News and updates, July 2007

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News and updates, July 2007	2007-08-02(Thu) 02:11

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News and updates, July 2007

Jul 31, 2007 (3rd): By Robert Backstrom / Msieve v. 1.25
7·10¹²²+3 = 7(0)₁₂₁3_<123> = 17³ · 37 · 34057 · 121139 · 447641 · 1966357949_<10> · C94
C94 = P41 · P53
P41 = 36803587049889567164794261972333592412847_<41>
P53 = 28812211472214508546521155757658327809127986705923647_<53>

Tue Jul 31 22:22:05 2007 Tue Jul 31 22:22:05 2007 Tue Jul 31 22:22:05 2007 Msieve v. 1.25 Tue Jul 31 22:22:05 2007 random seeds: 2df35130 45e71b74 Tue Jul 31 22:22:05 2007 factoring 1060392733017473507363436391125662056426006504379915175604094685956234092303916292830483893009 (94 digits) Tue Jul 31 22:22:05 2007 commencing quadratic sieve (93-digit input) Tue Jul 31 22:22:05 2007 using multiplier of 1 Tue Jul 31 22:22:05 2007 using 64kb Opteron sieve core Tue Jul 31 22:22:05 2007 sieve interval: 18 blocks of size 65536 Tue Jul 31 22:22:05 2007 processing polynomials in batches of 6 Tue Jul 31 22:22:05 2007 using a sieve bound of 1986401 (74118 primes) Tue Jul 31 22:22:05 2007 using large prime bound of 256245729 (27 bits) Tue Jul 31 22:22:05 2007 using double large prime bound of 1366412668937199 (42-51 bits) Tue Jul 31 22:22:05 2007 using trial factoring cutoff of 51 bits Tue Jul 31 22:22:05 2007 polynomial 'A' values have 12 factors Wed Aug 01 00:39:21 2007 74518 relations (18810 full + 55708 combined from 1024843 partial), need 74214 Wed Aug 01 00:39:22 2007 begin with 1043653 relations Wed Aug 01 00:39:23 2007 reduce to 190550 relations in 13 passes Wed Aug 01 00:39:23 2007 attempting to read 190550 relations Wed Aug 01 00:39:26 2007 recovered 190550 relations Wed Aug 01 00:39:26 2007 recovered 169642 polynomials Wed Aug 01 00:39:26 2007 attempting to build 74518 cycles Wed Aug 01 00:39:26 2007 found 74518 cycles in 5 passes Wed Aug 01 00:39:27 2007 distribution of cycle lengths: Wed Aug 01 00:39:27 2007 length 1 : 18810 Wed Aug 01 00:39:27 2007 length 2 : 13413 Wed Aug 01 00:39:27 2007 length 3 : 12787 Wed Aug 01 00:39:27 2007 length 4 : 10167 Wed Aug 01 00:39:27 2007 length 5 : 7362 Wed Aug 01 00:39:27 2007 length 6 : 4755 Wed Aug 01 00:39:27 2007 length 7 : 3092 Wed Aug 01 00:39:27 2007 length 9+: 4132 Wed Aug 01 00:39:27 2007 largest cycle: 20 relations Wed Aug 01 00:39:27 2007 matrix is 74118 x 74518 with weight 4440747 (avg 59.59/col) Wed Aug 01 00:39:28 2007 filtering completed in 3 passes Wed Aug 01 00:39:28 2007 matrix is 70053 x 70117 with weight 4190795 (avg 59.77/col) Wed Aug 01 00:39:29 2007 saving the first 48 matrix rows for later Wed Aug 01 00:39:29 2007 matrix is 70005 x 70117 with weight 3152619 (avg 44.96/col) Wed Aug 01 00:39:29 2007 matrix includes 64 packed rows Wed Aug 01 00:39:29 2007 using block size 21845 for processor cache size 512 kB Wed Aug 01 00:39:29 2007 commencing Lanczos iteration Wed Aug 01 00:40:15 2007 lanczos halted after 1108 iterations Wed Aug 01 00:40:15 2007 recovered 16 nontrivial dependencies Wed Aug 01 00:40:16 2007 prp41 factor: 36803587049889567164794261972333592412847 Wed Aug 01 00:40:16 2007 prp53 factor: 28812211472214508546521155757658327809127986705923647 Wed Aug 01 00:40:16 2007 elapsed time 02:18:11 AMD 64 3400+
Jul 31, 2007 (2nd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve v. 1.25
(2·10¹⁶⁴-17)/3 = (6)₁₆₃1_<164> = 29 · 107 · 210109 · C156
C156 = P45 · P54 · P58
P45 = 146792919660212633045160717534069008610074051_<45>
P54 = 135010317731924137634438672025990319457714916359755721_<54>
P58 = 5159531184859186656457275600237553641883637652588888601333_<58>

Number: n N=102254471776071177570846050856197117511781240018413760317596990300367300976872093287863039783787909447720167299911482751852977440673142905577002399944662743 ( 156 digits) SNFS difficulty: 165 digits. Divisors found: r1=146792919660212633045160717534069008610074051 (pp45) r2=135010317731924137634438672025990319457714916359755721 (pp54) r3=5159531184859186656457275600237553641883637652588888601333 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 50.11 hours. Scaled time: 72.91 units (timescale=1.455). Factorization parameters were as follows: name: KA_6_163_1 n: 102254471776071177570846050856197117511781240018413760317596990300367300976872093287863039783787909447720167299911482751852977440673142905577002399944662743 skew: 2.43 deg: 5 c5: 1 c0: -85 m: 1000000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2300001) Primes: RFBsize:250150, AFBsize:250371, largePrimes:7491975 encountered Relations: rels:7069787, finalFF:615528 Max relations in full relation-set: 28 Initial matrix: 500585 x 615528 with sparse part having weight 43347706. Pruned matrix : 408266 x 410832 with weight 26760517. Total sieving time: 44.47 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.99 hours. Total square root time: 0.43 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 50.11 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹³⁶+3 = 7(0)₁₃₅3_<137> = C137
C137 = P33 · P43 · P63
P33 = 189532579450789969799143826592293_<33>
P43 = 2381835865531583487969941738318774107993447_<43>
P63 = 155060912820934332646084226028944988675098343203271382941181793_<63>

Number: n N=70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 137 digits) SNFS difficulty: 136 digits. Divisors found: r1=189532579450789969799143826592293 (pp33) r2=2381835865531583487969941738318774107993447 (pp43) r3=155060912820934332646084226028944988675098343203271382941181793 (pp63) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.52 hours. Scaled time: 8.03 units (timescale=1.455). Factorization parameters were as follows: name: KA_7_0_135_3 n: 70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 skew: 0.53 deg: 5 c5: 70 c0: 3 m: 1000000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:78498, AFBsize:78021, largePrimes:6514103 encountered Relations: rels:5824178, finalFF:190944 Max relations in full relation-set: 28 Initial matrix: 156586 x 190944 with sparse part having weight 19426214. Pruned matrix : 147516 x 148362 with weight 12985709. Total sieving time: 4.77 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.53 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,75000 total time: 5.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹¹⁷+3 = 7(0)₁₁₆3_<118> = 31 · C117
C117 = P54 · P63
P54 = 796610382478821640289686993942482559318724926882166707_<54>
P63 = 283459086875391589955150402968360965955345854041338678737403759_<63>

Number: n N=225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613 ( 117 digits) SNFS difficulty: 117 digits. Divisors found: r1=796610382478821640289686993942482559318724926882166707 (pp54) r2=283459086875391589955150402968360965955345854041338678737403759 (pp63) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.23 hours. Scaled time: 1.78 units (timescale=1.451). Factorization parameters were as follows: name: KA_7_0_116_3 n: 225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613 skew: 0.34 deg: 5 c5: 700 c0: 3 m: 100000000000000000000000 type: snfs rlim: 600000 alim: 600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:49098, AFBsize:48976, largePrimes:3849937 encountered Relations: rels:3225255, finalFF:131768 Max relations in full relation-set: 28 Initial matrix: 98141 x 131768 with sparse part having weight 8495908. Pruned matrix : 84202 x 84756 with weight 3752118. Total sieving time: 1.07 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.05 hours. Total square root time: 0.04 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,600000,28,28,48,48,2.5,2.5,50000 total time: 1.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹³¹+3 = 7(0)₁₃₀3_<132> = 37 · 167 · 821 · 86381 · 8277265193_<10> · 1909043502241_<13> · 11221997190059_<14> · C85
C85 = P42 · P44
P42 = 245476063044641766698278446037400797293497_<42>
P44 = 36697498431299323192437388994595232599875443_<44>

Tue Jul 31 18:27:11 2007 Tue Jul 31 18:27:11 2007 Tue Jul 31 18:27:11 2007 Msieve v. 1.25 Tue Jul 31 18:27:11 2007 random seeds: 51a0e488 172d0ce2 Tue Jul 31 18:27:11 2007 factoring 9008357438502274995224625264375573726008762745952381754409588880984018651293713894171 (85 digits) Tue Jul 31 18:27:11 2007 commencing quadratic sieve (85-digit input) Tue Jul 31 18:27:11 2007 using multiplier of 59 Tue Jul 31 18:27:11 2007 using 64kb Opteron sieve core Tue Jul 31 18:27:11 2007 sieve interval: 6 blocks of size 65536 Tue Jul 31 18:27:11 2007 processing polynomials in batches of 17 Tue Jul 31 18:27:11 2007 using a sieve bound of 1442509 (54972 primes) Tue Jul 31 18:27:11 2007 using large prime bound of 115400720 (26 bits) Tue Jul 31 18:27:11 2007 using double large prime bound of 325068826146400 (41-49 bits) Tue Jul 31 18:27:11 2007 using trial factoring cutoff of 49 bits Tue Jul 31 18:27:11 2007 polynomial 'A' values have 11 factors Tue Jul 31 18:57:24 2007 55354 relations (16849 full + 38505 combined from 558450 partial), need 55068 Tue Jul 31 18:57:25 2007 begin with 575299 relations Tue Jul 31 18:57:25 2007 reduce to 126894 relations in 9 passes Tue Jul 31 18:57:25 2007 attempting to read 126894 relations Tue Jul 31 18:57:27 2007 recovered 126894 relations Tue Jul 31 18:57:27 2007 recovered 104607 polynomials Tue Jul 31 18:57:27 2007 attempting to build 55354 cycles Tue Jul 31 18:57:27 2007 found 55354 cycles in 5 passes Tue Jul 31 18:57:27 2007 distribution of cycle lengths: Tue Jul 31 18:57:27 2007 length 1 : 16849 Tue Jul 31 18:57:27 2007 length 2 : 11673 Tue Jul 31 18:57:27 2007 length 3 : 9808 Tue Jul 31 18:57:27 2007 length 4 : 6856 Tue Jul 31 18:57:27 2007 length 5 : 4419 Tue Jul 31 18:57:27 2007 length 6 : 2741 Tue Jul 31 18:57:27 2007 length 7 : 1489 Tue Jul 31 18:57:27 2007 length 9+: 1519 Tue Jul 31 18:57:27 2007 largest cycle: 18 relations Tue Jul 31 18:57:28 2007 matrix is 54972 x 55354 with weight 2949435 (avg 53.28/col) Tue Jul 31 18:57:28 2007 filtering completed in 3 passes Tue Jul 31 18:57:28 2007 matrix is 49563 x 49627 with weight 2651538 (avg 53.43/col) Tue Jul 31 18:57:29 2007 saving the first 48 matrix rows for later Tue Jul 31 18:57:29 2007 matrix is 49515 x 49627 with weight 2025706 (avg 40.82/col) Tue Jul 31 18:57:29 2007 matrix includes 64 packed rows Tue Jul 31 18:57:29 2007 commencing Lanczos iteration Tue Jul 31 18:58:45 2007 lanczos halted after 785 iterations Tue Jul 31 18:58:46 2007 recovered 12 nontrivial dependencies Tue Jul 31 18:58:46 2007 prp42 factor: 245476063044641766698278446037400797293497 Tue Jul 31 18:58:46 2007 prp44 factor: 36697498431299323192437388994595232599875443 Tue Jul 31 18:58:46 2007 elapsed time 00:31:35 AMD 64 3400+
7·10¹³³+3 = 7(0)₁₃₂3_<134> = 29 · 59 · 1741 · 19286399236854181_<17> · 46083256114156603252213_<23> · C89
C89 = P40 · P49
P40 = 8783383808652802647890907770843019907393_<40>
P49 = 3010184316154118713322706068056130317359871964857_<49>

Tue Jul 31 19:07:15 2007 Tue Jul 31 19:07:15 2007 Tue Jul 31 19:07:15 2007 Msieve v. 1.25 Tue Jul 31 19:07:15 2007 random seeds: d5724f40 7200004e Tue Jul 31 19:07:15 2007 factoring 26439604183568695431333540511848343933708312285905784586381054531841927202958085090487801 (89 digits) Tue Jul 31 19:07:15 2007 commencing quadratic sieve (89-digit input) Tue Jul 31 19:07:15 2007 using multiplier of 1 Tue Jul 31 19:07:15 2007 using 64kb Opteron sieve core Tue Jul 31 19:07:15 2007 sieve interval: 15 blocks of size 65536 Tue Jul 31 19:07:15 2007 processing polynomials in batches of 7 Tue Jul 31 19:07:15 2007 using a sieve bound of 1544831 (58667 primes) Tue Jul 31 19:07:15 2007 using large prime bound of 123586480 (26 bits) Tue Jul 31 19:07:15 2007 using double large prime bound of 367745783685200 (42-49 bits) Tue Jul 31 19:07:15 2007 using trial factoring cutoff of 49 bits Tue Jul 31 19:07:15 2007 polynomial 'A' values have 11 factors Tue Jul 31 19:50:38 2007 58799 relations (16800 full + 41999 combined from 610095 partial), need 58763 Tue Jul 31 19:50:38 2007 begin with 626895 relations Tue Jul 31 19:50:39 2007 reduce to 139283 relations in 10 passes Tue Jul 31 19:50:39 2007 attempting to read 139283 relations Tue Jul 31 19:50:40 2007 recovered 139283 relations Tue Jul 31 19:50:40 2007 recovered 109037 polynomials Tue Jul 31 19:50:40 2007 attempting to build 58799 cycles Tue Jul 31 19:50:41 2007 found 58799 cycles in 5 passes Tue Jul 31 19:50:41 2007 distribution of cycle lengths: Tue Jul 31 19:50:41 2007 length 1 : 16800 Tue Jul 31 19:50:41 2007 length 2 : 11719 Tue Jul 31 19:50:41 2007 length 3 : 10451 Tue Jul 31 19:50:41 2007 length 4 : 7497 Tue Jul 31 19:50:41 2007 length 5 : 5180 Tue Jul 31 19:50:41 2007 length 6 : 3241 Tue Jul 31 19:50:41 2007 length 7 : 1863 Tue Jul 31 19:50:41 2007 length 9+: 2048 Tue Jul 31 19:50:41 2007 largest cycle: 18 relations Tue Jul 31 19:50:41 2007 matrix is 58667 x 58799 with weight 3374117 (avg 57.38/col) Tue Jul 31 19:50:42 2007 filtering completed in 3 passes Tue Jul 31 19:50:42 2007 matrix is 53856 x 53920 with weight 3132205 (avg 58.09/col) Tue Jul 31 19:50:43 2007 saving the first 48 matrix rows for later Tue Jul 31 19:50:43 2007 matrix is 53808 x 53920 with weight 2508505 (avg 46.52/col) Tue Jul 31 19:50:43 2007 matrix includes 64 packed rows Tue Jul 31 19:50:43 2007 using block size 21568 for processor cache size 512 kB Tue Jul 31 19:50:43 2007 commencing Lanczos iteration Tue Jul 31 19:51:11 2007 lanczos halted after 852 iterations Tue Jul 31 19:51:11 2007 recovered 17 nontrivial dependencies Tue Jul 31 19:51:11 2007 prp40 factor: 8783383808652802647890907770843019907393 Tue Jul 31 19:51:11 2007 prp49 factor: 3010184316154118713322706068056130317359871964857 Tue Jul 31 19:51:11 2007 elapsed time 00:43:56 AMD 64 3400+
7·10¹⁰⁹+3 = 7(0)₁₀₈3_<110> = 61 · 283 · 6833 · 3752738047_<10> · C93
C93 = P35 · P58
P35 = 94998794192060872628935849323365693_<35>
P58 = 1664577444559100089652031980780871295487207378438987754367_<58>

Tue Jul 31 20:06:20 2007 Tue Jul 31 20:06:20 2007 Tue Jul 31 20:06:20 2007 Msieve v. 1.25 Tue Jul 31 20:06:20 2007 random seeds: 58a7aa10 e5a73f18 Tue Jul 31 20:06:20 2007 factoring 158132850072416566802699765435756674614463053664908574703804989105665472581049135992398731331 (93 digits) Tue Jul 31 20:06:20 2007 commencing quadratic sieve (92-digit input) Tue Jul 31 20:06:20 2007 using multiplier of 5 Tue Jul 31 20:06:20 2007 using 64kb Opteron sieve core Tue Jul 31 20:06:20 2007 sieve interval: 18 blocks of size 65536 Tue Jul 31 20:06:20 2007 processing polynomials in batches of 6 Tue Jul 31 20:06:20 2007 using a sieve bound of 1885601 (70588 primes) Tue Jul 31 20:06:20 2007 using large prime bound of 220615317 (27 bits) Tue Jul 31 20:06:20 2007 using double large prime bound of 1043624286913572 (42-50 bits) Tue Jul 31 20:06:20 2007 using trial factoring cutoff of 50 bits Tue Jul 31 20:06:20 2007 polynomial 'A' values have 12 factors Tue Jul 31 22:12:14 2007 71029 relations (18147 full + 52882 combined from 923968 partial), need 70684 Tue Jul 31 22:12:15 2007 begin with 942115 relations Tue Jul 31 22:12:16 2007 reduce to 179413 relations in 13 passes Tue Jul 31 22:12:16 2007 attempting to read 179413 relations Tue Jul 31 22:12:18 2007 recovered 179413 relations Tue Jul 31 22:12:18 2007 recovered 159146 polynomials Tue Jul 31 22:12:18 2007 attempting to build 71029 cycles Tue Jul 31 22:12:18 2007 found 71029 cycles in 5 passes Tue Jul 31 22:12:19 2007 distribution of cycle lengths: Tue Jul 31 22:12:19 2007 length 1 : 18147 Tue Jul 31 22:12:19 2007 length 2 : 13037 Tue Jul 31 22:12:19 2007 length 3 : 12364 Tue Jul 31 22:12:19 2007 length 4 : 9648 Tue Jul 31 22:12:19 2007 length 5 : 7028 Tue Jul 31 22:12:19 2007 length 6 : 4488 Tue Jul 31 22:12:19 2007 length 7 : 2773 Tue Jul 31 22:12:19 2007 length 9+: 3544 Tue Jul 31 22:12:19 2007 largest cycle: 18 relations Tue Jul 31 22:12:19 2007 matrix is 70588 x 71029 with weight 4271043 (avg 60.13/col) Tue Jul 31 22:12:20 2007 filtering completed in 3 passes Tue Jul 31 22:12:20 2007 matrix is 66489 x 66553 with weight 4008580 (avg 60.23/col) Tue Jul 31 22:12:21 2007 saving the first 48 matrix rows for later Tue Jul 31 22:12:21 2007 matrix is 66441 x 66553 with weight 3003773 (avg 45.13/col) Tue Jul 31 22:12:21 2007 matrix includes 64 packed rows Tue Jul 31 22:12:21 2007 using block size 21845 for processor cache size 512 kB Tue Jul 31 22:12:21 2007 commencing Lanczos iteration Tue Jul 31 22:13:01 2007 lanczos halted after 1053 iterations Tue Jul 31 22:13:02 2007 recovered 19 nontrivial dependencies Tue Jul 31 22:13:02 2007 prp35 factor: 94998794192060872628935849323365693 Tue Jul 31 22:13:02 2007 prp58 factor: 1664577444559100089652031980780871295487207378438987754367 Tue Jul 31 22:13:02 2007 elapsed time 02:06:42 AMD 64 3400+
Jul 31, 2007: By Sinkiti Sibata / Msieve v. 1.23
7·10¹¹⁵+3 = 7(0)₁₁₄3_<116> = 71 · 571 · 1753 · 41759 · 101687624751179_<15> · C90
C90 = P45 · P46
P45 = 229383234010881253145836095413674027664523319_<45>
P46 = 1011211039809810274754617373533701326457880829_<46>

Tue Jul 31 07:34:45 2007 Msieve v. 1.23 Tue Jul 31 07:34:45 2007 random seeds: f6cd87d8 a53fdc24 Tue Jul 31 07:34:45 2007 factoring 231954858579080269057677376740414939630659505325131391785225954643473927231021865193551451 (90 digits) Tue Jul 31 07:34:46 2007 commencing quadratic sieve (89-digit input) Tue Jul 31 07:34:46 2007 using multiplier of 11 Tue Jul 31 07:34:46 2007 using 64kb Pentium 2 sieve core Tue Jul 31 07:34:46 2007 sieve interval: 18 blocks of size 65536 Tue Jul 31 07:34:46 2007 processing polynomials in batches of 6 Tue Jul 31 07:34:46 2007 using a sieve bound of 1575269 (59601 primes) Tue Jul 31 07:34:46 2007 using large prime bound of 126021520 (26 bits) Tue Jul 31 07:34:46 2007 using double large prime bound of 380890718607520 (42-49 bits) Tue Jul 31 07:34:46 2007 using trial factoring cutoff of 49 bits Tue Jul 31 07:34:46 2007 polynomial 'A' values have 12 factors Tue Jul 31 17:16:16 2007 59785 relations (16189 full + 43596 combined from 628261 partial), need 59697 Tue Jul 31 17:16:20 2007 begin with 644450 relations Tue Jul 31 17:16:21 2007 reduce to 144357 relations in 9 passes Tue Jul 31 17:16:21 2007 attempting to read 144357 relations Tue Jul 31 17:16:29 2007 recovered 144357 relations Tue Jul 31 17:16:29 2007 recovered 122313 polynomials Tue Jul 31 17:16:29 2007 attempting to build 59785 cycles Tue Jul 31 17:16:30 2007 found 59785 cycles in 6 passes Tue Jul 31 17:16:34 2007 distribution of cycle lengths: Tue Jul 31 17:16:34 2007 length 1 : 16189 Tue Jul 31 17:16:34 2007 length 2 : 11643 Tue Jul 31 17:16:34 2007 length 3 : 10503 Tue Jul 31 17:16:34 2007 length 4 : 7913 Tue Jul 31 17:16:34 2007 length 5 : 5683 Tue Jul 31 17:16:34 2007 length 6 : 3388 Tue Jul 31 17:16:34 2007 length 7 : 2104 Tue Jul 31 17:16:34 2007 length 9+: 2362 Tue Jul 31 17:16:34 2007 largest cycle: 22 relations Tue Jul 31 17:16:35 2007 matrix is 59601 x 59785 with weight 3535144 (avg 59.13/col) Tue Jul 31 17:16:41 2007 filtering completed in 3 passes Tue Jul 31 17:16:41 2007 matrix is 55625 x 55687 with weight 3317745 (avg 59.58/col) Tue Jul 31 17:16:43 2007 saving the first 48 matrix rows for later Tue Jul 31 17:16:43 2007 matrix is 55577 x 55687 with weight 2590949 (avg 46.53/col) Tue Jul 31 17:16:43 2007 matrix includes 64 packed rows Tue Jul 31 17:16:43 2007 using block size 5461 for processor cache size 128 kB Tue Jul 31 17:16:44 2007 commencing Lanczos iteration Tue Jul 31 17:19:46 2007 lanczos halted after 879 iterations Tue Jul 31 17:19:47 2007 recovered 16 nontrivial dependencies Tue Jul 31 17:19:50 2007 prp45 factor: 229383234010881253145836095413674027664523319 Tue Jul 31 17:19:50 2007 prp46 factor: 1011211039809810274754617373533701326457880829 Tue Jul 31 17:19:50 2007 elapsed time 09:45:05
Jul 30, 2007 (2nd): The factor table of 700...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jul 30, 2007: By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(7·10¹⁶³-1)/3 = 2(3)₁₆₃_<164> = 31 · 26480968333_<11> · C152
C152 = P73 · P79
P73 = 6005499498342026296996247513568027884866123915015309416115316591128827611_<73>
P79 = 4732951939505968237884782724690167133167712747934122360855348805147547921808661_<79>

Number: n N=28423740498380012646351441222833046018885664846683919488791556370619977774011134692143246359762495624861587748954770936198932245142948442069275595738871 ( 152 digits) SNFS difficulty: 163 digits. Divisors found: r1=6005499498342026296996247513568027884866123915015309416115316591128827611 (pp73) r2=4732951939505968237884782724690167133167712747934122360855348805147547921808661 (pp79) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 62.00 hours. Scaled time: 84.63 units (timescale=1.365). Factorization parameters were as follows: name: KA_2_3_163 n: 28423740498380012646351441222833046018885664846683919488791556370619977774011134692143246359762495624861587748954770936198932245142948442069275595738871 skew: 0.17 deg: 5 c5: 7000 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2600001) Primes: RFBsize:250150, AFBsize:250186, largePrimes:7515166 encountered Relations: rels:7038514, finalFF:567391 Max relations in full relation-set: 28 Initial matrix: 500403 x 567391 with sparse part having weight 42599784. Pruned matrix : 449316 x 451882 with weight 30245743. Total sieving time: 56.37 hours. Total relation processing time: 0.29 hours. Matrix solve time: 5.04 hours. Total square root time: 0.30 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 62.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 29, 2007 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(2·10¹⁶⁰+1)/3 = (6)₁₅₉7_<160> = 227 · 419 · 1458595001_<10> · 16026242851179144358700459_<26> · C121
C121 = P48 · P74
P48 = 161463735175025949280548404486238854502944749577_<48>
P74 = 18570663712910018221335055151517350281831147548443709556829543800274598713_<74>

Number: 66667_160 N=2998488727765767306056724256898840427400661293190185342767414314752818203241712663724341297601486372223255855543951494401 ( 121 digits) SNFS difficulty: 160 digits. Divisors found: r1=161463735175025949280548404486238854502944749577 (pp48) r2=18570663712910018221335055151517350281831147548443709556829543800274598713 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.89 hours. Scaled time: 55.06 units (timescale=2.127). Factorization parameters were as follows: n: 2998488727765767306056724256898840427400661293190185342767414314752818203241712663724341297601486372223255855543951494401 m: 100000000000000000000000000000000 c5: 2 c0: 1 skew: 0.87 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:282707, largePrimes:5745066 encountered Relations: rels:5888263, finalFF:750273 Max relations in full relation-set: 28 Initial matrix: 565918 x 750273 with sparse part having weight 47378726. Pruned matrix : 416316 x 419209 with weight 29586910. Total sieving time: 24.83 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.93 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 25.89 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
(83·10¹⁵⁸+61)/9 = 9(2)₁₅₇9_<159> = 117545651888135840815842818880953169751_<39> · C121
C121 = P53 · P69
P53 = 19948874429255659337544510594592376405101429806260627_<53>
P69 = 393287929414931017949697007530034379610754908774038875145063023078177_<69>

Number: 92229_158 N=7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979 ( 121 digits) SNFS difficulty: 160 digits. Divisors found: r1=19948874429255659337544510594592376405101429806260627 (pp53) r2=393287929414931017949697007530034379610754908774038875145063023078177 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 38.31 hours. Scaled time: 82.06 units (timescale=2.142). Factorization parameters were as follows: n: 7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979 m: 20000000000000000000000000000000 c5: 10375 c0: 244 skew: 0.47 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 4200001) Primes: RFBsize:283146, AFBsize:283188, largePrimes:5761581 encountered Relations: rels:5805318, finalFF:660921 Max relations in full relation-set: 28 Initial matrix: 566401 x 660921 with sparse part having weight 47281694. Pruned matrix : 502096 x 504992 with weight 33891197. Total sieving time: 36.70 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.46 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 38.31 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 29, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(10¹⁶³-7)/3 = (3)₁₆₂1_<163> = 401 · 340687 · C155
C155 = P34 · P58 · P65
P34 = 1169754593539985501873975459730137_<34>
P58 = 1658788489453091556494815237092230110842898508302882101211_<58>
P65 = 12574566972385656776513038298834533485077579778495931368800832559_<65>

Number: n N=24399381113601954464601318101902556137967969424530421893773531937366173816979720120115908479199970449421545694400908832051620423776210184232870562715436013 ( 155 digits) SNFS difficulty: 163 digits. Divisors found: r1=1169754593539985501873975459730137 (pp34) r2=1658788489453091556494815237092230110842898508302882101211 (pp58) r3=12574566972385656776513038298834533485077579778495931368800832559 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.87 hours. Scaled time: 62.21 units (timescale=1.451). Factorization parameters were as follows: name: KA_3_162_1 n: 24399381113601954464601318101902556137967969424530421893773531937366173816979720120115908479199970449421545694400908832051620423776210184232870562715436013 skew: 0.37 deg: 5 c5: 1000 c0: -7 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:250150, AFBsize:249886, largePrimes:7373909 encountered Relations: rels:6949423, finalFF:611249 Max relations in full relation-set: 28 Initial matrix: 500102 x 611249 with sparse part having weight 41187658. Pruned matrix : 405991 x 408555 with weight 24372265. Total sieving time: 38.29 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.21 hours. Total square root time: 0.14 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 42.87 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(16·10¹⁶³-7)/9 = 1(7)₁₆₃_<164> = 257 · 423277 · C156
C156 = P41 · P51 · P64
P41 = 73711078007185859471835668366940479393171_<41>
P51 = 821912260604473840932297229077014953449618054109223_<51>
P64 = 2697500027586692927181515435498036599615808525035592363867652721_<64>

Number: n N=163425446216914956342510976477755726884460633328290330485790994496146586807310687393666786552509784278911484101296929939309989227903639425547667346331647893 ( 156 digits) SNFS difficulty: 164 digits. Divisors found: r1=73711078007185859471835668366940479393171 (pp41) r2=821912260604473840932297229077014953449618054109223 (pp51) r3=2697500027586692927181515435498036599615808525035592363867652721 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 61.71 hours. Scaled time: 73.69 units (timescale=1.194). Factorization parameters were as follows: name: KA_1_7_163 n: 163425446216914956342510976477755726884460633328290330485790994496146586807310687393666786552509784278911484101296929939309989227903639425547667346331647893 type: snfs skew: 0.43 deg: 5 c5: 500 c0: -7 m: 200000000000000000000000000000000 rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2600001) Primes: RFBsize:256726, AFBsize:256456, largePrimes:7276877 encountered Relations: rels:6788820, finalFF:601944 Max relations in full relation-set: 28 Initial matrix: 513248 x 601944 with sparse part having weight 36488675. Pruned matrix : 437144 x 439774 with weight 22807094. Total sieving time: 56.01 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.06 hours. Total square root time: 0.35 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000 total time: 61.71 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 28, 2007 (5th): By honeycrack7 / GGNFS-0.77.1-20060513-k8
4·10¹⁷⁰+3 = 4(0)₁₆₉3_<171> = 13 · 2332022449008725190543961_<25> · 9091674957193157331925985427613_<31> · C115
C115 = P52 · P63
P52 = 5519848976962319518553726010848147162459426482482457_<52>
P63 = 262913457234491688131920560141939578410279343647748980394630731_<63>
Jul 28, 2007 (4th): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
7·10¹⁵⁰-3 = 6(9)₁₄₉7_<151> = 23537 · 117047527 · C139
C139 = P55 · P84
P55 = 8764729519896434388185150658193376696083145995054647761_<55>
P84 = 289898636097657769901727571746993680083346617528438604091309287391756698440245150523_<84>

Number: 69997_150 N=2540883133582855129103294851665209412058385608097038665067689287721635183644657611078834087886540221297369512376354576518671195152189929003 ( 139 digits) SNFS difficulty: 150 digits. Divisors found: r1=8764729519896434388185150658193376696083145995054647761 (pp55) r2=289898636097657769901727571746993680083346617528438604091309287391756698440245150523 (pp84) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 26.99 hours. Scaled time: 18.41 units (timescale=0.682). Factorization parameters were as follows: name: 69997_150 n: 2540883133582855129103294851665209412058385608097038665067689287721635183644657611078834087886540221297369512376354576518671195152189929003 m: 1000000000000000000000000000000 c5: 7 c0: -3 skew: 0.84 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 1900001) Primes: RFBsize:176302, AFBsize:175733, largePrimes:5394959 encountered Relations: rels:5312038, finalFF:400934 Max relations in full relation-set: 0 Initial matrix: 352100 x 400934 with sparse part having weight 23256659. Pruned matrix : 317140 x 318964 with weight 17341814. Total sieving time: 23.86 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.81 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 26.99 hours. --------- CPU info (if available) ----------
Jul 28, 2007 (3rd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(2·10¹⁵⁹+43)/9 = (2)₁₅₈7_<159> = 239 · 809 · 4027 · 238547 · 885263 · C139
C139 = P45 · P94
P45 = 347764084623597453108213934934669011761877139_<45>
P94 = 3886229406208272471593857319229809807058694766986913068964477873900842341708025811926593810169_<94>

Number: 22227_159 N=1351491012087326549211979087569214053838808220524355993937154678565591119267140370025719121273819964452615804361909214924166342965666826491 ( 139 digits) SNFS difficulty: 160 digits. Divisors found: r1=347764084623597453108213934934669011761877139 (pp45) r2=3886229406208272471593857319229809807058694766986913068964477873900842341708025811926593810169 (pp94) Version: GGNFS-0.77.1-20050930-nocona Total time: 29.92 hours. Scaled time: 63.91 units (timescale=2.136). Factorization parameters were as follows: n: 1351491012087326549211979087569214053838808220524355993937154678565591119267140370025719121273819964452615804361909214924166342965666826491 m: 100000000000000000000000000000000 c5: 1 c0: 215 skew: 2.93 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3600001) Primes: RFBsize:283146, AFBsize:283892, largePrimes:5618226 encountered Relations: rels:5629970, finalFF:640876 Max relations in full relation-set: 28 Initial matrix: 567102 x 640876 with sparse part having weight 39940913. Pruned matrix : 509180 x 512079 with weight 28084715. Total sieving time: 27.43 hours. Total relation processing time: 0.09 hours. Matrix solve time: 2.35 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 29.92 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
2·10¹⁵⁹-9 = 1(9)₁₅₈1_<160> = 11 · 24691 · 52861 · 266261 · 4151011 · C138
C138 = P47 · P91
P47 = 40930808775623536636245772098276860041853369431_<47>
P91 = 3079296349757713797324715535825813229817563878384139018839754824005144136790174117702778331_<91>

