News and updates, October 2007

Since June 16, 2000

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News and updates, October 2007	2007-11-01(Thu) 22:30

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News and updates, October 2007

Oct 31, 2007 (5th): By Robert Backstrom / GGNFS, Msieve
9·10¹⁵⁷-7 = 8(9)₁₅₆3_<158> = 23 · 64057787 · C149
C149 = P73 · P76
P73 = 8547312778918799179387612593474476828728823510172134540253167241939987973_<73>
P76 = 7146824962215572093535969278319248184705372720242480746696150650147917691641_<76>

Number: n N=61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693 ( 149 digits) SNFS difficulty: 157 digits. Divisors found: Thu Nov 01 00:37:53 2007 prp73 factor: 8547312778918799179387612593474476828728823510172134540253167241939987973 Thu Nov 01 00:37:53 2007 prp76 factor: 7146824962215572093535969278319248184705372720242480746696150650147917691641 Thu Nov 01 00:37:53 2007 elapsed time 01:22:09 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 37.30 hours. Scaled time: 49.46 units (timescale=1.326). Factorization parameters were as follows: name: KA_8_9_156_3 n: 61086148328241023456170774434462215920080438294417426293679106525704877121001087183439811795314562241854476205041713894715231040563014033617462633693 skew: 0.38 deg: 5 c5: 900 c0: -7 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 special-q in [100000, 1900000) Primes: RFBsize:216816, AFBsize:216321, largePrimes:7229719 encountered Relations: rels:6721021, finalFF:520151 Max relations in full relation-set: 28 Initial matrix: 433201 x 520151 with sparse part having weight 46044664. Pruned matrix : 368182 x 370412 with weight 28093041. Total sieving time: 37.05 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 37.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 31, 2007 (4th): By Jo Yeong Uk / GGNFS, Msieve
9·10¹⁵⁰-7 = 8(9)₁₄₉3_<151> = 859 · 352963277 · 18139634852382632412042997_<26> · C115
C115 = P41 · P74
P41 = 55504280314514112186236174411054189440309_<41>
P74 = 29482533885016913889484106257918099812603456906714576053691076225565509087_<74>

Number: 89993_150 N=1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883 ( 115 digits) SNFS difficulty: 150 digits. Divisors found: r1=55504280314514112186236174411054189440309 (pp41) r2=29482533885016913889484106257918099812603456906714576053691076225565509087 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.99 hours. Scaled time: 27.87 units (timescale=2.146). Factorization parameters were as follows: n: 1636406825136139563104533988910623283706494518193323744963557735997068458160508983884811204786788623931439183587883 m: 1000000000000000000000000000000 c5: 9 c0: -7 skew: 0.95 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, 2000001) Primes: RFBsize:176302, AFBsize:176458, largePrimes:5472027 encountered Relations: rels:5419693, finalFF:513988 Max relations in full relation-set: 28 Initial matrix: 352824 x 513988 with sparse part having weight 44556647. Pruned matrix : 279117 x 280945 with weight 22936374. Total sieving time: 12.50 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.38 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 12.99 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
9·10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 · 15771126802857831503737789_<26> · 2469438507084583723424410362013_<31> · C93
C93 = P35 · P59
P35 = 29916323560200857306637278521712341_<35>
P59 = 32803016936544339453376593485631195739277624165372655627383_<59>

Wed Oct 31 08:32:17 2007 Wed Oct 31 08:32:17 2007 Wed Oct 31 08:32:17 2007 Msieve v. 1.28 Wed Oct 31 08:32:17 2007 random seeds: 78b84c31 5c438943 Wed Oct 31 08:32:17 2007 factoring 981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603 (93 digits) Wed Oct 31 08:32:17 2007 commencing quadratic sieve (93-digit input) Wed Oct 31 08:32:18 2007 using multiplier of 3 Wed Oct 31 08:32:18 2007 using 32kb Intel Core sieve core Wed Oct 31 08:32:18 2007 sieve interval: 36 blocks of size 32768 Wed Oct 31 08:32:18 2007 processing polynomials in batches of 6 Wed Oct 31 08:32:18 2007 using a sieve bound of 1953863 (72941 primes) Wed Oct 31 08:32:18 2007 using large prime bound of 244232875 (27 bits) Wed Oct 31 08:32:18 2007 using double large prime bound of 1253277823035125 (42-51 bits) Wed Oct 31 08:32:18 2007 using trial factoring cutoff of 51 bits Wed Oct 31 08:32:18 2007 polynomial 'A' values have 12 factors Wed Oct 31 09:57:24 2007 73505 relations (19333 full + 54172 combined from 979953 partial), need 73037 Wed Oct 31 09:57:24 2007 begin with 999286 relations Wed Oct 31 09:57:24 2007 reduce to 184209 relations in 11 passes Wed Oct 31 09:57:24 2007 attempting to read 184209 relations Wed Oct 31 09:57:26 2007 recovered 184209 relations Wed Oct 31 09:57:26 2007 recovered 160186 polynomials Wed Oct 31 09:57:26 2007 attempting to build 73505 cycles Wed Oct 31 09:57:26 2007 found 73505 cycles in 6 passes Wed Oct 31 09:57:26 2007 distribution of cycle lengths: Wed Oct 31 09:57:26 2007 length 1 : 19333 Wed Oct 31 09:57:26 2007 length 2 : 13661 Wed Oct 31 09:57:26 2007 length 3 : 12554 Wed Oct 31 09:57:26 2007 length 4 : 9800 Wed Oct 31 09:57:26 2007 length 5 : 7114 Wed Oct 31 09:57:26 2007 length 6 : 4591 Wed Oct 31 09:57:26 2007 length 7 : 2825 Wed Oct 31 09:57:26 2007 length 9+: 3627 Wed Oct 31 09:57:26 2007 largest cycle: 18 relations Wed Oct 31 09:57:26 2007 matrix is 72941 x 73505 with weight 4546757 (avg 61.86/col) Wed Oct 31 09:57:27 2007 filtering completed in 3 passes Wed Oct 31 09:57:27 2007 matrix is 68316 x 68380 with weight 4231949 (avg 61.89/col) Wed Oct 31 09:57:28 2007 saving the first 48 matrix rows for later Wed Oct 31 09:57:28 2007 matrix is 68268 x 68380 with weight 3299116 (avg 48.25/col) Wed Oct 31 09:57:28 2007 matrix includes 64 packed rows Wed Oct 31 09:57:28 2007 using block size 27352 for processor cache size 4096 kB Wed Oct 31 09:57:29 2007 commencing Lanczos iteration Wed Oct 31 09:57:50 2007 lanczos halted after 1081 iterations Wed Oct 31 09:57:50 2007 recovered 15 nontrivial dependencies Wed Oct 31 09:57:50 2007 prp35 factor: 29916323560200857306637278521712341 Wed Oct 31 09:57:50 2007 prp59 factor: 32803016936544339453376593485631195739277624165372655627383 Wed Oct 31 09:57:50 2007 elapsed time 01:25:33
Oct 31, 2007 (3rd): By Sinkiti Sibata / GGNFS
9·10¹⁴⁸-7 = 8(9)₁₄₇3_<149> = 53 · 839 · 3833 · 5333122741489_<13> · 380397540317863012963011373_<27> · C102
C102 = P48 · P55
P48 = 185048077381378285528736195447051909587258335893_<48>
P55 = 1406572115111896750750738223467919885903244947129739803_<55>

Number: 89993_148 N=260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079 ( 102 digits) SNFS difficulty: 148 digits. Divisors found: r1=185048077381378285528736195447051909587258335893 (pp48) r2=1406572115111896750750738223467919885903244947129739803 (pp55) Version: GGNFS-0.77.1-20060513-k8 Total time: 30.10 hours. Scaled time: 59.93 units (timescale=1.991). Factorization parameters were as follows: name: 89993_148 n: 260283465599715195282875769247700889484368036515112348257395053869878284353005891464605690479865649079 m: 100000000000000000000000000000 c5: 9000 c0: -7 skew: 0.24 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, 4250001) Primes: RFBsize:114155, AFBsize:114082, largePrimes:3049998 encountered Relations: rels:3108836, finalFF:263510 Max relations in full relation-set: 28 Initial matrix: 228304 x 263510 with sparse part having weight 32994625. Pruned matrix : 218898 x 220103 with weight 26198623. Total sieving time: 29.21 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.62 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 30.10 hours. --------- CPU info (if available) ----------
Oct 31, 2007 (2nd): By matsui / GMP-ECM, Msieve
(5·10¹⁹⁸+7)/3 = 1(6)₁₉₇9_<199> = 2671 · 2222089 · 43446912661062564370891697_<26> · 151432609261393100562428907767_<30> · C134
C134 = P38 · P43 · P53
P38 = 78356711420850326025452572618724188949_<38>
P43 = 5527668366912659164266442169275274462403349_<43>
P53 = 98540986433720343595658132228977073747961703420580549_<53>
(5·10¹⁷³+7)/3 = 1(6)₁₇₂9_<174> = 79 · 141073 · 154543 · 165887 · 63473899 · 133660440077_<12> · C137
C137 = P34 · C104
P34 = 1862230537518772176753410725489813_<34>
C104 = [36921943839998587914228808236155511843378747795412617433005313650028624835179704262350945849262592485273_<104>]
Oct 31, 2007: By Womack
(10³⁰⁹-1)/9 is divisible by 5294796903161592416528456780680376286484870226446771978908657527791_<67> and the cofactor is prime.
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 30, 2007 (5th): By Tyler Cadigan / Msieve, GGNFS
(64·10¹⁶³-1)/9 = 7(1)₁₆₃_<164> = 637330387763_<12> · 10957735036324101653_<20> · C134
C134 = P61 · P73
P61 = 5153208161696653721426359516088698419315495201808470280932923_<61>
P73 = 1975942751788253995617036939102852461531533982770011785041254696010379563_<73>

