News and updates, August 2009

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News and updates, August 2009

Aug 31, 2009 (5th): By Erik Branger / GGNFS, Msieve / Aug 31, 2009
(59·10¹⁵⁴-41)/9 = 6(5)₁₅₃1_<155> = 3797 · 159093639765504071562915217735497341_<36> · C117
C117 = P55 · P62
P55 = 2589791619531563881290259667937807775007827680200185973_<55>
P62 = 41903593307858982204461105941512747941924740493989831900396931_<62>

Number: 65551_154 N=108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863 ( 117 digits) SNFS difficulty: 156 digits. Divisors found: r1=2589791619531563881290259667937807775007827680200185973 (pp55) r2=41903593307858982204461105941512747941924740493989831900396931 (pp62) Version: Msieve v. 1.42 Total time: 46.92 hours. Scaled time: 18.02 units (timescale=0.384). Factorization parameters were as follows: n: 108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863 m: 10000000000000000000000000000000 deg: 5 c5: 59 c0: -410 skew: 1.47 type: snfs lss: 1 rlim: 2900000 alim: 2900000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 100000 Factor base limits: 2900000/2900000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1450000, 2950001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 551770 x 551994 Total sieving time: 45.21 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.05 hours. Time per square root: 0.55 hours. Prototype def-par.txt line would be: snfs ,156.000,5,0,0,0,0,0,0,0,0,2900000,2900000,27,27,50,50,2.4,2.4, total time: 46.92 hours. --------- CPU info (if available) ----------
Aug 31, 2009 (4th): By Sinkiti Sibata / Msieve / Aug 31, 2009
(59·10¹⁶⁷-41)/9 = 6(5)₁₆₆1_<168> = 3² · 13 · 31 · 6389 · 132096631 · C153
C153 = P47 · P106
P47 = 29066651586528410702821561866512390233285664069_<47>
P106 = 7367876067116486925377923809061947616100280902108981773894021319523839837975817484936114364116391604057203_<106>

Number: 65551_167 N=214159486575596141707211680720002581157646854390477143895630202872280827983759826601254749071627804247303991319745959188294916234845748005710716517739007 ( 153 digits) SNFS difficulty: 169 digits. Divisors found: r1=29066651586528410702821561866512390233285664069 (pp47) r2=7367876067116486925377923809061947616100280902108981773894021319523839837975817484936114364116391604057203 (pp106) Version: Msieve-1.40 Total time: 61.17 hours. Scaled time: 203.20 units (timescale=3.322). Factorization parameters were as follows: name: 65551_167 n: 214159486575596141707211680720002581157646854390477143895630202872280827983759826601254749071627804247303991319745959188294916234845748005710716517739007 m: 2000000000000000000000000000000000 deg: 5 c5: 1475 c0: -328 skew: 0.74 type: snfs lss: 1 rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2350000, 5550001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 935564 x 935811 Total sieving time: 59.13 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.66 hours. Time per square root: 0.27 hours. Prototype def-par.txt line would be: snfs,169.000,5,0,0,0,0,0,0,0,0,4700000,4700000,27,27,52,52,2.4,2.4,100000 total time: 61.17 hours. --------- CPU info (if available) ----------
Aug 31, 2009 (3rd): By Markus Tervooren / gnfs-lasieve4I14e, gnfs-lasieve4I15e, msieve 1.42 / Aug 31, 2009
8·10²³⁰-1 = 7(9)₂₃₀_<231> = 171847177 · C223
C223 = P70 · P74 · P80
P70 = 7194989070351007241001770794481202899232920377811344337193524816903113_<70>
P74 = 28405869825449471447004672858393144480378760112284964510299428948566224457_<74>
P80 = 22777672993897316831397692267111749997397458530603944165484429112280289213344407_<80>

Sieving took ~191 CPU-days @ 2.66Ghz Core 2 + 120 CPU-days @2.00 Ghz P4 Sat Aug 22 14:08:04 2009 commencing relation filtering Sat Aug 22 14:08:04 2009 estimated available RAM is 8010.2 MB Sat Aug 22 14:08:04 2009 commencing duplicate removal, pass 1 -- some errors snipped Sat Aug 22 14:19:35 2009 found 17364933 hash collisions in 92302860 relations Sat Aug 22 14:19:55 2009 added 419490 free relations Sat Aug 22 14:19:55 2009 commencing duplicate removal, pass 2 Sat Aug 22 14:24:57 2009 found 17849103 duplicates and 74873247 unique relations Sat Aug 22 14:24:57 2009 memory use: 426.4 MB Sat Aug 22 14:24:57 2009 reading ideals above 53280768 Sat Aug 22 14:24:57 2009 commencing singleton removal, initial pass Sat Aug 22 14:38:55 2009 memory use: 1193.5 MB Sat Aug 22 14:38:55 2009 reading all ideals from disk Sat Aug 22 14:39:25 2009 memory use: 1323.7 MB Sat Aug 22 14:39:34 2009 commencing in-memory singleton removal Sat Aug 22 14:39:42 2009 begin with 74873247 relations and 74233171 unique ideals Sat Aug 22 14:41:11 2009 reduce to 32087832 relations and 25064968 ideals in 19 passes Sat Aug 22 14:41:11 2009 max relations containing the same ideal: 21 Sat Aug 22 14:41:16 2009 reading ideals above 720000 Sat Aug 22 14:41:16 2009 commencing singleton removal, initial pass Sat Aug 22 14:48:39 2009 memory use: 596.8 MB Sat Aug 22 14:48:39 2009 reading all ideals from disk Sat Aug 22 14:49:00 2009 memory use: 1198.3 MB Sat Aug 22 14:49:10 2009 keeping 31255991 ideals with weight <= 200, target excess is 177317 Sat Aug 22 14:49:19 2009 commencing in-memory singleton removal Sat Aug 22 14:49:28 2009 begin with 32087840 relations and 31255991 unique ideals Sat Aug 22 14:51:30 2009 reduce to 32043145 relations and 31211249 ideals in 14 passes Sat Aug 22 14:51:30 2009 max relations containing the same ideal: 200 Sat Aug 22 14:52:11 2009 removing 3404380 relations and 3091276 ideals in 313104 cliques Sat Aug 22 14:52:12 2009 commencing in-memory singleton removal Sat Aug 22 14:52:21 2009 begin with 28638765 relations and 31211249 unique ideals Sat Aug 22 14:54:01 2009 reduce to 28324631 relations and 27801343 ideals in 13 passes Sat Aug 22 14:54:01 2009 max relations containing the same ideal: 192 Sat Aug 22 14:54:36 2009 removing 2504006 relations and 2190902 ideals in 313104 cliques Sat Aug 22 14:54:38 2009 commencing in-memory singleton removal Sat Aug 22 14:54:45 2009 begin with 25820625 relations and 27801343 unique ideals Sat Aug 22 14:56:01 2009 reduce to 25626526 relations and 25413937 ideals in 11 passes Sat Aug 22 14:56:01 2009 max relations containing the same ideal: 182 Sat Aug 22 14:56:43 2009 relations with 0 large ideals: 6650 Sat Aug 22 14:56:43 2009 relations with 1 large ideals: 776 Sat Aug 22 14:56:43 2009 relations with 2 large ideals: 9374 Sat Aug 22 14:56:43 2009 relations with 3 large ideals: 93183 Sat Aug 22 14:56:43 2009 relations with 4 large ideals: 547174 Sat Aug 22 14:56:43 2009 relations with 5 large ideals: 1991731 Sat Aug 22 14:56:43 2009 relations with 6 large ideals: 4560537 Sat Aug 22 14:56:43 2009 relations with 7+ large ideals: 18417101 Sat Aug 22 14:56:43 2009 commencing 2-way merge Sat Aug 22 14:57:27 2009 reduce to 15063412 relation sets and 14850827 unique ideals Sat Aug 22 14:57:27 2009 ignored 4 oversize relation sets Sat Aug 22 14:57:27 2009 commencing full merge Sat Aug 22 15:04:59 2009 memory use: 1764.4 MB Sat Aug 22 15:05:01 2009 found 7950941 cycles, need 7925027 Sat Aug 22 15:05:06 2009 weight of 7925027 cycles is about 554942333 (70.02/cycle) Sat Aug 22 15:05:06 2009 distribution of cycle lengths: Sat Aug 22 15:05:06 2009 1 relations: 1169843 Sat Aug 22 15:05:06 2009 2 relations: 1106346 Sat Aug 22 15:05:06 2009 3 relations: 1021429 Sat Aug 22 15:05:06 2009 4 relations: 874258 Sat Aug 22 15:05:06 2009 5 relations: 743662 Sat Aug 22 15:05:06 2009 6 relations: 615047 Sat Aug 22 15:05:06 2009 7 relations: 500678 Sat Aug 22 15:05:06 2009 8 relations: 404363 Sat Aug 22 15:05:06 2009 9 relations: 328390 Sat Aug 22 15:05:06 2009 10+ relations: 1161011 Sat Aug 22 15:05:06 2009 heaviest cycle: 26 relations Sat Aug 22 15:05:09 2009 commencing cycle optimization Sat Aug 22 15:05:30 2009 start with 42060266 relations Sat Aug 22 15:06:59 2009 pruned 704586 relations Sat Aug 22 15:06:59 2009 memory use: 1471.4 MB Sat Aug 22 15:06:59 2009 distribution of cycle lengths: Sat Aug 22 15:06:59 2009 1 relations: 1169843 Sat Aug 22 15:06:59 2009 2 relations: 1125822 Sat Aug 22 15:06:59 2009 3 relations: 1048997 Sat Aug 22 15:06:59 2009 4 relations: 885549 Sat Aug 22 15:06:59 2009 5 relations: 751949 Sat Aug 22 15:06:59 2009 6 relations: 615186 Sat Aug 22 15:06:59 2009 7 relations: 497737 Sat Aug 22 15:06:59 2009 8 relations: 399716 Sat Aug 22 15:06:59 2009 9 relations: 322988 Sat Aug 22 15:06:59 2009 10+ relations: 1107240 Sat Aug 22 15:06:59 2009 heaviest cycle: 26 relations Sat Aug 22 15:07:18 2009 RelProcTime: 3554 Sat Aug 22 15:07:18 2009 elapsed time 00:59:16 Sat Aug 22 15:45:07 2009 commencing linear algebra Sat Aug 22 15:45:08 2009 read 7925027 cycles Sat Aug 22 15:45:25 2009 cycles contain 25287775 unique relations Sat Aug 22 15:50:50 2009 read 25287775 relations Sat Aug 22 15:51:38 2009 using 20 quadratic characters above 1073741312 Sat Aug 22 15:54:07 2009 building initial matrix Sat Aug 22 15:59:14 2009 memory use: 3135.0 MB Sat Aug 22 15:59:21 2009 read 7925027 cycles Sat Aug 22 15:59:29 2009 matrix is 7924849 x 7925027 (2395.5 MB) with weight 696021674 (87.83/col) Sat Aug 22 15:59:29 2009 sparse part has weight 540796398 (68.24/col) Sat Aug 22 16:01:56 2009 filtering completed in 2 passes Sat Aug 22 16:01:58 2009 matrix is 7915028 x 7915206 (2394.8 MB) with weight 695762853 (87.90/col) Sat Aug 22 16:01:58 2009 sparse part has weight 540725492 (68.31/col) Sat Aug 22 16:03:01 2009 read 7915206 cycles Sat Aug 22 16:03:05 2009 matrix is 7915028 x 7915206 (2394.8 MB) with weight 695762853 (87.90/col) Sat Aug 22 16:03:05 2009 sparse part has weight 540725492 (68.31/col) Sat Aug 22 16:03:05 2009 saving the first 48 matrix rows for later Sat Aug 22 16:03:09 2009 matrix is 7914980 x 7915206 (2286.5 MB) with weight 561446210 (70.93/col) Sat Aug 22 16:03:09 2009 sparse part has weight 520247528 (65.73/col) Sat Aug 22 16:03:09 2009 matrix includes 64 packed rows Sat Aug 22 16:03:09 2009 using block size 65536 for processor cache size 4096 kB Sat Aug 22 16:03:42 2009 commencing Lanczos iteration (4 threads) Sat Aug 22 16:03:42 2009 memory use: 2480.9 MB Sun Aug 30 13:18:16 2009 lanczos halted after 125170 iterations (dim = 7914978) Sun Aug 30 13:18:31 2009 recovered 38 nontrivial dependencies Sun Aug 30 13:18:31 2009 BLanczosTime: 682404 Sun Aug 30 13:18:31 2009 elapsed time 189:33:27 Sun Aug 30 15:39:04 2009 commencing square root phase Sun Aug 30 15:39:04 2009 reading relations for dependency 5 Sun Aug 30 15:39:16 2009 read 3957653 cycles Sun Aug 30 15:39:31 2009 cycles contain 15233059 unique relations Sun Aug 30 15:44:24 2009 read 15233059 relations Sun Aug 30 15:47:18 2009 multiplying 12643428 relations Sun Aug 30 16:39:02 2009 sqrtTime: 11943 Sun Aug 30 16:39:02 2009 prp70 factor: 7194989070351007241001770794481202899232920377811344337193524816903113 Sun Aug 30 16:39:02 2009 prp74 factor: 28405869825449471447004672858393144480378760112284964510299428948566224457 Sun Aug 30 16:39:02 2009 prp80 factor: 22777672993897316831397692267111749997397458530603944165484429112280289213344407 Sun Aug 30 16:39:02 2009 elapsed time 03:19:06
c223 is the largest number factored by SNFS in our tables so far. Congratulations!!!
Aug 31, 2009 (2nd): By Robert Backstrom / GMP-ECM, GGNFS / Aug 31, 2009
(59·10¹⁷⁰-41)/9 = 6(5)₁₆₉1_<171> = 3 · 7 · 214170980453_<12> · 3324849806533_<13> · C146
C146 = P36 · P46 · P65
P36 = 804107783923129451039657356402486843_<36>
P46 = 2776050591687826340964640438188313241988097739_<46>
P65 = 19638843448420433381809909722623979282848939454441955452939170147_<65>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 43838688281452999209382287472067018505906351758921389540363873721972984740431326457383916438597688638236307286955968711139765929965483119754642619 (146 digits) Using B1=3242000, B2=5707206970, polynomial Dickson(6), sigma=2430415712 Step 1 took 38250ms Step 2 took 14281ms ********** Factor found in step 2: 804107783923129451039657356402486843 Found probable prime factor of 36 digits: 804107783923129451039657356402486843 Composite cofactor 54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633 has 110 digits Number: n N=54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633 ( 110 digits) Divisors found: r1=2776050591687826340964640438188313241988097739 (pp46) r2=19638843448420433381809909722623979282848939454441955452939170147 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 16.34 hours. Scaled time: 29.87 units (timescale=1.828). Factorization parameters were as follows: name: KA_6_5_169_1 n: 54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633 Y0: -1907280307381663206726 Y1: 332678452343 c0: 899049179931483930219743873 c1: -50751007675298549806423 c2: -1403077213923752919 c3: 75397464258793 c4: 482168956 c5: 2160 skew: 32525.21 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 20000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1600000, 2160001) Primes: RFBsize:230209, AFBsize:230958, largePrimes:16207647 encountered Relations: rels:14256599, finalFF:544460 Max relations in full relation-set: 48 Initial matrix: 461242 x 544460 with sparse part having weight 61863544. Pruned matrix : 397836 x 400206 with weight 37670194. Total sieving time: 13.78 hours. Total relation processing time: 0.51 hours. Matrix solve time: 1.82 hours. Total square root time: 0.22 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,28,28,56,56,2.6,2.6,100000 total time: 16.34 hours. --------- CPU info (if available) ----------
Jo Yeong Uk also found P36.

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 43838688281452999209382287472067018505906351758921389540363873721972984740431326457383916438597688638236307286955968711139765929965483119754642619 (146 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5417305544 Step 1 took 4727ms Step 2 took 4493ms ********** Factor found in step 2: 804107783923129451039657356402486843 Found probable prime factor of 36 digits: 804107783923129451039657356402486843 Composite cofactor 54518422975052135935953956558967048083415118898869480584619417866224478054192616489161192182019931353786997633 has 110 digits
Aug 31, 2009: By Dmitry Domanov / GGNFS/msieve 1.42 / Aug 31, 2009
(16·10²⁰²-7)/9 = 1(7)₂₀₂_<203> = 23663522088959665379_<20> · 41175088192813174267_<20> · 1085821989830191408574448787_<28> · C137
C137 = P46 · P92
P46 = 1081532647714971214037755172969779401345844853_<46>
P92 = 15536932645254557221822951817675878742208962257314811273026340883379604360838433963316815599_<92>

Sieving ~ 18.5 cpu-days Sun Aug 30 11:15:50 2009 Msieve v. 1.42 Sun Aug 30 11:15:50 2009 random seeds: bee3af00 d09e99d0 Sun Aug 30 11:15:50 2009 factoring 16803699901191332856731624940085075709418965141403433009136434244527057083294180228918835965492442107538029009528292583619187682264261947 (137 digits) Sun Aug 30 11:15:52 2009 searching for 15-digit factors Sun Aug 30 11:15:53 2009 commencing number field sieve (137-digit input) Sun Aug 30 11:15:53 2009 R0: -291093131217969603025891500 Sun Aug 30 11:15:53 2009 R1: 926622307161661 Sun Aug 30 11:15:53 2009 A0: -30036619351616900804396764665813653 Sun Aug 30 11:15:53 2009 A1: 42857501262580016590013505029 Sun Aug 30 11:15:53 2009 A2: 97333981214042173293399 Sun Aug 30 11:15:53 2009 A3: -72897361794663101 Sun Aug 30 11:15:53 2009 A4: -63509433778 Sun Aug 30 11:15:53 2009 A5: 8040 Sun Aug 30 11:15:53 2009 skew 1401827.32, size 3.338525e-013, alpha -6.680700, combined = 3.197034e-011 Sun Aug 30 11:15:53 2009 Sun Aug 30 11:15:53 2009 commencing relation filtering Sun Aug 30 11:15:53 2009 estimated available RAM is 4094.1 MB Sun Aug 30 11:15:53 2009 commencing duplicate removal, pass 1 Sun Aug 30 11:18:03 2009 error -6 reading relation 8603340 Sun Aug 30 11:21:44 2009 found 3672019 hash collisions in 23132690 relations Sun Aug 30 11:23:26 2009 added 121221 free relations Sun Aug 30 11:23:26 2009 commencing duplicate removal, pass 2 Sun Aug 30 11:24:44 2009 found 3326171 duplicates and 19927739 unique relations Sun Aug 30 11:24:44 2009 memory use: 106.6 MB Sun Aug 30 11:24:44 2009 reading ideals above 19595264 Sun Aug 30 11:24:59 2009 commencing singleton removal, initial pass Sun Aug 30 11:30:51 2009 memory use: 298.4 MB Sun Aug 30 11:30:51 2009 reading all ideals from disk Sun Aug 30 11:30:51 2009 memory use: 326.5 MB Sun Aug 30 11:30:53 2009 commencing in-memory singleton removal Sun Aug 30 11:30:56 2009 begin with 19927739 relations and 19184707 unique ideals Sun Aug 30 11:31:18 2009 reduce to 8405921 relations and 5821694 ideals in 19 passes Sun Aug 30 11:31:18 2009 max relations containing the same ideal: 28 Sun Aug 30 11:31:20 2009 reading ideals above 100000 Sun Aug 30 11:31:20 2009 commencing singleton removal, initial pass Sun Aug 30 11:34:58 2009 memory use: 149.2 MB Sun Aug 30 11:34:58 2009 reading all ideals from disk Sun Aug 30 11:34:59 2009 memory use: 326.5 MB Sun Aug 30 11:35:01 2009 keeping 8264605 ideals with weight <= 200, target excess is 44720 Sun Aug 30 11:35:04 2009 commencing in-memory singleton removal Sun Aug 30 11:35:06 2009 begin with 8407054 relations and 8264605 unique ideals Sun Aug 30 11:35:35 2009 reduce to 8284360 relations and 8136440 ideals in 13 passes Sun Aug 30 11:35:35 2009 max relations containing the same ideal: 200 Sun Aug 30 11:35:45 2009 removing 604136 relations and 556114 ideals in 48022 cliques Sun Aug 30 11:35:46 2009 commencing in-memory singleton removal Sun Aug 30 11:35:48 2009 begin with 7680224 relations and 8136440 unique ideals Sun Aug 30 11:36:08 2009 reduce to 7647797 relations and 7547616 ideals in 10 passes Sun Aug 30 11:36:08 2009 max relations containing the same ideal: 195 Sun Aug 30 11:36:18 2009 removing 436373 relations and 388351 ideals in 48022 cliques Sun Aug 30 11:36:18 2009 commencing in-memory singleton removal Sun Aug 30 11:36:20 2009 begin with 7211424 relations and 7547616 unique ideals Sun Aug 30 11:36:36 2009 reduce to 7192976 relations and 7140672 ideals in 8 passes Sun Aug 30 11:36:36 2009 max relations containing the same ideal: 186 Sun Aug 30 11:36:48 2009 relations with 0 large ideals: 129 Sun Aug 30 11:36:48 2009 relations with 1 large ideals: 111 Sun Aug 30 11:36:48 2009 relations with 2 large ideals: 1351 Sun Aug 30 11:36:48 2009 relations with 3 large ideals: 17575 Sun Aug 30 11:36:48 2009 relations with 4 large ideals: 127018 Sun Aug 30 11:36:48 2009 relations with 5 large ideals: 533702 Sun Aug 30 11:36:48 2009 relations with 6 large ideals: 1356073 Sun Aug 30 11:36:48 2009 relations with 7+ large ideals: 5157017 Sun Aug 30 11:36:48 2009 commencing 2-way merge Sun Aug 30 11:37:02 2009 reduce to 4228031 relation sets and 4175727 unique ideals Sun Aug 30 11:37:02 2009 commencing full merge Sun Aug 30 11:39:22 2009 memory use: 438.0 MB Sun Aug 30 11:39:23 2009 found 2185706 cycles, need 2181927 Sun Aug 30 11:39:24 2009 weight of 2181927 cycles is about 153056632 (70.15/cycle) Sun Aug 30 11:39:24 2009 distribution of cycle lengths: Sun Aug 30 11:39:24 2009 1 relations: 318590 Sun Aug 30 11:39:24 2009 2 relations: 287686 Sun Aug 30 11:39:24 2009 3 relations: 265305 Sun Aug 30 11:39:24 2009 4 relations: 224441 Sun Aug 30 11:39:24 2009 5 relations: 193393 Sun Aug 30 11:39:24 2009 6 relations: 158988 Sun Aug 30 11:39:24 2009 7 relations: 134476 Sun Aug 30 11:39:24 2009 8 relations: 111474 Sun Aug 30 11:39:24 2009 9 relations: 91852 Sun Aug 30 11:39:24 2009 10+ relations: 395722 Sun Aug 30 11:39:24 2009 heaviest cycle: 28 relations Sun Aug 30 11:39:25 2009 commencing cycle optimization Sun Aug 30 11:39:32 2009 start with 12568120 relations Sun Aug 30 11:40:11 2009 pruned 267617 relations Sun Aug 30 11:40:11 2009 memory use: 335.1 MB Sun Aug 30 11:40:11 2009 distribution of cycle lengths: Sun Aug 30 11:40:11 2009 1 relations: 318590 Sun Aug 30 11:40:11 2009 2 relations: 293890 Sun Aug 30 11:40:11 2009 3 relations: 273827 Sun Aug 30 11:40:11 2009 4 relations: 228287 Sun Aug 30 11:40:11 2009 5 relations: 196248 Sun Aug 30 11:40:11 2009 6 relations: 159693 Sun Aug 30 11:40:11 2009 7 relations: 134312 Sun Aug 30 11:40:11 2009 8 relations: 110397 Sun Aug 30 11:40:11 2009 9 relations: 90366 Sun Aug 30 11:40:11 2009 10+ relations: 376317 Sun Aug 30 11:40:11 2009 heaviest cycle: 28 relations Sun Aug 30 11:40:24 2009 RelProcTime: 1471 Sun Aug 30 11:40:24 2009 Sun Aug 30 11:40:24 2009 commencing linear algebra Sun Aug 30 11:40:26 2009 read 2181927 cycles Sun Aug 30 11:40:33 2009 cycles contain 7124612 unique relations Sun Aug 30 11:47:52 2009 read 7124612 relations Sun Aug 30 11:48:08 2009 using 20 quadratic characters above 268435034 Sun Aug 30 11:49:08 2009 building initial matrix Sun Aug 30 11:51:23 2009 memory use: 814.7 MB Sun Aug 30 11:51:31 2009 read 2181927 cycles Sun Aug 30 11:55:11 2009 matrix is 2181750 x 2181927 (629.4 MB) with weight 206833828 (94.79/col) Sun Aug 30 11:55:11 2009 sparse part has weight 147540980 (67.62/col) Sun Aug 30 11:55:51 2009 filtering completed in 2 passes Sun Aug 30 11:55:52 2009 matrix is 2180999 x 2181176 (629.4 MB) with weight 206805813 (94.81/col) Sun Aug 30 11:55:52 2009 sparse part has weight 147535633 (67.64/col) Sun Aug 30 11:56:09 2009 read 2181176 cycles Sun Aug 30 12:02:33 2009 matrix is 2180999 x 2181176 (629.4 MB) with weight 206805813 (94.81/col) Sun Aug 30 12:02:33 2009 sparse part has weight 147535633 (67.64/col) Sun Aug 30 12:02:33 2009 saving the first 48 matrix rows for later Sun Aug 30 12:02:35 2009 matrix is 2180951 x 2181176 (604.3 MB) with weight 164620917 (75.47/col) Sun Aug 30 12:02:35 2009 sparse part has weight 145323930 (66.63/col) Sun Aug 30 12:02:35 2009 matrix includes 64 packed rows Sun Aug 30 12:02:35 2009 using block size 65536 for processor cache size 4096 kB Sun Aug 30 12:02:59 2009 commencing Lanczos iteration (4 threads) Sun Aug 30 12:02:59 2009 memory use: 673.2 MB Sun Aug 30 20:35:43 2009 lanczos halted after 34495 iterations (dim = 2180951) Sun Aug 30 20:35:49 2009 recovered 28 nontrivial dependencies Sun Aug 30 20:35:52 2009 BLanczosTime: 32128 Sun Aug 30 20:35:52 2009 Sun Aug 30 20:35:52 2009 commencing square root phase Sun Aug 30 20:35:52 2009 reading relations for dependency 1 Sun Aug 30 20:35:54 2009 read 1092247 cycles Sun Aug 30 20:35:57 2009 cycles contain 4349405 unique relations Sun Aug 30 20:41:33 2009 read 4349405 relations Sun Aug 30 20:42:16 2009 multiplying 3565232 relations Sun Aug 30 21:00:27 2009 multiply complete, coefficients have about 168.77 million bits Sun Aug 30 21:00:37 2009 initial square root is modulo 1139683 Sun Aug 30 21:22:39 2009 reading relations for dependency 2 Sun Aug 30 21:22:40 2009 read 1091237 cycles Sun Aug 30 21:22:44 2009 cycles contain 4347764 unique relations Sun Aug 30 21:29:18 2009 read 4347764 relations Sun Aug 30 21:29:59 2009 multiplying 3563378 relations Sun Aug 30 21:48:03 2009 multiply complete, coefficients have about 168.68 million bits Sun Aug 30 21:48:13 2009 initial square root is modulo 1131341 Sun Aug 30 22:10:07 2009 reading relations for dependency 3 Sun Aug 30 22:10:08 2009 read 1090577 cycles Sun Aug 30 22:10:12 2009 cycles contain 4345517 unique relations Sun Aug 30 22:15:38 2009 read 4345517 relations Sun Aug 30 22:16:19 2009 multiplying 3563306 relations Sun Aug 30 22:34:24 2009 multiply complete, coefficients have about 168.68 million bits Sun Aug 30 22:34:35 2009 initial square root is modulo 1131191 Sun Aug 30 22:56:32 2009 reading relations for dependency 4 Sun Aug 30 22:56:33 2009 read 1090876 cycles Sun Aug 30 22:56:37 2009 cycles contain 4348230 unique relations Sun Aug 30 23:02:54 2009 read 4348230 relations Sun Aug 30 23:03:36 2009 multiplying 3564124 relations Sun Aug 30 23:21:43 2009 multiply complete, coefficients have about 168.72 million bits Sun Aug 30 23:21:53 2009 initial square root is modulo 1135019 Sun Aug 30 23:43:48 2009 sqrtTime: 11276 Sun Aug 30 23:43:48 2009 prp46 factor: 1081532647714971214037755172969779401345844853 Sun Aug 30 23:43:48 2009 prp92 factor: 15536932645254557221822951817675878742208962257314811273026340883379604360838433963316815599 Sun Aug 30 23:43:48 2009 elapsed time 12:27:58
Aug 30, 2009 (2nd): By Jo Yeong Uk / GMP-ECM, GGNFS, Msieve v1.39 / Aug 30, 2009
(43·10¹⁷⁰-61)/9 = 4(7)₁₆₉1_<171> = 3⁴ · 2297 · 86142190922609442826319581_<26> · C140
C140 = P35 · P105
P35 = 61205871025572349031057520850672879_<35>
P105 = 487047071018647562838374099050351413427398683541739940812874899307923729937987987488512016099910123356097_<105>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 29810140212150119020193034504540165336135631922025659778353692043960704366721925412459175875355132428078825083113940577992345976016177193263 (140 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2242790170 Step 1 took 13962ms Step 2 took 10124ms ********** Factor found in step 2: 61205871025572349031057520850672879 Found probable prime factor of 35 digits: 61205871025572349031057520850672879 Probable prime cofactor 487047071018647562838374099050351413427398683541739940812874899307923729937987987488512016099910123356097 has 105 digits
(59·10¹⁶⁵-41)/9 = 6(5)₁₆₄1_<166> = 15853671262377575120216579_<26> · C141
C141 = P46 · P95
P46 = 6340161287912131268161125425786578533212741867_<46>
P95 = 65219782716166814592146317374475128145739944922584322010120403135302390427100230848435276962207_<95>