Number: 19991_159 N=126038090055408555107408847579488891171318490786133096772283218499151669830811145264505896403808824896321957494548755525749518542444599661 ( 138 digits) SNFS difficulty: 160 digits. Divisors found: r1=40930808775623536636245772098276860041853369431 (pp47) r2=3079296349757713797324715535825813229817563878384139018839754824005144136790174117702778331 (pp91) Version: GGNFS-0.77.1-20050930-nocona Total time: 23.56 hours. Scaled time: 50.48 units (timescale=2.143). Factorization parameters were as follows: n: 126038090055408555107408847579488891171318490786133096772283218499151669830811145264505896403808824896321957494548755525749518542444599661 m: 100000000000000000000000000000000 c5: 1 c0: -45 skew: 2.14 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3300001) Primes: RFBsize:283146, AFBsize:283177, largePrimes:5644839 encountered Relations: rels:5726943, finalFF:702143 Max relations in full relation-set: 28 Initial matrix: 566387 x 702143 with sparse part having weight 41923918. Pruned matrix : 452126 x 455021 with weight 25213445. Total sieving time: 22.45 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.97 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 23.56 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 28, 2007 (2nd): By JMB / GMP-ECM B1=1000000
(25·10¹⁹⁷-7)/9 = 2(7)₁₉₇_<198> = 1373 · C195
C195 = P32 · C163
P32 = 85030629703280968207735306809773_<32>
C163 = [2379312940877966056839041692231255679976556971431892634670943410004573553981330698167952823566726167898725398615761464958869155626448416241982456084785127904775513_<163>]
Jul 28, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(2·10¹⁶²+1)/3 = (6)₁₆₁7_<162> = 89 · 5942153001947_<13> · C148
C148 = P54 · P94
P54 = 260109084099025462382032890421450150382266857071125187_<54>
P94 = 4846401432771397426216214806428116706548778140446303082763979669092372351100444829939195019827_<94>

Number: n N=1260593037854372908702191537268240612213565622246104193999268784722069543835151571262530708956084288244937923573974982203746499701928418153664082649 ( 148 digits) SNFS difficulty: 162 digits. Divisors found: r1=260109084099025462382032890421450150382266857071125187 (pp54) r2=4846401432771397426216214806428116706548778140446303082763979669092372351100444829939195019827 (pp94) Version: GGNFS-0.77.1-20051202-athlon Total time: 41.90 hours. Scaled time: 55.51 units (timescale=1.325). Factorization parameters were as follows: name: KA_6_161_7 n: 1260593037854372908702191537268240612213565622246104193999268784722069543835151571262530708956084288244937923573974982203746499701928418153664082649 skew: 0.35 deg: 5 c5: 200 c0: 1 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:250150, AFBsize:249566, largePrimes:7143893 encountered Relations: rels:6652480, finalFF:561530 Max relations in full relation-set: 48 Initial matrix: 499781 x 561530 with sparse part having weight 37610274. Pruned matrix : 446875 x 449437 with weight 24206431. Total sieving time: 36.44 hours. Total relation processing time: 0.22 hours. Matrix solve time: 5.14 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 41.90 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 27, 2007 (6th): By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
9·10¹⁶¹+1 = 9(0)₁₆₀1_<162> = 19² · 268115868282277_<15> · C145
C145 = P43 · P103
P43 = 1452612416148001223786387377375980929408933_<43>
P103 = 6401224184307784221531476143753944364302696193784598490179821129689892756268275790197304471135782300801_<103>

Number: n N=9298497728672348738654088152725043047653335440887426945669034198013979457141066603768096625347093326453497719648788386059162812868886287742455333 ( 145 digits) SNFS difficulty: 161 digits. Divisors found: r1=1452612416148001223786387377375980929408933 (pp43) r2=6401224184307784221531476143753944364302696193784598490179821129689892756268275790197304471135782300801 (pp103) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 50.93 hours. Scaled time: 54.65 units (timescale=1.073). Factorization parameters were as follows: name: KA_9_0_160_1 n: 9298497728672348738654088152725043047653335440887426945669034198013979457141066603768096625347093326453497719648788386059162812868886287742455333 skew: 0.41 deg: 5 c5: 90 c0: 1 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:250150, AFBsize:249956, largePrimes:7360513 encountered Relations: rels:6909886, finalFF:585073 Max relations in full relation-set: 28 Initial matrix: 500173 x 585073 with sparse part having weight 41263807. Pruned matrix : 430599 x 433163 with weight 26317605. Total sieving time: 45.72 hours. Total relation processing time: 0.26 hours. Matrix solve time: 4.79 hours. Total square root time: 0.16 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 50.93 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 27, 2007 (5th): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
5·10¹⁶³-3 = 4(9)₁₆₂7_<164> = 2833 · 184967 · 13315699 · C148
C148 = P35 · P113
P35 = 74998792236344109387450078891725779_<35>
P113 = 95545654112791421636906751022948221950213818775035727503822215288586505310116495426553720942470582028517007755987_<113>

Number: 49997_163 N=7165808661890840897859714216746508466161349306048122768370338285750348690423700476081529989454370863114686016738935169566343753929497072942549488873 ( 148 digits) SNFS difficulty: 164 digits. Divisors found: r1=74998792236344109387450078891725779 (pp35) r2=95545654112791421636906751022948221950213818775035727503822215288586505310116495426553720942470582028517007755987 (pp113) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 96.02 hours. Scaled time: 65.49 units (timescale=0.682). Factorization parameters were as follows: name: 49997_163 n: 7165808661890840897859714216746508466161349306048122768370338285750348690423700476081529989454370863114686016738935169566343753929497072942549488873 m: 500000000000000000000000000000000 c5: 8 c0: -15 skew: 1.13 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4550001) Primes: RFBsize:315948, AFBsize:315761, largePrimes:5791399 encountered Relations: rels:5931578, finalFF:709466 Max relations in full relation-set: 0 Initial matrix: 631774 x 709466 with sparse part having weight 36626735. Pruned matrix : 573328 x 576550 with weight 28530803. Total sieving time: 82.87 hours. Total relation processing time: 0.35 hours. Matrix solve time: 12.59 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 96.02 hours. --------- CPU info (if available) ----------
Jul 27, 2007 (4th): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
6·10¹⁶²-1 = 5(9)₁₆₂_<163> = 33413 · 15377792567_<11> · C149
C149 = P40 · P109
P40 = 8461863041793557423309640118101540415199_<40>
P109 = 1379989523873218126548187496324337406517253315539049102957670242333680936574239687581847686601665035459375931_<109>

Number: n N=11677282350125072565528496755056693390894578124346913826602577065368169930338426882409563592311243405998642515404383594961811857506465947731167175269 ( 149 digits) SNFS difficulty: 162 digits. Divisors found: r1=8461863041793557423309640118101540415199 (pp40) r2=1379989523873218126548187496324337406517253315539049102957670242333680936574239687581847686601665035459375931 (pp109) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.45 hours. Scaled time: 61.47 units (timescale=1.448). Factorization parameters were as follows: name: KA_5_9_162 n: 11677282350125072565528496755056693390894578124346913826602577065368169930338426882409563592311243405998642515404383594961811857506465947731167175269 skew: 0.28 deg: 5 c5: 600 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1900001) Primes: RFBsize:250150, AFBsize:249916, largePrimes:7325134 encountered Relations: rels:6881070, finalFF:592491 Max relations in full relation-set: 28 Initial matrix: 500132 x 592491 with sparse part having weight 39869074. Pruned matrix : 421848 x 424412 with weight 24612582. Total sieving time: 37.71 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.45 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 42.45 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(13·10¹⁶¹-1)/3 = 4(3)₁₆₁_<162> = 35591 · 56617483129_<11> · C147
C147 = P28 · P56 · P64
P28 = 6916321829686376333181913823_<28>
P56 = 11574884111412367178608580326121743923707807455418638553_<56>
P64 = 2686207161095289004338174437326230035207838243702836292283105613_<64>

Number: n N=215045989550297315654863919994251904257815223605138461618086564897394811789556878090551491142316445311255103555809184394301856619887795350638801947 ( 147 digits) SNFS difficulty: 162 digits. Divisors found: r1=6916321829686376333181913823 (pp28) r2=11574884111412367178608580326121743923707807455418638553 (pp56) r3=2686207161095289004338174437326230035207838243702836292283105613 (pp64) Version: GGNFS-0.77.1-20051202-athlon Total time: 61.29 hours. Scaled time: 58.97 units (timescale=0.962). Factorization parameters were as follows: name: KA_4_3_161 n: 215045989550297315654863919994251904257815223605138461618086564897394811789556878090551491142316445311255103555809184394301856619887795350638801947 type: snfs skew: 1 deg: 5 c5: 130 c0: -1 m: 100000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [1750000, 3750001) Primes: RFBsize:250150, AFBsize:250361, largePrimes:7677203 encountered Relations: rels:7173676, finalFF:581835 Max relations in full relation-set: 48 Initial matrix: 500578 x 581835 with sparse part having weight 54017180. Pruned matrix : 461516 x 464082 with weight 37017683. Total sieving time: 53.03 hours. Total relation processing time: 0.36 hours. Matrix solve time: 7.72 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000 total time: 61.29 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2400+ stepping 01 Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem) sisfb: Memory heap starting at 12288K, size 19960K Calibrating delay loop... 4010.80 BogoMIPS
Jul 27, 2007 (3rd): By JMB / GMP-ECM B1=1000000
(25·10¹⁸⁵-7)/9 = 2(7)₁₈₅_<186> = 809 · 1498561 · 4617297143_<10> · C167
C167 = P32 · P135
P32 = 54832091297347447631038216522501_<32>
P135 = 905006956151265763655758125706409102912355176390129079383960741381669849617325066992415304569102339104861501591003320417505261613287411_<135>
Jul 27, 2007 (2nd): By Jo Yeong Uk / Msieve v. 1.25, GGNFS-0.77.1-20050930-nocona
(25·10¹⁶⁵-7)/9 = 2(7)₁₆₅_<166> = 296987 · 1840206433618866165991_<22> · 26841431788288106581500307455836598045271854373_<47> · C93
C93 = P44 · P49
P44 = 47762472444603047641362563601969990683449099_<44>
P49 = 3964615152987551810337697840608378229741533181603_<49>

Fri Jul 27 00:00:02 2007 Fri Jul 27 00:00:02 2007 Fri Jul 27 00:00:02 2007 Msieve v. 1.25 Fri Jul 27 00:00:02 2007 random seeds: 2bd8376f a00d4807 Fri Jul 27 00:00:02 2007 factoring 189359821998023639433196029818337369944098310651646127033896205015214673371291949815173725697 (93 digits) Fri Jul 27 00:00:02 2007 commencing quadratic sieve (92-digit input) Fri Jul 27 00:00:02 2007 using multiplier of 1 Fri Jul 27 00:00:02 2007 using 32kb Intel Core sieve core Fri Jul 27 00:00:02 2007 sieve interval: 36 blocks of size 32768 Fri Jul 27 00:00:02 2007 processing polynomials in batches of 6 Fri Jul 27 00:00:02 2007 using a sieve bound of 1888763 (70588 primes) Fri Jul 27 00:00:02 2007 using large prime bound of 220985271 (27 bits) Fri Jul 27 00:00:02 2007 using double large prime bound of 1046776511774331 (42-50 bits) Fri Jul 27 00:00:02 2007 using trial factoring cutoff of 50 bits Fri Jul 27 00:00:02 2007 polynomial 'A' values have 12 factors Fri Jul 27 01:44:58 2007 70722 relations (18185 full + 52537 combined from 929745 partial), need 70684 Fri Jul 27 01:44:59 2007 begin with 947930 relations Fri Jul 27 01:44:59 2007 reduce to 179343 relations in 10 passes Fri Jul 27 01:44:59 2007 attempting to read 179343 relations Fri Jul 27 01:45:01 2007 recovered 179343 relations Fri Jul 27 01:45:01 2007 recovered 160005 polynomials Fri Jul 27 01:45:01 2007 attempting to build 70722 cycles Fri Jul 27 01:45:01 2007 found 70722 cycles in 6 passes Fri Jul 27 01:45:01 2007 distribution of cycle lengths: Fri Jul 27 01:45:01 2007 length 1 : 18185 Fri Jul 27 01:45:01 2007 length 2 : 12896 Fri Jul 27 01:45:01 2007 length 3 : 12122 Fri Jul 27 01:45:01 2007 length 4 : 9485 Fri Jul 27 01:45:01 2007 length 5 : 6891 Fri Jul 27 01:45:01 2007 length 6 : 4485 Fri Jul 27 01:45:01 2007 length 7 : 2866 Fri Jul 27 01:45:01 2007 length 9+: 3792 Fri Jul 27 01:45:01 2007 largest cycle: 24 relations Fri Jul 27 01:45:01 2007 matrix is 70588 x 70722 with weight 4300045 (avg 60.80/col) Fri Jul 27 01:45:02 2007 filtering completed in 3 passes Fri Jul 27 01:45:02 2007 matrix is 66700 x 66763 with weight 4091463 (avg 61.28/col) Fri Jul 27 01:45:03 2007 saving the first 48 matrix rows for later Fri Jul 27 01:45:03 2007 matrix is 66652 x 66763 with weight 3180982 (avg 47.65/col) Fri Jul 27 01:45:03 2007 matrix includes 64 packed rows Fri Jul 27 01:45:03 2007 using block size 26705 for processor cache size 4096 kB Fri Jul 27 01:45:03 2007 commencing Lanczos iteration Fri Jul 27 01:45:24 2007 lanczos halted after 1056 iterations Fri Jul 27 01:45:24 2007 recovered 17 nontrivial dependencies Fri Jul 27 01:45:25 2007 prp44 factor: 47762472444603047641362563601969990683449099 Fri Jul 27 01:45:25 2007 prp49 factor: 3964615152987551810337697840608378229741533181603 Fri Jul 27 01:45:25 2007 elapsed time 01:45:23
(25·10¹⁷⁶-7)/9 = 2(7)₁₇₆_<177> = 53 · 170174087 · 9924073470733_<13> · 5048202952542749191_<19> · 250364392061117480432331832411240313552347_<42> · C94
C94 = P37 · P57
P37 = 3963347185486060546396209546732592561_<37>
P57 = 619536279901870322724589710902400805635161682525735259507_<57>

Fri Jul 27 01:51:19 2007 Fri Jul 27 01:51:19 2007 Fri Jul 27 01:51:19 2007 Msieve v. 1.25 Fri Jul 27 01:51:19 2007 random seeds: a432810d 7a7c1870 Fri Jul 27 01:51:19 2007 factoring 2455437371255581962526922265114020960306360460563718242524031556201268139958057995992232727427 (94 digits) Fri Jul 27 01:51:19 2007 commencing quadratic sieve (94-digit input) Fri Jul 27 01:51:19 2007 using multiplier of 3 Fri Jul 27 01:51:19 2007 using 32kb Intel Core sieve core Fri Jul 27 01:51:19 2007 sieve interval: 36 blocks of size 32768 Fri Jul 27 01:51:19 2007 processing polynomials in batches of 6 Fri Jul 27 01:51:19 2007 using a sieve bound of 2023097 (75294 primes) Fri Jul 27 01:51:19 2007 using large prime bound of 271094998 (28 bits) Fri Jul 27 01:51:19 2007 using double large prime bound of 1512232961643520 (42-51 bits) Fri Jul 27 01:51:19 2007 using trial factoring cutoff of 51 bits Fri Jul 27 01:51:19 2007 polynomial 'A' values have 12 factors Fri Jul 27 03:46:55 2007 75609 relations (19298 full + 56311 combined from 1057051 partial), need 75390 Fri Jul 27 03:46:55 2007 begin with 1076349 relations Fri Jul 27 03:46:56 2007 reduce to 193033 relations in 11 passes Fri Jul 27 03:46:56 2007 attempting to read 193033 relations Fri Jul 27 03:46:58 2007 recovered 193033 relations Fri Jul 27 03:46:58 2007 recovered 172661 polynomials Fri Jul 27 03:46:58 2007 attempting to build 75609 cycles Fri Jul 27 03:46:58 2007 found 75609 cycles in 5 passes Fri Jul 27 03:46:58 2007 distribution of cycle lengths: Fri Jul 27 03:46:58 2007 length 1 : 19298 Fri Jul 27 03:46:58 2007 length 2 : 13639 Fri Jul 27 03:46:58 2007 length 3 : 12851 Fri Jul 27 03:46:58 2007 length 4 : 10149 Fri Jul 27 03:46:58 2007 length 5 : 7572 Fri Jul 27 03:46:58 2007 length 6 : 4979 Fri Jul 27 03:46:58 2007 length 7 : 3073 Fri Jul 27 03:46:58 2007 length 9+: 4048 Fri Jul 27 03:46:58 2007 largest cycle: 19 relations Fri Jul 27 03:46:58 2007 matrix is 75294 x 75609 with weight 4735754 (avg 62.63/col) Fri Jul 27 03:46:59 2007 filtering completed in 3 passes Fri Jul 27 03:46:59 2007 matrix is 71057 x 71120 with weight 4477233 (avg 62.95/col) Fri Jul 27 03:47:00 2007 saving the first 48 matrix rows for later Fri Jul 27 03:47:00 2007 matrix is 71009 x 71120 with weight 3452561 (avg 48.55/col) Fri Jul 27 03:47:00 2007 matrix includes 64 packed rows Fri Jul 27 03:47:00 2007 using block size 28448 for processor cache size 4096 kB Fri Jul 27 03:47:00 2007 commencing Lanczos iteration Fri Jul 27 03:47:26 2007 lanczos halted after 1125 iterations Fri Jul 27 03:47:26 2007 recovered 15 nontrivial dependencies Fri Jul 27 03:47:26 2007 prp37 factor: 3963347185486060546396209546732592561 Fri Jul 27 03:47:26 2007 prp57 factor: 619536279901870322724589710902400805635161682525735259507 Fri Jul 27 03:47:26 2007 elapsed time 01:56:07
(7·10¹⁸¹-1)/3 = 2(3)₁₈₁_<182> = C182
C182 = P50 · P59 · P74
P50 = 63260551995570788106768735871476130074461634746477_<50>
P59 = 25995503880899966863964451990659560723251183499345255736491_<59>
P74 = 14188796769082230791752762485216295330686733826011471336380633628674520219_<74>

Number: 23333_181 N=23333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 ( 182 digits) SNFS difficulty: 181 digits. Divisors found: r1=63260551995570788106768735871476130074461634746477 (pp50) r2=25995503880899966863964451990659560723251183499345255736491 (pp59) r3=14188796769082230791752762485216295330686733826011471336380633628674520219 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 251.75 hours. Scaled time: 538.99 units (timescale=2.141). Factorization parameters were as follows: n: 23333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 m: 1000000000000000000000000000000000000 c5: 70 c0: -1 skew: 0.43 type: snfs Factor base limits: 10000000/10000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [5000000, 9100001) Primes: RFBsize:664579, AFBsize:665975, largePrimes:11133286 encountered Relations: rels:11498215, finalFF:1574842 Max relations in full relation-set: 28 Initial matrix: 1330621 x 1574842 with sparse part having weight 97445326. Pruned matrix : 1107698 x 1114415 with weight 66130008. Total sieving time: 240.97 hours. Total relation processing time: 0.46 hours. Matrix solve time: 10.19 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,181,5,0,0,0,0,0,0,0,0,10000000,10000000,28,28,50,50,2.6,2.6,100000 total time: 251.75 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 27, 2007: By Wataru Sakai / GMP-ECM 6.1.1 B1=11000000
4·10¹⁹⁴+1 = 4(0)₁₉₃1_<195> = 721324202162977116296517293557_<30> · 230366834312643340988031253121778481_<36> · C130
C130 = P46 · P84
P46 = 4539551603725680577678687090612374940158174209_<46>
P84 = 530269411486144259272416902466941069870793165414892485082648513501276740375531374317_<84>
Jul 26, 2007 (5th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(8·10¹⁵⁸+1)/9 = (8)₁₅₇9_<158> = 251 · 19051 · 661553 · 16802878173815484403_<20> · C127
C127 = P36 · P91
P36 = 507720820294334799136631537333312339_<36>
P91 = 3293689718850709442805545468432778915791702568309037103083241191944222576426385744129092889_<91>

Number: 88889_158 N=1672274845849899157699286610421044576382314630035217679398866050298573807484823525552765996029264801596675892531763861780857371 ( 127 digits) SNFS difficulty: 160 digits. Divisors found: r1=507720820294334799136631537333312339 (pp36) r2=3293689718850709442805545468432778915791702568309037103083241191944222576426385744129092889 (pp91) Version: GGNFS-0.77.1-20050930-nocona Total time: 26.23 hours. Scaled time: 56.17 units (timescale=2.141). Factorization parameters were as follows: n: 1672274845849899157699286610421044576382314630035217679398866050298573807484823525552765996029264801596675892531763861780857371 m: 100000000000000000000000000000000 c5: 2 c0: 25 skew: 1.66 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3500001) Primes: RFBsize:283146, AFBsize:282402, largePrimes:5682679 encountered Relations: rels:5768719, finalFF:704676 Max relations in full relation-set: 28 Initial matrix: 565613 x 704676 with sparse part having weight 43802932. Pruned matrix : 450587 x 453479 with weight 27244630. Total sieving time: 25.05 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.04 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 26.23 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 26, 2007 (4th): By Alfred Reich
10⁵¹⁵+1 is divisible by 896048585318577702680084550566846611_<36>
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)
Jul 26, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
6·10¹⁶¹-1 = 5(9)₁₆₁_<162> = 43 · 836569 · 2898421 · C148
C148 = P43 · P48 · P58
P43 = 8293782204604425278695261694855447366239429_<43>
P48 = 373661139043910874867543028013950188940119372163_<48>
P58 = 1856902068363473523911678753942645197496692067981158293791_<58>

Number: n N=5754658547595349311495950603756779150156168225617883200618038320893662324167945261296559539792048549985733231130607693324550635705623295348791018257 ( 148 digits) SNFS difficulty: 161 digits. Divisors found: r1=8293782204604425278695261694855447366239429 (pp43) r2=373661139043910874867543028013950188940119372163 (pp48) r3=1856902068363473523911678753942645197496692067981158293791 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 38.23 hours. Scaled time: 50.61 units (timescale=1.324). Factorization parameters were as follows: name: KA_5_9_161 n: 5754658547595349311495950603756779150156168225617883200618038320893662324167945261296559539792048549985733231130607693324550635705623295348791018257 skew: 0.44 deg: 5 c5: 60 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:250150, AFBsize:249771, largePrimes:7114930 encountered Relations: rels:6634553, finalFF:568518 Max relations in full relation-set: 48 Initial matrix: 499988 x 568518 with sparse part having weight 37166803. Pruned matrix : 440914 x 443477 with weight 23182215. Total sieving time: 33.28 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.57 hours. Total square root time: 0.15 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 38.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
6·10¹⁶³+1 = 6(0)₁₆₂1_<164> = 17 · 353 · 383 · C158
C158 = P55 · P103
P55 = 5215147241069255739103596758994562191897609456843465301_<55>
P103 = 5005670690155230684429614037038784632521687552228111599112073609027731095334283017297356948767263632947_<103>

Number: n N=26105309689464288588977555089817493429076006914426359749441237600521758122993426247931698067728485635335799124863001510192165535509094872351561945941994872047 ( 158 digits) SNFS difficulty: 164 digits. Divisors found: r1=5215147241069255739103596758994562191897609456843465301 (pp55) r2=5005670690155230684429614037038784632521687552228111599112073609027731095334283017297356948767263632947 (pp103) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.28 hours. Scaled time: 75.62 units (timescale=1.195). Factorization parameters were as follows: name: KA_6_0_162_1 n: 26105309689464288588977555089817493429076006914426359749441237600521758122993426247931698067728485635335799124863001510192165535509094872351561945941994872047 type: snfs skew: 0.35 deg: 5 c5: 375 c0: 2 m: 200000000000000000000000000000000 rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2500001) Primes: RFBsize:256726, AFBsize:256771, largePrimes:7311903 encountered Relations: rels:6805144, finalFF:587598 Max relations in full relation-set: 28 Initial matrix: 513563 x 587598 with sparse part having weight 35738792. Pruned matrix : 452305 x 454936 with weight 23525858. Total sieving time: 57.84 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.04 hours. Total square root time: 0.12 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000 total time: 63.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 26, 2007 (2nd): By JMB / GMP-ECM B1=1000000
(25·10¹⁷⁶-7)/9 = 2(7)₁₇₆_<177> = 53 · 170174087 · 9924073470733_<13> · 5048202952542749191_<19> · C135
C135 = P42 · C94
P42 = 250364392061117480432331832411240313552347_<42>
C94 = [2455437371255581962526922265114020960306360460563718242524031556201268139958057995992232727427_<94>]
Jul 26, 2007: By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
7·10¹⁶⁰-3 = 6(9)₁₅₉7_<161> = 1023557 · 676040311822727_<15> · 225167822909311193771939915964703697_<36> · C105
C105 = P47 · P59
P47 = 26553121374225817669622704350957054548498613613_<47>
P59 = 16919655045991966846784423102442420227389002548091598746443_<59>

Number: 69997_160 N=449269654046257004984956784811621039356018734468246305859975642850924126367108968544894530278674215128559 ( 105 digits) Divisors found: r1=26553121374225817669622704350957054548498613613 (pp47) r2=16919655045991966846784423102442420227389002548091598746443 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.63 hours. Scaled time: 18.49 units (timescale=2.142). Factorization parameters were as follows: name: 69997_160 n: 449269654046257004984956784811621039356018734468246305859975642850924126367108968544894530278674215128559 skew: 10958.86 # norm 7.52e+14 c5: 43560 c4: -563864382 c3: -51657033522313 c2: 36279037644759719 c1: 357816660151572433929 c0: 516503811917770537490127 # alpha -6.49 Y1: 32038029803 Y0: -100619974011831009902 # Murphy_E 2.05e-09 # M 112706527664659458380579445234447723037480698246914182616771058378695853459900351089940084316930206294864 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1320001) Primes: RFBsize:135072, AFBsize:135315, largePrimes:4535175 encountered Relations: rels:4601948, finalFF:406094 Max relations in full relation-set: 28 Initial matrix: 270467 x 406094 with sparse part having weight 36895626. Pruned matrix : 194220 x 195636 with weight 16421677. Polynomial selection time: 0.43 hours. Total sieving time: 7.88 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 8.63 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 25, 2007 (4th): By Alban Nonymous
10¹¹⁴²+1 is divisible by 72902178953713285322996186513081_<32>
10¹¹⁷⁴+1 is divisible by 56360262697642563914567399981_<29>
10¹³⁴⁸+1 is divisible by 28060177869481210079003327188873_<32>
10¹³⁴⁸+1 is divisible by 87621827832372981614062571297033_<32>
10¹³⁸²+1 is divisible by 897720822084629349764719120861_<30>
10¹⁴¹⁵+1 is divisible by 21279344764661594183530203415321_<32>
10¹⁴³⁹+1 is divisible by 6652742443560007068799568102809_<31>
10¹⁴⁴⁸+1 is divisible by 3741284323572778169733000409441_<31>
10¹⁴⁵⁴+1 is divisible by 24474149875167364484471358364249_<32>
10¹⁷⁶⁸+1 is divisible by 54377311669469461225374918721_<29>
10¹⁸²⁸+1 is divisible by 99257142543720996230422229080081_<32>
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)
Jul 25, 2007 (3rd): By JMB / GMP-ECM B1=3000000
(25·10¹⁷¹-7)/9 = 2(7)₁₇₁_<172> = 17 · 2087 · 21787 · 105991859 · 5704794863611639_<16> · 514082498989493831_<18> · C122
C122 = P39 · P83
P39 = 197487969842997416603481017802302838281_<39>
P83 = 58538648152060113017157905351021224725745777751121568986210159879682035562955814559_<83>
(25·10¹⁶⁵-7)/9 = 2(7)₁₆₅_<166> = 296987 · 1840206433618866165991_<22> · C139
C139 = P47 · C93
P47 = 26841431788288106581500307455836598045271854373_<47>
C93 = [189359821998023639433196029818337369944098310651646127033896205015214673371291949815173725697_<93>]
(25·10¹⁶¹-7)/9 = 2(7)₁₆₁_<162> = 145934700643261_<15> · 253469408840513_<15> · C133
C133 = P37 · P97
P37 = 2540772921047677915010225799850512679_<37>
P97 = 2955612696837122473621797379554555189784507453027799522994334517349252054962930031497122170904691_<97>
Jul 25, 2007 (2nd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
7·10¹⁵⁸-3 = 6(9)₁₅₇7_<159> = 1303 · 2473 · 133346505599_<12> · C142
C142 = P65 · P77
P65 = 42315979991490290739022320497289947523549183832673097091435256957_<65>
P77 = 38498469586434182358752612193019411923606426698177641577645805015090636763441_<77>

Number: n N=1629100468722546348836181865908396777509268424093637341521060707834668285197254554652258415454552586334588148334243116907405481886978658509037 ( 142 digits) SNFS difficulty: 158 digits. Divisors found: r1=42315979991490290739022320497289947523549183832673097091435256957 (pp65) r2=38498469586434182358752612193019411923606426698177641577645805015090636763441 (pp77) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.97 hours. Scaled time: 51.83 units (timescale=1.441). Factorization parameters were as follows: name: KA_6_9_157_7 n: 1629100468722546348836181865908396777509268424093637341521060707834668285197254554652258415454552586334588148334243116907405481886978658509037 skew: 0.21 deg: 5 c5: 7000 c0: -3 m: 10000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:250150, AFBsize:249771, largePrimes:7127717 encountered Relations: rels:6646443, finalFF:562655 Max relations in full relation-set: 28 Initial matrix: 499988 x 562655 with sparse part having weight 34901852. Pruned matrix : 443280 x 445843 with weight 23027628. Total sieving time: 31.37 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.32 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 35.97 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹⁵⁹-3 = 6(9)₁₅₈7_<160> = 11480647 · C153
C153 = P37 · P117
P37 = 2123843629199706450095966417930509967_<37>
P117 = 287084098820217654683647609855563415797505527535490938568019121616173404487170471297898238166611115453129796922918453_<117>

Number: n N=609721734323858228547572275325597938861808049668280890441104930758693303609108441362233330577971781555516862420732908171464552476876956499054452244721051 ( 153 digits) SNFS difficulty: 160 digits. Divisors found: r1=2123843629199706450095966417930509967 (pp37) r2=287084098820217654683647609855563415797505527535490938568019121616173404487170471297898238166611115453129796922918453 (pp117) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 52.22 hours. Scaled time: 71.22 units (timescale=1.364). Factorization parameters were as follows: name: KA_6_9_158_7 n: 609721734323858228547572275325597938861808049668280890441104930758693303609108441362233330577971781555516862420732908171464552476876956499054452244721051 skew: 1.34 deg: 5 c5: 7 c0: -30 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2100001) Primes: RFBsize:250150, AFBsize:249671, largePrimes:7451024 encountered Relations: rels:7012972, finalFF:594936 Max relations in full relation-set: 28 Initial matrix: 499886 x 594936 with sparse part having weight 41833194. Pruned matrix : 422235 x 424798 with weight 26496990. Total sieving time: 46.74 hours. Total relation processing time: 0.26 hours. Matrix solve time: 4.28 hours. Total square root time: 0.93 hours, sqrts: 7. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 52.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 25, 2007: By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
(7·10¹⁵⁸-43)/9 = (7)₁₅₇3_<158> = 89 · 517482230513_<12> · 5274627333364848091_<19> · C126
C126 = P46 · P81
P46 = 2933276055435097150496053520245973899417083587_<46>
P81 = 109150408258221546428199289249059666027298203143441744801893598785485031825721717_<81>

Number: 77773_158 N=320168278984806550631540855094563858596255377566714042276093831735771608620605463361630935228187638716394639828145755590158879 ( 126 digits) SNFS difficulty: 159 digits. Divisors found: r1=2933276055435097150496053520245973899417083587 (pp46) r2=109150408258221546428199289249059666027298203143441744801893598785485031825721717 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 33.67 hours. Scaled time: 72.19 units (timescale=2.144). Factorization parameters were as follows: n: 320168278984806550631540855094563858596255377566714042276093831735771608620605463361630935228187638716394639828145755590158879 m: 20000000000000000000000000000000 c5: 875 c0: -172 skew: 0.72 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3900001) Primes: RFBsize:283146, AFBsize:283557, largePrimes:5672154 encountered Relations: rels:5680276, finalFF:635478 Max relations in full relation-set: 28 Initial matrix: 566770 x 635478 with sparse part having weight 40948383. Pruned matrix : 518482 x 521379 with weight 30154788. Total sieving time: 31.82 hours. Total relation processing time: 0.12 hours. Matrix solve time: 1.67 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 33.67 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 24, 2007 (2nd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
3·10¹⁶³-1 = 2(9)₁₆₃_<164> = 997 · 2287 · C158
C158 = P50 · P108
P50 = 45747879641691574163746483574403221719068934066339_<50>
P108 = 287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719_<108>

Number: n N=13157092615844911209360481970616703630787421293175547631087403004816811606660821993746872449442775199231274935431567987741098240063434729198526931910730003741 ( 158 digits) SNFS difficulty: 163 digits. Divisors found: r1=45747879641691574163746483574403221719068934066339 (pp50) r2=287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719 (pp108) Version: GGNFS-0.77.1-20051202-athlon Total time: 63.42 hours. Scaled time: 82.76 units (timescale=1.305). Factorization parameters were as follows: name: KA_2_9_163 n: 13157092615844911209360481970616703630787421293175547631087403004816811606660821993746872449442775199231274935431567987741098240063434729198526931910730003741 skew: 0.20 deg: 5 c5: 3000 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2600001) Primes: RFBsize:256726, AFBsize:256576, largePrimes:7639847 encountered Relations: rels:7209577, finalFF:633047 Max relations in full relation-set: 48 Initial matrix: 513369 x 633047 with sparse part having weight 51694938. Pruned matrix : 421670 x 424300 with weight 31990993. Total sieving time: 56.77 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.99 hours. Total square root time: 0.37 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.5,2.5,100000 total time: 63.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁴⁹-3 = 6(9)₁₄₈7_<150> = 73 · 139 · C146
C146 = P44 · P50 · P53
P44 = 79426057057573470993450111694681586724818267_<44>
P50 = 10135149856645968832942226206178100278444840800939_<50>
P53 = 85697312347290420035372811292253154086540948455681127_<53>

