603559456090055808011_<21> · 6987589127253189423927781_<25> · C89
C89 = P36 · P54
P36 = 215360073973402846985925692625318647_<36>
P54 = 147828512122673638011891093090638637018899493413484911_<54>

Wed Apr 16 13:56:32 2008 Msieve v. 1.33 Wed Apr 16 13:56:32 2008 random seeds: 051d1ddb 36376896 Wed Apr 16 13:56:32 2008 factoring 31836359306117074203320389250315624977093890041136677461587471134178603659539208101435417 (89 digits) Wed Apr 16 13:56:33 2008 searching for 15-digit factors Wed Apr 16 13:56:35 2008 commencing quadratic sieve (89-digit input) Wed Apr 16 13:56:35 2008 using multiplier of 1 Wed Apr 16 13:56:35 2008 using 64kb Pentium 4 sieve core Wed Apr 16 13:56:35 2008 sieve interval: 16 blocks of size 65536 Wed Apr 16 13:56:35 2008 processing polynomials in batches of 7 Wed Apr 16 13:56:35 2008 using a sieve bound of 1553807 (59000 primes) Wed Apr 16 13:56:35 2008 using large prime bound of 124304560 (26 bits) Wed Apr 16 13:56:35 2008 using double large prime bound of 371600775237280 (42-49 bits) Wed Apr 16 13:56:35 2008 using trial factoring cutoff of 49 bits Wed Apr 16 13:56:35 2008 polynomial 'A' values have 11 factors Wed Apr 16 15:44:03 2008 59162 relations (15809 full + 43353 combined from 628278 partial), need 59096 Wed Apr 16 15:44:05 2008 begin with 644087 relations Wed Apr 16 15:44:06 2008 reduce to 144799 relations in 10 passes Wed Apr 16 15:44:06 2008 attempting to read 144799 relations Wed Apr 16 15:44:09 2008 recovered 144799 relations Wed Apr 16 15:44:09 2008 recovered 122538 polynomials Wed Apr 16 15:44:10 2008 attempting to build 59162 cycles Wed Apr 16 15:44:10 2008 found 59162 cycles in 6 passes Wed Apr 16 15:44:10 2008 distribution of cycle lengths: Wed Apr 16 15:44:10 2008 length 1 : 15809 Wed Apr 16 15:44:10 2008 length 2 : 11122 Wed Apr 16 15:44:10 2008 length 3 : 10318 Wed Apr 16 15:44:10 2008 length 4 : 7943 Wed Apr 16 15:44:10 2008 length 5 : 5657 Wed Apr 16 15:44:10 2008 length 6 : 3567 Wed Apr 16 15:44:10 2008 length 7 : 2188 Wed Apr 16 15:44:10 2008 length 9+: 2558 Wed Apr 16 15:44:10 2008 largest cycle: 20 relations Wed Apr 16 15:44:10 2008 matrix is 59000 x 59162 (14.3 MB) with weight 3504517 (59.24/col) Wed Apr 16 15:44:10 2008 sparse part has weight 3504517 (59.24/col) Wed Apr 16 15:44:11 2008 filtering completed in 3 passes Wed Apr 16 15:44:11 2008 matrix is 55126 x 55190 (13.4 MB) with weight 3298366 (59.76/col) Wed Apr 16 15:44:11 2008 sparse part has weight 3298366 (59.76/col) Wed Apr 16 15:44:11 2008 saving the first 48 matrix rows for later Wed Apr 16 15:44:11 2008 matrix is 55078 x 55190 (9.4 MB) with weight 2687805 (48.70/col) Wed Apr 16 15:44:11 2008 sparse part has weight 2138294 (38.74/col) Wed Apr 16 15:44:11 2008 matrix includes 64 packed rows Wed Apr 16 15:44:11 2008 using block size 21845 for processor cache size 512 kB Wed Apr 16 15:44:12 2008 commencing Lanczos iteration Wed Apr 16 15:44:12 2008 memory use: 8.8 MB Wed Apr 16 15:44:43 2008 lanczos halted after 872 iterations (dim = 55078) Wed Apr 16 15:44:43 2008 recovered 17 nontrivial dependencies Wed Apr 16 15:44:44 2008 prp36 factor: 215360073973402846985925692625318647 Wed Apr 16 15:44:44 2008 prp54 factor: 147828512122673638011891093090638637018899493413484911 Wed Apr 16 15:44:44 2008 elapsed time 01:48:12
(16·10¹¹⁰-43)/9 = 1(7)₁₀₉3_<111> = 17 · 223 · 18191 · 2170920051541_<13> · C91
C91 = P30 · P61
P30 = 644318852795425173737822057861_<30>
P61 = 1842987738890828356532876930775288642859248655760493846825733_<61>

Wed Apr 16 15:55:31 2008 Msieve v. 1.33 Wed Apr 16 15:55:31 2008 random seeds: c0087b2b 2066460a Wed Apr 16 15:55:31 2008 factoring 1187471745638173122414222944023909080821371944500674767638801121464815734387399444709737113 (91 digits) Wed Apr 16 15:55:32 2008 searching for 15-digit factors Wed Apr 16 15:55:34 2008 commencing quadratic sieve (91-digit input) Wed Apr 16 15:55:34 2008 using multiplier of 23 Wed Apr 16 15:55:34 2008 using 64kb Pentium 4 sieve core Wed Apr 16 15:55:34 2008 sieve interval: 18 blocks of size 65536 Wed Apr 16 15:55:34 2008 processing polynomials in batches of 6 Wed Apr 16 15:55:34 2008 using a sieve bound of 1652509 (62297 primes) Wed Apr 16 15:55:34 2008 using large prime bound of 145420792 (27 bits) Wed Apr 16 15:55:34 2008 using double large prime bound of 492864656290952 (42-49 bits) Wed Apr 16 15:55:34 2008 using trial factoring cutoff of 49 bits Wed Apr 16 15:55:34 2008 polynomial 'A' values have 12 factors Wed Apr 16 18:22:20 2008 62911 relations (16720 full + 46191 combined from 692900 partial), need 62393 Wed Apr 16 18:22:23 2008 begin with 709620 relations Wed Apr 16 18:22:23 2008 reduce to 152950 relations in 9 passes Wed Apr 16 18:22:23 2008 attempting to read 152950 relations Wed Apr 16 18:22:27 2008 recovered 152950 relations Wed Apr 16 18:22:27 2008 recovered 131618 polynomials Wed Apr 16 18:22:28 2008 attempting to build 62911 cycles Wed Apr 16 18:22:28 2008 found 62911 cycles in 5 passes Wed Apr 16 18:22:28 2008 distribution of cycle lengths: Wed Apr 16 18:22:28 2008 length 1 : 16720 Wed Apr 16 18:22:28 2008 length 2 : 12357 Wed Apr 16 18:22:28 2008 length 3 : 11143 Wed Apr 16 18:22:28 2008 length 4 : 8369 Wed Apr 16 18:22:28 2008 length 5 : 5829 Wed Apr 16 18:22:28 2008 length 6 : 3720 Wed Apr 16 18:22:28 2008 length 7 : 2165 Wed Apr 16 18:22:28 2008 length 9+: 2608 Wed Apr 16 18:22:28 2008 largest cycle: 20 relations Wed Apr 16 18:22:28 2008 matrix is 62297 x 62911 (15.4 MB) with weight 3773523 (59.98/col) Wed Apr 16 18:22:28 2008 sparse part has weight 3773523 (59.98/col) Wed Apr 16 18:22:29 2008 filtering completed in 3 passes Wed Apr 16 18:22:29 2008 matrix is 57938 x 58002 (14.2 MB) with weight 3482288 (60.04/col) Wed Apr 16 18:22:29 2008 sparse part has weight 3482288 (60.04/col) Wed Apr 16 18:22:30 2008 saving the first 48 matrix rows for later Wed Apr 16 18:22:30 2008 matrix is 57890 x 58002 (8.5 MB) with weight 2661136 (45.88/col) Wed Apr 16 18:22:30 2008 sparse part has weight 1882903 (32.46/col) Wed Apr 16 18:22:30 2008 matrix includes 64 packed rows Wed Apr 16 18:22:30 2008 using block size 21845 for processor cache size 512 kB Wed Apr 16 18:22:30 2008 commencing Lanczos iteration Wed Apr 16 18:22:30 2008 memory use: 8.5 MB Wed Apr 16 18:23:03 2008 lanczos halted after 917 iterations (dim = 57890) Wed Apr 16 18:23:03 2008 recovered 19 nontrivial dependencies Wed Apr 16 18:23:05 2008 prp30 factor: 644318852795425173737822057861 Wed Apr 16 18:23:05 2008 prp61 factor: 1842987738890828356532876930775288642859248655760493846825733 Wed Apr 16 18:23:05 2008 elapsed time 02:27:34
Apr 16, 2008 (3rd): By Robert Backstrom / GMP-ECM, GGNFS
8·10¹⁶⁷+9 = 8(0)₁₆₆9_<168> = 7² · 967 · 59723 · 85525507 · 104791781467_<12> · C140
C140 = P38 · P102
P38 = 32070636141063417698309974804038142769_<38>
P102 = 983547553579979304561951273616176372155814093748174239324385537878449421978287184323475247763731622141_<102>
(16·10¹¹¹-43)/9 = 1(7)₁₁₀3_<112> = 3² · 10274066749_<11> · C101
C101 = P37 · P64
P37 = 2225084121385833837269896643903724031_<37>
P64 = 8640644676536263769574342271241601366043048979121263003270936663_<64>

Number: n N=19226161268297874886381163435979431186147422624412897339015610496841133983714092394936499375232048553 ( 101 digits) SNFS difficulty: 112 digits. Divisors found: r1=2225084121385833837269896643903724031 (pp37) r2=8640644676536263769574342271241601366043048979121263003270936663 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.67 hours. Scaled time: 1.22 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_7_110_3 n: 19226161268297874886381163435979431186147422624412897339015610496841133983714092394936499375232048553 skew: 1.54 deg: 5 c5: 5 c0: -43 m: 20000000000000000000000 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 10000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 170001) Primes: RFBsize:41538, AFBsize:41437, largePrimes:3529069 encountered Relations: rels:2913505, finalFF:95356 Max relations in full relation-set: 48 Initial matrix: 83040 x 95356 with sparse part having weight 7738673. Pruned matrix : 78525 x 79004 with weight 4764399. Total sieving time: 0.58 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Total square root time: 0.02 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,50000 total time: 0.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Apr 16, 2008 (2nd): By Jo Yeong Uk / GMP-ECM
8·10¹⁷⁰-1 = 7(9)₁₇₀_<171> = 79 · 5711 · 27751 · 271927760593_<12> · C150
C150 = P32 · P119
P32 = 14008580624750494404998711251129_<32>
P119 = 16773527998674156443599016288925581723244594369965881175195561165229044921073548889200126000428046790680088466419299393_<119>
(16·10¹⁴²-43)/9 = 1(7)₁₄₁3_<143> = 7 · 17 · 2709756296960221278752815673_<28> · C113
C113 = P34 · P80
P34 = 5500591316638770792347012316501127_<34>
P80 = 10022842335671191323150316599085734859085649805584448266612992605807362427757077_<80>
8·10¹⁷³-1 = 7(9)₁₇₃_<174> = 30169 · 829284774211_<12> · 528320520638157539_<18> · C140
C140 = P34 · P107
P34 = 2380128402987626355750914791239491_<34>
P107 = 25428896472579987859772918652405527101836770281382986409039510776347763971977279943001852490967033956157589_<107>
Apr 16, 2008: The factor table of 177...773 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Apr 15, 2008 (2nd): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
4·10¹⁹⁴+3 = 4(0)₁₉₃3_<195> = 13 · 487 · 10747520347_<11> · 1061459829998311_<16> · 56889821479343939004524558081383_<32> · C134
C134 = P37 · P98
P37 = 1097437743804222790112801602356295333_<37>
P98 = 88707711400317344925950831681572035023026603223066152620648506409066689217254920192657566027207151_<98>
(31·10¹⁶⁵-13)/9 = 3(4)₁₆₄3_<166> = 11 · 167881116341_<12> · 1805455694335159_<16> · C139
C139 = P49 · P90
P49 = 7347822245464475165282519977448389173180184038157_<49>
P90 = 140598010033950929058795866865500565051420080556908773879274375567266916603580233027144711_<90>

Number: n N=1033089185795502125725549943468951191075287560678144964465240476031654211528331590947854279300951567277909959275083588067187997223584737627 ( 139 digits) SNFS difficulty: 166 digits. Divisors found: Tue Apr 15 11:10:58 2008 prp49 factor: 7347822245464475165282519977448389173180184038157 Tue Apr 15 11:10:58 2008 prp90 factor: 140598010033950929058795866865500565051420080556908773879274375567266916603580233027144711 Tue Apr 15 11:10:58 2008 elapsed time 01:00:36 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 46.01 hours. Scaled time: 38.47 units (timescale=0.836). Factorization parameters were as follows: name: KA_3_4_164_3 n: 1033089185795502125725549943468951191075287560678144964465240476031654211528331590947854279300951567277909959275083588067187997223584737627 type: snfs deg: 5 c5: 31 c0: -13 skew: 0.84 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2900189) Primes: RFBsize:230209, AFBsize:231088, largePrimes:5568743 encountered Relations: rels:5432587, finalFF:503551 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 45.83 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000 total time: 46.01 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Apr 15, 2008: By Jo Yeong Uk / GGNFS
(5·10¹⁶⁸-11)/3 = 1(6)₁₆₇3_<169> = 4120200831685709_<16> · 23283723302621145827_<20> · 7002077822382344086391_<22> · C112
C112 = P36 · P76
P36 = 717427856562862178965744919216242153_<36>
P76 = 3458380435415848667465634528539779826524512908443732339648083491542419594767_<76>

Number: 16663_168 N=2481138462959330325490993384397680976466694579370363415914673815102702133510771942578531055673159342874803613351 ( 112 digits) Divisors found: r1=717427856562862178965744919216242153 (pp36) r2=3458380435415848667465634528539779826524512908443732339648083491542419594767 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.75 hours. Scaled time: 37.84 units (timescale=2.132). Factorization parameters were as follows: name: 16663_168 n: 2481138462959330325490993384397680976466694579370363415914673815102702133510771942578531055673159342874803613351 skew: 39431.34 # norm 3.83e+15 c5: 49140 c4: 25817859 c3: -129120732929669 c2: -13844558931293250 c1: -38168703002247717958437 c0: -14214612319618440379396535 # alpha -6.15 Y1: 948140859907 Y0: -2191003897547610215284 # Murphy_E 7.79e-10 # M 626313471121193201721002423945625760926830506962689097707011606329236140510462918777889081342378696446678369389 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 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: 50/50 Sieved algebraic special-q in [1400000, 2310001) Primes: RFBsize:203362, AFBsize:203549, largePrimes:7651451 encountered Relations: rels:7592999, finalFF:593633 Max relations in full relation-set: 28 Initial matrix: 406998 x 593633 with sparse part having weight 57772171. Pruned matrix : 279566 x 281664 with weight 33387440. Polynomial selection time: 0.93 hours. Total sieving time: 16.05 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.51 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 17.75 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
(5·10¹⁶²-11)/3 = 1(6)₁₆₁3_<163> = 79² · 1703047673933057999_<19> · 233440442843090372721489089_<27> · C114
C114 = P52 · P63
P52 = 1306190477930074137492388256168123171756279944035161_<52>
P63 = 514262846899694625766088991599592595724106922026482072425101233_<63>

Number: 16663_162 N=671725233773592668158357861381849172992458792903099915618738967360228871501589617429534879024002483836109936453513 ( 114 digits) Divisors found: r1=1306190477930074137492388256168123171756279944035161 (pp52) r2=514262846899694625766088991599592595724106922026482072425101233 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.21 hours. Scaled time: 43.07 units (timescale=2.131). Factorization parameters were as follows: name: 16663_162 n: 671725233773592668158357861381849172992458792903099915618738967360228871501589617429534879024002483836109936453513 skew: 78136.67 # norm 7.46e+15 c5: 10200 c4: 383189044 c3: -309484053417710 c2: -2304352732987123077 c1: 541567228155987031479672 c0: 5146408181504792994975174915 # alpha -6.63 Y1: 790123132007 Y0: -9198521293021626091202 # Murphy_E 6.63e-10 # M 149167548420111073124963642693625400845864591092677417612563808371518751186252456902329787959070180331393959520234 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 70000 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, 2800001) Primes: RFBsize:250150, AFBsize:249746, largePrimes:7531910 encountered Relations: rels:7489527, finalFF:657062 Max relations in full relation-set: 28 Initial matrix: 499975 x 657062 with sparse part having weight 55624613. Pruned matrix : 371906 x 374469 with weight 31096495. Polynomial selection time: 1.18 hours. Total sieving time: 17.97 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.78 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.4,2.4,70000 total time: 20.21 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
Apr 14, 2008 (4th): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(5·10¹⁶⁵-11)/3 = 1(6)₁₆₄3_<166> = C166
C166 = P79 · P87
P79 = 2245517242112414977206809019850729467395498042626696714518847161837856305294667_<79>
P87 = 742219491977176312144123372249810594188783117241757062443391872162301374408886058723989_<87>