Number: 65551_165 N=413503941583081550029323061610568526119686926032409887198149321241700574934648467048889309789763186916268930747752107818183593351933005620469 ( 141 digits) SNFS difficulty: 166 digits. Divisors found: r1=6340161287912131268161125425786578533212741867 r2=65219782716166814592146317374475128145739944922584322010120403135302390427100230848435276962207 Version: Total time: 25.78 hours. Scaled time: 61.36 units (timescale=2.380). Factorization parameters were as follows: n: 413503941583081550029323061610568526119686926032409887198149321241700574934648467048889309789763186916268930747752107818183593351933005620469 m: 1000000000000000000000000000000000 deg: 5 c5: 59 c0: -41 skew: 0.93 type: snfs lss: 1 rlim: 4600000 alim: 4600000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4600000/4600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2300000, 4400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10023616 Max relations in full relation-set: Initial matrix: Pruned matrix : 759607 x 759855 Total sieving time: 23.19 hours. Total relation processing time: 1.02 hours. Matrix solve time: 1.18 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4600000,4600000,27,27,51,51,2.4,2.4,100000 total time: 25.78 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Aug 30, 2009: By Sinkiti Sibata / Msieve / Aug 30, 2009
(59·10¹⁵¹-41)/9 = 6(5)₁₅₀1_<152> = 786086982781_<12> · 435721903752358018180169_<24> · C117
C117 = P49 · P68
P49 = 4559565812653039995170667321098441921755424461139_<49>
P68 = 41976479907500678916377186105933586601154615587003436570164974072481_<68>

Number: 65551_151 N=191394522721757338189978481862379468868860410055039494993662461032118366979363583455183244670769264779036865753815859 ( 117 digits) SNFS difficulty: 152 digits. Divisors found: r1=4559565812653039995170667321098441921755424461139 (pp49) r2=41976479907500678916377186105933586601154615587003436570164974072481 (pp68) Version: Msieve-1.40 Total time: 22.57 hours. Scaled time: 47.06 units (timescale=2.085). Factorization parameters were as follows: name: 65551_151 n: 191394522721757338189978481862379468868860410055039494993662461032118366979363583455183244670769264779036865753815859 m: 1000000000000000000000000000000 deg: 5 c5: 590 c0: -41 skew: 0.59 type: snfs lss: 1 rlim: 2500000 alim: 2500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1250000, 2150001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 467967 x 468215 Total sieving time: 21.24 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.76 hours. Time per square root: 0.43 hours. Prototype def-par.txt line would be: snfs,152.000,5,0,0,0,0,0,0,0,0,2500000,2500000,27,27,50,50,2.4,2.4,100000 total time: 22.57 hours. --------- CPU info (if available) ----------
Aug 29, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 29, 2009
(44·10¹⁶⁹-53)/9 = 4(8)₁₆₈3_<170> = 17 · 43 · 1630423 · 21750516732549499949_<20> · C142
C142 = P48 · P94
P48 = 489641797116893462699294028241035350517514338379_<48>
P94 = 3851628881325874837178721243483272939017889163594114474066555739511475683749623855910191557521_<94>

Number: 48883_169 N=1885918487279731334844061215429615053174211390022725930251012918160514773580971772193004553379869884756817593843749606903596980083631836398459 ( 142 digits) SNFS difficulty: 171 digits. Divisors found: r1=489641797116893462699294028241035350517514338379 r2=3851628881325874837178721243483272939017889163594114474066555739511475683749623855910191557521 Version: Total time: 33.52 hours. Scaled time: 78.24 units (timescale=2.334). Factorization parameters were as follows: n: 1885918487279731334844061215429615053174211390022725930251012918160514773580971772193004553379869884756817593843749606903596980083631836398459 m: 10000000000000000000000000000000000 deg: 5 c5: 22 c0: -265 skew: 1.64 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11061459 Max relations in full relation-set: Initial matrix: Pruned matrix : 921196 x 921444 Total sieving time: 30.41 hours. Total relation processing time: 0.79 hours. Matrix solve time: 1.88 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000 total time: 33.52 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672349) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
(59·10¹⁵⁹-41)/9 = 6(5)₁₅₈1_<160> = 1451 · 6917 · 37094443609_<11> · 2598169745728791720663187707556303091_<37> · C106
C106 = P48 · P58
P48 = 820889968246951339790540386495386854270140538021_<48>
P58 = 8255872609163889121125670485890992574796509420461607010047_<58>

Number: 65551_159 N=6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987 ( 106 digits) Divisors found: r1=820889968246951339790540386495386854270140538021 r2=8255872609163889121125670485890992574796509420461607010047 Version: Total time: 5.41 hours. Scaled time: 12.69 units (timescale=2.348). Factorization parameters were as follows: name: 65551_159 n: 6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987 skew: 12582.78 # norm 1.29e+15 c5: 262440 c4: -4659048357 c3: -146542938404236 c2: 790340887867501438 c1: 8313308791385384666564 c0: -14544187091187097192015545 # alpha -7.04 Y1: 86304481709 Y0: -120893981641063169426 # Murphy_E 1.67e-09 # M 233941627322368526897049390385975758084765376780110111644521819338376892631029209741812043543819236488285 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1850001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7132778 Max relations in full relation-set: Initial matrix: Pruned matrix : 299772 x 300020 Polynomial selection time: 0.38 hours. Total sieving time: 4.16 hours. Total relation processing time: 0.59 hours. Matrix solve time: 0.21 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 5.41 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.61 BogoMIPS (lpj=2673805) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672349) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
(59·10¹⁴⁹-41)/9 = 6(5)₁₄₈1_<150> = 3² · 13 · 19851087923_<11> · 26776182667895359173751_<23> · C116
C116 = P54 · P62
P54 = 652082745253715773516074932609579615606989934537126869_<54>
P62 = 16165455891393350287819085890362832406948198797702538297578619_<62>

Number: 65551_149 N=10541214855937628876152464065866311686150262293869601020055860706093425225533958519391800940530932095752139904813911 ( 116 digits) SNFS difficulty: 151 digits. Divisors found: r1=652082745253715773516074932609579615606989934537126869 r2=16165455891393350287819085890362832406948198797702538297578619 Version: Total time: 10.94 hours. Scaled time: 26.12 units (timescale=2.387). Factorization parameters were as follows: n: 10541214855937628876152464065866311686150262293869601020055860706093425225533958519391800940530932095752139904813911 m: 1000000000000000000000000000000 deg: 5 c5: 59 c0: -410 skew: 1.47 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7377549 Max relations in full relation-set: Initial matrix: Pruned matrix : 392381 x 392629 Total sieving time: 10.17 hours. Total relation processing time: 0.39 hours. Matrix solve time: 0.31 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 10.94 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673794) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
Aug 29, 2009 (4th): By Erik Branger / GGNFS, Msieve / Aug 29, 2009
(59·10¹⁴⁵-41)/9 = 6(5)₁₄₄1_<146> = 211 · 844447 · 37668119627_<11> · C127
C127 = P42 · P42 · P44
P42 = 549690954084227334046373836255244354233007_<42>
P42 = 721044887110064073265612393855556722934303_<42>
P44 = 24643354074993241023553893354420056835203009_<44>

Number: 65551_145 N=9767439025466310689382920239378941208099550425943607238692087452651281025110190773764650914274716357618807670061234159412815089 ( 127 digits) SNFS difficulty: 146 digits. Divisors found: r1=549690954084227334046373836255244354233007 (pp42) r2=721044887110064073265612393855556722934303 (pp42) r3=24643354074993241023553893354420056835203009 (pp44) Version: Msieve v. 1.41 Total time: 14.27 hours. Scaled time: 11.19 units (timescale=0.784). Factorization parameters were as follows: n: 9767439025466310689382920239378941208099550425943607238692087452651281025110190773764650914274716357618807670061234159412815089 m: 100000000000000000000000000000 deg: 5 c5: 59 c0: -41 skew: 0.93 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2180001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 318356 x 318596 Total sieving time: 13.32 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.52 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 14.27 hours. --------- CPU info (if available) ----------
(49·10¹⁷¹-13)/9 = 5(4)₁₇₀3_<172> = 1309907 · 1509331 · 186135721123313863044793461731766127889_<39> · C122
C122 = P41 · P81
P41 = 78118283689308132829443292403611291227803_<41>
P81 = 189385269551937878693181478095539023949471844401877418236197269245497479472145737_<81>

Number: 54443_171 N=14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811 ( 122 digits) Divisors found: r1=78118283689308132829443292403611291227803 (pp41) r2=189385269551937878693181478095539023949471844401877418236197269245497479472145737 (pp81) Version: Msieve v. 1.42 Total time: 94.54 hours. Scaled time: 84.14 units (timescale=0.890). Factorization parameters were as follows: name: 54443_171 n: 14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811 skew: 100801.55 # norm 2.51e+016 c5: 15540 c4: -3524203548 c3: -420650336721402 c2: 65567099398070687185 c1: 4319439315112807051384690 c0: -690078891322799688013927425 # alpha -5.18 Y1: 25679226421157 Y0: -248731969491594434266556 # Murphy_E 2.31e-010 # M 413839379239698306525414216049804652849438324257727581695754799129246235176693693402226716314260713159272150579379954349 type: gnfs rlim: 4700000 alim: 4700000 lpbr: 27 lpba: 27 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4700000/4700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 53/53 Sieved algebraic special-q in [2350000, 4750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : submatrix x not Polynomial selection time: 6.85 hours. Total sieving time: 82.76 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.47 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: gnfs,121,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4700000,4700000,27,27,53,53,2.5,2.5,100000 total time: 94.54 hours. --------- CPU info (if available) ----------
Aug 29, 2009 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM / Aug 29, 2009
(59·10¹³⁶-41)/9 = 6(5)₁₃₅1_<137> = 311 · C135
C135 = P38 · P44 · P54
P38 = 26179380007226157021127248101170405337_<38>
P44 = 14297798976196798020082250427539153295127879_<44>
P54 = 563145436761579883955917094967740928748812991722141367_<54>

Number: n N=210789567702750982493747767059664165773490532332976062879599857091818506609503394069310468024294390853876384423008217220435869953554841 ( 135 digits) SNFS difficulty: 137 digits. Divisors found: Sat Aug 29 01:44:27 2009 prp38 factor: 26179380007226157021127248101170405337 Sat Aug 29 01:44:27 2009 prp44 factor: 14297798976196798020082250427539153295127879 Sat Aug 29 01:44:27 2009 prp54 factor: 563145436761579883955917094967740928748812991722141367 Sat Aug 29 01:44:27 2009 elapsed time 00:16:47 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.02 hours. Scaled time: 7.32 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_5_135_1 n: 210789567702750982493747767059664165773490532332976062879599857091818506609503394069310468024294390853876384423008217220435869953554841 m: 1000000000000000000000000000 deg: 5 c5: 590 c0: -41 skew: 0.59 type: snfs lss: 1 rlim: 1380000 alim: 1380000 lpbr: 26 lpba: 26 mfbr: 56 mfba: 56 rlambda: 2.3 alambda: 2.3 qintsize: 50000 Factor base limits: 1380000/1380000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 56/56 Sieved special-q in [690000, 1461797) Primes: RFBsize:105690, AFBsize:105947, largePrimes:3177187 encountered Relations: rels:3014745, finalFF:214239 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 323499 hash collisions in 3418073 relations Msieve: matrix is 225284 x 225532 (60.0 MB) Total sieving time: 3.96 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1380000,1380000,26,26,56,56,2.3,2.3,75000 total time: 4.02 hours. --------- CPU info (if available) ----------
(59·10¹⁵⁸-41)/9 = 6(5)₁₅₇1_<159> = 3³ · 7 · 449 · 1478429 · 8960605669_<10> · 972619078189867_<15> · C123
C123 = P48 · P76
P48 = 217923913046764811356626710395989581702567843659_<48>
P76 = 2751159983487564578438662871520344645588319823419937844950095840125164584947_<76>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 599543549019282937413245056494763681133772472976550903769136303031395960534601089463284130350567362781324328315687520801073 (123 digits) Using B1=2958000, B2=4281751120, polynomial Dickson(6), sigma=962280220 Step 1 took 25656ms Step 2 took 10953ms ********** Factor found in step 2: 217923913046764811356626710395989581702567843659 Found probable prime factor of 48 digits: 217923913046764811356626710395989581702567843659 Probable prime cofactor 2751159983487564578438662871520344645588319823419937844950095840125164584947 has 76 digits
Aug 29, 2009 (2nd): By Sinkiti Sibata / Msieve / Aug 29, 2009
(59·10¹⁴⁸-41)/9 = 6(5)₁₄₇1_<149> = 26728403302199_<14> · 533273908107113_<15> · C121
C121 = P47 · P74
P47 = 90745693245729358517082419197212783245968267481_<47>
P74 = 50682745018821389408300370756291566831716285785457828913075299356070158233_<74>

Number: 65551_148 N=4599240832329483446438911438293912091197844869217679103966516381860976339020948840206178483537950205688304180256538321073 ( 121 digits) SNFS difficulty: 151 digits. Divisors found: r1=90745693245729358517082419197212783245968267481 (pp47) r2=50682745018821389408300370756291566831716285785457828913075299356070158233 (pp74) Version: Msieve-1.40 Total time: 21.67 hours. Scaled time: 43.75 units (timescale=2.019). Factorization parameters were as follows: name: 65551_148 n: 4599240832329483446438911438293912091197844869217679103966516381860976339020948840206178483537950205688304180256538321073 m: 500000000000000000000000000000 deg: 5 c5: 472 c0: -1025 skew: 1.17 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 *1 These parameters were not fully adjusted. The approximate expressions which were Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 2050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 437631 x 437879 Total sieving time: 20.54 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.67 hours. Time per square root: 0.33 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 21.67 hours. --------- CPU info (if available) ----------
Aug 29, 2009: By Dmitry Domanov / ECMNET / Aug 29, 2009
(59·10¹⁵³-41)/9 = 6(5)₁₅₂1_<154> = 71 · C152
C152 = P38 · C115
P38 = 31547078069965587199548803369110194703_<38>
C115 = [2926793035581032985985372497805728366509485826817219355709884856091272013245694366598974490036970962573306601872327_<115>]

C152=P38*C115 C152=31547078069965587199548803369110194703<38>*2926793035581032985985372497805728366509485826817219355709884856091272013245694366598974490036970962573306601872327<115>
(59·10¹⁵⁴-41)/9 = 6(5)₁₅₃1_<155> = 3797 · C152
C152 = P36 · C117
P36 = 159093639765504071562915217735497341_<36>
C117 = [108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863_<117>]

C152=P36*C117 C152=159093639765504071562915217735497341<36>*108521574776952115645717588039054192051980803534687113921049522702179053232133262478345190473870479199937478718448863<117>
Aug 28, 2009 (4th): By Jo Yeong Uk / GGNFS, Msieve v1.39, YAFU 1.10, GMP-ECM / Aug 28, 2009
(59·10¹¹⁰-41)/9 = 6(5)₁₀₉1_<111> = 3 · 7² · 103 · 16665469 · C100
C100 = P36 · P65
P36 = 100569868188240422212672513519393283_<36>
P65 = 25832683422264164337538558517870859590637727898173160332304112293_<65>

Number: 65551_110 N=2597989566725650502849872479791838917651440564302408490731586236718833328085585735067306147261927919 ( 100 digits) SNFS difficulty: 111 digits. Divisors found: r1=100569868188240422212672513519393283 r2=25832683422264164337538558517870859590637727898173160332304112293 Version: Total time: 0.38 hours. Scaled time: 0.91 units (timescale=2.388). Factorization parameters were as follows: n: 2597989566725650502849872479791838917651440564302408490731586236718833328085585735067306147261927919 m: 10000000000000000000000 deg: 5 c5: 59 c0: -41 skew: 0.93 type: snfs lss: 1 rlim: 320000 alim: 320000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 320000/320000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [160000, 300001) Primes: rational ideals reading, algebraic ideals reading, Relations: 1042212 Max relations in full relation-set: Initial matrix: Pruned matrix : 40915 x 41147 Total sieving time: 0.34 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,320000,320000,25,25,44,44,2.2,2.2,20000 total time: 0.38 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
(59·10¹³⁰-41)/9 = 6(5)₁₂₉1_<131> = 863 · 12380033 · 578081849930021_<15> · 1286027650661759_<16> · C91
C91 = P46 · P46
P46 = 1874536995577468817771844750195374139545485531_<46>
P46 = 4402944871230901384323087592619302612598638441_<46>

08/27/09 23:30:17 v1.10 @ 조영욱-PC, starting SIQS on c91: 8253483050610399201614656565498306273254000866702463502996230748570396254465732878865897171 08/27/09 23:30:17 v1.10 @ 조영욱-PC, random seeds: 131344719, 45773372 08/27/09 23:30:18 v1.10 @ 조영욱-PC, ==== sieve params ==== 08/27/09 23:30:18 v1.10 @ 조영욱-PC, n = 91 digits, 307 bits 08/27/09 23:30:18 v1.10 @ 조영욱-PC, factor base: 70662 primes (max prime = 1893187) 08/27/09 23:30:18 v1.10 @ 조영욱-PC, single large prime cutoff: 227182440 (120 * pmax) 08/27/09 23:30:18 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 08/27/09 23:30:18 v1.10 @ 조영욱-PC, double large prime cutoff: 1100207414487985 08/27/09 23:30:18 v1.10 @ 조영욱-PC, using 16 large prime slices of factor base 08/27/09 23:30:18 v1.10 @ 조영욱-PC, buckets hold 1024 elements 08/27/09 23:30:18 v1.10 @ 조영욱-PC, sieve interval: 11 blocks of size 65536 08/27/09 23:30:18 v1.10 @ 조영욱-PC, polynomial A has ~ 12 factors 08/27/09 23:30:18 v1.10 @ 조영욱-PC, using multiplier of 19 08/27/09 23:30:18 v1.10 @ 조영욱-PC, using small prime variation correction of 22 bits 08/27/09 23:30:18 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 08/27/09 23:30:18 v1.10 @ 조영욱-PC, trial factoring cutoff at 97 bits 08/27/09 23:30:18 v1.10 @ 조영욱-PC, ==== sieving started ==== 08/28/09 00:26:05 v1.10 @ 조영욱-PC, sieve time = 1542.6450, relation time = 702.4350, poly_time = 1100.0520 08/28/09 00:26:05 v1.10 @ 조영욱-PC, 70735 relations found: 20355 full + 50380 from 853952 partial, using 471953 polys (230 A polys) 08/28/09 00:26:05 v1.10 @ 조영욱-PC, on average, sieving found 1.85 rels/poly and 261.20 rels/sec 08/28/09 00:26:05 v1.10 @ 조영욱-PC, trial division touched 26612272 sieve locations out of 680458059776 08/28/09 00:26:05 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 08/28/09 00:26:05 v1.10 @ 조영욱-PC, begin with 874307 relations 08/28/09 00:26:06 v1.10 @ 조영욱-PC, reduce to 163723 relations in 9 passes 08/28/09 00:26:07 v1.10 @ 조영욱-PC, recovered 163723 relations 08/28/09 00:26:07 v1.10 @ 조영욱-PC, recovered 138447 polynomials 08/28/09 00:26:07 v1.10 @ 조영욱-PC, attempting to build 70735 cycles 08/28/09 00:26:07 v1.10 @ 조영욱-PC, found 70735 cycles in 4 passes 08/28/09 00:26:07 v1.10 @ 조영욱-PC, distribution of cycle lengths: 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 1 : 20355 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 2 : 15712 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 3 : 13220 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 4 : 8823 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 5 : 5767 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 6 : 3219 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 7 : 1799 08/28/09 00:26:07 v1.10 @ 조영욱-PC, length 9+: 1840 08/28/09 00:26:07 v1.10 @ 조영욱-PC, largest cycle: 19 relations 08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix is 70662 x 70735 (17.6 MB) with weight 4054145 (57.31/col) 08/28/09 00:26:08 v1.10 @ 조영욱-PC, sparse part has weight 4054145 (57.31/col) 08/28/09 00:26:08 v1.10 @ 조영욱-PC, filtering completed in 3 passes 08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix is 65082 x 65146 (16.4 MB) with weight 3786317 (58.12/col) 08/28/09 00:26:08 v1.10 @ 조영욱-PC, sparse part has weight 3786317 (58.12/col) 08/28/09 00:26:08 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix is 65034 x 65146 (11.3 MB) with weight 3022515 (46.40/col) 08/28/09 00:26:08 v1.10 @ 조영욱-PC, sparse part has weight 2318790 (35.59/col) 08/28/09 00:26:08 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 08/28/09 00:26:08 v1.10 @ 조영욱-PC, using block size 26058 for processor cache size 4096 kB 08/28/09 00:26:09 v1.10 @ 조영욱-PC, commencing Lanczos iteration 08/28/09 00:26:09 v1.10 @ 조영욱-PC, memory use: 9.9 MB 08/28/09 00:26:30 v1.10 @ 조영욱-PC, lanczos halted after 1030 iterations (dim = 65030) 08/28/09 00:26:30 v1.10 @ 조영욱-PC, recovered 15 nontrivial dependencies 08/28/09 00:26:31 v1.10 @ 조영욱-PC, prp46 = 4402944871230901384323087592619302612598638441 08/28/09 00:26:33 v1.10 @ 조영욱-PC, prp46 = 1874536995577468817771844750195374139545485531 08/28/09 00:26:33 v1.10 @ 조영욱-PC, Lanczos elapsed time = 25.0990 seconds. 08/28/09 00:26:33 v1.10 @ 조영욱-PC, Sqrt elapsed time = 3.2240 seconds. 08/28/09 00:26:33 v1.10 @ 조영욱-PC, SIQS elapsed time = 3375.6350 seconds. 08/28/09 00:26:33 v1.10 @ 조영욱-PC, 08/28/09 00:26:33 v1.10 @ 조영욱-PC,
(59·10¹²⁸-41)/9 = 6(5)₁₂₇1_<129> = 3 · 7 · 11273 · 807217798013115349249_<21> · C103
C103 = P35 · P69
P35 = 15687391337389820067594699621928049_<35>
P69 = 218680088493350538687823046086955801253237178180069851711522664388347_<69>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 3430520125890226509593731402569423321015647527360602456706265755347841481793027317214936054879428045003 (103 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6225541169 Step 1 took 3463ms Step 2 took 3682ms ********** Factor found in step 2: 15687391337389820067594699621928049 Found probable prime factor of 35 digits: 15687391337389820067594699621928049 Probable prime cofactor 218680088493350538687823046086955801253237178180069851711522664388347 has 69 digits
(59·10¹³²-41)/9 = 6(5)₁₃₁1_<133> = 19 · 83 · 2161 · 2602723 · C120
C120 = P35 · P86
P35 = 64762468536958753275997370026592189_<35>
P86 = 11412261060476583010801648653588374466659404427949117412495467433944876668021019371489_<86>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 739086197864674243080103063204723838549459620630445797290182833000541981305222698078503131350548820404722187029296699421 (120 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3807268069 Step 1 took 4180ms Step 2 took 4041ms ********** Factor found in step 2: 64762468536958753275997370026592189 Found probable prime factor of 35 digits: 64762468536958753275997370026592189 Probable prime cofactor 11412261060476583010801648653588374466659404427949117412495467433944876668021019371489 has 86 digits
(59·10¹⁶¹-41)/9 = 6(5)₁₆₀1_<162> = 3 · 13² · 29 · 4703 · 8394739 · 3133872767_<10> · 143369462659_<12> · 6687547849938316622715871634891_<31> · C96
C96 = P39 · P58
P39 = 356847838604780119196330765207415979007_<39>
P58 = 1053254630446441697498609349401656856796194164343781800341_<58>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 375851638375289155490915074834142837946749360995064073843851662872671638502051544695517521441387 (96 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5608720449 Step 1 took 2980ms Step 2 took 3260ms ********** Factor found in step 2: 356847838604780119196330765207415979007 Found probable prime factor of 39 digits: 356847838604780119196330765207415979007 Probable prime cofactor 1053254630446441697498609349401656856796194164343781800341 has 58 digits
(38·10¹⁶⁹-11)/9 = 4(2)₁₆₈1_<170> = 17² · 83 · 211 · 2339 · 244251602108399660808017_<24> · C137
C137 = P50 · P88
P50 = 12643456665765147374218786433570546868392699029511_<50>
P88 = 1154912892544551407467844162921108648037743984077350799609066744377902172336659747050721_<88>