Number: n N=68985907164679215531684241647777668276337833842515029072632305114812259781216122992017345028087119345619394895042869813738050655366118064452547551 ( 146 digits) SNFS difficulty: 150 digits. Divisors found: r1=79426057057573470993450111694681586724818267 (pp44) r2=10135149856645968832942226206178100278444840800939 (pp50) r3=85697312347290420035372811292253154086540948455681127 (pp53) Version: GGNFS-0.77.1-20051202-athlon Total time: 28.79 hours. Scaled time: 27.70 units (timescale=0.962). Factorization parameters were as follows: name: KA_6_9_148_7 n: 68985907164679215531684241647777668276337833842515029072632305114812259781216122992017345028087119345619394895042869813738050655366118064452547551 type: snfs skew: 1 deg: 5 c5: 7 c0: -30 m: 1000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2400001) Primes: RFBsize:216816, AFBsize:216451, largePrimes:7557334 encountered Relations: rels:7186983, finalFF:648300 Max relations in full relation-set: 48 Initial matrix: 433332 x 648300 with sparse part having weight 55843030. Pruned matrix : 303102 x 305332 with weight 30614410. Total sieving time: 24.47 hours. Total relation processing time: 0.27 hours. Matrix solve time: 3.92 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 28.79 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2400+ stepping 01 Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem) sisfb: Memory heap starting at 12288K, size 19960K Calibrating delay loop... 4010.80 BogoMIPS
Jul 24, 2007: By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000
7·10¹⁶⁰-3 = 6(9)₁₅₉7_<161> = 1023557 · 676040311822727_<15> · C141
C141 = P36 · C105
P36 = 225167822909311193771939915964703697_<36>
C105 = [449269654046257004984956784811621039356018734468246305859975642850924126367108968544894530278674215128559_<105>]
Jul 23, 2007 (5th): By Bruce Dodson
10²⁷¹+1 is divisible by 256031814642414583920091086688834271205176259587307504943_<57>, cofactor is prime.
Reference: ECMNET (Paul Zimmermann)
Jul 23, 2007 (4th): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
(73·10¹⁶²-1)/9 = 8(1)₁₆₂_<163> = 1423 · 19441 · C156
C156 = P39 · P55 · P63
P39 = 543595994789336592839503974042022463653_<39>
P55 = 3924592279844824544604200287483373227338892292932056637_<55>
P63 = 137431427308481583890246932087896925834997509780593354650152457_<63>

Number: n N=293195196143710420631604545613173914028188035172354414497687928953357773201281912052952080614926879909460680811214235894339953893730003460064788025275209177 ( 156 digits) SNFS difficulty: 163 digits. Divisors found: r1=543595994789336592839503974042022463653 (pp39) r2=3924592279844824544604200287483373227338892292932056637 (pp55) r3=137431427308481583890246932087896925834997509780593354650152457 (pp63) Version: GGNFS-0.77.1-20051202-athlon Total time: 69.55 hours. Scaled time: 100.51 units (timescale=1.445). Factorization parameters were as follows: name: KA_8_1_162 n: 293195196143710420631604545613173914028188035172354414497687928953357773201281912052952080614926879909460680811214235894339953893730003460064788025275209177 skew: 0.17 deg: 5 c5: 7300 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3200001) Primes: RFBsize:250150, AFBsize:251141, largePrimes:7701069 encountered Relations: rels:7215982, finalFF:564079 Max relations in full relation-set: 28 Initial matrix: 501358 x 564079 with sparse part having weight 45743064. Pruned matrix : 462725 x 465295 with weight 34374223. Total sieving time: 62.01 hours. Total relation processing time: 0.26 hours. Matrix solve time: 7.00 hours. Total square root time: 0.28 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 69.55 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹⁴⁰-3 = 6(9)₁₃₉7_<141> = 991 · 1057391 · 345418457 · C124
C124 = P59 · P66
P59 = 11250180495689321348084945885182355115543862335246134474303_<59>
P66 = 171903114767847828998563831031206474014001920428664101581017239147_<66>

Number: n N=1933941068909484585739512229673477136075976625781953413961591541199884613868795341283880692719104589317952297566427277139541 ( 124 digits) SNFS difficulty: 140 digits. Divisors found: r1=11250180495689321348084945885182355115543862335246134474303 (pp59) r2=171903114767847828998563831031206474014001920428664101581017239147 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.58 hours. Scaled time: 8.26 units (timescale=0.963). Factorization parameters were as follows: name: KA_6_9_139_7 n: 1933941068909484585739512229673477136075976625781953413961591541199884613868795341283880692719104589317952297566427277139541 type: snfs skew: 1 deg: 5 c5: 7 c0: -3 m: 10000000000000000000000000000 rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [1250000, 1850001) Primes: RFBsize:183072, AFBsize:182526, largePrimes:6512840 encountered Relations: rels:5911205, finalFF:420901 Max relations in full relation-set: 48 Initial matrix: 365663 x 420901 with sparse part having weight 26924881. Pruned matrix : 322386 x 324278 with weight 16005615. Total sieving time: 6.02 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.27 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.3,2.3,100000 total time: 8.58 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2400+ stepping 01 Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem) sisfb: Memory heap starting at 12288K, size 19960K Calibrating delay loop... 4010.80 BogoMIPS
(2·10¹⁶¹+7)/9 = (2)₁₆₀3_<161> = 1714933083439_<13> · C149
C149 = P32 · P117
P32 = 21393514829134244932337814471241_<32>
P117 = 605700824976428319254861005827037748162874928762405763234457258027843650353567084980102064536103816470993229797108377_<117>

Number: n N=12958069581152065089700334183735480199819753791816814760004627272433457888819522067048753782066853574073171870347608059491626405404996336087026685857 ( 149 digits) SNFS difficulty: 161 digits. Divisors found: r1=21393514829134244932337814471241 (pp32) r2=605700824976428319254861005827037748162874928762405763234457258027843650353567084980102064536103816470993229797108377 (pp117) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 37.29 hours. Scaled time: 50.87 units (timescale=1.364). Factorization parameters were as follows: name: KA_2_160_3 n: 12958069581152065089700334183735480199819753791816814760004627272433457888819522067048753782066853574073171870347608059491626405404996336087026685857 skew: 0.81 deg: 5 c5: 20 c0: 7 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:250150, AFBsize:249316, largePrimes:7126735 encountered Relations: rels:6696335, finalFF:602076 Max relations in full relation-set: 28 Initial matrix: 499532 x 602076 with sparse part having weight 35432862. Pruned matrix : 408966 x 411527 with weight 19865620. Total sieving time: 33.82 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.16 hours. Total square root time: 0.12 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 37.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁴⁶-3 = 6(9)₁₄₅7_<147> = 17 · C146
C146 = P58 · P89
P58 = 2772341545407390176277168504286752739988576758255116308281_<58>
P89 = 14852596591660026569344293574475374603014785217941966344202020052222211474146804385683861_<89>

Number: n N=41176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941 ( 146 digits) SNFS difficulty: 146 digits. Divisors found: r1=2772341545407390176277168504286752739988576758255116308281 (pp58) r2=14852596591660026569344293574475374603014785217941966344202020052222211474146804385683861 (pp89) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.83 hours. Scaled time: 18.57 units (timescale=1.447). Factorization parameters were as follows: name: KA_6_9_145_7 n: 41176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941 skew: 0.53 deg: 5 c5: 70 c0: -3 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:183072, AFBsize:182426, largePrimes:7031056 encountered Relations: rels:6506072, finalFF:476292 Max relations in full relation-set: 28 Initial matrix: 365565 x 476292 with sparse part having weight 34230439. Pruned matrix : 282716 x 284607 with weight 19056754. Total sieving time: 10.50 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.04 hours. Total square root time: 0.11 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 12.83 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(86·10¹⁶²+31)/9 = 9(5)₁₆₁9_<163> = 13 · 137 · 191 · 733 · C155
C155 = P56 · P100
P56 = 15748989216219619926851701365192338858672015860064422379_<56>
P100 = 2433335515280598540281314498084827557020483327676703163289609599551700916484623909357190520150067147_<100>

Number: n N=38322574789598358592787335737630181268537088962417700159555639086291479506619682708714377535238568925490441405819861474435299782420863402913266182619482713 ( 155 digits) SNFS difficulty: 163 digits. Divisors found: r1=15748989216219619926851701365192338858672015860064422379 (pp56) r2=2433335515280598540281314498084827557020483327676703163289609599551700916484623909357190520150067147 (pp100) Version: GGNFS-0.77.1-20051202-athlon Total time: 72.01 hours. Scaled time: 86.12 units (timescale=1.196). Factorization parameters were as follows: name: KA_9_5_161_9 n: 38322574789598358592787335737630181268537088962417700159555639086291479506619682708714377535238568925490441405819861474435299782420863402913266182619482713 type: snfs skew: 0.32 deg: 5 c5: 8600 c0: 31 m: 100000000000000000000000000000000 rlim: 3600000 alim: 3600000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2800001) Primes: RFBsize:256726, AFBsize:257352, largePrimes:7397949 encountered Relations: rels:6878522, finalFF:577657 Max relations in full relation-set: 28 Initial matrix: 514145 x 577657 with sparse part having weight 36827281. Pruned matrix : 463389 x 466023 with weight 25709396. Total sieving time: 65.41 hours. Total relation processing time: 0.31 hours. Matrix solve time: 5.74 hours. Total square root time: 0.55 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3600000,3600000,28,28,48,48,2.3,2.3,100000 total time: 72.01 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 23, 2007 (3rd): By Sinkiti Sibata / Msieve v. 1.23, GGNFS-0.77.1-20060722-pentium4
7·10¹⁴⁵-3 = 6(9)₁₄₄7_<146> = 135899 · 2882653 · 4137260381_<10> · 769330598837417_<15> · 213310674409584473_<18> · C93
C93 = P41 · P52
P41 = 38419676520928330018576887493317188578379_<41>
P52 = 6850105473822077822398812945194215058951502092829389_<52>

Sun Jul 22 08:36:10 2007 Msieve v. 1.23 Sun Jul 22 08:36:10 2007 random seeds: 3eab88d0 395fcfcd Sun Jul 22 08:36:10 2007 factoring 263178836438484716512595291995766692784822600963980076573334298726819222124062974186701180431 (93 digits) Sun Jul 22 08:36:11 2007 commencing quadratic sieve (93-digit input) Sun Jul 22 08:36:11 2007 using multiplier of 1 Sun Jul 22 08:36:11 2007 using 64kb Pentium 2 sieve core Sun Jul 22 08:36:12 2007 sieve interval: 18 blocks of size 65536 Sun Jul 22 08:36:12 2007 processing polynomials in batches of 6 Sun Jul 22 08:36:12 2007 using a sieve bound of 1923127 (71422 primes) Sun Jul 22 08:36:12 2007 using large prime bound of 232698367 (27 bits) Sun Jul 22 08:36:12 2007 using double large prime bound of 1148756443608092 (42-51 bits) Sun Jul 22 08:36:12 2007 using trial factoring cutoff of 51 bits Sun Jul 22 08:36:12 2007 polynomial 'A' values have 12 factors Mon Jul 23 02:26:32 2007 71761 relations (17892 full + 53869 combined from 964161 partial), need 71518 Mon Jul 23 02:26:37 2007 begin with 982053 relations Mon Jul 23 02:26:39 2007 reduce to 183833 relations in 10 passes Mon Jul 23 02:26:39 2007 attempting to read 183833 relations Mon Jul 23 02:26:48 2007 recovered 183833 relations Mon Jul 23 02:26:48 2007 recovered 165542 polynomials Mon Jul 23 02:26:49 2007 attempting to build 71761 cycles Mon Jul 23 02:26:49 2007 found 71761 cycles in 6 passes Mon Jul 23 02:26:55 2007 distribution of cycle lengths: Mon Jul 23 02:26:55 2007 length 1 : 17892 Mon Jul 23 02:26:55 2007 length 2 : 12817 Mon Jul 23 02:26:55 2007 length 3 : 12407 Mon Jul 23 02:26:55 2007 length 4 : 9896 Mon Jul 23 02:26:55 2007 length 5 : 7008 Mon Jul 23 02:26:55 2007 length 6 : 4784 Mon Jul 23 02:26:55 2007 length 7 : 2999 Mon Jul 23 02:26:55 2007 length 9+: 3958 Mon Jul 23 02:26:55 2007 largest cycle: 20 relations Mon Jul 23 02:26:57 2007 matrix is 71422 x 71761 with weight 4423886 (avg 61.65/col) Mon Jul 23 02:27:03 2007 filtering completed in 3 passes Mon Jul 23 02:27:03 2007 matrix is 67649 x 67713 with weight 4191481 (avg 61.90/col) Mon Jul 23 02:27:06 2007 saving the first 48 matrix rows for later Mon Jul 23 02:27:07 2007 matrix is 67601 x 67713 with weight 3220413 (avg 47.56/col) Mon Jul 23 02:27:07 2007 matrix includes 64 packed rows Mon Jul 23 02:27:07 2007 using block size 5461 for processor cache size 128 kB Mon Jul 23 02:27:07 2007 commencing Lanczos iteration Mon Jul 23 02:31:49 2007 lanczos halted after 1071 iterations Mon Jul 23 02:31:50 2007 recovered 17 nontrivial dependencies Mon Jul 23 02:31:51 2007 prp41 factor: 38419676520928330018576887493317188578379 Mon Jul 23 02:31:51 2007 prp52 factor: 6850105473822077822398812945194215058951502092829389 Mon Jul 23 02:31:51 2007 elapsed time 17:55:41
5·10¹⁶¹-3 = 4(9)₁₆₀7_<162> = 509 · 1747 · C156
C156 = P44 · P49 · P64
P44 = 84102469602460672319344905855931567246447997_<44>
P49 = 2165440703043832390582601658352828177598414559503_<49>
P64 = 3087480849537780573910857739142506288073610114206777292982835929_<64>

Number: 49997_161 N=562288649753773800272822452860531047892373454127929664437379599942871473185016581892281238789370045534134857060602346093162232645804258324402315279744226139 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: r1=84102469602460672319344905855931567246447997 (pp44) r2=2165440703043832390582601658352828177598414559503 (pp49) r3=3087480849537780573910857739142506288073610114206777292982835929 (pp64) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 84.32 hours. Scaled time: 57.59 units (timescale=0.683). Factorization parameters were as follows: name: 49997_161 n: 562288649753773800272822452860531047892373454127929664437379599942871473185016581892281238789370045534134857060602346093162232645804258324402315279744226139 m: 100000000000000000000000000000000 c5: 50 c0: -3 skew: 0.57 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4250001) Primes: RFBsize:315948, AFBsize:315546, largePrimes:5795947 encountered Relations: rels:5955594, finalFF:716832 Max relations in full relation-set: 0 Initial matrix: 631559 x 716832 with sparse part having weight 35018298. Pruned matrix : 561436 x 564657 with weight 26268658. Total sieving time: 72.28 hours. Total relation processing time: 0.33 hours. Matrix solve time: 11.50 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 84.32 hours. --------- CPU info (if available) ----------
Jul 23, 2007 (2nd): By JMB / GMP-ECM B1=1000000
(25·10¹⁷³-7)/9 = 2(7)₁₇₃_<174> = 6169017583_<10> · 20358471981247_<14> · C151
C151 = P33 · P119
P33 = 147538874768229210393236316231919_<33>
P119 = 14990973816674434798810951647946982968321498302818159656670508001237850390226986288400829699930440359734410720309273583_<119>
(25·10¹⁶⁸-7)/9 = 2(7)₁₆₈_<169> = 467 · 1951 · 669181 · 754597 · 1164052117_<10> · 947954614376246137517748334624309_<33> · C109
C109 = P30 · P79
P30 = 927132501806373661426134175901_<30>
P79 = 5901506603211846125449705047676356701978336662915489305427354655975488018446161_<79>
(25·10¹⁸⁰-7)/9 = 2(7)₁₈₀_<181> = 29 · 1431838763_<10> · C170
C170 = P38 · P133
P38 = 18470961602412156590684680364912916293_<38>
P133 = 3621728413595020127934729686179752937236914591769684906994555969901118223512872261753854263218760544399218998367476041945127627646307_<133>
Jul 23, 2007: By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GMP-ECM 6.1.2 B1=1000000
7·10¹⁴²-3 = 6(9)₁₄₁7_<143> = 41 · 684820152391010899426909_<24> · C118
C118 = P42 · P76
P42 = 293996872467290101398339992619243102794207_<42>
P76 = 8479982205197969383707708914235563099398323494880780373423205897700123689959_<76>

Number: 69997_142 N=2493088246906476884084912070409326850502294819795549558679381121592194090497586991463738201828121886276619548249267513 ( 118 digits) SNFS difficulty: 142 digits. Divisors found: r1=293996872467290101398339992619243102794207 (pp42) r2=8479982205197969383707708914235563099398323494880780373423205897700123689959 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 7.68 hours. Scaled time: 16.37 units (timescale=2.132). Factorization parameters were as follows: n: 2493088246906476884084912070409326850502294819795549558679381121592194090497586991463738201828121886276619548249267513 m: 10000000000000000000000000000 c5: 700 c0: -3 skew: 0.34 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1250001) Primes: RFBsize:114155, AFBsize:114337, largePrimes:2621896 encountered Relations: rels:2599825, finalFF:287405 Max relations in full relation-set: 28 Initial matrix: 228559 x 287405 with sparse part having weight 18474157. Pruned matrix : 199501 x 200707 with weight 10381351. Total sieving time: 7.49 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 7.68 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹⁵³-3 = 6(9)₁₅₂7_<154> = 23² · 10303 · 4132288063902465163_<19> · 73545936976938384659_<20> · C109
C109 = P33 · P77
P33 = 368950902030040136294932320283019_<33>
P77 = 11454095970935197036364142614850850481119263863106296451412205403591388218697_<77>
7·10¹⁴³-3 = 6(9)₁₄₂7_<144> = 1390760561015147597115111631999_<31> · C114
C114 = P48 · P67
P48 = 176985412377038489455150177398295039807447995083_<48>
P67 = 2843859925569024851779496154354305448575151654276681477679351507241_<67>

Number: 69997_143 N=503321721669367848389014004967846324275133410824146226320877399025698826072432114856210091439057067468359606896003 ( 114 digits) SNFS difficulty: 144 digits. Divisors found: r1=176985412377038489455150177398295039807447995083 (pp48) r2=2843859925569024851779496154354305448575151654276681477679351507241 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.45 hours. Scaled time: 22.29 units (timescale=2.133). Factorization parameters were as follows: n: 503321721669367848389014004967846324275133410824146226320877399025698826072432114856210091439057067468359606896003 m: 20000000000000000000000000000 c5: 875 c0: -12 skew: 0.42 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1450001) Primes: RFBsize:114155, AFBsize:114347, largePrimes:2712236 encountered Relations: rels:2714874, finalFF:310280 Max relations in full relation-set: 28 Initial matrix: 228569 x 310280 with sparse part having weight 22031944. Pruned matrix : 197851 x 199057 with weight 11694112. Total sieving time: 10.24 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.14 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,144,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 10.45 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹⁴⁸-3 = 6(9)₁₄₇7_<149> = 311 · 7912579919_<10> · C137
C137 = P30 · P43 · P65
P30 = 301037510767131424181611457969_<30>
P43 = 5434594245435338312688573491110293470744533_<43>
P65 = 17387286194393844709918894508724977643672044365413394191742373729_<65>

Number: 69997_148 N=28445890993355795785465713412766066538152730750893507917803289805207609319238261618681814513715015288973371527222324093744020519559325733 ( 137 digits) SNFS difficulty: 149 digits. Divisors found: r1=301037510767131424181611457969 (pp30) r2=5434594245435338312688573491110293470744533 (pp43) r3=17387286194393844709918894508724977643672044365413394191742373729 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.60 hours. Scaled time: 27.00 units (timescale=2.143). Factorization parameters were as follows: n: 28445890993355795785465713412766066538152730750893507917803289805207609319238261618681814513715015288973371527222324093744020519559325733 m: 200000000000000000000000000000 c5: 875 c0: -12 skew: 0.42 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1725001) Primes: RFBsize:135072, AFBsize:135518, largePrimes:3840968 encountered Relations: rels:3910546, finalFF:354284 Max relations in full relation-set: 28 Initial matrix: 270657 x 354284 with sparse part having weight 33819268. Pruned matrix : 244258 x 245675 with weight 20068683. Total sieving time: 12.20 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.31 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 12.60 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 22, 2007 (6th): By JMB / GMP-ECM B1=1000000
(25·10¹⁶²-7)/9 = 2(7)₁₆₂_<163> = 31 · 193 · 419 · 5655980505619_<13> · C144
C144 = P30 · P114
P30 = 757834905954475759153120346779_<30>
P114 = 258512748121660648679500730489730055051223230946990605506285956104708110213970081444008373211813972771066168890501_<114>
(25·10¹⁶⁸-7)/9 = 2(7)₁₆₈_<169> = 467 · 1951 · 669181 · 754597 · 1164052117_<10> · C142
C142 = P33 · C109
P33 = 947954614376246137517748334624309_<33>
C109 = [5471478581462633018677789162246038606727580138540073007104958991038578407898337844421297328962275304272166061_<109>]
Jul 22, 2007 (5th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
7·10¹³¹-3 = 6(9)₁₃₀7_<132> = 23 · 43 · 200357 · 686073298051849_<15> · C109
C109 = P49 · P61
P49 = 3492650375317905457798484924118526607821958419517_<49>
P61 = 1474251565366503210694631337567966010127470661351122913594633_<61>

Number: 69997_131 N=5149045283090327070069279376634643521531392220622868283592793023104111216823296932910173748751679693893652261 ( 109 digits) SNFS difficulty: 131 digits. Divisors found: r1=3492650375317905457798484924118526607821958419517 (pp49) r2=1474251565366503210694631337567966010127470661351122913594633 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.06 hours. Scaled time: 6.56 units (timescale=2.144). Factorization parameters were as follows: n: 5149045283090327070069279376634643521531392220622868283592793023104111216823296932910173748751679693893652261 m: 100000000000000000000000000 c5: 70 c0: -3 skew: 0.53 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1150001) Primes: RFBsize:78498, AFBsize:78021, largePrimes:1557428 encountered Relations: rels:1555267, finalFF:175874 Max relations in full relation-set: 28 Initial matrix: 156586 x 175874 with sparse part having weight 11502732. Pruned matrix : 150400 x 151246 with weight 8326009. Total sieving time: 2.95 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.07 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 3.06 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹⁵⁸-1 = 4(9)₁₅₈_<159> = 929 · 2039 · 195480696444471195235091_<24> · C130
C130 = P55 · P75
P55 = 3914379888823857856496565940348441055481401908952110819_<55>
P75 = 344961172633478712235231612125560933379158026766703661954210221883077707201_<75>

Number: 49999_158 N=1350309076581584038910089762282315799270660996144707824782483833075965830415212667287719844360646971845236733069095577551786307619 ( 130 digits) SNFS difficulty: 160 digits. Divisors found: r1=3914379888823857856496565940348441055481401908952110819 (pp55) r2=344961172633478712235231612125560933379158026766703661954210221883077707201 (pp75) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.89 hours. Scaled time: 53.09 units (timescale=2.133). Factorization parameters were as follows: n: 1350309076581584038910089762282315799270660996144707824782483833075965830415212667287719844360646971845236733069095577551786307619 m: 100000000000000000000000000000000 c5: 1 c0: -20 skew: 1.82 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3400001) Primes: RFBsize:283146, AFBsize:282402, largePrimes:5586780 encountered Relations: rels:5610115, finalFF:652381 Max relations in full relation-set: 28 Initial matrix: 565612 x 652381 with sparse part having weight 39533074. Pruned matrix : 493839 x 496731 with weight 26115813. Total sieving time: 23.41 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.35 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 24.89 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹³⁶-3 = 6(9)₁₃₅7_<137> = 1911173014322791_<16> · C122
C122 = P40 · P82
P40 = 6688529150867410750543674810071273572433_<40>
P82 = 5476050080158143153708958738926903788962439257212131688978965251785087525399823499_<82>

Number: 69997_136 N=36626720592747561803500026700296649794252768847574024237934710155034041818228816099980837330026827983143189237441392003067 ( 122 digits) SNFS difficulty: 136 digits. Divisors found: r1=6688529150867410750543674810071273572433 (pp40) r2=5476050080158143153708958738926903788962439257212131688978965251785087525399823499 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.99 hours. Scaled time: 10.69 units (timescale=2.143). Factorization parameters were as follows: n: 36626720592747561803500026700296649794252768847574024237934710155034041818228816099980837330026827983143189237441392003067 m: 1000000000000000000000000000 c5: 70 c0: -3 skew: 0.53 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [700000, 1650001) Primes: RFBsize:107126, AFBsize:106428, largePrimes:1903120 encountered Relations: rels:2018723, finalFF:271339 Max relations in full relation-set: 28 Initial matrix: 213621 x 271339 with sparse part having weight 20879664. Pruned matrix : 192022 x 193154 with weight 12401408. Total sieving time: 4.80 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 total time: 4.99 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 22, 2007 (4th): By Yousuke Koide
(10⁸⁵³-1)/9 is divisible by 446687009597873860118984450851524186409_<39>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jul 22, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
7·10¹³²-3 = 6(9)₁₃₁7_<133> = 41 · 761 · 823 · 8863 · 6082088060418354263973053_<25> · C97
C97 = P35 · P63
P35 = 27212650857151474320206035877612519_<35>
P63 = 185834091366309855618215438086593893231210033409435324983518879_<63>

Number: n N=5057038245707377286077394752451829803112566267314143247542799158823686682115360518604401883246201 ( 97 digits) SNFS difficulty: 132 digits. Divisors found: r1=27212650857151474320206035877612519 (pp35) r2=185834091366309855618215438086593893231210033409435324983518879 (pp63) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.60 hours. Scaled time: 5.40 units (timescale=0.963). Factorization parameters were as follows: name: KA_6_9_131_7 n: 5057038245707377286077394752451829803112566267314143247542799158823686682115360518604401883246201 type: snfs skew: 1 deg: 5 c5: 700 c0: -3 m: 100000000000000000000000000 rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [1250000, 1750001) Primes: RFBsize:183072, AFBsize:183021, largePrimes:5616253 encountered Relations: rels:5027789, finalFF:431914 Max relations in full relation-set: 48 Initial matrix: 366160 x 431914 with sparse part having weight 16649644. Pruned matrix : 301469 x 303363 with weight 9063422. Total sieving time: 4.17 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.20 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.2,2.2,50000 total time: 5.60 hours. --------- CPU info (if available) ---------- CPU: AMD Athlon(tm) XP 2400+ stepping 01 Memory: 901612k/917504k available (1069k kernel code, 15504k reserved, 459k data, 96k init, 0k highmem) sisfb: Memory heap starting at 12288K, size 19960K Calibrating delay loop... 4010.80 BogoMIPS
Jul 22, 2007 (2nd): By Jo Yeong Uk / Msieve v. 1.25, GGNFS-0.77.1-20050930-nocona
7·10¹¹⁶-3 = 6(9)₁₁₅7_<117> = 257 · 271861 · 9968346863_<10> · 5492745356335264771_<19> · C81
C81 = P35 · P46
P35 = 38690791643388328103740921502952607_<35>
P46 = 4729310014865205650831153297596976512403898451_<46>

Sat Jul 21 23:59:36 2007 Sat Jul 21 23:59:36 2007 Sat Jul 21 23:59:36 2007 Msieve v. 1.25 Sat Jul 21 23:59:36 2007 random seeds: 59986908 0149e5dc Sat Jul 21 23:59:36 2007 factoring 182980748402139428556729916605951877285225472985237924125874449528521933893711757 (81 digits) Sat Jul 21 23:59:36 2007 commencing quadratic sieve (80-digit input) Sat Jul 21 23:59:36 2007 using multiplier of 7 Sat Jul 21 23:59:36 2007 using 32kb Intel Core sieve core Sat Jul 21 23:59:36 2007 sieve interval: 12 blocks of size 32768 Sat Jul 21 23:59:36 2007 processing polynomials in batches of 17 Sat Jul 21 23:59:36 2007 using a sieve bound of 1305643 (50294 primes) Sat Jul 21 23:59:36 2007 using large prime bound of 129258657 (26 bits) Sat Jul 21 23:59:36 2007 using trial factoring cutoff of 27 bits Sat Jul 21 23:59:36 2007 polynomial 'A' values have 10 factors Sun Jul 22 00:11:15 2007 50465 relations (25708 full + 24757 combined from 274294 partial), need 50390 Sun Jul 22 00:11:15 2007 begin with 300002 relations Sun Jul 22 00:11:15 2007 reduce to 72144 relations in 2 passes Sun Jul 22 00:11:15 2007 attempting to read 72144 relations Sun Jul 22 00:11:16 2007 recovered 72144 relations Sun Jul 22 00:11:16 2007 recovered 61871 polynomials Sun Jul 22 00:11:16 2007 attempting to build 50465 cycles Sun Jul 22 00:11:16 2007 found 50465 cycles in 1 passes Sun Jul 22 00:11:16 2007 distribution of cycle lengths: Sun Jul 22 00:11:16 2007 length 1 : 25708 Sun Jul 22 00:11:16 2007 length 2 : 24757 Sun Jul 22 00:11:16 2007 largest cycle: 2 relations Sun Jul 22 00:11:16 2007 matrix is 50294 x 50465 with weight 1573880 (avg 31.19/col) Sun Jul 22 00:11:16 2007 filtering completed in 4 passes Sun Jul 22 00:11:16 2007 matrix is 42972 x 43036 with weight 1314047 (avg 30.53/col) Sun Jul 22 00:11:16 2007 saving the first 48 matrix rows for later Sun Jul 22 00:11:16 2007 matrix is 42924 x 43036 with weight 1004755 (avg 23.35/col) Sun Jul 22 00:11:16 2007 matrix includes 64 packed rows Sun Jul 22 00:11:16 2007 commencing Lanczos iteration Sun Jul 22 00:11:41 2007 lanczos halted after 680 iterations Sun Jul 22 00:11:41 2007 recovered 9 nontrivial dependencies Sun Jul 22 00:11:41 2007 prp35 factor: 38690791643388328103740921502952607 Sun Jul 22 00:11:41 2007 prp46 factor: 4729310014865205650831153297596976512403898451 Sun Jul 22 00:11:41 2007 elapsed time 00:12:05
7·10¹²⁷-3 = 6(9)₁₂₆7_<128> = 41² · 151 · 2347 · 39819539 · 55136742586585039706768971261_<29> · C83
C83 = P33 · P50
P33 = 996661217419669522960891631306797_<33>
P50 = 53697664591766885637251106829273235075760230423267_<50>

Sun Jul 22 00:13:13 2007 Sun Jul 22 00:13:13 2007 Sun Jul 22 00:13:13 2007 Msieve v. 1.25 Sun Jul 22 00:13:13 2007 random seeds: 103aacd2 23967dbd Sun Jul 22 00:13:13 2007 factoring 53518379764623465702863279224822425408675308236078968242775516646260859391644045799 (83 digits) Sun Jul 22 00:13:13 2007 commencing quadratic sieve (83-digit input) Sun Jul 22 00:13:13 2007 using multiplier of 5 Sun Jul 22 00:13:13 2007 using 32kb Intel Core sieve core Sun Jul 22 00:13:13 2007 sieve interval: 12 blocks of size 32768 Sun Jul 22 00:13:13 2007 processing polynomials in batches of 17 Sun Jul 22 00:13:13 2007 using a sieve bound of 1372627 (52647 primes) Sun Jul 22 00:13:13 2007 using large prime bound of 122163803 (26 bits) Sun Jul 22 00:13:13 2007 using trial factoring cutoff of 27 bits Sun Jul 22 00:13:13 2007 polynomial 'A' values have 11 factors Sun Jul 22 00:33:32 2007 52785 relations (26977 full + 25808 combined from 279646 partial), need 52743 Sun Jul 22 00:33:33 2007 begin with 306623 relations Sun Jul 22 00:33:33 2007 reduce to 75331 relations in 2 passes Sun Jul 22 00:33:33 2007 attempting to read 75331 relations Sun Jul 22 00:33:33 2007 recovered 75331 relations Sun Jul 22 00:33:33 2007 recovered 68714 polynomials Sun Jul 22 00:33:33 2007 attempting to build 52785 cycles Sun Jul 22 00:33:33 2007 found 52785 cycles in 1 passes Sun Jul 22 00:33:33 2007 distribution of cycle lengths: Sun Jul 22 00:33:33 2007 length 1 : 26977 Sun Jul 22 00:33:33 2007 length 2 : 25808 Sun Jul 22 00:33:33 2007 largest cycle: 2 relations Sun Jul 22 00:33:33 2007 matrix is 52647 x 52785 with weight 1723884 (avg 32.66/col) Sun Jul 22 00:33:33 2007 filtering completed in 4 passes Sun Jul 22 00:33:33 2007 matrix is 45365 x 45429 with weight 1454573 (avg 32.02/col) Sun Jul 22 00:33:34 2007 saving the first 48 matrix rows for later Sun Jul 22 00:33:34 2007 matrix is 45317 x 45429 with weight 1108107 (avg 24.39/col) Sun Jul 22 00:33:34 2007 matrix includes 64 packed rows Sun Jul 22 00:33:34 2007 commencing Lanczos iteration Sun Jul 22 00:34:03 2007 lanczos halted after 718 iterations Sun Jul 22 00:34:03 2007 recovered 10 nontrivial dependencies Sun Jul 22 00:34:03 2007 prp33 factor: 996661217419669522960891631306797 Sun Jul 22 00:34:03 2007 prp50 factor: 53697664591766885637251106829273235075760230423267 Sun Jul 22 00:34:03 2007 elapsed time 00:20:50
7·10¹³⁴-3 = 6(9)₁₃₃7_<135> = 127 · 186103 · 284041 · 67139650373_<11> · 224080515702813399469184201_<27> · C85
C85 = P40 · P46
P40 = 1657367916841120248990423676418651639587_<40>
P46 = 4181747575834472305239024549045571460403317707_<46>