Number: n N=1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 166 digits) SNFS difficulty: 165 digits. Divisors found: Mon Apr 14 12:44:39 2008 prp79 factor: 2245517242112414977206809019850729467395498042626696714518847161837856305294667 Mon Apr 14 12:44:39 2008 prp87 factor: 742219491977176312144123372249810594188783117241757062443391872162301374408886058723989 Mon Apr 14 12:44:39 2008 elapsed time 01:37:42 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 60.64 hours. Scaled time: 79.13 units (timescale=1.305). Factorization parameters were as follows: name: KA_1_6_164_3 n: 1666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 skew: 1.17 deg: 5 c5: 5 c0: -11 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2700199) Primes: RFBsize:216816, AFBsize:217082, largePrimes:7364083 encountered Relations: rels:6800164, finalFF:446721 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 60.37 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 60.64 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
9·10¹⁶⁵-1 = 8(9)₁₆₅_<166> = 1139239 · 3500008777892854273507_<22> · C139
C139 = P66 · P74
P66 = 107006813752674037531328510242074918993021462449577391740200262799_<66>
P74 = 21093424816570316132097077241926854067827836439105917046567434042812717837_<74>

Number: n N=2257140180752772341749697563476673520949004624616088331617541248692208685477716800333936267810500726303368685688650280142696027086834845763 ( 139 digits) SNFS difficulty: 165 digits. Divisors found: Mon Apr 14 14:15:03 2008 prp66 factor: 107006813752674037531328510242074918993021462449577391740200262799 Mon Apr 14 14:15:03 2008 prp74 factor: 21093424816570316132097077241926854067827836439105917046567434042812717837 Mon Apr 14 14:15:03 2008 elapsed time 00:46:12 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 38.69 hours. Scaled time: 32.38 units (timescale=0.837). Factorization parameters were as follows: name: KA_8_9_165 n: 2257140180752772341749697563476673520949004624616088331617541248692208685477716800333936267810500726303368685688650280142696027086834845763 type: snfs deg: 5 c5: 9 c0: -1 skew: 0.72 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2500363) Primes: RFBsize:230209, AFBsize:230192, largePrimes:5532216 encountered Relations: rels:5417337, finalFF:495898 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 38.51 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000 total time: 38.69 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(28·10¹⁷⁰+17)/9 = 3(1)₁₆₉3_<171> = 1364116464566141004805456799576331094877_<40> · C132
C132 = P35 · P97
P35 = 23585939755509836363182840530964787_<35>
P97 = 9669652926621334818015115351221646782123712466665679277267133617240759474730728542857515285098287_<97>
Apr 14, 2008 (3rd): By Sinkiti Sibata / GGNFS
(5·10¹⁴⁸-11)/3 = 1(6)₁₄₇3_<149> = 19 · 47 · 21136991855671866611141813801269_<32> · C114
C114 = P44 · P71
P44 = 77581006255394308296816310422507819092440721_<44>
P71 = 11381479025872568962993334130062892789418939418216468034738922176619159_<71>

Number: 16663_148 N=882986595501858891160847091201028575717445778711899220284603910447793803044973296304248132142102675473785400373639 ( 114 digits) SNFS difficulty: 149 digits. Divisors found: r1=77581006255394308296816310422507819092440721 (pp44) r2=11381479025872568962993334130062892789418939418216468034738922176619159 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 30.17 hours. Scaled time: 20.43 units (timescale=0.677). Factorization parameters were as follows: name: 16663_148 n: 882986595501858891160847091201028575717445778711899220284603910447793803044973296304248132142102675473785400373639 m: 500000000000000000000000000000 c5: 8 c0: -55 skew: 1.47 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 3650001) Primes: RFBsize:114155, AFBsize:114253, largePrimes:2934910 encountered Relations: rels:2944993, finalFF:258683 Max relations in full relation-set: 28 Initial matrix: 228473 x 258683 with sparse part having weight 30088083. Pruned matrix : 220063 x 221269 with weight 24230101. Total sieving time: 27.97 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.87 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 30.17 hours. --------- CPU info (if available) ----------
Apr 14, 2008 (2nd): By Jo Yeong Uk / GGNFS
(5·10¹⁷⁰-11)/3 = 1(6)₁₆₉3_<171> = C171
C171 = P67 · P104
P67 = 2804670536816483766033030070325032866365359271873179603347962930801_<67>
P104 = 59424686243485168857371524605765216738985593764108704179128271614469158986252195899906766898342583066263_<104>

Number: 16663_170 N=166666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 ( 171 digits) SNFS difficulty: 170 digits. Divisors found: r1=2804670536816483766033030070325032866365359271873179603347962930801 (pp67) r2=59424686243485168857371524605765216738985593764108704179128271614469158986252195899906766898342583066263 (pp104) Version: GGNFS-0.77.1-20050930-nocona Total time: 77.89 hours. Scaled time: 167.32 units (timescale=2.148). Factorization parameters were as follows: n: 166666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666663 m: 10000000000000000000000000000000000 c5: 5 c0: -11 skew: 1.17 type: snfs Factor base limits: 7000000/7000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved algebraic special-q in [3500000, 7400001) Primes: RFBsize:476648, AFBsize:476585, largePrimes:6660039 encountered Relations: rels:7150884, finalFF:1119821 Max relations in full relation-set: 28 Initial matrix: 953298 x 1119821 with sparse part having weight 64956325. Pruned matrix : 810449 x 815279 with weight 45109511. Total sieving time: 73.83 hours. Total relation processing time: 0.13 hours. Matrix solve time: 3.86 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,7000000,7000000,27,27,49,49,2.6,2.6,100000 total time: 77.89 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407670) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Total of 4 processors activated (19246.09 BogoMIPS).
Apr 14, 2008: Jason Papadopoulos's Msieve Version 1.35 was released.
HOW TO for Japanese
Apr 13, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(5·10¹⁵⁹-11)/3 = 1(6)₁₅₈3_<160> = 66617 · 21944655402216352685141777_<26> · C130
C130 = P57 · P73
P57 = 249338152176387828895115662897439191770188346492207387691_<57>
P73 = 4572420640210901723153537570503316526388708355459392492824185811297632077_<73>

Number: n N=1140078913403362475426734419368691054460014958124652265589751664211254989625522656680600371254324341321370031223969601514216564207 ( 130 digits) SNFS difficulty: 160 digits. Divisors found: r1=249338152176387828895115662897439191770188346492207387691 (pp57) r2=4572420640210901723153537570503316526388708355459392492824185811297632077 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 22.36 hours. Scaled time: 40.90 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_6_158_3 n: 1140078913403362475426734419368691054460014958124652265589751664211254989625522656680600371254324341321370031223969601514216564207 skew: 1.86 deg: 5 c5: 1 c0: -22 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:216816, AFBsize:216967, largePrimes:7093950 encountered Relations: rels:6596572, finalFF:526491 Max relations in full relation-set: 48 Initial matrix: 433847 x 526491 with sparse part having weight 41986594. Pruned matrix : 359802 x 362035 with weight 24165523. Total sieving time: 21.11 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.06 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 22.36 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
5·10¹⁶⁴-3 = 4(9)₁₆₃7_<165> = 7 · 17 · 265628159462057789779216016761_<30> · C134
C134 = P65 · P70
P65 = 14415395583187368964117409453669561022245725587364267441064003881_<65>
P70 = 1097292384810779781467311229833121140205885608438153270649880660837643_<70>

Number: n N=15817903797466449690025501204524752190149137263149117955395138235556021194425072941823375150554994336662924330944593886562016862892483 ( 134 digits) SNFS difficulty: 165 digits. Divisors found: Sun Apr 13 15:27:18 2008 prp65 factor: 14415395583187368964117409453669561022245725587364267441064003881 Sun Apr 13 15:27:18 2008 prp70 factor: 1097292384810779781467311229833121140205885608438153270649880660837643 Sun Apr 13 15:27:18 2008 elapsed time 00:48:41 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.01 hours. Scaled time: 51.37 units (timescale=1.834). Factorization parameters were as follows: name: KA_4_9_163_7 n: 15817903797466449690025501204524752190149137263149117955395138235556021194425072941823375150554994336662924330944593886562016862892483 skew: 1.43 deg: 5 c5: 1 c0: -6 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2000261) Primes: RFBsize:230209, AFBsize:230282, largePrimes:7108660 encountered Relations: rels:6564318, finalFF:502203 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 27.86 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 28.01 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(2·10¹⁷⁷+43)/9 = (2)₁₇₆7_<177> = 5555233 · 4431534533_<10> · 9207448973929_<13> · 2993559071886717761227_<22> · C126
C126 = P38 · P88
P38 = 96018067606635797646393749559985680613_<38>
P88 = 3410758378305553129463494314744010333879148182725934296703293055767983843116651912665817_<88>
Apr 12, 2008 (2nd): By Sinkiti Sibata / GGNFS
(5·10¹⁴⁵-11)/3 = 1(6)₁₄₄3_<146> = 13 · 29 · 136045673 · 524365382060364953_<18> · C117
C117 = P48 · P69
P48 = 782208664539194981412341792228712859716363821171_<48>
P69 = 792256901871551573562908486122649158368373345051205572768889156804581_<69>

Number: 16663_145 N=619710213184906401442171112855315553108109013330960148072201601903639776804276018815261015424998164044556841277584351 ( 117 digits) SNFS difficulty: 145 digits. Divisors found: r1=782208664539194981412341792228712859716363821171 (pp48) r2=792256901871551573562908486122649158368373345051205572768889156804581 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 16.78 hours. Scaled time: 11.36 units (timescale=0.677). Factorization parameters were as follows: name: 16663_145 n: 619710213184906401442171112855315553108109013330960148072201601903639776804276018815261015424998164044556841277584351 m: 100000000000000000000000000000 c5: 5 c0: -11 skew: 1.17 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2250001) Primes: RFBsize:100021, AFBsize:100464, largePrimes:2713581 encountered Relations: rels:2665288, finalFF:225945 Max relations in full relation-set: 28 Initial matrix: 200550 x 225945 with sparse part having weight 23304396. Pruned matrix : 193546 x 194612 with weight 18417270. Total sieving time: 15.37 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.17 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 16.78 hours. --------- CPU info (if available) ----------
(5·10¹³⁴-11)/3 = 1(6)₁₃₃3_<135> = 17 · 73 · 50664461 · 775886330194411_<15> · C109
C109 = P55 · P55
P55 = 1514562294684404165773916125751733937523450013323054647_<55>
P55 = 2255736153622223157008861495416148949542640027113330839_<55>

Number: 16663_134 N=3416452925032645934485143394771495867369932302980206841897365478739597445039157195025694908555018430187358833 ( 109 digits) SNFS difficulty: 135 digits. Divisors found: r1=1514562294684404165773916125751733937523450013323054647 (pp55) r2=2255736153622223157008861495416148949542640027113330839 (pp55) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.96 hours. Scaled time: 4.71 units (timescale=0.677). Factorization parameters were as follows: name: 16663_134 n: 3416452925032645934485143394771495867369932302980206841897365478739597445039157195025694908555018430187358833 m: 1000000000000000000000000000 c5: 1 c0: -22 skew: 1.86 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:64044, largePrimes:1509703 encountered Relations: rels:1514301, finalFF:179475 Max relations in full relation-set: 28 Initial matrix: 142606 x 179475 with sparse part having weight 12642214. Pruned matrix : 129762 x 130539 with weight 7432855. Total sieving time: 6.54 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.28 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.96 hours. --------- CPU info (if available) ----------
Apr 12, 2008: By Robert Backstrom / GGNFS, Msieve
(5·10¹⁵³-11)/3 = 1(6)₁₅₂3_<154> = 3819031 · C147
C147 = P41 · P50 · P57
P41 = 24146838789382262583920577322514279965903_<41>
P50 = 28350609396736902451470157465466104446889245761819_<50>
P57 = 637489278118176076476491206382010478850794755031832879789_<57>

Number: n N=436410876650822333378981911031009349404774841227176911281072781725696038253333546301841138934632022276505916465895842863455852195666038496850815473 ( 147 digits) SNFS difficulty: 154 digits. Divisors found: Sat Apr 12 10:45:05 2008 prp41 factor: 24146838789382262583920577322514279965903 Sat Apr 12 10:45:05 2008 prp50 factor: 28350609396736902451470157465466104446889245761819 Sat Apr 12 10:45:05 2008 prp57 factor: 637489278118176076476491206382010478850794755031832879789 Sat Apr 12 10:45:05 2008 elapsed time 00:27:23 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 16.36 hours. Scaled time: 13.73 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_6_152_3 n: 436410876650822333378981911031009349404774841227176911281072781725696038253333546301841138934632022276505916465895842863455852195666038496850815473 type: snfs deg: 5 c5: 8 c0: -55 skew: 1.47 m: 5000000000000000000000000000000 rlim: 2400000 alim: 2400000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 1099990) Primes: RFBsize:176302, AFBsize:176364, largePrimes:5290147 encountered Relations: rels:5091653, finalFF:422983 Max relations in full relation-set: 28 Initial matrix: 352731 x 422983 with sparse part having weight 32754194. Pruned matrix : Total sieving time: 16.23 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,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.5,2.5,100000 total time: 16.36 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(4·10¹⁶⁷+11)/3 = 1(3)₁₆₆7_<168> = 9293 · C164
C164 = P45 · P53 · P67
P45 = 224864619045978638314145645571117372544626209_<45>
P53 = 23565455558677248911299805619150071026683171590171297_<53>
P67 = 2707608271774091657130405693450396883166513443249779410037377585533_<67>

Number: n N=14347716919545177373650417877255281753291007568420675060081064600595430252161124861006492341906094192761576814089458014993364180924710355464686681731769432189102909 ( 164 digits) SNFS difficulty: 167 digits. Divisors found: Sat Apr 12 21:37:02 2008 prp45 factor: 224864619045978638314145645571117372544626209 Sat Apr 12 21:37:02 2008 prp53 factor: 23565455558677248911299805619150071026683171590171297 Sat Apr 12 21:37:02 2008 prp67 factor: 2707608271774091657130405693450396883166513443249779410037377585533 Sat Apr 12 21:37:02 2008 elapsed time 01:43:43 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.71 hours. Scaled time: 92.25 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_3_166_7 n: 14347716919545177373650417877255281753291007568420675060081064600595430252161124861006492341906094192761576814089458014993364180924710355464686681731769432189102909 skew: 0.97 deg: 5 c5: 25 c0: 22 m: 2000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300127) Primes: RFBsize:230209, AFBsize:229923, largePrimes:7513121 encountered Relations: rels:6955203, finalFF:510760 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 63.46 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 63.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Apr 11, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(5·10¹⁴³-11)/3 = 1(6)₁₄₂3_<144> = 7² · 67 · 331 · C138
C138 = P38 · P100
P38 = 28798534375392779303628140531657338781_<38>
P100 = 5325734193132791638248472962622411091501534140325790522239722750062612132583107197711871318984210851_<100>

Number: n N=153373339235139427101498488198995159230667060529401822504715463314784361686235571019678106170546858775976459032907476919613045200043312631 ( 138 digits) SNFS difficulty: 144 digits. Divisors found: Fri Apr 11 06:57:45 2008 prp38 factor: 28798534375392779303628140531657338781 Fri Apr 11 06:57:45 2008 prp100 factor: 5325734193132791638248472962622411091501534140325790522239722750062612132583107197711871318984210851 Fri Apr 11 06:57:45 2008 elapsed time 00:23:37 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.52 hours. Scaled time: 13.08 units (timescale=1.739). Factorization parameters were as follows: name: KA_1_6_142_3 n: 153373339235139427101498488198995159230667060529401822504715463314784361686235571019678106170546858775976459032907476919613045200043312631 type: snfs skew: 1.47 deg: 5 c5: 8 c0: -55 m: 50000000000000000000000000000 rlim: 1300000 alim: 1300000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1299990) Primes: RFBsize:100021, AFBsize:100094, largePrimes:5326819 encountered Relations: rels:4686212, finalFF:250627 Max relations in full relation-set: 28 Initial matrix: 200180 x 250627 with sparse part having weight 20240544. Pruned matrix : Total sieving time: 7.38 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1300000,1300000,28,28,48,48,2.3,2.3,100000 total time: 7.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(4·10¹⁶⁶+17)/3 = 1(3)₁₆₅9_<167> = 23 · 14934599 · C158
C158 = P40 · P49 · P70
P40 = 4174243305008880150142804690262251278349_<40>
P49 = 7364569572438135830466677565409660399752515893267_<49>
P70 = 1262676814439812792538853247661616472122117327064522172690220773124829_<70>