Number: 42221_169 N=14602091109620515869366332015142728586054934512934342589581239347419963235977351626438610141371466520699267476440359057526064881192827431 ( 137 digits) SNFS difficulty: 171 digits. Divisors found: r1=12643456665765147374218786433570546868392699029511 r2=1154912892544551407467844162921108648037743984077350799609066744377902172336659747050721 Version: Total time: 39.39 hours. Scaled time: 94.03 units (timescale=2.387). Factorization parameters were as follows: n: 14602091109620515869366332015142728586054934512934342589581239347419963235977351626438610141371466520699267476440359057526064881192827431 m: 10000000000000000000000000000000000 deg: 5 c5: 19 c0: -55 skew: 1.24 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 5900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11130436 Max relations in full relation-set: Initial matrix: Pruned matrix : 1006398 x 1006645 Total sieving time: 35.52 hours. Total relation processing time: 1.32 hours. Matrix solve time: 2.29 hours. Time per square root: 0.26 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000 total time: 39.39 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5344.67 BogoMIPS (lpj=2672339) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342)
(59·10¹⁵⁹-41)/9 = 6(5)₁₅₈1_<160> = 1451 · 6917 · 37094443609_<11> · C143
C143 = P37 · C106
P37 = 2598169745728791720663187707556303091_<37>
C106 = [6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987_<106>]

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 17608219878832569939402941493323999511486423867559456103886959410813000481338848062703009217991518592534765451863274229281547530390998016286817 (143 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=6442492946 Step 1 took 4048ms Step 2 took 2450ms ********** Factor found in step 2: 2598169745728791720663187707556303091 Found probable prime factor of 37 digits: 2598169745728791720663187707556303091 Composite cofactor 6777163003987420249369446581356217664161110220076196504409799447202003922532945122069823146006361732496987 has 106 digits
Aug 28, 2009 (3rd): By Robert Backstrom / GGNFS, GMP-ECM, Msieve / Aug 28, 2009
(59·10¹¹⁸-41)/9 = 6(5)₁₁₇1_<119> = 71 · C117
C117 = P48 · P70
P48 = 342040803041321313688302451689958483852221604999_<48>
P70 = 2699437247460560632206497429854420932366137288553121858772250208311119_<70>

Number: n N=923317683881064162754303599374021909233176838810641627543035993740219092331768388106416275430359937402190923317683881 ( 117 digits) SNFS difficulty: 121 digits. Divisors found: r1=342040803041321313688302451689958483852221604999 (pp48) r2=2699437247460560632206497429854420932366137288553121858772250208311119 (pp70) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.60 hours. Scaled time: 2.91 units (timescale=1.823). Factorization parameters were as follows: name: KA_6_5_117_1 n: 923317683881064162754303599374021909233176838810641627543035993740219092331768388106416275430359937402190923317683881 m: 500000000000000000000000 deg: 5 c5: 472 c0: -1025 skew: 1.17 type: snfs lss: 1 rlim: 740000 alim: 740000 mfbr: 56 mfba: 56 rlambda: 2.2 alambda: 2.2 qintsize: 50000 Factor base limits: 740000/740000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 56/56 Sieved rational special-q in [370000, 720001) Primes: RFBsize:59531, AFBsize:59694, largePrimes:1359196 encountered Relations: rels:1337738, finalFF:155412 Max relations in full relation-set: 48 Initial matrix: 119292 x 155412 with sparse part having weight 7787649. Pruned matrix : 106776 x 107436 with weight 4030051. Total sieving time: 1.49 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Total square root time: 0.05 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,740000,740000,25,25,56,56,2.2,2.2,50000 total time: 1.60 hours. --------- CPU info (if available) ----------
(59·10¹¹⁹-41)/9 = 6(5)₁₁₈1_<120> = 3 · 13 · 547 · 556399 · 31606445333_<11> · C100
C100 = P34 · P67
P34 = 1238586755744250042256057931648171_<34>
P67 = 1410811987959398448543925216694404844029838755220880952470146831371_<67>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 1747413043131727277788190198313073799579267718733141705256364062479384714596122432332591695237572441 (100 digits) Using B1=726000, B2=696728352, polynomial Dickson(3), sigma=672678217 Step 1 took 5031ms Step 2 took 2625ms ********** Factor found in step 2: 1238586755744250042256057931648171 Found probable prime factor of 34 digits: 1238586755744250042256057931648171 Probable prime cofactor 1410811987959398448543925216694404844029838755220880952470146831371 has 67 digits
(16·10²²¹-61)/9 = 1(7)₂₂₀1_<222> = 3 · 11 · C220
C220 = P74 · P147
P74 = 40547480142119922688518914038786161136818885750756170028782710211441154919_<74>
P147 = 132861656712651410768724637841254958549779105856049539596201523367987125563433527252580925341831118918802493988686721629211532202122209163723587773_<147>

Number: n N=5387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387 ( 220 digits) SNFS difficulty: 222 digits. Divisors found: Fri Aug 28 17:17:55 2009 prp74 factor: 40547480142119922688518914038786161136818885750756170028782710211441154919 Fri Aug 28 17:17:55 2009 prp147 factor: 132861656712651410768724637841254958549779105856049539596201523367987125563433527252580925341831118918802493988686721629211532202122209163723587773 Fri Aug 28 17:17:55 2009 elapsed time 67:04:23 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 174.43 hours. Scaled time: 351.30 units (timescale=2.014). Factorization parameters were as follows: name: KA_1_7_220_1 n: 5387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387205387 m: 10000000000000000000000000000000000000 deg: 6 c6: 8 c0: -305 skew: 1.83 type: snfs lss: 1 rlim: 36000000 alim: 36000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 36000000/36000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [18000000, 54149990) Primes: RFBsize:2204262, AFBsize:2201981, largePrimes:38297939 encountered Relations: rels:36171342, finalFF:1790359 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 9529631 hash collisions in 52517034 relations Msieve: matrix is 5639739 x 5639987 (1521.0 MB) Total sieving time: 172.55 hours. Total relation processing time: 1.88 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,222,6,0,0,0,0,0,0,0,0,36000000,36000000,29,29,58,58,2.6,2.6,100000 total time: 174.43 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352028k/3407296k available (3120k kernel code, 53984k reserved, 1898k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.41 BogoMIPS (lpj=2830706) Calibrating delay using timer specific routine.. 5660.90 BogoMIPS (lpj=2830451) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Total of 4 processors activated (22644.14 BogoMIPS).
c220 is the third largest number factored by SNFS in our tables so far. Congratulations!
Aug 28, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.3, yafu, Msieve / Aug 28, 2009
(59·10¹⁴²-41)/9 = 6(5)₁₄₁1_<143> = 131 · 1402671779_<10> · 3596836632895354892741_<22> · C110
C110 = P31 · P39 · P42
P31 = 1279201868994144050132194828067_<31>
P39 = 137662433006997570220530848318162243587_<39>
P42 = 563257402843915535764008602767320453683491_<42>

Input number is 99188525553478613740693018714173592981572951837275851680687204631968974415083826327584353647304252763642664539 (110 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3055685713 Step 1 took 2305ms Step 2 took 1920ms ********** Factor found in step 2: 1279201868994144050132194828067 Found probable prime factor of 31 digits: 1279201868994144050132194828067 Composite cofactor has 80 digits starting SIQS on c80: 77539384484695965128406068996129563971417687858859427676654726298502214942522217 ==== sieve params ==== n = 80 digits, 266 bits ... Lanczos elapsed time = 4.8700 seconds. Sqrt elapsed time = 0.5300 seconds. SIQS elapsed time = 379.4000 seconds. ***factors found*** PRP39 = 137662433006997570220530848318162243587 PRP42 = 563257402843915535764008602767320453683491
(59·10¹⁴⁷-41)/9 = 6(5)₁₄₆1_<148> = 3863 · 28901 · 8004709 · 77945136156599114050070531_<26> · C107
C107 = P33 · P75
P33 = 266941962748313436907550064124241_<33>
P75 = 352549827314674485749210699129788765635093418756045159371124172879548044443_<75>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1124467645 Step 1 took 6828ms Step 2 took 4264ms ********** Factor found in step 2: 266941962748313436907550064124241 Found probable prime factor of 33 digits: 266941962748313436907550064124241 Probable prime cofactor has 75 digits
(59·10¹⁸⁵-41)/9 = 6(5)₁₈₄1_<186> = 3³ · 13 · C184
C184 = P31 · P153
P31 = 3314037138425310906358457868773_<31>
P153 = 563566299183015474614878269645043450470219877270863059769326842164610494746548875667368937571772996793911384692710424597648306758405487025010001461232237_<153>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3092775926 Step 1 took 8885ms Step 2 took 4720ms ********** Factor found in step 2: 3314037138425310906358457868773 Found probable prime factor of 31 digits: 3314037138425310906358457868773 Probable prime cofactor has 153 digits
(59·10¹⁷⁶-41)/9 = 6(5)₁₇₅1_<177> = 3² · 7 · 241 · 47977 · 93149814203_<11> · C157
C157 = P38 · P120
P38 = 38625847807622427747634970352985604971_<38>
P120 = 250125980536769192609880404461832864559611828012339046983407808013266788748920882215142885060832727293121873895915028897_<120>

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=1022211378 Step 1 took 7720ms Step 2 took 4092ms ********** Factor found in step 2: 38625847807622427747634970352985604971 Found probable prime factor of 38 digits: 38625847807622427747634970352985604971 Probable prime cofactor has 120 digits
(59·10¹⁴⁰-41)/9 = 6(5)₁₃₉1_<141> = 3² · 7 · 2319241 · C133
C133 = P34 · P36 · P64
P34 = 1121072026810203394520355219374897_<34>
P36 = 665636968570409833311374016398251961_<36>
P64 = 6012458927193535206829524119375218118645993092105672468842645041_<64>

SNFS difficulty: 141 digits. Divisors found: r1=1121072026810203394520355219374897 (pp34) r2=665636968570409833311374016398251961 (pp36) r3=6012458927193535206829524119375218118645993092105672468842645041 (pp64) Version: Msieve v. 1.43 Total time: 2.99 hours. Scaled time: 7.17 units (timescale=2.400). Factorization parameters were as follows: n: 4486659100532058682304100237524721368070693704956523410204305520201252181384187214255470781348572114315447299528442166629976061308697 m: 10000000000000000000000000000 deg: 5 c5: 59 c0: -41 skew: 0.93 type: snfs lss: 1 rlim: 1610000 alim: 1610000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1610000/1610000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [805000, 1605001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 251292 x 251517 Total sieving time: 2.84 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1610000,1610000,26,26,48,48,2.3,2.3,100000 total time: 2.99 hours.
Aug 28, 2009: By Erik Branger / GGNFS, Msieve / Aug 28, 2009
(59·10¹¹¹-41)/9 = 6(5)₁₁₀1_<112> = C112
C112 = P34 · P79
P34 = 2453439594373098072663247600625437_<34>
P79 = 2671985717761528403081198923694369774910242295609051984693196496700468164596523_<79>

Number: 65551_111 N=6555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 ( 112 digits) SNFS difficulty: 112 digits. Divisors found: r1=2453439594373098072663247600625437 (pp34) r2=2671985717761528403081198923694369774910242295609051984693196496700468164596523 (pp79) Version: Msieve v. 1.41 Total time: 1.74 hours. Scaled time: 1.37 units (timescale=0.788). Factorization parameters were as follows: n: 6555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555551 m: 10000000000000000000000 deg: 5 c5: 590 c0: -41 skew: 0.59 type: snfs lss: 1 rlim: 530000 alim: 530000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 530000/530000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [265000, 465001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 53595 x 53823 Total sieving time: 1.69 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,112.000,5,0,0,0,0,0,0,0,0,530000,530000,25,25,45,45,2.2,2.2,50000 total time: 1.74 hours. --------- CPU info (if available) ----------
Aug 27, 2009 (3rd): By Serge Batalov / GMP-ECM 6.2.3 / Aug 27, 2009
4·10²⁴³+9 = 4(0)₂₄₂9_<244> = 211 · 761 · C239
C239 = P42 · P198
P42 = 127566948277192337869764297638109721127023_<42>
P198 = 195278627055004260165165796713698923970426519764143364350420080659555185314378363696270057757429282480559027603944657848259735353558435498871600913917817557530384015450970490735110900823076695659173_<198>

Run 578 out of 1000: Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3161935447 Step 1 took 57743ms Step 2 took 20450ms ********** Factor found in step 2: 127566948277192337869764297638109721127023 Found probable prime factor of 42 digits: 127566948277192337869764297638109721127023 Probable prime cofactor has 198 digits
4·10²⁰⁴+9 = 4(0)₂₀₃9_<205> = 13³ · 3163073222102835073_<19> · C183
C183 = P33 · C151
P33 = 104371341092297168434106963028253_<33>
C151 = [5514922642801281170779376780759437194775023248270464884245911662908683979158794827643748726590188350303750194354785166138207825960686703194983314150313_<151>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3928819928 Step 1 took 12684ms Step 2 took 6453ms ********** Factor found in step 2: 104371341092297168434106963028253 Found probable prime factor of 33 digits: 104371341092297168434106963028253 Composite cofactor has 151 digits
Aug 27, 2009 (2nd): Factorizations of 655...551 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Aug 27, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 27, 2009
(34·10¹⁶⁹+11)/9 = 3(7)₁₆₈9_<170> = 3³ · 13 · 6316473139_<10> · 407799232266689_<15> · 75988493960251357_<17> · C126
C126 = P53 · P74
P53 = 18996040647697883281745471417581144798771086079754053_<53>
P74 = 28946583100012908073644120379111826298817121794389208345765758626662639919_<74>

Number: 37779_169 N=549870469179809804400773189900652481997984884146536985427414341642160967172160491609374388356461473305517418822641431219841707 ( 126 digits) SNFS difficulty: 171 digits. Divisors found: r1=18996040647697883281745471417581144798771086079754053 r2=28946583100012908073644120379111826298817121794389208345765758626662639919 Version: Total time: 35.34 hours. Scaled time: 84.18 units (timescale=2.382). Factorization parameters were as follows: n: 549870469179809804400773189900652481997984884146536985427414341642160967172160491609374388356461473305517418822641431219841707 m: 10000000000000000000000000000000000 deg: 5 c5: 17 c0: 55 skew: 1.26 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11191619 Max relations in full relation-set: Initial matrix: Pruned matrix : 933173 x 933421 Total sieving time: 32.04 hours. Total relation processing time: 1.13 hours. Matrix solve time: 1.94 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,52,52,2.4,2.4,100000 total time: 35.34 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672380)
Aug 26, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 26, 2009
(37·10¹⁸⁷+71)/9 = 4(1)₁₈₆9_<188> = 7 · 131² · 347 · 449 · 787 · 3793 · 54751 · 98240367022528967_<17> · 11521275019116676381_<20> · C131
C131 = P39 · P92
P39 = 469202909278931356117976919565489527769_<39>
P92 = 25307073155146640842672255497156160022227569263192069413856806792430390779517568555111001253_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3909651050 Step 1 took 38287ms Step 2 took 14195ms ********** Factor found in step 2: 469202909278931356117976919565489527769 Found probable prime factor of 39 digits: 469202909278931356117976919565489527769 Probable prime cofactor 25307073155146640842672255497156160022227569263192069413856806792430390779517568555111001253 has 92 digits
(7·10²⁰⁵-43)/9 = (7)₂₀₄3_<205> = 3⁴ · 17 · C202
C202 = P62 · P69 · P72
P62 = 62604108974342978505062826478040576438184094528258457506805873_<62>
P69 = 662021298149734281561229659528509403900190047328271154405447199062439_<69>
P72 = 136284601949026682390730569825694949184102512515689530468924678839170267_<72>

Number: 77773_205 N=5648349874929395626563382554667957718066650528524166868393447914145081901073186476236585169047042685386911966432663600419591704994755103687565561203905430484951182118938110223513273622206084079722423949 ( 202 digits) SNFS difficulty: 205 digits. Divisors found: r1=62604108974342978505062826478040576438184094528258457506805873 r2=662021298149734281561229659528509403900190047328271154405447199062439 r3=136284601949026682390730569825694949184102512515689530468924678839170267 Version: Total time: 1118.63 hours. Scaled time: 2254.03 units (timescale=2.015). Factorization parameters were as follows: n: 5648349874929395626563382554667957718066650528524166868393447914145081901073186476236585169047042685386911966432663600419591704994755103687565561203905430484951182118938110223513273622206084079722423949 m: 100000000000000000000000000000000000000000 deg: 5 c5: 7 c0: -43 skew: 1.44 type: snfs lss: 1 rlim: 18900000 alim: 18900000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 18900000/18900000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [9450000, 21450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3577131 x 3577378 Total sieving time: 1118.63 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,205,5,0,0,0,0,0,0,0,0,18900000,18900000,29,29,56,56,2.6,2.6,100000 total time: 1118.63 hours. --------- CPU info (if available) ----------
Aug 26, 2009: By Erik Branger / GGNFS, Msieve / Aug 26, 2009
(34·10¹⁶²+11)/9 = 3(7)₁₆₁9_<163> = 47 · 459443 · 67124546794083294248340603185287579_<35> · C121
C121 = P60 · P62
P60 = 106851167940478740045730236724328448611032403830368245522011_<60>
P62 = 24391935925025616413012597364043838783569401954353983491549671_<62>

Number: 37779_162 N=2606306841918308784669025209898688038053573715705451307168694698444179234703434235423308619590868129220762915004730308381 ( 121 digits) SNFS difficulty: 164 digits. Divisors found: r1=106851167940478740045730236724328448611032403830368245522011 (pp60) r2=24391935925025616413012597364043838783569401954353983491549671 (pp62) Version: Msieve v. 1.42 Total time: 59.21 hours. Scaled time: 23.39 units (timescale=0.395). Factorization parameters were as follows: n: 2606306841918308784669025209898688038053573715705451307168694698444179234703434235423308619590868129220762915004730308381 m: 200000000000000000000000000000000 deg: 5 c5: 425 c0: 44 skew: 0.64 type: snfs lss: 1 rlim: 3800000 alim: 3800000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3800000/3800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1900000, 4100001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 728523 x 728749 Total sieving time: 56.59 hours. Total relation processing time: 0.26 hours. Matrix solve time: 2.13 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,164.000,5,0,0,0,0,0,0,0,0,3800000,3800000,27,27,51,51,2.4,2.4,100000 total time: 59.21 hours. --------- CPU info (if available) ----------
Aug 25, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 25, 2009
(32·10¹⁶⁹-23)/9 = 3(5)₁₆₈3_<170> = 3² · 11 · 1823 · 2846155130424323406378163_<25> · C140
C140 = P49 · P92
P49 = 3054037465657598396665128463543860241767984014899_<49>
P92 = 22664841036145811481509986875433404714496667158274671465882815159605493593530416205438845997_<92>

Number: 35559_169 N=69219273677563090593398149236428754097982185713146430612942470417139285929049376313365862167983876981615989343694701114817723025993414509303 ( 140 digits) SNFS difficulty: 171 digits. Divisors found: r1=3054037465657598396665128463543860241767984014899 r2=22664841036145811481509986875433404714496667158274671465882815159605493593530416205438845997 Version: Total time: 26.26 hours. Scaled time: 62.73 units (timescale=2.389). Factorization parameters were as follows: n: 69219273677563090593398149236428754097982185713146430612942470417139285929049376313365862167983876981615989343694701114817723025993414509303 m: 20000000000000000000000000000000000 deg: 5 c5: 1 c0: -230 skew: 2.97 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 4800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 10687531 Max relations in full relation-set: Initial matrix: Pruned matrix : 861414 x 861662 Total sieving time: 23.85 hours. Total relation processing time: 0.67 hours. Matrix solve time: 1.66 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000 total time: 26.26 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.62 BogoMIPS (lpj=2673813) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672386) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Aug 25, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 25, 2009
8·10¹⁹⁸+3 = 8(0)₁₉₇3_<199> = 11 · 53 · C197
C197 = P43 · P155
P43 = 1350678383321052486001773788083398163612589_<43>
P155 = 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969_<155>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=184675988 Step 1 took 75436ms Step 2 took 22771ms ********** Factor found in step 2: 1350678383321052486001773788083398163612589 Found probable prime factor of 43 digits: 1350678383321052486001773788083398163612589 Probable prime cofactor 10159433288577617053454552915986316337776945515442442225397613087026136705762770406500515286186663991881893416281217389552885939501195077102302205387682969 has 155 digits
Aug 25, 2009: By Dmitry Domanov / ECMNET, GMP-ECM, GGNFS/msieve 1.42 / Aug 25, 2009
(16·10²⁴⁴-7)/9 = 1(7)₂₄₄_<245> = 357131 · 5718499 · 50074501 · 49725910634419_<14> · C211
C211 = P50 · P162
P50 = 18626347316752091887613730912259192759279958920129_<50>
P162 = 187689856289552606645258672395266771629129914562572777562468039096119103199366120307762823572047220965155854278003711101806936593196982626950879534048742843552783_<162>

C211=P50*P162 C211=18626347316752091887613730912259192759279958920129<50>*187689856289552606645258672395266771629129914562572777562468039096119103199366120307762823572047220965155854278003711101806936593196982626950879534048742843552783<162> Method=ECM B1=11000000 Sigma=1786901496
(2·10²⁰⁵+1)/3 = (6)₂₀₄7_<205> = 7 · C204
C204 = P50 · P155
P50 = 48640687651801423804337056354992853346324870893769_<50>
P155 = 19579923688551731244546269150496163178660313660002447546455753332835083003773596869975317881941326532491200104594142764296885809934157623594946146289883349_<155>