Sun Jul 22 01:59:47 2007 Sun Jul 22 01:59:47 2007 Sun Jul 22 01:59:47 2007 Msieve v. 1.25 Sun Jul 22 01:59:47 2007 random seeds: 7b30c364 1c9cc3ef Sun Jul 22 01:59:47 2007 factoring 6930694268516183887694709958969040895366115620435867716462445489842053938330019267009 (85 digits) Sun Jul 22 01:59:47 2007 commencing quadratic sieve (85-digit input) Sun Jul 22 01:59:48 2007 using multiplier of 1 Sun Jul 22 01:59:48 2007 using 32kb Intel Core sieve core Sun Jul 22 01:59:48 2007 sieve interval: 12 blocks of size 32768 Sun Jul 22 01:59:48 2007 processing polynomials in batches of 17 Sun Jul 22 01:59:48 2007 using a sieve bound of 1434241 (54497 primes) Sun Jul 22 01:59:48 2007 using large prime bound of 116173521 (26 bits) Sun Jul 22 01:59:48 2007 using double large prime bound of 328997602795950 (41-49 bits) Sun Jul 22 01:59:48 2007 using trial factoring cutoff of 49 bits Sun Jul 22 01:59:48 2007 polynomial 'A' values have 11 factors Sun Jul 22 02:21:27 2007 54900 relations (16114 full + 38786 combined from 570398 partial), need 54593 Sun Jul 22 02:21:27 2007 begin with 586512 relations Sun Jul 22 02:21:27 2007 reduce to 128737 relations in 9 passes Sun Jul 22 02:21:27 2007 attempting to read 128737 relations Sun Jul 22 02:21:28 2007 recovered 128737 relations Sun Jul 22 02:21:28 2007 recovered 106037 polynomials Sun Jul 22 02:21:28 2007 attempting to build 54900 cycles Sun Jul 22 02:21:28 2007 found 54900 cycles in 5 passes Sun Jul 22 02:21:28 2007 distribution of cycle lengths: Sun Jul 22 02:21:28 2007 length 1 : 16114 Sun Jul 22 02:21:28 2007 length 2 : 11199 Sun Jul 22 02:21:28 2007 length 3 : 9754 Sun Jul 22 02:21:28 2007 length 4 : 6903 Sun Jul 22 02:21:28 2007 length 5 : 4674 Sun Jul 22 02:21:28 2007 length 6 : 2887 Sun Jul 22 02:21:28 2007 length 7 : 1597 Sun Jul 22 02:21:28 2007 length 9+: 1772 Sun Jul 22 02:21:28 2007 largest cycle: 19 relations Sun Jul 22 02:21:29 2007 matrix is 54497 x 54900 with weight 2829346 (avg 51.54/col) Sun Jul 22 02:21:29 2007 filtering completed in 3 passes Sun Jul 22 02:21:29 2007 matrix is 49646 x 49710 with weight 2569219 (avg 51.68/col) Sun Jul 22 02:21:29 2007 saving the first 48 matrix rows for later Sun Jul 22 02:21:30 2007 matrix is 49598 x 49710 with weight 1887856 (avg 37.98/col) Sun Jul 22 02:21:30 2007 matrix includes 64 packed rows Sun Jul 22 02:21:30 2007 commencing Lanczos iteration Sun Jul 22 02:22:14 2007 lanczos halted after 786 iterations Sun Jul 22 02:22:14 2007 recovered 15 nontrivial dependencies Sun Jul 22 02:22:15 2007 prp40 factor: 1657367916841120248990423676418651639587 Sun Jul 22 02:22:15 2007 prp46 factor: 4181747575834472305239024549045571460403317707 Sun Jul 22 02:22:15 2007 elapsed time 00:22:28
7·10¹²⁶-3 = 6(9)₁₂₅7_<127> = C127
C127 = P49 · P79
P49 = 3733064887567996534792974929164593204373697227583_<49>
P79 = 1875134831787061276782822033581045574929236611892954682370632550609251043832259_<79>

Number: 69997_126 N=6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 127 digits) SNFS difficulty: 126 digits. Divisors found: r1=3733064887567996534792974929164593204373697227583 (pp49) r2=1875134831787061276782822033581045574929236611892954682370632550609251043832259 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.18 hours. Scaled time: 4.65 units (timescale=2.128). Factorization parameters were as follows: n: 6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 10000000000000000000000000 c5: 70 c0: -3 skew: 0.53 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 950001) Primes: RFBsize:78498, AFBsize:78021, largePrimes:1558333 encountered Relations: rels:1597125, finalFF:213619 Max relations in full relation-set: 28 Initial matrix: 156586 x 213619 with sparse part having weight 11148790. Pruned matrix : 132114 x 132960 with weight 5515036. Total sieving time: 2.10 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.18 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹⁰⁹-3 = 6(9)₁₀₈7_<110> = 23 · 73 · 8689 · C103
C103 = P42 · P62
P42 = 228859484167433722234911564635934681814193_<42>
P62 = 20965664506503249718202161151414441563687134934979206768443859_<62>

Number: 69997_109 N=4798191164185807622283101367066353705790409115027790780495023898762004988610807815924387635993589890787 ( 103 digits) SNFS difficulty: 110 digits. Divisors found: r1=228859484167433722234911564635934681814193 (pp42) r2=20965664506503249718202161151414441563687134934979206768443859 (pp62) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.61 hours. Scaled time: 1.31 units (timescale=2.143). Factorization parameters were as follows: n: 4798191164185807622283101367066353705790409115027790780495023898762004988610807815924387635993589890787 m: 10000000000000000000000 c5: 7 c0: -30 skew: 1.34 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 300001) Primes: RFBsize:30757, AFBsize:30494, largePrimes:983606 encountered Relations: rels:888199, finalFF:73849 Max relations in full relation-set: 28 Initial matrix: 61316 x 73849 with sparse part having weight 3415148. Pruned matrix : 56457 x 56827 with weight 2004983. Total sieving time: 0.58 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.61 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹²¹-3 = 6(9)₁₂₀7_<122> = 47653 · 1369371443767_<13> · C106
C106 = P35 · P71
P35 = 36358147136114613307985190682380569_<35>
P71 = 29504263852952324258374435890140498246794971645497980237929073951677863_<71>

Number: 69997_121 N=1072720366308388454659014573709742439750797378507314566568561935551101727969483113552373319637988658644047 ( 106 digits) SNFS difficulty: 121 digits. Divisors found: r1=36358147136114613307985190682380569 (pp35) r2=29504263852952324258374435890140498246794971645497980237929073951677863 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.34 hours. Scaled time: 2.86 units (timescale=2.142). Factorization parameters were as follows: n: 1072720366308388454659014573709742439750797378507314566568561935551101727969483113552373319637988658644047 m: 1000000000000000000000000 c5: 70 c0: -3 skew: 0.53 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 540001) Primes: RFBsize:49098, AFBsize:48796, largePrimes:2105450 encountered Relations: rels:2178868, finalFF:179576 Max relations in full relation-set: 28 Initial matrix: 97961 x 179576 with sparse part having weight 18093782. Pruned matrix : 84353 x 84906 with weight 6257540. Total sieving time: 1.27 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.34 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹²³-3 = 6(9)₁₂₂7_<124> = 173 · 61027 · 713562389 · C108
C108 = P54 · P55
P54 = 135311009685237351278540689388809518241159030458513113_<54>
P55 = 6866964940815089427027581044049877493885455562590216551_<55>

Number: 69997_123 N=929175959614815900163066670327570369604706388965383155597477001152268117687211419282352024355512064143133263 ( 108 digits) SNFS difficulty: 124 digits. Divisors found: r1=135311009685237351278540689388809518241159030458513113 (pp54) r2=6866964940815089427027581044049877493885455562590216551 (pp55) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.38 hours. Scaled time: 2.94 units (timescale=2.131). Factorization parameters were as follows: n: 929175959614815900163066670327570369604706388965383155597477001152268117687211419282352024355512064143133263 m: 2000000000000000000000000 c5: 875 c0: -12 skew: 0.42 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 540001) Primes: RFBsize:49098, AFBsize:49241, largePrimes:2087615 encountered Relations: rels:2138687, finalFF:167675 Max relations in full relation-set: 28 Initial matrix: 98406 x 167675 with sparse part having weight 16330556. Pruned matrix : 86136 x 86692 with weight 6130758. Total sieving time: 1.31 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.38 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹²⁴-3 = 6(9)₁₂₃7_<125> = 12435393851_<11> · C115
C115 = P49 · P67
P49 = 1653859776119932304506498458736364717902994881823_<49>
P67 = 3403610153505365266823631691628573931926592430091798145981178781689_<67>

Number: 69997_124 N=5629093926475911824338727170724976501590661199557369773249492232749066308603561735312182192338670303366493671339047 ( 115 digits) SNFS difficulty: 125 digits. Divisors found: r1=1653859776119932304506498458736364717902994881823 (pp49) r2=3403610153505365266823631691628573931926592430091798145981178781689 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.76 hours. Scaled time: 3.78 units (timescale=2.145). Factorization parameters were as follows: n: 5629093926475911824338727170724976501590661199557369773249492232749066308603561735312182192338670303366493671339047 m: 10000000000000000000000000 c5: 7 c0: -30 skew: 1.34 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 850001) Primes: RFBsize:78498, AFBsize:77956, largePrimes:1482727 encountered Relations: rels:1490685, finalFF:186596 Max relations in full relation-set: 28 Initial matrix: 156519 x 186596 with sparse part having weight 8875261. Pruned matrix : 140381 x 141227 with weight 5293869. Total sieving time: 1.69 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.76 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
7·10¹³⁰-3 = 6(9)₁₂₉7_<131> = 17 · 6967 · 22159 · C122
C122 = P56 · P67
P56 = 12377339630211913014729356379781933602404602590397460483_<56>
P67 = 2154893656072748577302512740902433579438090282103291765000036292359_<67>

Number: 69997_130 N=26671850648201471139952050436640275593130415064623068809555644373410921858636706510104666244043064581907285529588537349397 ( 122 digits) SNFS difficulty: 130 digits. Divisors found: r1=12377339630211913014729356379781933602404602590397460483 (pp56) r2=2154893656072748577302512740902433579438090282103291765000036292359 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.95 hours. Scaled time: 4.18 units (timescale=2.143). Factorization parameters were as follows: n: 26671850648201471139952050436640275593130415064623068809555644373410921858636706510104666244043064581907285529588537349397 m: 100000000000000000000000000 c5: 7 c0: -3 skew: 0.84 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78031, largePrimes:1497101 encountered Relations: rels:1513263, finalFF:193250 Max relations in full relation-set: 28 Initial matrix: 156594 x 193250 with sparse part having weight 9535488. Pruned matrix : 138779 x 139625 with weight 5365586. Total sieving time: 1.88 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.95 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 22, 2007: By Kenichiro Yamaguchi / Msieve v. 1.25
7·10¹³⁷-3 = 6(9)₁₃₆7_<138> = 19 · 41 · 83 · 14431 · 32687 · 220474522090692269_<18> · 3088175041540998887_<19> · C89
C89 = P41 · P48
P41 = 53204897233454695830562193693392037137397_<41>
P48 = 633576518273911287795959707919898837003414686923_<48>

C89=P41*P48 P41=53204897233454695830562193693392037137397 P48=633576518273911287795959707919898837003414686923 Sun Jul 22 01:55:34 2007 Msieve v. 1.25 Sun Jul 22 01:55:34 2007 random seeds: 1d6eae68 a4f7c8cb Sun Jul 22 01:55:34 2007 factoring 33709373544293481213343982315692544285548550722517329478640267756974328368014399890159431 (89 digits) Sun Jul 22 01:55:34 2007 commencing quadratic sieve (89-digit input) Sun Jul 22 01:55:34 2007 using multiplier of 5 Sun Jul 22 01:55:34 2007 using 32kb Pentium M sieve core Sun Jul 22 01:55:34 2007 sieve interval: 32 blocks of size 32768 Sun Jul 22 01:55:34 2007 processing polynomials in batches of 7 Sun Jul 22 01:55:34 2007 using a sieve bound of 1556189 (58911 primes) Sun Jul 22 01:55:34 2007 using large prime bound of 124495120 (26 bits) Sun Jul 22 01:55:34 2007 using double large prime bound of 372626841652480 (42-49 bits) Sun Jul 22 01:55:34 2007 using trial factoring cutoff of 49 bits Sun Jul 22 01:55:34 2007 polynomial 'A' values have 11 factors Sun Jul 22 03:49:04 2007 59251 relations (15409 full + 43842 combined from 635927 partial), need 59007 Sun Jul 22 03:49:06 2007 begin with 651336 relations Sun Jul 22 03:49:07 2007 reduce to 146490 relations in 10 passes Sun Jul 22 03:49:07 2007 attempting to read 146490 relations Sun Jul 22 03:49:13 2007 recovered 146490 relations Sun Jul 22 03:49:13 2007 recovered 128156 polynomials Sun Jul 22 03:49:13 2007 attempting to build 59251 cycles Sun Jul 22 03:49:13 2007 found 59251 cycles in 5 passes Sun Jul 22 03:49:13 2007 distribution of cycle lengths: Sun Jul 22 03:49:13 2007 length 1 : 15409 Sun Jul 22 03:49:13 2007 length 2 : 11060 Sun Jul 22 03:49:13 2007 length 3 : 10314 Sun Jul 22 03:49:14 2007 length 4 : 8027 Sun Jul 22 03:49:14 2007 length 5 : 5815 Sun Jul 22 03:49:14 2007 length 6 : 3624 Sun Jul 22 03:49:14 2007 length 7 : 2227 Sun Jul 22 03:49:14 2007 length 9+: 2775 Sun Jul 22 03:49:15 2007 largest cycle: 18 relations Sun Jul 22 03:49:15 2007 matrix is 58911 x 59251 with weight 3663344 (avg 61.83/col) Sun Jul 22 03:49:17 2007 filtering completed in 4 passes Sun Jul 22 03:49:17 2007 matrix is 55380 x 55444 with weight 3442544 (avg 62.09/col) Sun Jul 22 03:49:18 2007 saving the first 48 matrix rows for later Sun Jul 22 03:49:18 2007 matrix is 55332 x 55444 with weight 2837873 (avg 51.18/col) Sun Jul 22 03:49:18 2007 matrix includes 64 packed rows Sun Jul 22 03:49:18 2007 using block size 22177 for processor cache size 2048 kB Sun Jul 22 03:49:18 2007 commencing Lanczos iteration Sun Jul 22 03:50:16 2007 lanczos halted after 876 iterations Sun Jul 22 03:50:16 2007 recovered 19 nontrivial dependencies Sun Jul 22 03:50:17 2007 prp41 factor: 53204897233454695830562193693392037137397 Sun Jul 22 03:50:17 2007 prp48 factor: 633576518273911287795959707919898837003414686923 Sun Jul 22 03:50:17 2007 elapsed time 01:54:43
7·10¹⁷⁶-3 = 6(9)₁₇₅7_<177> = 127 · 1427 · 1823167117_<10> · 3122832099875424913_<19> · 4959902390670157503819923_<25> · 96538958547137354194163712683_<29> · C91
C91 = P42 · P49
P42 = 226468883271578475618379567962241702278977_<42>
P49 = 6256204756417669062376992564657832577417523732181_<49>

C91=P42*P49 P42=226468883271578475618379567962241702278977 P49=6256204756417669062376992564657832577417523732181 Sun Jul 22 11:36:57 2007 Msieve v. 1.25 Sun Jul 22 11:36:57 2007 random seeds: afc45a78 7d8aa159 Sun Jul 22 11:36:57 2007 factoring 1416835704704247144924541052389267917368021881114236322739410829329143705256446130294658837 (91 digits) Sun Jul 22 11:36:58 2007 commencing quadratic sieve (90-digit input) Sun Jul 22 11:36:58 2007 using multiplier of 5 Sun Jul 22 11:36:58 2007 using 32kb Pentium M sieve core Sun Jul 22 11:36:58 2007 sieve interval: 36 blocks of size 32768 Sun Jul 22 11:36:58 2007 processing polynomials in batches of 6 Sun Jul 22 11:36:58 2007 using a sieve bound of 1652491 (62295 primes) Sun Jul 22 11:36:58 2007 using large prime bound of 145419208 (27 bits) Sun Jul 22 11:36:58 2007 using double large prime bound of 492854925172808 (42-49 bits) Sun Jul 22 11:36:58 2007 using trial factoring cutoff of 49 bits Sun Jul 22 11:36:58 2007 polynomial 'A' values have 12 factors Sun Jul 22 14:18:41 2007 62560 relations (15701 full + 46859 combined from 707243 partial), need 62391 Sun Jul 22 14:18:54 2007 begin with 722944 relations Sun Jul 22 14:18:55 2007 reduce to 155793 relations in 10 passes Sun Jul 22 14:18:55 2007 attempting to read 155793 relations Sun Jul 22 14:19:06 2007 recovered 155793 relations Sun Jul 22 14:19:06 2007 recovered 138792 polynomials Sun Jul 22 14:19:06 2007 attempting to build 62560 cycles Sun Jul 22 14:19:06 2007 found 62560 cycles in 5 passes Sun Jul 22 14:19:06 2007 distribution of cycle lengths: Sun Jul 22 14:19:06 2007 length 1 : 15701 Sun Jul 22 14:19:06 2007 length 2 : 11811 Sun Jul 22 14:19:06 2007 length 3 : 11050 Sun Jul 22 14:19:06 2007 length 4 : 8666 Sun Jul 22 14:19:06 2007 length 5 : 6156 Sun Jul 22 14:19:06 2007 length 6 : 3886 Sun Jul 22 14:19:06 2007 length 7 : 2377 Sun Jul 22 14:19:06 2007 length 9+: 2913 Sun Jul 22 14:19:06 2007 largest cycle: 17 relations Sun Jul 22 14:19:07 2007 matrix is 62295 x 62560 with weight 3738751 (avg 59.76/col) Sun Jul 22 14:19:08 2007 filtering completed in 3 passes Sun Jul 22 14:19:08 2007 matrix is 59024 x 59088 with weight 3551902 (avg 60.11/col) Sun Jul 22 14:19:09 2007 saving the first 48 matrix rows for later Sun Jul 22 14:19:09 2007 matrix is 58976 x 59088 with weight 2711102 (avg 45.88/col) Sun Jul 22 14:19:09 2007 matrix includes 64 packed rows Sun Jul 22 14:19:09 2007 using block size 23635 for processor cache size 2048 kB Sun Jul 22 14:19:09 2007 commencing Lanczos iteration Sun Jul 22 14:20:07 2007 lanczos halted after 934 iterations Sun Jul 22 14:20:07 2007 recovered 17 nontrivial dependencies Sun Jul 22 14:20:08 2007 prp42 factor: 226468883271578475618379567962241702278977 Sun Jul 22 14:20:08 2007 prp49 factor: 6256204756417669062376992564657832577417523732181 Sun Jul 22 14:20:08 2007 elapsed time 02:43:11
Jul 21, 2007 (3rd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
2·10¹⁵⁸-3 = 1(9)₁₅₇7_<159> = 571 · 8308493 · 627908707 · 19547338624799_<14> · C127
C127 = P48 · P79
P48 = 765613002593259893435771444351052001550447832917_<48>
P79 = 4486195411014709158764439342476979691484480174887014872203008588690204116766979_<79>

Number: 19997_158 N=3434689538847075156669170246694359027751302650612112051029535669072282263120505215768659729098715953969223080215754614814847743 ( 127 digits) SNFS difficulty: 158 digits. Divisors found: r1=765613002593259893435771444351052001550447832917 (pp48) r2=4486195411014709158764439342476979691484480174887014872203008588690204116766979 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.75 hours. Scaled time: 53.09 units (timescale=2.145). Factorization parameters were as follows: n: 3434689538847075156669170246694359027751302650612112051029535669072282263120505215768659729098715953969223080215754614814847743 m: 20000000000000000000000000000000 c5: 125 c0: -6 skew: 0.54 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3400001) Primes: RFBsize:283146, AFBsize:282582, largePrimes:5753873 encountered Relations: rels:5897488, finalFF:751668 Max relations in full relation-set: 28 Initial matrix: 565793 x 751668 with sparse part having weight 45568672. Pruned matrix : 412610 x 415502 with weight 27462155. Total sieving time: 23.64 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.98 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 24.75 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 21, 2007 (2nd): By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
(28·10¹⁶⁰+17)/9 = 3(1)₁₅₉3_<161> = 3 · 601 · 604411 · 92915322557_<11> · C141
C141 = P50 · P91
P50 = 40211844589201070870193753925177566929720034091471_<50>
P91 = 7640927890799418264376357335504587466320927492331080493247053896348840184348910650404572763_<91>

Number: n N=307255804862118138238800959977993782051356232749794701698253135356472234511279752884270077185205828579676440295689321401915567074990617204373 ( 141 digits) SNFS difficulty: 161 digits. Divisors found: r1=40211844589201070870193753925177566929720034091471 (pp50) r2=7640927890799418264376357335504587466320927492331080493247053896348840184348910650404572763 (pp91) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 43.45 hours. Scaled time: 59.31 units (timescale=1.365). Factorization parameters were as follows: name: KA_3_1_159_3 n: 307255804862118138238800959977993782051356232749794701698253135356472234511279752884270077185205828579676440295689321401915567074990617204373 skew: 0.91 deg: 5 c5: 28 c0: 17 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:250150, AFBsize:251161, largePrimes:7385460 encountered Relations: rels:7003197, finalFF:646856 Max relations in full relation-set: 28 Initial matrix: 501377 x 646856 with sparse part having weight 41926338. Pruned matrix : 377245 x 379815 with weight 22916317. Total sieving time: 40.00 hours. Total relation processing time: 0.27 hours. Matrix solve time: 2.85 hours. Total square root time: 0.33 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 43.45 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(2·10¹⁶⁰+61)/9 = (2)₁₅₉9_<160> = 3 · 10103 · 15613457 · 416632441 · C140
C140 = P49 · P91
P49 = 2936151587344808656346302770353734642204342157279_<49>
P91 = 3838709524601464946084217929761401324614789430983800435309597156231900651034036787115571447_<91>

Number: n N=11271033064014227117251631716765959674881912246034154599682541233752667463468895884880810622635796812902030044764864707565008915372835612713 ( 140 digits) SNFS difficulty: 160 digits. Divisors found: r1=2936151587344808656346302770353734642204342157279 (pp49) r2=3838709524601464946084217929761401324614789430983800435309597156231900651034036787115571447 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.68 hours. Scaled time: 57.78 units (timescale=1.323). Factorization parameters were as follows: name: KA_2_159_9 n: 11271033064014227117251631716765959674881912246034154599682541233752667463468895884880810622635796812902030044764864707565008915372835612713 skew: 1.98 deg: 5 c5: 2 c0: 61 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:250150, AFBsize:250287, largePrimes:7344485 encountered Relations: rels:6910066, finalFF:610929 Max relations in full relation-set: 48 Initial matrix: 500504 x 610929 with sparse part having weight 44987741. Pruned matrix : 407031 x 409597 with weight 25737146. Total sieving time: 38.85 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.52 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 43.68 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 21, 2007: The factor table of 699...997 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jul 20, 2007 (4th): By Bruce Dodson / Jul 17, 2007
10³²²+1 is divisible by 1009805096139614383066323378818605356821967673241_<49>, cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jul 20, 2007 (3rd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
2·10¹⁸⁹+3 = 2(0)₁₈₈3_<190> = 211 · 617 · 186762743 · 3025939986458771807_<19> · 299721566142829669823_<21> · 6007634365195440036739_<22> · C116
C116 = P57 · P59
P57 = 419817276608201618522516989479656415256109781516871114787_<57>
P59 = 35960856659366982010140181518614170249139085672467809368871_<59>

Number: 20003_189 N=15096988907233357495521287258396184736155032772962973177413972069504983979832606332318573583018636209111156665595477 ( 116 digits) Divisors found: r1=419817276608201618522516989479656415256109781516871114787 (pp57) r2=35960856659366982010140181518614170249139085672467809368871 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 26.59 hours. Scaled time: 56.99 units (timescale=2.143). Factorization parameters were as follows: name: 20003_189 n: 15096988907233357495521287258396184736155032772962973177413972069504983979832606332318573583018636209111156665595477 skew: 41912.62 # norm 2.16e+15 c5: 6360 c4: -1373737086 c3: -45296079427237 c2: 3778123322489630234 c1: -16523333732336258468648 c0: -33305705182922434771711568 # alpha -4.95 Y1: 311998665473 Y0: -18840262728057601590579 # Murphy_E 5.40e-10 # M 9806237666384931345996401187694326584755524337853627549119046455930816589581929721798263470708982718933220092999579 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3225001) Primes: RFBsize:256726, AFBsize:256878, largePrimes:7669673 encountered Relations: rels:7649278, finalFF:642547 Max relations in full relation-set: 28 Initial matrix: 513683 x 642547 with sparse part having weight 57962084. Pruned matrix : 414171 x 416803 with weight 36292501. Total sieving time: 25.12 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.19 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 26.59 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 20, 2007 (2nd): By suberi / GMP-ECM 6.1.2 B1=3000000
5·10¹⁸⁵+3 = 5(0)₁₈₄3_<186> = 7 · 505752502245677956259_<21> · C165
C165 = P38 · P127
P38 = 18507977608619856746602644452748137837_<38>
P127 = 7630885880694883788242610766381704283225279287936847958869670360168616422552526506424965632629458726936822609309848264083247763_<127>
Jul 20, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(4·10¹⁶⁰-13)/9 = (4)₁₅₉3_<160> = 3² · 305111482118759_<15> · C145
C145 = P46 · P100
P46 = 1599713742434510285313677046167755092936978823_<46>
P100 = 1011752171645268180409456572991158703185507059827665215709520041736230600671785104494834474709153811_<100>

Number: n N=1618513852918894982244660695192826276506442011651985662185105820561633856669307795206595456944773683156646273494967998942230092499261817156744453 ( 145 digits) SNFS difficulty: 160 digits. Divisors found: r1=1599713742434510285313677046167755092936978823 (pp46) r2=1011752171645268180409456572991158703185507059827665215709520041736230600671785104494834474709153811 (pp100) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.16 hours. Scaled time: 56.97 units (timescale=1.320). Factorization parameters were as follows: name: KA_4_159_3 n: 1618513852918894982244660695192826276506442011651985662185105820561633856669307795206595456944773683156646273494967998942230092499261817156744453 skew: 1.27 deg: 5 c5: 4 c0: -13 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:250150, AFBsize:250321, largePrimes:7367990 encountered Relations: rels:6945136, finalFF:621444 Max relations in full relation-set: 48 Initial matrix: 500535 x 621444 with sparse part having weight 45008824. Pruned matrix : 398253 x 400819 with weight 25062427. Total sieving time: 38.50 hours. Total relation processing time: 0.23 hours. Matrix solve time: 4.36 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 43.16 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(2·10¹⁶⁰-17)/3 = (6)₁₅₉1_<160> = 727 · 1583 · 95988095509_<11> · C143
C143 = P45 · P99
P45 = 101750434942955870404274154756703815926783363_<45>
P99 = 593116172250912842488653172573804937639666230962446807900778437541739835324711444191625551399818163_<99>

Number: n N=60349828498231515075105017277191802863759950651617645337907466391569953750527359884165767483560724325965640457676728648881641211444679693622169 ( 143 digits) SNFS difficulty: 160 digits. Divisors found: r1=101750434942955870404274154756703815926783363 (pp45) r2=593116172250912842488653172573804937639666230962446807900778437541739835324711444191625551399818163 (pp99) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.20 hours. Scaled time: 58.17 units (timescale=1.447). Factorization parameters were as follows: name: KA_6_159_1 n: 60349828498231515075105017277191802863759950651617645337907466391569953750527359884165767483560724325965640457676728648881641211444679693622169 skew: 1.53 deg: 5 c5: 2 c0: -17 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1900001) Primes: RFBsize:250150, AFBsize:249961, largePrimes:7392335 encountered Relations: rels:6971314, finalFF:612340 Max relations in full relation-set: 28 Initial matrix: 500176 x 612340 with sparse part having weight 42132816. Pruned matrix : 405751 x 408315 with weight 24833572. Total sieving time: 35.40 hours. Total relation processing time: 0.21 hours. Matrix solve time: 4.23 hours. Total square root time: 0.36 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 40.20 hours. --------- CPU info (if available) ----------
5·10¹⁶⁶+3 = 5(0)₁₆₅3_<167> = 58411 · C166
C162 = P69 · P94
P69 = 205212516206615635610167665320053000460472202204809200220862876866413_<69>
P94 = 4171300883176815364229387134807678863679793387097531618573030009987940624111825593896704727821_<94>

Number: n N=856003150091592337059800380065398640666997654551368749036996456146958620807724572426426529249627638629710157333378986834671551591309856020270154594168906541576073 ( 162 digits) SNFS difficulty: 166 digits. Divisors found: r1=205212516206615635610167665320053000460472202204809200220862876866413 (pp69) r2=4171300883176815364229387134807678863679793387097531618573030009987940624111825593896704727821 (pp94) Version: GGNFS-0.77.1-20051202-athlon Total time: 80.81 hours. Scaled time: 96.49 units (timescale=1.194). Factorization parameters were as follows: name: KA_5_0_165_3 n: 856003150091592337059800380065398640666997654551368749036996456146958620807724572426426529249627638629710157333378986834671551591309856020270154594168906541576073 type: snfs skew: 0.57 deg: 5 c5: 50 c0: 3 m: 1000000000000000000000000000000000 rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3000001) Primes: RFBsize:283146, AFBsize:283047, largePrimes:7663698 encountered Relations: rels:7215429, finalFF:636030 Max relations in full relation-set: 28 Initial matrix: 566258 x 636030 with sparse part having weight 42205013. Pruned matrix : 510577 x 513472 with weight 29645883. Total sieving time: 71.79 hours. Total relation processing time: 0.33 hours. Matrix solve time: 7.83 hours. Total square root time: 0.87 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 80.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 19, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp
(25·10¹⁶⁰-7)/9 = 2(7)₁₆₀_<161> = 3 · 27947 · 7306883 · 138621983 · C141
C141 = P69 · P72
P69 = 883323744340659477525559747044983470768166295315797627245668926714929_<69>
P72 = 370302704851532106577899935747396428452827041176147028833284274712784437_<72>

Number: n N=327097171788929430479622084869129690697740912748786682229340262241719606549744366710334791145444653101642953787249946765260803343440926759973 ( 141 digits) SNFS difficulty: 161 digits. Divisors found: r1=883323744340659477525559747044983470768166295315797627245668926714929 (pp69) r2=370302704851532106577899935747396428452827041176147028833284274712784437 (pp72) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 36.41 hours. Scaled time: 49.70 units (timescale=1.365). Factorization parameters were as follows: name: KA_2_7_160 n: 327097171788929430479622084869129690697740912748786682229340262241719606549744366710334791145444653101642953787249946765260803343440926759973 skew: 0.78 deg: 5 c5: 25 c0: -7 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:250150, AFBsize:250196, largePrimes:7112312 encountered Relations: rels:6671455, finalFF:592115 Max relations in full relation-set: 28 Initial matrix: 500410 x 592115 with sparse part having weight 34549711. Pruned matrix : 418302 x 420868 with weight 20091437. Total sieving time: 33.04 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.04 hours. Total square root time: 0.10 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 36.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 19, 2007 (2nd): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
5·10¹⁶¹+3 = 5(0)₁₆₀3_<162> = 7² · 1447 · 180463 · 26314542158435393005535533221629_<32> · C121
C121 = P59 · P63
P59 = 11706943567107084998551285511603272813010623152246453284257_<59>
P63 = 126846321501220363453898438705886991913400990993746411945018359_<63>

Number: 50003_161 N=1484982727509908854740212306941041004792973008825939876458829727780821383869898582890053749715127694042906997885710674263 ( 121 digits) SNFS difficulty: 161 digits. Divisors found: r1=11706943567107084998551285511603272813010623152246453284257 (pp59) r2=126846321501220363453898438705886991913400990993746411945018359 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 80.52 hours. Scaled time: 54.99 units (timescale=0.683). Factorization parameters were as follows: name: 50003_161 n: 1484982727509908854740212306941041004792973008825939876458829727780821383869898582890053749715127694042906997885710674263 m: 100000000000000000000000000000000 c5: 50 c0: 3 skew: 0.57 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4150001) Primes: RFBsize:315948, AFBsize:315546, largePrimes:5714501 encountered Relations: rels:5824294, finalFF:708200 Max relations in full relation-set: 0 Initial matrix: 631559 x 708200 with sparse part having weight 36699917. Pruned matrix : 568992 x 572213 with weight 27259397. Total sieving time: 67.88 hours. Total relation processing time: 0.32 hours. Matrix solve time: 12.11 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 80.52 hours. --------- CPU info (if available) ----------
Jul 19, 2007: By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
5·10¹⁵⁷-3 = 4(9)₁₅₆7_<158> = 170751714607368696896080865604341002901_<39> · C120
C120 = P50 · P70
P50 = 35723845046279761616907730154034566105895929934169_<50>
P70 = 8196845212810478814820742135146474925279643255860336587608186692950513_<70>

Number: 49997_157 N=292822828250781602016000167325285828040891795200764250827620597365088252659542353359323090342351116997142479928464778697 ( 120 digits) SNFS difficulty: 159 digits. Divisors found: r1=35723845046279761616907730154034566105895929934169 (pp50) r2=8196845212810478814820742135146474925279643255860336587608186692950513 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.71 hours. Scaled time: 53.00 units (timescale=2.145). Factorization parameters were as follows: n: 292822828250781602016000167325285828040891795200764250827620597365088252659542353359323090342351116997142479928464778697 m: 50000000000000000000000000000000 c5: 4 c0: -75 skew: 1.8 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3400001) Primes: RFBsize:283146, AFBsize:282917, largePrimes:5641286 encountered Relations: rels:5700798, finalFF:682263 Max relations in full relation-set: 28 Initial matrix: 566127 x 682263 with sparse part having weight 40514085. Pruned matrix : 469219 x 472113 with weight 25366768. Total sieving time: 23.34 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.24 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 24.71 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 18, 2007 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
5·10¹⁹⁶+3 = 5(0)₁₉₅3_<197> = 53 · 4831 · 81435758513_<11> · 620177514568967_<15> · 8335212300603379_<16> · 35165888307807931_<17> · 1724266535012524133_<19> · C115
C115 = P47 · P69
P47 = 18149768500139575450781954504934682959012295193_<47>
P69 = 421514178392323250396382121254673947852157285795193589239114535798571_<69>