Mon Oct 29 19:58:09 2007 Mon Oct 29 19:58:09 2007 Mon Oct 29 19:58:09 2007 Msieve v. 1.29 Mon Oct 29 19:58:09 2007 random seeds: 79db1e80 385338a0 Mon Oct 29 19:58:09 2007 factoring 10182444315560575705513301530834416904561566048028307675788338594283441380448622210798637965512347107701350195485846065970978973052649 (134 digits) Mon Oct 29 19:58:10 2007 commencing number field sieve (133-digit input) Mon Oct 29 19:58:10 2007 R0: -400000000000000000000000000000000 Mon Oct 29 19:58:10 2007 R1: 1 Mon Oct 29 19:58:10 2007 A0: -2 Mon Oct 29 19:58:10 2007 A1: 0 Mon Oct 29 19:58:10 2007 A2: 0 Mon Oct 29 19:58:10 2007 A3: 0 Mon Oct 29 19:58:10 2007 A4: 0 Mon Oct 29 19:58:10 2007 A5: 125 Mon Oct 29 19:58:10 2007 size score = 2.442337e-011, Murphy alpha = 0.284179, combined = 2.221603e-011 Mon Oct 29 20:01:42 2007 restarting with 5837456 relations Mon Oct 29 20:01:48 2007 factor base loaded: Mon Oct 29 20:01:48 2007 348513 rational ideals (max prime = 4999999) Mon Oct 29 20:01:48 2007 316326 algebraic ideals (max prime = 4499969) Mon Oct 29 20:01:48 2007 added 15854 free relations Mon Oct 29 20:01:48 2007 Mon Oct 29 20:01:48 2007 commencing relation filtering Mon Oct 29 20:01:48 2007 commencing duplicate removal, pass 1 Mon Oct 29 20:01:52 2007 error -14 reading relation 62058 Mon Oct 29 20:06:03 2007 found 79763 hash collisions in 5853309 relations Mon Oct 29 20:06:03 2007 commencing duplicate removal, pass 2 Mon Oct 29 20:09:59 2007 found 17169 duplicates and 5836140 unique relations Mon Oct 29 20:09:59 2007 memory use: 37.8 MB Mon Oct 29 20:10:05 2007 ignoring smallest 282973 rational and 283029 algebraic ideals Mon Oct 29 20:10:05 2007 filtering ideals above 3997355 Mon Oct 29 20:10:05 2007 need 962203 more relations than ideals Mon Oct 29 20:10:05 2007 commencing singleton removal, pass 1 Mon Oct 29 20:14:14 2007 relations with 0 large ideals: 103993 Mon Oct 29 20:14:14 2007 relations with 1 large ideals: 760328 Mon Oct 29 20:14:14 2007 relations with 2 large ideals: 2000058 Mon Oct 29 20:14:14 2007 relations with 3 large ideals: 1934872 Mon Oct 29 20:14:14 2007 relations with 4 large ideals: 844689 Mon Oct 29 20:14:14 2007 relations with 5 large ideals: 173568 Mon Oct 29 20:14:14 2007 relations with 6 large ideals: 17913 Mon Oct 29 20:14:14 2007 relations with 7+ large ideals: 719 Mon Oct 29 20:14:14 2007 5836140 relations and about 5716455 large ideals Mon Oct 29 20:14:14 2007 commencing singleton removal, pass 2 Mon Oct 29 20:18:32 2007 found 3032525 singletons Mon Oct 29 20:18:32 2007 current dataset: 2803615 relations and about 2113481 large ideals Mon Oct 29 20:18:32 2007 commencing singleton removal, pass 3 Mon Oct 29 20:22:13 2007 found 448303 singletons Mon Oct 29 20:22:13 2007 current dataset: 2355312 relations and about 1639581 large ideals Mon Oct 29 20:22:13 2007 commencing singleton removal, final pass Mon Oct 29 20:26:10 2007 memory use: 77.5 MB Mon Oct 29 20:26:10 2007 commencing in-memory singleton removal Mon Oct 29 20:26:11 2007 begin with 2355312 relations and 1708927 unique ideals Mon Oct 29 20:26:17 2007 reduce to 2069330 relations and 1416639 ideals in 11 passes Mon Oct 29 20:26:17 2007 max relations containing the same ideal: 35 Mon Oct 29 20:26:18 2007 dataset has 15.3% excess relations Mon Oct 29 20:26:22 2007 ignoring smallest 256574 rational and 256498 algebraic ideals Mon Oct 29 20:26:22 2007 filtering ideals above 3597619 Mon Oct 29 20:26:22 2007 need 611282 more relations than ideals Mon Oct 29 20:26:22 2007 commencing singleton removal, final pass Mon Oct 29 20:29:45 2007 memory use: 93.6 MB Mon Oct 29 20:29:45 2007 commencing in-memory singleton removal Mon Oct 29 20:29:46 2007 begin with 2355312 relations and 1761848 unique ideals Mon Oct 29 20:29:53 2007 reduce to 2068928 relations and 1469137 ideals in 11 passes Mon Oct 29 20:29:53 2007 max relations containing the same ideal: 35 Mon Oct 29 20:29:54 2007 dataset has 6.0% excess relations Mon Oct 29 20:29:54 2007 relations with 0 large ideals: 68851 Mon Oct 29 20:29:54 2007 relations with 1 large ideals: 298085 Mon Oct 29 20:29:54 2007 relations with 2 large ideals: 616837 Mon Oct 29 20:29:54 2007 relations with 3 large ideals: 631687 Mon Oct 29 20:29:54 2007 relations with 4 large ideals: 341963 Mon Oct 29 20:29:54 2007 relations with 5 large ideals: 94801 Mon Oct 29 20:29:54 2007 relations with 6 large ideals: 15793 Mon Oct 29 20:29:54 2007 relations with 7+ large ideals: 911 Mon Oct 29 20:29:54 2007 commencing 2-way merge Mon Oct 29 20:30:00 2007 reduce to 1298002 relation sets and 698213 unique ideals Mon Oct 29 20:30:00 2007 ignored 2 oversize relation sets Mon Oct 29 20:30:00 2007 commencing full merge Mon Oct 29 20:30:59 2007 found 664054 cycles, need 590413 Mon Oct 29 20:31:00 2007 weight of 590413 cycles is about 38798316 (65.71/cycle) Mon Oct 29 20:31:00 2007 distribution of cycle lengths: Mon Oct 29 20:31:00 2007 1 relations: 100601 Mon Oct 29 20:31:00 2007 2 relations: 68982 Mon Oct 29 20:31:00 2007 3 relations: 62992 Mon Oct 29 20:31:00 2007 4 relations: 55520 Mon Oct 29 20:31:00 2007 5 relations: 50346 Mon Oct 29 20:31:00 2007 6 relations: 44152 Mon Oct 29 20:31:00 2007 7 relations: 39232 Mon Oct 29 20:31:00 2007 8 relations: 34235 Mon Oct 29 20:31:00 2007 9 relations: 30168 Mon Oct 29 20:31:00 2007 10+ relations: 104185 Mon Oct 29 20:31:00 2007 heaviest cycle: 17 relations Mon Oct 29 20:31:00 2007 commencing cycle optimization Mon Oct 29 20:31:02 2007 start with 3228434 relations Mon Oct 29 20:31:22 2007 pruned 92753 relations Mon Oct 29 20:31:22 2007 distribution of cycle lengths: Mon Oct 29 20:31:22 2007 1 relations: 100601 Mon Oct 29 20:31:22 2007 2 relations: 70333 Mon Oct 29 20:31:22 2007 3 relations: 65309 Mon Oct 29 20:31:22 2007 4 relations: 56690 Mon Oct 29 20:31:22 2007 5 relations: 52216 Mon Oct 29 20:31:22 2007 6 relations: 45474 Mon Oct 29 20:31:22 2007 7 relations: 40433 Mon Oct 29 20:31:22 2007 8 relations: 35072 Mon Oct 29 20:31:22 2007 9 relations: 30464 Mon Oct 29 20:31:22 2007 10+ relations: 93821 Mon Oct 29 20:31:22 2007 heaviest cycle: 17 relations Mon Oct 29 20:31:25 2007 Mon Oct 29 20:31:25 2007 commencing linear algebra Mon Oct 29 20:31:27 2007 read 590413 cycles Mon Oct 29 20:31:31 2007 cycles contain 1626805 unique relations Mon Oct 29 20:35:42 2007 read 1626805 relations Mon Oct 29 20:35:52 2007 using 32 quadratic characters above 134216228 Mon Oct 29 20:38:40 2007 read 590413 cycles Mon Oct 29 20:40:52 2007 filtering completed in 3 passes Mon Oct 29 20:40:53 2007 matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col) Mon Oct 29 20:42:11 2007 read 585316 cycles Mon Oct 29 20:44:43 2007 matrix is 585116 x 585316 with weight 52706044 (avg 90.05/col) Mon Oct 29 20:44:43 2007 saving the first 48 matrix rows for later Mon Oct 29 20:44:44 2007 matrix is 585068 x 585316 with weight 39821171 (avg 68.03/col) Mon Oct 29 20:44:44 2007 matrix includes 64 packed rows Mon Oct 29 20:44:44 2007 using block size 21845 for processor cache size 512 kB Mon Oct 29 20:44:55 2007 commencing Lanczos iteration Mon Oct 29 23:39:22 2007 lanczos halted after 9254 iterations (dim = 585068) Mon Oct 29 23:39:40 2007 recovered 51 nontrivial dependencies Mon Oct 29 23:39:49 2007 Mon Oct 29 23:39:49 2007 commencing square root phase Mon Oct 29 23:39:49 2007 reading relations for dependency 1 Mon Oct 29 23:40:38 2007 read 292046 cycles Mon Oct 29 23:40:40 2007 cycles contain 983974 unique relations Mon Oct 29 23:45:16 2007 read 983974 relations Mon Oct 29 23:45:37 2007 multiplying 1554024 relations Mon Oct 29 23:58:13 2007 multiply complete, coefficients have about 43.64 million bits Mon Oct 29 23:58:15 2007 initial square root is modulo 1843111 Tue Oct 30 00:16:39 2007 prp61 factor: 5153208161696653721426359516088698419315495201808470280932923 Tue Oct 30 00:16:39 2007 prp73 factor: 1975942751788253995617036939102852461531533982770011785041254696010379563 Tue Oct 30 00:16:39 2007 elapsed time 04:18:30
Oct 30, 2007 (4th): By Sinkiti Sibata / GGNFS
(8·10¹⁶⁹+7)/3 = 2(6)₁₆₈9_<170> = 29 · 2731 · 3853 · 6101 · C158
C158 = P39 · P119
P39 = 662045957785193703483721009542997210001_<39>
P119 = 21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827_<119>

Number: 26669_169 N=14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827 ( 158 digits) SNFS difficulty: 170 digits. Divisors found: r1=662045957785193703483721009542997210001 (pp39) r2=21635197395131458368660666363246008064391683714979718942359200843611409545192525720721351020928312546549349492289471827 (pp119) Version: GGNFS-0.77.1-20060513-k8 Total time: 139.76 hours. Scaled time: 279.94 units (timescale=2.003). Factorization parameters were as follows: name: 26669_169 n: 14323494981331534264770233164626933360731902226623376107836718853298476108817106742366885509525113696497209270753439876022351249265426627408162506926892141827 m: 10000000000000000000000000000000000 c5: 4 c0: 35 skew: 1.54 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 7100001) Primes: RFBsize:412849, AFBsize:412831, largePrimes:6055936 encountered Relations: rels:6345700, finalFF:951274 Max relations in full relation-set: 28 Initial matrix: 825744 x 951274 with sparse part having weight 56560583. Pruned matrix : 721298 x 725490 with weight 40805496. Total sieving time: 133.63 hours. Total relation processing time: 0.31 hours. Matrix solve time: 5.58 hours. Time per square root: 0.24 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 139.76 hours. --------- CPU info (if available) ----------
Oct 30, 2007 (3rd): By Jo Yeong Uk / GGNFS
9·10¹⁴³-7 = 8(9)₁₄₂3_<144> = 1777 · 1725179 · 133421887 · C127
C127 = P39 · P89
P39 = 156872632499525723095280260098133461577_<39>
P89 = 14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429_<89>