sieving ~43 cpu-days Mon Aug 24 23:16:31 2009 Msieve v. 1.42 Mon Aug 24 23:16:31 2009 random seeds: ddd8b5c8 ded37060 Mon Aug 24 23:16:31 2009 factoring 952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952380952381 (204 digits) Mon Aug 24 23:16:33 2009 searching for 15-digit factors Mon Aug 24 23:16:35 2009 commencing number field sieve (204-digit input) Mon Aug 24 23:16:35 2009 R0: -100000000000000000000000000000000000000000 Mon Aug 24 23:16:35 2009 R1: 1 Mon Aug 24 23:16:35 2009 A0: 1 Mon Aug 24 23:16:35 2009 A1: 0 Mon Aug 24 23:16:35 2009 A2: 0 Mon Aug 24 23:16:35 2009 A3: 0 Mon Aug 24 23:16:35 2009 A4: 0 Mon Aug 24 23:16:35 2009 A5: 2 Mon Aug 24 23:16:35 2009 skew 0.87, size 5.998329e-014, alpha 1.449076, combined = 1.362059e-011 Mon Aug 24 23:16:35 2009 Mon Aug 24 23:16:35 2009 commencing relation filtering Mon Aug 24 23:16:35 2009 estimated available RAM is 4094.1 MB Mon Aug 24 23:16:35 2009 commencing duplicate removal, pass 1 Mon Aug 24 23:22:00 2009 error -11 reading relation 30239153 Mon Aug 24 23:24:55 2009 found 4896193 hash collisions in 46646507 relations Mon Aug 24 23:26:17 2009 added 731191 free relations Mon Aug 24 23:26:17 2009 commencing duplicate removal, pass 2 Mon Aug 24 23:29:41 2009 found 3615445 duplicates and 43762252 unique relations Mon Aug 24 23:29:41 2009 memory use: 197.2 MB Mon Aug 24 23:29:41 2009 reading ideals above 26935296 Mon Aug 24 23:29:41 2009 commencing singleton removal, initial pass Mon Aug 24 23:43:52 2009 memory use: 596.8 MB Mon Aug 24 23:43:52 2009 reading all ideals from disk Mon Aug 24 23:43:53 2009 memory use: 754.2 MB Mon Aug 24 23:43:59 2009 commencing in-memory singleton removal Mon Aug 24 23:44:05 2009 begin with 43762252 relations and 38545902 unique ideals Mon Aug 24 23:44:57 2009 reduce to 24714676 relations and 17302634 ideals in 13 passes Mon Aug 24 23:44:57 2009 max relations containing the same ideal: 60 Mon Aug 24 23:45:03 2009 reading ideals above 720000 Mon Aug 24 23:45:04 2009 commencing singleton removal, initial pass Tue Aug 25 00:02:10 2009 memory use: 532.8 MB Tue Aug 25 00:02:10 2009 reading all ideals from disk Tue Aug 25 00:02:12 2009 memory use: 850.5 MB Tue Aug 25 00:02:19 2009 keeping 20528578 ideals with weight <= 200, target excess is 132773 Tue Aug 25 00:02:26 2009 commencing in-memory singleton removal Tue Aug 25 00:02:33 2009 begin with 24714716 relations and 20528578 unique ideals Tue Aug 25 00:03:33 2009 reduce to 24711529 relations and 20525237 ideals in 8 passes Tue Aug 25 00:03:33 2009 max relations containing the same ideal: 200 Tue Aug 25 00:04:04 2009 removing 2497614 relations and 2097614 ideals in 400000 cliques Tue Aug 25 00:04:06 2009 commencing in-memory singleton removal Tue Aug 25 00:04:13 2009 begin with 22213915 relations and 20525237 unique ideals Tue Aug 25 00:05:13 2009 reduce to 22061876 relations and 18272637 ideals in 9 passes Tue Aug 25 00:05:13 2009 max relations containing the same ideal: 192 Tue Aug 25 00:05:41 2009 removing 1868490 relations and 1468490 ideals in 400000 cliques Tue Aug 25 00:05:43 2009 commencing in-memory singleton removal Tue Aug 25 00:05:49 2009 begin with 20193386 relations and 18272637 unique ideals Tue Aug 25 00:06:32 2009 reduce to 20096884 relations and 16706033 ideals in 7 passes Tue Aug 25 00:06:32 2009 max relations containing the same ideal: 183 Tue Aug 25 00:06:58 2009 removing 1673961 relations and 1273961 ideals in 400000 cliques Tue Aug 25 00:06:59 2009 commencing in-memory singleton removal Tue Aug 25 00:07:05 2009 begin with 18422923 relations and 16706033 unique ideals Tue Aug 25 00:07:49 2009 reduce to 18338178 relations and 15345854 ideals in 8 passes Tue Aug 25 00:07:49 2009 max relations containing the same ideal: 172 Tue Aug 25 00:08:12 2009 removing 1558416 relations and 1158416 ideals in 400000 cliques Tue Aug 25 00:08:13 2009 commencing in-memory singleton removal Tue Aug 25 00:08:19 2009 begin with 16779762 relations and 15345854 unique ideals Tue Aug 25 00:08:48 2009 reduce to 16693317 relations and 14099363 ideals in 6 passes Tue Aug 25 00:08:48 2009 max relations containing the same ideal: 164 Tue Aug 25 00:09:10 2009 removing 1492815 relations and 1092815 ideals in 400000 cliques Tue Aug 25 00:09:11 2009 commencing in-memory singleton removal Tue Aug 25 00:09:16 2009 begin with 15200502 relations and 14099363 unique ideals Tue Aug 25 00:09:47 2009 reduce to 15116492 relations and 12920846 ideals in 7 passes Tue Aug 25 00:09:47 2009 max relations containing the same ideal: 153 Tue Aug 25 00:10:06 2009 removing 1440970 relations and 1040970 ideals in 400000 cliques Tue Aug 25 00:10:07 2009 commencing in-memory singleton removal Tue Aug 25 00:10:12 2009 begin with 13675522 relations and 12920846 unique ideals Tue Aug 25 00:10:36 2009 reduce to 13585042 relations and 11787407 ideals in 6 passes Tue Aug 25 00:10:36 2009 max relations containing the same ideal: 143 Tue Aug 25 00:10:53 2009 removing 1414062 relations and 1014062 ideals in 400000 cliques Tue Aug 25 00:10:54 2009 commencing in-memory singleton removal Tue Aug 25 00:10:58 2009 begin with 12170980 relations and 11787407 unique ideals Tue Aug 25 00:11:23 2009 reduce to 12073653 relations and 10673537 ideals in 7 passes Tue Aug 25 00:11:23 2009 max relations containing the same ideal: 129 Tue Aug 25 00:11:39 2009 removing 1385748 relations and 985748 ideals in 400000 cliques Tue Aug 25 00:11:40 2009 commencing in-memory singleton removal Tue Aug 25 00:11:43 2009 begin with 10687905 relations and 10673537 unique ideals Tue Aug 25 00:12:02 2009 reduce to 10581657 relations and 9578472 ideals in 6 passes Tue Aug 25 00:12:02 2009 max relations containing the same ideal: 118 Tue Aug 25 00:12:16 2009 removing 1370298 relations and 970298 ideals in 400000 cliques Tue Aug 25 00:12:17 2009 commencing in-memory singleton removal Tue Aug 25 00:12:19 2009 begin with 9211359 relations and 9578472 unique ideals Tue Aug 25 00:12:38 2009 reduce to 9094789 relations and 8487968 ideals in 7 passes Tue Aug 25 00:12:38 2009 max relations containing the same ideal: 106 Tue Aug 25 00:12:50 2009 removing 1358293 relations and 958293 ideals in 400000 cliques Tue Aug 25 00:12:51 2009 commencing in-memory singleton removal Tue Aug 25 00:12:54 2009 begin with 7736496 relations and 8487968 unique ideals Tue Aug 25 00:13:09 2009 reduce to 7598810 relations and 7386845 ideals in 7 passes Tue Aug 25 00:13:09 2009 max relations containing the same ideal: 92 Tue Aug 25 00:13:20 2009 removing 293684 relations and 235736 ideals in 57948 cliques Tue Aug 25 00:13:20 2009 commencing in-memory singleton removal Tue Aug 25 00:13:22 2009 begin with 7305126 relations and 7386845 unique ideals Tue Aug 25 00:13:33 2009 reduce to 7298052 relations and 7143994 ideals in 5 passes Tue Aug 25 00:13:33 2009 max relations containing the same ideal: 89 Tue Aug 25 00:13:37 2009 relations with 0 large ideals: 2925 Tue Aug 25 00:13:37 2009 relations with 1 large ideals: 486 Tue Aug 25 00:13:37 2009 relations with 2 large ideals: 9057 Tue Aug 25 00:13:37 2009 relations with 3 large ideals: 78455 Tue Aug 25 00:13:37 2009 relations with 4 large ideals: 369097 Tue Aug 25 00:13:37 2009 relations with 5 large ideals: 1033882 Tue Aug 25 00:13:37 2009 relations with 6 large ideals: 1870884 Tue Aug 25 00:13:37 2009 relations with 7+ large ideals: 3933266 Tue Aug 25 00:13:37 2009 commencing 2-way merge Tue Aug 25 00:13:51 2009 reduce to 4877616 relation sets and 4723558 unique ideals Tue Aug 25 00:13:51 2009 commencing full merge Tue Aug 25 00:16:24 2009 memory use: 535.7 MB Tue Aug 25 00:16:25 2009 found 2596663 cycles, need 2575758 Tue Aug 25 00:16:26 2009 weight of 2575758 cycles is about 180583247 (70.11/cycle) Tue Aug 25 00:16:26 2009 distribution of cycle lengths: Tue Aug 25 00:16:26 2009 1 relations: 279212 Tue Aug 25 00:16:26 2009 2 relations: 299234 Tue Aug 25 00:16:26 2009 3 relations: 313601 Tue Aug 25 00:16:26 2009 4 relations: 299542 Tue Aug 25 00:16:26 2009 5 relations: 280947 Tue Aug 25 00:16:26 2009 6 relations: 247235 Tue Aug 25 00:16:26 2009 7 relations: 208707 Tue Aug 25 00:16:26 2009 8 relations: 169480 Tue Aug 25 00:16:26 2009 9 relations: 134175 Tue Aug 25 00:16:26 2009 10+ relations: 343625 Tue Aug 25 00:16:26 2009 heaviest cycle: 20 relations Tue Aug 25 00:16:28 2009 commencing cycle optimization Tue Aug 25 00:16:35 2009 start with 14016520 relations Tue Aug 25 00:17:18 2009 pruned 414403 relations Tue Aug 25 00:17:18 2009 memory use: 357.6 MB Tue Aug 25 00:17:18 2009 distribution of cycle lengths: Tue Aug 25 00:17:18 2009 1 relations: 279212 Tue Aug 25 00:17:18 2009 2 relations: 305935 Tue Aug 25 00:17:18 2009 3 relations: 325203 Tue Aug 25 00:17:18 2009 4 relations: 308910 Tue Aug 25 00:17:18 2009 5 relations: 290433 Tue Aug 25 00:17:18 2009 6 relations: 253052 Tue Aug 25 00:17:18 2009 7 relations: 211890 Tue Aug 25 00:17:18 2009 8 relations: 169290 Tue Aug 25 00:17:18 2009 9 relations: 131652 Tue Aug 25 00:17:18 2009 10+ relations: 300181 Tue Aug 25 00:17:18 2009 heaviest cycle: 20 relations Tue Aug 25 00:17:33 2009 RelProcTime: 3658 Tue Aug 25 00:17:33 2009 Tue Aug 25 00:17:33 2009 commencing linear algebra Tue Aug 25 00:17:35 2009 read 2575758 cycles Tue Aug 25 00:17:42 2009 cycles contain 7222300 unique relations Tue Aug 25 00:27:08 2009 read 7222300 relations Tue Aug 25 00:27:26 2009 using 20 quadratic characters above 536866442 Tue Aug 25 00:28:29 2009 building initial matrix Tue Aug 25 00:30:54 2009 memory use: 846.8 MB Tue Aug 25 00:31:01 2009 read 2575758 cycles Tue Aug 25 00:33:17 2009 matrix is 2575581 x 2575758 (730.1 MB) with weight 226524143 (87.94/col) Tue Aug 25 00:33:17 2009 sparse part has weight 173363652 (67.31/col) Tue Aug 25 00:34:04 2009 filtering completed in 2 passes Tue Aug 25 00:34:05 2009 matrix is 2575290 x 2575467 (730.1 MB) with weight 226516174 (87.95/col) Tue Aug 25 00:34:05 2009 sparse part has weight 173361396 (67.31/col) Tue Aug 25 00:34:30 2009 read 2575467 cycles Tue Aug 25 00:41:23 2009 matrix is 2575290 x 2575467 (730.1 MB) with weight 226516174 (87.95/col) Tue Aug 25 00:41:23 2009 sparse part has weight 173361396 (67.31/col) Tue Aug 25 00:41:24 2009 saving the first 48 matrix rows for later Tue Aug 25 00:41:26 2009 matrix is 2575242 x 2575467 (690.6 MB) with weight 178986811 (69.50/col) Tue Aug 25 00:41:26 2009 sparse part has weight 165592916 (64.30/col) Tue Aug 25 00:41:26 2009 matrix includes 64 packed rows Tue Aug 25 00:41:26 2009 using block size 65536 for processor cache size 4096 kB Tue Aug 25 00:41:52 2009 commencing Lanczos iteration (4 threads) Tue Aug 25 00:41:52 2009 memory use: 786.1 MB Tue Aug 25 14:23:24 2009 lanczos halted after 40727 iterations (dim = 2575240) Tue Aug 25 14:23:33 2009 recovered 35 nontrivial dependencies Tue Aug 25 14:23:38 2009 BLanczosTime: 50765 Tue Aug 25 14:23:38 2009 Tue Aug 25 14:23:38 2009 commencing square root phase Tue Aug 25 14:23:38 2009 reading relations for dependency 1 Tue Aug 25 14:23:42 2009 read 1285922 cycles Tue Aug 25 14:23:46 2009 cycles contain 4488674 unique relations Tue Aug 25 14:32:25 2009 read 4488674 relations Tue Aug 25 14:33:06 2009 multiplying 3608038 relations Tue Aug 25 14:41:39 2009 multiply complete, coefficients have about 90.10 million bits Tue Aug 25 14:41:41 2009 initial square root is modulo 2935241 Tue Aug 25 14:52:21 2009 sqrtTime: 1723 Tue Aug 25 14:52:21 2009 prp50 factor: 48640687651801423804337056354992853346324870893769 Tue Aug 25 14:52:21 2009 prp155 factor: 19579923688551731244546269150496163178660313660002447546455753332835083003773596869975317881941326532491200104594142764296885809934157623594946146289883349 Tue Aug 25 14:52:21 2009 elapsed time 15:35:50
Aug 24, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.42 / Aug 24, 2009
(16·10²⁰⁰+17)/3 = 5(3)₁₉₉9_<201> = 7 · 11 · 53 · 1867 · 2162879 · 6576017627_<10> · 49830784277_<11> · 16059890440978574700941544301_<29> · C139
C139 = P43 · P48 · P49
P43 = 5465589490197817703795797688544120931163749_<43>
P48 = 298131801644473477455962103738371299534531237091_<48>
P49 = 3774044422137398794264282715509644849768141470003_<49>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1866420656 Step 1 took 42771ms Step 2 took 14797ms ********** Factor found in step 2: 5465589490197817703795797688544120931163749 Found probable prime factor of 43 digits: 5465589490197817703795797688544120931163749 Composite cofactor 1125162663058098504797405482943005184164299914993771206716128207364181036419506148377602857481273 has 97 digits ------------------------------- Sun Aug 23 13:25:48 2009 Msieve v. 1.42 Sun Aug 23 13:25:48 2009 random seeds: 5c7374a8 5ef10529 Sun Aug 23 13:25:48 2009 factoring 1125162663058098504797405482943005184164299914993771206716128207364181036419506148377602857481273 (97 digits) Sun Aug 23 13:25:49 2009 searching for 15-digit factors Sun Aug 23 13:25:50 2009 commencing quadratic sieve (97-digit input) Sun Aug 23 13:25:50 2009 using multiplier of 1 Sun Aug 23 13:25:50 2009 using 64kb Pentium 3 sieve core Sun Aug 23 13:25:50 2009 sieve interval: 18 blocks of size 65536 Sun Aug 23 13:25:50 2009 processing polynomials in batches of 6 Sun Aug 23 13:25:50 2009 using a sieve bound of 2334881 (85864 primes) Sun Aug 23 13:25:50 2009 using large prime bound of 350232150 (28 bits) Sun Aug 23 13:25:50 2009 using double large prime bound of 2397953724173250 (43-52 bits) Sun Aug 23 13:25:50 2009 using trial factoring cutoff of 52 bits Sun Aug 23 13:25:50 2009 polynomial 'A' values have 12 factors Sun Aug 23 22:43:02 2009 86190 relations (20613 full + 65577 combined from 1302314 partial), need 85960 Sun Aug 23 22:43:09 2009 begin with 1322927 relations Sun Aug 23 22:43:11 2009 reduce to 227316 relations in 13 passes Sun Aug 23 22:43:11 2009 attempting to read 227316 relations Sun Aug 23 22:43:23 2009 recovered 227316 relations Sun Aug 23 22:43:23 2009 recovered 213982 polynomials Sun Aug 23 22:43:24 2009 attempting to build 86190 cycles Sun Aug 23 22:43:24 2009 found 86190 cycles in 6 passes Sun Aug 23 22:43:24 2009 distribution of cycle lengths: Sun Aug 23 22:43:24 2009 length 1 : 20613 Sun Aug 23 22:43:24 2009 length 2 : 14554 Sun Aug 23 22:43:24 2009 length 3 : 14469 Sun Aug 23 22:43:24 2009 length 4 : 11952 Sun Aug 23 22:43:24 2009 length 5 : 8905 Sun Aug 23 22:43:24 2009 length 6 : 6215 Sun Aug 23 22:43:24 2009 length 7 : 3905 Sun Aug 23 22:43:24 2009 length 9+: 5577 Sun Aug 23 22:43:24 2009 largest cycle: 19 relations Sun Aug 23 22:43:24 2009 matrix is 85864 x 86190 (23.8 MB) with weight 5890275 (68.34/col) Sun Aug 23 22:43:24 2009 sparse part has weight 5890275 (68.34/col) Sun Aug 23 22:43:27 2009 filtering completed in 3 passes Sun Aug 23 22:43:27 2009 matrix is 82166 x 82230 (22.8 MB) with weight 5637674 (68.56/col) Sun Aug 23 22:43:27 2009 sparse part has weight 5637674 (68.56/col) Sun Aug 23 22:43:27 2009 saving the first 48 matrix rows for later Sun Aug 23 22:43:27 2009 matrix is 82118 x 82230 (16.2 MB) with weight 4678949 (56.90/col) Sun Aug 23 22:43:27 2009 sparse part has weight 3758275 (45.70/col) Sun Aug 23 22:43:27 2009 matrix includes 64 packed rows Sun Aug 23 22:43:27 2009 using block size 32892 for processor cache size 1024 kB Sun Aug 23 22:43:28 2009 commencing Lanczos iteration Sun Aug 23 22:43:28 2009 memory use: 15.2 MB Sun Aug 23 22:44:47 2009 lanczos halted after 1300 iterations (dim = 82116) Sun Aug 23 22:44:48 2009 recovered 15 nontrivial dependencies Sun Aug 23 22:44:48 2009 prp48 factor: 298131801644473477455962103738371299534531237091 Sun Aug 23 22:44:48 2009 prp49 factor: 3774044422137398794264282715509644849768141470003 Sun Aug 23 22:44:48 2009 elapsed time 09:19:00
Aug 24, 2009: By Dmitry Domanov / ECMNET / Aug 24, 2009
(16·10²⁰⁸-7)/9 = 1(7)₂₀₈_<209> = 613 · 155312749 · 122870845801218751_<18> · C181
C181 = P44 · P137
P44 = 33196494245589085028001912695928770935280171_<44>
P137 = 45779265693588795907442339030823949447819912433245685072037175910245588951267538385400947054816041565951371323741983261114872494043160301_<137>

C181=P44*P137 C181=33196494245589085028001912695928770935280171<44>*45779265693588795907442339030823949447819912433245685072037175910245588951267538385400947054816041565951371323741983261114872494043160301<137>
Aug 23, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 23, 2009
(32·10¹⁶⁹+13)/9 = 3(5)₁₆₈7_<170> = 31 · 37² · 197 · 647 · 6581 · 5064601914373430809_<19> · C138
C138 = P64 · P74
P64 = 2662996647046263982196858217327530760359601577131613151314289971_<64>
P74 = 74056638451825662200473333254579946422969866696922537212821981772723385623_<74>

Number: 35557_169 N=197212579888729164471309556399936640756410330307724816872021002362065422823075007141756856489734111483154757167846859583742889531474486933 ( 138 digits) SNFS difficulty: 171 digits. Divisors found: r1=2662996647046263982196858217327530760359601577131613151314289971 r2=74056638451825662200473333254579946422969866696922537212821981772723385623 Version: Total time: 30.05 hours. Scaled time: 71.60 units (timescale=2.383). Factorization parameters were as follows: n: 197212579888729164471309556399936640756410330307724816872021002362065422823075007141756856489734111483154757167846859583742889531474486933 m: 20000000000000000000000000000000000 deg: 5 c5: 1 c0: 130 skew: 2.65 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 5100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11119594 Max relations in full relation-set: Initial matrix: Pruned matrix : 850829 x 851077 Total sieving time: 27.63 hours. Total relation processing time: 0.71 hours. Matrix solve time: 1.48 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000 total time: 30.05 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673801) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672346) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672380) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340)
Aug 23, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 23, 2009
(28·10¹⁹⁵+53)/9 = 3(1)₁₉₄7_<196> = 3 · 59 · 395953 · 42767503850028819725441309_<26> · 352426542677057137608275426464363_<33> · C130
C130 = P38 · P92
P38 = 83818878880914915377013698879274119363_<38>
P92 = 35137774993989565829855092330752915371536012111459064937383666423536942780985993383926108817_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3984559737 Step 1 took 38183ms Step 2 took 14303ms ********** Factor found in step 2: 83818878880914915377013698879274119363 Found probable prime factor of 38 digits: 83818878880914915377013698879274119363 Probable prime cofactor 35137774993989565829855092330752915371536012111459064937383666423536942780985993383926108817 has 92 digits
Aug 23, 2009: By Justin Card / gmp-ecm 6.2 / Aug 23, 2009
(64·10²⁰³+53)/9 = 7(1)₂₀₂7_<204> = 3³ · 11² · 2069 · 7103 · 24324049 · 336174101 · 3482198767_<10> · C168
C168 = P37 · P132
P37 = 3980843238588010489892024931548862143_<37>
P132 = 130664397334782295209650590742356899679167397610942074331579761558024231657405938067573861191185006433921905590657151181446661170297_<132>

Run 52 out of 4480: Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=194726714 Step 1 took 63016ms Step 2 took 25201ms ********** Factor found in step 2: 3980843238588010489892024931548862143 Found probable prime factor of 37 digits: 3980843238588010489892024931548862143 Probable prime cofactor 130664397334782295209650590742356899679167397610942074331579761558024231657405938067573861191185006433921905590657151181446661170297 has 132 digits
Aug 22, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1, Msieve v. 1.42 / Aug 22, 2009
(13·10¹⁷²+23)/9 = 1(4)₁₇₁7_<173> = 149371 · 167722932457097_<15> · 44064556377957406403542099_<26> · C128
C128 = P36 · P41 · P52
P36 = 149913770606299879910229935179747037_<36>
P41 = 50877483285356724843669322116346571593229_<41>
P52 = 1715479597622848701658232150207211689815887239314303_<52>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=789472094 Step 1 took 38413ms Step 2 took 14089ms ********** Factor found in step 2: 149913770606299879910229935179747037 Found probable prime factor of 36 digits: 149913770606299879910229935179747037 Composite cofactor 87279284554426964743980580315959098898746362920358811195503822260589842067230516396197654387 has 92 digits ------------------------------- Tue Aug 18 20:18:26 2009 Msieve v. 1.42 Tue Aug 18 20:18:26 2009 random seeds: 6d03c3f8 644abe73 Tue Aug 18 20:18:26 2009 factoring 87279284554426964743980580315959098898746362920358811195503822260589842067230516396197654387 (92 digits) Tue Aug 18 20:18:27 2009 searching for 15-digit factors Tue Aug 18 20:18:28 2009 commencing quadratic sieve (92-digit input) Tue Aug 18 20:18:28 2009 using multiplier of 3 Tue Aug 18 20:18:28 2009 using 64kb Pentium 3 sieve core Tue Aug 18 20:18:28 2009 sieve interval: 18 blocks of size 65536 Tue Aug 18 20:18:28 2009 processing polynomials in batches of 6 Tue Aug 18 20:18:28 2009 using a sieve bound of 1855349 (69378 primes) Tue Aug 18 20:18:28 2009 using large prime bound of 209654437 (27 bits) Tue Aug 18 20:18:28 2009 using double large prime bound of 952154221467417 (42-50 bits) Tue Aug 18 20:18:28 2009 using trial factoring cutoff of 50 bits Tue Aug 18 20:18:28 2009 polynomial 'A' values have 12 factors Tue Aug 18 23:33:35 2009 69929 relations (17625 full + 52304 combined from 894203 partial), need 69474 Tue Aug 18 23:33:39 2009 begin with 911828 relations Tue Aug 18 23:33:40 2009 reduce to 177278 relations in 11 passes Tue Aug 18 23:33:40 2009 attempting to read 177278 relations Tue Aug 18 23:33:47 2009 recovered 177278 relations Tue Aug 18 23:33:47 2009 recovered 158770 polynomials Tue Aug 18 23:33:47 2009 attempting to build 69929 cycles Tue Aug 18 23:33:47 2009 found 69929 cycles in 5 passes Tue Aug 18 23:33:47 2009 distribution of cycle lengths: Tue Aug 18 23:33:47 2009 length 1 : 17625 Tue Aug 18 23:33:47 2009 length 2 : 12725 Tue Aug 18 23:33:47 2009 length 3 : 11937 Tue Aug 18 23:33:47 2009 length 4 : 9581 Tue Aug 18 23:33:47 2009 length 5 : 7001 Tue Aug 18 23:33:47 2009 length 6 : 4657 Tue Aug 18 23:33:47 2009 length 7 : 2783 Tue Aug 18 23:33:47 2009 length 9+: 3620 Tue Aug 18 23:33:47 2009 largest cycle: 19 relations Tue Aug 18 23:33:47 2009 matrix is 69378 x 69929 (17.2 MB) with weight 4231188 (60.51/col) Tue Aug 18 23:33:47 2009 sparse part has weight 4231188 (60.51/col) Tue Aug 18 23:33:49 2009 filtering completed in 3 passes Tue Aug 18 23:33:49 2009 matrix is 65612 x 65676 (16.1 MB) with weight 3968846 (60.43/col) Tue Aug 18 23:33:49 2009 sparse part has weight 3968846 (60.43/col) Tue Aug 18 23:33:49 2009 saving the first 48 matrix rows for later Tue Aug 18 23:33:49 2009 matrix is 65564 x 65676 (9.3 MB) with weight 2999864 (45.68/col) Tue Aug 18 23:33:49 2009 sparse part has weight 2045539 (31.15/col) Tue Aug 18 23:33:49 2009 matrix includes 64 packed rows Tue Aug 18 23:33:49 2009 using block size 26270 for processor cache size 1024 kB Tue Aug 18 23:33:50 2009 commencing Lanczos iteration Tue Aug 18 23:33:50 2009 memory use: 10.1 MB Tue Aug 18 23:34:24 2009 lanczos halted after 1038 iterations (dim = 65562) Tue Aug 18 23:34:24 2009 recovered 16 nontrivial dependencies Tue Aug 18 23:34:25 2009 prp41 factor: 50877483285356724843669322116346571593229 Tue Aug 18 23:34:25 2009 prp52 factor: 1715479597622848701658232150207211689815887239314303 Tue Aug 18 23:34:25 2009 elapsed time 03:15:59
Aug 22, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 22, 2009
7·10¹⁶⁹+9 = 7(0)₁₆₈9_<170> = 19 · 197 · 1218731 · 76893204345311_<14> · 5094367215912347_<16> · C131
C131 = P62 · P70
P62 = 14895146820296515742340476222921748580100430093472165449145387_<62>
P70 = 2629949201635387234251242596490670534870085851462962353425228926560387_<70>

Number: 70009_169 N=39173479488280698301566650872036774199426866136397189452808421112916404369440174985140115774837583709302975448240597911414597984769 ( 131 digits) SNFS difficulty: 170 digits. Divisors found: r1=14895146820296515742340476222921748580100430093472165449145387 r2=2629949201635387234251242596490670534870085851462962353425228926560387 Version: Total time: 34.98 hours. Scaled time: 83.07 units (timescale=2.375). Factorization parameters were as follows: n: 39173479488280698301566650872036774199426866136397189452808421112916404369440174985140115774837583709302975448240597911414597984769 m: 10000000000000000000000000000000000 deg: 5 c5: 7 c0: 90 skew: 1.67 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 5600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11269680 Max relations in full relation-set: Initial matrix: Pruned matrix : 925303 x 925551 Total sieving time: 32.31 hours. Total relation processing time: 0.81 hours. Matrix solve time: 1.77 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000 total time: 34.98 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672348) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343)
Aug 22, 2009: Factorizations of Phi_n(10) is available. It is the origin of Factorizations of 11...11 (Repunit) and Factorizations of 100...001.
Aug 21, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 21, 2009
(52·10¹⁹⁹+11)/9 = 5(7)₁₉₈9_<200> = 4547 · 15254923091918551452759372589_<29> · 1731348293684325255443601154609_<31> · C138
C138 = P37 · P102
P37 = 1786826983403462415473402018217405391_<37>
P102 = 269251983922852962675309422494691188138974240910425994172961541962117182925129658737872261636387448427_<102>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1647347969 Step 1 took 42593ms Step 2 took 14619ms ********** Factor found in step 2: 1786826983403462415473402018217405391 Found probable prime factor of 37 digits: 1786826983403462415473402018217405391 Probable prime cofactor 269251983922852962675309422494691188138974240910425994172961541962117182925129658737872261636387448427 has 102 digits
(46·10¹⁷¹+53)/9 = 5(1)₁₇₀7_<172> = 7 · 43 · 1373 · 8081 · 21174365965009_<14> · C149
C149 = P33 · P117
P33 = 605173586951071077503844970287679_<33>
P117 = 119432576933846853692398300562496450873677590281019524438614039543969108708295893722582025789172845080826012999716619_<117>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=43475544 Step 1 took 47342ms Step 2 took 16749ms ********** Factor found in step 2: 605173586951071077503844970287679 Found probable prime factor of 33 digits: 605173586951071077503844970287679 Probable prime cofactor 119432576933846853692398300562496450873677590281019524438614039543969108708295893722582025789172845080826012999716619 has 117 digits
Aug 21, 2009: By Serge Batalov and Bruce Dodson / Aug 20, 2009
c175 from 10²⁴¹+1 was splitted into p62 and p114.
Aug 20, 2009: By Dmitry Domanov / ECMNET / Aug 20, 2009
(53·10¹⁹⁶-71)/9 = 5(8)₁₉₅1_<197> = 3² · 4973 · 74797 · 122655881 · C180
C180 = P39 · P142
P39 = 112054989341662601618892514165224888241_<39>
P142 = 1279878186755975199770625717338893764280326490898655144840134732459923961450639607812280526526379705342401644682052605125245400793894469473609_<142>

C180=P39*P142 C180=112054989341662601618892514165224888241<39>*1279878186755975199770625717338893764280326490898655144840134732459923961450639607812280526526379705342401644682052605125245400793894469473609<142>
(53·10²⁰²-71)/9 = 5(8)₂₀₁1_<203> = 3 · 19 · 857 · 1259 · 1004317 · 71365367 · C182
C182 = P42 · C140
P42 = 779769064987480193874703347294131196204883_<42>
C140 = [17132771907515894174556863898939580232543643866401830701290571585218041096109532000936311816177590847856617333605840706370680024403860034243_<140>]

C182=P42*C140 C182=779769064987480193874703347294131196204883<42>*17132771907515894174556863898939580232543643866401830701290571585218041096109532000936311816177590847856617333605840706370680024403860034243<140>
(53·10¹⁹⁰-71)/9 = 5(8)₁₈₉1_<191> = 3 · 61 · 173 · 39203873 · 211360399 · C171
C171 = P36 · C136
P36 = 168914326803248671710673803592753171_<36>
C136 = [1328975843267167003533199181021679263944069843997313562305346088568990122619806818358213686861743331804899354370025982954624757057766927_<136>]

C171=P36*C136 C171=168914326803248671710673803592753171<36>*1328975843267167003533199181021679263944069843997313562305346088568990122619806818358213686861743331804899354370025982954624757057766927<136>
Aug 18, 2009 (3rd): By Wataru Sakai / Msieve / Aug 18, 2009
(19·10¹⁸⁵-7)/3 = 6(3)₁₈₄1_<186> = 307 · 2129 · C180
C180 = P44 · P47 · P90
P44 = 92441972095372479843278989499675612962293661_<44>
P47 = 46224877490952496513455145253411202856771657321_<47>
P90 = 226763597697597739551036386348904373582419249675420678746058970902269764864275707817984317_<90>