Number: n N=38816585897454376370203041341417520056828335718762951002257396990744760548637933715654773052226878857184125827938004994260332153467299638252418262869453947707 ( 158 digits) SNFS difficulty: 166 digits. Divisors found: Fri Apr 11 07:07:03 2008 prp40 factor: 4174243305008880150142804690262251278349 Fri Apr 11 07:07:03 2008 prp49 factor: 7364569572438135830466677565409660399752515893267 Fri Apr 11 07:07:03 2008 prp70 factor: 1262676814439812792538853247661616472122117327064522172690220773124829 Fri Apr 11 07:07:03 2008 elapsed time 00:55:29 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 54.76 hours. Scaled time: 45.78 units (timescale=0.836). Factorization parameters were as follows: name: KA_1_3_165_9 n: 38816585897454376370203041341417520056828335718762951002257396990744760548637933715654773052226878857184125827938004994260332153467299638252418262869453947707 type: snfs deg: 5 c5: 40 c0: 17 skew: 0.84 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3300001) Primes: RFBsize:230209, AFBsize:230272, largePrimes:5779326 encountered Relations: rels:5745407, finalFF:535328 Max relations in full relation-set: 28 Initial matrix: 460547 x 535328 with sparse part having weight 49032993. Pruned matrix : Total sieving time: 54.57 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000 total time: 54.76 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(4·10¹⁹⁷+41)/9 = (4)₁₉₆9_<197> = 23 · 71² · 149 · 233 · 677664049 · 2468169467_<10> · 22402204398569599_<17> · 4434981126357605717_<19> · C134
C134 = P40 · P95
P40 = 2078833007212834249538418304107943881613_<40>
P95 = 31962386728259488329238937951744272406806378777600988877444685328307968295581798047594803451847_<95>
(5·10¹⁵⁰-11)/3 = 1(6)₁₄₉3_<151> = 17 · 73 · C148
C148 = P60 · P88
P60 = 421508304886553720011487693851764078006034468054366993384417_<60>
P88 = 3186183852220802244203025392870376136376593039760043939060786645463566852296231191997279_<88>

Number: n N=1343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343 ( 148 digits) SNFS difficulty: 150 digits. Divisors found: r1=421508304886553720011487693851764078006034468054366993384417 (pp60) r2=3186183852220802244203025392870376136376593039760043939060786645463566852296231191997279 (pp88) Version: GGNFS-0.77.1-20051202-athlon Total time: 10.06 hours. Scaled time: 18.40 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_6_149_3 n: 1343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343002954606500134300295460650013430029546065001343 skew: 1.17 deg: 5 c5: 5 c0: -11 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:148933, AFBsize:149461, largePrimes:6183051 encountered Relations: rels:5595336, finalFF:372683 Max relations in full relation-set: 48 Initial matrix: 298459 x 372683 with sparse part having weight 30927493. Pruned matrix : 243552 x 245108 with weight 16516457. Total sieving time: 9.53 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.40 hours. Total square root time: 0.03 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 10.06 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(5·10¹⁵¹-11)/3 = 1(6)₁₅₀3_<152> = 13 · 61 · 19826901180373766972341_<23> · C127
C127 = P44 · P83
P44 = 46530459068806937674122576450802907831043811_<44>
P83 = 22781555975659239394922705505015311151556624542606348511511085464549559681088943041_<83>

Number: n N=1060036257849146338773355785054145385311743017990749268402929154561767396758361119623350696044828967927053540184320041754569251 ( 127 digits) SNFS difficulty: 151 digits. Divisors found: r1=46530459068806937674122576450802907831043811 (pp44) r2=22781555975659239394922705505015311151556624542606348511511085464549559681088943041 (pp83) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.84 hours. Scaled time: 23.49 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_6_150_3 n: 1060036257849146338773355785054145385311743017990749268402929154561767396758361119623350696044828967927053540184320041754569251 skew: 0.74 deg: 5 c5: 50 c0: -11 m: 1000000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:148933, AFBsize:149221, largePrimes:6479496 encountered Relations: rels:5837996, finalFF:344927 Max relations in full relation-set: 48 Initial matrix: 298219 x 344927 with sparse part having weight 33847276. Pruned matrix : 270062 x 271617 with weight 21493159. Total sieving time: 12.13 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.56 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 12.84 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Apr 11, 2008: By Sinkiti Sibata / Msieve, GGNFS
(5·10¹⁵⁴-11)/3 = 1(6)₁₅₃3_<155> = 20747 · 1103982904122717018242570941_<28> · 514096729678132664523698534537_<30> · C94
C94 = P45 · P49
P45 = 585300977028591004285181609982549579278364431_<45>
P49 = 2418282339557813003254540703695423879556104787327_<49>

Thu Apr 10 21:13:18 2008 Msieve v. 1.33 Thu Apr 10 21:13:18 2008 random seeds: 5f0a8418 665aa333 Thu Apr 10 21:13:18 2008 factoring 1415423016074174819521263294353965449508917291651641663096371423565430400347476027033656365937 (94 digits) Thu Apr 10 21:13:20 2008 searching for 15-digit factors Thu Apr 10 21:13:21 2008 commencing quadratic sieve (94-digit input) Thu Apr 10 21:13:22 2008 using multiplier of 1 Thu Apr 10 21:13:22 2008 using 64kb Pentium 4 sieve core Thu Apr 10 21:13:22 2008 sieve interval: 18 blocks of size 65536 Thu Apr 10 21:13:22 2008 processing polynomials in batches of 6 Thu Apr 10 21:13:22 2008 using a sieve bound of 1983061 (74118 primes) Thu Apr 10 21:13:22 2008 using large prime bound of 255814869 (27 bits) Thu Apr 10 21:13:22 2008 using double large prime bound of 1362279921846333 (42-51 bits) Thu Apr 10 21:13:22 2008 using trial factoring cutoff of 51 bits Thu Apr 10 21:13:22 2008 polynomial 'A' values have 12 factors Fri Apr 11 03:21:49 2008 74217 relations (17169 full + 57048 combined from 1052711 partial), need 74214 Fri Apr 11 03:21:52 2008 begin with 1069880 relations Fri Apr 11 03:21:54 2008 reduce to 197432 relations in 11 passes Fri Apr 11 03:21:54 2008 attempting to read 197432 relations Fri Apr 11 03:22:00 2008 recovered 197432 relations Fri Apr 11 03:22:00 2008 recovered 184174 polynomials Fri Apr 11 03:22:00 2008 attempting to build 74217 cycles Fri Apr 11 03:22:00 2008 found 74217 cycles in 5 passes Fri Apr 11 03:22:00 2008 distribution of cycle lengths: Fri Apr 11 03:22:00 2008 length 1 : 17169 Fri Apr 11 03:22:00 2008 length 2 : 12312 Fri Apr 11 03:22:00 2008 length 3 : 12345 Fri Apr 11 03:22:00 2008 length 4 : 10360 Fri Apr 11 03:22:00 2008 length 5 : 7835 Fri Apr 11 03:22:00 2008 length 6 : 5380 Fri Apr 11 03:22:00 2008 length 7 : 3675 Fri Apr 11 03:22:00 2008 length 9+: 5141 Fri Apr 11 03:22:00 2008 largest cycle: 19 relations Fri Apr 11 03:22:01 2008 matrix is 74118 x 74217 (19.0 MB) with weight 4695268 (63.26/col) Fri Apr 11 03:22:01 2008 sparse part has weight 4695268 (63.26/col) Fri Apr 11 03:22:02 2008 filtering completed in 3 passes Fri Apr 11 03:22:02 2008 matrix is 71310 x 71374 (18.4 MB) with weight 4545762 (63.69/col) Fri Apr 11 03:22:02 2008 sparse part has weight 4545762 (63.69/col) Fri Apr 11 03:22:03 2008 saving the first 48 matrix rows for later Fri Apr 11 03:22:03 2008 matrix is 71262 x 71374 (10.9 MB) with weight 3510302 (49.18/col) Fri Apr 11 03:22:03 2008 sparse part has weight 2421855 (33.93/col) Fri Apr 11 03:22:03 2008 matrix includes 64 packed rows Fri Apr 11 03:22:03 2008 using block size 21845 for processor cache size 512 kB Fri Apr 11 03:22:04 2008 commencing Lanczos iteration Fri Apr 11 03:22:04 2008 memory use: 11.1 MB Fri Apr 11 03:22:53 2008 lanczos halted after 1128 iterations (dim = 71260) Fri Apr 11 03:22:53 2008 recovered 15 nontrivial dependencies Fri Apr 11 03:22:54 2008 prp45 factor: 585300977028591004285181609982549579278364431 Fri Apr 11 03:22:54 2008 prp49 factor: 2418282339557813003254540703695423879556104787327 Fri Apr 11 03:22:54 2008 elapsed time 06:09:36
(5·10¹²⁹-11)/3 = 1(6)₁₂₈3_<130> = 258787 · C124
C124 = P37 · P88
P37 = 5066833232812900348371444210929217377_<37>
P88 = 1271070628221685741151778990506755714714922860599778130191770040148883980132610080516237_<88>

Number: 16663_129 N=6440302900326008132814502531683070118153797009380945204614863446257604387649559934102820723864284785042010095818826551050349 ( 124 digits) SNFS difficulty: 130 digits. Divisors found: r1=5066833232812900348371444210929217377 (pp37) r2=1271070628221685741151778990506755714714922860599778130191770040148883980132610080516237 (pp88) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 4.48 hours. Scaled time: 3.03 units (timescale=0.677). Factorization parameters were as follows: name: 16663_129 n: 6440302900326008132814502531683070118153797009380945204614863446257604387649559934102820723864284785042010095818826551050349 m: 100000000000000000000000000 c5: 1 c0: -22 skew: 1.86 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 850001) Primes: RFBsize:63951, AFBsize:64044, largePrimes:1431982 encountered Relations: rels:1420951, finalFF:163891 Max relations in full relation-set: 28 Initial matrix: 128059 x 163891 with sparse part having weight 9321009. Pruned matrix : 116287 x 116991 with weight 5139628. Total sieving time: 4.18 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.18 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.48 hours. --------- CPU info (if available) ----------
(5·10¹³³-11)/3 = 1(6)₁₃₂3_<134> = 13 · 5693 · 929178817187244089_<18> · C111
C111 = P47 · P64
P47 = 26383737838315756222354254062173633796804502149_<47>
P64 = 9186045454305410246170305021305223071642869327656871729015051787_<64>

Number: 16663_133 N=242362215037246103331022315073602170502581559779716014453310837872533146895368113827105214017523348267987790263 ( 111 digits) SNFS difficulty: 134 digits. Divisors found: r1=26383737838315756222354254062173633796804502149 (pp47) r2=9186045454305410246170305021305223071642869327656871729015051787 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 7.41 hours. Scaled time: 5.02 units (timescale=0.677). Factorization parameters were as follows: name: 16663_133 n: 242362215037246103331022315073602170502581559779716014453310837872533146895368113827105214017523348267987790263 m: 500000000000000000000000000 c5: 8 c0: -55 skew: 1.47 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1150001) Primes: RFBsize:78498, AFBsize:64019, largePrimes:1542285 encountered Relations: rels:1556716, finalFF:188341 Max relations in full relation-set: 28 Initial matrix: 142582 x 188341 with sparse part having weight 14359518. Pruned matrix : 127065 x 127841 with weight 7978424. Total sieving time: 6.99 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.28 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 7.41 hours. --------- CPU info (if available) ----------
Apr 10, 2008 (6th): By suberi / GGNFS
(61·10¹⁶⁴-7)/9 = 6(7)₁₆₄_<165> = 317 · 3495769463_<10> · 4497534330479_<13> · 110614628030592113_<18> · C124
C124 = P46 · P78
P46 = 5132819123667913656014282950111020599968382579_<46>
P78 = 239520267690880254444053983762177434375240421775507117542386875504206305181039_<78>

Number: 67777_164 N=1229414210509808080396481586136781304990112987408467724961865348285630111489772284606331844141937676322340980381636608719581 ( 124 digits) SNFS difficulty: 166 digits. Divisors found: r1=5132819123667913656014282950111020599968382579 (pp46) r2=239520267690880254444053983762177434375240421775507117542386875504206305181039 (pp78) Version: GGNFS-0.77.1-20060722-k8 Total time: 148.21 hours. Scaled time: 280.42 units (timescale=1.892). Factorization parameters were as follows: n: 1229414210509808080396481586136781304990112987408467724961865348285630111489772284606331844141937676322340980381636608719581 m: 1000000000000000000000000000000000 c5: 61 c0: -70 skew: 1.03 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, ) Primes: RFBsize:348513, AFBsize:347762, largePrimes:6076829 encountered Relations: rels:6274668, finalFF:827831 Max relations in full relation-set: 32 Initial matrix: 696340 x 827831 with sparse part having weight 69285818. Pruned matrix : 599091 x 602636 with weight 51254532. Total sieving time: 144.01 hours. Total relation processing time: 0.25 hours. Matrix solve time: 3.82 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 148.21 hours. --------- CPU info (if available) ---------- Memory: 896148k/915904k available (2823k kernel code, 19044k reserved, 1312k data, 204k init) Calibrating delay using timer specific routine.. 3594.37 BogoMIPS (lpj=7188757) Calibrating delay using timer specific routine.. 3591.04 BogoMIPS (lpj=7182090)
Apr 10, 2008 (5th): By Jo Yeong Uk / GMP-ECM, Msieve
(5·10¹⁴¹-11)/3 = 1(6)₁₄₀3_<142> = 149 · 173273 · 92704098020668750136839_<23> · C111
C111 = P32 · P34 · P46
P32 = 15188722265464115071522657576259_<32>
P34 = 7712334843403732256679766516486637_<34>
P46 = 5944639679663139196197290964556363337121607987_<46>

Thu Apr 10 09:23:24 2008 Thu Apr 10 09:23:24 2008 Thu Apr 10 09:23:24 2008 Msieve v. 1.34 Thu Apr 10 09:23:24 2008 random seeds: f379aa7d 8ca47774 Thu Apr 10 09:23:24 2008 factoring 45847051732946429718609863722692727709273793212213606054363232586927611237969719 (80 digits) Thu Apr 10 09:23:24 2008 no P-1/P+1/ECM available, skipping Thu Apr 10 09:23:24 2008 commencing quadratic sieve (80-digit input) Thu Apr 10 09:23:24 2008 using multiplier of 5 Thu Apr 10 09:23:24 2008 using 32kb Intel Core sieve core Thu Apr 10 09:23:24 2008 sieve interval: 12 blocks of size 32768 Thu Apr 10 09:23:24 2008 processing polynomials in batches of 17 Thu Apr 10 09:23:24 2008 using a sieve bound of 1262311 (48647 primes) Thu Apr 10 09:23:24 2008 using large prime bound of 126231100 (26 bits) Thu Apr 10 09:23:24 2008 using trial factoring cutoff of 27 bits Thu Apr 10 09:23:24 2008 polynomial 'A' values have 10 factors Thu Apr 10 09:38:17 2008 48752 relations (24624 full + 24128 combined from 267948 partial), need 48743 Thu Apr 10 09:38:17 2008 begin with 292572 relations Thu Apr 10 09:38:17 2008 reduce to 69970 relations in 2 passes Thu Apr 10 09:38:17 2008 attempting to read 69970 relations Thu Apr 10 09:38:18 2008 recovered 69970 relations Thu Apr 10 09:38:18 2008 recovered 60666 polynomials Thu Apr 10 09:38:18 2008 attempting to build 48752 cycles Thu Apr 10 09:38:18 2008 found 48752 cycles in 1 passes Thu Apr 10 09:38:18 2008 distribution of cycle lengths: Thu Apr 10 09:38:18 2008 length 1 : 24624 Thu Apr 10 09:38:18 2008 length 2 : 24128 Thu Apr 10 09:38:18 2008 largest cycle: 2 relations Thu Apr 10 09:38:18 2008 matrix is 48647 x 48752 (7.2 MB) with weight 1506429 (30.90/col) Thu Apr 10 09:38:18 2008 sparse part has weight 1506429 (30.90/col) Thu Apr 10 09:38:18 2008 filtering completed in 4 passes Thu Apr 10 09:38:18 2008 matrix is 41826 x 41890 (6.1 MB) with weight 1269861 (30.31/col) Thu Apr 10 09:38:18 2008 sparse part has weight 1269861 (30.31/col) Thu Apr 10 09:38:18 2008 saving the first 48 matrix rows for later Thu Apr 10 09:38:18 2008 matrix is 41778 x 41890 (4.4 MB) with weight 957728 (22.86/col) Thu Apr 10 09:38:18 2008 sparse part has weight 728581 (17.39/col) Thu Apr 10 09:38:18 2008 matrix includes 64 packed rows Thu Apr 10 09:38:18 2008 commencing Lanczos iteration Thu Apr 10 09:38:18 2008 memory use: 6.0 MB Thu Apr 10 09:38:40 2008 lanczos halted after 662 iterations (dim = 41759) Thu Apr 10 09:38:40 2008 recovered 8 nontrivial dependencies Thu Apr 10 09:38:41 2008 prp34 factor: 7712334843403732256679766516486637 Thu Apr 10 09:38:41 2008 prp46 factor: 5944639679663139196197290964556363337121607987 Thu Apr 10 09:38:41 2008 elapsed time 00:15:17
Apr 10, 2008 (4th): By matsui / GGNFS
8·10¹⁷⁷-7 = 7(9)₁₇₆3_<178> = 19 · 73 · C175
C175 = P69 · P106
P69 = 845024513588440108342229237258611536863418925832842805605254098132291_<69>
P106 = 6825653191658678389031719639341109854130190201976846345079951503520340161289026704590084570366199203022329_<106>