Number: 89993_143 N=2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533 ( 127 digits) SNFS difficulty: 145 digits. Divisors found: r1=156872632499525723095280260098133461577 (pp39) r2=14026414070177028542787457357907396822775755157120560213926799915579235133672913797156429 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.59 hours. Scaled time: 20.58 units (timescale=2.146). Factorization parameters were as follows: n: 2200360499717057804285186354000826515700652096122032856111785933419856092599249419038475136935920236563158160790423597130028533 m: 100000000000000000000000000000 c5: 9 c0: -700 skew: 2.39 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1400001) Primes: RFBsize:114155, AFBsize:114082, largePrimes:3411338 encountered Relations: rels:3448077, finalFF:323928 Max relations in full relation-set: 28 Initial matrix: 228301 x 323928 with sparse part having weight 30228512. Pruned matrix : 199683 x 200888 with weight 15655341. Total sieving time: 9.35 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.17 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 9.59 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
9·10¹⁴⁴-7 = 8(9)₁₄₃3_<145> = 30380069764762946805547503800941_<32> · C114
C114 = P40 · P74
P40 = 5793759319832245415885975057146558926953_<40>
P74 = 51132060310818176689028811056072205332653270314035794978186101297841513141_<74>

Number: 89993_144 N=296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373 ( 114 digits) SNFS difficulty: 145 digits. Divisors found: r1=5793759319832245415885975057146558926953 (pp40) r2=51132060310818176689028811056072205332653270314035794978186101297841513141 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 8.87 hours. Scaled time: 19.03 units (timescale=2.146). Factorization parameters were as follows: n: 296246850968027270505132871619611111688006744457888000889843536883278888233053939988057668145613936858002808589373 m: 100000000000000000000000000000 c5: 9 c0: -70 skew: 1.51 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1350001) Primes: RFBsize:114155, AFBsize:114417, largePrimes:3343512 encountered Relations: rels:3328593, finalFF:281277 Max relations in full relation-set: 28 Initial matrix: 228636 x 281277 with sparse part having weight 25879845. Pruned matrix : 211599 x 212806 with weight 16431801. Total sieving time: 8.61 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.19 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 8.87 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
9·10¹⁵³-7 = 8(9)₁₅₂3_<154> = 235483 · 15771126802857831503737789_<26> · C124
C124 = P31 · C93
P31 = 2469438507084583723424410362013_<31>
C93 = [981345668424409173005139032359911659122268552148212314853518231679477196677844688222808633603_<93>]
9·10¹⁴⁶-7 = 8(9)₁₄₅3_<147> = 19 · 307 · 2243 · 17371526793899_<14> · 28598478520519_<14> · C114
C114 = P44 · P70
P44 = 64299853807288749095977974116352073454267827_<44>
P70 = 2153427995281495420234041605616327252058426335937525315582533212837981_<70>

Number: 89993_146 N=138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287 ( 114 digits) SNFS difficulty: 146 digits. Divisors found: r1=64299853807288749095977974116352073454267827 (pp44) r2=2153427995281495420234041605616327252058426335937525315582533212837981 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.37 hours. Scaled time: 22.21 units (timescale=2.143). Factorization parameters were as follows: n: 138465105281123041720280097879537854129018147941456341438827168511391802940627666355587781402709904235851131937287 m: 100000000000000000000000000000 c5: 90 c0: -7 skew: 0.6 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:135493, largePrimes:3715295 encountered Relations: rels:3729829, finalFF:320257 Max relations in full relation-set: 28 Initial matrix: 270632 x 320257 with sparse part having weight 29075311. Pruned matrix : 251639 x 253056 with weight 19777051. Total sieving time: 10.00 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.28 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 10.37 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 30, 2007 (2nd): By Robert Backstrom / GGNFS, Msieve
8·10¹⁶⁷-7 = 7(9)₁₆₆3_<168> = 15137 · C164
C164 = P41 · P123
P41 = 70835644003123593484318087394932806885707_<41>
P123 = 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227_<123>

Number: n N=52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489 ( 164 digits) SNFS difficulty: 167 digits. Divisors found: Tue Oct 30 07:24:05 2007 prp41 factor: 70835644003123593484318087394932806885707 Tue Oct 30 07:24:05 2007 prp123 factor: 746102215179633311919695276118227149695996068322953673178010306203699906940184998267472539948678240767141330911324215957227 Tue Oct 30 07:24:05 2007 elapsed time 02:09:23 (Msieve 1.28) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 78.72 hours. Scaled time: 102.80 units (timescale=1.306). Factorization parameters were as follows: name: KA_7_9_166_3 n: 52850630904406421351654885380194226068573693598467331703772213780802008323974367444011362885644447380590605800356741758604743344123670476316311025962872431789654489 skew: 0.78 deg: 5 c5: 25 c0: -7 m: 2000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3100001) Primes: RFBsize:216816, AFBsize:216906, largePrimes:7450046 encountered Relations: rels:6889776, finalFF:446877 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 78.46 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 78.72 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
9·10¹⁴¹-7 = 8(9)₁₄₀3_<142> = 2467639565737_<13> · C130
C130 = P62 · P68
P62 = 53727058137272382231521263461791395461691665958866250660772681_<62>
P68 = 67884046657300958448660911774042029705347021611364740350454114167369_<68>

Number: n N=3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289 ( 130 digits) SNFS difficulty: 141 digits. Divisors found: Tue Oct 30 09:24:32 2007 prp62 factor: 53727058137272382231521263461791395461691665958866250660772681 Tue Oct 30 09:24:32 2007 prp68 factor: 67884046657300958448660911774042029705347021611364740350454114167369 Tue Oct 30 09:24:32 2007 elapsed time 00:50:42 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.66 hours. Scaled time: 9.64 units (timescale=1.447). Factorization parameters were as follows: name: KA_8_9_140_3 n: 3647210121350119518190235337345061800537587608749415529958760713265023919457085448117350162821494933357724078360429982102496846289 skew: 0.60 deg: 5 c5: 90 c0: -7 m: 10000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 9500000) Primes: RFBsize:148933, AFBsize:149225, largePrimes:6523890 encountered Relations: rels:5928439, finalFF:382643 Max relations in full relation-set: 28 Initial matrix: 298225 x 382643 with sparse part having weight 26922338. Pruned matrix : 236427 x 237982 with weight 14528939. Total sieving time: 6.49 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 6.66 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Oct 30, 2007: By matsui / GMP-ECM
(5·10¹⁸¹+7)/3 = 1(6)₁₈₀9_<182> = 19 · 167393 · C175
C175 = P38 · P138
P38 = 15723245803923831841763637804116393807_<38>
P138 = 333284910953414496865344254925662573105861000375900329621890909608385992777196180707248922993978075855583628204941899412869920935091825201_<138>
Oct 29, 2007 (3rd): By Robert Backstrom / GGNFS, Msieve 1.28, GMP-ECM
9·10¹⁸⁴-7 = 8(9)₁₈₃3_<185> = 31 · 311 · 22091 · 37100458201_<11> · 1275537910469_<13> · 282209150413571_<15> · 480434327015263_<15> · 14873984820428774119490711269_<29> · C97
C97 = P39 · P58
P39 = 593474640229445793717454630072648349617_<39>
P58 = 7461012807353624814862644671648910980191120545663272451503_<58>

Number: n N=4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351 ( 97 digits) Divisors found: r1=593474640229445793717454630072648349617 (pp39) r2=7461012807353624814862644671648910980191120545663272451503 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.00 hours. Scaled time: 11.63 units (timescale=1.453). Factorization parameters were as follows: name: n n: 4427921891591479845215021556692579780756319432292202349671112615670635805041615039103114621124351 m: 13069795307958322129988 deg: 4 c4: 151748640 c3: 1255715867918 c2: -263120823138764827 c1: -4731771597968022768 c0: 240860015889048958069487 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.565 # E(F1,F2) = 2.428134e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1193586766. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 60000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 1180001) Primes: RFBsize:92938, AFBsize:92740, largePrimes:1863035 encountered Relations: rels:1930390, finalFF:234741 Max relations in full relation-set: 28 Initial matrix: 185753 x 234741 with sparse part having weight 16859853. Pruned matrix : 163671 x 164663 with weight 9437558. Polynomial selection time: 0.17 hours. Total sieving time: 7.24 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.44 hours. Total square root time: 0.06 hours, sqrts: 2. Prototype def-par.txt line would be: gnfs,96,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 8.00 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
9·10¹⁴⁰-7 = 8(9)₁₃₉3_<141> = 47 · 109 · 167 · 617 · C133
C133 = P33 · P101
P33 = 153337616869490449763658859895879_<33>
P101 = 11119053224090329768606633153477332542273472771580149117582678104067239138069306589653736225297573611_<101>
(89·10¹⁶⁴+1)/9 = 9(8)₁₆₃9_<165> = 17 · 19597 · 7888299157_<10> · C150
C150 = P42 · P109
P42 = 270666531521708051044165587427652002648199_<42>
P109 = 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927_<109>

Number: n N=376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473 ( 150 digits) SNFS difficulty: 166 digits. Divisors found: Mon Oct 29 21:17:16 2007 prp42 factor: 270666531521708051044165587427652002648199 Mon Oct 29 21:17:16 2007 prp109 factor: 1390244075564748945696789150673380726874059327867465501106095914306348058416858266414264460951086291348664927 Mon Oct 29 21:17:16 2007 elapsed time 02:10:55 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 74.57 hours. Scaled time: 98.88 units (timescale=1.326). Factorization parameters were as follows: name: KA_9_8_163_9 n: 376292541901713990156240140280107136920403712406844501532612508891705603189038511185276004611331447762586551055990351376936771061312168024647111016473 skew: 0.65 deg: 5 c5: 89 c0: 10 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 special-q in [100000, 3500000) Primes: RFBsize:250150, AFBsize:249266, largePrimes:7709961 encountered Relations: rels:7186570, finalFF:561747 Max relations in full relation-set: 28 Initial matrix: 499481 x 561747 with sparse part having weight 51822639. Pruned matrix : 473183 x 475744 with weight 37331802. Total sieving time: 74.27 hours. Total relation processing time: 0.30 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 74.57 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
9·10¹⁴⁵-7 = 8(9)₁₄₄3_<146> = 97 · 3307 · 3767 · C137
C137 = P29 · P108
P29 = 88689612345000909646591931059_<29>
P108 = 839785174596700619416492075514766572936766799231731694119293012984478206119418982501449042954689673043155839_<108>
Oct 29, 2007 (2nd): By Jo Yeong Uk / GGNFS, GMP-ECM
9·10¹³⁸-7 = 8(9)₁₃₇3_<139> = 113 · 1039 · 21012038995387387919_<20> · C115
C115 = P55 · P60
P55 = 8324111480329451493669984302302012442668075809611357389_<55>
P60 = 438270694932342412379485394874876095508458992349269934992589_<60>