Number: 63331_185 N=968987800443592415171492990903244528151390573992673432241488079665077016680359994267672170007379607090746727498700791357036814906500327160881044507649648690922981279665689008975377 ( 180 digits) SNFS difficulty: 186 digits. Divisors found: r1=92441972095372479843278989499675612962293661 r2=46224877490952496513455145253411202856771657321 r3=226763597697597739551036386348904373582419249675420678746058970902269764864275707817984317 Version: Total time: 214.40 hours. Scaled time: 429.87 units (timescale=2.005). Factorization parameters were as follows: n: 968987800443592415171492990903244528151390573992673432241488079665077016680359994267672170007379607090746727498700791357036814906500327160881044507649648690922981279665689008975377 m: 10000000000000000000000000000000000000 deg: 5 c5: 19 c0: -7 skew: 0.82 type: snfs lss: 1 rlim: 8900000 alim: 8900000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8900000/8900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4450000, 6650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1532242 x 1532490 Total sieving time: 214.40 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8900000,8900000,28,28,54,54,2.5,2.5,100000 total time: 214.40 hours. --------- CPU info (if available) ----------
(4·10²⁰⁰-31)/9 = (4)₁₉₉1_<200> = 221047 · C195
C195 = P46 · P52 · P98
P46 = 6099950637964487344624524200296949847675258491_<46>
P52 = 2617574360209393093008226658654893652993339169215851_<52>
P98 = 12592370931196073272289411784959848587864333346912734305442667923493511107809613626421022457004183_<98>

Number: 44441_200 N=201063323385725408824568731737795330605909351605968162628058487310139673664172978798375207283719952971288660078826875933373646529672171277802659364046761297119818158330329949940259060039016337903 ( 195 digits) SNFS difficulty: 200 digits. Divisors found: r1=6099950637964487344624524200296949847675258491 r2=2617574360209393093008226658654893652993339169215851 r3=12592370931196073272289411784959848587864333346912734305442667923493511107809613626421022457004183 Version: Total time: 732.85 hours. Scaled time: 1472.29 units (timescale=2.009). Factorization parameters were as follows: n: 201063323385725408824568731737795330605909351605968162628058487310139673664172978798375207283719952971288660078826875933373646529672171277802659364046761297119818158330329949940259060039016337903 m: 10000000000000000000000000000000000000000 deg: 5 c5: 4 c0: -31 skew: 1.51 type: snfs lss: 1 rlim: 15400000 alim: 15400000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 15400000/15400000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7700000, 15500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2968446 x 2968694 Total sieving time: 732.85 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15400000,15400000,29,29,56,56,2.6,2.6,100000 total time: 732.85 hours. --------- CPU info (if available) ----------
Aug 18, 2009 (2nd): By Dmitry Domanov / ECMNET / Aug 18, 2009
(53·10¹⁹³-71)/9 = 5(8)₁₉₂1_<194> = 3 · 17 · 2131 · 122614102349_<12> · 157528172059_<12> · C167
C167 = P33 · P134
P33 = 386318917324635401637343670457937_<33>
P134 = 72616464843759242682094782381797010874803934727294295921255817042629723671550851219691527308314086340987245476998440916635306218917703_<134>

C167=P33*P134 C167=386318917324635401637343670457937<33>*72616464843759242682094782381797010874803934727294295921255817042629723671550851219691527308314086340987245476998440916635306218917703<134>
Aug 18, 2009: By Robert Backstrom / GGNFS, Msieve / Aug 18, 2009
10²¹²+3 = 1(0)₂₁₁3_<213> = 19 · 313 · C209
C209 = P53 · P156
P53 = 72100344457846728686995566050906079023204339527194013_<53>
P156 = 233219425899999887904779450574060410914770791909686397507236849819912243596530554293769515201797100091341545546091157355719851915551928373643299913434059373_<156>

Number: n N=16815200941651252732470153018328569026399865478392466789978140238775853371447788801076172860265680174878089793173028417689591390617117874558600975281654615772658483268875063057003531192197746763073818732133849 ( 209 digits) SNFS difficulty: 213 digits. Divisors found: Tue Aug 18 04:27:28 2009 prp53 factor: 72100344457846728686995566050906079023204339527194013 Tue Aug 18 04:27:28 2009 prp156 factor: 233219425899999887904779450574060410914770791909686397507236849819912243596530554293769515201797100091341545546091157355719851915551928373643299913434059373 Tue Aug 18 04:27:28 2009 elapsed time 30:40:57 (Msieve 1.39 - dependency 9) ... Msieve: warning: no irreducible prime found, switching to small primes Msieve: Newton iteration failed several times (see at end, below) ... Version: GGNFS-0.77.1-20050930-k8 Total time: 65.90 hours. Scaled time: 132.86 units (timescale=2.016). Factorization parameters were as follows: name: KA_1_0_211_3 n: 16815200941651252732470153018328569026399865478392466789978140238775853371447788801076172860265680174878089793173028417689591390617117874558600975281654615772658483268875063057003531192197746763073818732133849 m: 200000000000000000000000000000000000 deg: 6 c6: 25 c0: 48 skew: 1.11 type: snfs lss: 1 rlim: 25000000 alim: 25000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 25000000/25000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [12500000, 27749990) Primes: RFBsize:1565927, AFBsize:1566435, largePrimes:40192350 encountered Relations: rels:39845888, finalFF:1905146 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 9102934 hash collisions in 52197256 relations Msieve: matrix is 3731532 x 3731780 (996.2 MB) Total sieving time: 64.23 hours. Total relation processing time: 1.67 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,213,6,0,0,0,0,0,0,0,0,25000000,25000000,29,29,58,58,2.6,2.6,100000 total time: 65.90 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352028k/3407296k available (3120k kernel code, 53984k reserved, 1898k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5661.97 BogoMIPS (lpj=2830989) Calibrating delay using timer specific routine.. 5660.88 BogoMIPS (lpj=2830443) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Total of 4 processors activated (22644.69 BogoMIPS). ... Msieve: warning: no irreducible prime found, switching to small primes Msieve: Newton iteration failed several times: ... Tue Aug 18 02:20:00 2009 reading relations for dependency 7 Tue Aug 18 02:20:10 2009 read 1866396 cycles Tue Aug 18 02:20:17 2009 cycles contain 6394091 unique relations Tue Aug 18 02:21:41 2009 read 6394091 relations Tue Aug 18 02:22:18 2009 multiplying 5186178 relations Tue Aug 18 02:32:05 2009 multiply complete, coefficients have about 148.72 million bits Tue Aug 18 02:32:07 2009 warning: no irreducible prime found, switching to small primes Tue Aug 18 02:56:28 2009 initial square root is modulo 53 Tue Aug 18 03:18:43 2009 Newton iteration failed to converge Tue Aug 18 03:18:43 2009 algebraic square root failed Tue Aug 18 03:18:43 2009 reading relations for dependency 8 Tue Aug 18 03:18:53 2009 read 1865384 cycles Tue Aug 18 03:19:00 2009 cycles contain 6392057 unique relations Tue Aug 18 03:20:24 2009 read 6392057 relations Tue Aug 18 03:21:01 2009 multiplying 5184576 relations Tue Aug 18 03:30:49 2009 multiply complete, coefficients have about 148.68 million bits Tue Aug 18 03:30:50 2009 warning: no irreducible prime found, switching to small primes Tue Aug 18 03:30:50 2009 initial square root is modulo 53 Tue Aug 18 03:53:06 2009 Newton iteration failed to converge Tue Aug 18 03:53:06 2009 algebraic square root failed Tue Aug 18 03:53:06 2009 reading relations for dependency 9 Tue Aug 18 03:53:16 2009 read 1866216 cycles Tue Aug 18 03:53:23 2009 cycles contain 6390913 unique relations Tue Aug 18 03:54:47 2009 read 6390913 relations Tue Aug 18 03:55:25 2009 multiplying 5183958 relations Tue Aug 18 04:05:12 2009 multiply complete, coefficients have about 148.66 million bits Tue Aug 18 04:05:13 2009 warning: no irreducible prime found, switching to small primes Tue Aug 18 04:05:13 2009 initial square root is modulo 53 Tue Aug 18 04:27:28 2009 prp53 factor: 72100344457846728686995566050906079023204339527194013 Tue Aug 18 04:27:28 2009 prp156 factor: 233219425899999887904779450574060410914770791909686397507236849819912243596530554293769515201797100091341545546091157355719851915551928373643299913434059373 Tue Aug 18 04:27:28 2009 elapsed time 30:40:57
Aug 17, 2009 (5th): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 17, 2009
9·10¹⁹⁵-7 = 8(9)₁₉₄3_<196> = 17 · 439 · 119183 · 1271399 · 242885213 · 461827684596426570878380861037770727_<36> · C137
C137 = P47 · P90
P47 = 90273726781308008410859820613528673953162767949_<47>
P90 = 785941965246821725517634354985618196758423193048763238517231673375963788322474444838897417_<90>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1202030130 Step 1 took 156685ms Step 2 took 47668ms ********** Factor found in step 2: 90273726781308008410859820613528673953162767949 Found probable prime factor of 47 digits: 90273726781308008410859820613528673953162767949 Probable prime cofactor 785941965246821725517634354985618196758423193048763238517231673375963788322474444838897417 has 90 digits
Aug 17, 2009 (4th): By Sinkiti Sibata / Msieve / Aug 17, 2009
(58·10¹⁸⁰+41)/9 = 6(4)₁₇₉9_<181> = 11 · 1627 · C177
C177 = P34 · P144
P34 = 1280000823649561544625004925310473_<34>
P144 = 281316364893573382047531009276426345002478941203207649965104069424638937150544933870763338855019543891400117696494924919567782620672341626777329_<144>

Number: 64449_180 N=360085178769874528940294152340864080261744674774791554140048301080876372824744060146641584871455799544305997901572578892800158934147870841171394336729309071042322425235762666617 ( 177 digits) SNFS difficulty: 181 digits. Divisors found: r1=1280000823649561544625004925310473 (pp34) r2=281316364893573382047531009276426345002478941203207649965104069424638937150544933870763338855019543891400117696494924919567782620672341626777329 (pp144) Version: Msieve-1.40 Total time: 139.70 hours. Scaled time: 468.96 units (timescale=3.357). Factorization parameters were as follows: name: 64449_180 n: 360085178769874528940294152340864080261744674774791554140048301080876372824744060146641584871455799544305997901572578892800158934147870841171394336729309071042322425235762666617 m: 1000000000000000000000000000000000000 deg: 5 c5: 58 c0: 41 skew: 0.93 type: snfs lss: 1 rlim: 7500000 alim: 7500000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7500000/7500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3750000, 6050001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1433571 x 1433819 Total sieving time: 134.91 hours. Total relation processing time: 0.17 hours. Matrix solve time: 4.50 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,181.000,5,0,0,0,0,0,0,0,0,7500000,7500000,28,28,53,53,2.5,2.5,100000 total time: 139.70 hours. --------- CPU info (if available) ----------
Aug 17, 2009 (3rd): By Justin Card / ggnfs, msieve / Aug 17, 2009
(8·10¹⁹⁷+7)/3 = 2(6)₁₉₆9_<198> = 13 · 29 · 73 · 113786895756473091763216512239_<30> · C164
C164 = P70 · P95
P70 = 2325412411440405653690878974819812220657268033511965719935728303192037_<70>
P95 = 36619489557764519846267534525547256193377038956838686278299696905702216244880052542768324514023_<95>

Number: 26669_197 N=85155415518237946102479936799298669533177788063631844025863034765370542187259018971925248551625065434263578805689864621162022682754722142419580647352642227668434851 ( 164 digits) SNFS difficulty: 197 digits. Divisors found: r1=2325412411440405653690878974819812220657268033511965719935728303192037 (pp70) r2=36619489557764519846267534525547256193377038956838686278299696905702216244880052542768324514023 (pp95) Version: Msieve-1.40 Total time: 342.90 hours. Scaled time: 684.42 units (timescale=1.996). Factorization parameters were as follows: n: 85155415518237946102479936799298669533177788063631844025863034765370542187259018971925248551625065434263578805689864621162022682754722142419580647352642227668434851 m: 2000000000000000000000000000000000000000 deg: 5 c5: 25 c0: 7 skew: 0.78 type: snfs lss: 1 rlim: 13900000 alim: 13900000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 Factor base limits: 13900000/13900000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6950000, 12650001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2445649 x 2445874 Total sieving time: 297.25 hours. Total relation processing time: 0.41 hours. Matrix solve time: 43.74 hours. Time per square root: 1.50 hours. Prototype def-par.txt line would be: snfs,197.000,5,0,0,0,0,0,0,0,0,13900000,13900000,28,28,55,55,2.5,2.5,100000 total time: 342.90 hours. --------- CPU info (if available) ---------- [ 0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init) [ 0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297) [ 0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305) [ 0.231806] Total of 2 processors activated (8004.80 BogoMIPS).
Aug 17, 2009 (2nd): By Ignacio Santos / GGNFS, Msieve / Aug 17, 2009
(5·10²⁰⁰+13)/9 = (5)₁₉₉7_<200> = 3 · 19 · C198
C198 = P89 · P110
P89 = 52593328804790143359951630636697845044104157190753524779891824241888335192056207024750447_<89>
P110 = 18531986690048427358425949212844400767279971081177871933577024616257238836726538482785916221117286551415305283_<110>

Number: 55557_200 N=974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711501 ( 198 digits) SNFS difficulty: 200 digits. Divisors found: r1=52593328804790143359951630636697845044104157190753524779891824241888335192056207024750447 (pp89) r2=18531986690048427358425949212844400767279971081177871933577024616257238836726538482785916221117286551415305283 (pp110) Version: Msieve-1.40 Total time: 509.70 hours. Scaled time: 888.93 units (timescale=1.744). Factorization parameters were as follows: n: 974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711500974658869395711501 m: 10000000000000000000000000000000000000000 deg: 5 c5: 5 c0: 13 skew: 1.21 type: snfs lss: 1 rlim: 15500000 alim: 15500000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 15500000/15500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7750000, 15350001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 3174393 x 3174619 Total sieving time: 490.48 hours. Total relation processing time: 0.41 hours. Matrix solve time: 18.45 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,200.000,5,0,0,0,0,0,0,0,0,15500000,15500000,29,29,56,56,2.6,2.6,100000 total time: 509.70 hours.
Aug 17, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 17, 2009
(61·10¹⁷¹-7)/9 = 6(7)₁₇₁_<172> = 3 · 2803 · 3690984696370158400897064979949717_<34> · C135
C135 = P35 · P101
P35 = 18349916058226002381325132005750817_<35>
P101 = 11900539403604735254297165860871207760195905493929857397119064848185233384993512653727172540270521877_<101>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 218373899103757824771934513730446408208901986048652105451130131357315856486078756863651890930918440628821417715447161662433665809123509 (135 digits) Using B1=50000, B2=12746592, polynomial x^2, sigma=5473602807 Step 1 took 202ms Step 2 took 234ms ********** Factor found in step 2: 18349916058226002381325132005750817 Found probable prime factor of 35 digits: 18349916058226002381325132005750817 Probable prime cofactor 11900539403604735254297165860871207760195905493929857397119064848185233384993512653727172540270521877 has 101 digits
Aug 16, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 16, 2009
(25·10¹⁶⁹+11)/9 = 2(7)₁₆₈9_<170> = 29 · 467052151217671807_<18> · 25562040522225893199206593_<26> · C125
C125 = P51 · P75
P51 = 726341733161813647858156175202119648900783529862783_<51>
P75 = 110458109920047163481828000865195622785385713219451478383234067978685288847_<75>

Number: 27779_169 N=80230335001105177866805283220394479113117091317066824102441316262293178583056975568401818887106425370321835996839030630281201 ( 125 digits) SNFS difficulty: 170 digits. Divisors found: r1=726341733161813647858156175202119648900783529862783 r2=110458109920047163481828000865195622785385713219451478383234067978685288847 Version: Total time: 34.73 hours. Scaled time: 82.09 units (timescale=2.364). Factorization parameters were as follows: n: 80230335001105177866805283220394479113117091317066824102441316262293178583056975568401818887106425370321835996839030630281201 m: 10000000000000000000000000000000000 deg: 5 c5: 5 c0: 22 skew: 1.34 type: snfs lss: 1 rlim: 5600000 alim: 5600000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 5600000/5600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2800000, 5500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11038674 Max relations in full relation-set: Initial matrix: Pruned matrix : 973380 x 973628 Total sieving time: 31.10 hours. Total relation processing time: 1.44 hours. Matrix solve time: 1.98 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,5600000,5600000,27,27,52,52,2.4,2.4,100000 total time: 34.73 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673791) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672381) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Aug 16, 2009: By Dmitry Domanov / ECMNET / Aug 16, 2009
(23·10²⁰⁵+31)/9 = 2(5)₂₀₄9_<206> = 40545719773789_<14> · C192
C192 = P34 · C159
P34 = 4202462726885897525922861991796773_<34>
C159 = [149981068011369458327294192549304395213719767345838336061005720263500366352537864270906566505780532829539650383016948492667426233305737362820224459405598540247_<159>]

C192=P34*C159 C192=4202462726885897525922861991796773<34>*149981068011369458327294192549304395213719767345838336061005720263500366352537864270906566505780532829539650383016948492667426233305737362820224459405598540247<159>
Aug 15, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 15, 2009
(58·10¹⁶⁸+41)/9 = 6(4)₁₆₇9_<169> = 11² · 17 · 336340635039131954550293537507006243_<36> · C130
C130 = P61 · P70
P61 = 6468180746247313164919651472070638965886398620871300817741023_<61>
P70 = 1440090234293645015127160651757741514630147400069989660127682788576013_<70>

Number: 64449_168 N=9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299 ( 130 digits) SNFS difficulty: 171 digits. Divisors found: r1=6468180746247313164919651472070638965886398620871300817741023 r2=1440090234293645015127160651757741514630147400069989660127682788576013 Version: Total time: 39.52 hours. Scaled time: 94.28 units (timescale=2.386). Factorization parameters were as follows: n: 9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: 2050 skew: 2.34 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3100000, 6100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11320930 Max relations in full relation-set: Initial matrix: Pruned matrix : 971090 x 971338 Total sieving time: 36.11 hours. Total relation processing time: 1.20 hours. Matrix solve time: 1.97 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000 total time: 39.52 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.58 BogoMIPS (lpj=2673791) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672381) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672342) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672382)
Aug 15, 2009: By Serge Batalov / GMP-ECM 6.2.3 / Aug 15, 2009
(73·10²⁴⁹-1)/9 = 8(1)₂₄₉_<250> = 17 · 5443 · 15809 · C241
C241 = P38 · C204
P38 = 32607769874736976738779806206337465479_<38>
C204 = [170046461128108574995927236581628482215136764041055238483652624154293003769490480684917928338533050156473440999584084450662282572700445782394777642120172552258120330384289238781876693262128523142851830971_<204>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3778736387 Step 1 took 5244ms Step 2 took 2780ms ********** Factor found in step 2: 32607769874736976738779806206337465479 Found probable prime factor of 38 digits: 32607769874736976738779806206337465479 Composite cofactor has 204 digits
Aug 14, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.3 / Aug 14, 2009
(73·10²¹⁶-1)/9 = 8(1)₂₁₆_<217> = 71 · 28808051 · C208
C208 = P34 · P175
P34 = 3620576061701876499733072865659927_<34>
P175 = 1095293345497329293397673211340210417659625724719865891699257885248592552342275988711289537372777550314530400518083640878622741178698608241670961162797540046118753399114398333_<175>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2394144579 Step 1 took 12049ms ********** Factor found in step 1: 3620576061701876499733072865659927 Found probable prime factor of 34 digits: 3620576061701876499733072865659927 Probable prime cofactor has 175 digits
(73·10²⁴²-1)/9 = 8(1)₂₄₂_<243> = 6661 · 5768443348883_<13> · 2433133368010550753_<19> · C208
C208 = P33 · C176
P33 = 146337898716429751088899432223507_<33>
C176 = [59287011032147246415404357711918292857582091957106148141677454653007379683860195517172477070080575255441763542889691583392291227603304875315501329180227976487363263981212546307_<176>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=380702607 Step 1 took 11965ms Step 2 took 5392ms ********** Factor found in step 2: 146337898716429751088899432223507 Found probable prime factor of 33 digits: 146337898716429751088899432223507 Composite cofactor has 176 digits
Aug 14, 2009: By Dmitry Domanov / ECMNET / Aug 14, 2009
(23·10¹⁹⁴+31)/9 = 2(5)₁₉₃9_<195> = 7 · 19 · 37 · 1801 · C188
C188 = P39 · P45 · P104
P39 = 829120576370272477495488439345330306211_<39>
P45 = 373665017540682988557616909862451034443569869_<45>
P104 = 93071800242908434411113725305788079538407132412622804537132101554811430232078431135405103826930054200481_<104>

C188=P39*P45*P104 C188=829120576370272477495488439345330306211<39>*373665017540682988557616909862451034443569869<45>*93071800242908434411113725305788079538407132412622804537132101554811430232078431135405103826930054200481<104>
Aug 13, 2009 (6th): By Andreas Tete / Msieve v. 1.42, GGNFS / Aug 13, 2009
(58·10¹⁶³+41)/9 = 6(4)₁₆₂9_<164> = 3 · 53 · 337 · 41203 · 158613152738522987_<18> · 1748203055833034139767_<22> · C117
C117 = P41 · P76
P41 = 35354718772917701681492033166427827343819_<41>
P76 = 2977495823399103642870676144152784725505450903763932457717703309648252436651_<76>

Thu Aug 13 14:51:14 2009 Thu Aug 13 14:51:14 2009 Thu Aug 13 14:51:14 2009 Msieve v. 1.42 Thu Aug 13 14:51:14 2009 random seeds: 6239ca34 0a4dea92 Thu Aug 13 14:51:14 2009 factoring 105268527483812339334342341086979371310318838050297559395543654117627237975927554198893362237003523082233591893910169 (117 digits) Thu Aug 13 14:51:15 2009 searching for 15-digit factors Thu Aug 13 14:51:16 2009 commencing number field sieve (117-digit input) Thu Aug 13 14:51:16 2009 R0: -29317831392317037372404 Thu Aug 13 14:51:16 2009 R1: 1913949221161 Thu Aug 13 14:51:16 2009 A0: -728982585579479297678902795 Thu Aug 13 14:51:16 2009 A1: 1550972593082845957057335 Thu Aug 13 14:51:16 2009 A2: -9804057744669819423 Thu Aug 13 14:51:16 2009 A3: -515744502109505 Thu Aug 13 14:51:16 2009 A4: 525317832 Thu Aug 13 14:51:16 2009 A5: 4860 Thu Aug 13 14:51:16 2009 skew 119821.42, size 4.205158e-011, alpha -6.397800, combined = 4.770932e-010 Thu Aug 13 14:51:16 2009 Thu Aug 13 14:51:16 2009 commencing relation filtering Thu Aug 13 14:51:16 2009 estimated available RAM is 3069.5 MB Thu Aug 13 14:51:16 2009 commencing duplicate removal, pass 1 Thu Aug 13 14:51:23 2009 error -11 reading relation 454382 Thu Aug 13 14:53:02 2009 found 1086882 hash collisions in 9055892 relations Thu Aug 13 14:53:29 2009 added 59696 free relations Thu Aug 13 14:53:29 2009 commencing duplicate removal, pass 2 Thu Aug 13 14:54:05 2009 found 703872 duplicates and 8411715 unique relations Thu Aug 13 14:54:05 2009 memory use: 41.3 MB Thu Aug 13 14:54:05 2009 reading ideals above 100000 Thu Aug 13 14:54:05 2009 commencing singleton removal, initial pass Thu Aug 13 14:56:27 2009 memory use: 149.2 MB Thu Aug 13 14:56:27 2009 reading all ideals from disk Thu Aug 13 14:56:43 2009 memory use: 289.6 MB Thu Aug 13 14:56:45 2009 keeping 8758426 ideals with weight <= 200, target excess is 44355 Thu Aug 13 14:56:47 2009 commencing in-memory singleton removal Thu Aug 13 14:56:49 2009 begin with 8411715 relations and 8758426 unique ideals Thu Aug 13 14:57:02 2009 reduce to 3547796 relations and 3091338 ideals in 13 passes Thu Aug 13 14:57:02 2009 max relations containing the same ideal: 115 Thu Aug 13 14:57:07 2009 removing 928378 relations and 725875 ideals in 202503 cliques Thu Aug 13 14:57:07 2009 commencing in-memory singleton removal Thu Aug 13 14:57:08 2009 begin with 2619418 relations and 3091338 unique ideals Thu Aug 13 14:57:13 2009 reduce to 2479610 relations and 2216512 ideals in 8 passes Thu Aug 13 14:57:13 2009 max relations containing the same ideal: 89 Thu Aug 13 14:57:16 2009 removing 715041 relations and 512538 ideals in 202503 cliques Thu Aug 13 14:57:16 2009 commencing in-memory singleton removal Thu Aug 13 14:57:16 2009 begin with 1764569 relations and 2216512 unique ideals Thu Aug 13 14:57:19 2009 reduce to 1631712 relations and 1560558 ideals in 8 passes Thu Aug 13 14:57:19 2009 max relations containing the same ideal: 68 Thu Aug 13 14:57:21 2009 removing 118317 relations and 98615 ideals in 19702 cliques Thu Aug 13 14:57:21 2009 commencing in-memory singleton removal Thu Aug 13 14:57:22 2009 begin with 1513395 relations and 1560558 unique ideals Thu Aug 13 14:57:24 2009 reduce to 1507858 relations and 1456319 ideals in 6 passes Thu Aug 13 14:57:24 2009 max relations containing the same ideal: 67 Thu Aug 13 14:57:24 2009 relations with 0 large ideals: 175 Thu Aug 13 14:57:24 2009 relations with 1 large ideals: 1081 Thu Aug 13 14:57:24 2009 relations with 2 large ideals: 9840 Thu Aug 13 14:57:24 2009 relations with 3 large ideals: 54246 Thu Aug 13 14:57:24 2009 relations with 4 large ideals: 176982 Thu Aug 13 14:57:24 2009 relations with 5 large ideals: 349708 Thu Aug 13 14:57:24 2009 relations with 6 large ideals: 426938 Thu Aug 13 14:57:24 2009 relations with 7+ large ideals: 488888 Thu Aug 13 14:57:24 2009 commencing 2-way merge Thu Aug 13 14:57:27 2009 reduce to 954045 relation sets and 902506 unique ideals Thu Aug 13 14:57:27 2009 commencing full merge Thu Aug 13 14:57:53 2009 memory use: 95.9 MB Thu Aug 13 14:57:53 2009 found 477338 cycles, need 470706 Thu Aug 13 14:57:53 2009 weight of 470706 cycles is about 33244760 (70.63/cycle) Thu Aug 13 14:57:53 2009 distribution of cycle lengths: Thu Aug 13 14:57:53 2009 1 relations: 46902 Thu Aug 13 14:57:53 2009 2 relations: 48364 Thu Aug 13 14:57:53 2009 3 relations: 51540 Thu Aug 13 14:57:53 2009 4 relations: 50100 Thu Aug 13 14:57:53 2009 5 relations: 46810 Thu Aug 13 14:57:53 2009 6 relations: 42132 Thu Aug 13 14:57:53 2009 7 relations: 36419 Thu Aug 13 14:57:53 2009 8 relations: 30854 Thu Aug 13 14:57:53 2009 9 relations: 26007 Thu Aug 13 14:57:53 2009 10+ relations: 91578 Thu Aug 13 14:57:53 2009 heaviest cycle: 21 relations Thu Aug 13 14:57:53 2009 commencing cycle optimization Thu Aug 13 14:57:55 2009 start with 2871862 relations Thu Aug 13 14:58:05 2009 pruned 81938 relations Thu Aug 13 14:58:05 2009 memory use: 72.8 MB Thu Aug 13 14:58:05 2009 distribution of cycle lengths: Thu Aug 13 14:58:05 2009 1 relations: 46902 Thu Aug 13 14:58:05 2009 2 relations: 49463 Thu Aug 13 14:58:05 2009 3 relations: 53366 Thu Aug 13 14:58:05 2009 4 relations: 51651 Thu Aug 13 14:58:05 2009 5 relations: 48234 Thu Aug 13 14:58:05 2009 6 relations: 43133 Thu Aug 13 14:58:05 2009 7 relations: 37001 Thu Aug 13 14:58:05 2009 8 relations: 31076 Thu Aug 13 14:58:05 2009 9 relations: 26045 Thu Aug 13 14:58:05 2009 10+ relations: 83835 Thu Aug 13 14:58:05 2009 heaviest cycle: 21 relations Thu Aug 13 14:58:05 2009 RelProcTime: 409 Thu Aug 13 14:58:05 2009 Thu Aug 13 14:58:05 2009 commencing linear algebra Thu Aug 13 14:58:06 2009 read 470706 cycles Thu Aug 13 14:58:07 2009 cycles contain 1474652 unique relations Thu Aug 13 14:58:43 2009 read 1474652 relations Thu Aug 13 14:58:47 2009 using 20 quadratic characters above 134213298 Thu Aug 13 14:58:58 2009 building initial matrix Thu Aug 13 14:59:26 2009 memory use: 167.9 MB Thu Aug 13 14:59:28 2009 read 470706 cycles Thu Aug 13 14:59:28 2009 matrix is 470527 x 470706 (135.6 MB) with weight 45098600 (95.81/col) Thu Aug 13 14:59:28 2009 sparse part has weight 31768393 (67.49/col) Thu Aug 13 14:59:36 2009 filtering completed in 2 passes Thu Aug 13 14:59:36 2009 matrix is 470306 x 470485 (135.5 MB) with weight 45089323 (95.84/col) Thu Aug 13 14:59:36 2009 sparse part has weight 31765638 (67.52/col) Thu Aug 13 14:59:38 2009 read 470485 cycles Thu Aug 13 14:59:39 2009 matrix is 470306 x 470485 (135.5 MB) with weight 45089323 (95.84/col) Thu Aug 13 14:59:39 2009 sparse part has weight 31765638 (67.52/col) Thu Aug 13 14:59:39 2009 saving the first 48 matrix rows for later Thu Aug 13 14:59:40 2009 matrix is 470258 x 470485 (129.3 MB) with weight 35913518 (76.33/col) Thu Aug 13 14:59:40 2009 sparse part has weight 31066595 (66.03/col) Thu Aug 13 14:59:40 2009 matrix includes 64 packed rows Thu Aug 13 14:59:40 2009 using block size 65536 for processor cache size 3072 kB Thu Aug 13 14:59:44 2009 commencing Lanczos iteration Thu Aug 13 14:59:44 2009 memory use: 130.2 MB Thu Aug 13 15:39:12 2009 lanczos halted after 7439 iterations (dim = 470256) Thu Aug 13 15:39:14 2009 recovered 29 nontrivial dependencies Thu Aug 13 15:39:14 2009 BLanczosTime: 2469 Thu Aug 13 15:39:14 2009 Thu Aug 13 15:39:14 2009 commencing square root phase Thu Aug 13 15:39:14 2009 reading relations for dependency 1 Thu Aug 13 15:39:14 2009 read 235617 cycles Thu Aug 13 15:39:15 2009 cycles contain 924126 unique relations Thu Aug 13 15:39:48 2009 read 924126 relations Thu Aug 13 15:39:53 2009 multiplying 737592 relations Thu Aug 13 15:41:37 2009 multiply complete, coefficients have about 31.47 million bits Thu Aug 13 15:41:38 2009 initial square root is modulo 1088586883 Thu Aug 13 15:44:50 2009 sqrtTime: 336 Thu Aug 13 15:44:50 2009 prp41 factor: 35354718772917701681492033166427827343819 Thu Aug 13 15:44:50 2009 prp76 factor: 2977495823399103642870676144152784725505450903763932457717703309648252436651 Thu Aug 13 15:44:50 2009 elapsed time 00:53:36 Thu Aug 13 15:44:50 2009 total time ~ 41,11 hours
Aug 13, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 13, 2009
(58·10¹⁶¹+41)/9 = 6(4)₁₆₀9_<162> = 13 · 229 · C159
C159 = P40 · P119
P40 = 3654704663721431785734998256008161717483_<40>
P119 = 59231722451106549788320435782143534486295223609948241326485620953755925134115062706023714637202558162648631578274012739_<119>