N=5767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739 ( 175 digits) SNFS difficulty: 177 digits. Divisors found: r1=845024513588440108342229237258611536863418925832842805605254098132291 (pp69) r2=6825653191658678389031719639341109854130190201976846345079951503520340161289026704590084570366199203022329 (pp106) Version: GGNFS-0.77.1-20060513-prescott Total time: 228.94 hours. Scaled time: 386.00 units (timescale=1.686). Factorization parameters were as follows: n: 5767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739005046863734679163662581110310021629416005767844268204758471521268925739 m: 200000000000000000000000000000000000 c5: 25 c0: -7 skew: 0.78 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 12000001) Primes: RFBsize:501962, AFBsize:501206, largePrimes:6478564 encountered Relations: rels:6931375, finalFF:1126384 Max relations in full relation-set: 28 Initial matrix: 1003232 x 1126384 with sparse part having weight 71657504. Pruned matrix : 899663 x 904743 with weight 55336059. Total sieving time: 212.90 hours. Total relation processing time: 0.14 hours. Matrix solve time: 15.65 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 228.94 hours.
Apr 10, 2008 (3rd): By Sinkiti Sibata / Msieve, GGNFS
(5·10¹⁴⁴-11)/3 = 1(6)₁₄₃3_<145> = 372005757821_<12> · 1993489673710399_<16> · 164034934577678887904605096215469_<33> · C86
C86 = P31 · P56
P31 = 1009810979515396265762537150309_<31>
P56 = 13567775824120341503281816335779422365608641008294822157_<56>

Thu Apr 10 06:45:04 2008 Msieve v. 1.33 Thu Apr 10 06:45:04 2008 random seeds: 4d5118a6 bb53e94c Thu Apr 10 06:45:04 2008 factoring 13700888994800274861698196701203613805538875258560664517465359702368373723918732596513 (86 digits) Thu Apr 10 06:45:05 2008 searching for 15-digit factors Thu Apr 10 06:45:07 2008 commencing quadratic sieve (86-digit input) Thu Apr 10 06:45:07 2008 using multiplier of 17 Thu Apr 10 06:45:07 2008 using 64kb Pentium 4 sieve core Thu Apr 10 06:45:07 2008 sieve interval: 6 blocks of size 65536 Thu Apr 10 06:45:07 2008 processing polynomials in batches of 17 Thu Apr 10 06:45:07 2008 using a sieve bound of 1442429 (54984 primes) Thu Apr 10 06:45:07 2008 using large prime bound of 115394320 (26 bits) Thu Apr 10 06:45:07 2008 using double large prime bound of 325036373888400 (41-49 bits) Thu Apr 10 06:45:07 2008 using trial factoring cutoff of 49 bits Thu Apr 10 06:45:07 2008 polynomial 'A' values have 11 factors Thu Apr 10 07:35:14 2008 55128 relations (16556 full + 38572 combined from 563178 partial), need 55080 Thu Apr 10 07:35:17 2008 begin with 579734 relations Thu Apr 10 07:35:17 2008 reduce to 127826 relations in 12 passes Thu Apr 10 07:35:17 2008 attempting to read 127826 relations Thu Apr 10 07:35:21 2008 recovered 127826 relations Thu Apr 10 07:35:21 2008 recovered 106966 polynomials Thu Apr 10 07:35:21 2008 attempting to build 55128 cycles Thu Apr 10 07:35:21 2008 found 55128 cycles in 5 passes Thu Apr 10 07:35:21 2008 distribution of cycle lengths: Thu Apr 10 07:35:21 2008 length 1 : 16556 Thu Apr 10 07:35:21 2008 length 2 : 11240 Thu Apr 10 07:35:21 2008 length 3 : 9653 Thu Apr 10 07:35:21 2008 length 4 : 7016 Thu Apr 10 07:35:21 2008 length 5 : 4631 Thu Apr 10 07:35:21 2008 length 6 : 2772 Thu Apr 10 07:35:21 2008 length 7 : 1589 Thu Apr 10 07:35:21 2008 length 9+: 1671 Thu Apr 10 07:35:21 2008 largest cycle: 20 relations Thu Apr 10 07:35:21 2008 matrix is 54984 x 55128 (12.1 MB) with weight 2963153 (53.75/col) Thu Apr 10 07:35:21 2008 sparse part has weight 2963153 (53.75/col) Thu Apr 10 07:35:22 2008 filtering completed in 3 passes Thu Apr 10 07:35:22 2008 matrix is 49629 x 49691 (11.1 MB) with weight 2706362 (54.46/col) Thu Apr 10 07:35:22 2008 sparse part has weight 2706362 (54.46/col) Thu Apr 10 07:35:22 2008 saving the first 48 matrix rows for later Thu Apr 10 07:35:22 2008 matrix is 49581 x 49691 (6.8 MB) with weight 2076867 (41.80/col) Thu Apr 10 07:35:22 2008 sparse part has weight 1488655 (29.96/col) Thu Apr 10 07:35:22 2008 matrix includes 64 packed rows Thu Apr 10 07:35:22 2008 commencing Lanczos iteration Thu Apr 10 07:35:22 2008 memory use: 8.7 MB Thu Apr 10 07:37:04 2008 lanczos halted after 786 iterations (dim = 49581) Thu Apr 10 07:37:05 2008 recovered 18 nontrivial dependencies Thu Apr 10 07:37:05 2008 prp31 factor: 1009810979515396265762537150309 Thu Apr 10 07:37:05 2008 prp56 factor: 13567775824120341503281816335779422365608641008294822157 Thu Apr 10 07:37:05 2008 elapsed time 00:52:01
(5·10¹³⁸-11)/3 = 1(6)₁₃₇3_<139> = 337 · 17600112488381_<14> · 64322575613083129_<17> · 1246141681788805723_<19> · C88
C88 = P36 · P52
P36 = 566733070758170868253771341604578479_<36>
P52 = 6185773308782255639310478822145178597967633181529103_<52>

Thu Apr 10 07:48:01 2008 Msieve v. 1.33 Thu Apr 10 07:48:01 2008 random seeds: 6c3c1403 9c5365fb Thu Apr 10 07:48:01 2008 factoring 3505682302300098820331687118529707211660926175889383687226721329786765058955918985974337 (88 digits) Thu Apr 10 07:48:02 2008 searching for 15-digit factors Thu Apr 10 07:48:04 2008 commencing quadratic sieve (88-digit input) Thu Apr 10 07:48:04 2008 using multiplier of 17 Thu Apr 10 07:48:04 2008 using 64kb Pentium 4 sieve core Thu Apr 10 07:48:04 2008 sieve interval: 13 blocks of size 65536 Thu Apr 10 07:48:04 2008 processing polynomials in batches of 8 Thu Apr 10 07:48:04 2008 using a sieve bound of 1510507 (57667 primes) Thu Apr 10 07:48:04 2008 using large prime bound of 120840560 (26 bits) Thu Apr 10 07:48:04 2008 using double large prime bound of 353169224858800 (42-49 bits) Thu Apr 10 07:48:04 2008 using trial factoring cutoff of 49 bits Thu Apr 10 07:48:04 2008 polynomial 'A' values have 11 factors Thu Apr 10 09:21:58 2008 58012 relations (16032 full + 41980 combined from 609335 partial), need 57763 Thu Apr 10 09:22:01 2008 begin with 625367 relations Thu Apr 10 09:22:01 2008 reduce to 139986 relations in 9 passes Thu Apr 10 09:22:01 2008 attempting to read 139986 relations Thu Apr 10 09:22:05 2008 recovered 139986 relations Thu Apr 10 09:22:05 2008 recovered 119002 polynomials Thu Apr 10 09:22:05 2008 attempting to build 58012 cycles Thu Apr 10 09:22:05 2008 found 58011 cycles in 4 passes Thu Apr 10 09:22:05 2008 distribution of cycle lengths: Thu Apr 10 09:22:05 2008 length 1 : 16032 Thu Apr 10 09:22:05 2008 length 2 : 11280 Thu Apr 10 09:22:05 2008 length 3 : 10151 Thu Apr 10 09:22:05 2008 length 4 : 7452 Thu Apr 10 09:22:05 2008 length 5 : 5389 Thu Apr 10 09:22:05 2008 length 6 : 3403 Thu Apr 10 09:22:05 2008 length 7 : 1988 Thu Apr 10 09:22:05 2008 length 9+: 2316 Thu Apr 10 09:22:05 2008 largest cycle: 18 relations Thu Apr 10 09:22:06 2008 matrix is 57667 x 58011 (14.0 MB) with weight 3443627 (59.36/col) Thu Apr 10 09:22:06 2008 sparse part has weight 3443627 (59.36/col) Thu Apr 10 09:22:07 2008 filtering completed in 3 passes Thu Apr 10 09:22:07 2008 matrix is 53492 x 53555 (13.0 MB) with weight 3196363 (59.68/col) Thu Apr 10 09:22:07 2008 sparse part has weight 3196363 (59.68/col) Thu Apr 10 09:22:07 2008 saving the first 48 matrix rows for later Thu Apr 10 09:22:07 2008 matrix is 53444 x 53555 (9.6 MB) with weight 2662668 (49.72/col) Thu Apr 10 09:22:07 2008 sparse part has weight 2200954 (41.10/col) Thu Apr 10 09:22:07 2008 matrix includes 64 packed rows Thu Apr 10 09:22:07 2008 using block size 21422 for processor cache size 512 kB Thu Apr 10 09:22:08 2008 commencing Lanczos iteration Thu Apr 10 09:22:08 2008 memory use: 8.7 MB Thu Apr 10 09:22:37 2008 lanczos halted after 846 iterations (dim = 53440) Thu Apr 10 09:22:38 2008 recovered 15 nontrivial dependencies Thu Apr 10 09:22:38 2008 prp36 factor: 566733070758170868253771341604578479 Thu Apr 10 09:22:38 2008 prp52 factor: 6185773308782255639310478822145178597967633181529103 Thu Apr 10 09:22:38 2008 elapsed time 01:34:37
(5·10¹³⁶-11)/3 = 1(6)₁₃₅3_<137> = 79 · 367 · 134401 · 4789658941_<10> · 396271367827_<12> · 198762889748084687_<18> · C89
C89 = P34 · P55
P34 = 8068301980104416383890347409737059_<34>
P55 = 1405200720180081873965164341710238376930548187931746661_<55>

Thu Apr 10 09:33:05 2008 Msieve v. 1.33 Thu Apr 10 09:33:05 2008 random seeds: 0142229e 3af44813 Thu Apr 10 09:33:05 2008 factoring 11337583753073106518116561988542402958930646986405793606004811557150675788314536611209999 (89 digits) Thu Apr 10 09:33:06 2008 searching for 15-digit factors Thu Apr 10 09:33:08 2008 commencing quadratic sieve (89-digit input) Thu Apr 10 09:33:08 2008 using multiplier of 3 Thu Apr 10 09:33:08 2008 using 64kb Pentium 4 sieve core Thu Apr 10 09:33:08 2008 sieve interval: 14 blocks of size 65536 Thu Apr 10 09:33:08 2008 processing polynomials in batches of 8 Thu Apr 10 09:33:08 2008 using a sieve bound of 1533307 (58333 primes) Thu Apr 10 09:33:08 2008 using large prime bound of 122664560 (26 bits) Thu Apr 10 09:33:08 2008 using double large prime bound of 362822632808640 (42-49 bits) Thu Apr 10 09:33:08 2008 using trial factoring cutoff of 49 bits Thu Apr 10 09:33:08 2008 polynomial 'A' values have 11 factors Thu Apr 10 11:40:42 2008 58719 relations (15129 full + 43590 combined from 628696 partial), need 58429 Thu Apr 10 11:40:45 2008 begin with 643825 relations Thu Apr 10 11:40:45 2008 reduce to 144836 relations in 11 passes Thu Apr 10 11:40:45 2008 attempting to read 144836 relations Thu Apr 10 11:40:49 2008 recovered 144836 relations Thu Apr 10 11:40:49 2008 recovered 127614 polynomials Thu Apr 10 11:40:49 2008 attempting to build 58719 cycles Thu Apr 10 11:40:49 2008 found 58719 cycles in 5 passes Thu Apr 10 11:40:49 2008 distribution of cycle lengths: Thu Apr 10 11:40:49 2008 length 1 : 15129 Thu Apr 10 11:40:49 2008 length 2 : 11176 Thu Apr 10 11:40:49 2008 length 3 : 10479 Thu Apr 10 11:40:49 2008 length 4 : 7871 Thu Apr 10 11:40:49 2008 length 5 : 5641 Thu Apr 10 11:40:49 2008 length 6 : 3557 Thu Apr 10 11:40:49 2008 length 7 : 2180 Thu Apr 10 11:40:49 2008 length 9+: 2686 Thu Apr 10 11:40:49 2008 largest cycle: 17 relations Thu Apr 10 11:40:50 2008 matrix is 58333 x 58719 (14.4 MB) with weight 3540941 (60.30/col) Thu Apr 10 11:40:50 2008 sparse part has weight 3540941 (60.30/col) Thu Apr 10 11:40:51 2008 filtering completed in 3 passes Thu Apr 10 11:40:51 2008 matrix is 54761 x 54825 (13.5 MB) with weight 3321850 (60.59/col) Thu Apr 10 11:40:51 2008 sparse part has weight 3321850 (60.59/col) Thu Apr 10 11:40:51 2008 saving the first 48 matrix rows for later Thu Apr 10 11:40:51 2008 matrix is 54713 x 54825 (9.5 MB) with weight 2731547 (49.82/col) Thu Apr 10 11:40:51 2008 sparse part has weight 2167317 (39.53/col) Thu Apr 10 11:40:51 2008 matrix includes 64 packed rows Thu Apr 10 11:40:51 2008 using block size 21845 for processor cache size 512 kB Thu Apr 10 11:40:52 2008 commencing Lanczos iteration Thu Apr 10 11:40:52 2008 memory use: 8.8 MB Thu Apr 10 11:41:28 2008 lanczos halted after 866 iterations (dim = 54712) Thu Apr 10 11:41:28 2008 recovered 17 nontrivial dependencies Thu Apr 10 11:41:29 2008 prp34 factor: 8068301980104416383890347409737059 Thu Apr 10 11:41:29 2008 prp55 factor: 1405200720180081873965164341710238376930548187931746661 Thu Apr 10 11:41:29 2008 elapsed time 02:08:24
(5·10¹¹⁹-11)/3 = 1(6)₁₁₈3_<120> = 7 · 733 · 34313 · C111
C111 = P39 · P73
P39 = 101104783942079007388364625845026040897_<39>
P73 = 9363028368878613663743614793519812822060379795258031152047919513400120493_<73>

Number: 16663_119 N=946646960279028659715896214466534268244143257606707337535752891397296333493000489535755981252974684242545802221 ( 111 digits) SNFS difficulty: 120 digits. Divisors found: r1=101104783942079007388364625845026040897 (pp39) r2=9363028368878613663743614793519812822060379795258031152047919513400120493 (pp73) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.13 hours. Scaled time: 1.43 units (timescale=0.675). Factorization parameters were as follows: name: 16663_119 n: 946646960279028659715896214466534268244143257606707337535752891397296333493000489535755981252974684242545802221 m: 1000000000000000000000000 c5: 1 c0: -22 skew: 1.86 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64044, largePrimes:2132126 encountered Relations: rels:2254968, finalFF:263067 Max relations in full relation-set: 28 Initial matrix: 113206 x 263067 with sparse part having weight 22310391. Pruned matrix : 81108 x 81738 with weight 4690802. Total sieving time: 1.92 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.10 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.13 hours. --------- CPU info (if available) ----------
(5·10¹²⁴-11)/3 = 1(6)₁₂₃3_<125> = 155782489099_<12> · C114
C114 = P35 · P79
P35 = 79040799952020878573456251998858247_<35>
P79 = 1353563964903948324773516845167090881007930444243617150102530821798840472293571_<79>