Number: 89993_138 N=3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121 ( 115 digits) SNFS difficulty: 140 digits. Divisors found: r1=8324111480329451493669984302302012442668075809611357389 (pp55) r2=438270694932342412379485394874876095508458992349269934992589 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.25 hours. Scaled time: 13.42 units (timescale=2.146). Factorization parameters were as follows: n: 3648214123178278233256210719479595987622179900672256982789110923572726048983147685427800495148109948692769945390121 m: 10000000000000000000000000000 c5: 9 c0: -700 skew: 2.39 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114082, largePrimes:3249074 encountered Relations: rels:3266483, finalFF:322988 Max relations in full relation-set: 28 Initial matrix: 228301 x 322988 with sparse part having weight 26878127. Pruned matrix : 191188 x 192393 with weight 12738220. Total sieving time: 6.06 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.13 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.25 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
9·10¹⁴⁹-7 = 8(9)₁₄₈3_<150> = C150
C150 = P38 · P42 · P72
P38 = 35794409962129142828512220689799871821_<38>
P42 = 123028439265110134626156384131454479013793_<42>
P72 = 204372184460583650412981392697490828081020379007054396748321776875537981_<72>

Number: 89993_149 N=899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 150 digits) SNFS difficulty: 150 digits. Divisors found: r1=35794409962129142828512220689799871821 (pp38) r2=123028439265110134626156384131454479013793 (pp42) r3=204372184460583650412981392697490828081020379007054396748321776875537981 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 12.84 hours. Scaled time: 27.54 units (timescale=2.146). Factorization parameters were as follows: n: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 1000000000000000000000000000000 c5: 9 c0: -70 skew: 1.51 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, 2000001) Primes: RFBsize:176302, AFBsize:176833, largePrimes:5402800 encountered Relations: rels:5281314, finalFF:455491 Max relations in full relation-set: 28 Initial matrix: 353199 x 455491 with sparse part having weight 38566153. Pruned matrix : 301756 x 303585 with weight 22658433. Total sieving time: 12.29 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.44 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 12.84 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
9·10¹³⁹-7 = 8(9)₁₃₈3_<140> = 31 · 34319 · C134
C134 = P41 · P93
P41 = 95880034599375142177521603584056943225357_<41>
P93 = 882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941_<93>

Number: 89993_139 N=84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937 ( 134 digits) SNFS difficulty: 140 digits. Divisors found: r1=95880034599375142177521603584056943225357 (pp41) r2=882303513756038409718500891576339947944242061119473046440639355414422699311396515924957852941 (pp93) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.16 hours. Scaled time: 13.12 units (timescale=2.129). Factorization parameters were as follows: n: 84595291426079224430368205705670422384290090413567580828451088412418964760421434942931076456284443207891048784224670054864746228224937 m: 10000000000000000000000000000 c5: 9 c0: -70 skew: 1.51 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114417, largePrimes:3350084 encountered Relations: rels:3437732, finalFF:383556 Max relations in full relation-set: 28 Initial matrix: 228636 x 383556 with sparse part having weight 32672853. Pruned matrix : 174534 x 175741 with weight 12890921. Total sieving time: 5.98 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.16 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407677) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405128) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405120) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405122) Total of 4 processors activated (19246.09 BogoMIPS).
9·10¹⁹⁷-7 = 8(9)₁₉₆3_<198> = C198
C198 = P33 · C166
P33 = 104572749495411191273052631155941_<33>
C166 = [8606448662225270711938618675616267002791985751466136050473524371365139986511632740091624538638242280156899111248894398265050813422371895877062117828590480106511274373_<166>]
Oct 29, 2007: By Sinkiti Sibata / GGNFS
9·10¹³⁷-7 = 8(9)₁₃₆3_<138> = 227 · 2521 · C133
C133 = P39 · P94
P39 = 221091843902924979644001926922716807503_<39>
P94 = 7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093_<94>

Number: 89993_137 N=1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779 ( 133 digits) SNFS difficulty: 137 digits. Divisors found: r1=221091843902924979644001926922716807503 (pp39) r2=7113299338479217992920918313593338363891253403625902931023690166695268837106428754985186805093 (pp94) Version: GGNFS-0.77.1-20060513-k8 Total time: 13.09 hours. Scaled time: 26.31 units (timescale=2.010). Factorization parameters were as follows: name: 89993_137 n: 1572692466977826783651687062158048603186973912526844986693274293293165602769336690740510985256881840120083807034129173969493261012779 m: 1000000000000000000000000000 c5: 900 c0: -7 skew: 0.38 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 2125001) Primes: RFBsize:78498, AFBsize:63823, largePrimes:1683910 encountered Relations: rels:1718050, finalFF:173211 Max relations in full relation-set: 28 Initial matrix: 142385 x 173211 with sparse part having weight 19269917. Pruned matrix : 135154 x 135929 with weight 13734266. Total sieving time: 12.78 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 13.09 hours. --------- CPU info (if available) ----------
Oct 28, 2007 (5th): By JMB / GMP-ECM
(2·10¹⁶⁴+43)/9 = (2)₁₆₃7_<164> = 3³ · 17² · 2309 · 631311078642593_<15> · C142
C142 = P36 · P106
P36 = 212146409889374522698249183584805409_<36>
P106 = 9209220022038251514752208083059669039690403032046144718649809261395595313649005423325208968370329688568373_<106>
Oct 28, 2007 (4th): By Robert Backstrom / GGNFS, GMP-ECM
9·10¹²⁰-7 = 8(9)₁₁₉3_<121> = C121
C121 = P56 · P66
P56 = 20354029401725849662526304753223971301497103511422609997_<56>
P66 = 442172889817918611600780346173978409068598975005735222119428696669_<66>

Number: n N=8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 121 digits) SNFS difficulty: 120 digits. Divisors found: r1=20354029401725849662526304753223971301497103511422609997 (pp56) r2=442172889817918611600780346173978409068598975005735222119428696669 (pp66) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.55 hours. Scaled time: 2.24 units (timescale=1.442). Factorization parameters were as follows: name: KA_8_9_119_3 n: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 skew: 0.95 deg: 5 c5: 9 c0: -7 m: 1000000000000000000000000 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, 250001) Primes: RFBsize:78498, AFBsize:78361, largePrimes:4232731 encountered Relations: rels:3638568, finalFF:200786 Max relations in full relation-set: 28 Initial matrix: 156923 x 200786 with sparse part having weight 10194178. Pruned matrix : 122805 x 123653 with weight 4620848. Total sieving time: 1.31 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.13 hours. Total square root time: 0.05 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 1.55 hours. --------- CPU info (if available) ----------
9·10¹²⁴-7 = 8(9)₁₂₃3_<125> = 31 · 83 · 859 · C119
C119 = P39 · P80
P39 = 514997239710717504843060243797163586321_<39>
P80 = 79068710858248681348102914984733040362741538735234491408794076224567905858038519_<80>

Number: n N=40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599 ( 119 digits) SNFS difficulty: 125 digits. Divisors found: r1=514997239710717504843060243797163586321 (pp39) r2=79068710858248681348102914984733040362741538735234491408794076224567905858038519 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.17 hours. Scaled time: 3.15 units (timescale=1.454). Factorization parameters were as follows: name: KA_8_9_123_3 n: 40720167839482908161995686376886870777262039256956475117488995374641379744069220665756646323172444933890807512599498599 skew: 1.51 deg: 5 c5: 9 c0: -70 m: 10000000000000000000000000 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, 350001) Primes: RFBsize:78498, AFBsize:78806, largePrimes:4616754 encountered Relations: rels:3996538, finalFF:211076 Max relations in full relation-set: 28 Initial matrix: 157368 x 211076 with sparse part having weight 12304449. Pruned matrix : 125655 x 126505 with weight 5315318. Total sieving time: 1.90 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.16 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 2.17 hours. --------- CPU info (if available) ----------
9·10¹²³-7 = 8(9)₁₂₂3_<124> = 283 · 449 · 18553 · C115
C115 = P33 · P83
P33 = 335087805245091568482853093222231_<33>
P83 = 11392970303565490307790042441076114728020253883982388272289002974166360045042039653_<83>
Oct 28, 2007 (3rd): By Sinkiti Sibata / GGNFS
9·10¹⁰³-7 = 8(9)₁₀₂3_<104> = 8969263 · 22129553 · C90
C90 = P34 · P57
P34 = 3138341068996635669510657500009591_<34>
P57 = 144481741911394492878214372456463812416287949515103488657_<57>

Number: 89993_103 N=453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287 ( 90 digits) SNFS difficulty: 103 digits. Divisors found: r1=3138341068996635669510657500009591 (pp34) r2=144481741911394492878214372456463812416287949515103488657 (pp57) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.16 hours. Scaled time: 2.33 units (timescale=2.010). Factorization parameters were as follows: name: 89993_103 n: 453432984360701811730662361842066998814076709622439235119159164702296684015661335059709287 m: 100000000000000000000 c5: 9000 c0: -7 skew: 0.24 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 350001) Primes: RFBsize:37706, AFBsize:41552, largePrimes:1383872 encountered Relations: rels:1489916, finalFF:267931 Max relations in full relation-set: 28 Initial matrix: 79325 x 267931 with sparse part having weight 10896930. Pruned matrix : 39729 x 40189 with weight 1773397. Total sieving time: 1.10 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.00 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 1.16 hours. --------- CPU info (if available) ----------
9·10¹¹⁰-7 = 8(9)₁₀₉3_<111> = 19 · 41551595117_<11> · C100
C100 = P29 · P71
P29 = 41281949109330068117018801413_<29>
P71 = 27614743514922133541815936402538216668321370424896711617313719193012707_<71>

Number: 89993_110 N=1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991 ( 100 digits) SNFS difficulty: 110 digits. Divisors found: r1=41281949109330068117018801413 (pp29) r2=27614743514922133541815936402538216668321370424896711617313719193012707 (pp71) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.60 hours. Scaled time: 3.20 units (timescale=2.003). Factorization parameters were as follows: name: 89993_110 n: 1139990436450218045364874916232246048513796723724260459114263780638570351214091539941676577618554991 m: 10000000000000000000000 c5: 9 c0: -7 skew: 0.95 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 450001) Primes: RFBsize:49098, AFBsize:63908, largePrimes:2384591 encountered Relations: rels:2925739, finalFF:659504 Max relations in full relation-set: 28 Initial matrix: 113070 x 659504 with sparse part having weight 48577546. Pruned matrix : 58429 x 59058 with weight 4920438. Total sieving time: 1.50 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.02 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,110,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.60 hours. --------- CPU info (if available) ----------
9·10¹³³-7 = 8(9)₁₃₂3_<134> = 264101 · 534617 · C123
C123 = P39 · P85
P39 = 182955127132944612210518087078849494903_<39>
P85 = 3484055901363921062151806188107621607898929991774539197434850631713521731052250641243_<85>