Number: 64449_161 N=216474452282312544321277945732094203709924233941701190609487552718993767028701526518120404583286679356548352181539954465718657858395849662225208076736461015937 ( 159 digits) SNFS difficulty: 162 digits. Divisors found: r1=3654704663721431785734998256008161717483 r2=59231722451106549788320435782143534486295223609948241326485620953755925134115062706023714637202558162648631578274012739 Version: Total time: 18.03 hours. Scaled time: 42.94 units (timescale=2.381). Factorization parameters were as follows: n: 216474452282312544321277945732094203709924233941701190609487552718993767028701526518120404583286679356548352181539954465718657858395849662225208076736461015937 m: 100000000000000000000000000000000 deg: 5 c5: 580 c0: 41 skew: 0.59 type: snfs lss: 1 rlim: 4000000 alim: 4000000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [2000000, 3500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9614060 Max relations in full relation-set: Initial matrix: Pruned matrix : 672370 x 672618 Total sieving time: 16.52 hours. Total relation processing time: 0.51 hours. Matrix solve time: 0.92 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,51,51,2.4,2.4,100000 total time: 18.03 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.59 BogoMIPS (lpj=2673798) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672340) Calibrating delay using timer specific routine.. 5344.77 BogoMIPS (lpj=2672387)
Aug 13, 2009 (4th): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 13, 2009
(49·10¹⁷¹-13)/9 = 5(4)₁₇₀3_<172> = 1309907 · 1509331 · C160
C160 = P39 · C122
P39 = 186135721123313863044793461731766127889_<39>
C122 = [14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811_<122>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2313565796 Step 1 took 52141ms Step 2 took 17706ms ********** Factor found in step 2: 186135721123313863044793461731766127889 Found probable prime factor of 39 digits: 186135721123313863044793461731766127889 Composite cofactor 14794452213434372946420738528169896579615815849117777730825714913852145946553387018597884831622546553977005766909682325811 has 122 digits
Aug 13, 2009 (3rd): By Dmitry Domanov / ECMNET / Aug 13, 2009
(16·10²¹⁰-7)/9 = 1(7)₂₁₀_<211> = 2306753 · 707999891526611_<15> · 34982088008588268790615606126668383363_<38> · C152
C152 = P43 · P110
P43 = 1742276401997614863682400832116335307416429_<43>
P110 = 17859956858070459648332660652295189478614882396823687035320140864284662019894144474128047165289895725299940797_<110>

C152=P43*P110 C152=1742276401997614863682400832116335307416429<43>*17859956858070459648332660652295189478614882396823687035320140864284662019894144474128047165289895725299940797<110>
Aug 13, 2009 (2nd): By Robert Backstrom / GGNFS, Msieve / Aug 13, 2009
(25·10²¹⁵-1)/3 = 8(3)₂₁₅_<216> = 468653 · C211
C211 = P47 · P165
P47 = 10837959565633376609020155979327155879453500933_<47>
P165 = 164066466998120886009170753099955422048842327500144372228690573743783715684021657284565055073307989853343982097643796221647012749477812858299698290812380055168396917_<165>

Number: n N=1778145735401956956070553977747573008885749868950659300875772337600171840003869245120234658336409525455578718867335391714836634638705680606617973923848419477381630616540027127391339292255321812371484516973823561 ( 211 digits) SNFS difficulty: 216 digits. Divisors found: Thu Aug 13 17:10:17 2009 prp47 factor: 10837959565633376609020155979327155879453500933 Thu Aug 13 17:10:17 2009 prp165 factor: 164066466998120886009170753099955422048842327500144372228690573743783715684021657284565055073307989853343982097643796221647012749477812858299698290812380055168396917 Thu Aug 13 17:10:17 2009 elapsed time 69:23:21 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 148.72 hours. Scaled time: 299.67 units (timescale=2.015). Factorization parameters were as follows: name: KA_8_3_215 n: 1778145735401956956070553977747573008885749868950659300875772337600171840003869245120234658336409525455578718867335391714836634638705680606617973923848419477381630616540027127391339292255321812371484516973823561 m: 1000000000000000000000000000000000000 deg: 6 c6: 5 c0: -2 skew: 0.86 type: snfs lss: 1 rlim: 29000000 alim: 29000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 29000000/29000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [14500000, 41549990) Primes: RFBsize:1799676, AFBsize:1800322, largePrimes:38147337 encountered Relations: rels:34668211, finalFF:912109 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 9105302 hash collisions in 49974295 relations Msieve: matrix is 5732590 x 5732838 (1550.1 MB) Total sieving time: 147.03 hours. Total relation processing time: 1.69 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,216,6,0,0,0,0,0,0,0,0,29000000,29000000,29,29,58,58,2.6,2.6,100000 total time: 148.72 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352028k/3407296k available (3120k kernel code, 53984k reserved, 1898k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5662.12 BogoMIPS (lpj=2831063) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830445) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830459) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830460) Total of 4 processors activated (22644.85 BogoMIPS).
Aug 13, 2009: By Serge Batalov, Bruce Dodson / Msieve / Aug 12, 2009
c253 from 10³⁹³+1 was splitted into p119 and p134. Congratulations!
Aug 12, 2009 (2nd): By Robert Backstrom / GGNFS, Msieve / Aug 12, 2009
(58·10¹⁵²+41)/9 = 6(4)₁₅₁9_<153> = 11 · 17 · 16007 · C147
C147 = P68 · P80
P68 = 11070022447903046623645328650347018977427326705944677000437857521689_<68>
P80 = 19448469542909211426583031757749301794789777521107886109243313377103525520008349_<80>

Number: n N=215294994417363674931136225643408162820625750446894872679180279899083069754724435213485959666858464810831238754316525438718302869648420675728581461 ( 147 digits) SNFS difficulty: 154 digits. Divisors found: Wed Aug 12 12:03:18 2009 prp68 factor: 11070022447903046623645328650347018977427326705944677000437857521689 Wed Aug 12 12:03:18 2009 prp80 factor: 19448469542909211426583031757749301794789777521107886109243313377103525520008349 Wed Aug 12 12:03:18 2009 elapsed time 01:52:28 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.90 hours. Scaled time: 18.76 units (timescale=0.943). Factorization parameters were as follows: name: KA_6_4_151_9 n: 215294994417363674931136225643408162820625750446894872679180279899083069754724435213485959666858464810831238754316525438718302869648420675728581461 m: 2000000000000000000000000000000 deg: 5 c5: 725 c0: 164 skew: 0.74 type: snfs lss: 1 rlim: 2600000 alim: 2600000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2600000/2600000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [1300000, 2050001) Primes: RFBsize:189880, AFBsize:189046, largePrimes:27535725 encountered Relations: rels:24932402, finalFF:456925 Max relations in full relation-set: 28 Initial matrix: 378993 x 456925 with sparse part having weight 73195773. Pruned matrix : Msieve: found 2077426 hash collisions in 26024074 relations Msieve: matrix is 475387 x 475634 (127.1 MB) Total sieving time: 19.20 hours. Total relation processing time: 0.70 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2600000,2600000,29,29,58,58,2.6,2.6,100000 total time: 19.90 hours. --------- CPU info (if available) ----------
Aug 12, 2009: By Dmitry Domanov / ECMNET / Aug 12, 2009
(58·10¹⁶⁸+41)/9 = 6(4)₁₆₇9_<169> = 11² · 17 · C166
C166 = P36 · C130
P36 = 336340635039131954550293537507006243_<36>
C130 = [9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299_<130>]

C166=P36*C130 C166=336340635039131954550293537507006243<36>*9314763926316936870617423027014862687838866087875593973448170193850377580272582112388416930433089994630940974221974276541583881299<130>
(16·10²³⁰-7)/9 = 1(7)₂₃₀_<231> = 3² · 140681 · 1402277 · C219
C219 = P43 · P176
P43 = 3944281709221934348316789231845083597207091_<43>
P176 = 25386204870744998992688276663987897077304779888008176579483498199145614420279845835462036189475927778331120836559408570910727745551926370892296621414363814700980634305953356159_<176>

C219=P43*P176 C219=3944281709221934348316789231845083597207091<43>*25386204870744998992688276663987897077304779888008176579483498199145614420279845835462036189475927778331120836559408570910727745551926370892296621414363814700980634305953356159<176>
Aug 11, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 11, 2009
(58·10¹⁴⁸+41)/9 = 6(4)₁₄₇9_<149> = 3² · 7² · 11 · 7655322337515029619053_<22> · C124
C124 = P50 · P74
P50 = 37355104026158289925635199403391287893388509054633_<50>
P74 = 46455889216811801389017392632315875552686098951001099958910251693636540751_<74>

Number: 64449_148 N=1735364574321690008200642197598958580298118964657785245246879331636960268082291614275971412554302452221654247232075389849383 ( 124 digits) SNFS difficulty: 151 digits. Divisors found: r1=37355104026158289925635199403391287893388509054633 r2=46455889216811801389017392632315875552686098951001099958910251693636540751 Version: Total time: 7.25 hours. Scaled time: 17.32 units (timescale=2.388). Factorization parameters were as follows: n: 1735364574321690008200642197598958580298118964657785245246879331636960268082291614275971412554302452221654247232075389849383 m: 1000000000000000000000000000000 deg: 5 c5: 29 c0: 2050 skew: 2.34 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6663329 Max relations in full relation-set: Initial matrix: Pruned matrix : 391208 x 391456 Total sieving time: 6.67 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.31 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 7.25 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673788) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672383) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672343) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344)
(58·10¹⁷⁵+41)/9 = 6(4)₁₇₄9_<176> = 3² · 113 · 180799 · 18369017 · 20724731513_<11> · 194278867157_<12> · 4211528010489493_<16> · C124
C124 = P40 · P84
P40 = 2202184715456389693063837224368295327739_<40>
P84 = 510945617062227781245498909898705264220997982507792737736799211040862361156935490637_<84>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 1125196628323871537050544410903193876581153579714044972724099733552508728126037056929993269101100025133827011425034680879743 (124 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2028390863 Step 1 took 3343ms Step 2 took 2092ms ********** Factor found in step 2: 2202184715456389693063837224368295327739 Found probable prime factor of 40 digits: 2202184715456389693063837224368295327739 Probable prime cofactor 510945617062227781245498909898705264220997982507792737736799211040862361156935490637 has 84 digits
Aug 11, 2009 (4th): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 11, 2009
(4·10¹⁷²+11)/3 = 1(3)₁₇₁7_<173> = 89 · 44298394983828534317971_<23> · C148
C148 = P36 · P113
P36 = 147668611851868658810324482778075801_<36>
P113 = 22901954443464829237690488724952674774172113307515222316314785504936376877185871170914885048443823739100628195923_<113>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1532346831 Step 1 took 46999ms Step 2 took 16538ms ********** Factor found in step 2: 147668611851868658810324482778075801 Found probable prime factor of 36 digits: 147668611851868658810324482778075801 Probable prime cofactor 22901954443464829237690488724952674774172113307515222316314785504936376877185871170914885048443823739100628195923 has 113 digits
Aug 11, 2009 (3rd): By Robert Backstrom / GGNFS / Aug 11, 2009
(58·10¹⁸⁹+41)/9 = 6(4)₁₈₈9_<190> = 53 · 71 · 1009 · 12964271 · 39384977 · 1248374028769795019_<19> · 41054055524932111007_<20> · 261420106563786798596455219_<27> · C105
C105 = P43 · P62
P43 = 3339319253796127630188959796136480948753637_<43>
P62 = 74299122286499570025192389670970928627261334898949097017828959_<62>

Number: n N=248108489591460980312417272537903441658361226851702740557431060424235449229527746069508933855398695173883 ( 105 digits) Divisors found: r1=3339319253796127630188959796136480948753637 (pp43) r2=74299122286499570025192389670970928627261334898949097017828959 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.55 hours. Scaled time: 15.64 units (timescale=1.829). Factorization parameters were as follows: name: KA_6_4_188_9 n: 248108489591460980312417272537903441658361226851702740557431060424235449229527746069508933855398695173883 Y0: -136270219024381679450 Y1: 45562200853 c0: -684169272975852034269820119 c1: 45234606651522858406119 c2: 188909143076621294 c3: -34709869262836 c4: 106646558 c5: 5280 skew: 46076.58 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [1250000, 1950001) Primes: RFBsize:183072, AFBsize:183774, largePrimes:14525770 encountered Relations: rels:12546494, finalFF:474415 Max relations in full relation-set: 48 Initial matrix: 366932 x 474415 with sparse part having weight 52901740. Pruned matrix : 288929 x 290827 with weight 26572457. Total sieving time: 7.25 hours. Total relation processing time: 0.39 hours. Matrix solve time: 0.76 hours. Total square root time: 0.15 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,56,56,2.6,2.6,150000 total time: 8.55 hours. --------- CPU info (if available) ----------
Aug 11, 2009 (2nd): By Sinkiti Sibata / Msieve / Aug 11, 2009
(58·10¹⁶⁶+41)/9 = 6(4)₁₆₅9_<167> = 3³ · 7 · 11 · 215443 · 4093637 · C152
C152 = P72 · P80
P72 = 706604938908288596762603928693621117476374747431908877267657716973583417_<72>
P80 = 49740782017038381446898408076325283314020354933960390731754594066785632705466473_<80>

Number: 64449_166 N=35147082238399905566036355276072819135190316906897480108713199435188564513655611555102672917103076788399563036475073085609589123129960373650671362278241 ( 152 digits) SNFS difficulty: 168 digits. Divisors found: r1=706604938908288596762603928693621117476374747431908877267657716973583417 (pp72) r2=49740782017038381446898408076325283314020354933960390731754594066785632705466473 (pp80) Version: Msieve-1.40 Total time: 43.05 hours. Scaled time: 143.74 units (timescale=3.339). Factorization parameters were as follows: name: 64449_166 n: 35147082238399905566036355276072819135190316906897480108713199435188564513655611555102672917103076788399563036475073085609589123129960373650671362278241 m: 2000000000000000000000000000000000 deg: 5 c5: 145 c0: 328 skew: 1.18 type: snfs lss: 1 rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [2250000, 4450001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 842623 x 842871 Total sieving time: 41.52 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.36 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,168.000,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,52,52,2.4,2.4,100000 total time: 43.05 hours. --------- CPU info (if available) ----------
Aug 11, 2009: By Serge Batalov / PFGW / Aug 10, 2009
(64·10⁸³⁴⁶¹-1)/9 = 7(1)₈₃₄₆₁_<83462>
Aug 10, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 10, 2009
(58·10¹⁴⁶+41)/9 = 6(4)₁₄₅9_<147> = 11² · 139 · 30586547 · 8854610330194782473_<19> · C117
C117 = P46 · P72
P46 = 1044143941895224076008252929168616516373419781_<46>
P72 = 135495551116589058893468838756066885759317128660887029717156341753187261_<72>

Number: 64449_146 N=141476858852141129982085096165096307405123624215597661573103210099884666813868205468677251665186249925639019054609841 ( 117 digits) SNFS difficulty: 147 digits. Divisors found: r1=1044143941895224076008252929168616516373419781 r2=135495551116589058893468838756066885759317128660887029717156341753187261 Version: Total time: 6.16 hours. Scaled time: 14.51 units (timescale=2.355). Factorization parameters were as follows: n: 141476858852141129982085096165096307405123624215597661573103210099884666813868205468677251665186249925639019054609841 m: 100000000000000000000000000000 deg: 5 c5: 580 c0: 41 skew: 0.59 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1500000, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6811242 Max relations in full relation-set: Initial matrix: Pruned matrix : 372186 x 372434 Total sieving time: 5.31 hours. Total relation processing time: 0.50 hours. Matrix solve time: 0.28 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,49,49,2.3,2.3,75000 total time: 6.16 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Aug 10, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 10, 2009
(58·10¹⁷⁰+41)/9 = 6(4)₁₆₉9_<171> = 11 · 8442103296703_<13> · 6243174303238469933530387_<25> · C133
C133 = P52 · P81
P52 = 1268227929841860533189429196657056691419100472647721_<52>
P81 = 876474658081602209257265498268798224770709796472774664205322953842768425268663639_<81>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1249571775 Step 1 took 37981ms Step 2 took 13962ms ********** Factor found in step 2: 1268227929841860533189429196657056691419100472647721 Found probable prime factor of 52 digits: 1268227929841860533189429196657056691419100472647721 Probable prime cofactor 876474658081602209257265498268798224770709796472774664205322953842768425268663639 has 81 digits
Aug 10, 2009: By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 10, 2009
(58·10¹⁴²+41)/9 = 6(4)₁₄₁9_<143> = 3 · 7 · 11 · 13229 · 126653 · 15815032747_<11> · C122
C122 = P57 · P65
P57 = 522074508523921921621312471446082179548893172922272368021_<57>
P65 = 20166402113362492556571937451567880430507687069249483258274948441_<65>

Number: 64449_142 N=10528364472029503674546930418450190626108381180174211115822246930224941166469042970442458502269726972756776294182752205261 ( 122 digits) SNFS difficulty: 144 digits. Divisors found: r1=522074508523921921621312471446082179548893172922272368021 r2=20166402113362492556571937451567880430507687069249483258274948441 Version: Total time: 4.72 hours. Scaled time: 11.29 units (timescale=2.390). Factorization parameters were as follows: n: 10528364472029503674546930418450190626108381180174211115822246930224941166469042970442458502269726972756776294182752205261 m: 20000000000000000000000000000 deg: 5 c5: 725 c0: 164 skew: 0.74 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4703864 Max relations in full relation-set: Initial matrix: Pruned matrix : 321444 x 321692 Total sieving time: 4.07 hours. Total relation processing time: 0.42 hours. Matrix solve time: 0.21 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,50000 total time: 4.72 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Aug 9, 2009 (5th): By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Aug 9, 2009
(58·10¹⁴¹+41)/9 = 6(4)₁₄₀9_<142> = 13417 · 11465492388766613_<17> · 85492832353215785749_<20> · C102
C102 = P48 · P55
P48 = 297188596750020055603166795930122343745013718293_<48>
P55 = 1648828582186947758223219615219991321258882551942718717_<55>

Number: 64449_141 N=490013052621464118683651322907303005438915081644290634464703535904536125332452737523019513099576390081 ( 102 digits) Divisors found: r1=297188596750020055603166795930122343745013718293 r2=1648828582186947758223219615219991321258882551942718717 Version: Total time: 3.55 hours. Scaled time: 8.48 units (timescale=2.391). Factorization parameters were as follows: name: 64449_141 n: 490013052621464118683651322907303005438915081644290634464703535904536125332452737523019513099576390081 skew: 2999.04 # norm 2.87e+14 c5: 285840 c4: -580998390 c3: -39809786971105 c2: 13101624497222693 c1: 51794700540962006453 c0: -6871927561416625019595 # alpha -6.32 Y1: 42203408671 Y0: -17652952443475187786 # Murphy_E 2.92e-09 # M 43468290854972797452314451564270390388087360027321479264612436286247719101896379620470713861572886086 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1350001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4920370 Max relations in full relation-set: Initial matrix: Pruned matrix : 221588 x 221836 Polynomial selection time: 0.22 hours. Total sieving time: 2.86 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.11 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.55 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(58·10²⁰⁰+41)/9 = 6(4)₁₉₉9_<201> = 11 · 17 · 107 · 2377 · 932774347987103381_<18> · 13826677866082240683703_<23> · 21474065269491482871681097_<26> · 9617476601959055323120190872597_<31> · C97
C97 = P48 · P50
P48 = 105112228249013874195504102675707517143167052699_<48>
P50 = 48395817392296351722664742435602568363350373923061_<50>

Number: 64449_200 N=5086992204036649549554802325517951171974055226822069754918148594115667379490630513181229558391639 ( 97 digits) Divisors found: r1=105112228249013874195504102675707517143167052699 r2=48395817392296351722664742435602568363350373923061 Version: Total time: 1.81 hours. Scaled time: 4.32 units (timescale=2.386). Factorization parameters were as follows: name: 64449_200 n: 5086992204036649549554802325517951171974055226822069754918148594115667379490630513181229558391639 skew: 4251.50 # norm 3.00e+13 c5: 88920 c4: -552671486 c3: -4344467514261 c2: 3144978948596562 c1: 41332925549711484436 c0: 1886464308075611431704 # alpha -5.85 Y1: 3492390701 Y0: -2246431410188375885 # Murphy_E 4.64e-09 # M 1588946694778192353638204469934463977067134430662642725994726068441844085253881674329972420828066 type: gnfs rlim: 1000000 alim: 1000000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [500000, 850001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3998077 Max relations in full relation-set: Initial matrix: Pruned matrix : 145180 x 145428 Polynomial selection time: 0.11 hours. Total sieving time: 1.49 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.05 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: gnfs,96,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1000000,1000000,26,26,49,49,2.5,2.5,50000 total time: 1.81 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(58·10¹⁴⁹+41)/9 = 6(4)₁₄₈9_<150> = 13 · 421 · 673 · 100732103 · 10121236004206718958491_<23> · C114
C114 = P34 · P81
P34 = 1696102823243283336102096639983899_<34>
P81 = 101179223498410154287697137052894881945104457224269718891386984074813463313174703_<81>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 171610366629216617736141540111186208266328445401431653663190700487849543363369209052931064897099041336492494106997 (114 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=8045793004 Step 1 took 2679ms Step 2 took 1931ms ********** Factor found in step 2: 1696102823243283336102096639983899 Found probable prime factor of 34 digits: 1696102823243283336102096639983899 Probable prime cofactor 101179223498410154287697137052894881945104457224269718891386984074813463313174703 has 81 digits
(58·10¹³⁹+41)/9 = 6(4)₁₃₈9_<140> = 3³ · 31 · 354401 · 54080105661919_<14> · C118
C118 = P48 · P71
P48 = 240281321672102092031822941423701958764184969789_<48>
P71 = 16718893984341374478344248259057953266891108617477674510284921115332047_<71>