Number: 50003_196 N=7650384757347202203321962443218518173640546585406568276655144521369399383167952622184566026725961406618337839569203 ( 115 digits) Divisors found: r1=18149768500139575450781954504934682959012295193 (pp47) r2=421514178392323250396382121254673947852157285795193589239114535798571 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 23.37 hours. Scaled time: 49.86 units (timescale=2.134). Factorization parameters were as follows: name: 50003_196 n: 7650384757347202203321962443218518173640546585406568276655144521369399383167952622184566026725961406618337839569203 skew: 19553.70 # norm 3.28e+15 c5: 16920 c4: -3549394118 c3: -96775513274836 c2: -922030925486182961 c1: 11391841096341814490596 c0: -17247691065672184548477665 # alpha -5.74 Y1: 678599985437 Y0: -13522515818159374759236 # Murphy_E 6.05e-10 # M 1884377264941917291735930955710612016215991487489349721733252967878467057857630059934213163822258669912389565149551 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 2925001) Primes: RFBsize:256726, AFBsize:255896, largePrimes:7598169 encountered Relations: rels:7604204, finalFF:692093 Max relations in full relation-set: 28 Initial matrix: 512710 x 692093 with sparse part having weight 60076442. Pruned matrix : 368783 x 371410 with weight 33519290. Polynomial selection time: 1.33 hours. Total sieving time: 20.87 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.88 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 23.37 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 18, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
(25·10¹⁵⁹-1)/3 = 8(3)₁₅₉_<160> = 13 · 67 · 2236664243479_<13> · C145
C145 = P68 · P77
P68 = 85262497941625226303736633385477406332679270895304586298374767884871_<68>
P77 = 50169728633912464831848958683943349449579452577543046686850278491362296324547_<77>

Number: n N=4277596384380857709493007778877230054219181915921345009085918406957522336511160704245123636854674964203757729951971401133102929893914016547228437 ( 145 digits) SNFS difficulty: 160 digits. Divisors found: r1=85262497941625226303736633385477406332679270895304586298374767884871 (pp68) r2=50169728633912464831848958683943349449579452577543046686850278491362296324547 (pp77) Version: GGNFS-0.77.1-20051202-athlon Total time: 32.10 hours. Scaled time: 42.47 units (timescale=1.323). Factorization parameters were as follows: name: KA_8_3_159 n: 4277596384380857709493007778877230054219181915921345009085918406957522336511160704245123636854674964203757729951971401133102929893914016547228437 skew: 0.83 deg: 5 c5: 5 c0: -2 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:250150, AFBsize:249566, largePrimes:6976915 encountered Relations: rels:6496813, finalFF:566255 Max relations in full relation-set: 48 Initial matrix: 499781 x 566255 with sparse part having weight 34478584. Pruned matrix : 438189 x 440751 with weight 21194488. Total sieving time: 27.82 hours. Total relation processing time: 0.20 hours. Matrix solve time: 4.02 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 32.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(67·10¹⁶⁰+23)/9 = 7(4)₁₅₉7_<161> = 61 · 173 · 401199361 · C149
C149 = P59 · P91
P59 = 10926374007313810829354105515688558278231191096957190128523_<59>
P91 = 1609237188318111563993645016667268783331795663193421462542500398194843294512175283899466533_<91>

Number: n N=17583127386041774296839855493344250162140468475916165432870626962320083118392473075736410533833904510381392754713628615579892796163624551333407220759 ( 149 digits) SNFS difficulty: 161 digits. Divisors found: r1=10926374007313810829354105515688558278231191096957190128523 (pp59) r2=1609237188318111563993645016667268783331795663193421462542500398194843294512175283899466533 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.67 hours. Scaled time: 53.17 units (timescale=1.450). Factorization parameters were as follows: name: KA_7_4_159_7 n: 17583127386041774296839855493344250162140468475916165432870626962320083118392473075736410533833904510381392754713628615579892796163624551333407220759 skew: 0.81 deg: 5 c5: 67 c0: 23 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:250150, AFBsize:249876, largePrimes:7232989 encountered Relations: rels:6812085, finalFF:613709 Max relations in full relation-set: 28 Initial matrix: 500091 x 613709 with sparse part having weight 37971848. Pruned matrix : 402209 x 404773 with weight 21189373. Total sieving time: 32.31 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.89 hours. Total square root time: 0.28 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 36.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(34·10¹⁵⁹-7)/9 = 3(7)₁₅₉_<160>= 3² · 71 · 9849193859_<10> · C147
C147 = P38 · P110
P38 = 15789711189493102093850282846783373661_<38>
P110 = 38015497418106844664862291991531816509233084067775500201987562671218032336050381463628044115703545766523286857_<110>

Number: n N=600253724956827777777889593571298375324011458737641410037337583447615653917558424232237914428509235194183545143746268503264957812846753488921273477 ( 147 digits) SNFS difficulty: 161 digits. Divisors found: r1=15789711189493102093850282846783373661 (pp38) r2=38015497418106844664862291991531816509233084067775500201987562671218032336050381463628044115703545766523286857 (pp110) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 45.27 hours. Scaled time: 61.80 units (timescale=1.365). Factorization parameters were as follows: name: KA_3_7_159 n: 600253724956827777777889593571298375324011458737641410037337583447615653917558424232237914428509235194183545143746268503264957812846753488921273477 skew: 1.16 deg: 5 c5: 17 c0: -35 m: 100000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2000001) Primes: RFBsize:250150, AFBsize:249491, largePrimes:7263434 encountered Relations: rels:6782000, finalFF:559844 Max relations in full relation-set: 28 Initial matrix: 499706 x 559844 with sparse part having weight 36936566. Pruned matrix : 449732 x 452294 with weight 25239638. Total sieving time: 40.93 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.98 hours. Total square root time: 0.14 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 45.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 17, 2007 (2nd): By Yousuke Koide
10⁸⁶³+1 is divisible by 1584705713225403483147160166143_<31>
10¹³²⁹+1 is divisible by558143308808597896050937412527393543_<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jul 17, 2007: By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs
5·10¹⁷⁹-3 = 4(9)₁₇₈7_<180> = 1900472818297_<13> · 143368179663990121285177_<24> · 806484427355480910242618688187_<30> · C115
C115 = P33 · P82
P33 = 621517573913879824531937479098749_<33>
P82 = 3661054312333149079554418503387457027608632989634573487936702648419063794797276451_<82>

Number: 49997_179 N=2275409594168246455928757421586717932537118162223751052838379676300521807658832201602602122092595306083443281259799 ( 115 digits) Divisors found: r1=621517573913879824531937479098749 (pp33) r2=3661054312333149079554418503387457027608632989634573487936702648419063794797276451 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 25.17 hours. Scaled time: 53.93 units (timescale=2.143). Factorization parameters were as follows: name: 49997_179 n: 2275409594168246455928757421586717932537118162223751052838379676300521807658832201602602122092595306083443281259799 skew: 48196.28 # norm 2.56e+15 c5: 17100 c4: -244455031 c3: -4688970535978 c2: 2873460003022738472 c1: -73570840875606184789656 c0: -1602366182681329256539047600 # alpha -5.29 Y1: 1286465858737 Y0: -10587973502887367643287 # Murphy_E 5.24e-10 # M 1767462674691911687831046393184802436937077927791968598803245797389906802841504982740536471287350721141060325879747 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3075001) Primes: RFBsize:256726, AFBsize:256075, largePrimes:7543117 encountered Relations: rels:7471856, finalFF:627137 Max relations in full relation-set: 28 Initial matrix: 512887 x 627137 with sparse part having weight 54070246. Pruned matrix : 419748 x 422376 with weight 33364516. Polynomial selection time: 1.32 hours. Total sieving time: 22.33 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.22 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 25.17 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 16, 2007 (4th): By Robert Backstrom / GMP-ECM 5.0 B1=891500, GGNFS-0.77.1-20060513-athlon-xp, GGNFS-0.77.1-20051202-athlon
5·10¹⁵¹+3 = 5(0)₁₅₀3_<152> = 443 · 947 · C147
C147 = P35 · P40 · P73
P35 = 16270985621257205906905273044911329_<35>
P40 = 1985841848915255165882503532099473704607_<40>
P73 = 3688567872296026104787199609577180339676172266118012744852132484083849981_<73>

Number: n N=7324912443369749282814026596498825470913846589987658708241984849562150308735119605514615544006418914029296562467 ( 112 digits) SNFS difficulty: 151 digits. Divisors found: r1=1985841848915255165882503532099473704607 (pp40) r2=3688567872296026104787199609577180339676172266118012744852132484083849981 (pp73) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 19.96 hours. Scaled time: 27.26 units (timescale=1.366). Factorization parameters were as follows: name: KA_5_0_150_3 n: 7324912443369749282814026596498825470913846589987658708241984849562150308735119605514615544006418914029296562467 # n: 119183545043037178115040725017341205803761909415738425490023145444447357819989940908798367662167090562808536402230162494845311676888642046524488643 skew: 0.57 deg: 5 c5: 50 c0: 3 m: 1000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:216816, AFBsize:216516, largePrimes:6804261 encountered Relations: rels:6450784, finalFF:626071 Max relations in full relation-set: 28 Initial matrix: 433397 x 626071 with sparse part having weight 36162324. Pruned matrix : 263684 x 265914 with weight 16092660. Total sieving time: 17.97 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.70 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 19.96 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
5·10¹⁵⁷+3 = 5(0)₁₅₆3_<158> = 53 · 149 · C154
C154 = P77 · P78
P77 = 13437119575793745653860491268913351112372015271429983467581637225087533319599_<77>
P78 = 471196096929417376262628665137399248660726397583286864726053838970722199918901_<78>

Number: n N=6331518298087881473977459794858807141952640243130302646574648600734456122578194250981385336203621628466506268203115107002659237685196910219070533113840699 ( 154 digits) SNFS difficulty: 157 digits. Divisors found: r1=13437119575793745653860491268913351112372015271429983467581637225087533319599 (pp77) r2=471196096929417376262628665137399248660726397583286864726053838970722199918901 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.27 hours. Scaled time: 38.69 units (timescale=1.322). Factorization parameters were as follows: name: KA_5_0_156_3 n: 6331518298087881473977459794858807141952640243130302646574648600734456122578194250981385336203621628466506268203115107002659237685196910219070533113840699 skew: 0.36 deg: 5 c5: 500 c0: 3 m: 10000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1200001) Primes: RFBsize:250150, AFBsize:249916, largePrimes:7074187 encountered Relations: rels:6675409, finalFF:633608 Max relations in full relation-set: 48 Initial matrix: 500132 x 633608 with sparse part having weight 36398161. Pruned matrix : 379352 x 381916 with weight 17859403. Total sieving time: 26.08 hours. Total relation processing time: 0.20 hours. Matrix solve time: 2.92 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 29.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
5·10¹⁵⁸+3 = 5(0)₁₅₇3_<159> = 23535093831695777_<17> · C143
C143 = P43 · P100
P43 = 3336615942677038549001641449007892174836007_<43>
P100 = 6367190586858022590177464026314548769045456613292917746979423848926661873487443619330012203341779877_<100>

Number: n N=21244869622173647341125524581467461321857532311440306649055866165271370428262898974355677169015308439811677066930201131833443993338133967631139 ( 143 digits) SNFS difficulty: 159 digits. Divisors found: r1=3336615942677038549001641449007892174836007 (pp43) r2=6367190586858022590177464026314548769045456613292917746979423848926661873487443619330012203341779877 (pp100) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.31 hours. Scaled time: 42.38 units (timescale=1.446). Factorization parameters were as follows: name: KA_5_0_157_3 n: 21244869622173647341125524581467461321857532311440306649055866165271370428262898974355677169015308439811677066930201131833443993338133967631139 skew: 1.13 deg: 5 c5: 8 c0: 15 m: 50000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:250150, AFBsize:249771, largePrimes:7121193 encountered Relations: rels:6715214, finalFF:623828 Max relations in full relation-set: 28 Initial matrix: 499986 x 623828 with sparse part having weight 35936151. Pruned matrix : 388924 x 391487 with weight 18826913. Total sieving time: 25.99 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.08 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 29.31 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
5·10¹⁵²+3 = 5(0)₁₅₁3_<153> = 14869 · C149
C149 = P57 · P93
P57 = 135268966532217716081858222979343678676268459159986363363_<57>
P93 = 248593672856895851344394797338957581879512075361661154360125070884478563005695290561420504349_<93>

Number: n N=33627009213800524581343735288183468962270495662115811419732329006658147824332503867106059587060326854529558141098930661107001143318313269217835765687 ( 149 digits) SNFS difficulty: 152 digits. Divisors found: r1=135268966532217716081858222979343678676268459159986363363 (pp57) r2=248593672856895851344394797338957581879512075361661154360125070884478563005695290561420504349 (pp93) Version: GGNFS-0.77.1-20051202-athlon Total time: 24.70 hours. Scaled time: 29.56 units (timescale=1.197). Factorization parameters were as follows: name: KA_5_0_151_3 n: 33627009213800524581343735288183468962270495662115811419732329006658147824332503867106059587060326854529558141098930661107001143318313269217835765687 type: snfs skew: 0.36 deg: 5 c5: 500 c0: 3 m: 1000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:216816, AFBsize:216936, largePrimes:6041357 encountered Relations: rels:5535427, finalFF:506590 Max relations in full relation-set: 28 Initial matrix: 433818 x 506590 with sparse part having weight 22617044. Pruned matrix : 360584 x 362817 with weight 12620042. Total sieving time: 22.48 hours. Total relation processing time: 0.19 hours. Matrix solve time: 1.96 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 24.70 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 16, 2007 (3rd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs, GGNFS-0.77.1-20050930-nocona
(7·10¹⁶⁰-1)/3 = 2(3)₁₆₀_<161> = 767759 · 101791091 · 144095279191_<12> · 35667897961095649947526145377069_<32> · C104
C104 = P50 · P54
P50 = 62240253527047472580312971081891307447294255689341_<50>
P54 = 933347736560011308158563114276369605838717858921125863_<54>

Number: 23333_160 N=58091799752391019095159666661111369201684177850360308694417611514513839600421435152360645238364888526283 ( 104 digits) Divisors found: r1=62240253527047472580312971081891307447294255689341 (pp50) r2=933347736560011308158563114276369605838717858921125863 (pp54) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.76 hours. Scaled time: 14.49 units (timescale=2.143). Factorization parameters were as follows: name: 23333_160 n: 58091799752391019095159666661111369201684177850360308694417611514513839600421435152360645238364888526283 skew: 3825.25 # norm 1.63e+14 c5: 583440 c4: 2326542356 c3: -1039085397060 c2: -24696191837440549 c1: -63642552109250830002 c0: 197660511380706138491336 # alpha -5.58 Y1: 23540119783 Y0: -39776221118266163853 # Murphy_E 2.00e-09 # M 24646029232970984534273208895494097189591808184433543572167780495792969620406958018181523786806597925930 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1800001) Primes: RFBsize:135072, AFBsize:135103, largePrimes:4502987 encountered Relations: rels:4540682, finalFF:378476 Max relations in full relation-set: 28 Initial matrix: 270263 x 378476 with sparse part having weight 34673689. Pruned matrix : 213384 x 214799 with weight 18092350. Polynomial selection time: 0.39 hours. Total sieving time: 6.00 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.20 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 6.76 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
(8·10¹⁵⁷+1)/9 = (8)₁₅₆9_<157> = 3 · 167 · 643 · 386810729226965311961660138063_<30> · C122
C122 = P57 · P66
P57 = 584698862250581133160768195196298297489539613970663689401_<57>
P66 = 122002299998521265446868714174191654500476089207312611183964015921_<66>

Number: 88889_157 N=71334606001089460171433505241882854150874389311670197254671100147853471919307059160203441539544459417073704994902162953321 ( 122 digits) SNFS difficulty: 157 digits. Divisors found: r1=584698862250581133160768195196298297489539613970663689401 (pp57) r2=122002299998521265446868714174191654500476089207312611183964015921 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.80 hours. Scaled time: 42.41 units (timescale=2.142). Factorization parameters were as follows: n: 71334606001089460171433505241882854150874389311670197254671100147853471919307059160203441539544459417073704994902162953321 m: 20000000000000000000000000000000 c5: 25 c0: 1 skew: 0.53 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2700001) Primes: RFBsize:216816, AFBsize:216556, largePrimes:5671234 encountered Relations: rels:5704347, finalFF:614436 Max relations in full relation-set: 28 Initial matrix: 433436 x 614436 with sparse part having weight 47552480. Pruned matrix : 325242 x 327473 with weight 29562975. Total sieving time: 19.05 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.62 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 19.80 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 16, 2007 (2nd): By JMB / GMP-ECM B1=1000000
5·10¹⁸⁰+3 = 5(0)₁₇₉3_<181> = 3636511 · 10065320359_<11> · 170781899320909_<15> · C150
C150 = P35 · P116
P35 = 28365504652386968928074018263317721_<35>
P116 = 28198443896462682489337688478809235310463625892214771261649188513799597672988910349570886709139480460830651399289823_<116>
Jul 16, 2007: By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000
(89·10¹⁵⁹+1)/9 = 9(8)₁₅₈9_<160> = 11 · 1607 · 117727 · 9898242372013_<13> · C138
C138 = P36 · P102
P36 = 748314670082521201732646760076033103_<36>
P102 = 641535236229688185049707266010883443210404427579829424348071950643837839950313319024896633402043943969_<102>
Jul 15, 2007 (5th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GGNFS-0.77.1-20050930-nocona gnfs, GMP-ECM 6.1.2 B1=1000000
5·10¹⁴⁹+3 = 5(0)₁₄₈3_<150> = 7 · 1931 · C146
C146 = P70 · P76
P70 = 5243209539041849099760187057760329315540666673453359958582230909941313_<70>
P76 = 7054926221581529213954354507669417037749392705948230321975121930804768049743_<76>

Number: 50003_149 N=36990456462232743952060368424946363838129762521269512465783827772434711844344159206924613449729969667825700969149959310497891543981652733594732559 ( 146 digits) SNFS difficulty: 150 digits. Divisors found: r1=5243209539041849099760187057760329315540666673453359958582230909941313 (pp70) r2=7054926221581529213954354507669417037749392705948230321975121930804768049743 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.32 hours. Scaled time: 22.11 units (timescale=2.143). Factorization parameters were as follows: n: 36990456462232743952060368424946363838129762521269512465783827772434711844344159206924613449729969667825700969149959310497891543981652733594732559 m: 1000000000000000000000000000000 c5: 1 c0: 6 skew: 1.43 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1575001) Primes: RFBsize:135072, AFBsize:135038, largePrimes:3902867 encountered Relations: rels:4084643, finalFF:460007 Max relations in full relation-set: 28 Initial matrix: 270174 x 460007 with sparse part having weight 43534247. Pruned matrix : 208806 x 210220 with weight 19236951. Total sieving time: 10.03 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.21 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 10.32 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹⁶⁵+3 = 5(0)₁₆₄3_<166> = 107 · 3347 · 76127449 · 526115281 · 8629342554611_<13> · 669110924591646330515236469_<27> · C104
C104 = P44 · P60
P44 = 90824126989341694860705521906459719377905473_<44>
P60 = 664708541046310574292268644887995665738412289611807142993429_<60>

Number: 50003_165 N=60371572942890158021797115986528632028025448079180506843525853489532798120896719516288434944161422136917 ( 104 digits) Divisors found: r1=90824126989341694860705521906459719377905473 (pp44) r2=664708541046310574292268644887995665738412289611807142993429 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.17 hours. Scaled time: 13.22 units (timescale=2.141). Factorization parameters were as follows: name: 50003_165 n: 60371572942890158021797115986528632028025448079180506843525853489532798120896719516288434944161422136917 skew: 7512.98 # norm 2.02e+14 c5: 166500 c4: -1914787896 c3: -27411196426603 c2: 131255323836306125 c1: 909402917800101582079 c0: -10830259771894865408765 # alpha -5.96 Y1: 44183744759 Y0: -51509164741546869936 # Murphy_E 2.11e-09 # M 17593451203521667606384512745223636260136127566053466928071642609603807329680876842845993513292579249217 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1680001) Primes: RFBsize:135072, AFBsize:134796, largePrimes:4380469 encountered Relations: rels:4317631, finalFF:327814 Max relations in full relation-set: 28 Initial matrix: 269947 x 327814 with sparse part having weight 26520107. Pruned matrix : 232660 x 234073 with weight 15995712. Polynomial selection time: 0.39 hours. Total sieving time: 5.42 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.22 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 6.17 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
(71·10¹⁵⁹-17)/9 = 7(8)₁₅₈7_<160> = 3² · 11 · 19 · 1109 · 3623 · 5261 · 267040418211849516599855437_<27> · C120
C120 = P35 · P86
P35 = 40952345579027162659509811761961327_<35>
P86 = 18142748524569935341717716457506943467605125808300221525169648512901304619161112676899_<86>
(7·10¹⁶⁰-1)/3 = 2(3)₁₆₀_<161> = 767759 · 101791091 · 144095279191_<12> · C136
C136 = P32 · C104
P32 = 35667897961095649947526145377069_<32>
C104 = [58091799752391019095159666661111369201684177850360308694417611514513839600421435152360645238364888526283_<104>]
Jul 15, 2007 (4th): By suberi / GMP-ECM 6.1.2 B1=1000000
5·10¹⁷³+3 = 5(0)₁₇₂3_<174> = 7 · 313 · 169061906987_<12> · C160
C160 = P32 · P128
P32 = 59249254073379949902901368057587_<32>
P128 = 22782373957682117221393919745453826568924577598689253992144435924521117243880060681895434415464594199441242777852408944634407357_<128>
Jul 15, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GGNFS-0.77.1-20060513-athlon-xp
(19·10¹⁵⁷-1)/9 = 2(1)₁₅₇_<158> = 3 · 7 · 4129 · 4139 · 136082245808735331544874467_<27> · C123
C123 = P61 · P62
P61 = 6186192101868302643109806651993561689864386250254698505182203_<61>
P62 = 69875771724775887872374741822268114523219808403456062141215761_<62>

Number: n N=432264947155761060829306720543648014786687216349608237446155217915853935721724780996199161863813705702775908099453240301483 ( 123 digits) SNFS difficulty: 158 digits. Divisors found: r1=6186192101868302643109806651993561689864386250254698505182203 (pp61) r2=69875771724775887872374741822268114523219808403456062141215761 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.81 hours. Scaled time: 54.75 units (timescale=1.195). Factorization parameters were as follows: name: KA_2_1_157 n: 432264947155761060829306720543648014786687216349608237446155217915853935721724780996199161863813705702775908099453240301483 type: snfs skew: 0.22 deg: 5 c5: 1900 c0: -1 m: 10000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:250150, AFBsize:249896, largePrimes:6865713 encountered Relations: rels:6360045, finalFF:568119 Max relations in full relation-set: 28 Initial matrix: 500113 x 568119 with sparse part having weight 30885928. Pruned matrix : 436560 x 439124 with weight 19548005. Total sieving time: 41.67 hours. Total relation processing time: 0.24 hours. Matrix solve time: 3.79 hours. Total square root time: 0.11 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000 total time: 45.81 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
5·10¹³⁶+3 = 5(0)₁₃₅3_<137> = 229 · 82132721813_<11> · C124
C124 = P58 · P66
P58 = 5824999790723064946307734440392437977214744000689735893063_<58>
P66 = 456375574500296265791802787296814526424506695836333278231520021053_<66>

Number: n N=2658387625955344283447253598161736872225766192093870684024282834889948633340957531901645111619482902526329350996955516655339 ( 124 digits) SNFS difficulty: 136 digits. Divisors found: r1=5824999790723064946307734440392437977214744000689735893063 (pp58) r2=456375574500296265791802787296814526424506695836333278231520021053 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.26 hours. Scaled time: 6.96 units (timescale=1.324). Factorization parameters were as follows: name: KA_5_0_135_3 n: 2658387625955344283447253598161736872225766192093870684024282834889948633340957531901645111619482902526329350996955516655339 skew: 0.57 deg: 5 c5: 50 c0: 3 m: 1000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 500001) Primes: RFBsize:183072, AFBsize:182856, largePrimes:5537962 encountered Relations: rels:5074935, finalFF:454061 Max relations in full relation-set: 48 Initial matrix: 365993 x 454061 with sparse part having weight 18698401. Pruned matrix : 276551 x 278444 with weight 8183715. Total sieving time: 4.18 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.82 hours. Total square root time: 0.13 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,75000 total time: 5.26 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(73·10¹⁷⁸-1)/9 = 8(1)₁₇₈_<179> = 3 · C179
C179 = P76 · P104
P76 = 1916119867312670924752148611535640415033386450801802237208935853302075657931_<76>
P104 = 14110305674642407281721016340336939892095295727428257624280415428343597811358551505074904645162638085927_<104>

Number: n N=27037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037 ( 179 digits) SNFS difficulty: 179 digits. Divisors found: r1=1916119867312670924752148611535640415033386450801802237208935853302075657931 (pp76) r2=14110305674642407281721016340336939892095295727428257624280415428343597811358551505074904645162638085927 (pp104) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 432.02 hours. Scaled time: 590.57 units (timescale=1.367). Factorization parameters were as follows: name: KA_8_1_178 n: 27037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037037 skew: 0.11 deg: 5 c5: 73000 c0: -1 m: 100000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 17500001) Primes: RFBsize:380800, AFBsize:380932, largePrimes:10269650 encountered Relations: rels:10024620, finalFF:853883 Max relations in full relation-set: 28 Initial matrix: 761799 x 853883 with sparse part having weight 106544632. Pruned matrix : 703884 x 707756 with weight 90829890. Total sieving time: 405.67 hours. Total relation processing time: 1.62 hours. Matrix solve time: 24.13 hours. Total square root time: 0.60 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,179,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 432.02 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
5·10¹³⁷+3 = 5(0)₁₃₆3_<138> = 7 · 3343 · 1231884389_<10> · C125
C125 = P56 · P70
P56 = 14133656423605033089328341238732583072598888641345800951_<56>
P70 = 1227188017945406154897963678957290689881567366655657179710045847933577_<70>

Number: n N=17344653812805218322201570213942926988367052498223811015981967787777496609303098136878312186566884764798888346267889311431727 ( 125 digits) SNFS difficulty: 137 digits. Divisors found: r1=14133656423605033089328341238732583072598888641345800951 (pp56) r2=1227188017945406154897963678957290689881567366655657179710045847933577 (pp70) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.48 hours. Scaled time: 7.74 units (timescale=1.195). Factorization parameters were as follows: name: KA_5_0_136_3 n: 17344653812805218322201570213942926988367052498223811015981967787777496609303098136878312186566884764798888346267889311431727 type: snfs skew: 0.36 deg: 5 c5: 500 c0: 3 m: 1000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:148933, AFBsize:148735, largePrimes:5741066 encountered Relations: rels:5246168, finalFF:473203 Max relations in full relation-set: 28 Initial matrix: 297734 x 473203 with sparse part having weight 21419198. Pruned matrix : 149345 x 150897 with weight 8231855. Total sieving time: 5.80 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.48 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,75000 total time: 6.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
5·10¹⁴⁴+3 = 5(0)₁₄₃3_<145> = 53 · C143
C143 = P67 · P77
P67 = 8915485535218874463020966252542555006448848732763244901456195853393_<67>
P77 = 10581546262269091742312886939766011985159784242637011168380827339866200032807_<77>

Number: n N=94339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264151 ( 143 digits) SNFS difficulty: 145 digits. Divisors found: r1=8915485535218874463020966252542555006448848732763244901456195853393 (pp67) r2=10581546262269091742312886939766011985159784242637011168380827339866200032807 (pp77) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.42 hours. Scaled time: 9.79 units (timescale=1.320). Factorization parameters were as follows: name: KA_5_0_143_3 n: 94339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264150943396226415094339622641509433962264151 skew: 1.43 deg: 5 c5: 1 c0: 6 m: 100000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:183072, AFBsize:183151, largePrimes:6364163 encountered Relations: rels:5878097, finalFF:499432 Max relations in full relation-set: 48 Initial matrix: 366287 x 499432 with sparse part having weight 26509055. Pruned matrix : 248154 x 250049 with weight 10949064. Total sieving time: 6.14 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.04 hours. Total square root time: 0.08 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 7.42 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
5·10¹⁵⁴+3 = 5(0)₁₅₃3_<155> = 31 · 4021 · C150
C150 = P36 · P115
P36 = 167160802616143494509108495516497129_<36>
P115 = 2399605173928420299498820740137566306845129879546122780196166540333527775067120892884179276851300720910497809301857_<115>

Number: n N=401119926835725345163697042141659513361304762898011247402748473738678390065061652132754650985551660235377173067203632542057424328725802440413634868553 ( 150 digits) SNFS difficulty: 155 digits. Divisors found: r1=167160802616143494509108495516497129 (pp36) r2=2399605173928420299498820740137566306845129879546122780196166540333527775067120892884179276851300720910497809301857 (pp115) Version: GGNFS-0.77.1-20051202-athlon Total time: 18.03 hours. Scaled time: 26.12 units (timescale=1.449). Factorization parameters were as follows: name: KA_5_0_153_3 n: 401119926835725345163697042141659513361304762898011247402748473738678390065061652132754650985551660235377173067203632542057424328725802440413634868553 skew: 1.43 deg: 5 c5: 1 c0: 6 m: 10000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 800001) Primes: RFBsize:216816, AFBsize:216821, largePrimes:6423682 encountered Relations: rels:5914055, finalFF:487619 Max relations in full relation-set: 28 Initial matrix: 433701 x 487619 with sparse part having weight 27166609. Pruned matrix : 381771 x 384003 with weight 17076701. Total sieving time: 15.26 hours. Total relation processing time: 0.14 hours. Matrix solve time: 2.48 hours. Total square root time: 0.15 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 18.03 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Jul 15, 2007 (2nd): By Jo Yeong Uk / Msieve v. 1.21, GGNFS-0.77.1-20050930-nocona gnfs 5·10¹⁶⁰+3 = 5(0)₁₅₉3_<161> = 2207 · 7760503636757_<13> · 120355074834623_<15> · 82551714075637674821552052888550681_<35> · C96
C96 = P43 · P54
P43 = 1770092901260328461943147499208826822490849_<43>
P54 = 165993545605717346668480035353143215370070055379374031_<54>

Sat Jul 14 21:15:30 2007 Sat Jul 14 21:15:30 2007 Sat Jul 14 21:15:30 2007 Msieve v. 1.21 Sat Jul 14 21:15:30 2007 random seeds: 7cf136d0 06e41b3c Sat Jul 14 21:15:30 2007 factoring 293823996731712864770458618120875378669709169546409049689172378069092682226620668855969845742319 (96 digits) Sat Jul 14 21:15:30 2007 commencing quadratic sieve (96-digit input) Sat Jul 14 21:15:30 2007 using multiplier of 1 Sat Jul 14 21:15:30 2007 using 32kb Intel Core sieve core Sat Jul 14 21:15:30 2007 sieve interval: 36 blocks of size 32768 Sat Jul 14 21:15:30 2007 processing polynomials in batches of 6 Sat Jul 14 21:15:30 2007 using a sieve bound of 2258261 (83529 primes) Sat Jul 14 21:15:30 2007 using large prime bound of 338739150 (28 bits) Sat Jul 14 21:15:30 2007 using double large prime bound of 2258175411908100 (43-52 bits) Sat Jul 14 21:15:30 2007 using trial factoring cutoff of 52 bits Sat Jul 14 21:15:30 2007 polynomial 'A' values have 12 factors Sun Jul 15 00:30:57 2007 83772 relations (20431 full + 63341 combined from 1261659 partial), need 83625 Sun Jul 15 00:30:57 2007 begin with 1282090 relations Sun Jul 15 00:30:58 2007 reduce to 219241 relations in 10 passes Sun Jul 15 00:30:58 2007 attempting to read 219241 relations Sun Jul 15 00:31:00 2007 recovered 219241 relations Sun Jul 15 00:31:00 2007 recovered 203549 polynomials Sun Jul 15 00:31:00 2007 attempting to build 83772 cycles Sun Jul 15 00:31:00 2007 found 83772 cycles in 6 passes Sun Jul 15 00:31:00 2007 distribution of cycle lengths: Sun Jul 15 00:31:00 2007 length 1 : 20431 Sun Jul 15 00:31:00 2007 length 2 : 14459 Sun Jul 15 00:31:00 2007 length 3 : 13979 Sun Jul 15 00:31:00 2007 length 4 : 11430 Sun Jul 15 00:31:00 2007 length 5 : 8505 Sun Jul 15 00:31:00 2007 length 6 : 5874 Sun Jul 15 00:31:00 2007 length 7 : 3781 Sun Jul 15 00:31:00 2007 length 9+: 5313 Sun Jul 15 00:31:00 2007 largest cycle: 25 relations Sun Jul 15 00:31:00 2007 matrix is 83529 x 83772 with weight 5702285 (avg 68.07/col) Sun Jul 15 00:31:01 2007 filtering completed in 3 passes Sun Jul 15 00:31:01 2007 matrix is 82006 x 82070 with weight 5508650 (avg 67.12/col) Sun Jul 15 00:31:02 2007 saving the first 48 matrix rows for later Sun Jul 15 00:31:02 2007 matrix is 81958 x 82070 with weight 4517163 (avg 55.04/col) Sun Jul 15 00:31:02 2007 matrix includes 32 packed rows Sun Jul 15 00:31:02 2007 using block size 32828 for processor cache size 4096 kB Sun Jul 15 00:31:40 2007 lanczos halted after 1298 iterations Sun Jul 15 00:31:40 2007 recovered 16 nontrivial dependencies Sun Jul 15 00:31:40 2007 prp43 factor: 1770092901260328461943147499208826822490849 Sun Jul 15 00:31:40 2007 prp54 factor: 165993545605717346668480035353143215370070055379374031 Sun Jul 15 00:31:40 2007 elapsed time 03:16:10
5·10¹⁵⁶+3 = 5(0)₁₅₅3_<157> = 17 · 19 · 353 · 9781 · 2903959 · 3738923 · 48999199953669556762469285191647229_<35> · C100
C100 = P44 · P57
P44 = 16220542161012079506892689114089790259652611_<44>
P57 = 519539008028015605717126723388083053475004321678810798119_<57>