Number: 89993_133 N=637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429 ( 123 digits) SNFS difficulty: 133 digits. Divisors found: r1=182955127132944612210518087078849494903 (pp39) r2=3484055901363921062151806188107621607898929991774539197434850631713521731052250641243 (pp85) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.85 hours. Scaled time: 13.77 units (timescale=2.010). Factorization parameters were as follows: name: 89993_133 n: 637425890372322111870552134461924960577827615567570996460983077035726280509113823885139408501711796643783835904368410084429 m: 100000000000000000000000000 c5: 9000 c0: -7 skew: 0.24 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1225001) Primes: RFBsize:78498, AFBsize:63803, largePrimes:1569153 encountered Relations: rels:1588445, finalFF:190481 Max relations in full relation-set: 28 Initial matrix: 142368 x 190481 with sparse part having weight 15782385. Pruned matrix : 127348 x 128123 with weight 8890552. Total sieving time: 6.62 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.85 hours. --------- CPU info (if available) ----------
9·10¹²²-7 = 8(9)₁₂₁3_<123> = 53 · 4483 · 916879 · 2468335253078521_<16> · C97
C97 = P38 · P59
P38 = 21496643135387952418448986201888231937_<38>
P59 = 77859405334185056592558073314508609031087592802266287870129_<59>

Number: 89993_122 N=1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873 ( 97 digits) SNFS difficulty: 122 digits. Divisors found: r1=21496643135387952418448986201888231937 (pp38) r2=77859405334185056592558073314508609031087592802266287870129 (pp59) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.78 hours. Scaled time: 5.54 units (timescale=1.991). Factorization parameters were as follows: name: 89993_122 n: 1673715851202497322218396988251980025978426972094963254178577242866898726074527843954613286109873 m: 1000000000000000000000000 c5: 900 c0: -7 skew: 0.38 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63823, largePrimes:2113012 encountered Relations: rels:2116801, finalFF:142981 Max relations in full relation-set: 28 Initial matrix: 112985 x 142981 with sparse part having weight 12791337. Pruned matrix : 105117 x 105745 with weight 7557577. Total sieving time: 2.61 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,122,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.78 hours. --------- CPU info (if available) ----------
9·10¹²⁷-7 = 8(9)₁₂₆3_<128> = 16927 · 2815289 · 34549727 · C110
C110 = P53 · P58
P53 = 18928495665651195086151678397725759673977330546366127_<53>
P58 = 2887877797068484257309586094965034801453924030197429437839_<58>

Number: 89993_127 N=54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553 ( 110 digits) SNFS difficulty: 127 digits. Divisors found: r1=18928495665651195086151678397725759673977330546366127 (pp53) r2=2887877797068484257309586094965034801453924030197429437839 (pp58) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.41 hours. Scaled time: 8.86 units (timescale=2.010). Factorization parameters were as follows: name: 89993_127 n: 54663182364741125803462775792405445851485144937413141458737770402786616920134187641356901510330757177881679553 m: 10000000000000000000000000 c5: 900 c0: -7 skew: 0.38 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63823, largePrimes:1546280 encountered Relations: rels:1577253, finalFF:198015 Max relations in full relation-set: 28 Initial matrix: 127838 x 198015 with sparse part having weight 14562521. Pruned matrix : 108690 x 109393 with weight 6383787. Total sieving time: 4.25 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.41 hours. --------- CPU info (if available) ----------
9·10¹¹⁹-7 = 8(9)₁₁₈3_<120> = 61 · 823 · 1004981 · 1446682233738538319_<19> · C92
C92 = P41 · P51
P41 = 45567990874948473844291875103339917072403_<41>
P51 = 270596365668481699029128282701225154281973286874043_<51>

Number: 89993_119 N=12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329 ( 92 digits) SNFS difficulty: 120 digits. Divisors found: r1=45567990874948473844291875103339917072403 (pp41) r2=270596365668481699029128282701225154281973286874043 (pp51) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.11 hours. Scaled time: 4.20 units (timescale=1.991). Factorization parameters were as follows: name: 89993_119 n: 12330532721575594545992327055219422353381614259277089538199489555365772207883504963972335329 m: 1000000000000000000000000 c5: 9 c0: -70 skew: 1.51 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64228, largePrimes:1981105 encountered Relations: rels:1934715, finalFF:128846 Max relations in full relation-set: 28 Initial matrix: 113390 x 128846 with sparse part having weight 9933260. Pruned matrix : 107064 x 107694 with weight 6957791. Total sieving time: 1.96 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.06 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.11 hours. --------- CPU info (if available) ----------
Oct 28, 2007 (2nd): By Sinkiti Sibata / PRIMO
(5·10²⁸⁴⁷+1)/3 is prime.
Oct 28, 2007: The factor table of 899...993 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.
Oct 27, 2007: By Yousuke Koide
10¹¹²¹+1 is divisible by 162578197086018239450239785966343_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 26, 2007 (3rd): By Sinkiti Sibata / GGNFS
(8·10¹⁶³+7)/3 = 2(6)₁₆₂9_<164> = 17 · 9672675193889_<13> · 2132690377238720580097964644733_<31> · C119
C119 = P32 · P88
P32 = 16241366780245493793149978382913_<32>
P88 = 4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897_<88>

Number: 26669_163 N=76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961 ( 119 digits) SNFS difficulty: 163 digits. Divisors found: r1=16241366780245493793149978382913 (pp32) r2=4681907431777497416749516436722604837221873429043948077027598629819267084782903500320897 (pp88) Version: GGNFS-0.77.1-20060513-k8 Total time: 89.67 hours. Scaled time: 179.08 units (timescale=1.997). Factorization parameters were as follows: name: 26669_163 n: 76040575830655542110535543314902372731075646666123180911982484874925096768258162409352851616275001258339376508641632961 m: 200000000000000000000000000000000 c5: 250 c0: 7 skew: 0.49 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, 5150001) Primes: RFBsize:315948, AFBsize:316791, largePrimes:5926048 encountered Relations: rels:6075527, finalFF:765961 Max relations in full relation-set: 28 Initial matrix: 632805 x 765961 with sparse part having weight 56904865. Pruned matrix : 534793 x 538021 with weight 40888773. Total sieving time: 85.28 hours. Total relation processing time: 0.25 hours. Matrix solve time: 3.92 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 89.67 hours. --------- CPU info (if available) ----------
Oct 26, 2007 (2nd): By Jo Yeong Uk / Msieve, GGNFS
(82·10¹⁶¹+71)/9 = 9(1)₁₆₀9_<162> = 11 · 23 · 3748991 · 2671832954149_<13> · 5966029856099_<13> · 302592140766530934908888222616061079_<36> · C93
C93 = P40 · P53
P40 = 3850694069121437110112555389391787483611_<40>
P53 = 51718395086698620503380784735167544390948057134540087_<53>

Fri Oct 26 00:04:24 2007 Fri Oct 26 00:04:24 2007 Fri Oct 26 00:04:24 2007 Msieve v. 1.28 Fri Oct 26 00:04:24 2007 random seeds: bb05f469 520cf979 Fri Oct 26 00:04:24 2007 factoring 199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157 (93 digits) Fri Oct 26 00:04:24 2007 commencing quadratic sieve (92-digit input) Fri Oct 26 00:04:24 2007 using multiplier of 53 Fri Oct 26 00:04:24 2007 using 32kb Intel Core sieve core Fri Oct 26 00:04:24 2007 sieve interval: 36 blocks of size 32768 Fri Oct 26 00:04:24 2007 processing polynomials in batches of 6 Fri Oct 26 00:04:24 2007 using a sieve bound of 1879931 (70588 primes) Fri Oct 26 00:04:24 2007 using large prime bound of 219951927 (27 bits) Fri Oct 26 00:04:24 2007 using double large prime bound of 1037982177167364 (42-50 bits) Fri Oct 26 00:04:24 2007 using trial factoring cutoff of 50 bits Fri Oct 26 00:04:24 2007 polynomial 'A' values have 12 factors Fri Oct 26 01:38:35 2007 70852 relations (18438 full + 52414 combined from 913373 partial), need 70684 Fri Oct 26 01:38:35 2007 begin with 931811 relations Fri Oct 26 01:38:36 2007 reduce to 176982 relations in 10 passes Fri Oct 26 01:38:36 2007 attempting to read 176982 relations Fri Oct 26 01:38:37 2007 recovered 176982 relations Fri Oct 26 01:38:37 2007 recovered 157867 polynomials Fri Oct 26 01:38:38 2007 attempting to build 70852 cycles Fri Oct 26 01:38:38 2007 found 70852 cycles in 5 passes Fri Oct 26 01:38:38 2007 distribution of cycle lengths: Fri Oct 26 01:38:38 2007 length 1 : 18438 Fri Oct 26 01:38:38 2007 length 2 : 13138 Fri Oct 26 01:38:38 2007 length 3 : 12424 Fri Oct 26 01:38:38 2007 length 4 : 9444 Fri Oct 26 01:38:38 2007 length 5 : 6893 Fri Oct 26 01:38:38 2007 length 6 : 4449 Fri Oct 26 01:38:38 2007 length 7 : 2721 Fri Oct 26 01:38:38 2007 length 9+: 3345 Fri Oct 26 01:38:38 2007 largest cycle: 17 relations Fri Oct 26 01:38:38 2007 matrix is 70588 x 70852 with weight 4361172 (avg 61.55/col) Fri Oct 26 01:38:38 2007 filtering completed in 3 passes Fri Oct 26 01:38:38 2007 matrix is 66408 x 66472 with weight 4123761 (avg 62.04/col) Fri Oct 26 01:38:39 2007 saving the first 48 matrix rows for later Fri Oct 26 01:38:39 2007 matrix is 66360 x 66472 with weight 3167656 (avg 47.65/col) Fri Oct 26 01:38:39 2007 matrix includes 64 packed rows Fri Oct 26 01:38:39 2007 using block size 26588 for processor cache size 4096 kB Fri Oct 26 01:38:41 2007 commencing Lanczos iteration Fri Oct 26 01:39:01 2007 lanczos halted after 1051 iterations Fri Oct 26 01:39:01 2007 recovered 17 nontrivial dependencies Fri Oct 26 01:39:01 2007 prp40 factor: 3850694069121437110112555389391787483611 Fri Oct 26 01:39:01 2007 prp53 factor: 51718395086698620503380784735167544390948057134540087 Fri Oct 26 01:39:01 2007 elapsed time 01:34:37
10¹⁶⁰-3 = (9)₁₅₉7_<160> = 13 · 383 · 52771123082243438120761219452533939_<35> · C122
C122 = P55 · P68
P55 = 3104829324566476660204837376960208819056316254480075411_<55>
P68 = 12258118210972106300910696745912453876036288591144435630300652094167_<68>