Number: 64449_139 N=4017237943453302397946339277421751791024513472930215399935475761833309366097049405279496394556016946350294521398528083 ( 118 digits) SNFS difficulty: 141 digits. Divisors found: r1=240281321672102092031822941423701958764184969789 r2=16718893984341374478344248259057953266891108617477674510284921115332047 Version: Total time: 2.70 hours. Scaled time: 6.45 units (timescale=2.387). Factorization parameters were as follows: n: 4017237943453302397946339277421751791024513472930215399935475761833309366097049405279496394556016946350294521398528083 m: 10000000000000000000000000000 deg: 5 c5: 29 c0: 205 skew: 1.48 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [950000, 1550001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4087260 Max relations in full relation-set: Initial matrix: Pruned matrix : 225814 x 226062 Total sieving time: 2.35 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,48,48,2.3,2.3,50000 total time: 2.70 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(58·10¹⁵⁴+41)/9 = 6(4)₁₅₃9_<155> = 3 · 7 · 11 · 31 · 71 · 5855357 · C143
C143 = P38 · P106
P38 = 19602950039461147737333838041523754911_<38>
P106 = 1104278583638193529919243527908672991914078598007534915906542790083954395182929626640133526640510031759077_<106>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 21647117904706426189450950955016520273027057886377657995652670021137134050778094557363598017537468435215087853257755032275763510326739547577147 (143 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=127652953 Step 1 took 4052ms Step 2 took 2504ms ********** Factor found in step 2: 19602950039461147737333838041523754911 Found probable prime factor of 38 digits: 19602950039461147737333838041523754911 Probable prime cofactor 1104278583638193529919243527908672991914078598007534915906542790083954395182929626640133526640510031759077 has 106 digits
(58·10¹⁵⁹+41)/9 = 6(4)₁₅₈9_<160> = 47 · C159
C159 = P32 · P127
P32 = 21092604873221414521443936704579_<32>
P127 = 6500659357516210823212559424126325115688797215821254650858989687046391572429678404166908697240963504783993737251101929522190373_<127>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 137115839243498817966903073286052009456264775413711583924349881796690307328605200945626477541371158392434988179669030732860520094562647754137115839243498817967 (159 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1988145448 Step 1 took 4787ms Step 2 took 2705ms ********** Factor found in step 2: 21092604873221414521443936704579 Found probable prime factor of 32 digits: 21092604873221414521443936704579 Probable prime cofactor 6500659357516210823212559424126325115688797215821254650858989687046391572429678404166908697240963504783993737251101929522190373 has 127 digits
(58·10¹⁴⁰+41)/9 = 6(4)₁₃₉9_<141> = 11 · 19 · 127 · 2801 · 517961019025123_<15> · C119
C119 = P44 · P75
P44 = 28571814345470798457850196642434401668480249_<44>
P75 = 585716518304778674109618639218066670643040948267599228491642409925313514109_<75>

Number: 64449_140 N=16734983620079684836530558211268541781736781482763673605856165874596688227525266870848902799120670143654113023649333141 ( 119 digits) SNFS difficulty: 141 digits. Divisors found: r1=28571814345470798457850196642434401668480249 r2=585716518304778674109618639218066670643040948267599228491642409925313514109 Version: Total time: 3.15 hours. Scaled time: 7.52 units (timescale=2.385). Factorization parameters were as follows: n: 16734983620079684836530558211268541781736781482763673605856165874596688227525266870848902799120670143654113023649333141 m: 10000000000000000000000000000 deg: 5 c5: 58 c0: 41 skew: 0.93 type: snfs lss: 1 rlim: 1900000 alim: 1900000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1900000/1900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [950000, 1650001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3952668 Max relations in full relation-set: Initial matrix: Pruned matrix : 274683 x 274930 Total sieving time: 2.65 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.17 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1900000,1900000,26,26,48,48,2.3,2.3,50000 total time: 3.15 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(43·10²⁰⁰+11)/9 = 4(7)₁₉₉9_<201> = C201
C201 = P91 · P111
P91 = 2174373058099133778955027754091881176658176439236542612023908234704073354923429801680431157_<91>
P111 = 219731281160859097400420474569740172057755221825684698747872340583961067609816288201669884937774558773451626247_<111>

Number: 47779_200 N=477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 ( 201 digits) SNFS difficulty: 201 digits. Divisors found: r1=2174373058099133778955027754091881176658176439236542612023908234704073354923429801680431157 r2=219731281160859097400420474569740172057755221825684698747872340583961067609816288201669884937774558773451626247 Version: Total time: 448.74 hours. Scaled time: 1069.34 units (timescale=2.383). Factorization parameters were as follows: n: 477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779 m: 10000000000000000000000000000000000000000 deg: 5 c5: 43 c0: 11 skew: 0.76 type: snfs lss: 1 rlim: 20000000 alim: 20000000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 20000000/20000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [10000000, 19500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 39359230 Max relations in full relation-set: Initial matrix: Pruned matrix : 3461402 x 3461650 Total sieving time: 402.68 hours. Total relation processing time: 11.76 hours. Matrix solve time: 33.25 hours. Time per square root: 1.06 hours. Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,20000000,20000000,29,29,56,56,2.6,2.6,100000 total time: 448.74 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Aug 9, 2009 (4th): By Wataru Sakai / Msieve / Aug 9, 2009
(55·10¹⁸²+71)/9 = 6(1)₁₈₁9_<183> = 81629 · C178
C178 = P87 · P92
P87 = 268968386937796209285255055537985514655500461536626239747662232571641324962733344449049_<87>
P92 = 27833925818601073393361973681889386756037781086677916726445315318676185387360456995972477139_<92>

Number: 61119_182 N=7486446129575409610691189541843108590220523479536820383823287203213454913218477637985410958251492865416838514634641011296366623517513519841124001410174216407295337577467702790811 ( 178 digits) SNFS difficulty: 184 digits. Divisors found: r1=268968386937796209285255055537985514655500461536626239747662232571641324962733344449049 r2=27833925818601073393361973681889386756037781086677916726445315318676185387360456995972477139 Version: Total time: 310.69 hours. Scaled time: 624.49 units (timescale=2.010). Factorization parameters were as follows: n: 7486446129575409610691189541843108590220523479536820383823287203213454913218477637985410958251492865416838514634641011296366623517513519841124001410174216407295337577467702790811 m: 2000000000000000000000000000000000000 deg: 5 c5: 1375 c0: 568 skew: 0.84 type: snfs lss: 1 rlim: 8400000 alim: 8400000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 8400000/8400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4200000, 7800001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1285146 x 1285394 Total sieving time: 310.69 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,184,5,0,0,0,0,0,0,0,0,8400000,8400000,28,28,54,54,2.5,2.5,100000 total time: 310.69 hours. --------- CPU info (if available) ----------
(4·10¹⁹⁹-7)/3 = 1(3)₁₉₈1_<200> = 11 · 313 · C196
C196 = P80 · P117
P80 = 14245284449048868649167658171982103265194892503790476016535809966373146771405253_<80>
P117 = 271850783034045904709166657548054817831235558520384314653175768959548794237356697623685222130093654997355896460223789_<117>

Number: 13331_199 N=3872591732016652144447671604221124987898150837447962048601026236808984412818278632975118598121793009971923709942879271952754380869396843837738406428502275147642559783134863007067479910930390163617 ( 196 digits) SNFS difficulty: 200 digits. Divisors found: r1=14245284449048868649167658171982103265194892503790476016535809966373146771405253 r2=271850783034045904709166657548054817831235558520384314653175768959548794237356697623685222130093654997355896460223789 Version: Total time: 513.72 hours. Scaled time: 1035.14 units (timescale=2.015). Factorization parameters were as follows: n: 3872591732016652144447671604221124987898150837447962048601026236808984412818278632975118598121793009971923709942879271952754380869396843837738406428502275147642559783134863007067479910930390163617 m: 10000000000000000000000000000000000000000 deg: 5 c5: 2 c0: -35 skew: 1.77 type: snfs lss: 1 rlim: 15300000 alim: 15300000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6 Factor base limits: 15300000/15300000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7650000, 12650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2913154 x 2913400 Total sieving time: 513.72 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,200,5,0,0,0,0,0,0,0,0,15300000,15300000,29,29,56,56,2.6,2.6,100000 total time: 513.72 hours. --------- CPU info (if available) ----------
(37·10¹⁹³-1)/9 = 4(1)₁₉₃_<194> = 541 · C191
C191 = P95 · P97
P95 = 16982086357914803637623741673240335869987959520338455554555164416476118201559316006982399568593_<95>
P97 = 4474771923497334638554968073323091298281184099854318393507188833675114725959431699712597968081347_<97>

Number: 41111_193 N=75990963236804271924419798726637913329225713698911480796878209077839392072294105565824604641610186896693366194290408708153624974327377284863421647155473403162867118504826453070445676730334771 ( 191 digits) SNFS difficulty: 196 digits. Divisors found: r1=16982086357914803637623741673240335869987959520338455554555164416476118201559316006982399568593 r2=4474771923497334638554968073323091298281184099854318393507188833675114725959431699712597968081347 Version: Total time: 650.69 hours. Scaled time: 1307.89 units (timescale=2.010). Factorization parameters were as follows: n: 75990963236804271924419798726637913329225713698911480796878209077839392072294105565824604641610186896693366194290408708153624974327377284863421647155473403162867118504826453070445676730334771 m: 1000000000000000000000000000000000000000 deg: 5 c5: 37 c0: -100 skew: 1.22 type: snfs lss: 1 rlim: 13200000 alim: 13200000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 13200000/13200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6600000, 13700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2320654 x 2320902 Total sieving time: 650.69 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,196,5,0,0,0,0,0,0,0,0,13200000,13200000,28,28,55,55,2.5,2.5,100000 total time: 650.69 hours. --------- CPU info (if available) ----------
Aug 9, 2009 (3rd): By matsui / Msieve / Aug 9, 2009
9·10¹⁹⁶+7 = 9(0)₁₉₅7_<197> = 379 · 84347 · C190
C190 = P70 · P121
P70 = 2793581839990665879086071955488871732154051874807346381894557450536389_<70>
P121 = 1007795141038902862381302247759455291325233747340278362348189347943401583915173253582538601189245685674010445568232328851_<121>

N=2815358204437110888169498828388683223496303888263062566049476542013136899326513138510337041233079345271557408923240290854030465241384276593552961095221889797933295592935240223410560590059039 ( 190 digits) SNFS difficulty: 196 digits. Divisors found: r1=2793581839990665879086071955488871732154051874807346381894557450536389 (pp70) r2=1007795141038902862381302247759455291325233747340278362348189347943401583915173253582538601189245685674010445568232328851 (pp121) Version: Msieve v. 1.42 Total time: 502.44 hours. Scaled time: 1121.95 units (timescale=2.233). Factorization parameters were as follows: n: 2815358204437110888169498828388683223496303888263062566049476542013136899326513138510337041233079345271557408923240290854030465241384276593552961095221889797933295592935240223410560590059039 m: 1000000000000000000000000000000000000000 deg: 5 c5: 90 c0: 7 skew: 0.60 type: snfs lss: 1 rlim: 13400000 alim: 13400000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5 qintsize: 300000 Factor base limits: 13400000/13400000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6700000, 14800001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2655010 x 2655235 Total sieving time: 488.23 hours. Total relation processing time: 0.20 hours. Matrix solve time: 13.50 hours. Time per square root: 0.51 hours. Prototype def-par.txt line would be: snfs,196.000,5,0,0,0,0,0,0,0,0,13400000,13400000,28,28,55,55,2.5,2.5,100000 total time: 502.44 hours.
Aug 9, 2009 (2nd): By Sinkiti Sibata / Msieve / Aug 9, 2009
(58·10¹⁴⁷+41)/9 = 6(4)₁₄₆9_<148> = 107 · 691 · 1870639 · 15308009 · C130
C130 = P57 · P74
P57 = 104226810757989487023155307155618642769595857629037983413_<57>
P74 = 29203541189843452413587717044503298257109696168892743916901538636843884779_<74>

Number: 64449_147 N=3043791961056964650204073474298058150487255812058742155043591009507435709246375658619967190325348574728898111100942827283085170727 ( 130 digits) SNFS difficulty: 149 digits. Divisors found: r1=104226810757989487023155307155618642769595857629037983413 (pp57) r2=29203541189843452413587717044503298257109696168892743916901538636843884779 (pp74) Version: Msieve-1.40 Total time: 10.41 hours. Scaled time: 34.93 units (timescale=3.357). Factorization parameters were as follows: name: 64449_147 n: 3043791961056964650204073474298058150487255812058742155043591009507435709246375658619967190325348574728898111100942827283085170727 m: 200000000000000000000000000000 deg: 5 c5: 725 c0: 164 skew: 0.74 type: snfs lss: 1 rlim: 2200000 alim: 2200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1100000, 2700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 368768 x 369016 Total sieving time: 10.10 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.24 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,149.000,5,0,0,0,0,0,0,0,0,2200000,2200000,26,26,49,49,2.3,2.3,100000 total time: 10.41 hours. --------- CPU info (if available) ----------
Aug 9, 2009: Many small prime numbers up to 215 digits in the primesize.txt were proved by Robert Backstrom.
Aug 8, 2009 (5th): By Jo Yeong Uk / YAFU 1.10, Msieve, GGNFS, GMP-ECM / Aug 8, 2009
(58·10¹²⁰+41)/9 = 6(4)₁₁₉9_<121> = 11 · 17 · 1432943 · 13858699 · 96751818844475480137_<20> · C86
C86 = P40 · P46
P40 = 4171154534180201577214509051813439982857_<40>
P46 = 4300085410829145193862369954805882431917303879_<46>

08/08/09 14:59:52 v1.10 @ 조영욱-PC, starting SIQS on c86: 17936320758742123847911845494663667844121370803322423565926859018744477965975419602303 08/08/09 14:59:52 v1.10 @ 조영욱-PC, random seeds: 3513321531, 909715568 08/08/09 14:59:52 v1.10 @ 조영욱-PC, ==== sieve params ==== 08/08/09 14:59:52 v1.10 @ 조영욱-PC, n = 86 digits, 287 bits 08/08/09 14:59:52 v1.10 @ 조영욱-PC, factor base: 56921 primes (max prime = 1493971) 08/08/09 14:59:52 v1.10 @ 조영욱-PC, single large prime cutoff: 164336810 (110 * pmax) 08/08/09 14:59:52 v1.10 @ 조영욱-PC, double large prime range from 43 to 50 bits 08/08/09 14:59:52 v1.10 @ 조영욱-PC, double large prime cutoff: 614218275674814 08/08/09 14:59:52 v1.10 @ 조영욱-PC, using 15 large prime slices of factor base 08/08/09 14:59:52 v1.10 @ 조영욱-PC, buckets hold 1024 elements 08/08/09 14:59:52 v1.10 @ 조영욱-PC, sieve interval: 9 blocks of size 65536 08/08/09 14:59:52 v1.10 @ 조영욱-PC, polynomial A has ~ 11 factors 08/08/09 14:59:52 v1.10 @ 조영욱-PC, using multiplier of 13 08/08/09 14:59:52 v1.10 @ 조영욱-PC, using small prime variation correction of 24 bits 08/08/09 14:59:52 v1.10 @ 조영욱-PC, using SSE2 for trial division and x128 sieve scanning 08/08/09 14:59:52 v1.10 @ 조영욱-PC, trial factoring cutoff at 91 bits 08/08/09 14:59:52 v1.10 @ 조영욱-PC, ==== sieving started ==== 08/08/09 15:17:13 v1.10 @ 조영욱-PC, sieve time = 453.0300, relation time = 269.1360, poly_time = 318.0120 08/08/09 15:17:13 v1.10 @ 조영욱-PC, 57094 relations found: 20657 full + 36437 from 472011 partial, using 168286 polys (164 A polys) 08/08/09 15:17:13 v1.10 @ 조영욱-PC, on average, sieving found 2.93 rels/poly and 473.28 rels/sec 08/08/09 15:17:13 v1.10 @ 조영욱-PC, trial division touched 15023845 sieve locations out of 198518243328 08/08/09 15:17:13 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 08/08/09 15:17:13 v1.10 @ 조영욱-PC, begin with 492668 relations 08/08/09 15:17:13 v1.10 @ 조영욱-PC, reduce to 111147 relations in 8 passes 08/08/09 15:17:14 v1.10 @ 조영욱-PC, recovered 111147 relations 08/08/09 15:17:14 v1.10 @ 조영욱-PC, recovered 81457 polynomials 08/08/09 15:17:14 v1.10 @ 조영욱-PC, attempting to build 57094 cycles 08/08/09 15:17:14 v1.10 @ 조영욱-PC, found 57094 cycles in 4 passes 08/08/09 15:17:14 v1.10 @ 조영욱-PC, distribution of cycle lengths: 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 1 : 20657 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 2 : 16661 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 3 : 10075 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 4 : 5301 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 5 : 2549 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 6 : 1083 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 7 : 461 08/08/09 15:17:14 v1.10 @ 조영욱-PC, length 9+: 307 08/08/09 15:17:14 v1.10 @ 조영욱-PC, largest cycle: 14 relations 08/08/09 15:17:14 v1.10 @ 조영욱-PC, matrix is 56921 x 57094 (11.8 MB) with weight 2647073 (46.36/col) 08/08/09 15:17:14 v1.10 @ 조영욱-PC, sparse part has weight 2647073 (46.36/col) 08/08/09 15:17:14 v1.10 @ 조영욱-PC, filtering completed in 3 passes 08/08/09 15:17:14 v1.10 @ 조영욱-PC, matrix is 48448 x 48508 (10.3 MB) with weight 2307516 (47.57/col) 08/08/09 15:17:14 v1.10 @ 조영욱-PC, sparse part has weight 2307516 (47.57/col) 08/08/09 15:17:14 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 08/08/09 15:17:15 v1.10 @ 조영욱-PC, matrix is 48400 x 48508 (7.3 MB) with weight 1823058 (37.58/col) 08/08/09 15:17:15 v1.10 @ 조영욱-PC, sparse part has weight 1420269 (29.28/col) 08/08/09 15:17:15 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 08/08/09 15:17:15 v1.10 @ 조영욱-PC, using block size 19403 for processor cache size 4096 kB 08/08/09 15:17:15 v1.10 @ 조영욱-PC, commencing Lanczos iteration 08/08/09 15:17:15 v1.10 @ 조영욱-PC, memory use: 6.5 MB 08/08/09 15:17:24 v1.10 @ 조영욱-PC, lanczos halted after 766 iterations (dim = 48398) 08/08/09 15:17:24 v1.10 @ 조영욱-PC, recovered 17 nontrivial dependencies 08/08/09 15:17:25 v1.10 @ 조영욱-PC, prp40 = 4171154534180201577214509051813439982857 08/08/09 15:17:26 v1.10 @ 조영욱-PC, prp46 = 4300085410829145193862369954805882431917303879 08/08/09 15:17:26 v1.10 @ 조영욱-PC, Lanczos elapsed time = 10.8730 seconds. 08/08/09 15:17:26 v1.10 @ 조영욱-PC, Sqrt elapsed time = 2.5110 seconds. 08/08/09 15:17:26 v1.10 @ 조영욱-PC, SIQS elapsed time = 1054.3570 seconds. 08/08/09 15:17:26 v1.10 @ 조영욱-PC, 08/08/09 15:17:26 v1.10 @ 조영욱-PC,
(58·10¹²⁴+41)/9 = 6(4)₁₂₃9_<125> = 3 · 7 · 11² · 31 · 53 · 3336601 · 4436867425279643_<16> · C97
C97 = P48 · P49
P48 = 267492333084733470268984029104710701455232281551_<48>
P49 = 3898083961532116929988497717471694102623444454411_<49>

Number: 64449_124 N=1042707573430406393491906031296711719332378538641660681551632980630039511373360505714837935871461 ( 97 digits) SNFS difficulty: 126 digits. Divisors found: r1=267492333084733470268984029104710701455232281551 r2=3898083961532116929988497717471694102623444454411 Version: Total time: 0.79 hours. Scaled time: 1.89 units (timescale=2.388). Factorization parameters were as follows: n: 1042707573430406393491906031296711719332378538641660681551632980630039511373360505714837935871461 m: 10000000000000000000000000 deg: 5 c5: 29 c0: 205 skew: 1.48 type: snfs lss: 1 rlim: 800000 alim: 800000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [400000, 600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 2446613 Max relations in full relation-set: Initial matrix: Pruned matrix : 95442 x 95690 Total sieving time: 0.70 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,800000,800000,26,26,46,46,2.3,2.3,40000 total time: 0.79 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(58·10¹³⁵+41)/9 = 6(4)₁₃₄9_<136> = 1439 · 53697084205907_<14> · C119
C119 = P52 · P68
P52 = 1128787256771068110891967257486158744224357811724497_<52>
P68 = 73885954557658207227978625191186478807384791934220624008771044803029_<68>

Number: 64449_135 N=83401523959050804924972610883019020772103327350516411471050111549524066031956548155738313342090261880249108256179101413 ( 119 digits) SNFS difficulty: 136 digits. Divisors found: r1=1128787256771068110891967257486158744224357811724497 r2=73885954557658207227978625191186478807384791934220624008771044803029 Version: Total time: 2.26 hours. Scaled time: 5.40 units (timescale=2.388). Factorization parameters were as follows: n: 83401523959050804924972610883019020772103327350516411471050111549524066031956548155738313342090261880249108256179101413 m: 1000000000000000000000000000 deg: 5 c5: 58 c0: 41 skew: 0.93 type: snfs lss: 1 rlim: 1400000 alim: 1400000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [700000, 1250001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3548779 Max relations in full relation-set: Initial matrix: Pruned matrix : 194905 x 195153 Total sieving time: 1.95 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,26,26,48,48,2.3,2.3,50000 total time: 2.26 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(58·10¹³⁸+41)/9 = 6(4)₁₃₇9_<139> = 11 · 1907 · 33947487199_<11> · C124
C124 = P36 · P89
P36 = 619682416402246260242658300172564813_<36>
P89 = 14603780594971380709213275235955179207952396770027290460063940971518463105065496294225451_<89>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 9049706047700098778472617130075705484325248766095900478012943598748454740374814077391893881246699892749334477158507931655663 (124 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=3967165505 Step 1 took 4212ms Step 2 took 4149ms ********** Factor found in step 2: 619682416402246260242658300172564813 Found probable prime factor of 36 digits: 619682416402246260242658300172564813 Probable prime cofactor 14603780594971380709213275235955179207952396770027290460063940971518463105065496294225451 has 89 digits
(58·10¹³⁷+41)/9 = 6(4)₁₃₆9_<138> = 13² · 53 · 89 · 2371780942173151_<16> · C117
C117 = P35 · P83
P35 = 14884551379367473034365581346771321_<35>
P83 = 22899319608705534678406447304938033748166187889155106711843604195847753505863147003_<83>

Number: 64449_137 N=340846099268334589063925286498769963997410140964630221918445886354506313410431118519162224524675570357048474447500963 ( 117 digits) SNFS difficulty: 139 digits. Divisors found: r1=14884551379367473034365581346771321 r2=22899319608705534678406447304938033748166187889155106711843604195847753505863147003 Version: Total time: 3.14 hours. Scaled time: 7.51 units (timescale=2.389). Factorization parameters were as follows: n: 340846099268334589063925286498769963997410140964630221918445886354506313410431118519162224524675570357048474447500963 m: 2000000000000000000000000000 deg: 5 c5: 725 c0: 164 skew: 0.74 type: snfs lss: 1 rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [900000, 1600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 3960377 Max relations in full relation-set: Initial matrix: Pruned matrix : 243100 x 243348 Total sieving time: 2.71 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.13 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,50000 total time: 3.14 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
(58·10¹⁴⁴+41)/9 = 6(4)₁₄₃9_<145> = 11 · 199 · 6581 · 10586419 · 178413835756643_<15> · 13295261417971829_<17> · C101
C101 = P46 · P55
P46 = 3550330562770319439823346494483581255745491313_<46>
P55 = 5017698363791318288256268260704825461570233445854479429_<55>

Number: 64449_144 N=17814487855730942101864005469134517687896385849816384316995836597205299202233380008914073671456700277 ( 101 digits) Divisors found: r1=3550330562770319439823346494483581255745491313 r2=5017698363791318288256268260704825461570233445854479429 Version: Total time: 2.62 hours. Scaled time: 6.24 units (timescale=2.384). Factorization parameters were as follows: name: 64449_144 n: 17814487855730942101864005469134517687896385849816384316995836597205299202233380008914073671456700277 skew: 1770.95 # norm 5.81e+13 c5: 602640 c4: 1871645292 c3: 8704689514020 c2: -3695448870658363 c1: -15197534558257118770 c0: 5588911043113068396936 # alpha -5.76 Y1: 62518557167 Y0: -7836839010963824795 # Murphy_E 3.24e-09 # M 16121912846489293313346083522004164419855127380897457966767740960635640065692258082666037901042514449 type: gnfs rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [600000, 1100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4181672 Max relations in full relation-set: Initial matrix: Pruned matrix : 208491 x 208739 Polynomial selection time: 0.19 hours. Total sieving time: 2.06 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.10 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,49,49,2.5,2.5,50000 total time: 2.62 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Aug 8, 2009 (4th): By Sinkiti Sibata / Msieve / Aug 8, 2009
(58·10¹¹⁷+41)/9 = 6(4)₁₁₆9_<118> = 6981103 · 20052849473375479961204639_<26> · C86
C86 = P37 · P50
P37 = 2158588796290758972254217158621260613_<37>
P50 = 21326295670555186762106081990279592452723366079869_<50>

at Aug 08 15:22:45 2009 Msieve v. 1.42 Sat Aug 08 15:22:45 2009 random seeds: ac5f2114 ee093235 Sat Aug 08 15:22:45 2009 factoring 46034702900844545055529893009178313512466417637783840356525323468254990122504821899697 (86 digits) Sat Aug 08 15:22:47 2009 searching for 15-digit factors Sat Aug 08 15:22:47 2009 commencing quadratic sieve (86-digit input) Sat Aug 08 15:22:48 2009 using multiplier of 1 Sat Aug 08 15:22:48 2009 using 32kb Intel Core sieve core Sat Aug 08 15:22:48 2009 sieve interval: 16 blocks of size 32768 Sat Aug 08 15:22:48 2009 processing polynomials in batches of 13 Sat Aug 08 15:22:48 2009 using a sieve bound of 1459427 (55667 primes) Sat Aug 08 15:22:48 2009 using large prime bound of 116754160 (26 bits) Sat Aug 08 15:22:48 2009 using double large prime bound of 331963366994880 (41-49 bits) Sat Aug 08 15:22:48 2009 using trial factoring cutoff of 49 bits Sat Aug 08 15:22:48 2009 polynomial 'A' values have 11 factors Sat Aug 08 15:56:44 2009 56109 relations (16197 full + 39912 combined from 581509 partial), need 55763 Sat Aug 08 15:56:46 2009 begin with 597706 relations Sat Aug 08 15:56:46 2009 reduce to 132368 relations in 10 passes Sat Aug 08 15:56:46 2009 attempting to read 132368 relations Sat Aug 08 15:56:48 2009 recovered 132368 relations Sat Aug 08 15:56:48 2009 recovered 108695 polynomials Sat Aug 08 15:56:48 2009 attempting to build 56109 cycles Sat Aug 08 15:56:48 2009 found 56109 cycles in 6 passes Sat Aug 08 15:56:48 2009 distribution of cycle lengths: Sat Aug 08 15:56:48 2009 length 1 : 16197 Sat Aug 08 15:56:48 2009 length 2 : 11144 Sat Aug 08 15:56:48 2009 length 3 : 10111 Sat Aug 08 15:56:48 2009 length 4 : 7157 Sat Aug 08 15:56:48 2009 length 5 : 4913 Sat Aug 08 15:56:48 2009 length 6 : 2935 Sat Aug 08 15:56:48 2009 length 7 : 1722 Sat Aug 08 15:56:48 2009 length 9+: 1930 Sat Aug 08 15:56:48 2009 largest cycle: 18 relations Sat Aug 08 15:56:48 2009 matrix is 55667 x 56109 (12.0 MB) with weight 2917724 (52.00/col) Sat Aug 08 15:56:48 2009 sparse part has weight 2917724 (52.00/col) Sat Aug 08 15:56:49 2009 filtering completed in 3 passes Sat Aug 08 15:56:49 2009 matrix is 50596 x 50660 (10.9 MB) with weight 2647779 (52.27/col) Sat Aug 08 15:56:49 2009 sparse part has weight 2647779 (52.27/col) Sat Aug 08 15:56:49 2009 saving the first 48 matrix rows for later Sat Aug 08 15:56:49 2009 matrix is 50548 x 50660 (6.1 MB) with weight 1968508 (38.86/col) Sat Aug 08 15:56:49 2009 sparse part has weight 1285742 (25.38/col) Sat Aug 08 15:56:49 2009 matrix includes 64 packed rows Sat Aug 08 15:56:49 2009 using block size 20264 for processor cache size 1024 kB Sat Aug 08 15:56:50 2009 commencing Lanczos iteration Sat Aug 08 15:56:50 2009 memory use: 7.0 MB Sat Aug 08 15:57:03 2009 lanczos halted after 801 iterations (dim = 50546) Sat Aug 08 15:57:04 2009 recovered 16 nontrivial dependencies Sat Aug 08 15:57:04 2009 prp37 factor: 2158588796290758972254217158621260613 Sat Aug 08 15:57:04 2009 prp50 factor: 21326295670555186762106081990279592452723366079869 Sat Aug 08 15:57:04 2009 elapsed time 00:34:19
(58·10¹²⁸+41)/9 = 6(4)₁₂₇9_<129> = 11 · C128
C128 = P32 · P45 · P52
P32 = 39898048673574179603199844885073_<32>
P45 = 649715236944848403995371739583303968875535713_<45>
P52 = 2260050228906597591554901754728515026209895212840691_<52>