Number: 50003_156 N=8427204384008820376729101935985157281095142510409891407641557472295423610841518758316232116592238709 ( 100 digits) Divisors found: r1=16220542161012079506892689114089790259652611 (pp44) r2=519539008028015605717126723388083053475004321678810798119 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.73 hours. Scaled time: 7.99 units (timescale=2.143). Factorization parameters were as follows: name: 50003_156 n: 8427204384008820376729101935985157281095142510409891407641557472295423610841518758316232116592238709 skew: 3444.23 # norm 9.10e+13 c5: 173280 c4: -628911052 c3: 10329441200556 c2: -274954422866913 c1: -77119095993536940626 c0: -44666410367268089640360 # alpha -6.59 Y1: 27461304337 Y0: -8657410638244314449 # Murphy_E 3.57e-09 # M 7478100621744003382968441551055951149169645585010492469244137615838640289772215551370324908911734284 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [750000, 1250001) Primes: RFBsize:114155, AFBsize:113396, largePrimes:3918665 encountered Relations: rels:3901134, finalFF:350563 Max relations in full relation-set: 28 Initial matrix: 227632 x 350563 with sparse part having weight 27724694. Pruned matrix : 160476 x 161678 with weight 11045630. Polynomial selection time: 0.25 hours. Total sieving time: 3.27 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000 total time: 3.73 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹⁵⁹+3 = 5(0)₁₅₈3_<160> = C160
C160 = P44 · P116
P44 = 83066365779588590821426749068056416859826527_<44>
P116 = 60192834405048939466899798943567903902651745875844194867985009267232595787118690954252254004124505688435636777703389_<116>

Number: 50003_159 N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 160 digits) SNFS difficulty: 160 digits. Divisors found: r1=83066365779588590821426749068056416859826527 (pp44) r2=60192834405048939466899798943567903902651745875844194867985009267232595787118690954252254004124505688435636777703389 (pp116) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.58 hours. Scaled time: 51.97 units (timescale=2.114). Factorization parameters were as follows: n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 100000000000000000000000000000000 c5: 1 c0: 6 skew: 1.43 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2000000, 3400001) Primes: RFBsize:283146, AFBsize:283322, largePrimes:5636652 encountered Relations: rels:5694712, finalFF:681230 Max relations in full relation-set: 28 Initial matrix: 566532 x 681230 with sparse part having weight 41699472. Pruned matrix : 471507 x 474403 with weight 26271016. Total sieving time: 23.28 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.18 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 24.58 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 15, 2007: By JMB / GGNFS
5·10¹⁴⁵+3 = 5(0)₁₄₄3_<146> = 10903 · 323797439456498340561904697913457873787_<39> · C104
C104 = P46 · P58
P46 = 2465188889777582684991267296272427043966702509_<46>
P58 = 5745136880246153704523428561631148137811827694096870119147_<58>
Jul 14, 2007 (8th): By JMB / GMP-ECM B1=1000000
5·10¹⁷⁸+3 = 5(0)₁₇₇3_<179> = 61 · 5813 · C174
C174 = P34 · C141
P34 = 1266095772152669053113048638910331_<34>
C141 = [111371299677925599229304910106423605557497863192994526047063490147240879819809490792264436773201047749707743497289808646191385677866285614841_<141>]
5·10¹⁷²+3 = 5(0)₁₇₁3_<173> = 17 · 9089719 · 870832992287_<12> · 13385200156201_<14> · 47347314846917_<14> · 724273923844727_<15> · C111
C111 = P36 · P76
P36 = 199380097814707075827853407010411667_<36>
P76 = 4060045237533688631179618384328067264911276818684333348445532508588775649451_<76>
5·10¹⁷⁹+3 = 5(0)₁₇₈3_<180> = 7 · 6581 · 274649101458389267214457_<24> · 17442996660668102907927206569_<29> · C124
C124 = P38 · P86
P38 = 58420054131152676580667221137068677907_<38>
P86 = 38780985245897447564182837100518071852832635692767107596372080155550102208945138108939_<86>
5·10¹⁴⁵+3 = 5(0)₁₄₄3_<146> = 10903 · C142
C142 = P39 · C104
P39 = 323797439456498340561904697913457873787_<39>
C104 = [14162847607434260658361502210554839882035030992737898227692191559764168402119735000385403725547533839823_<104>]
Jul 14, 2007 (7th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, GMP-ECM 6.1.2 B1=1000000
5·10¹³⁰+3 = 5(0)₁₂₉3_<131> = 349 · C129
C129 = P45 · P84
P45 = 223050252687486781077222133508703494233225969_<45>
P84 = 642305820856559171936319435779114051384175861818268799381835937621892642342986131663_<84>

Number: 50003_130 N=143266475644699140401146131805157593123209169054441260744985673352435530085959885386819484240687679083094555873925501432664756447 ( 129 digits) SNFS difficulty: 130 digits. Divisors found: r1=223050252687486781077222133508703494233225969 (pp45) r2=642305820856559171936319435779114051384175861818268799381835937621892642342986131663 (pp84) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.97 hours. Scaled time: 4.23 units (timescale=2.144). Factorization parameters were as follows: n: 143266475644699140401146131805157593123209169054441260744985673352435530085959885386819484240687679083094555873925501432664756447 m: 100000000000000000000000000 c5: 5 c0: 3 skew: 0.9 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78421, largePrimes:1491823 encountered Relations: rels:1505178, finalFF:190379 Max relations in full relation-set: 28 Initial matrix: 156984 x 190379 with sparse part having weight 9500964. Pruned matrix : 140981 x 141829 with weight 5530242. Total sieving time: 1.90 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.97 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹³¹+3 = 5(0)₁₃₀3_<132> = 7 · 53 · 4048842607_<10> · C120
C120 = P48 · P72
P48 = 523541404697611061806834745219853229328170446317_<48>
P72 = 635790693115827427508005325491084683125703813484245526914108384957137147_<72>

Number: 50003_131 N=332862752567528046530685118837102160591749923555522639241418808436225983242944407127183464433987927779293409445570037599 ( 120 digits) SNFS difficulty: 131 digits. Divisors found: r1=523541404697611061806834745219853229328170446317 (pp48) r2=635790693115827427508005325491084683125703813484245526914108384957137147 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.42 hours. Scaled time: 5.12 units (timescale=2.118). Factorization parameters were as follows: n: 332862752567528046530685118837102160591749923555522639241418808436225983242944407127183464433987927779293409445570037599 m: 100000000000000000000000000 c5: 50 c0: 3 skew: 0.57 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 1000001) Primes: RFBsize:78498, AFBsize:78466, largePrimes:1559164 encountered Relations: rels:1595536, finalFF:210853 Max relations in full relation-set: 28 Initial matrix: 157029 x 210853 with sparse part having weight 10838743. Pruned matrix : 135540 x 136389 with weight 5520586. Total sieving time: 2.34 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 2.42 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹³²+3 = 5(0)₁₃₁3_<133> = 16187 · C129
C129 = P59 · P71
P59 = 18572566704029876782615951371188489713635855833627934104693_<59>
P71 = 16631511131550278291805996309948604657716454712748581690326108061640533_<71>

Number: 50003_132 N=308889849879532958546982146166676962994995984431951566071538889232099833199481065052202384629641069994439982702168406746154321369 ( 129 digits) SNFS difficulty: 134 digits. Divisors found: r1=18572566704029876782615951371188489713635855833627934104693 (pp59) r2=16631511131550278291805996309948604657716454712748581690326108061640533 (pp71) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.52 hours. Scaled time: 5.41 units (timescale=2.144). Factorization parameters were as follows: n: 308889849879532958546982146166676962994995984431951566071538889232099833199481065052202384629641069994439982702168406746154321369 m: 500000000000000000000000000 c5: 4 c0: 75 skew: 1.8 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [700000, 1150001) Primes: RFBsize:107126, AFBsize:106673, largePrimes:1795749 encountered Relations: rels:1865223, finalFF:245894 Max relations in full relation-set: 28 Initial matrix: 213863 x 245894 with sparse part having weight 12440753. Pruned matrix : 192707 x 193840 with weight 7862026. Total sieving time: 2.38 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,134,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 total time: 2.52 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹³³+3 = 5(0)₁₃₂3_<134> = 11057031539_<11> · C124
C124 = P42 · P82
P42 = 886544732452880113982144287654486535090287_<42>
P82 = 5100711993689431955514377563639991758308507294250704290195426082082810455667928671_<82>

Number: 50003_133 N=4522009349764594173325890157795994688624718772270474935469929475797618053624329089471361776496421369211037031120835260918577 ( 124 digits) SNFS difficulty: 135 digits. Divisors found: r1=886544732452880113982144287654486535090287 (pp42) r2=5100711993689431955514377563639991758308507294250704290195426082082810455667928671 (pp82) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.78 hours. Scaled time: 5.91 units (timescale=2.128). Factorization parameters were as follows: n: 4522009349764594173325890157795994688624718772270474935469929475797618053624329089471361776496421369211037031120835260918577 m: 1000000000000000000000000000 c5: 1 c0: 60 skew: 2.27 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [700000, 1200001) Primes: RFBsize:107126, AFBsize:106993, largePrimes:1858990 encountered Relations: rels:1990762, finalFF:296586 Max relations in full relation-set: 28 Initial matrix: 214183 x 296586 with sparse part having weight 15830089. Pruned matrix : 168876 x 170010 with weight 7418709. Total sieving time: 2.66 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 total time: 2.78 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
(19·10¹⁶⁰-1)/9 = 2(1)₁₆₀_<161> = 3² · 15418862204910161_<17> · C144
C144 = P33 · P111
P33 = 198440143099519652057552815018259_<33>
P111 = 766631611792914428985345616031997540862285764082560979052617179307561469122129221254517402352149820216246478021_<111>
Jul 14, 2007 (6th): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(89·10¹⁵⁸+1)/9 = 9(8)₁₅₇9_<159> = 19 · 1301 · 153009010613_<12> · C144
C144 = P63 · P81
P63 = 424900550000295550092866554354772812998171689914130662333763053_<63>
P81 = 615335965218209178221823895527708916744280900160476438475349268969266385168270279_<81>

Number: n N=261456590056179812443165367795872934768914215004307843412220192729070446047275621879186181977133609132560926795382217178649634421230505048201787 ( 144 digits) SNFS difficulty: 159 digits. Divisors found: r1=424900550000295550092866554354772812998171689914130662333763053 (pp63) r2=615335965218209178221823895527708916744280900160476438475349268969266385168270279 (pp81) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.67 hours. Scaled time: 48.65 units (timescale=1.445). Factorization parameters were as follows: name: KA_9_8_157_9 n: 261456590056179812443165367795872934768914215004307843412220192729070446047275621879186181977133609132560926795382217178649634421230505048201787 skew: 0.10 deg: 5 c5: 89000 c0: 1 m: 10000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:250150, AFBsize:249496, largePrimes:6906833 encountered Relations: rels:6429793, finalFF:563547 Max relations in full relation-set: 28 Initial matrix: 499713 x 563547 with sparse part having weight 31998849. Pruned matrix : 438837 x 441399 with weight 20235550. Total sieving time: 28.59 hours. Total relation processing time: 0.20 hours. Matrix solve time: 4.48 hours. Total square root time: 0.40 hours, sqrts: 6. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 33.67 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(7·10¹⁵⁷-61)/9 = (7)₁₅₆1_<157> = 536746193918741_<15> · 74325871959677983_<17> · C126
C126 = P57 · P69
P57 = 664828967518681180559161523946360773815099210144871733241_<57>
P69 = 293249047514706248599001187604405935292797388117330624974946437107177_<69>

Number: n N=194960461485038834727296645467655591808226295435757088586794057750949454544474226631511051570795485756565910575024330070570657 ( 126 digits) SNFS difficulty: 157 digits. Divisors found: r1=664828967518681180559161523946360773815099210144871733241 (pp57) r2=293249047514706248599001187604405935292797388117330624974946437107177 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.28 hours. Scaled time: 57.26 units (timescale=1.323). Factorization parameters were as follows: name: KA_7_156_1 n: 194960461485038834727296645467655591808226295435757088586794057750949454544474226631511051570795485756565910575024330070570657 skew: 0.61 deg: 5 c5: 700 c0: -61 m: 10000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1800001) Primes: RFBsize:250150, AFBsize:249972, largePrimes:7243078 encountered Relations: rels:6755304, finalFF:568264 Max relations in full relation-set: 48 Initial matrix: 500189 x 568264 with sparse part having weight 39667025. Pruned matrix : 443449 x 446013 with weight 25263932. Total sieving time: 37.86 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.05 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 43.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 14, 2007 (5th): By Jo Yeong Uk / Msieve v. 1.21, GMP-ECM 6.1.2 B1=1000000
5·10¹⁶⁸+3 = 5(0)₁₆₇3_<169> = 30261601 · 890150258236321_<15> · 498727304848409587637_<21> · 142978063635046612431340573579_<30> · C97
C97 = P44 · P54
P44 = 12718944880656352612135685179437522176294183_<44>
P54 = 204659137232336784991399810699824456814839775637627027_<54>

Sat Jul 14 01:19:05 2007 Sat Jul 14 01:19:05 2007 Sat Jul 14 01:19:05 2007 Msieve v. 1.21 Sat Jul 14 01:19:05 2007 random seeds: 2c6b3972 03752bf5 Sat Jul 14 01:19:05 2007 factoring 2603048285780775881221905377785187247573247246016520013086521779141708972201219207045854783683941 (97 digits) Sat Jul 14 01:19:05 2007 commencing quadratic sieve (97-digit input) Sat Jul 14 01:19:06 2007 using multiplier of 61 Sat Jul 14 01:19:06 2007 using 32kb Intel Core sieve core Sat Jul 14 01:19:06 2007 sieve interval: 36 blocks of size 32768 Sat Jul 14 01:19:06 2007 processing polynomials in batches of 6 Sat Jul 14 01:19:06 2007 using a sieve bound of 2361367 (87059 primes) Sat Jul 14 01:19:06 2007 using large prime bound of 354205050 (28 bits) Sat Jul 14 01:19:06 2007 using double large prime bound of 2447138225130900 (43-52 bits) Sat Jul 14 01:19:06 2007 using trial factoring cutoff of 52 bits Sat Jul 14 01:19:06 2007 polynomial 'A' values have 13 factors Sat Jul 14 05:43:47 2007 87427 relations (21313 full + 66114 combined from 1303942 partial), need 87155 Sat Jul 14 05:43:48 2007 begin with 1325255 relations Sat Jul 14 05:43:48 2007 reduce to 228294 relations in 12 passes Sat Jul 14 05:43:48 2007 attempting to read 228294 relations Sat Jul 14 05:43:50 2007 recovered 228294 relations Sat Jul 14 05:43:50 2007 recovered 215876 polynomials Sat Jul 14 05:43:51 2007 attempting to build 87427 cycles Sat Jul 14 05:43:51 2007 found 87427 cycles in 6 passes Sat Jul 14 05:43:51 2007 distribution of cycle lengths: Sat Jul 14 05:43:51 2007 length 1 : 21313 Sat Jul 14 05:43:51 2007 length 2 : 15209 Sat Jul 14 05:43:51 2007 length 3 : 14610 Sat Jul 14 05:43:51 2007 length 4 : 12030 Sat Jul 14 05:43:51 2007 length 5 : 8885 Sat Jul 14 05:43:51 2007 length 6 : 6060 Sat Jul 14 05:43:51 2007 length 7 : 3877 Sat Jul 14 05:43:51 2007 length 9+: 5443 Sat Jul 14 05:43:51 2007 largest cycle: 25 relations Sat Jul 14 05:43:51 2007 matrix is 87059 x 87427 with weight 5727486 (avg 65.51/col) Sat Jul 14 05:43:51 2007 filtering completed in 3 passes Sat Jul 14 05:43:51 2007 matrix is 85635 x 85699 with weight 5541486 (avg 64.66/col) Sat Jul 14 05:43:53 2007 saving the first 48 matrix rows for later Sat Jul 14 05:43:53 2007 matrix is 85587 x 85699 with weight 4247055 (avg 49.56/col) Sat Jul 14 05:43:53 2007 matrix includes 32 packed rows Sat Jul 14 05:43:53 2007 using block size 34279 for processor cache size 4096 kB Sat Jul 14 05:44:30 2007 lanczos halted after 1355 iterations Sat Jul 14 05:44:30 2007 recovered 14 nontrivial dependencies Sat Jul 14 05:44:30 2007 prp44 factor: 12718944880656352612135685179437522176294183 Sat Jul 14 05:44:30 2007 prp54 factor: 204659137232336784991399810699824456814839775637627027 Sat Jul 14 05:44:30 2007 elapsed time 04:25:25
5·10¹²⁷+3 = 5(0)₁₂₆3_<128> = 1063 · 19759 · 9528013351973_<13> · C108
C108 = P36 · P73
P36 = 231486198826356536297596881484840829_<36>
P73 = 1079305320539789652825036330387473369897040690627974500945419108513238427_<73>
5·10¹²⁶+3 = 5(0)₁₂₅3_<127> = 23 · 32869 · C121
C121 = P40 · P82
P40 = 1771845148714035530042375961149100976639_<40>
P82 = 3732758672015730547173100481173208742246650750942529540645311897013388939508906671_<82>
5·10¹⁷⁷+3 = 5(0)₁₇₆3_<178> = C178
C178 = P30 · C149
P30 = 176218992155079534631185354899_<30>
C149 = [28373786155806670640998399527341074498848269897625772403660234914777229704006772677455191720133985486886631783071384944023777763803864984794834905297_<149>]
Jul 14, 2007 (4th): By JMB / GMP-ECM B1=1000000
5·10¹⁸⁷+3 = 5(0)₁₈₆3_<188> = 43951 · 881623824379321_<15> · C169
C169 = P34 · P135
P34 = 7538781648531214385240912695837561_<34>
P135 = 171165708092478089670945899225361876860032835861904429144861641040302889862809476562441735553451758084446668158294751605231000217623613_<135>
5·10¹⁵⁶+3 = 5(0)₁₅₅3_<157> = 17 · 19 · 353 · 9781 · 2903959 · 3738923 · C135
C135 = P35 · C100
P35 = 48999199953669556762469285191647229_<35>
C100 = [8427204384008820376729101935985157281095142510409891407641557472295423610841518758316232116592238709_<100>]
5·10¹⁶¹+3 = 5(0)₁₆₀3_<162> = 7² · 1447 · 180463 · C152
C152 = P32 · C121
P32 = 26314542158435393005535533221629_<32>
C121 = [1484982727509908854740212306941041004792973008825939876458829727780821383869898582890053749715127694042906997885710674263_<121>]
Jul 14, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
5·10¹²⁸+3 = 5(0)₁₂₇3_<129> = 824220383604228418854258476629_<30> · C99
C99 = P39 · P60
P39 = 778977109190834486013530928931812523699_<39>
P60 = 778756989881128479103802248680558442310201163296540906795693_<60>

Number: n N=606633868739757406203256446479850116767816318805314527242598676929677564111420625371388633713628407 ( 99 digits) SNFS difficulty: 129 digits. Divisors found: r1=778977109190834486013530928931812523699 (pp39) r2=778756989881128479103802248680558442310201163296540906795693 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.38 hours. Scaled time: 3.45 units (timescale=1.449). Factorization parameters were as follows: name: KA_5_0_127_3 n: 606633868739757406203256446479850116767816318805314527242598676929677564111420625371388633713628407 skew: 1.13 deg: 5 c5: 8 c0: 15 m: 50000000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 400001) Primes: RFBsize:78498, AFBsize:78351, largePrimes:5398510 encountered Relations: rels:4800608, finalFF:256002 Max relations in full relation-set: 28 Initial matrix: 156914 x 256002 with sparse part having weight 19788163. Pruned matrix : 117925 x 118773 with weight 6523826. Total sieving time: 2.01 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.18 hours. Total square root time: 0.04 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 2.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Jul 14, 2007 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
5·10¹¹⁰+3 = 5(0)₁₀₉3_<111> = 181 · 140869 · 11063288894785937_<17> · C88
C88 = P31 · P57
P31 = 6039261878537983804809377055481_<31>
P57 = 293499849169094259922144875395852639709254512750131598291_<57>

Number: 50003_110 N=1772522450443559105303400406863312386769861079139349751622786142722504963484025911782971 ( 88 digits) SNFS difficulty: 110 digits. Divisors found: r1=6039261878537983804809377055481 (pp31) r2=293499849169094259922144875395852639709254512750131598291 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.51 hours. Scaled time: 1.08 units (timescale=2.144). Factorization parameters were as follows: n: 1772522450443559105303400406863312386769861079139349751622786142722504963484025911782971 m: 10000000000000000000000 c5: 5 c0: 3 skew: 0.9 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 280001) Primes: RFBsize:30757, AFBsize:30494, largePrimes:1050943 encountered Relations: rels:988188, finalFF:104048 Max relations in full relation-set: 28 Initial matrix: 61316 x 104048 with sparse part having weight 4750487. Pruned matrix : 47929 x 48299 with weight 1555471. Total sieving time: 0.48 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.51 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹¹⁴+3 = 5(0)₁₁₃3_<115> = 316469363851_<12> · C104
C104 = P31 · P32 · P42
P31 = 1081354250785203149101117499513_<31>
P32 = 33280544906954346861035663714839_<32>
P42 = 439015556833735689338180321004768868727479_<42>

Number: 50003_114 N=15799317631118626468490249640104333120774198019987032630994473961208379779282675169509041640621008750953 ( 104 digits) SNFS difficulty: 115 digits. Divisors found: r1=1081354250785203149101117499513 (pp31) r2=33280544906954346861035663714839 (pp32) r3=439015556833735689338180321004768868727479 (pp42) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.54 hours. Scaled time: 1.15 units (timescale=2.143). Factorization parameters were as follows: n: 15799317631118626468490249640104333120774198019987032630994473961208379779282675169509041640621008750953 m: 100000000000000000000000 c5: 1 c0: 6 skew: 1.43 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 300001) Primes: RFBsize:30757, AFBsize:30754, largePrimes:976509 encountered Relations: rels:884427, finalFF:74434 Max relations in full relation-set: 28 Initial matrix: 61575 x 74434 with sparse part having weight 3217169. Pruned matrix : 56872 x 57243 with weight 1876427. Total sieving time: 0.51 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.54 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹¹⁹+3 = 5(0)₁₁₈3_<120> = 7² · 71843 · C114
C114 = P47 · P67
P47 = 90543020753040293576959578835244863827338385803_<47>
P67 = 1568680455115318344001740770037613906724896970510571219229245382643_<67>

Number: 50003_119 N=142033067002394961575794383842091044900345339199109623109575386464873660166570699657728715137628621594650693817329 ( 114 digits) SNFS difficulty: 120 digits. Divisors found: r1=90543020753040293576959578835244863827338385803 (pp47) r2=1568680455115318344001740770037613906724896970510571219229245382643 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.79 hours. Scaled time: 1.69 units (timescale=2.143). Factorization parameters were as follows: n: 142033067002394961575794383842091044900345339199109623109575386464873660166570699657728715137628621594650693817329 m: 1000000000000000000000000 c5: 1 c0: 6 skew: 1.43 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 420001) Primes: RFBsize:49098, AFBsize:49231, largePrimes:1971794 encountered Relations: rels:2027062, finalFF:202354 Max relations in full relation-set: 28 Initial matrix: 98393 x 202354 with sparse part having weight 16943511. Pruned matrix : 76211 x 76766 with weight 4142003. Total sieving time: 0.74 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.79 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 14, 2007: By JMB / GMP-ECM B1=1000000
5·10¹⁶⁰+3 = 5(0)₁₅₉3_<161> = 2207 · 7760503636757_<13> · 120355074834623_<15> · C131
C131 = P35 · C96
P35 = 82551714075637674821552052888550681_<35>
C96 = [293823996731712864770458618120875378669709169546409049689172378069092682226620668855969845742319_<96>]
Jul 13, 2007 (6th): By Bruce Dodson / Jul 12, 2007
10³³⁷+1 is divisible by 1687858617956114857563779160203327248258725852773131_<52>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jul 13, 2007 (5th): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v. 1.21, GGNFS-0.77.1-20050930-nocona gnfs
5·10¹²³+3 = 5(0)₁₂₂3_<124> = C124
C124 = P47 · P78
P47 = 29103572282156559112182740936226932631374490509_<47>
P78 = 171800215847231475291585450337672992777067604341481417436023086954002453065167_<78>

Number: 50003_123 N=5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 ( 124 digits) SNFS difficulty: 125 digits. Divisors found: r1=29103572282156559112182740936226932631374490509 (pp47) r2=171800215847231475291585450337672992777067604341481417436023086954002453065167 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.06 hours. Scaled time: 2.26 units (timescale=2.129). Factorization parameters were as follows: n: 5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 m: 10000000000000000000000000 c5: 1 c0: 60 skew: 2.27 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 480001) Primes: RFBsize:49098, AFBsize:48986, largePrimes:1922445 encountered Relations: rels:1871417, finalFF:110397 Max relations in full relation-set: 28 Initial matrix: 98148 x 110397 with sparse part having weight 9157899. Pruned matrix : 94827 x 95381 with weight 6835596. Total sieving time: 0.99 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.06 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
5·10¹³⁵+3 = 5(0)₁₃₄3_<136> = 29 · 97 · 293 · 12415969 · 8179360663_<10> · 3544624710199_<13> · 502246085292724499_<18> · C83
C83 = P33 · P51
P33 = 103888204664039275506234925332227_<33>
P51 = 322982960901345113517889401979443805784667940709243_<51>

Fri Jul 13 23:04:56 2007 Fri Jul 13 23:04:56 2007 Fri Jul 13 23:04:56 2007 Msieve v. 1.21 Fri Jul 13 23:04:56 2007 random seeds: d29e7421 231acc36 Fri Jul 13 23:04:56 2007 factoring 33554119945116336385337462642964476014723803391219875848421325898095952849784674161 (83 digits) Fri Jul 13 23:04:56 2007 commencing quadratic sieve (83-digit input) Fri Jul 13 23:04:56 2007 using multiplier of 1 Fri Jul 13 23:04:56 2007 using 32kb Intel Core sieve core Fri Jul 13 23:04:56 2007 sieve interval: 12 blocks of size 32768 Fri Jul 13 23:04:56 2007 processing polynomials in batches of 17 Fri Jul 13 23:04:56 2007 using a sieve bound of 1372829 (52647 primes) Fri Jul 13 23:04:56 2007 using large prime bound of 122181781 (26 bits) Fri Jul 13 23:04:56 2007 using trial factoring cutoff of 27 bits Fri Jul 13 23:04:56 2007 polynomial 'A' values have 10 factors Fri Jul 13 23:21:48 2007 52748 relations (27073 full + 25675 combined from 277937 partial), need 52743 Fri Jul 13 23:21:48 2007 begin with 305010 relations Fri Jul 13 23:21:48 2007 reduce to 75223 relations in 2 passes Fri Jul 13 23:21:48 2007 attempting to read 75223 relations Fri Jul 13 23:21:48 2007 recovered 75223 relations Fri Jul 13 23:21:48 2007 recovered 67365 polynomials Fri Jul 13 23:21:48 2007 attempting to build 52748 cycles Fri Jul 13 23:21:48 2007 found 52748 cycles in 1 passes Fri Jul 13 23:21:48 2007 distribution of cycle lengths: Fri Jul 13 23:21:48 2007 length 1 : 27073 Fri Jul 13 23:21:48 2007 length 2 : 25675 Fri Jul 13 23:21:48 2007 largest cycle: 2 relations Fri Jul 13 23:21:48 2007 matrix is 52647 x 52748 with weight 1615124 (avg 30.62/col) Fri Jul 13 23:21:48 2007 filtering completed in 4 passes Fri Jul 13 23:21:48 2007 matrix is 45423 x 45487 with weight 1365016 (avg 30.01/col) Fri Jul 13 23:21:49 2007 saving the first 48 matrix rows for later Fri Jul 13 23:21:49 2007 matrix is 45375 x 45487 with weight 1103284 (avg 24.25/col) Fri Jul 13 23:21:49 2007 matrix includes 32 packed rows Fri Jul 13 23:22:10 2007 lanczos halted after 719 iterations Fri Jul 13 23:22:10 2007 recovered 9 nontrivial dependencies Fri Jul 13 23:22:11 2007 prp33 factor: 103888204664039275506234925332227 Fri Jul 13 23:22:11 2007 prp51 factor: 322982960901345113517889401979443805784667940709243 Fri Jul 13 23:22:11 2007 elapsed time 00:17:15
5·10¹²⁴+3 = 5(0)₁₂₃3_<125> = 17 · 31 · 139 · 199 · 353 · 17749 · 4211985913711273004737734377_<28> · C84
C84 = P33 · P52
P33 = 128040753937687879477084697015491_<33>
P52 = 1015097562328485295738336683852546474132803693053831_<52>

Fri Jul 13 23:24:22 2007 Fri Jul 13 23:24:22 2007 Fri Jul 13 23:24:22 2007 Msieve v. 1.21 Fri Jul 13 23:24:22 2007 random seeds: 1a661020 c160427d Fri Jul 13 23:24:22 2007 factoring 129973857200848371297919511176220553709357372754369950897383608306308229333303896021 (84 digits) Fri Jul 13 23:24:23 2007 commencing quadratic sieve (83-digit input) Fri Jul 13 23:24:23 2007 using multiplier of 1 Fri Jul 13 23:24:23 2007 using 32kb Intel Core sieve core Fri Jul 13 23:24:23 2007 sieve interval: 12 blocks of size 32768 Fri Jul 13 23:24:23 2007 processing polynomials in batches of 17 Fri Jul 13 23:24:23 2007 using a sieve bound of 1388659 (53235 primes) Fri Jul 13 23:24:23 2007 using large prime bound of 120813333 (26 bits) Fri Jul 13 23:24:23 2007 using trial factoring cutoff of 27 bits Fri Jul 13 23:24:23 2007 polynomial 'A' values have 11 factors Fri Jul 13 23:45:21 2007 53475 relations (27195 full + 26280 combined from 283677 partial), need 53331 Fri Jul 13 23:45:21 2007 begin with 310872 relations Fri Jul 13 23:45:21 2007 reduce to 76468 relations in 2 passes Fri Jul 13 23:45:21 2007 attempting to read 76468 relations Fri Jul 13 23:45:21 2007 recovered 76468 relations Fri Jul 13 23:45:21 2007 recovered 69986 polynomials Fri Jul 13 23:45:21 2007 attempting to build 53475 cycles Fri Jul 13 23:45:21 2007 found 53475 cycles in 1 passes Fri Jul 13 23:45:21 2007 distribution of cycle lengths: Fri Jul 13 23:45:21 2007 length 1 : 27195 Fri Jul 13 23:45:21 2007 length 2 : 26280 Fri Jul 13 23:45:21 2007 largest cycle: 2 relations Fri Jul 13 23:45:21 2007 matrix is 53235 x 53475 with weight 1691816 (avg 31.64/col) Fri Jul 13 23:45:22 2007 filtering completed in 4 passes Fri Jul 13 23:45:22 2007 matrix is 46232 x 46296 with weight 1435739 (avg 31.01/col) Fri Jul 13 23:45:22 2007 saving the first 48 matrix rows for later Fri Jul 13 23:45:22 2007 matrix is 46184 x 46296 with weight 1076659 (avg 23.26/col) Fri Jul 13 23:45:22 2007 matrix includes 32 packed rows Fri Jul 13 23:45:47 2007 lanczos halted after 732 iterations Fri Jul 13 23:45:47 2007 recovered 12 nontrivial dependencies Fri Jul 13 23:45:47 2007 prp33 factor: 128040753937687879477084697015491 Fri Jul 13 23:45:47 2007 prp52 factor: 1015097562328485295738336683852546474132803693053831 Fri Jul 13 23:45:47 2007 elapsed time 00:21:25
5·10¹⁶⁵-3 = 4(9)₁₆₄7_<166> = 19 · 57057317 · 98215463 · 2605629635761_<13> · 3946732535812616137099_<22> · C115
C115 = P34 · P81
P34 = 7543512127570632979961763022705421_<34>
P81 = 605342568468243602479097354297941125861779312424902349610895360925921457852332187_<81>

Number: 49997_165 N=4566409006574951863433979568362754800728318400898293602723291780776693632787788274495993362803824147636639137685727 ( 115 digits) Divisors found: r1=7543512127570632979961763022705421 (pp34) r2=605342568468243602479097354297941125861779312424902349610895360925921457852332187 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 27.02 hours. Scaled time: 57.56 units (timescale=2.130). Factorization parameters were as follows: name: 49997_165 n: 4566409006574951863433979568362754800728318400898293602723291780776693632787788274495993362803824147636639137685727 skew: 37063.96 # norm 4.73e+15 c5: 62160 c4: -3621719066 c3: -306726077373988 c2: 4532051020693653061 c1: 228973543810823218638998 c0: 1468727302885487696151709760 # alpha -5.55 Y1: 1746324969367 Y0: -9401858279023299564901 # Murphy_E 5.17e-10 # M 1002986331347959461341605441671137184505700766449988056152747414018476686730995147030702035468882560833614505929064 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3150001) Primes: RFBsize:256726, AFBsize:256682, largePrimes:7522227 encountered Relations: rels:7394243, finalFF:577903 Max relations in full relation-set: 28 Initial matrix: 513492 x 577903 with sparse part having weight 50045594. Pruned matrix : 462271 x 464902 with weight 35767881. Polynomial selection time: 1.34 hours. Total sieving time: 23.99 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.38 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 27.02 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
Jul 13, 2007 (4th): The factor table of 500...003 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jul 13, 2007 (3rd): By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs
5·10¹⁵⁸-3 = 4(9)₁₅₇7_<159> = 7 · 2111 · 80552352457081_<14> · 5710039315042630712188991_<25> · C116
C116 = P54 · P63
P54 = 467341027637686776935113873903056598872599949645184321_<54>
P63 = 157410063903105298144279249626151629802510455702264743972251571_<63>