Number: 16663_124 N=106986778572237188918038053454011120432923406069133029873611126531552369406827118389351077489337777850129398430037 ( 114 digits) SNFS difficulty: 125 digits. Divisors found: r1=79040799952020878573456251998858247 (pp35) r2=1353563964903948324773516845167090881007930444243617150102530821798840472293571 (pp79) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 3.07 hours. Scaled time: 2.07 units (timescale=0.675). Factorization parameters were as follows: name: 16663_124 n: 106986778572237188918038053454011120432923406069133029873611126531552369406827118389351077489337777850129398430037 m: 10000000000000000000000000 c5: 1 c0: -22 skew: 1.86 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:64044, largePrimes:2230601 encountered Relations: rels:2398863, finalFF:282622 Max relations in full relation-set: 28 Initial matrix: 113206 x 282622 with sparse part having weight 27237143. Pruned matrix : 84072 x 84702 with weight 6352895. Total sieving time: 2.83 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.13 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.07 hours. --------- CPU info (if available) ----------
Apr 10, 2008 (2nd): By Robert Backstrom / GMP-ECM, Msieve, GGNFS
(5·10¹³⁰-11)/3 = 1(6)₁₂₉3_<131> = 19 · 197 · 14107 · 191413 · 649724783 · 14480781147778646998269769_<26> · C84
C84 = P38 · P46
P38 = 53531600126183563743099708638553112189_<38>
P46 = 3274094258896914280404842697764802626556431917_<46>
8·10¹⁶³+9 = 8(0)₁₆₂9_<164> = 503 · 1087 · 399924341 · 29222738487023707_<17> · C134
C134 = P56 · P78
P56 = 36035228405537339175432279337085862878520760605668457943_<56>
P78 = 347429290363042316932943294898674175631435388823749992448700892981477531332209_<78>

Number: n N=12519693833005982629763709812980179231976207191212881316914731579887782131176373995769271932131678712789550263792631222521491477786087 ( 134 digits) SNFS difficulty: 163 digits. Divisors found: Thu Apr 10 07:25:28 2008 prp56 factor: 36035228405537339175432279337085862878520760605668457943 Thu Apr 10 07:25:28 2008 prp78 factor: 347429290363042316932943294898674175631435388823749992448700892981477531332209 Thu Apr 10 07:25:28 2008 elapsed time 01:12:32 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 51.50 hours. Scaled time: 90.43 units (timescale=1.756). Factorization parameters were as follows: name: KA_8_0_162_9 n: 12519693833005982629763709812980179231976207191212881316914731579887782131176373995769271932131678712789550263792631222521491477786087 type: snfs skew: 0.51 deg: 5 c5: 250 c0: 9 m: 200000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2599990) Primes: RFBsize:230209, AFBsize:229672, largePrimes:7298720 encountered Relations: rels:6770473, finalFF:539596 Max relations in full relation-set: 28 Initial matrix: 459948 x 539596 with sparse part having weight 38448691. Pruned matrix : Total sieving time: 51.26 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 51.50 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(5·10¹⁰⁹-11)/3 = 1(6)₁₀₈3_<110> = 13 · 313 · 2312775383_<10> · C97
C97 = P38 · P59
P38 = 58445511121979509375071556501778835511_<38>
P59 = 30302359249263881160048008087323480234166016216705306154379_<59>
(5·10¹²⁵-11)/3 = 1(6)₁₂₄3_<126> = 7 · 89 · 556121386394051411573_<21> · C102
C102 = P31 · P72
P31 = 2082317813011810225828417141867_<31>
P72 = 231017080921821034361454488681781206591379258747165236540837184499456591_<72>
(5·10¹¹⁵-11)/3 = 1(6)₁₁₄3_<116> = 13 · 243311 · 6251989363_<10> · 415576023843179_<15> · C85
C85 = P39 · P47
P39 = 101724403988483751381031110691554232729_<39>
P47 = 19936539876112083560045113778507889458461515877_<47>

Thu Apr 10 08:23:12 2008 Thu Apr 10 08:23:12 2008 Thu Apr 10 08:23:12 2008 Msieve v. 1.34 Thu Apr 10 08:23:12 2008 random seeds: 37c399e0 09f2c22c Thu Apr 10 08:23:12 2008 factoring 2028032636490141387528493438386065303545798771129933058079434458815434399092986538333 (85 digits) Thu Apr 10 08:23:12 2008 searching for 15-digit factors Thu Apr 10 08:23:13 2008 commencing quadratic sieve (85-digit input) Thu Apr 10 08:23:13 2008 using multiplier of 37 Thu Apr 10 08:23:13 2008 using 64kb Opteron sieve core Thu Apr 10 08:23:13 2008 sieve interval: 6 blocks of size 65536 Thu Apr 10 08:23:13 2008 processing polynomials in batches of 17 Thu Apr 10 08:23:13 2008 using a sieve bound of 1426129 (54372 primes) Thu Apr 10 08:23:13 2008 using large prime bound of 116942578 (26 bits) Thu Apr 10 08:23:13 2008 using double large prime bound of 332928269126164 (41-49 bits) Thu Apr 10 08:23:13 2008 using trial factoring cutoff of 49 bits Thu Apr 10 08:23:13 2008 polynomial 'A' values have 11 factors Thu Apr 10 08:47:08 2008 54480 relations (16137 full + 38343 combined from 569033 partial), need 54468 Thu Apr 10 08:47:08 2008 begin with 585169 relations Thu Apr 10 08:47:09 2008 reduce to 127178 relations in 10 passes Thu Apr 10 08:47:09 2008 attempting to read 127178 relations Thu Apr 10 08:47:10 2008 recovered 127178 relations Thu Apr 10 08:47:10 2008 recovered 106669 polynomials Thu Apr 10 08:47:10 2008 attempting to build 54480 cycles Thu Apr 10 08:47:10 2008 found 54480 cycles in 5 passes Thu Apr 10 08:47:10 2008 distribution of cycle lengths: Thu Apr 10 08:47:10 2008 length 1 : 16137 Thu Apr 10 08:47:10 2008 length 2 : 11237 Thu Apr 10 08:47:10 2008 length 3 : 9540 Thu Apr 10 08:47:10 2008 length 4 : 6859 Thu Apr 10 08:47:10 2008 length 5 : 4566 Thu Apr 10 08:47:10 2008 length 6 : 2788 Thu Apr 10 08:47:10 2008 length 7 : 1597 Thu Apr 10 08:47:10 2008 length 9+: 1756 Thu Apr 10 08:47:10 2008 largest cycle: 19 relations Thu Apr 10 08:47:11 2008 matrix is 54372 x 54480 (11.8 MB) with weight 2874410 (52.76/col) Thu Apr 10 08:47:11 2008 sparse part has weight 2874410 (52.76/col) Thu Apr 10 08:47:11 2008 filtering completed in 3 passes Thu Apr 10 08:47:11 2008 matrix is 49520 x 49584 (10.8 MB) with weight 2639553 (53.23/col) Thu Apr 10 08:47:11 2008 sparse part has weight 2639553 (53.23/col) Thu Apr 10 08:47:11 2008 saving the first 48 matrix rows for later Thu Apr 10 08:47:11 2008 matrix is 49472 x 49584 (6.4 MB) with weight 1990780 (40.15/col) Thu Apr 10 08:47:11 2008 sparse part has weight 1368376 (27.60/col) Thu Apr 10 08:47:11 2008 matrix includes 64 packed rows Thu Apr 10 08:47:11 2008 commencing Lanczos iteration Thu Apr 10 08:47:11 2008 memory use: 8.2 MB Thu Apr 10 08:47:59 2008 lanczos halted after 783 iterations (dim = 49462) Thu Apr 10 08:47:59 2008 recovered 11 nontrivial dependencies Thu Apr 10 08:47:59 2008 prp39 factor: 101724403988483751381031110691554232729 Thu Apr 10 08:47:59 2008 prp47 factor: 19936539876112083560045113778507889458461515877 Thu Apr 10 08:47:59 2008 elapsed time 00:24:47
(5·10¹⁰²-11)/3 = 1(6)₁₀₁3_<103> = 17 · 47 · 73 · C98
C98 = P41 · P57
P41 = 42247654314238814538592060301512367110661_<41>
P57 = 676357809987191111919877049341177444192239827754611671229_<57>

Number: n N=28574530949074470942559477886170498511266937553220063892651202130517027562992553477234671192872369 ( 98 digits) SNFS difficulty: 102 digits. Divisors found: r1=42247654314238814538592060301512367110661 (pp41) r2=676357809987191111919877049341177444192239827754611671229 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.41 hours. Scaled time: 0.73 units (timescale=1.753). Factorization parameters were as follows: name: KA_1_6_101_3 n: 28574530949074470942559477886170498511266937553220063892651202130517027562992553477234671192872369 type: snfs skew: 0.47 deg: 5 c5: 500 c0: -11 m: 100000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 300001) Primes: RFBsize:41538, AFBsize:41853, largePrimes:2461385 encountered Relations: rels:1937861, finalFF:105591 Max relations in full relation-set: 28 Initial matrix: 83457 x 105591 with sparse part having weight 2650651. Pruned matrix : 56554 x 57035 with weight 1104019. Total sieving time: 0.35 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.2,2.2,20000 total time: 0.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(5·10¹²⁶-11)/3 = 1(6)₁₂₅3_<127> = 73 · 103 · 151 · 8036239 · C114
C114 = P42 · P73
P42 = 136601909891494683571867166667984462907181_<42>
P73 = 1337217654640463702420039415634113857360702296152706815677177592790424453_<73>

Number: n N=182666485564512480286199842770473113380890893561775030331297841982007142001745032870406824625614600794059331696993 ( 114 digits) SNFS difficulty: 126 digits. Divisors found: r1=136601909891494683571867166667984462907181 (pp42) r2=1337217654640463702420039415634113857360702296152706815677177592790424453 (pp73) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.66 hours. Scaled time: 3.03 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_6_125_3 n: 182666485564512480286199842770473113380890893561775030331297841982007142001745032870406824625614600794059331696993 skew: 0.74 deg: 5 c5: 50 c0: -11 m: 10000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 25000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 300001) Primes: RFBsize:78498, AFBsize:78657, largePrimes:4602854 encountered Relations: rels:3926609, finalFF:176847 Max relations in full relation-set: 48 Initial matrix: 157220 x 176847 with sparse part having weight 12529569. Pruned matrix : 145751 x 146601 with weight 7887455. Total sieving time: 1.48 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 1.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(14·10¹⁷⁰+31)/9 = 1(5)₁₆₉9_<171> = 3⁴ · 173 · 241 · 1063 · 947388505673668601_<18> · 329773997817300200297648891_<27> · C117
C117 = P43 · P74
P43 = 4570257576393376741108870562574935143559999_<43>
P74 = 30347219042826632639068219128539563087330388614267880782603290658707817769_<74>

Number: n N=138694607752947776402054601038374261634077577246418128378721610395375037159280518817908354940816419747823675209822231 ( 117 digits) Divisors found: Thu Apr 10 19:09:13 2008 prp43 factor: 4570257576393376741108870562574935143559999 Thu Apr 10 19:09:13 2008 prp74 factor: 30347219042826632639068219128539563087330388614267880782603290658707817769 Thu Apr 10 19:09:13 2008 elapsed time 01:18:33 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 49.69 hours. Scaled time: 64.80 units (timescale=1.304). Factorization parameters were as follows: name: KA_1_5_169_9 n: 138694607752947776402054601038374261634077577246418128378721610395375037159280518817908354940816419747823675209822231 skew: 94836.36 # norm 1.77e+16 c5: 1920 c4: 4251138112 c3: -309124278511618 c2: -29561456463897609891 c1: 487127672626518629193186 c0: 32056092180814696347161000619 # alpha -6.09 Y1: 31913420429 Y0: -37303665233241543560500 # Murphy_E 4.26e-10 # M 30440368514637758849034089320960643934931022425993500010937446988681486641564356323500538790935064017609701630427635 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 2020001) Primes: RFBsize:315948, AFBsize:316044, largePrimes:6564918 encountered Relations: rels:6479500, finalFF:721077 Max relations in full relation-set: 28 Initial matrix: 632068 x 721077 with sparse part having weight 38916166. Pruned matrix : Total sieving time: 49.37 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 49.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(5·10¹³⁵-11)/3 = 1(6)₁₃₄3_<136> = 2309 · C132
C132 = P51 · P81
P51 = 769471589341802815698410458609829329351462222537643_<51>
P81 = 938063477252786787981200026222114693270614493438014472876357993296728209029600049_<81>

Number: n N=721813194745199942254944420384004619604446369279630431644290457629565468456763389634762523458928829218998123285693662480150137144507 ( 132 digits) SNFS difficulty: 135 digits. Divisors found: r1=769471589341802815698410458609829329351462222537643 (pp51) r2=938063477252786787981200026222114693270614493438014472876357993296728209029600049 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.40 hours. Scaled time: 4.40 units (timescale=1.834). Factorization parameters were as follows: name: KA_1_6_134_3 n: 721813194745199942254944420384004619604446369279630431644290457629565468456763389634762523458928829218998123285693662480150137144507 skew: 1.17 deg: 5 c5: 5 c0: -11 m: 1000000000000000000000000000 type: snfs rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 25000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 475001) Primes: RFBsize:92938, AFBsize:93450, largePrimes:5497865 encountered Relations: rels:4850841, finalFF:262120 Max relations in full relation-set: 48 Initial matrix: 186453 x 262120 with sparse part having weight 23107069. Pruned matrix : 153848 x 154844 with weight 9218030. Total sieving time: 2.18 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.12 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000 total time: 2.40 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Apr 10, 2008: The factor table of 166...663 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Apr 9, 2008: By Robert Backstrom / GGNFS, Msieve
4·10¹⁶⁴+9 = 4(0)₁₆₃9_<165> = 433 · 325501909 · 155697059191893120469_<21> · C134
C134 = P58 · P76
P58 = 2480292169582768150613622571493155466576298122188305452881_<58>
P76 = 7349119396569529045017568501654084454037447639806748910113839336437017179473_<76>

Number: n N=18227963292640241073752649952343065729223968280713818502150062554437260230889566308369202243770405504513631798743471894619440521911713 ( 134 digits) SNFS difficulty: 165 digits. Divisors found: r1=2480292169582768150613622571493155466576298122188305452881 (pp58) r2=7349119396569529045017568501654084454037447639806748910113839336437017179473 (pp76) Version: GGNFS-0.77.1-20051202-athlon Total time: 46.42 hours. Scaled time: 84.63 units (timescale=1.823). Factorization parameters were as follows: name: KA_4_0_163_9 n: 18227963292640241073752649952343065729223968280713818502150062554437260230889566308369202243770405504513631798743471894619440521911713 skew: 1.86 deg: 5 c5: 2 c0: 45 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3100001) Primes: RFBsize:230209, AFBsize:230302, largePrimes:7625564 encountered Relations: rels:7110539, finalFF:542315 Max relations in full relation-set: 48 Initial matrix: 460576 x 542315 with sparse part having weight 55660953. Pruned matrix : 428423 x 430789 with weight 36977980. Total sieving time: 44.05 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.04 hours. Total square root time: 0.13 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 46.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(16·10¹⁶³-1)/3 = 5(3)₁₆₃_<164> = 9203 · 649751 · 754067 · 210126893 · 1470754547_<10> · C131
C131 = P40 · P46 · P46
P40 = 5241938648266082638689856097053647927227_<40>
P46 = 1203492293151321834268051001544618500679611569_<46>
P46 = 6066739234889810264566998524928554913682222871_<46>

Number: n N=38272829910055922554986494307292612701700316471903274256011625905419437445035817954191202482574294773808756113465281446661881046973 ( 131 digits) SNFS difficulty: 164 digits. Divisors found: Wed Apr 09 22:10:04 2008 prp40 factor: 5241938648266082638689856097053647927227 Wed Apr 09 22:10:04 2008 prp46 factor: 1203492293151321834268051001544618500679611569 Wed Apr 09 22:10:04 2008 prp46 factor: 6066739234889810264566998524928554913682222871 Wed Apr 09 22:10:04 2008 elapsed time 01:02:53 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.31 hours. Scaled time: 59.09 units (timescale=1.829). Factorization parameters were as follows: name: KA_5_3_163 n: 38272829910055922554986494307292612701700316471903274256011625905419437445035817954191202482574294773808756113465281446661881046973 skew: 0.29 deg: 5 c5: 500 c0: -1 m: 200000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2299990) Primes: RFBsize:230209, AFBsize:229657, largePrimes:7314015 encountered Relations: rels:6796872, finalFF:529923 Max relations in full relation-set: 28 Initial matrix: 459932 x 529922 with sparse part having weight 46577315. Pruned matrix : Total sieving time: 32.13 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 32.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Apr 8, 2008: By Sinkiti Sibata / GGNFS
(14·10¹⁵²+31)/9 = 1(5)₁₅₁9_<153> = 3² · 17 · 67 · 123377 · 127319953639_<12> · 56178496930208414688605633_<26> · C107
C107 = P39 · P69
P39 = 111313093274540417476741014421320134743_<39>
P69 = 154479995522690870591367172547336505227910968599671963282858372345637_<69>