Number: 99997_160 N=38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637 ( 122 digits) SNFS difficulty: 160 digits. Divisors found: r1=3104829324566476660204837376960208819056316254480075411 (pp55) r2=12258118210972106300910696745912453876036288591144435630300652094167 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.28 hours. Scaled time: 51.72 units (timescale=2.130). Factorization parameters were as follows: n: 38059364885428552053660274073288904257094149099533297652419641952424130876827819709343439432012909374053370298093233227637 m: 100000000000000000000000000000000 c5: 1 c0: -3 skew: 1.25 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:282992, largePrimes:5668831 encountered Relations: rels:5757196, finalFF:705905 Max relations in full relation-set: 28 Initial matrix: 566202 x 705905 with sparse part having weight 43019303. Pruned matrix : 449468 x 452363 with weight 26383924. Total sieving time: 23.17 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.99 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: 24.28 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 26, 2007: By Robert Backstrom / GGNFS, Msieve
(68·10¹⁵⁹+13)/9 = 7(5)₁₅₈7_<160> = 3 · 11 · 4815673 · 4744027650700422249483517_<25> · C128
C128 = P43 · P85
P43 = 1817556499049832315979311388016701905830557_<43>
P85 = 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717_<85>

Number: n N=10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369 ( 128 digits) SNFS difficulty: 161 digits. Divisors found: Fri Oct 26 04:07:36 2007 prp43 factor: 1817556499049832315979311388016701905830557 Fri Oct 26 04:07:36 2007 prp85 factor: 5513918500405508167982559945335390530223566166104141567423964571081382710408776663717 Fri Oct 26 04:07:36 2007 elapsed time 01:12:41 (Msieve 1.28) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 35.05 hours. Scaled time: 45.84 units (timescale=1.308). Factorization parameters were as follows: name: KA_7_5_158_7 n: 10021858405643136835110663638106493348996711376408485617314301858636084358685512690994172006148128480343234388008600600371800369 skew: 1.14 deg: 5 c5: 34 c0: 65 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1700001) Primes: RFBsize:216816, AFBsize:216756, largePrimes:7052915 encountered Relations: rels:6510490, finalFF:471406 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 34.83 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 35.05 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 25, 2007 (4th): By Robert Backstrom / GGNFS, Msieve
(8·10¹⁶⁷+7)/3 = 2(6)₁₆₆9_<168> = 13 · C167
C167 = P41 · P127
P41 = 13118854935330807737302880871625861715191_<41>
P127 = 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343_<127>

Number: n N=20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513 ( 167 digits) SNFS difficulty: 167 digits. Divisors found: Fri Oct 26 00:52:24 2007 prp41 factor: 13118854935330807737302880871625861715191 Fri Oct 26 00:52:24 2007 prp127 factor: 1563613639600265717122264555652120246875230542463041437585843162802180545583168901897596747095254252168082117302855188658610343 Fri Oct 26 00:52:24 2007 elapsed time 02:20:14 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 68.58 hours. Scaled time: 82.23 units (timescale=1.199). Factorization parameters were as follows: name: KA_2_6_166_9 n: 20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513 type: snfs skew: 0.78 deg: 5 c5: 25 c0: 7 m: 2000000000000000000000000000000000 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 special-q in [100000, 2800001) Primes: RFBsize:250150, AFBsize:250196, largePrimes:7501352 encountered Relations: rels:7006091, finalFF:549114 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 68.27 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.6,2.6,100000 total time: 68.58 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Oct 25, 2007 (3rd): By Sinkiti Sibata / PRIMO
(26·10²⁶⁸⁸-11)/3 is prime.
Oct 25, 2007 (2nd): By Jo Yeong Uk / GMP-ECM
(46·10¹⁶¹-1)/9 = 5(1)₁₆₁_<162> = 17 · 29 · 47 · 724447 · 855857254801063_<15> · 3172216729960337_<16> · C122
C122 = P31 · P91
P31 = 8979918563026048055214325630447_<31>
P91 = 1248899066404055568679090185969582597135314562972683825422549780576518206214842043840714379_<91>
(82·10¹⁶¹+71)/9 = 9(1)₁₆₀9_<162> = 11 · 23 · 3748991 · 2671832954149_<13> · 5966029856099_<13> · C128
C128 = P36 · C93
P36 = 302592140766530934908888222616061079_<36>
C93 = [199151717224829651201838246240894378459227321597236742980797132267408631739729758957535014157_<93>]
Oct 25, 2007: By Robert Backstrom / GGNFS, Msieve
10¹⁶⁶+9 = 1(0)₁₆₅9_<167> = 6841 · 3298055297_<10> · C153
C153 = P47 · P106
P47 = 96175707342105206747325741564689382490429756801_<47>
P106 = 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817_<106>

Number: n N=443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417 ( 153 digits) SNFS difficulty: 166 digits. Divisors found: Thu Oct 25 15:40:05 2007 prp47 factor: 96175707342105206747325741564689382490429756801 Thu Oct 25 15:40:05 2007 prp106 factor: 4608473425480966721109597553701118029210118730372926247354918207318621993190226935764939329385047887076817 Thu Oct 25 15:40:05 2007 elapsed time 01:54:23 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 62.44 hours. Scaled time: 82.79 units (timescale=1.326). Factorization parameters were as follows: name: KA_1_0_165_9 n: 443223191462926543459909958595746661943719852080722467101166627816472353539797980148447621698392127726651524401212365554604364053039646401916272115182417 skew: 0.98 deg: 5 c5: 10 c0: 9 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 special-q in [100000, 2900000) Primes: RFBsize:250150, AFBsize:250021, largePrimes:7553576 encountered Relations: rels:7043754, finalFF:563405 Max relations in full relation-set: 28 Initial matrix: 500238 x 563405 with sparse part having weight 49550458. Pruned matrix : 457419 x 459984 with weight 35024031. Total sieving time: 62.12 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 62.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 24, 2007 (5th): By Jo Yeong Uk / GGNFS, GMP-ECM
(10¹⁶⁰+11)/3 = (3)₁₅₉7_<160> = 2357 · 3547 · 6483784428566166293003_<22> · C131
C131 = P65 · P66
P65 = 98546042989459507145454598033560826513496496641717463749658701161_<65>
P66 = 624008085251487858816186117499534910163524917199921025095545919941_<66>

Number: 33337_160 N=61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501 ( 131 digits) SNFS difficulty: 160 digits. Divisors found: r1=98546042989459507145454598033560826513496496641717463749658701161 (pp65) r2=624008085251487858816186117499534910163524917199921025095545919941 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.41 hours. Scaled time: 51.96 units (timescale=2.129). Factorization parameters were as follows: n: 61493527594963435585105940425622344176908261835783977623937353322902951931684135308791965353024017933025951725442269952202949751501 m: 100000000000000000000000000000000 c5: 1 c0: 11 skew: 1.62 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:283048, largePrimes:5715875 encountered Relations: rels:5844133, finalFF:739067 Max relations in full relation-set: 28 Initial matrix: 566258 x 739067 with sparse part having weight 45560931. Pruned matrix : 423383 x 426278 with weight 27548907. Total sieving time: 23.43 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.85 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 24.41 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(28·10¹⁵⁹-1)/9 = 3(1)₁₅₉_<160> = 3³ · 97 · 717667 · 31119047 · 4319493713_<10> · C134
C134 = P51 · P83
P51 = 691407189640250229701631872793975317289967702892453_<51>
P83 = 17810004148297787657731990085303963501623195591076357396769870762158063825273702029_<83>

Number: 31111_159 N=12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137 ( 134 digits) SNFS difficulty: 161 digits. Divisors found: r1=691407189640250229701631872793975317289967702892453 (pp51) r2=17810004148297787657731990085303963501623195591076357396769870762158063825273702029 (pp83) Version: GGNFS-0.77.1-20050930-nocona Total time: 31.18 hours. Scaled time: 66.89 units (timescale=2.145). Factorization parameters were as follows: n: 12313964915655771746286044453350809950290851202515862861599384612499767983759056219534341024515693473314812267723013626438858554887137 m: 100000000000000000000000000000000 c5: 14 c0: -5 skew: 0.81 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, 3800001) Primes: RFBsize:283146, AFBsize:284317, largePrimes:5680047 encountered Relations: rels:5727480, finalFF:670051 Max relations in full relation-set: 28 Initial matrix: 567529 x 670051 with sparse part having weight 43786702. Pruned matrix : 489700 x 492601 with weight 29899843. Total sieving time: 29.75 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.29 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 31.18 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(2·10¹⁶²+43)/9 = (2)₁₆₁7_<162> = 79 · 3074539183721_<13> · 92026938157876922867_<20> · C127
C127 = P31 · P97
P31 = 7374950638373593966200740279443_<31>
P97 = 1348050841856743517595672702299157137569123136816328878609841055467622001119053294651183847225613_<97>
(4·10¹⁶²-13)/9 = (4)₁₆₁3_<162> = 4795407827859115566133901_<25> · C137
C137 = P30 · P108
P30 = 732132950352080637131122456739_<30>
P108 = 126590752328295613964062194725925454032813432338962666501971716450553063422318328708874925852644810865626637_<108>
(5·10¹⁶²-41)/9 = (5)₁₆₁1_<162> = 17 · 7802477 · 1221834755184846949_<19> · C136
C136 = P29 · P107
P29 = 74150969555284684198040824859_<29>
P107 = 46229241501927787031803827366761897615314009076339630433468603502437500587889723061122144734719131912055229_<107>
3·10¹⁶³-7 = 2(9)₁₆₂3_<164> = 41 · 43 · 73 · 433163734125755498123_<21> · C138
C138 = P33 · P105
P33 = 984803325251956195887249668731139_<33>
P105 = 546442521935781460110773913223987286991730594097092602213887622250012599971203648826978554376441175284731_<105>
Oct 24, 2007 (4th): By Sinkiti Sibata / GGNFS
(8·10¹⁵⁸+7)/3 = 2(6)₁₅₇9_<159> = 453968096244493_<15> · C144
C144 = P56 · P88
P56 = 77025991204399032295102167879033530984020107406191788251_<56>
P88 = 7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083_<88>