Number: 49997_158 N=73564181024991174831410187304979775278602449566930735136444638612241727301463214510006040339766493271745851676818291 ( 116 digits) Divisors found: r1=467341027637686776935113873903056598872599949645184321 (pp54) r2=157410063903105298144279249626151629802510455702264743972251571 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 75.59 hours. Scaled time: 51.55 units (timescale=0.682). Factorization parameters were as follows: name: 49997_158 n: 73564181024991174831410187304979775278602449566930735136444638612241727301463214510006040339766493271745851676818291 skew: 42822.68 # norm 5.10e+15 c5: 37680 c4: 38633798 c3: -353231884823776 c2: 649944449545850313 c1: 316689536566344976014916 c0: 2229243313064835235066218784 # alpha -5.41 Y1: 756740286929 Y0: -18118035169349655294225 # Murphy_E 4.48e-10 # M 18062748841787132536527980613922191917491498627232287844155502604722767071327377360711903467081749263690925827819192 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3690001) Primes: RFBsize:315948, AFBsize:316005, largePrimes:7444584 encountered Relations: rels:7386540, finalFF:708105 Max relations in full relation-set: 0 Initial matrix: 632036 x 708105 with sparse part having weight 58435719. Pruned matrix : 566947 x 570171 with weight 38719113. Total sieving time: 58.58 hours. Total relation processing time: 0.57 hours. Matrix solve time: 15.99 hours. Time per square root: 0.46 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 75.59 hours. --------- CPU info (if available) ----------
Jul 13, 2007 (2nd): By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000
(7·10¹⁵⁸-61)/9 = (7)₁₅₇1_<158> = 469891 · 36460481 · 4181947377644793050081_<22> · C124
C124 = P35 · P89
P35 = 19452134249342894566208338343315587_<35>
P89 = 55807194183615693406796837297244974493029600283991480615392292095590717453155106764298483_<89>
Jul 13, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon, GMP-ECM 5.0 B1=1221000
(64·10¹⁵⁷-1)/9 = 7(1)₁₅₇_<158> = 8564115301768762508376928872997_<31> · C127
C127 = P57 · P71
P57 = 311235374037474312294580186612322910045517898252957252213_<57>
P71 = 26678782543165187104805765400094072904958914109911757415689580416168751_<71>

Number: n N=8303380863686457181005966020913589977121038158477222397503411687450746021165003481262209392026801408206039035454342249876195963 ( 127 digits) SNFS difficulty: 158 digits. Divisors found: r1=311235374037474312294580186612322910045517898252957252213 (pp57) r2=26678782543165187104805765400094072904958914109911757415689580416168751 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.20 hours. Scaled time: 42.30 units (timescale=1.449). Factorization parameters were as follows: name: KA_7_1_157 n: 8303380863686457181005966020913589977121038158477222397503411687450746021165003481262209392026801408206039035454342249876195963 skew: 0.35 deg: 5 c5: 200 c0: -1 m: 20000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1300001) Primes: RFBsize:250150, AFBsize:249566, largePrimes:7196272 encountered Relations: rels:6819995, finalFF:650477 Max relations in full relation-set: 28 Initial matrix: 499781 x 650477 with sparse part having weight 38973134. Pruned matrix : 364784 x 367346 with weight 19461875. Total sieving time: 25.94 hours. Total relation processing time: 0.19 hours. Matrix solve time: 2.83 hours. Total square root time: 0.23 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 29.20 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(13·10¹⁶⁰-1)/3 = 4(3)₁₆₀_<161> = 61 · 10722039721_<11> · C149
C149 = P40 · P46 · P65
P40 = 1478358147879228767608167158274095081731_<40>
P46 = 1068416170500962398505260990592751451937327749_<46>
P65 = 41946404360747518012731992568602333958344340144878162072473881247_<65>

Number: n N=44816216713394732869400742251936381608859550861620422044292600609519547873818196195562696333410057367543823003 ( 110 digits) SNFS difficulty: 161 digits. Divisors found: r1=1068416170500962398505260990592751451937327749 (pp46) r2=41946404360747518012731992568602333958344340144878162072473881247 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 41.22 hours. Scaled time: 49.26 units (timescale=1.195). Factorization parameters were as follows: name: KA_4_3_160 n: 44816216713394732869400742251936381608859550861620422044292600609519547873818196195562696333410057367543823003 # n: 66254419135368374354145868844236142720498084646190457527394820437684299192700760966498827238982222849523472761840642307270779277283858346731482858193 type: snfs skew: 0.60 deg: 5 c5: 13 c0: -1 m: 100000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:250150, AFBsize:249271, largePrimes:6713157 encountered Relations: rels:6239590, finalFF:580304 Max relations in full relation-set: 28 Initial matrix: 499486 x 580304 with sparse part having weight 30086204. Pruned matrix : 422637 x 425198 with weight 17790023. Total sieving time: 37.50 hours. Total relation processing time: 0.30 hours. Matrix solve time: 3.33 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000 total time: 41.22 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 12, 2007 (3rd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(2·10¹⁶⁴+61)/9 = (2)₁₆₃9_<164> = 8599 · C160
C160 = P65 · P96
P65 = 22651222927647321814936310172131574319011957238861315512443742367_<65>
P96 = 114090079554391502386878822975570247933855139052610776246086403516712638744974826517502878472813_<96>

Number: n N=2584279825819539739763021539972348205863730924784535669522295874197258079104805468336111434146089338553578581488803607654636844077476709178069801398095385768371 ( 160 digits) SNFS difficulty: 165 digits. Divisors found: r1=22651222927647321814936310172131574319011957238861315512443742367 (pp65) r2=114090079554391502386878822975570247933855139052610776246086403516712638744974826517502878472813 (pp96) Version: GGNFS-0.77.1-20051202-athlon Total time: 61.85 hours. Scaled time: 81.83 units (timescale=1.323). Factorization parameters were as follows: name: KA_2_163_9 n: 2584279825819539739763021539972348205863730924784535669522295874197258079104805468336111434146089338553578581488803607654636844077476709178069801398095385768371 skew: 3.14 deg: 5 c5: 1 c0: 305 m: 1000000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2500001) Primes: RFBsize:283146, AFBsize:282858, largePrimes:7623038 encountered Relations: rels:7210159, finalFF:669993 Max relations in full relation-set: 48 Initial matrix: 566068 x 669993 with sparse part having weight 44463704. Pruned matrix : 477178 x 480072 with weight 26963646. Total sieving time: 55.32 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.10 hours. Total square root time: 0.18 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 61.85 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 12, 2007 (2nd): By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, GGNFS-0.77.1-20050930-pentium3 gnfs
(43·10¹⁶⁰-7)/9 = 4(7)₁₆₀_<161> = 5007179 · 7008751163_<10> · C145
C145 = P28 · C117
P28 = 4421264001211142317908244507_<28>
C117 = [307925559846392608191890342655880287652240774038193999902100985083530393790025178760683643373658220133542015572724043_<117>]
5·10¹⁷¹-3 = 4(9)₁₇₀7_<172> = 46000847 · 6121638571_<10> · 958447987411_<12> · 6312681043024475375491430161_<28> · C115
C115 = P45 · P71
P45 = 241198112402284085400049735671995479639288153_<45>
P71 = 12166907050378837298642013658257125610939904245160777794608634185199787_<71>

Number: 49997_171 N=2934635014325417516096701273747698164950838782296104637022869061437943116969747674977296282584317681872004767223411 ( 115 digits) Divisors found: r1=241198112402284085400049735671995479639288153 (pp45) r2=12166907050378837298642013658257125610939904245160777794608634185199787 (pp71) Version: GGNFS-0.77.1-20050930-pentium3 Total time: 26.09 hours. Scaled time: 7.75 units (timescale=0.297). Factorization parameters were as follows: name: 49997_171 n: 2934635014325417516096701273747698164950838782296104637022869061437943116969747674977296282584317681872004767223411 skew: 74056.80 # norm 1.29e+16 c5: 33600 c4: -3746392840 c3: -544442683811411 c2: 17054315618171851220 c1: 1217441680378892041663324 c0: -19655107573523269710901021680 # alpha -6.40 Y1: 1547472681557 Y0: -9732950247591089513527 # Murphy_E 5.29e-10 # M 1529526105085601883212096215779823540361348901810900877749446168933591385261591139256845661451207162190541862940240 type: gnfs rlim: 3600000 alim: 3600000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3600000/3600000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1800000, 3150000) Primes: RFBsize:256726, AFBsize:257300, largePrimes:7660466 encountered Relations: rels:7701963, finalFF:702520 Max relations in full relation-set: 28 Initial matrix: 514107 x 702520 with sparse part having weight 63078489. Pruned matrix : 368728 x 371362 with weight 37331473. Total sieving time: 23.97 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.93 hours. Time per square root: 1.02 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3600000,3600000,27,27,50,50,2.4,2.4,75000 total time: 26.09 hours. --------- CPU info (if available) ----------
Jul 12, 2007: By Jo Yeong Uk / Msieve v. 1.21
5·10¹⁵⁹-3 = 4(9)₁₅₈7_<160> = 23 · 10611966307_<11> · 4368534516821_<13> · 5006536233163_<13> · 3603669365157562557541028774720347_<34> · C90
C90 = P42 · P49
P42 = 191027376246576260076013368620556928804243_<42>
P49 = 1360606753360105851237415658886311322045879676319_<49>

Thu Jul 12 08:25:38 2007 Thu Jul 12 08:25:38 2007 Thu Jul 12 08:25:38 2007 Msieve v. 1.21 Thu Jul 12 08:25:38 2007 random seeds: 3396b730 2c6be133 Thu Jul 12 08:25:38 2007 factoring 259913138197753528521831503031382370167660110953871390680307688669870475962297396553821517 (90 digits) Thu Jul 12 08:25:38 2007 commencing quadratic sieve (90-digit input) Thu Jul 12 08:25:38 2007 using multiplier of 29 Thu Jul 12 08:25:38 2007 using 32kb Intel Core sieve core Thu Jul 12 08:25:38 2007 sieve interval: 36 blocks of size 32768 Thu Jul 12 08:25:38 2007 processing polynomials in batches of 6 Thu Jul 12 08:25:38 2007 using a sieve bound of 1584931 (59872 primes) Thu Jul 12 08:25:38 2007 using large prime bound of 126794480 (26 bits) Thu Jul 12 08:25:38 2007 using double large prime bound of 385106280791040 (42-49 bits) Thu Jul 12 08:25:38 2007 using trial factoring cutoff of 49 bits Thu Jul 12 08:25:38 2007 polynomial 'A' values have 12 factors Thu Jul 12 09:21:20 2007 60317 relations (16443 full + 43874 combined from 635017 partial), need 59968 Thu Jul 12 09:21:20 2007 begin with 651460 relations Thu Jul 12 09:21:20 2007 reduce to 145915 relations in 10 passes Thu Jul 12 09:21:20 2007 attempting to read 145915 relations Thu Jul 12 09:21:22 2007 recovered 145915 relations Thu Jul 12 09:21:22 2007 recovered 124747 polynomials Thu Jul 12 09:21:22 2007 attempting to build 60317 cycles Thu Jul 12 09:21:22 2007 found 60317 cycles in 6 passes Thu Jul 12 09:21:22 2007 distribution of cycle lengths: Thu Jul 12 09:21:22 2007 length 1 : 16443 Thu Jul 12 09:21:22 2007 length 2 : 11820 Thu Jul 12 09:21:22 2007 length 3 : 10631 Thu Jul 12 09:21:22 2007 length 4 : 7828 Thu Jul 12 09:21:22 2007 length 5 : 5627 Thu Jul 12 09:21:22 2007 length 6 : 3460 Thu Jul 12 09:21:22 2007 length 7 : 2063 Thu Jul 12 09:21:22 2007 length 9+: 2445 Thu Jul 12 09:21:22 2007 largest cycle: 20 relations Thu Jul 12 09:21:22 2007 matrix is 59872 x 60317 with weight 3587835 (avg 59.48/col) Thu Jul 12 09:21:22 2007 filtering completed in 3 passes Thu Jul 12 09:21:22 2007 matrix is 58252 x 58316 with weight 3393360 (avg 58.19/col) Thu Jul 12 09:21:23 2007 saving the first 48 matrix rows for later Thu Jul 12 09:21:23 2007 matrix is 58204 x 58316 with weight 2649013 (avg 45.43/col) Thu Jul 12 09:21:23 2007 matrix includes 32 packed rows Thu Jul 12 09:21:23 2007 using block size 23326 for processor cache size 4096 kB Thu Jul 12 09:21:39 2007 lanczos halted after 922 iterations Thu Jul 12 09:21:39 2007 recovered 17 nontrivial dependencies Thu Jul 12 09:21:39 2007 prp42 factor: 191027376246576260076013368620556928804243 Thu Jul 12 09:21:39 2007 prp49 factor: 1360606753360105851237415658886311322045879676319 Thu Jul 12 09:21:39 2007 elapsed time 00:56:01
Jul 11, 2007 (4th): By Maksym Voznyy
(10²⁷⁰³⁴³-1)/9 is PRP.
Jul 11, 2007 (3rd): By Jo Yeong Uk / Msieve v. 1.21
(2·10¹⁵⁸+61)/9 = (2)₁₅₇9_<158> = 313251391 · 4232920182402397664794465973_<28> · 8180004382945353667194983565175097_<34> · C88
C88 = P37 · P52
P37 = 1173816789875564874460017932751680269_<37>
P52 = 1745422399702334476184140689167794733731023214569971_<52>

Wed Jul 11 19:35:21 2007 Wed Jul 11 19:35:21 2007 Wed Jul 11 19:35:21 2007 Msieve v. 1.21 Wed Jul 11 19:35:21 2007 random seeds: 5b524611 d566dca2 Wed Jul 11 19:35:21 2007 factoring 2048806118195499354913542723718755940102140970322140966978079897796843232293172520602199 (88 digits) Wed Jul 11 19:35:21 2007 commencing quadratic sieve (88-digit input) Wed Jul 11 19:35:21 2007 using multiplier of 35 Wed Jul 11 19:35:21 2007 using 32kb Intel Core sieve core Wed Jul 11 19:35:21 2007 sieve interval: 25 blocks of size 32768 Wed Jul 11 19:35:21 2007 processing polynomials in batches of 9 Wed Jul 11 19:35:21 2007 using a sieve bound of 1516987 (57667 primes) Wed Jul 11 19:35:21 2007 using large prime bound of 121358960 (26 bits) Wed Jul 11 19:35:21 2007 using double large prime bound of 355901048223760 (42-49 bits) Wed Jul 11 19:35:21 2007 using trial factoring cutoff of 49 bits Wed Jul 11 19:35:21 2007 polynomial 'A' values have 11 factors Wed Jul 11 20:23:35 2007 57807 relations (15424 full + 42383 combined from 616759 partial), need 57763 Wed Jul 11 20:23:36 2007 begin with 632183 relations Wed Jul 11 20:23:36 2007 reduce to 141408 relations in 12 passes Wed Jul 11 20:23:36 2007 attempting to read 141408 relations Wed Jul 11 20:23:37 2007 recovered 141408 relations Wed Jul 11 20:23:37 2007 recovered 123274 polynomials Wed Jul 11 20:23:37 2007 attempting to build 57807 cycles Wed Jul 11 20:23:37 2007 found 57807 cycles in 5 passes Wed Jul 11 20:23:37 2007 distribution of cycle lengths: Wed Jul 11 20:23:37 2007 length 1 : 15424 Wed Jul 11 20:23:37 2007 length 2 : 11026 Wed Jul 11 20:23:37 2007 length 3 : 10054 Wed Jul 11 20:23:37 2007 length 4 : 7830 Wed Jul 11 20:23:37 2007 length 5 : 5352 Wed Jul 11 20:23:37 2007 length 6 : 3440 Wed Jul 11 20:23:37 2007 length 7 : 2150 Wed Jul 11 20:23:37 2007 length 9+: 2531 Wed Jul 11 20:23:37 2007 largest cycle: 17 relations Wed Jul 11 20:23:37 2007 matrix is 57667 x 57807 with weight 3502421 (avg 60.59/col) Wed Jul 11 20:23:38 2007 filtering completed in 4 passes Wed Jul 11 20:23:38 2007 matrix is 56148 x 56212 with weight 3349462 (avg 59.59/col) Wed Jul 11 20:23:38 2007 saving the first 48 matrix rows for later Wed Jul 11 20:23:39 2007 matrix is 56100 x 56212 with weight 2776045 (avg 49.39/col) Wed Jul 11 20:23:39 2007 matrix includes 32 packed rows Wed Jul 11 20:23:39 2007 using block size 22484 for processor cache size 4096 kB Wed Jul 11 20:23:54 2007 lanczos halted after 888 iterations Wed Jul 11 20:23:54 2007 recovered 19 nontrivial dependencies Wed Jul 11 20:23:55 2007 prp37 factor: 1173816789875564874460017932751680269 Wed Jul 11 20:23:55 2007 prp52 factor: 1745422399702334476184140689167794733731023214569971 Wed Jul 11 20:23:55 2007 elapsed time 00:48:34
(23·10¹⁵⁷+1)/3 = 7(6)₁₅₆7_<158> = 7² · 11 · 103 · 3931093 · 187918820385783433750403_<24> · 20896654878601350360268149361_<29> · C95
C95 = P41 · P55
P41 = 78193602897564757645098493674472199158583_<41>
P55 = 1144060525373511021818728474775835114113368172612932063_<55>

Wed Jul 11 20:25:41 2007 Wed Jul 11 20:25:41 2007 Wed Jul 11 20:25:41 2007 Msieve v. 1.21 Wed Jul 11 20:25:41 2007 random seeds: 124ff28c e04ddd07 Wed Jul 11 20:25:41 2007 factoring 89458214411835630370906446629114652455106051226197501160191146683705663732977188286693142346729 (95 digits) Wed Jul 11 20:25:41 2007 commencing quadratic sieve (95-digit input) Wed Jul 11 20:25:42 2007 using multiplier of 6 Wed Jul 11 20:25:42 2007 using 32kb Intel Core sieve core Wed Jul 11 20:25:42 2007 sieve interval: 36 blocks of size 32768 Wed Jul 11 20:25:42 2007 processing polynomials in batches of 6 Wed Jul 11 20:25:42 2007 using a sieve bound of 2196599 (81150 primes) Wed Jul 11 20:25:42 2007 using large prime bound of 329489850 (28 bits) Wed Jul 11 20:25:42 2007 using double large prime bound of 2148402323041500 (43-51 bits) Wed Jul 11 20:25:42 2007 using trial factoring cutoff of 51 bits Wed Jul 11 20:25:42 2007 polynomial 'A' values have 12 factors Wed Jul 11 23:02:25 2007 81576 relations (20604 full + 60972 combined from 1201596 partial), need 81246 Wed Jul 11 23:02:25 2007 begin with 1222200 relations Wed Jul 11 23:02:26 2007 reduce to 209892 relations in 12 passes Wed Jul 11 23:02:26 2007 attempting to read 209892 relations Wed Jul 11 23:02:28 2007 recovered 209892 relations Wed Jul 11 23:02:28 2007 recovered 192187 polynomials Wed Jul 11 23:02:28 2007 attempting to build 81576 cycles Wed Jul 11 23:02:28 2007 found 81576 cycles in 6 passes Wed Jul 11 23:02:28 2007 distribution of cycle lengths: Wed Jul 11 23:02:28 2007 length 1 : 20604 Wed Jul 11 23:02:28 2007 length 2 : 14493 Wed Jul 11 23:02:28 2007 length 3 : 13853 Wed Jul 11 23:02:28 2007 length 4 : 11006 Wed Jul 11 23:02:28 2007 length 5 : 8296 Wed Jul 11 23:02:28 2007 length 6 : 5403 Wed Jul 11 23:02:28 2007 length 7 : 3318 Wed Jul 11 23:02:28 2007 length 9+: 4603 Wed Jul 11 23:02:28 2007 largest cycle: 19 relations Wed Jul 11 23:02:28 2007 matrix is 81150 x 81576 with weight 5566718 (avg 68.24/col) Wed Jul 11 23:02:29 2007 filtering completed in 4 passes Wed Jul 11 23:02:29 2007 matrix is 79471 x 79535 with weight 5325669 (avg 66.96/col) Wed Jul 11 23:02:30 2007 saving the first 48 matrix rows for later Wed Jul 11 23:02:30 2007 matrix is 79423 x 79535 with weight 4374458 (avg 55.00/col) Wed Jul 11 23:02:30 2007 matrix includes 32 packed rows Wed Jul 11 23:02:30 2007 using block size 31814 for processor cache size 4096 kB Wed Jul 11 23:03:05 2007 lanczos error: not all columns used Wed Jul 11 23:03:05 2007 lanczos halted after 1257 iterations Wed Jul 11 23:03:05 2007 linear algebra failed; retrying... Wed Jul 11 23:03:40 2007 lanczos halted after 1258 iterations Wed Jul 11 23:03:40 2007 recovered 18 nontrivial dependencies Wed Jul 11 23:03:41 2007 prp41 factor: 78193602897564757645098493674472199158583 Wed Jul 11 23:03:41 2007 prp55 factor: 1144060525373511021818728474775835114113368172612932063 Wed Jul 11 23:03:41 2007 elapsed time 02:38:00
5·10¹⁵⁹-3 = 4(9)₁₅₈7_<160> = 23 · 10611966307_<11> · 4368534516821_<13> · 5006536233163_<13> · C123
C123 = P34 · C90
P34 = 3603669365157562557541028774720347_<34>
C90 = [259913138197753528521831503031382370167660110953871390680307688669870475962297396553821517_<90>]
Jul 11, 2007 (2nd): By Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, GGNFS-0.77.1-20050930-nocona gnfs
(7·10¹⁵⁷-1)/3 = 2(3)₁₅₇_<158> = 61 · 1279 · 14635063 · 3987383581_<10> · 4581360201133_<13> · C124
C124 = P42 · P83
P42 = 111804472216234621446149216648206991096293_<42>
P83 = 10005531849149209867385888327748278326019822739848288047545094990750961458768022501_<83>
(7·10¹⁵⁹-61)/9 = (7)₁₅₈1_<159> = 3³ · 43 · 263 · 349831 · 17126917 · 28619057539265783684510425072387757_<35> · C107
C107 = P33 · P74
P33 = 797403209935797539434823436791693_<33>
P74 = 18629310032851632076163322531678663673503016373642711951312754825678195311_<74>

Number: 77771_159 N=14855071619085049328530992857412182242694733285669768452444236785568599716426578493792762350613756076351523 ( 107 digits) Divisors found: r1=797403209935797539434823436791693 (pp33) r2=18629310032851632076163322531678663673503016373642711951312754825678195311 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.49 hours. Scaled time: 22.36 units (timescale=2.132). Factorization parameters were as follows: name: 77771_159 n: 14855071619085049328530992857412182242694733285669768452444236785568599716426578493792762350613756076351523 skew: 17252.59 # norm 4.53e+14 c5: 24360 c4: 1552062034 c3: -12155455866301 c2: -501419086915678603 c1: 4107034064874536958069 c0: -110865863932083856105047 # alpha -5.86 Y1: 159151859009 Y0: -227528404968347614694 # Murphy_E 1.61e-09 # M 13177898755741697868442278760361905096607553508203604547219497232778306454584708936145593728319772417207638 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [900000, 1440001) Primes: RFBsize:135072, AFBsize:135225, largePrimes:4558581 encountered Relations: rels:4599743, finalFF:363106 Max relations in full relation-set: 28 Initial matrix: 270381 x 363106 with sparse part having weight 34524026. Pruned matrix : 218438 x 219853 with weight 18421094. Polynomial selection time: 0.54 hours. Total sieving time: 9.58 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.21 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 10.49 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.36 BogoMIPS (lpj=2407683) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405129) Total of 4 processors activated (19246.12 BogoMIPS).
(23·10¹⁵⁷+1)/3 = 7(6)₁₅₆7_<158> = 7² · 11 · 103 · 3931093 · 187918820385783433750403_<24> · C124
C124 = P29 · C95
P29 = 20896654878601350360268149361_<29>
C95 = [89458214411835630370906446629114652455106051226197501160191146683705663732977188286693142346729_<95>]
3·10¹⁵⁹-1 = 2(9)₁₅₉_<160> = 1321 · 6967 · 398760584767619777_<18> · C135
C135 = P34 · P102
P34 = 1365996837467415111026906770750469_<34>
P102 = 598426350404332450433128876484310209991358869759713755798077815328602741567697247226824883321819832989_<102>
(2·10¹⁵⁸+61)/9 = (2)₁₅₇9_<158> = 313251391 · 4232920182402397664794465973_<28> · C122
C122 = P34 · C88
P34 = 8180004382945353667194983565175097_<34>
C88 = [2048806118195499354913542723718755940102140970322140966978079897796843232293172520602199_<88>]
Jul 11, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
5·10¹⁵⁶-3 = 4(9)₁₅₅7_<157> = 1973 · 2053063 · C148
C148 = P53 · P95
P53 = 88666131158617287229707084514778242205719232955907723_<53>
P95 = 13921399093960280961780774878816447259601802769512930326480215435970153126193617396031190315661_<95>

Number: n N=1234356597976538139280142028842356943894606126781952641732207333922863854916604980909466777183418645194248264906713195221843429918982863975157749903 ( 148 digits) SNFS difficulty: 156 digits. Divisors found: r1=88666131158617287229707084514778242205719232955907723 (pp53) r2=13921399093960280961780774878816447259601802769512930326480215435970153126193617396031190315661 (pp95) Version: GGNFS-0.77.1-20051202-athlon Total time: 33.75 hours. Scaled time: 40.30 units (timescale=1.194). Factorization parameters were as follows: name: KA_4_9_155_7 n: 1234356597976538139280142028842356943894606126781952641732207333922863854916604980909466777183418645194248264906713195221843429918982863975157749903 type: snfs skew: 0.57 deg: 5 c5: 50 c0: -3 m: 10000000000000000000000000000000 rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:250150, AFBsize:250256, largePrimes:6432804 encountered Relations: rels:5951628, finalFF:565359 Max relations in full relation-set: 28 Initial matrix: 500471 x 565359 with sparse part having weight 25798180. Pruned matrix : 434020 x 436586 with weight 15831361. Total sieving time: 30.40 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.06 hours. Total square root time: 0.08 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000 total time: 33.75 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
5·10¹⁶²-3 = 4(9)₁₆₁7_<163> = C163
C163 = P49 · P114
P49 = 8544406184158733288717788329856875808280189100763_<49>
P114 = 585178172974730942884427619934926129351771486625491327311590996532550927049973737667478017100778019085012646208519_<114>

Number: n N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 163 digits) SNFS difficulty: 162 digits. Divisors found: r1=8544406184158733288717788329856875808280189100763 (pp49) r2=585178172974730942884427619934926129351771486625491327311590996532550927049973737667478017100778019085012646208519 (pp114) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.47 hours. Scaled time: 63.03 units (timescale=1.450). Factorization parameters were as follows: name: KA_4_9_161_7 n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 skew: 0.36 deg: 5 c5: 500 c0: -3 m: 100000000000000000000000000000000 type: snfs rlim: 4000000 alim: 4000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1900001) Primes: RFBsize:283146, AFBsize:282917, largePrimes:7337299 encountered Relations: rels:6908627, finalFF:639847 Max relations in full relation-set: 28 Initial matrix: 566129 x 639847 with sparse part having weight 37255811. Pruned matrix : 497961 x 500855 with weight 23972880. Total sieving time: 37.76 hours. Total relation processing time: 0.22 hours. Matrix solve time: 5.18 hours. Total square root time: 0.30 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,28,28,48,48,2.5,2.5,100000 total time: 43.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Jul 10, 2007 (2nd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
5·10¹⁵⁰-3 = 4(9)₁₄₉7_<151> = 67 · 3116051 · 28212754553911189_<17> · C126
C126 = P61 · P65
P61 = 9067846705098386264105687808083859986016022518939144596253611_<61>
P65 = 93614039200569581281008047873083290213666429881740082969167944179_<65>

Number: n N=848877756915836047327005956367688030754050414861578135676328925892022810228355445983559089497621983270454716296031158175180369 ( 126 digits) SNFS difficulty: 150 digits. Divisors found: r1=9067846705098386264105687808083859986016022518939144596253611 (pp61) r2=93614039200569581281008047873083290213666429881740082969167944179 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 15.95 hours. Scaled time: 21.05 units (timescale=1.320). Factorization parameters were as follows: name: KA_4_9_149_7 n: 848877756915836047327005956367688030754050414861578135676328925892022810228355445983559089497621983270454716296031158175180369 skew: 0.90 deg: 5 c5: 5 c0: -3 m: 1000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 700001) Primes: RFBsize:250150, AFBsize:249871, largePrimes:6181244 encountered Relations: rels:5785296, finalFF:582205 Max relations in full relation-set: 48 Initial matrix: 500086 x 582205 with sparse part having weight 24719108. Pruned matrix : 412540 x 415104 with weight 13084779. Total sieving time: 13.54 hours. Total relation processing time: 0.15 hours. Matrix solve time: 2.16 hours. Total square root time: 0.10 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 15.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Jul 10, 2007: By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
5·10¹⁴⁶-3 = 4(9)₁₄₅7_<147> = 7 · 797 · 239329 · 93483761128799642385893_<23> · C115
C115 = P45 · P71
P45 = 128452413621408811962701715902967521602390963_<45>
P71 = 31184577944989473183131805515755584538817242291977209687873566291246313_<71>

Number: 49997_146 N=4005734304798850622326249951143037423616711644650164979183042659808685924415865726837714445893729270428277958269419 ( 115 digits) Divisors found: r1=128452413621408811962701715902967521602390963 (pp45) r2=31184577944989473183131805515755584538817242291977209687873566291246313 (pp71) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 62.55 hours. Scaled time: 41.60 units (timescale=0.665). Factorization parameters were as follows: name: 49997_146 n: 4005734304798850622326249951143037423616711644650164979183042659808685924415865726837714445893729270428277958269419 skew: 36021.67 # norm 2.21e+16 c5: 39600 c4: -5544913316 c3: 808385282931308 c2: 4256940067114749501 c1: -289150373904486983283538 c0: -1001954365526770591150788255 # alpha -6.85 Y1: 195581790739 Y0: -10022997639641682506218 # Murphy_E 5.45e-10 # M 830918682632186915924213558878628963560867949599055263643356419771358536458349787830192216066526682747955092642640 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2950001) Primes: RFBsize:250150, AFBsize:250336, largePrimes:7615163 encountered Relations: rels:7554461, finalFF:563033 Max relations in full relation-set: 0 Initial matrix: 500568 x 563033 with sparse part having weight 41679643. Pruned matrix : 450560 x 453126 with weight 30186049. Polynomial selection time: 2.62 hours. Total sieving time: 50.83 hours. Total relation processing time: 0.45 hours. Matrix solve time: 8.26 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 62.55 hours. --------- CPU info (if available) ----------
Jul 9, 2007 (2nd): By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
5·10¹⁴⁹-3 = 4(9)₁₄₈7_<150> = 29 · 6983106863_<10> · C139
C139 = P48 · P92
P48 = 208747880384388120276325252490914165886057736101_<48>
P92 = 11827725694599174236257190431349303144204489375682681972938043512380134113838243183754907011_<92>

Number: n N=2469012668515542318460277664481179790737291307383604284844296502512716634601796579368377536357106844920154402705397083070678261616432704111 ( 139 digits) SNFS difficulty: 150 digits. Divisors found: r1=208747880384388120276325252490914165886057736101 (pp48) r2=11827725694599174236257190431349303144204489375682681972938043512380134113838243183754907011 (pp92) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.93 hours. Scaled time: 18.71 units (timescale=1.447). Factorization parameters were as follows: name: KA_4_9_148_7 n: 2469012668515542318460277664481179790737291307383604284844296502512716634601796579368377536357106844920154402705397083070678261616432704111 skew: 1.43 deg: 5 c5: 1 c0: -6 m: 1000000000000000000000000000000 type: snfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:250150, AFBsize:250351, largePrimes:5947139 encountered Relations: rels:5574191, finalFF:579093 Max relations in full relation-set: 28 Initial matrix: 500565 x 579093 with sparse part having weight 22226434. Pruned matrix : 404909 x 407475 with weight 11698567. Total sieving time: 10.91 hours. Total relation processing time: 0.13 hours. Matrix solve time: 1.85 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 12.93 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Jul 9, 2007: By Robert Backstrom / GGNFS-0.77.1-20051202-athlon
(5·10¹⁷⁹-17)/3 = 1(6)₁₇₈1_<180> = 11 · C179
C179 = P88 · P91
P88 = 1639019173770832049695358993053022960848462753158292470147701013746739785573856983124029_<88>
P91 = 9244257415644875817165595378275105183625338529342101678091693130990885547247677848761743419_<91>

Number: n N=15151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151 ( 179 digits) SNFS difficulty: 180 digits. Divisors found: r1=1639019173770832049695358993053022960848462753158292470147701013746739785573856983124029 (pp88) r2=9244257415644875817165595378275105183625338529342101678091693130990885547247677848761743419 (pp91) Version: GGNFS-0.77.1-20051202-athlon Total time: 227.13 hours. Scaled time: 330.25 units (timescale=1.454). Factorization parameters were as follows: name: KA_1_6_178_1 n: 15151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151515151 skew: 2.02 deg: 5 c5: 1 c0: -34 m: 1000000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 3200001) Primes: RFBsize:380800, AFBsize:380652, largePrimes:8184922 encountered Relations: rels:7889387, finalFF:860871 Max relations in full relation-set: 28 Initial matrix: 761516 x 860871 with sparse part having weight 49715353. Pruned matrix : 669290 x 673161 with weight 32998412. Total sieving time: 216.42 hours. Total relation processing time: 0.31 hours. Matrix solve time: 10.21 hours. Total square root time: 0.20 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,180,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 227.13 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
P88 is the largest factor found by GGNFS so far in our tables. Congratulations!
(4·10¹⁷⁴+23)/9 = (4)₁₇₃7_<174> = 3 · C174
C174 = P66 · P108
P66 = 431698729585373966167026238230882951903861668583514905584774408843_<66>
P108 = 343174853190875443246946483687163515522963880644358945766137050568648583698244978599326968646362907761905343_<108>