Number: 15559_152 N=17195646150667874950992453422444333642975476026069684108426569369939091078615552957010779914767445808166291 ( 107 digits) SNFS difficulty: 153 digits. Divisors found: r1=111313093274540417476741014421320134743 (pp39) r2=154479995522690870591367172547336505227910968599671963282858372345637 (pp69) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 51.75 hours. Scaled time: 34.93 units (timescale=0.675). Factorization parameters were as follows: name: 15559_152 n: 17195646150667874950992453422444333642975476026069684108426569369939091078615552957010779914767445808166291 m: 1000000000000000000000000000000 c5: 1400 c0: 31 skew: 0.47 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2600001) Primes: RFBsize:176302, AFBsize:175914, largePrimes:5759456 encountered Relations: rels:5717101, finalFF:466652 Max relations in full relation-set: 28 Initial matrix: 352283 x 466652 with sparse part having weight 48829191. Pruned matrix : 312843 x 314668 with weight 30625407. Total sieving time: 46.57 hours. Total relation processing time: 0.28 hours. Matrix solve time: 4.73 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 51.75 hours. --------- CPU info (if available) ----------
Apr 7, 2008 (2nd): By Robert Backstrom / GGNFS, Msieve
(14·10¹⁵³+31)/9 = 1(5)₁₅₂9_<154> = 61 · 541 · 23624025645827704817_<20> · C130
C130 = P62 · P69
P62 = 12618987396929809067039217391491187497627561020701168808432897_<62>
P69 = 158117527310291680588589078011395917240084089263123655628504089737791_<69>

Number: n N=1995283084362275608981993720845150085222935999336634693921193036336245407655677090547930521602073409192525797082004482958348510527 ( 130 digits) SNFS difficulty: 154 digits. Divisors found: r1=12618987396929809067039217391491187497627561020701168808432897 (pp62) r2=158117527310291680588589078011395917240084089263123655628504089737791 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 21.43 hours. Scaled time: 39.19 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_5_152_9 n: 1995283084362275608981993720845150085222935999336634693921193036336245407655677090547930521602073409192525797082004482958348510527 skew: 0.59 deg: 5 c5: 875 c0: 62 m: 2000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:183072, AFBsize:183212, largePrimes:7007383 encountered Relations: rels:6444936, finalFF:443762 Max relations in full relation-set: 48 Initial matrix: 366350 x 443762 with sparse part having weight 44001931. Pruned matrix : 316482 x 318377 with weight 26418976. Total sieving time: 19.91 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.94 hours. Total square root time: 0.41 hours, sqrts: 8. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 21.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(14·10¹⁶⁴+31)/9 = 1(5)₁₆₃9_<165> = 3 · 3167 · 3557 · 2115203 · C151
C151 = P51 · P100
P51 = 292044997922927091627528286394099949348817998187813_<51>
P100 = 7451273714795980303658961535674894947248661146078209917201810829662662013768700449007211187583249433_<100>

Number: n N=2176107216560753301911443296557873067276016343298831494475440440002350484312812223305933949454487812090080679805129498136087304244961797327267959760029 ( 151 digits) SNFS difficulty: 165 digits. Divisors found: Mon Apr 7 19:21:33 2008 prp51 factor: 292044997922927091627528286394099949348817998187813 Mon Apr 7 19:21:33 2008 prp100 factor: 7451273714795980303658961535674894947248661146078209917201810829662662013768700449007211187583249433 Mon Apr 7 19:21:33 2008 elapsed time 00:56:16 (Msieve 1.34) Version: GGNFS-0.77.1-20050930-k8 Total time: 58.46 hours. Scaled time: 49.16 units (timescale=0.841). Factorization parameters were as follows: name: KA_1_5_163_9 n: 2176107216560753301911443296557873067276016343298831494475440440002350484312812223305933949454487812090080679805129498136087304244961797327267959760029 type: snfs deg: 5 c5: 7 c0: 155 skew: 1.86 m: 1000000000000000000000000000000000 rlim: 3200000 alim: 3200000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3700369) Primes: RFBsize:230209, AFBsize:229318, largePrimes:5754763 encountered Relations: rels:5663009, finalFF:469183 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 58.27 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,27,27,48,48,2.5,2.5,100000 total time: 58.46 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(14·10¹⁶⁵+31)/9 = 1(5)₁₆₄9_<166> = 76012247 · 1729666074743_<13> · C146
C146 = P68 · P78
P68 = 67547527870814968644720759872728356155144540584072588165080323596693_<68>
P78 = 175158101286561444194143776900975745196879694692553333454908567390260925183803_<78>

Number: n N=11831496728453040368588747027393946948515280652340570548132594078197001463889134283214599455363721462782675641132374892459492277581995839067963479 ( 146 digits) SNFS difficulty: 166 digits. Divisors found: Mon Apr 07 20:40:51 2008 prp68 factor: 67547527870814968644720759872728356155144540584072588165080323596693 Mon Apr 07 20:40:51 2008 prp78 factor: 175158101286561444194143776900975745196879694692553333454908567390260925183803 Mon Apr 07 20:40:51 2008 elapsed time 01:01:41 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 50.67 hours. Scaled time: 92.93 units (timescale=1.834). Factorization parameters were as follows: name: KA_1_5_164_9 n: 11831496728453040368588747027393946948515280652340570548132594078197001463889134283214599455363721462782675641132374892459492277581995839067963479 skew: 1.17 deg: 5 c5: 14 c0: 31 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3400001) Primes: RFBsize:230209, AFBsize:230543, largePrimes:7686963 encountered Relations: rels:7146455, finalFF:522792 Max relations in full relation-set: 28 Initial matrix: 460818 x 522792 with sparse part having weight 59672004. Pruned matrix : Total sieving time: 50.44 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 50.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Apr 7, 2008: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(14·10¹⁵⁷+31)/9 = 1(5)₁₅₆9_<158> = 93463993209661_<14> · C144
C144 = P47 · P98
P47 = 16264286654890748144075190501147967098201002951_<47>
P98 = 10233075398052231822492848466935430038785598384068263986570291327906585563875283488105494739268469_<98>

Number: n N=166433671635031744544481049109629997491990532133453025037392323621256408259802421916610388923754892468719810052105215109107568842740899850252019 ( 144 digits) SNFS difficulty: 158 digits. Divisors found: Mon Apr 07 01:06:15 2008 prp47 factor: 16264286654890748144075190501147967098201002951 Mon Apr 07 01:06:15 2008 prp98 factor: 10233075398052231822492848466935430038785598384068263986570291327906585563875283488105494739268469 Mon Apr 07 01:06:15 2008 elapsed time 02:22:14 (Msieve 1.34, Dep=8) Version: GGNFS-0.77.1-20051202-athlon Total time: 47.92 hours. Scaled time: 84.11 units (timescale=1.755). Factorization parameters were as follows: name: KA_1_5_156_9 n: 166433671635031744544481049109629997491990532133453025037392323621256408259802421916610388923754892468719810052105215109107568842740899850252019 type: snfs skew: 0.47 deg: 5 c5: 1400 c0: 31 m: 10000000000000000000000000000000 rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2400001) Primes: RFBsize:183072, AFBsize:182717, largePrimes:7075797 encountered Relations: rels:6427225, finalFF:371726 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 47.69 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.3,2.3,100000 total time: 47.92 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(46·10¹⁹⁴-1)/9 = 5(1)₁₉₄_<195> = 7 · 73 · 59809 · 41535100907534041_<17> · 735190796811265416174712160511408781_<36> · C135
C135 = P34 · P102
P34 = 2131759063791372047774111469573847_<34>
P102 = 256906108706152053755199843207572059233131041311072028161736752737669098210183763610380354496349308547_<102>
Apr 6, 2008: By Jo Yeong Uk / GGNFS
(14·10¹⁵⁶+31)/9 = 1(5)₁₅₅9_<157> = 846400273673407_<15> · 5647119458626703_<16> · C126
C126 = P39 · P88
P39 = 181595105240033914022977640506121267719_<39>
P88 = 1792167585191447108689726343859434077154164335650452972726213569904570307167543559971441_<88>

Number: 15559_156 N=325448861240618282863068539156450995311385946677891062779075151268243362097776381667860754237370696771018560283140022355213079 ( 126 digits) SNFS difficulty: 157 digits. Divisors found: r1=181595105240033914022977640506121267719 (pp39) r2=1792167585191447108689726343859434077154164335650452972726213569904570307167543559971441 (pp88) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.96 hours. Scaled time: 53.59 units (timescale=2.147). Factorization parameters were as follows: n: 325448861240618282863068539156450995311385946677891062779075151268243362097776381667860754237370696771018560283140022355213079 m: 10000000000000000000000000000000 c5: 140 c0: 31 skew: 0.74 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3100001) Primes: RFBsize:216816, AFBsize:216762, largePrimes:5719874 encountered Relations: rels:5700036, finalFF:548025 Max relations in full relation-set: 28 Initial matrix: 433645 x 548025 with sparse part having weight 48656988. Pruned matrix : 380612 x 382844 with weight 32093823. Total sieving time: 24.02 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.80 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 24.96 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4042900k/4718592k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19246.09 BogoMIPS).
(14·10¹⁶⁶+31)/9 = 1(5)₁₆₅9_<167> = 14762153720019369394560342817_<29> · 25959036563720881399909794087532397_<35> · C104
C104 = P49 · P55
P49 = 9597033958947512940770715759079012159641836757583_<49>
P55 = 4229706193320175468626508490317354141097461889488396877_<55>

Number: 15559_166 N=40592633973664338092756074639611100697720162425602675161336639117666924326656515110040772765234343268291 ( 104 digits) Divisors found: r1=9597033958947512940770715759079012159641836757583 (pp49) r2=4229706193320175468626508490317354141097461889488396877 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.75 hours. Scaled time: 12.23 units (timescale=2.128). Factorization parameters were as follows: name: 15559_166 n: 40592633973664338092756074639611100697720162425602675161336639117666924326656515110040772765234343268291 skew: 26811.40 # norm 3.74e+14 c5: 15120 c4: 6077326 c3: -23724512303077 c2: 86864477756364696 c1: 8298547771000702870996 c0: 33119074129593578932976192 # alpha -6.43 Y1: 72405459907 Y0: -76873924976831669127 # Murphy_E 2.13e-09 # M 1233879129425926695567871031059691043818742592710023171099250854072614931552306628519699357283862227743 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1680001) Primes: RFBsize:135072, AFBsize:134910, largePrimes:4428331 encountered Relations: rels:4423357, finalFF:366133 Max relations in full relation-set: 28 Initial matrix: 270065 x 366133 with sparse part having weight 30992146. Pruned matrix : 212490 x 213904 with weight 16099938. Polynomial selection time: 0.39 hours. Total sieving time: 5.03 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.18 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 5.75 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4042900k/4718592k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.26 BogoMIPS (lpj=2405130) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19246.09 BogoMIPS).
Apr 5, 2008 (4th): By matsui / GGNFS
7·10¹⁷⁵+3 = 7(0)₁₇₄3_<176> = 113 · 487 · 8389 · C168
C168 = P50 · P118
P50 = 15382421157285425929466447017738051797673565880227_<50>
P118 = 9857249360937578381060501178705637693417639727420036892990380567114305681621039301876173072701917734426786021572283771_<118>

N=151628361122324449605999010616279199054547780878970071028724500558327034384345390656706742598481954467220514093835588185333846845161508345996485657487401215720241896017 ( 168 digits) SNFS difficulty: 175 digits. Divisors found: r1=15382421157285425929466447017738051797673565880227 (pp50) r2=9857249360937578381060501178705637693417639727420036892990380567114305681621039301876173072701917734426786021572283771 (pp118) Version: GGNFS-0.77.1-20060513-prescott Total time: 186.17 hours. Scaled time: 315.56 units (timescale=1.695). Factorization parameters were as follows: n: 151628361122324449605999010616279199054547780878970071028724500558327034384345390656706742598481954467220514093835588185333846845161508345996485657487401215720241896017 m: 100000000000000000000000000000000000 c5: 7 c0: 3 skew: 0.84 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10600001) Primes: RFBsize:501962, AFBsize:500771, largePrimes:6392766 encountered Relations: rels:6833029, finalFF:1124040 Max relations in full relation-set: 28 Initial matrix: 1002798 x 1124040 with sparse part having weight 66158404. Pruned matrix : 898702 x 903779 with weight 50386598. Total sieving time: 171.47 hours. Total relation processing time: 0.15 hours. Matrix solve time: 14.30 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 186.17 hours.
Apr 5, 2008 (3rd): By Robert Backstrom / GMP-ECM
(52·10¹⁶³-7)/9 = 5(7)₁₆₃_<164> = 3 · 19 · 89 · 4463 · 2537021 · 55830371 · 1248226627_<10> · C134
C134 = P37 · P97
P37 = 6420478316845888866764229697079609081_<37>
P97 = 2248089943587469434480299083386367776545352478097162371514379969035559192349878360635205285279419_<97>
(14·10¹⁶²+31)/9 = 1(5)₁₆₁9_<163> = 29 · 3806347 · 26170223 · C147
C147 = P38 · P40 · P70
P38 = 50365446354722171931533546718702257843_<38>
P40 = 3543988444207413403410274704260989655419_<40>
P70 = 3016801554260539634880325171364479046731365413823735186731506096436023_<70>
Apr 5, 2008 (2nd): By Sinkiti Sibata / GGNFS
(14·10¹³⁰+31)/9 = 1(5)₁₂₉9_<131> = 523 · 517830371 · 22205400930628594589_<20> · C100
C100 = P39 · P62
P39 = 223052339348662090783561338193275827047_<39>
P62 = 11596606412490730336161701177308159280832170437567286305560181_<62>

Number: 15559_130 N=2586650188811753255072196313522140231922638767244339815312972931926665126576983403300759137406015507 ( 100 digits) SNFS difficulty: 131 digits. Divisors found: r1=223052339348662090783561338193275827047 (pp39) r2=11596606412490730336161701177308159280832170437567286305560181 (pp62) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.44 hours. Scaled time: 4.35 units (timescale=0.675). Factorization parameters were as follows: name: 15559_130 n: 2586650188811753255072196313522140231922638767244339815312972931926665126576983403300759137406015507 m: 100000000000000000000000000 c5: 14 c0: 31 skew: 1.17 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63629, largePrimes:1507105 encountered Relations: rels:1507107, finalFF:169181 Max relations in full relation-set: 28 Initial matrix: 127646 x 169181 with sparse part having weight 13212589. Pruned matrix : 116035 x 116737 with weight 7300210. Total sieving time: 6.08 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.23 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.44 hours. --------- CPU info (if available) ----------
(14·10¹³⁴+31)/9 = 1(5)₁₃₃9_<135> = 3² · 29 · 5014409 · 329843551356450621367_<21> · C105
C105 = P40 · P66
P40 = 1306557661964407021017588295478647094717_<40>
P66 = 275796458917595587577783322712081943077119699195249979743129914969_<66>

Number: 15559_134 N=360343976541436324001467268397547805706577207259650798154874784983464628358958156247401923595203099118773 ( 105 digits) SNFS difficulty: 135 digits. Divisors found: r1=1306557661964407021017588295478647094717 (pp40) r2=275796458917595587577783322712081943077119699195249979743129914969 (pp66) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 10.14 hours. Scaled time: 6.84 units (timescale=0.674). Factorization parameters were as follows: name: 15559_134 n: 360343976541436324001467268397547805706577207259650798154874784983464628358958156247401923595203099118773 m: 1000000000000000000000000000 c5: 7 c0: 155 skew: 1.86 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1450001) Primes: RFBsize:78498, AFBsize:63449, largePrimes:1554550 encountered Relations: rels:1547172, finalFF:162708 Max relations in full relation-set: 28 Initial matrix: 142012 x 162708 with sparse part having weight 14524899. Pruned matrix : 135927 x 136701 with weight 10750022. Total sieving time: 9.55 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.43 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 10.14 hours. --------- CPU info (if available) ----------
Apr 5, 2008: By Tyler Cadigan / GGNFS, Msieve
(25·10¹⁸¹-1)/3 = 8(3)₁₈₁_<182> = 69591715019881213_<17> · 747152275895293013_<18> · C148
C148 = P46 · P102
P46 = 1780413985668047124967711027196123828460629329_<46>
P102 = 900183594319564916679896379547677509715284513197543620154816703452344181111024772817941782678605403333_<102>

Number: 83333_181 N=1602699460995484998900532952740942402090779344283258132988336035926159888755217576890505832750581638436871049644705615184704800910461748317054153557 ( 148 digits) SNFS difficulty: 182 digits. Divisors found: r1=1780413985668047124967711027196123828460629329 r2=900183594319564916679896379547677509715284513197543620154816703452344181111024772817941782678605403333 Version: Total time: 331.70 hours. Scaled time: 850.47 units (timescale=2.564). Factorization parameters were as follows: n: 1602699460995484998900532952740942402090779344283258132988336035926159888755217576890505832750581638436871049644705615184704800910461748317054153557 m: 1000000000000000000000000000000000000 c5: 250 c0: -1 skew: 0.33 type: snfs Y0: -1000000000000000000000000000000000000 Y1: 1Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 9300001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 873628 x 873876 Total sieving time: 331.70 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 331.70 hours. --------- CPU info (if available) ----------
Apr 4, 2008 (3rd): By Sinkiti Sibata / GGNFS
(14·10¹³⁸+31)/9 = 1(5)₁₃₇9_<139> = 23 · 587 · 22085650154593_<14> · 214708517662039_<15> · C107
C107 = P38 · P70
P38 = 18889071044965985559683161450105284079_<38>
P70 = 1286321494635454249284329017256606479419057950477955932294681889062123_<70>