Number: 26669_158 N=587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833 ( 144 digits) SNFS difficulty: 158 digits. Divisors found: r1=77025991204399032295102167879033530984020107406191788251 (pp56) r2=7626163354920877208117873161490105884353828530163763489424107667430447229492870343004083 (pp88) Version: GGNFS-0.77.1-20060513-k8 Total time: 59.71 hours. Scaled time: 118.95 units (timescale=1.992). Factorization parameters were as follows: name: 26669_158 n: 587412791499445703414789501643028537938176365461039166386707531445737063824203352653873977007985725071863227998012464875392047576593221164428833 m: 20000000000000000000000000000000 c5: 250 c0: 7 skew: 0.49 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:284107, largePrimes:5971981 encountered Relations: rels:6202849, finalFF:822675 Max relations in full relation-set: 28 Initial matrix: 567319 x 822675 with sparse part having weight 58139262. Pruned matrix : 388038 x 390938 with weight 44121525. Total sieving time: 56.94 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.38 hours. Time per square root: 0.19 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: 59.71 hours. --------- CPU info (if available) ----------
Oct 24, 2007 (3rd): By Robert Backstrom / GGNFS
(8·10¹⁵²+7)/3 = 2(6)₁₅₁9_<153> = 61 · C151
C151 = P39 · P113
P39 = 421869844046731851658147807645650077819_<39>
P113 = 10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691_<113>

Number: n N=4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929 ( 151 digits) SNFS difficulty: 152 digits. Divisors found: r1=421869844046731851658147807645650077819 (pp39) r2=10362401487434351205807812414291785916154078462280535061673815273435490140412383670255796593884378838685001402691 (pp113) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 16.95 hours. Scaled time: 22.10 units (timescale=1.304). Factorization parameters were as follows: name: KA_2_6_151_9 n: 4371584699453551912568306010928961748633879781420765027322404371584699453551912568306010928961748633879781420765027322404371584699453551912568306010929 skew: 0.78 deg: 5 c5: 25 c0: 7 m: 2000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 750001) Primes: RFBsize:203362, AFBsize:203182, largePrimes:6399966 encountered Relations: rels:5939023, finalFF:511751 Max relations in full relation-set: 28 Initial matrix: 406608 x 511751 with sparse part having weight 27504928. Pruned matrix : 311614 x 313711 with weight 13508229. Total sieving time: 15.13 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.56 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 16.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 24, 2007 (2nd): By Kurt Beschorner
10⁷⁵³+1 is divisible by 1756473376297178637489284481878718601_<37>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 24, 2007: By Yousuke Koide
10¹³⁷¹+1 is divisible by 127539278618607069275328998039143_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 23, 2007: By Sinkiti Sibata / GGNFS
(8·10¹⁴⁶+7)/3 = 2(6)₁₄₅9_<147> = 2167165829_<10> · C138
C138 = P64 · P74
P64 = 4143397241869544226241437570296544113990642586158773224155313511_<64>
P74 = 29697508503653602939343659106341885529158177653874575739404674525553127951_<74>

Number: 26669_146 N=123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961 ( 138 digits) SNFS difficulty: 147 digits. Divisors found: r1=4143397241869544226241437570296544113990642586158773224155313511 (pp64) r2=29697508503653602939343659106341885529158177653874575739404674525553127951 (pp74) Version: GGNFS-0.77.1-20060513-k8 Total time: 19.70 hours. Scaled time: 39.37 units (timescale=1.998). Factorization parameters were as follows: name: 26669_146 n: 123048574824435673891693992129047484472249246906461197560099895182809596923866349254192982509723148032649543343582622844440699543102045961 m: 200000000000000000000000000000 c5: 5 c0: 14 skew: 1.23 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, 2850001) Primes: RFBsize:114155, AFBsize:114392, largePrimes:2877121 encountered Relations: rels:2886374, finalFF:288594 Max relations in full relation-set: 28 Initial matrix: 228612 x 288594 with sparse part having weight 30123579. Pruned matrix : 210472 x 211679 with weight 20270448. Total sieving time: 18.98 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.51 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 19.70 hours. --------- CPU info (if available) ----------
Oct 23, 2007 (2nd): By Jo Yeong Uk / GGNFS
(8·10¹⁶⁵+7)/3 = 2(6)₁₆₄9_<166> = 73 · 9803 · 19961 · 3844331 · 12325751 · 106692540971_<12> · 5524900734469672569379_<22> · C109
C109 = P33 · P36 · P42
P33 = 161800001655869356136898432615667_<33>
P36 = 226209579099872731684276944664364189_<36>
P42 = 182609076402191723318653867302508477992533_<42>

Number: 26669_165 N=6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579 ( 109 digits) Divisors found: r1=161800001655869356136898432615667 (pp33) r2=226209579099872731684276944664364189 (pp36) r3=182609076402191723318653867302508477992533 (pp42) Version: GGNFS-0.77.1-20050930-nocona Total time: 14.55 hours. Scaled time: 30.77 units (timescale=2.114). Factorization parameters were as follows: name: 26669_165 n: 6683621898604490720408773048442746311375034340493821379268599844292684440397247763706382879797337575415946579 skew: 30844.34 # norm 3.88e+15 c5: 32640 c4: -6377134016 c3: 10966983900756 c2: 6023277967525827220 c1: 20338186144994372135593 c0: -322736910701913843682752030 # alpha -6.58 Y1: 391238345143 Y0: -728218088733067565453 # Murphy_E 1.05e-09 # M 2458195276530130644457672644483945265068481024582090432931298737948038172243268879673145326804447368387365992 type: gnfs rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 60000 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1200000, 1920001) Primes: RFBsize:176302, AFBsize:175803, largePrimes:7512919 encountered Relations: rels:7327983, finalFF:490794 Max relations in full relation-set: 28 Initial matrix: 352190 x 490794 with sparse part having weight 47989971. Pruned matrix : 258659 x 260483 with weight 27043110. Polynomial selection time: 0.68 hours. Total sieving time: 13.24 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.38 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 14.55 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 23, 2007: By Robert Backstrom / GGNFS, Msieve
(64·10¹⁶⁰+53)/9 = 7(1)₁₅₉7_<161> = 23 · 191 · 114769 · 748180586440778137_<18> · C135
C135 = P43 · P92
P43 = 2272678914182122391159400004256881975433059_<43>
P92 = 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647_<92>

Number: n N=188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173 ( 135 digits) SNFS difficulty: 161 digits. Divisors found: Tue Oct 23 03:14:29 2007 prp43 factor: 2272678914182122391159400004256881975433059 Tue Oct 23 03:14:29 2007 prp92 factor: 82948234356112188698160244749473598135682577177508948629769483777144299322248884566566919647 Tue Oct 23 03:14:29 2007 elapsed time 01:10:32 (Msieve 1.28) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 38.03 hours. Scaled time: 49.78 units (timescale=1.309). Factorization parameters were as follows: name: KA_7_1_159_7 n: 188514703189773269056083345014625106760612761414432617373683190484568696824418797686302626998621689259459609264199987578100566480410173 skew: 1.93 deg: 5 c5: 2 c0: 53 m: 200000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1700000) Primes: RFBsize:216816, AFBsize:216946, largePrimes:7083358 encountered Relations: rels:6573818, finalFF:499435 Max relations in full relation-set: 28 Initial matrix: 433827 x 499435 with sparse part having weight 36087703. Pruned matrix : 381360 x 383593 with weight 23854377. Total sieving time: 37.83 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 38.03 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(8·10¹⁶⁰+7)/3 = 2(6)₁₅₉9_<161> = 49843 · C156
C156 = P70 · P86
P70 = 8206529381083043352109674031409945933677801693490815409442456291123149_<70>
P86 = 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067_<86>

Number: n N=535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983 ( 156 digits) SNFS difficulty: 161 digits. Divisors found: Tue Oct 23 23:09:38 2007 prp70 factor: 8206529381083043352109674031409945933677801693490815409442456291123149 Tue Oct 23 23:09:38 2007 prp86 factor: 65193609889480326298653585942015762338033823753726962763716880835878142163048859303067 Tue Oct 23 23:09:38 2007 elapsed time 01:04:53 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.34 hours. Scaled time: 52.83 units (timescale=1.454). Factorization parameters were as follows: name: KA_2_6_159_9 n: 535013275016886356492720475626801490011970922028502832226524620642149683339017849380387750871068488386868099164710524379886175925740157427656173718810397983 skew: 1.95 deg: 5 c5: 1 c0: 28 m: 200000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1800000) Primes: RFBsize:203362, AFBsize:203227, largePrimes:7259162 encountered Relations: rels:6779635, finalFF:504684 Max relations in full relation-set: 28 Initial matrix: 406653 x 504684 with sparse part having weight 41751576. Pruned matrix : 337714 x 339811 with weight 26445618. Total sieving time: 36.12 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 36.34 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Oct 22, 2007 (4th): By Sinkiti Sibata / PRIMO
(85·10²⁵⁸⁰-13)/9 is prime.
Oct 22, 2007 (3rd): By Jo Yeong Uk / GGNFS
(8·10¹⁵⁴+7)/3 = 2(6)₁₅₃9_<155> = 17224619 · 55682718131_<11> · 46415095754141034190321569677_<29> · C108
C108 = P35 · P73
P35 = 63976167233321490585818587278762619_<35>
P73 = 9363133420441845598841194850047950471022696892436041111098985547200676067_<73>

Number: 26669_154 N=599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473 ( 108 digits) Divisors found: r1=63976167233321490585818587278762619 (pp35) r2=9363133420441845598841194850047950471022696892436041111098985547200676067 (pp73) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.65 hours. Scaled time: 22.83 units (timescale=2.144). Factorization parameters were as follows: name: 26669_154 n: 599017389534088974031064754543587991849505713299448734373260781981910865693172098475924868395465908007539473 skew: 21354.62 # norm 6.78e+14 c5: 32400 c4: 104238510 c3: -63159803819065 c2: 42231149150739894 c1: 10386860579266260178521 c0: 1573011234854712440644311 # alpha -5.93 Y1: 268163654693 Y0: -450172247251438281950 # Murphy_E 1.31e-09 # M 353372238522770296188352642033280019967747150736232710020604793608863613888916745569090484185353683588909139 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:135004, largePrimes:4543413 encountered Relations: rels:4565506, finalFF:355041 Max relations in full relation-set: 28 Initial matrix: 270157 x 355041 with sparse part having weight 33355043. Pruned matrix : 221309 x 222723 with weight 18208925. Polynomial selection time: 0.60 hours. Total sieving time: 9.69 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,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 10.65 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹⁵⁷+7)/3 = 2(6)₁₅₆9_<158>; = 71 · 73 · 4423 · 17761 · 463849 · 131698991 · C133
C133 = P48 · P85
P48 = 272730925941823417805548362043843409679870198107_<48>
P85 = 3931060343889521523931450002903303012283257053146040409429479768292617881055891882137_<85>