Number: n N=148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 ( 174 digits) SNFS difficulty: 175 digits. Divisors found: r1=431698729585373966167026238230882951903861668583514905584774408843 (pp66) r2=343174853190875443246946483687163515522963880644358945766137050568648583698244978599326968646362907761905343 (pp108) Version: GGNFS-0.77.1-20051202-athlon Total time: 219.68 hours. Scaled time: 290.86 units (timescale=1.324). Factorization parameters were as follows: name: KA_4_173_7 n: 148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149 skew: 2.25 deg: 5 c5: 2 c0: 115 m: 100000000000000000000000000000000000 type: snfs rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 8500001) Primes: RFBsize:380800, AFBsize:380192, largePrimes:9150545 encountered Relations: rels:8710774, finalFF:854421 Max relations in full relation-set: 48 Initial matrix: 761057 x 854421 with sparse part having weight 74383121. Pruned matrix : 692647 x 696516 with weight 56412545. Total sieving time: 199.12 hours. Total relation processing time: 0.62 hours. Matrix solve time: 19.49 hours. Total square root time: 0.45 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.5,2.5,100000 total time: 219.68 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(7·10¹⁷⁴-61)/9 = (7)₁₇₃1_<174> = 3 · C174
C174 = P66 · P108
P66 = 592183130436863192470465165361108333811673611186266348002248596759_<66>
P108 = 437802507254807238882928297138447646164159872834322448723319030478316704747682896028097705022390728332298223_<108>

Number: n N=259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257 ( 174 digits) SNFS difficulty: 175 digits. Divisors found: r1=592183130436863192470465165361108333811673611186266348002248596759 (pp66) r2=437802507254807238882928297138447646164159872834322448723319030478316704747682896028097705022390728332298223 (pp108) Version: GGNFS-0.77.1-20051202-athlon Total time: 333.18 hours. Scaled time: 397.82 units (timescale=1.194). Factorization parameters were as follows: name: KA_7_173_1 n: 259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259257 type: snfs skew: 2.44 deg: 5 c5: 7 c0: -610 m: 100000000000000000000000000000000000 rlim: 5500000 alim: 5500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 11600001) Primes: RFBsize:380800, AFBsize:381368, largePrimes:8890149 encountered Relations: rels:8648810, finalFF:860116 Max relations in full relation-set: 28 Initial matrix: 762233 x 860116 with sparse part having weight 86306908. Pruned matrix : 693173 x 697048 with weight 70123858. Total sieving time: 307.41 hours. Total relation processing time: 0.72 hours. Matrix solve time: 24.26 hours. Total square root time: 0.79 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,5500000,5500000,28,28,48,48,2.6,2.6,100000 total time: 333.18 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Jul 8, 2007: By Yousuke Koide
10¹²⁷⁸+1 is divisible by 40006639726526214492389221911263641_<35>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jul 7, 2007 (3rd): By Torbjörn Granlund
(10⁸⁵⁷-1)/9 is divisible by 600675575158100017424925351819839677_<36>, cofactor is probably prime
10⁵³¹+1 is divisible by 216300405364911283995901633078340436727_<39>
10⁸⁴¹+1 is divisible by 1630777462352881403814023114519396413_<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Jul 7, 2007 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
5·10¹⁴⁷-3 = 4(9)₁₄₆7_<148> = 19 · 139 · 601 · 13681 · 40487 · 354995006736248519_<18> · C116
C116 = P47 · P70
P47 = 10067361505415681618873296936552921933923299611_<47>
P70 = 1591313628803614731260135467601813388393486021881617569796951585055279_<70>

Number: 49997_147 N=16020329569660849975695435240487629364228641450318647485024030704932582906631343798326668419485613524001679514196469 ( 116 digits) SNFS difficulty: 149 digits. Divisors found: r1=10067361505415681618873296936552921933923299611 (pp47) r2=1591313628803614731260135467601813388393486021881617569796951585055279 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.23 hours. Scaled time: 19.79 units (timescale=2.144). Factorization parameters were as follows: n: 16020329569660849975695435240487629364228641450318647485024030704932582906631343798326668419485613524001679514196469 m: 500000000000000000000000000000 c5: 4 c0: -75 skew: 1.8 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: RFBsize:135072, AFBsize:134758, largePrimes:3616122 encountered Relations: rels:3602120, finalFF:311536 Max relations in full relation-set: 28 Initial matrix: 269894 x 311536 with sparse part having weight 26078125. Pruned matrix : 251458 x 252871 with weight 18101350. Total sieving time: 8.87 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.28 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 9.23 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
5·10¹⁴⁸-3 = 4(9)₁₄₇7_<149> = 17 · 61 · 3907 · 184094837 · C134
C134 = P42 · P46 · P47
P42 = 856199339682423221681610853181988817318913_<42>
P46 = 1556144666064391456467500163826224366444427919_<46>
P47 = 50313134072976025481264005755700033644273942497_<47>

Number: 49997_148 N=67035712232671026578085702644158591186552652917191706966233004080754358180856116346537407110225442792919527957856093621681551793501359 ( 134 digits) SNFS difficulty: 150 digits. Divisors found: r1=856199339682423221681610853181988817318913 (pp42) r2=1556144666064391456467500163826224366444427919 (pp46) r3=50313134072976025481264005755700033644273942497 (pp47) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.81 hours. Scaled time: 22.89 units (timescale=2.117). Factorization parameters were as follows: n: 67035712232671026578085702644158591186552652917191706966233004080754358180856116346537407110225442792919527957856093621681551793501359 m: 1000000000000000000000000000000 c5: 1 c0: -60 skew: 2.27 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1575001) Primes: RFBsize:135072, AFBsize:134688, largePrimes:3788068 encountered Relations: rels:3897704, finalFF:405595 Max relations in full relation-set: 28 Initial matrix: 269824 x 405595 with sparse part having weight 37011153. Pruned matrix : 222190 x 223603 with weight 17763617. Total sieving time: 10.40 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.33 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 10.81 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
Jul 7, 2007: By Sinkiti Sibata / GGNFS-0.77.1-20060513-k8, GGNFS-0.77.1-20060722-pentium4
(32·10¹⁸⁶-23)/9 = 3(5)₁₈₅3_<187> = C187
C187 = P77 · P111
P77 = 22505468127454808181216964200487999120781593821049054585465704599969960629843_<77>
P111 = 157986296282283153038019270956995707149770776451983434848501382962868901158389576269567185495417338509918446971_<111>

Number: 35553_186 N=3555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 ( 187 digits) SNFS difficulty: 187 digits. Divisors found: r1=22505468127454808181216964200487999120781593821049054585465704599969960629843 (pp77) r2=157986296282283153038019270956995707149770776451983434848501382962868901158389576269567185495417338509918446971 (pp111) Version: GGNFS-0.77.1-20060513-k8 Total time: 935.90 hours. Scaled time: 1881.16 units (timescale=2.010). Factorization parameters were as follows: name: 35553_186 n: 3555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 m: 20000000000000000000000000000000000000 c5: 10 c0: -23 skew: 1.18 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 14600001) Primes: RFBsize:501962, AFBsize:502936, largePrimes:6862780 encountered Relations: rels:7364860, finalFF:1143693 Max relations in full relation-set: 28 Initial matrix: 1004964 x 1143693 with sparse part having weight 105432265. Pruned matrix : 897970 x 903058 with weight 86536058. Total sieving time: 920.03 hours. Total relation processing time: 0.64 hours. Matrix solve time: 14.83 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 935.90 hours. --------- CPU info (if available) ----------
3·10¹⁶⁴-1 = 2(9)₁₆₄_<165> = 13 · 2591 · C160
C160 = P47 · P50 · P65
P47 = 20864331285956384714363476632186247632145067881_<47>
P50 = 16745773198975668201316866017478902963614694091371_<50>
P65 = 25491818321127692702503378138106307806982680946323585329451086103_<65>

Number: 29999_164 N=8906570079862245049431463943235460024344624884956803135112668111510257399875308018881928569307959504794703559659175251610604756108422646438856396401745687735653 ( 160 digits) SNFS difficulty: 165 digits. Divisors found: r1=20864331285956384714363476632186247632145067881 (pp47) r2=16745773198975668201316866017478902963614694091371 (pp50) r3=25491818321127692702503378138106307806982680946323585329451086103 (pp65) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 125.82 hours. Scaled time: 85.56 units (timescale=0.680). Factorization parameters were as follows: name: 29999_164 n: 8906570079862245049431463943235460024344624884956803135112668111510257399875308018881928569307959504794703559659175251610604756108422646438856396401745687735653 m: 1000000000000000000000000000000000 c5: 3 c0: -10 skew: 1.27 type: snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2500000, 5400001) Primes: RFBsize:348513, AFBsize:348501, largePrimes:5894099 encountered Relations: rels:6079819, finalFF:784956 Max relations in full relation-set: 0 Initial matrix: 697079 x 784956 with sparse part having weight 43312634. Pruned matrix : 626895 x 630444 with weight 33519435. Total sieving time: 107.99 hours. Total relation processing time: 0.41 hours. Matrix solve time: 17.17 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 125.82 hours. --------- CPU info (if available) ----------
Jul 6, 2007 (4th): By Alban Nonymous
10¹⁰⁶³+1 is divisible by 2928852075918417027638457828557_<31>
10¹²¹⁷+1 is divisible by 1097021863038561688666089244771_<31>
10¹²⁴⁹+1 is divisible by 83933507135165614961893401401_<29>, cofactor is probably prime
10¹⁴²⁰+1 is divisible by 33233412196028093809254651841_<29>
10¹⁴⁸⁰+1 is divisible by 2922137698079622949054068972641_<31>
10¹⁶⁴³+1 is divisible by 1393949954184795816301811495623_<31>
10¹⁷⁰⁶+1 is divisible by 2585176909735148567915152915961_<31>
10¹⁷³⁷+1 is divisible by 5337159554189680210862121006289_<31>
10¹⁸⁴¹+1 is divisible by 1221836164173949226042017629809_<31>
10¹⁹²⁵+1 is divisible by 1358137502639759693901685682201_<31>
10¹⁹³⁹+1 is divisible by 8672844768252056198113722386329_<31>, cofactor is probably prime
10¹⁹⁴¹+1 is divisible by 315539166618894730521025791493_<30>
10¹⁹⁴²+1 is divisible by 817080761838450112158972131041_<30>
Reference: Factorizations of numbers of the form 10^n+1 (Alfred Reich)
Jul 6, 2007 (3rd): By Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, GGNFS-0.77.1-20050930-nocona
5·10¹⁵⁷-3 = 4(9)₁₅₆7_<158> = C158
C158 = P39 · C120
P39 = 170751714607368696896080865604341002901_<39>
C120 = [292822828250781602016000167325285828040891795200764250827620597365088252659542353359323090342351116997142479928464778697_<120>]
5·10¹⁴³-3 = 4(9)₁₄₂7_<144> = 409 · C142
C142 = P61 · P81
P61 = 2935742145013115478236491256387688161775892870102820487172343_<61>
P81 = 416417323846778387561709274459675711946255835461780664134795831916578834221071331_<81>

Number: 49997_143 N=1222493887530562347188264058679706601466992665036674816625916870415647921760391198044009779951100244498777506112469437652811735941320293398533 ( 142 digits) SNFS difficulty: 145 digits. Divisors found: r1=2935742145013115478236491256387688161775892870102820487172343 (pp61) r2=416417323846778387561709274459675711946255835461780664134795831916578834221071331 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.13 hours. Scaled time: 17.41 units (timescale=2.143). Factorization parameters were as follows: n: 1222493887530562347188264058679706601466992665036674816625916870415647921760391198044009779951100244498777506112469437652811735941320293398533 m: 100000000000000000000000000000 c5: 1 c0: -60 skew: 2.27 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 1300001) Primes: RFBsize:114155, AFBsize:113882, largePrimes:2653193 encountered Relations: rels:2644766, finalFF:300265 Max relations in full relation-set: 28 Initial matrix: 228101 x 300265 with sparse part having weight 19434761. Pruned matrix : 195584 x 196788 with weight 10280185. Total sieving time: 7.95 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.12 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,50000 total time: 8.13 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
Jul 6, 2007 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v. 1.21, GMP-ECM 6.1.2
5·10¹²⁰-3 = 4(9)₁₁₉7_<121> = 109 · C119
C119 = P38 · P81
P38 = 71651015110439976712949381761124614909_<38>
P81 = 640208091432102618875345096934692490876535014728092248096211914729816834699112037_<81>

Number: 49997_120 N=45871559633027522935779816513761467889908256880733944954128440366972477064220183486238532110091743119266055045871559633 ( 119 digits) SNFS difficulty: 120 digits. Divisors found: r1=71651015110439976712949381761124614909 (pp38) r2=640208091432102618875345096934692490876535014728092248096211914729816834699112037 (pp81) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.93 hours. Scaled time: 1.99 units (timescale=2.125). Factorization parameters were as follows: n: 45871559633027522935779816513761467889908256880733944954128440366972477064220183486238532110091743119266055045871559633 m: 1000000000000000000000000 c5: 5 c0: -3 skew: 0.9 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 450001) Primes: RFBsize:49098, AFBsize:48956, largePrimes:2046876 encountered Relations: rels:2149382, finalFF:235375 Max relations in full relation-set: 28 Initial matrix: 98119 x 235375 with sparse part having weight 21516547. Pruned matrix : 73294 x 73848 with weight 4654054. Total sieving time: 0.88 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.93 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
5·10¹²⁸-3 = 4(9)₁₂₇7_<129> = 7 · 1871 · 142184699 · C117
C117 = P52 · P65
P52 = 9755302500995483441296854824102920959702641390257253_<52>
P65 = 27523557876492693925945733984595465953928510734994989947908285283_<65>

Number: 49997_128 N=268500632988843114399137334497132172339031733517253072560760156230954193300391203370973608509515917709832913483907599 ( 117 digits) SNFS difficulty: 130 digits. Divisors found: r1=9755302500995483441296854824102920959702641390257253 (pp52) r2=27523557876492693925945733984595465953928510734994989947908285283 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.77 hours. Scaled time: 3.76 units (timescale=2.128). Factorization parameters were as follows: n: 268500632988843114399137334497132172339031733517253072560760156230954193300391203370973608509515917709832913483907599 m: 100000000000000000000000000 c5: 1 c0: -60 skew: 2.27 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [500000, 850001) Primes: RFBsize:78498, AFBsize:78351, largePrimes:1470489 encountered Relations: rels:1481355, finalFF:188290 Max relations in full relation-set: 28 Initial matrix: 156913 x 188290 with sparse part having weight 8758854. Pruned matrix : 139088 x 139936 with weight 5115713. Total sieving time: 1.69 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.05 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,44,44,2.2,2.2,50000 total time: 1.77 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
5·10¹⁵⁴-3 = 4(9)₁₅₃7_<155> = 223 · 421 · 2256879067_<10> · 7689247183_<10> · 7976152762042959475996039114316239979_<37> · C94
C94 = P46 · P49
P46 = 2921647769384774308532275896959632201186400323_<46>
P49 = 1316950995804027485247023644858332723329794421707_<49>

Fri Jul 6 00:56:55 2007 Fri Jul 6 00:56:55 2007 Fri Jul 6 00:56:55 2007 Msieve v. 1.21 Fri Jul 6 00:56:55 2007 random seeds: d977a1fa f013ce09 Fri Jul 6 00:56:55 2007 factoring 3847666939279894172268033897682969407262717898287172366419424639735420453122353902836783011361 (94 digits) Fri Jul 6 00:56:55 2007 commencing quadratic sieve (94-digit input) Fri Jul 6 00:56:55 2007 using multiplier of 1 Fri Jul 6 00:56:55 2007 using 32kb Intel Core sieve core Fri Jul 6 00:56:55 2007 sieve interval: 36 blocks of size 32768 Fri Jul 6 00:56:55 2007 processing polynomials in batches of 6 Fri Jul 6 00:56:55 2007 using a sieve bound of 2025281 (75006 primes) Fri Jul 6 00:56:55 2007 using large prime bound of 271387654 (28 bits) Fri Jul 6 00:56:55 2007 using double large prime bound of 1515172741378278 (42-51 bits) Fri Jul 6 00:56:55 2007 using trial factoring cutoff of 51 bits Fri Jul 6 00:56:55 2007 polynomial 'A' values have 12 factors Fri Jul 6 03:02:27 2007 75317 relations (18669 full + 56648 combined from 1068446 partial), need 75102 Fri Jul 6 03:02:28 2007 begin with 1087115 relations Fri Jul 6 03:02:28 2007 reduce to 195099 relations in 11 passes Fri Jul 6 03:02:28 2007 attempting to read 195099 relations Fri Jul 6 03:02:30 2007 recovered 195099 relations Fri Jul 6 03:02:30 2007 recovered 176930 polynomials Fri Jul 6 03:02:30 2007 attempting to build 75317 cycles Fri Jul 6 03:02:30 2007 found 75316 cycles in 5 passes Fri Jul 6 03:02:30 2007 distribution of cycle lengths: Fri Jul 6 03:02:30 2007 length 1 : 18669 Fri Jul 6 03:02:30 2007 length 2 : 13325 Fri Jul 6 03:02:30 2007 length 3 : 12721 Fri Jul 6 03:02:30 2007 length 4 : 10305 Fri Jul 6 03:02:30 2007 length 5 : 7536 Fri Jul 6 03:02:30 2007 length 6 : 4964 Fri Jul 6 03:02:30 2007 length 7 : 3344 Fri Jul 6 03:02:30 2007 length 9+: 4452 Fri Jul 6 03:02:30 2007 largest cycle: 19 relations Fri Jul 6 03:02:30 2007 matrix is 75006 x 75316 with weight 4694209 (avg 62.33/col) Fri Jul 6 03:02:30 2007 filtering completed in 3 passes Fri Jul 6 03:02:30 2007 matrix is 73619 x 73683 with weight 4526930 (avg 61.44/col) Fri Jul 6 03:02:32 2007 saving the first 48 matrix rows for later Fri Jul 6 03:02:32 2007 matrix is 73571 x 73683 with weight 3487432 (avg 47.33/col) Fri Jul 6 03:02:32 2007 matrix includes 32 packed rows Fri Jul 6 03:02:32 2007 using block size 29473 for processor cache size 4096 kB Fri Jul 6 03:02:58 2007 lanczos halted after 1165 iterations Fri Jul 6 03:02:58 2007 recovered 15 nontrivial dependencies Fri Jul 6 03:02:59 2007 prp46 factor: 2921647769384774308532275896959632201186400323 Fri Jul 6 03:02:59 2007 prp49 factor: 1316950995804027485247023644858332723329794421707 Fri Jul 6 03:02:59 2007 elapsed time 02:06:04
5·10¹⁷⁵-3 = 4(9)₁₇₄7_<176> = C176
C176 = P38 · C138
P38 = 82494503209048359090450275383194039527_<38>
C138 = [606100989217373462581008360915327251534574087696954550955083284282765441327791625110225200206880593890686186829406312682705912893389087611_<138>]
5·10¹⁴²-3 = 4(9)₁₄₁7_<143> = 71 · 2143 · 2343611 · 1711248061_<10> · 2674951691_<10> · 1461605018313863471_<19> · C95
C95 = P34 · P61
P34 = 8731327716744500293395495818364077_<34>
P61 = 2400295605687202500809285138795364428820556768937793554302027_<61>

Fri Jul 6 08:21:10 2007 Fri Jul 6 08:21:10 2007 Fri Jul 6 08:21:10 2007 Msieve v. 1.21 Fri Jul 6 08:21:10 2007 random seeds: 58e36f1b b3909a7e Fri Jul 6 08:21:10 2007 factoring 20957767550316699204490665365600675841056124504326905194322448749729894011632283651292705084079 (95 digits) Fri Jul 6 08:21:10 2007 commencing quadratic sieve (95-digit input) Fri Jul 6 08:21:10 2007 using multiplier of 39 Fri Jul 6 08:21:10 2007 using 32kb Intel Core sieve core Fri Jul 6 08:21:10 2007 sieve interval: 36 blocks of size 32768 Fri Jul 6 08:21:10 2007 processing polynomials in batches of 6 Fri Jul 6 08:21:10 2007 using a sieve bound of 2128177 (78814 primes) Fri Jul 6 08:21:10 2007 using large prime bound of 310713842 (28 bits) Fri Jul 6 08:21:10 2007 using double large prime bound of 1933076650188010 (43-51 bits) Fri Jul 6 08:21:10 2007 using trial factoring cutoff of 51 bits Fri Jul 6 08:21:10 2007 polynomial 'A' values have 12 factors Fri Jul 6 10:59:50 2007 78971 relations (19724 full + 59247 combined from 1157803 partial), need 78910 Fri Jul 6 10:59:51 2007 begin with 1177527 relations Fri Jul 6 10:59:51 2007 reduce to 203965 relations in 11 passes Fri Jul 6 10:59:51 2007 attempting to read 203965 relations Fri Jul 6 10:59:53 2007 recovered 203965 relations Fri Jul 6 10:59:53 2007 recovered 187676 polynomials Fri Jul 6 10:59:53 2007 attempting to build 78971 cycles Fri Jul 6 10:59:53 2007 found 78971 cycles in 6 passes Fri Jul 6 10:59:53 2007 distribution of cycle lengths: Fri Jul 6 10:59:53 2007 length 1 : 19724 Fri Jul 6 10:59:53 2007 length 2 : 13855 Fri Jul 6 10:59:53 2007 length 3 : 13538 Fri Jul 6 10:59:53 2007 length 4 : 10684 Fri Jul 6 10:59:53 2007 length 5 : 7791 Fri Jul 6 10:59:53 2007 length 6 : 5465 Fri Jul 6 10:59:53 2007 length 7 : 3347 Fri Jul 6 10:59:53 2007 length 9+: 4567 Fri Jul 6 10:59:53 2007 largest cycle: 21 relations Fri Jul 6 10:59:54 2007 matrix is 78814 x 78971 with weight 5395208 (avg 68.32/col) Fri Jul 6 10:59:54 2007 filtering completed in 3 passes Fri Jul 6 10:59:54 2007 matrix is 77248 x 77312 with weight 5215318 (avg 67.46/col) Fri Jul 6 10:59:55 2007 saving the first 48 matrix rows for later Fri Jul 6 10:59:55 2007 matrix is 77200 x 77312 with weight 4324622 (avg 55.94/col) Fri Jul 6 10:59:55 2007 matrix includes 32 packed rows Fri Jul 6 10:59:55 2007 using block size 30924 for processor cache size 4096 kB Fri Jul 6 11:00:30 2007 lanczos halted after 1222 iterations Fri Jul 6 11:00:30 2007 recovered 18 nontrivial dependencies Fri Jul 6 11:00:31 2007 prp34 factor: 8731327716744500293395495818364077 Fri Jul 6 11:00:31 2007 prp61 factor: 2400295605687202500809285138795364428820556768937793554302027 Fri Jul 6 11:00:31 2007 elapsed time 02:39:21
5·10¹³⁷-3 = 4(9)₁₃₆7_<138> = 23 · 163 · 39461 · 93871607 · C122
C122 = P31 · P37 · P54
P31 = 5891496177752933541219267704741_<31>
P37 = 7812216930943689316265896059629904893_<37>
P54 = 782262172768407880210825956642975867414150295248290803_<54>

Number: 49997_137 N=36004121990432414722179291080937945766418689524785810698872912601379557840153318452414515762972516047917479488800024533539 ( 122 digits) SNFS difficulty: 139 digits. Divisors found: r1=5891496177752933541219267704741 (pp31) r2=7812216930943689316265896059629904893 (pp37) r3=782262172768407880210825956642975867414150295248290803 (pp54) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.00 hours. Scaled time: 8.58 units (timescale=2.145). Factorization parameters were as follows: n: 36004121990432414722179291080937945766418689524785810698872912601379557840153318452414515762972516047917479488800024533539 m: 5000000000000000000000000000 c5: 4 c0: -75 skew: 1.8 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [700000, 1450001) Primes: RFBsize:107126, AFBsize:106673, largePrimes:1867994 encountered Relations: rels:1987379, finalFF:283262 Max relations in full relation-set: 28 Initial matrix: 213863 x 283262 with sparse part having weight 17166479. Pruned matrix : 184846 x 185979 with weight 9061365. Total sieving time: 3.84 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.10 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,139,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,45,45,2.3,2.3,50000 total time: 4.00 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
Jul 6, 2007: By Kenichiro Yamaguchi / Msieve v. 1.25
5·10¹²²-3 = 4(9)₁₂₁7_<123> = 7 · 2446494083906698889244510653_<28> · C95
C95 = P43 · P52
P43 = 6303845095126307972819884509608992783019357_<43>
P52 = 4631506328102789383103305306718062753677381160084451_<52>

Thu Jul 05 23:38:40 2007 Thu Jul 05 23:38:40 2007 Thu Jul 05 23:38:40 2007 Msieve v. 1.25 Thu Jul 05 23:38:40 2007 random seeds: c91b51d8 af500c75 Thu Jul 05 23:38:40 2007 factoring 29196298449457225683898977265132542300678896172777155830274719264937835884224090396632887718007 (95 digits) Thu Jul 05 23:38:41 2007 commencing quadratic sieve (95-digit input) Thu Jul 05 23:38:41 2007 using multiplier of 7 Thu Jul 05 23:38:41 2007 using 32kb Pentium M sieve core Thu Jul 05 23:38:41 2007 sieve interval: 36 blocks of size 32768 Thu Jul 05 23:38:41 2007 processing polynomials in batches of 6 Thu Jul 05 23:38:41 2007 using a sieve bound of 2115527 (78824 primes) Thu Jul 05 23:38:41 2007 using large prime bound of 308866942 (28 bits) Thu Jul 05 23:38:41 2007 using double large prime bound of 1912443258076426 (43-51 bits) Thu Jul 05 23:38:41 2007 using trial factoring cutoff of 51 bits Thu Jul 05 23:38:41 2007 polynomial 'A' values have 12 factors Fri Jul 06 04:10:53 2007 79253 relations (19388 full + 59865 combined from 1166604 partial), need 78920 Fri Jul 06 04:10:55 2007 begin with 1185992 relations Fri Jul 06 04:10:56 2007 reduce to 206355 relations in 10 passes Fri Jul 06 04:10:56 2007 attempting to read 206355 relations Fri Jul 06 04:11:00 2007 recovered 206355 relations Fri Jul 06 04:11:00 2007 recovered 189200 polynomials Fri Jul 06 04:11:00 2007 attempting to build 79253 cycles Fri Jul 06 04:11:00 2007 found 79252 cycles in 5 passes Fri Jul 06 04:11:00 2007 distribution of cycle lengths: Fri Jul 06 04:11:00 2007 length 1 : 19388 Fri Jul 06 04:11:00 2007 length 2 : 13782 Fri Jul 06 04:11:00 2007 length 3 : 13535 Fri Jul 06 04:11:00 2007 length 4 : 10814 Fri Jul 06 04:11:00 2007 length 5 : 8041 Fri Jul 06 04:11:00 2007 length 6 : 5414 Fri Jul 06 04:11:00 2007 length 7 : 3423 Fri Jul 06 04:11:00 2007 length 9+: 4855 Fri Jul 06 04:11:00 2007 largest cycle: 23 relations Fri Jul 06 04:11:01 2007 matrix is 78824 x 79252 with weight 5331274 (avg 67.27/col) Fri Jul 06 04:11:02 2007 filtering completed in 4 passes Fri Jul 06 04:11:02 2007 matrix is 75026 x 75090 with weight 5058349 (avg 67.36/col) Fri Jul 06 04:11:02 2007 saving the first 48 matrix rows for later Fri Jul 06 04:11:02 2007 matrix is 74978 x 75090 with weight 4132765 (avg 55.04/col) Fri Jul 06 04:11:02 2007 matrix includes 64 packed rows Fri Jul 06 04:11:02 2007 using block size 30036 for processor cache size 2048 kB Fri Jul 06 04:11:02 2007 commencing Lanczos iteration Fri Jul 06 04:11:51 2007 lanczos halted after 1187 iterations Fri Jul 06 04:11:51 2007 recovered 17 nontrivial dependencies Fri Jul 06 04:11:52 2007 prp43 factor: 6303845095126307972819884509608992783019357 Fri Jul 06 04:11:52 2007 prp52 factor: 4631506328102789383103305306718062753677381160084451 Fri Jul 06 04:11:52 2007 elapsed time 04:33:12
Jul 5, 2007 (2nd): By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona
5·10¹⁰⁶-3 = 4(9)₁₀₅7_<107> = C107
C107 = P53 · P54
P53 = 51379467791652406382241099912651400334898984400190777_<53>
P54 = 973151380289763769238966237755432094392232133691333861_<54>

Number: 49997_106 N=49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 107 digits) SNFS difficulty: 106 digits. Divisors found: r1=51379467791652406382241099912651400334898984400190777 (pp53) r2=973151380289763769238966237755432094392232133691333861 (pp54) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.45 hours. Scaled time: 0.96 units (timescale=2.145). Factorization parameters were as follows: n: 49999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 1000000000000000000000 c5: 50 c0: -3 skew: 0.57 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 260001) Primes: RFBsize:30757, AFBsize:30789, largePrimes:1045486 encountered Relations: rels:987914, finalFF:108071 Max relations in full relation-set: 28 Initial matrix: 61611 x 108071 with sparse part having weight 4604823. Pruned matrix : 46229 x 46601 with weight 1394879. Total sieving time: 0.43 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.45 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
5·10¹¹³-3 = 4(9)₁₁₂7_<114> = C114
C114 = P48 · P66
P48 = 907436158859512909422687304965377963070381712507_<48>
P66 = 551002949483974443730009627016215019549109574303626681725606916071_<66>

Number: 49997_113 N=499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 114 digits) SNFS difficulty: 115 digits. Divisors found: r1=907436158859512909422687304965377963070381712507 (pp48) r2=551002949483974443730009627016215019549109574303626681725606916071 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.63 hours. Scaled time: 1.34 units (timescale=2.143). Factorization parameters were as follows: n: 499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 100000000000000000000000 c5: 1 c0: -60 skew: 2.27 type: snfs Factor base limits: 360000/360000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [180000, 320001) Primes: RFBsize:30757, AFBsize:30699, largePrimes:1057310 encountered Relations: rels:986957, finalFF:96871 Max relations in full relation-set: 28 Initial matrix: 61520 x 96871 with sparse part having weight 4430990. Pruned matrix : 51748 x 52119 with weight 1665807. Total sieving time: 0.60 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.63 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
5·10¹²³-3 = 4(9)₁₂₂7_<124> = C124
C124 = P59 · P66
P59 = 41339256942088911622012358254358042113678371404430757997789_<59>
P66 = 120950408155723983526356287938613353278226690610618708055828192673_<66>

Number: 49997_123 N=4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 ( 124 digits) SNFS difficulty: 125 digits. Divisors found: r1=41339256942088911622012358254358042113678371404430757997789 (pp59) r2=120950408155723983526356287938613353278226690610618708055828192673 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.04 hours. Scaled time: 2.23 units (timescale=2.145). Factorization parameters were as follows: n: 4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 m: 10000000000000000000000000 c5: 1 c0: -60 skew: 2.27 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 480001) Primes: RFBsize:49098, AFBsize:48986, largePrimes:1922284 encountered Relations: rels:1871231, finalFF:110151 Max relations in full relation-set: 28 Initial matrix: 98148 x 110151 with sparse part having weight 9092255. Pruned matrix : 94832 x 95386 with weight 6810840. Total sieving time: 0.97 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 1.04 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
5·10¹¹⁸-3 = 4(9)₁₁₇7_<119> = 2887441 · C113
C113 = P56 · P57
P56 = 63010830359033312483466077306764627266644155646127728707_<56>
P57 = 274815790254415776711435696262112720520718579760139674831_<57>

Number: 49997_118 N=17316371139704672753486564747123837335550752379009649028326466237751697783608392344640115590240631756631564073517 ( 113 digits) SNFS difficulty: 120 digits. Divisors found: r1=63010830359033312483466077306764627266644155646127728707 (pp56) r2=274815790254415776711435696262112720520718579760139674831 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.78 hours. Scaled time: 1.68 units (timescale=2.145). Factorization parameters were as follows: n: 17316371139704672753486564747123837335550752379009649028326466237751697783608392344640115590240631756631564073517 m: 1000000000000000000000000 c5: 1 c0: -60 skew: 2.27 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [300000, 420001) Primes: RFBsize:49098, AFBsize:48986, largePrimes:1903519 encountered Relations: rels:1888791, finalFF:147578 Max relations in full relation-set: 28 Initial matrix: 98148 x 147578 with sparse part having weight 11914433. Pruned matrix : 85032 x 85586 with weight 4763073. Total sieving time: 0.73 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,46,46,2.4,2.4,30000 total time: 0.78 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 4043036k/4718592k available (2106k kernel code, 0k reserved, 1299k data, 196k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Total of 4 processors activated (19246.09 BogoMIPS).
Jul 5, 2007: The factor table of 499...997 was extended to n=200. Those composite numbers had been tested 430 times by GMP-ECM B1=250000. So, unknown prime factors of them are probably greater than 10³⁰.
Jul 2, 2007 (2nd): By Torbjörn Granlund
10⁷⁹⁹+1 is divisible by 84381206263904600374587469219832511232219_<41>
10⁸⁹¹+1 is divisible by 22663213771462227811088536403512441819_<38>
10⁹⁴⁴+1 is divisible by 4859846047732923587514032493793_<31>
(10⁸¹⁵-1)/9 is divisible by 3664950640511701126041972679226717351_<37>
Reference: Factoring and Prime Identification (Torbjörn Granlund)
Jul 2, 2007: By suberi / GMP-ECM 6.1.2 B1=11000000
4·10¹⁹⁵-3 = 3(9)₁₉₄7_<196> = 7 · 101197 · C190
C190 = P37 · P154
P37 = 3771194733060677910727165656242155763_<37>
P154 = 1497322513815848534027864445072580097326790638319429568818602330439582708603315019200778229678277949703995368212735241456117614079298626340503579378845661_<154>
Jul 1, 2007: By Torbjörn Granlund
(10⁵⁰⁷-1)/9 is divisible by 82638297310634344310411757401076652003_<38>
10⁶⁸⁰+1 is divisible by 1516395051122929541850783680941040161_<37>
10⁶⁹¹+1 is divisible by 26578194229497643738821679856668807_<35>
10⁷⁵⁹+1 is divisible by 2832165561296805799533565929552471103_<37>
By Yousuke Koide
10¹²³³+1 is divisible by 14881155992657195128437244984378939_<35>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

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