Number: 64449_128 N=58585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585859 ( 128 digits) SNFS difficulty: 131 digits. Divisors found: r1=39898048673574179603199844885073 (pp32) r2=649715236944848403995371739583303968875535713 (pp45) r3=2260050228906597591554901754728515026209895212840691 (pp52) Version: Msieve-1.40 Total time: 2.46 hours. Scaled time: 8.09 units (timescale=3.287). Factorization parameters were as follows: name: 64449_128 n: 58585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585858585859 m: 50000000000000000000000000 deg: 5 c5: 464 c0: 1025 skew: 1.17 type: snfs lss: 1 rlim: 1070000 alim: 1070000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1070000/1070000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [535000, 985001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 147934 x 148182 Total sieving time: 2.37 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.04 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,131.000,5,0,0,0,0,0,0,0,0,1070000,1070000,26,26,47,47,2.3,2.3,50000 total time: 2.46 hours. --------- CPU info (if available) ----------
Aug 8, 2009 (3rd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 8, 2009
(14·10¹⁷¹+13)/9 = 1(5)₁₇₀7_<172> = 3 · 9761352401_<10> · 291815750197_<12> · 5862396613066093442304343_<25> · C125
C125 = P33 · P92
P33 = 335286451551713195473353730926391_<33>
P92 = 92609246362301408513269952814555626164032637076591129306358448623522057405639132520561888379_<92>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3294866312 Step 1 took 34035ms Step 2 took 13670ms ********** Factor found in step 2: 335286451551713195473353730926391 Found probable prime factor of 33 digits: 335286451551713195473353730926391 Probable prime cofactor 92609246362301408513269952814555626164032637076591129306358448623522057405639132520561888379 has 92 digits
Aug 8, 2009 (2nd): By Serge Batalov / GMP-ECM 6.2.1, Msieve / Aug 8, 2009
(58·10²⁰⁰+41)/9 = 6(4)₁₉₉9_<201> = 11 · 17 · 107 · 2377 · 932774347987103381_<18> · 13826677866082240683703_<23> · 21474065269491482871681097_<26> · C128
C128 = P31 · C97
P31 = 9617476601959055323120190872597_<31>
C97 = [5086992204036649549554802325517951171974055226822069754918148594115667379490630513181229558391639_<97>]

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1094701982 Step 1 took 2496ms Step 2 took 2004ms ********** Factor found in step 2: 9617476601959055323120190872597 Found probable prime factor of 31 digits: 9617476601959055323120190872597 Composite cofactor has 97 digits
(58·10¹⁹²+41)/9 = 6(4)₁₉₁9_<193> = 11 · 139 · 24107297 · 440052311 · 10402068055283_<14> · C161
C161 = P30 · P131
P30 = 389330198417547379466454031507_<30>
P131 = 98104152943332266788674463871533087097832143310616650750836727883467574943205234124279264185234168457469978071068936557397216769703_<131>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=131367667 Step 1 took 3576ms Step 2 took 2408ms ********** Factor found in step 2: 389330198417547379466454031507 Found probable prime factor of 30 digits: 389330198417547379466454031507 Probable prime cofactor 9810415294333226678867446387153308709783214331061665075083672788346757494320523412427926418523416845746997807106 8936557397216769703 has 131 digits
(58·10²⁰³+41)/9 = 6(4)₂₀₂9_<204> = 13 · 4562672679804431624287_<22> · C182
C182 = P35 · P147
P35 = 51152262708347907152704942961133901_<35>
P147 = 212401690156098939939913557892512052200649177854946363470388068645251151818923654748302693711054147745443858651608553980275034876545681804713872679_<147>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=2588790684 Step 1 took 4076ms Step 2 took 2652ms ********** Factor found in step 2: 51152262708347907152704942961133901 Found probable prime factor of 35 digits: 51152262708347907152704942961133901 Probable prime cofactor has 147 digits
(58·10¹⁰⁴+41)/9 = 6(4)₁₀₃9_<105> = 11 · 17 · 19 · 109 · 842887 · C94
C94 = P36 · P58
P36 = 550869718097003447204551975703287171_<36>
P58 = 3583814511051657908982940011891001026899175054919974150481_<58>

SNFS difficulty: 105 digits. Divisors found: r1=550869718097003447204551975703287171 (pp36) r2=3583814511051657908982940011891001026899175054919974150481 (pp58) Version: Msieve v. 1.43 Total time: 0.32 hours. Scaled time: 0.76 units (timescale=2.400). Factorization parameters were as follows: n: 1974214889414977037467608582187196548946406411233375487631192692026183614045274001659910779251 m: 100000000000000000000000000 deg: 4 c4: 58 c0: 41 skew: 0.92 type: snfs lss: 1 rlim: 410000 alim: 410000 lpbr: 25 lpba: 25 mfbr: 44 mfba: 44 rlambda: 2.2 alambda: 2.2 Factor base limits: 410000/410000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [205000, 305001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 38641 x 38889 Total sieving time: 0.30 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,105.000,4,0,0,0,0,0,0,0,0,410000,410000,25,25,44,44,2.2,2.2,20000 total time: 0.32 hours.
(58·10¹⁷⁹+41)/9 = 6(4)₁₇₈9_<180> = 13 · 257 · 8101 · 115998234137_<12> · 26557839579002128971173217971_<29> · C133
C133 = P32 · P102
P32 = 12168445837390283378749132344323_<32>
P102 = 635171702715363223405943616590905150867918196427406156053354992650488343086622847098876838786815913809_<102>

Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=4122123285 Step 1 took 2544ms Step 2 took 1992ms ********** Factor found in step 2: 12168445837390283378749132344323 Found probable prime factor of 32 digits: 12168445837390283378749132344323 Probable prime cofactor has 102 digits
(58·10¹¹²+41)/9 = 6(4)₁₁₁9_<113> = 3⁵ · 7 · 11 · 181 · 19411741 · C99
C99 = P45 · P55
P45 = 108154283898859034137377190207499452312048313_<45>
P55 = 9063620148804105342986892378964642781241934655305454783_<55>

SNFS difficulty: 114 digits. Divisors found: r1=108154283898859034137377190207499452312048313 (pp45) r2=9063620148804105342986892378964642781241934655305454783 (pp55) Version: Msieve v. 1.43 Total time: 0.57 hours. Scaled time: 1.36 units (timescale=2.400). Factorization parameters were as follows: n: 980269346725178173569345476627308050099291195661372298815557195739472378690464284127582580732931079 m: 20000000000000000000000 deg: 5 c5: 725 c0: 164 skew: 0.74 type: snfs lss: 1 rlim: 560000 alim: 560000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 560000/560000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [280000, 480001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 52644 x 52877 Total sieving time: 0.54 hours. Total relation processing time: 0.01 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,114.000,5,0,0,0,0,0,0,0,0,560000,560000,25,25,45,45,2.2,2.2,50000 total time: 0.57 hours.
(58·10¹⁹⁷+41)/9 = 6(4)₁₉₆9_<198> = 13 · 933299923 · 8436592305409_<13> · 111772795484434550519_<21> · C155
C155 = P34 · C122
P34 = 5087832120754440156018956894208167_<34>
C122 = [11070951636149765536840257253607829444595086747622399008620240727882623901740891490497776510088174513384413377746808577543_<122>]

Using B1=2000000, B2=2853999340, polynomial Dickson(6), sigma=3097237382 Step 1 took 7492ms ********** Factor found in step 1: 5087832120754440156018956894208167 Found probable prime factor of 34 digits: 5087832120754440156018956894208167 Composite cofactor has 122 digits
Aug 8, 2009: Factorizations of 644...449 have been extended up to n=205. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.
Aug 7, 2009 (2nd): By Wataru Sakai / GMP-ECM 6.2.1 / Aug 7, 2009
(52·10¹⁷¹-43)/9 = 5(7)₁₇₀3_<172> = 19 · 30158387489_<11> · 570722929894025945844003120791_<30> · C131
C131 = P37 · P94
P37 = 5740582896936804596177972515586571449_<37>
P94 = 3077639887964649309299233949920934152559049053053399717566063157179476351969374735826702962817_<94>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1753045546 Step 1 took 38331ms Step 2 took 13954ms ********** Factor found in step 2: 5740582896936804596177972515586571449 Found probable prime factor of 37 digits: 5740582896936804596177972515586571449 Probable prime cofactor 3077639887964649309299233949920934152559049053053399717566063157179476351969374735826702962817 has 94 digits
Aug 7, 2009: By Justin Card / ggnfs, msieve / Aug 7, 2009
(8·10¹⁸⁷+7)/3 = 2(6)₁₈₆9_<188> = 109 · 334385738359_<12> · 1156043727761581055051_<22> · C153
C153 = P50 · P104
P50 = 50479019016684754981287962531941919871490137032437_<50>
P104 = 12537453051487436307735149209875880318604212209305100871443655159262572184508170463967147425732527050177_<104>

Number: 26669_187 N=632878331006826607892921413052373101493750270973351039252297873320440059704872140878402857753484859895707714576386291447104887955102355026445584175591349 ( 153 digits) SNFS difficulty: 187 digits. Divisors found: r1=50479019016684754981287962531941919871490137032437 (pp50) r2=12537453051487436307735149209875880318604212209305100871443655159262572184508170463967147425732527050177 (pp104) Version: Msieve-1.40 Total time: 154.81 hours. Scaled time: 313.18 units (timescale=2.023). Factorization parameters were as follows: n: 632878331006826607892921413052373101493750270973351039252297873320440059704872140878402857753484859895707714576386291447104887955102355026445584175591349 m: 20000000000000000000000000000000000000 deg: 5 c5: 25 c0: 7 skew: 0.78 type: snfs lss: 1 rlim: 9500000 alim: 9500000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 9500000/9500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [4750000, 7550001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1798825 x 1799050 Total sieving time: 137.64 hours. Total relation processing time: 0.31 hours. Matrix solve time: 16.50 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: snfs,187.000,5,0,0,0,0,0,0,0,0,9500000,9500000,28,28,54,54,2.5,2.5,100000 total time: 154.81 hours. --------- CPU info (if available) ---------- [ 0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init) [ 0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297) [ 0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305) [ 0.231806] Total of 2 processors activated (8004.80 BogoMIPS).
Aug 4, 2009 (2nd): By Robert Backstrom / GGNFS, Msieve / Aug 4, 2009
4·10²¹³+9 = 4(0)₂₁₂9_<214> = 89 · 211 · C210
C210 = P40 · P57 · P114
P40 = 4912330291777329830182920462792184153201_<40>
P57 = 209197765948292508715840081366263723462559353816430654219_<57>
P114 = 207273092529491319737806399512561945738725389466995842008096844701461670330893312911176031446241487096666609893809_<114>

Number: n N=213003887320943607220831780179988284786197348101602854252090100644336759145854411843016135044464561478246978007348634112572554449118696416209595825123808509505298471697108472229618190531977208584056659034027371 ( 210 digits) SNFS difficulty: 213 digits. Divisors found: Tue Aug 4 04:37:56 2009 prp40 factor: 4912330291777329830182920462792184153201 Tue Aug 4 04:37:56 2009 prp57 factor: 209197765948292508715840081366263723462559353816430654219 Tue Aug 4 04:37:56 2009 prp114 factor: 207273092529491319737806399512561945738725389466995842008096844701461670330893312911176031446241487096666609893809 Tue Aug 4 04:37:56 2009 elapsed time 44:31:12 (Msieve 1.39 - dependency 7) Version: GGNFS-0.77.1-20050930-k8 Total time: 120.93 hours. Scaled time: 184.54 units (timescale=1.526). Factorization parameters were as follows: name: KA_4_0_212_9 n: 213003887320943607220831780179988284786197348101602854252090100644336759145854411843016135044464561478246978007348634112572554449118696416209595825123808509505298471697108472229618190531977208584056659034027371 m: 200000000000000000000000000000000000 deg: 6 c6: 125 c0: 18 skew: 0.72 type: snfs lss: 1 rlim: 26000000 alim: 26000000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 26000000/26000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [13000000, 37049990) Primes: RFBsize:1624527, AFBsize:1624093, largePrimes:39831436 encountered Relations: rels:39025275, finalFF:1913417 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7571502 hash collisions in 47357091 relations Msieve: matrix is 4518042 x 4518290 (1229.8 MB) Total sieving time: 119.25 hours. Total relation processing time: 1.68 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,213,6,0,0,0,0,0,0,0,0,26000000,26000000,29,29,58,58,2.6,2.6,100000 total time: 120.93 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3352036k/3407296k available (3118k kernel code, 53976k reserved, 1895k data, 424k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830492) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830448) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830455) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830458) Total of 4 processors activated (22643.70 BogoMIPS).
(53·10¹⁸⁵-71)/9 = 5(8)₁₈₄1_<186> = 23 · 233 · C183
C183 = P45 · P138
P45 = 215325522097885785506678338135721202120862759_<45>
P138 = 510333519255213660531524689794452061284434462061881762456420580789577174717938354675826912683331869019878654674813170859867374521644491401_<138>

Number: n N=109887831477680330078165495220916008376355456034500632373369824386805166801434761875142543177624349484771205241442225954261781841554187141050361800501751985237710186394642449876635359 ( 183 digits) SNFS difficulty: 186 digits. Divisors found: Tue Aug 04 22:42:53 2009 prp45 factor: 215325522097885785506678338135721202120862759 Tue Aug 04 22:42:53 2009 prp138 factor: 510333519255213660531524689794452061284434462061881762456420580789577174717938354675826912683331869019878654674813170859867374521644491401 Tue Aug 04 22:42:53 2009 elapsed time 03:07:10 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 125.56 hours. Scaled time: 333.98 units (timescale=2.660). Factorization parameters were as follows: name: KA_5_8_184_1 n: 109887831477680330078165495220916008376355456034500632373369824386805166801434761875142543177624349484771205241442225954261781841554187141050361800501751985237710186394642449876635359 m: 10000000000000000000000000000000000000 deg: 5 c5: 53 c0: -71 skew: 1.06 type: snfs lss: 1 rlim: 9200000 alim: 9200000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9200000/9200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4600000, 6800333) Primes: RFBsize:614917, AFBsize:614931, largePrimes:21290734 encountered Relations: rels:21649629, finalFF:1102807 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2166378 hash collisions in 23132561 relations Msieve: matrix is 1494834 x 1495082 (404.5 MB) Total sieving time: 124.87 hours. Total relation processing time: 0.69 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9200000,9200000,28,28,56,56,2.5,2.5,100000 total time: 125.56 hours. --------- CPU info (if available) ----------
Aug 4, 2009: By Jo Yeong Uk / GMP-ECM / Aug 4, 2009
(8·10¹⁷³-71)/9 = (8)₁₇₂1_<173> = 3² · 13 · 17 · 43 · 73819349 · 689479898902332034363_<21> · C140
C140 = P41 · P99
P41 = 33715138294680734832618454572413769091987_<41>
P99 = 605658021115666294214978686237465472994827629075929272382467836621789553075490427237044226574344187_<99>

GMP-ECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 20419843941197353791040696092597137963865400866495972289330486942965055929496647996235911574909705507595684650681311127191200053805001729569 (140 digits) Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=5942098668 Step 1 took 996ms Step 2 took 562ms ********** Factor found in step 2: 33715138294680734832618454572413769091987 Found probable prime factor of 41 digits: 33715138294680734832618454572413769091987 Probable prime cofactor 605658021115666294214978686237465472994827629075929272382467836621789553075490427237044226574344187 has 99 digits
Aug 3, 2009 (3rd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 3, 2009
(49·10¹⁶⁸-13)/9 = 5(4)₁₆₇3_<169> = 23 · 1447 · 11261 · 12853 · 2308951277_<10> · 5036853781320968279371_<22> · C125
C125 = P46 · P80
P46 = 4436645900924865896891648618121442838385371837_<46>
P80 = 21905181562068919290990994467028446773934788898829226150669261394310130185658329_<80>

Number: 54443_168 N=97185533986368021681783378062396574919435537754075193262983788450856674826360508129284134177950827777893612589454003301080373 ( 125 digits) SNFS difficulty: 171 digits. Divisors found: r1=4436645900924865896891648618121442838385371837 r2=21905181562068919290990994467028446773934788898829226150669261394310130185658329 Version: Total time: 46.73 hours. Scaled time: 111.36 units (timescale=2.383). Factorization parameters were as follows: n: 97185533986368021681783378062396574919435537754075193262983788450856674826360508129284134177950827777893612589454003301080373 m: 10000000000000000000000000000000000 deg: 5 c5: 49 c0: -1300 skew: 1.93 type: snfs lss: 1 rlim: 6200000 alim: 6200000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 6200000/6200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3100000, 6600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11417062 Max relations in full relation-set: Initial matrix: Pruned matrix : 1034547 x 1034795 Total sieving time: 42.04 hours. Total relation processing time: 2.01 hours. Matrix solve time: 2.54 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6200000,6200000,27,27,52,52,2.4,2.4,100000 total time: 46.73 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Aug 3, 2009 (2nd): By Justin Card / ggnfs, msieve 1.42 / Aug 3, 2009
(56·10¹⁷⁰-11)/9 = 6(2)₁₆₉1_<171> = 3 · 761 · 4228649 · 10979083 · 1343420723_<10> · 12114269027672661198796230498491836711_<38> · C108
C108 = P49 · P60
P49 = 1944800934677037047463766918371467712069304130887_<49>
P60 = 185475900387806551829482684307834368733260784549539663636751_<60>

Number: 62221_170 N=360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137 ( 108 digits) Divisors found: r1=1944800934677037047463766918371467712069304130887 (pp49) r2=185475900387806551829482684307834368733260784549539663636751 (pp60) Version: Msieve-1.40 Total time: 8.69 hours. Scaled time: 17.57 units (timescale=2.021). Factorization parameters were as follows: n: 360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137 skew: 33882.38 Y0: -844453122631185029679 Y1: 158724253097 c0: 3030270268952056684732360 c1: 1682226644659762561296 c2: -88344194390410036 c3: 2546804784059 c4: 57899656 c5: 840 type: gnfs 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, 2600001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 328483 x 328708 Total sieving time: 8.15 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.26 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 8.69 hours. --------- CPU info (if available) ---------- [ 0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init) [ 0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297) [ 0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305) [ 0.231806] Total of 2 processors activated (8004.80 BogoMIPS).
Aug 3, 2009: By Serge Batalov / PFGW 3.2 / Aug 2, 2009
(4·10¹⁰³⁷⁰³-1)/3 = 1(3)₁₀₃₇₀₃_<103704> is PRP.
This is the largest unprovable near-repdigit PRP in our tables so far. Congratulations!
Aug 2, 2009 (2nd): By Justin Card / ggnfs, msieve / Aug 2, 2009
(8·10¹⁸²+7)/3 = 2(6)₁₈₁9_<183> = 146833703 · 769436999 · 22087156719475884876001_<23> · C144
C144 = P49 · P95
P49 = 1313874628553225970702945084785841581827031259121_<49>
P95 = 81334757462238608757273597406493936479682614546275200441982222523538919383871427624411039249037_<95>

Number: 26669_182 N=106863674249165476277135950768201346179664064572388256062379170668048285931254966336140306142687056863527571470316756489216772473680220396716477 ( 144 digits) SNFS difficulty: 182 digits. Divisors found: r1=1313874628553225970702945084785841581827031259121 (pp49) r2=81334757462238608757273597406493936479682614546275200441982222523538919383871427624411039249037 (pp95) Version: Msieve-1.40 Total time: 108.67 hours. Scaled time: 219.84 units (timescale=2.023). Factorization parameters were as follows: n: 106863674249165476277135950768201346179664064572388256062379170668048285931254966336140306142687056863527571470316756489216772473680220396716477 m: 2000000000000000000000000000000000000 deg: 5 c5: 25 c0: 7 skew: 0.78 type: snfs lss: 1 rlim: 7800000 alim: 7800000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 7800000/7800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3900000, 6000001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1285649 x 1285897 Total sieving time: 100.57 hours. Total relation processing time: 0.37 hours. Matrix solve time: 7.27 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: snfs,182.000,5,0,0,0,0,0,0,0,0,7800000,7800000,28,28,53,53,2.5,2.5,100000 total time: 108.67 hours. --------- CPU info (if available) ---------- [ 0.138978] CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.231791] CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ stepping 01 [ 0.004000] Memory: 986784k/1014720k available (2225k kernel code, 27548k reserved, 1080k data, 392k init) [ 0.084027] Calibrating delay using timer specific routine.. 4004.64 BogoMIPS (lpj=8009297) [ 0.152009] Calibrating delay using timer specific routine.. 4000.15 BogoMIPS (lpj=8000305) [ 0.231806] Total of 2 processors activated (8004.80 BogoMIPS).
Aug 2, 2009: By Robert Backstrom / GGNFS, Msieve / Aug 2, 2009
(13·10¹⁸⁴+41)/9 = 1(4)₁₈₃9_<185> = 163 · 1579 · C179
C179 = P71 · P108
P71 = 92587192841326317904370509461876612279913187413506323373335331228760777_<71>
P108 = 606150114546001300708435303470338784608990441248267320938295610733948093243853858789867890785546836431405881_<108>

Number: n N=56121737546262659229241324766565949733054796832834497427681744850722653712042818295513757812253792858120362131987102361300521975329747586009800582198271191460171050421927539929537 ( 179 digits) SNFS difficulty: 185 digits. Divisors found: Sun Aug 02 08:53:24 2009 prp71 factor: 92587192841326317904370509461876612279913187413506323373335331228760777 Sun Aug 02 08:53:24 2009 prp108 factor: 606150114546001300708435303470338784608990441248267320938295610733948093243853858789867890785546836431405881 Sun Aug 02 08:53:24 2009 elapsed time 03:35:50 (Msieve 1.39 - dependency 2) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 147.60 hours. Scaled time: 384.64 units (timescale=2.606). Factorization parameters were as follows: name: KA_1_4_183_9 n: 56121737546262659229241324766565949733054796832834497427681744850722653712042818295513757812253792858120362131987102361300521975329747586009800582198271191460171050421927539929537 m: 5000000000000000000000000000000000000 deg: 5 c5: 208 c0: 205 skew: 1.00 type: snfs lss: 1 rlim: 8800000 alim: 8800000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved special-q in [4400000, 7035647) Primes: RFBsize:590006, AFBsize:590266, largePrimes:21302773 encountered Relations: rels:21438521, finalFF:1122149 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 2374612 hash collisions in 23329475 relations Msieve: matrix is 1562449 x 1562697 (420.7 MB) Total sieving time: 146.75 hours. Total relation processing time: 0.84 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,8800000,8800000,28,28,56,56,2.5,2.5,100000 total time: 147.60 hours. --------- CPU info (if available) ----------
Aug 1, 2009 (2nd): By Jo Yeong Uk / GGNFS, Msieve v1.39 / Aug 1, 2009
(29·10¹⁶⁸-11)/9 = 3(2)₁₆₇1_<169> = 47 · 1354711 · 33098700893973541_<17> · 80197477465388443_<17> · C128
C128 = P46 · P83
P46 = 1100732423272300277487241527837358243053560351_<46>
P83 = 17320385646653016613128923249554916759743959254925800399695761532181811650257807901_<83>

Number: 32221_168 N=19065110064851142634598305011711690781910600659166456675477203921277050640697856822512892845451487883248668975816575374668133251 ( 128 digits) SNFS difficulty: 171 digits. Divisors found: r1=1100732423272300277487241527837358243053560351 r2=17320385646653016613128923249554916759743959254925800399695761532181811650257807901 Version: Total time: 45.11 hours. Scaled time: 107.72 units (timescale=2.388). Factorization parameters were as follows: n: 19065110064851142634598305011711690781910600659166456675477203921277050640697856822512892845451487883248668975816575374668133251 m: 10000000000000000000000000000000000 deg: 5 c5: 29 c0: -1100 skew: 2.07 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved rational special-q in [3000000, 6400001) Primes: rational ideals reading, algebraic ideals reading, Relations: 11391845 Max relations in full relation-set: Initial matrix: Pruned matrix : 1021901 x 1022149 Total sieving time: 40.54 hours. Total relation processing time: 1.96 hours. Matrix solve time: 2.48 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,52,52,2.4,2.4,100000 total time: 45.11 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673789) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5344.75 BogoMIPS (lpj=2672379) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672345)
Aug 1, 2009: By Wataru Sakai / GMP-ECM 6.2.1 / Aug 1, 2009
(56·10¹⁷⁰-11)/9 = 6(2)₁₆₉1_<171> = 3 · 761 · 4228649 · 10979083 · 1343420723_<10> · C145
C145 = P38 · C108
P38 = 12114269027672661198796230498491836711_<38>
C108 = [360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137_<108>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2365907108 Step 1 took 47029ms Step 2 took 15502ms ********** Factor found in step 2: 12114269027672661198796230498491836711 Found probable prime factor of 38 digits: 12114269027672661198796230498491836711 Composite cofactor 360713704434271200183541622591615185634374495249172894015298812631314181864019058110537097267991345727428137 has 108 digits

More: July 2009