Number: 15559_138 N=24297418098835928184871286994621343003982194045684419344835498431243228852905498778636408028046235793839717 ( 107 digits) SNFS difficulty: 139 digits. Divisors found: r1=18889071044965985559683161450105284079 (pp38) r2=1286321494635454249284329017256606479419057950477955932294681889062123 (pp70) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 21.58 hours. Scaled time: 14.57 units (timescale=0.675). Factorization parameters were as follows: name: 15559_138 n: 24297418098835928184871286994621343003982194045684419344835498431243228852905498778636408028046235793839717 m: 2000000000000000000000000000 c5: 875 c0: 62 skew: 0.59 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2800001) Primes: RFBsize:78498, AFBsize:63759, largePrimes:1746679 encountered Relations: rels:1808224, finalFF:167624 Max relations in full relation-set: 28 Initial matrix: 142323 x 167624 with sparse part having weight 20269469. Pruned matrix : 136875 x 137650 with weight 15512291. Total sieving time: 20.76 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.59 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 21.58 hours. --------- CPU info (if available) ----------
Apr 4, 2008 (2nd): By JMB / GMP-ECM
(14·10¹⁶⁶+31)/9 = 1(5)₁₆₅9_<167> = 14762153720019369394560342817_<29> · C139
C139 = P35 · C104
P35 = 25959036563720881399909794087532397_<35>
C104 = [40592633973664338092756074639611100697720162425602675161336639117666924326656515110040772765234343268291_<104>]
Apr 4, 2008: By Robert Backstrom / GGNFS, Msieve
(67·10¹⁶³+23)/9 = 7(4)₁₆₂7_<164> = 7 · 11 · 15981307 · 550172091423481695139_<21> · C135
C135 = P60 · P75
P60 = 173899319743099863715074733204526874599504106558134328664339_<60>
P75 = 632314053644234448964586908637373660241500036550939211425372049855075000713_<75>

Number: n N=109958983792734326039438991504943363864512677413094518012785059431448235356759293336664332882078371346096185002361452719220446762673707 ( 135 digits) SNFS difficulty: 164 digits. Divisors found: Fri Apr 4 07:32:32 2008 prp60 factor: 173899319743099863715074733204526874599504106558134328664339 Fri Apr 4 07:32:32 2008 prp75 factor: 632314053644234448964586908637373660241500036550939211425372049855075000713 Fri Apr 4 07:32:32 2008 elapsed time 00:45:38 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 43.82 hours. Scaled time: 36.68 units (timescale=0.837). Factorization parameters were as follows: name: KA_7_4_162_7 n: 109958983792734326039438991504943363864512677413094518012785059431448235356759293336664332882078371346096185002361452719220446762673707 type: snfs deg: 5 c5: 67000 c0: 23 skew: 0.20 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2699990) Primes: RFBsize:216816, AFBsize:217321, largePrimes:5672603 encountered Relations: rels:5598931, finalFF:511786 Max relations in full relation-set: 28 Initial matrix: 434204 x 511786 with sparse part having weight 45127507. Pruned matrix : Total sieving time: 43.62 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 43.82 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
7·10¹⁶³+1 = 7(0)₁₆₂1_<164> = 2621 · 637097 · 6177922939_<10> · 156791141329_<12> · C134
C134 = P51 · P84
P51 = 402780568113496127134113047287312945816114000773181_<51>
P84 = 107446665123360825440701365404164787206317314310967090805791720700790075639081056243_<84>

Number: n N=43277428820287843704931976867461084748542006794075993513996138833643569977396426813266834171274514636681677977157534242400032147018983 ( 134 digits) SNFS difficulty: 163 digits. Divisors found: Fri Apr 4 12:59:40 2008 prp51 factor: 402780568113496127134113047287312945816114000773181 Fri Apr 4 12:59:40 2008 prp84 factor: 107446665123360825440701365404164787206317314310967090805791720700790075639081056243 Fri Apr 4 12:59:40 2008 elapsed time 00:46:52 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 46.82 hours. Scaled time: 39.19 units (timescale=0.837). Factorization parameters were as follows: name: KA_7_0_162_1 n: 43277428820287843704931976867461084748542006794075993513996138833643569977396426813266834171274514636681677977157534242400032147018983 type: snfs deg: 5 c5: 7000 c0: 1 skew: 0.17 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2800000) Primes: RFBsize:216816, AFBsize:216861, largePrimes:5723566 encountered Relations: rels:5651846, finalFF:500770 Max relations in full relation-set: 28 Initial matrix: 433744 x 500770 with sparse part having weight 45553627. Pruned matrix : 406474 x 408706 with weight 33499165. Total sieving time: 46.61 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 46.82 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(13·10¹⁶³+23)/9 = 1(4)₁₆₂7_<164> = 3517 · 18983905542455313683_<20> · C141
C141 = P57 · P84
P57 = 290489182949177909802781675636329039795637507570364531197_<57>
P84 = 744754172766735844931657694994085417458424028852613801213846101237458452241664067741_<84>

Number: n N=216343031144999981427906166521244760111099649120079328867161315613682148972954519919802708175175124782467477196706782976510301435255515815977 ( 141 digits) SNFS difficulty: 164 digits. Divisors found: Fri Apr 04 22:01:13 2008 prp57 factor: 290489182949177909802781675636329039795637507570364531197 Fri Apr 04 22:01:13 2008 prp84 factor: 744754172766735844931657694994085417458424028852613801213846101237458452241664067741 Fri Apr 04 22:01:13 2008 elapsed time 01:07:56 (Msieve 1.34) Version: GGNFS-0.77.1-20051202-athlon Total time: 59.80 hours. Scaled time: 109.37 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_4_162_7 n: 216343031144999981427906166521244760111099649120079328867161315613682148972954519919802708175175124782467477196706782976510301435255515815977 skew: 0.28 deg: 5 c5: 13000 c0: 23 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 4100293) Primes: RFBsize:216816, AFBsize:217281, largePrimes:7819749 encountered Relations: rels:7249599, finalFF:485822 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 59.59 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 59.80 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(22·10¹⁶⁵-1)/3 = 7(3)₁₆₅_<166> = 23 · 17497 · 274487009 · 25658674533179_<14> · C139
C139 = P65 · P75
P65 = 22933717666057774298302333628801575787136259295500785394358195651_<65>
P75 = 112818292849299160345823913937988573038591955291961894176315107848186283963_<75>

Number: n N=2587342875772451627047024007058209064159419996689996703791353347801727846113147460534304001711336122904729486466052945321623131575397644913 ( 139 digits) SNFS difficulty: 166 digits. Divisors found: Sat Apr 05 00:36:54 2008 prp65 factor: 22933717666057774298302333628801575787136259295500785394358195651 Sat Apr 05 00:36:54 2008 prp75 factor: 112818292849299160345823913937988573038591955291961894176315107848186283963 Sat Apr 05 00:36:54 2008 elapsed time 01:27:54 (Msieve 1.34) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 61.02 hours. Scaled time: 79.45 units (timescale=1.302). Factorization parameters were as follows: name: KA_7_3_165 n: 2587342875772451627047024007058209064159419996689996703791353347801727846113147460534304001711336122904729486466052945321623131575397644913 skew: 0.54 deg: 5 c5: 22 c0: -1 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2800247) Primes: RFBsize:216816, AFBsize:216967, largePrimes:7383104 encountered Relations: rels:6815983, finalFF:485019 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 60.76 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 61.02 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Apr 3, 2008 (5th): By JMB / GMP-ECM
(14·10¹⁴⁸+31)/9 = 1(5)₁₄₇9_<149> = 9949 · 54403 · 826856108189_<12> · 64934003080483_<14> · C114
C114 = P34 · P81
P34 = 2499113539947715325949124365216803_<34>
P81 = 214188003419738864023748273782105619197066640540736946746378416198577330759441277_<81>
Apr 3, 2008 (4th): By Sinkiti Sibata / GGNFS
(13·10¹⁶⁰+41)/9 = 1(4)₁₅₉9_<161> = 13177488726749_<14> · 107919830762963_<15> · 6948432863413003_<16> · C118
C118 = P44 · P74
P44 = 58318421562202336729024884964580815360748989_<44>
P74 = 25065380822971939726203162891930045767767595089719334854800459231611917481_<74>

Number: 14449_160 N=1461773445451219721817054132646300865765733841567085507878396932965774862914627039808990861227821796075443086622176709 ( 118 digits) SNFS difficulty: 161 digits. Divisors found: r1=58318421562202336729024884964580815360748989 (pp44) r2=25065380822971939726203162891930045767767595089719334854800459231611917481 (pp74) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 78.30 hours. Scaled time: 52.85 units (timescale=0.675). Factorization parameters were as follows: name: 14449_160 n: 1461773445451219721817054132646300865765733841567085507878396932965774862914627039808990861227821796075443086622176709 m: 100000000000000000000000000000000 c5: 13 c0: 41 skew: 1.26 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3900001) Primes: RFBsize:283146, AFBsize:282373, largePrimes:5738534 encountered Relations: rels:5817356, finalFF:694775 Max relations in full relation-set: 28 Initial matrix: 565586 x 694775 with sparse part having weight 46693987. Pruned matrix : 469450 x 472341 with weight 31381838. Total sieving time: 68.01 hours. Total relation processing time: 0.32 hours. Matrix solve time: 9.75 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 78.30 hours. --------- CPU info (if available) ----------
(14·10¹²⁰+31)/9 = 1(5)₁₁₉9_<121> = 17 · 107 · 50466277 · C110
C110 = P49 · P62
P49 = 1421577012344853500890676274711460113354683750921_<49>
P62 = 11920134834947284852618265683350810943104485024229298831379833_<62>

Number: 15559_120 N=16945389665412174607218409292531530192930180494329638763325905364366947215583860888478225208800730066514576193 ( 110 digits) SNFS difficulty: 121 digits. Divisors found: r1=1421577012344853500890676274711460113354683750921 (pp49) r2=11920134834947284852618265683350810943104485024229298831379833 (pp62) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.59 hours. Scaled time: 1.75 units (timescale=0.675). Factorization parameters were as follows: name: 15559_120 n: 16945389665412174607218409292531530192930180494329638763325905364366947215583860888478225208800730066514576193 m: 1000000000000000000000000 c5: 14 c0: 31 skew: 1.17 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:49098, AFBsize:63629, largePrimes:2164814 encountered Relations: rels:2280226, finalFF:244401 Max relations in full relation-set: 28 Initial matrix: 112793 x 244401 with sparse part having weight 22393749. Pruned matrix : 86473 x 87100 with weight 5524265. Total sieving time: 2.35 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.12 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.59 hours. --------- CPU info (if available) ----------
(14·10¹²⁹+31)/9 = 1(5)₁₂₈9_<130> = 331 · 647 · 1181 · 320796426397_<12> · C110
C110 = P43 · P67
P43 = 4707523717355474776435082396044989377741827_<43>
P67 = 4072689638852448957226819815433219768108727767837548269928546344633_<67>

Number: 15559_129 N=19172283068325806568537723586178607998494065432808843189221587559772708200225606297331105435664949712841064491 ( 110 digits) SNFS difficulty: 130 digits. Divisors found: r1=4707523717355474776435082396044989377741827 (pp43) r2=4072689638852448957226819815433219768108727767837548269928546344633 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.23 hours. Scaled time: 4.21 units (timescale=0.675). Factorization parameters were as follows: name: 15559_129 n: 19172283068325806568537723586178607998494065432808843189221587559772708200225606297331105435664949712841064491 m: 100000000000000000000000000 c5: 7 c0: 155 skew: 1.86 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63449, largePrimes:1489289 encountered Relations: rels:1474945, finalFF:157286 Max relations in full relation-set: 28 Initial matrix: 127465 x 157286 with sparse part having weight 12062069. Pruned matrix : 118994 x 119695 with weight 7467431. Total sieving time: 5.86 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.24 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 6.23 hours. --------- CPU info (if available) ----------
Apr 3, 2008 (3rd): By Robert Backstrom / Msieve, GMP-ECM, GGNFS
(14·10¹⁵⁸+31)/9 = 1(5)₁₅₇9_<159> = 3 · 53 · 127 · 7280174849_<10> · 109124535209_<12> · 21948898589324162190187_<23> · 33736169926864163126149367_<26> · C86
C86 = P41 · P45
P41 = 18462693075720592159694382676395345089159_<41>
P45 = 709278681425545386232340021289077175661076813_<45>

Thu Apr 03 02:41:55 2008 Thu Apr 03 02:41:55 2008 Thu Apr 03 02:41:55 2008 Msieve v. 1.33 Thu Apr 03 02:41:55 2008 random seeds: 42b0e064 b812c0af Thu Apr 03 02:41:55 2008 factoring 13095194600311648587363642228835280059379349527210239503556304027577051905401432570267 (86 digits) Thu Apr 03 02:41:56 2008 searching for 15-digit factors Thu Apr 03 02:41:57 2008 commencing quadratic sieve (86-digit input) Thu Apr 03 02:41:57 2008 using multiplier of 3 Thu Apr 03 02:41:57 2008 using 64kb Opteron sieve core Thu Apr 03 02:41:57 2008 sieve interval: 6 blocks of size 65536 Thu Apr 03 02:41:57 2008 processing polynomials in batches of 17 Thu Apr 03 02:41:57 2008 using a sieve bound of 1442509 (54992 primes) Thu Apr 03 02:41:57 2008 using large prime bound of 115400720 (26 bits) Thu Apr 03 02:41:57 2008 using double large prime bound of 325068826146400 (41-49 bits) Thu Apr 03 02:41:57 2008 using trial factoring cutoff of 49 bits Thu Apr 03 02:41:57 2008 polynomial 'A' values have 11 factors Thu Apr 03 03:20:45 2008 55145 relations (16138 full + 39007 combined from 573077 partial), need 55088 Thu Apr 03 03:20:45 2008 begin with 589214 relations Thu Apr 03 03:20:46 2008 reduce to 130017 relations in 10 passes Thu Apr 03 03:20:46 2008 attempting to read 130017 relations Thu Apr 03 03:20:47 2008 recovered 130017 relations Thu Apr 03 03:20:47 2008 recovered 111360 polynomials Thu Apr 03 03:20:47 2008 attempting to build 55144 cycles Thu Apr 03 03:20:47 2008 found 55143 cycles in 5 passes Thu Apr 03 03:20:48 2008 distribution of cycle lengths: Thu Apr 03 03:20:48 2008 length 1 : 16138 Thu Apr 03 03:20:48 2008 length 2 : 11055 Thu Apr 03 03:20:48 2008 length 3 : 9584 Thu Apr 03 03:20:48 2008 length 4 : 7023 Thu Apr 03 03:20:48 2008 length 5 : 4907 Thu Apr 03 03:20:48 2008 length 6 : 2885 Thu Apr 03 03:20:48 2008 length 7 : 1679 Thu Apr 03 03:20:48 2008 length 9+: 1872 Thu Apr 03 03:20:48 2008 largest cycle: 18 relations Thu Apr 03 03:20:48 2008 matrix is 54992 x 55143 (12.0 MB) with weight 2919220 (52.94/col) Thu Apr 03 03:20:48 2008 sparse part has weight 2919220 (52.94/col) Thu Apr 03 03:20:49 2008 filtering completed in 4 passes Thu Apr 03 03:20:49 2008 matrix is 50096 x 50160 (11.0 MB) with weight 2691005 (53.65/col) Thu Apr 03 03:20:49 2008 sparse part has weight 2691005 (53.65/col) Thu Apr 03 03:20:50 2008 saving the first 48 matrix rows for later Thu Apr 03 03:20:50 2008 matrix is 50048 x 50160 (6.5 MB) with weight 2016906 (40.21/col) Thu Apr 03 03:20:50 2008 sparse part has weight 1390909 (27.73/col) Thu Apr 03 03:20:50 2008 matrix includes 64 packed rows Thu Apr 03 03:20:50 2008 using block size 20064 for processor cache size 512 kB Thu Apr 03 03:20:50 2008 commencing Lanczos iteration Thu Apr 03 03:20:50 2008 memory use: 6.8 MB Thu Apr 03 03:21:10 2008 lanczos halted after 792 iterations (dim = 50039) Thu Apr 03 03:21:10 2008 recovered 12 nontrivial dependencies Thu Apr 03 03:21:11 2008 prp41 factor: 18462693075720592159694382676395345089159 Thu Apr 03 03:21:11 2008 prp45 factor: 709278681425545386232340021289077175661076813 Thu Apr 03 03:21:11 2008 elapsed time 00:39:16
(14·10¹²²+31)/9 = 1(5)₁₂₁9_<123> = 3 · 157 · C120
C120 = P35 · P86
P35 = 10603836885495071034474476095145129_<35>
P86 = 31145949892586395406949575512425987474943569710446787657049654966993983919833639672201_<86>
(14·10¹⁴⁷+31)/9 = 1(5)₁₄₆9_<148> = 781077391688879_<15> · C133
C133 = P35 · P98
P35 = 48666565188027890092729966818877889_<35>
P98 = 40922368653085930485059904571405162735697559903875161667841200639610533122749207940850079133777289_<98>
(14·10¹⁵⁰+31)/9 = 1(5)₁₄₉9_<151> = 39569 · 18139119101745599_<17> · C130
C130 = P33 · P97
P33 = 335061822392136720484534754789419_<33>
P97 = 6468287466652218202909758335139916011634361647250202124939424960816497412784711946727546397178331_<97>
(14·10¹⁴⁰+31)/9 = 1(5)₁₃₉9_<141> = 3 · 233 · 241 · 5903 · C132
C132 = P40 · P42 · P51
P40 = 3145814278159836132977122915782215478379_<40>
P42 = 136993138600366227200200711944926574507283_<42>
P51 = 362983287496566443500422296301603020385805008326731_<51>

Number: n N=156429452288643464911081002531058371361509167836384377115150014761470851983993732172191342450556465613504105350691617341742398323867 ( 132 digits) SNFS difficulty: 141 digits. Divisors found: r1=3145814278159836132977122915782215478379 (pp40) r2=136993138600366227200200711944926574507283 (pp42) r3=362983287496566443500422296301603020385805008326731 (pp51) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.22 hours. Scaled time: 12.66 units (timescale=1.752). Factorization parameters were as follows: name: KA_1_5_139_9 n: 156429452288643464911081002531058371361509167836384377115150014761470851983993732172191342450556465613504105350691617341742398323867 type: snfs skew: 1.17 deg: 5 c5: 14 c0: 31 m: 10000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 950001) Primes: RFBsize:148933, AFBsize:148581, largePrimes:5725582 encountered Relations: rels:5089339, finalFF:358359 Max relations in full relation-set: 28 Initial matrix: 297580 x 358359 with sparse part having weight 19209340. Pruned matrix : 245434 x 246985 with weight 10431835. Total sieving time: 6.09 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.87 hours. Total square root time: 0.12 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 7.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Apr 3, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, GGNFS
(14·10¹⁵⁵+31)/9 = 1(5)₁₅₄9_<156> = 3 · 54905849 · 154308125187053473_<18> · C130
C130 = P31 · P99
P31 = 7674360746381837411521751272723_<31>
P99 = 797470552787996185165803170580988931064736161642896696883978483018377247210575889135871920756199543_<99>
(14·10¹⁴⁶+31)/9 = 1(5)₁₄₅9_<147> = 3 · 83 · 2017 · 157915345952665151_<18> · 585854257405781501_<18> · C106
C106 = P39 · P67
P39 = 788446662848643115165841844345577532321_<39>
P67 = 4246137320921946481553619461943257958828954529607621070878133125813_<67>

Number: 15559_146 N=3347852800677986669372738417402636472582245561438340610458401501686074563594432546426620601309782766901973 ( 106 digits) SNFS difficulty: 147 digits. Divisors found: r1=788446662848643115165841844345577532321 (pp39) r2=4246137320921946481553619461943257958828954529607621070878133125813 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.94 hours. Scaled time: 21.33 units (timescale=2.145). Factorization parameters were as follows: n: 3347852800677986669372738417402636472582245561438340610458401501686074563594432546426620601309782766901973 m: 100000000000000000000000000000 c5: 140 c0: 31 skew: 0.74 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1575001) Primes: RFBsize:135072, AFBsize:134614, largePrimes:3693349 encountered Relations: rels:3686817, finalFF:304236 Max relations in full relation-set: 28 Initial matrix: 269753 x 304236 with sparse part having weight 27282670. Pruned matrix : 256253 x 257665 with weight 20349781. Total sieving time: 9.58 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.27 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 9.94 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).
Apr 3, 2008: By Jo Yeong Uk / GGNFS, GMP-ECM
(14·10¹⁰⁴+31)/9 = 1(5)₁₀₃9_<105> = 3 · 17 · 415039 · 960259 · C91
C91 = P31 · P61
P31 = 6123112702612974422656257278677_<31>
P61 = 1249872758938303891586631981770280688173300314576830254317117_<61>

Number: 15559_104 N=7653111766905052625714127478056069869442270615205235958642237021066340455316087033400214209 ( 91 digits) SNFS difficulty: 105 digits. Divisors found: r1=6123112702612974422656257278677 (pp31) r2=1249872758938303891586631981770280688173300314576830254317117 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.41 hours. Scaled time: 0.87 units (timescale=2.135). Factorization parameters were as follows: n: 7653111766905052625714127478056069869442270615205235958642237021066340455316087033400214209 m: 1000000000000000000000 c5: 7 c0: 155 skew: 1.86 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 260001) Primes: RFBsize:30757, AFBsize:30265, largePrimes:962732 encountered Relations: rels:875648, finalFF:78657 Max relations in full relation-set: 28 Initial matrix: 61087 x 78657 with sparse part having weight 3216591. Pruned matrix : 52909 x 53278 with weight 1608056. Total sieving time: 0.39 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,105,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.41 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).
(14·10¹⁰⁹+31)/9 = 1(5)₁₀₈9_<110> = 19 · 55335037 · C101
C101 = P46 · P55
P46 = 9501681575912170966662527503987525172261786003_<46>
P55 = 1557152862759509908452930886474382752596857671286405051_<55>

Number: 15559_109 N=14795570666960928585241814337133228280279517122079409846942244753399146743476713502376399618540301153 ( 101 digits) SNFS difficulty: 110 digits. Divisors found: r1=9501681575912170966662527503987525172261786003 (pp46) r2=1557152862759509908452930886474382752596857671286405051 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.67 hours. Scaled time: 1.44 units (timescale=2.146). Factorization parameters were as follows: n: 14795570666960928585241814337133228280279517122079409846942244753399146743476713502376399618540301153 m: 10000000000000000000000 c5: 7 c0: 155 skew: 1.86 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 320001) Primes: RFBsize:30757, AFBsize:30265, largePrimes:1063994 encountered Relations: rels:991255, finalFF:96554 Max relations in full relation-set: 28 Initial matrix: 61087 x 96554 with sparse part having weight 4661689. Pruned matrix : 51141 x 51510 with weight 1737634. Total sieving time: 0.65 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.67 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).
(14·10¹⁸⁰+31)/9 = 1(5)₁₇₉9_<181> = C181
C181 = P33 · P148
P33 = 224540162641475926200940032590041_<33>
P148 = 6927738615916639493795372224802362230619590881114688329834073792904549303518808372499279890767099431963254595662524485909980595129219530776688881599_<148>
(14·10¹¹⁰+31)/9 = 1(5)₁₀₉9_<111> = 3 · 241 · 4723 · C104
C104 = P46 · P59
P46 = 1303282840472408036468985773035703330564633891_<46>
P59 = 34953494903639795656060613382861445837052916896715844002181_<59>

Number: 15559_110 N=45554290122453511114807516366761624584426921010585482934533181273112904583513232105843701083030470516271 ( 104 digits) SNFS difficulty: 111 digits. Divisors found: r1=1303282840472408036468985773035703330564633891 (pp46) r2=34953494903639795656060613382861445837052916896715844002181 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.60 hours. Scaled time: 1.27 units (timescale=2.130). Factorization parameters were as follows: n: 45554290122453511114807516366761624584426921010585482934533181273112904583513232105843701083030470516271 m: 10000000000000000000000 c5: 14 c0: 31 skew: 1.17 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 300001) Primes: RFBsize:30757, AFBsize:30605, largePrimes:979923 encountered Relations: rels:884896, finalFF:73064 Max relations in full relation-set: 28 Initial matrix: 61428 x 73064 with sparse part having weight 3324838. Pruned matrix : 56970 x 57341 with weight 2019227. Total sieving time: 0.57 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.60 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).
(14·10¹¹²+31)/9 = 1(5)₁₁₁9_<113> = 277 · 1367 · 332573 · C102
C102 = P37 · P65
P37 = 6092182038573200834431033938985160341_<37>
P65 = 20275771240622793997064761967146282229636836482089466349375858957_<65>

Number: 15559_112 N=123523689370341250516149913321329516008019385631608532341465796759702347383365229527627429013246024337 ( 102 digits) SNFS difficulty: 113 digits. Divisors found: r1=6092182038573200834431033938985160341 (pp37) r2=20275771240622793997064761967146282229636836482089466349375858957 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.81 hours. Scaled time: 1.72 units (timescale=2.135). Factorization parameters were as follows: n: 123523689370341250516149913321329516008019385631608532341465796759702347383365229527627429013246024337 m: 20000000000000000000000 c5: 175 c0: 124 skew: 0.93 type: snfs Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [225000, 375001) Primes: RFBsize:37706, AFBsize:37740, largePrimes:1287788 encountered Relations: rels:1247576, finalFF:110750 Max relations in full relation-set: 28 Initial matrix: 75513 x 110750 with sparse part having weight 8140654. Pruned matrix : 67086 x 67527 with weight 3384017. Total sieving time: 0.77 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.3,2.3,25000 total time: 0.81 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).
(14·10¹¹⁵+31)/9 = 1(5)₁₁₄9_<116> = 3279678159671671397_<19> · C97
C97 = P39 · P59
P39 = 467835898086147901719587583613501434971_<39>
P59 = 10138197686463485465002382573752151496026773591252758195457_<59>

Number: 15559_115 N=4743012819621551624636543784883103395485170841183928305043751488713980500978238376905549993126747 ( 97 digits) SNFS difficulty: 116 digits. Divisors found: r1=467835898086147901719587583613501434971 (pp39) r2=10138197686463485465002382573752151496026773591252758195457 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.75 hours. Scaled time: 1.60 units (timescale=2.122). Factorization parameters were as follows: n: 4743012819621551624636543784883103395485170841183928305043751488713980500978238376905549993126747 m: 100000000000000000000000 c5: 14 c0: 31 skew: 1.17 type: snfs Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [225000, 375001) Primes: RFBsize:37706, AFBsize:37565, largePrimes:1292652 encountered Relations: rels:1256566, finalFF:114016 Max relations in full relation-set: 28 Initial matrix: 75337 x 114016 with sparse part having weight 8559587. Pruned matrix : 66510 x 66950 with weight 3395592. Total sieving time: 0.71 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,450000,450000,25,25,44,44,2.3,2.3,25000 total time: 0.75 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167492k/8912896k available (2127k kernel code, 0k reserved, 1314k data, 212k init) Calibrating delay using timer specific routine.. 4815.33 BogoMIPS (lpj=2407668) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.08 BogoMIPS).
Apr 2, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(14·10¹⁶³+13)/9 = 1(5)₁₆₂7_<164> = 88001 · C159
C159 = P59 · P100
P59 = 49844159806140022457656033933584078006954093974713327381627_<59>
P100 = 3546366690789890875339022615239880757403094877861401298222832779627443194683536889140462772150874591_<100>

Number: n N=176765668066903280139493364343081959927223049233026392376854303423319684498534738872916848167129413933427524182174697509750520511761861291980267900996074539557 ( 159 digits) SNFS difficulty: 164 digits. Divisors found: Thu Apr 03 01:28:54 2008 prp59 factor: 49844159806140022457656033933584078006954093974713327381627 Thu Apr 03 01:28:54 2008 prp100 factor: 3546366690789890875339022615239880757403094877861401298222832779627443194683536889140462772150874591 Thu Apr 03 01:28:54 2008 elapsed time 02:02:23 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 70.94 hours. Scaled time: 124.29 units (timescale=1.752). Factorization parameters were as follows: name: KA_1_5_162_7 n: 176765668066903280139493364343081959927223049233026392376854303423319684498534738872916848167129413933427524182174697509750520511761861291980267900996074539557 type: snfs skew: 0.49 deg: 5 c5: 875 c0: 26 m: 200000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3500383) Primes: RFBsize:216816, AFBsize:217331, largePrimes:7559625 encountered Relations: rels:6970216, finalFF:449362 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 70.68 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 70.94 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Apr 2, 2008 (2nd): The factor table of 155...559 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Apr 2, 2008: By Robert Backstrom / GMP-ECM
(13·10¹⁷⁷+41)/9 = 1(4)₁₇₆9_<178> = 3 · 7 · 31 · 23894417 · 387048321879097_<15> · 102901558413798602757536612189167_<33> · C121
C121 = P45 · P76
P45 = 332959311000289726554119341499581353472911353_<45>
P76 = 7002370898982811465985212519192627896899356817719697064270507631837030185901_<76>
Apr 1, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(13·10¹⁶⁵+41)/9 = 1(4)₁₆₄9_<166> = 3² · 7³ · 17 · 311 · C158
C158 = P35 · P124
P35 = 16314950226194202535821847388584579_<35>
P124 = 5424617863803991143762455161408372822546229535063185548695922017790727738160207197999393097074876903892876721001455128856499_<124>
(14·10¹⁵²+13)/9 = 1(5)₁₅₁7_<153> = 63788093921_<11> · C142
C142 = P54 · P89
P54 = 173460172689027899665086107807131828832709509246937443_<54>
P89 = 14058731181313703042304048180548635368310516923726637061756330334276648276290706574486519_<89>

Number: n N=2438629938499296133491619142929611093991847945494523527378368041823708212062716661647080595097808104570147460693796634688057769776161039830917 ( 142 digits) SNFS difficulty: 153 digits. Divisors found: Tue Apr 01 07:40:21 2008 prp54 factor: 173460172689027899665086107807131828832709509246937443 Tue Apr 01 07:40:21 2008 prp89 factor: 14058731181313703042304048180548635368310516923726637061756330334276648276290706574486519 Tue Apr 01 07:40:21 2008 elapsed time 00:53:45 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 29.91 hours. Scaled time: 39.03 units (timescale=1.305). Factorization parameters were as follows: name: KA_1_5_151_7 n: 2438629938499296133491619142929611093991847945494523527378368041823708212062716661647080595097808104570147460693796634688057769776161039830917 skew: 0.39 deg: 5 c5: 1400 c0: 13 m: 1000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1200000 ) Primes: RFBsize:203362, AFBsize:203057, largePrimes:7157192 encountered Relations: rels:6740859, finalFF:571144 Max relations in full relation-set: 28 Initial matrix: 406486 x 571144 with sparse part having weight 41884449. Pruned matrix : 277790 x 279886 with weight 22751566. Total sieving time: 27.09 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.62 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 29.91 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(14·10¹⁶²-23)/9 = 1(5)₁₆₁3_<163> = 17² · 30817 · 372124977656909_<15> · C141
C141 = P48 · P93
P48 = 472035414783518016243135774561543103921057694177_<48>
P93 = 994337733365949129428898253056275129686355332723981707011105870757951405338818661021405862917_<93>

Number: n N=469362624404298939135494109270052332408386538926431489548931993834927472197048244992417935599677767202896447674317093792319483188200971134309 ( 141 digits) SNFS difficulty: 163 digits. Divisors found: Tue Apr 1 16:01:03 2008 prp48 factor: 472035414783518016243135774561543103921057694177 Tue Apr 1 16:01:03 2008 prp93 factor: 994337733365949129428898253056275129686355332723981707011105870757951405338818661021405862917 Tue Apr 1 16:01:03 2008 elapsed time 00:46:15 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 37.68 hours. Scaled time: 31.61 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_5_161_3 n: 469362624404298939135494109270052332408386538926431489548931993834927472197048244992417935599677767202896447674317093792319483188200971134309 type: snfs deg: 5 c5: 1400 c0: -23 skew: 0.44 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2400001) Primes: RFBsize:216816, AFBsize:216901, largePrimes:5556168 encountered Relations: rels:5418684, finalFF:465647 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 37.50 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 37.68 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(11·10¹⁶⁵+61)/9 = 1(2)₁₆₄9_<166> = 409 · 80599 · C158
C158 = P50 · P54 · P55
P50 = 84487268400846963130771961910946989225423105211073_<50>
P54 = 404346314135854308052527269390940411387810076224120869_<54>
P55 = 1085306631461643435651060404463146659487393443172166287_<55>

Number: n N=37076370572108520285117694169011671267321814898181595809391309168633542846173451775619238671177620592167679409414133382357732851260970228149682256009783901419 ( 158 digits) SNFS difficulty: 166 digits. Divisors found: Wed Apr 2 00:28:00 2008 prp50 factor: 84487268400846963130771961910946989225423105211073 Wed Apr 2 00:28:00 2008 prp54 factor: 404346314135854308052527269390940411387810076224120869 Wed Apr 2 00:28:00 2008 prp55 factor: 1085306631461643435651060404463146659487393443172166287 Wed Apr 2 00:28:00 2008 elapsed time 00:53:00 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 45.93 hours. Scaled time: 38.49 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_2_164_9 n: 37076370572108520285117694169011671267321814898181595809391309168633542846173451775619238671177620592167679409414133382357732851260970228149682256009783901419 type: snfs deg: 5 c5: 11 c0: 61 skew: 1.41 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2900001) Primes: RFBsize:216816, AFBsize:216278, largePrimes:5612922 encountered Relations: rels:5482602, finalFF:460483 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 45.74 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 45.93 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).

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