Number: 26669_157 N=1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659 ( 133 digits) SNFS difficulty: 157 digits. Divisors found: r1=272730925941823417805548362043843409679870198107 (pp48) r2=3931060343889521523931450002903303012283257053146040409429479768292617881055891882137 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 19.84 hours. Scaled time: 42.45 units (timescale=2.140). Factorization parameters were as follows: n: 1072121727522171991711117449162947893294510889614725272405934873471024006838246193709580176818241416588454805181432061281055284514659 m: 20000000000000000000000000000000 c5: 25 c0: 7 skew: 0.78 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:216906, largePrimes:5656803 encountered Relations: rels:5671985, finalFF:600758 Max relations in full relation-set: 28 Initial matrix: 433786 x 600758 with sparse part having weight 46380712. Pruned matrix : 331528 x 333760 with weight 28777533. Total sieving time: 19.11 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.61 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: 19.84 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 22, 2007 (2nd): By Sinkiti Sibata / GGNFS
(8·10¹⁵⁰+7)/3 = 2(6)₁₄₉9_<151> = 19 · 19173023 · 221211127 · C134
C134 = P52 · P83
P52 = 3153611510488812690844381411841100171038865591531757_<52>
P83 = 10493234479791580568317662070396265616908097303633122206670593944661297064473922083_<83>

Number: 26669_150 N=33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831 ( 134 digits) SNFS difficulty: 150 digits. Divisors found: r1=3153611510488812690844381411841100171038865591531757 (pp52) r2=10493234479791580568317662070396265616908097303633122206670593944661297064473922083 (pp83) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.11 hours. Scaled time: 42.22 units (timescale=2.000). Factorization parameters were as follows: name: 26669_150 n: 33091585037728817063066885723269305783539863851825906597312108108442540229578000079303679297783978010391230631520577621957205438089831 m: 1000000000000000000000000000000 c5: 8 c0: 7 skew: 0.97 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:176343, largePrimes:5664697 encountered Relations: rels:5756890, finalFF:642726 Max relations in full relation-set: 28 Initial matrix: 352710 x 642726 with sparse part having weight 56826393. Pruned matrix : 241016 x 242843 with weight 25378288. Total sieving time: 20.10 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.75 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 21.11 hours. --------- CPU info (if available) ----------
(8·10¹⁴³+7)/3 = 2(6)₁₄₂9_<144> = 13² · 3517 · 62776679931694823_<17> · C121
C121 = P47 · P75
P47 = 20021116406067209554446200468334668005750140859_<47>
P75 = 356962853960238997946851914156890231498548267914175830313090442617598040829_<75>

Number: 26669_143 N=7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111 ( 121 digits) SNFS difficulty: 143 digits. Divisors found: r1=20021116406067209554446200468334668005750140859 (pp47) r2=356962853960238997946851914156890231498548267914175830313090442617598040829 (pp75) Version: GGNFS-0.77.1-20060513-k8 Total time: 17.14 hours. Scaled time: 34.23 units (timescale=1.997). Factorization parameters were as follows: nama: 26669_143 n: 7146794851779914387843228963979571845388741890295760803609820465560862056129003230767892770563281325758005179009183132111 m: 20000000000000000000000000000 c5: 250 c0: 7 skew: 0.49 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2550001) Primes: RFBsize:100021, AFBsize:100373, largePrimes:2900939 encountered Relations: rels:2943333, finalFF:278741 Max relations in full relation-set: 28 Initial matrix: 200460 x 278741 with sparse part having weight 32014645. Pruned matrix : 180795 x 181861 with weight 19476116. Total sieving time: 16.50 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.43 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 17.14 hours. --------- CPU info (if available) ----------
Oct 22, 2007: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(13·10¹⁶⁵-1)/3 = 4(3)₁₆₅_<166> = 7 · 801331 · C159
C159 = P77 · P83
P77 = 20581230672475861430727158263255086663302501457153191742856250309416063163917_<77>
P83 = 37535376232092446430954426168419670162044288493908322073297750728833564783295676597_<83>

Number: n N=772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449 ( 159 digits) SNFS difficulty: 166 digits. Divisors found: Mon Oct 22 02:26:02 2007 prp77 factor: 20581230672475861430727158263255086663302501457153191742856250309416063163917 Mon Oct 22 02:26:02 2007 prp83 factor: 37535376232092446430954426168419670162044288493908322073297750728833564783295676597 Mon Oct 22 02:26:02 2007 elapsed time 02:07:00 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 54.52 hours. Scaled time: 65.37 units (timescale=1.199). Factorization parameters were as follows: name: KA_4_3_165 n: 772524236610862487060961848534025324889524577294050832451318642418200528394692853574389419127735753449721834821125875633937845433469588781189106148455031750449 type: snfs skew: 0.60 deg: 5 c5: 13 c0: -1 m: 1000000000000000000000000000000000 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 special-q in [100000, 2300001) Primes: RFBsize:250150, AFBsize:249271, largePrimes:7324010 encountered Relations: rels:6828395, finalFF:550183 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 54.23 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 54.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
(8·10¹⁶²+7)/3 = 2(6)₁₆₁9_<163> = 23 · 2417 · C158
C158 = P38 · P121
P38 = 13758431094795674099921153836784941879_<38>
P121 = 3486545464024582803252161746345501308393073883180459970373351716778246003294776444321266822336985947908508412928696412621_<121>
Oct 21, 2007 (5th): By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(2·10¹⁶⁵+1)/3 = (6)₁₆₄7_<165> = 1907 · 25763 · 1950089 · C151
C151 = P38 · P54 · P61
P38 = 11159480313913593484408359509139419441_<38>
P54 = 145144015245287700460200196670856548838130894793891909_<54>
P61 = 4295998076553065365533511361350566844970496455322403010819807_<61>

prp38 factor: 11159480313913593484408359509139419441 prp54 factor: 145144015245287700460200196670856548838130894793891909 prp61 factor: 4295998076553065365533511361350566844970496455322403010819807 GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM] Input number is 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283 (151 digits) Using B1=1361500, B2=1303162716, polynomial Dickson(6), sigma=52991453 Step 1 took 19547ms Step 2 took 9719ms ********** Factor found in step 2: 11159480313913593484408359509139419441 Found probable prime factor of 38 digits: 11159480313913593484408359509139419441 Composite cofactor 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563 has 114 digits Number: n N=623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563 ( 114 digits) SNFS difficulty: 165 digits. Divisors found: Sun Oct 21 14:25:53 2007 prp54 factor: 145144015245287700460200196670856548838130894793891909 Sun Oct 21 14:25:53 2007 prp61 factor: 4295998076553065365533511361350566844970496455322403010819807 Sun Oct 21 14:25:53 2007 elapsed time 01:41:00 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.08 hours. Scaled time: 62.64 units (timescale=1.454). Factorization parameters were as follows: name: KA_6_164_7 n: 623538410316944757090120947223253498225421302104017860093686064012093871425660741494485547326568250544542234241563 # n: 6958364614900921735999678821358908199403904875839651413675026093315854699909592774863910249349186886963352504343210374853320078119407677971416772426283 skew: 0.87 deg: 5 c5: 2 c0: 1 m: 1000000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300001) Primes: RFBsize:203362, AFBsize:203032, largePrimes:7214058 encountered Relations: rels:6650540, finalFF:426929 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 42.87 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 43.08 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(8·10¹⁶⁵-53)/9 = (8)₁₆₄3_<165> = 6403993 · C159
C159 = P45 · P114
P45 = 350982021485651168585060151283338980210340619_<45>
P114 = 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649_<114>

Number: n N=138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731 ( 159 digits) SNFS difficulty: 165 digits. Divisors found: Sun Oct 21 20:17:38 2007 prp45 factor: 350982021485651168585060151283338980210340619 Sun Oct 21 20:17:38 2007 prp114 factor: 395468373808917744465660761189260784883193175621159446317143996419722368165129799067011823208112320581081097991649 Sun Oct 21 20:17:38 2007 elapsed time 01:35:15 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 47.74 hours. Scaled time: 63.31 units (timescale=1.326). Factorization parameters were as follows: name: KA_8_164_3 n: 138802289273097095654053477086700264801802389366897947716196580616013928948530844566645979920479127458273125671575357575951268043061397613783914018783107490731 skew: 1.46 deg: 5 c5: 8 c0: -53 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 special-q in [100000, 2200000) Primes: RFBsize:250150, AFBsize:250051, largePrimes:7311231 encountered Relations: rels:6818524, finalFF:565781 Max relations in full relation-set: 28 Initial matrix: 500266 x 565781 with sparse part having weight 42203089. Pruned matrix : 447352 x 449917 with weight 27775961. Total sieving time: 47.50 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 47.74 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 21, 2007 (4th): By anonymous / GMP-ECM
(5·10¹⁹⁰+7)/3 = 1(6)₁₈₉9_<191> = 983 · 3110537 · 4168826771_<10> · 54213944958939972267302651_<26> · C146
C146 = P29 · P117
P29 = 95241712200343898401070633893_<29>
P117 = 253225715089880357003437152506851618536597279889801230013665252373632182359449182088181293413579341092522759275175463_<117>
Oct 21, 2007 (3rd): By Sinkiti Sibata / GGNFS
(8·10¹³⁰+7)/3 = 2(6)₁₂₉9_<131> = 359 · C128
C128 = P33 · P96
P33 = 682633639211723545834566164085833_<33>
P96 = 108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227_<96>

Number: 26669_130 N=74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091 ( 128 digits) SNFS difficulty: 130 digits. Divisors found: r1=682633639211723545834566164085833 (pp33) r2=108814456650602300245382079887888010720933070751698732192617045113744525935607329203942293274227 (pp96) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.74 hours. Scaled time: 7.43 units (timescale=1.987). Factorization parameters were as follows: name: 26669_130 n: 74280408542246982358402971216341689879294336118848653667595171773444753946146703806870937790157845868152274837511606313834726091 m: 100000000000000000000000000 c5: 8 c0: 7 skew: 0.97 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 850001) Primes: RFBsize:63951, AFBsize:64073, largePrimes:1455357 encountered Relations: rels:1452260, finalFF:170662 Max relations in full relation-set: 28 Initial matrix: 128089 x 170662 with sparse part having weight 10762332. Pruned matrix : 114592 x 115296 with weight 5636879. Total sieving time: 3.59 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.07 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 3.74 hours. --------- CPU info (if available) ----------
(8·10¹³³+7)/3 = 2(6)₁₃₂9_<134> = 73 · 523 · 30253 · 694831 · 1145213 · C113
C113 = P42 · P72
P42 = 133271547249140168413145147446888048704353_<42>
P72 = 217707224173432323868406589757746873580273750494054826756936569259268393_<72>

Number: 26669_133 N=29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729 ( 113 digits) SNFS difficulty: 133 digits. Divisors found: r1=133271547249140168413145147446888048704353 (pp42) r2=217707224173432323868406589757746873580273750494054826756936569259268393 (pp72) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.92 hours. Scaled time: 13.77 units (timescale=1.988). Factorization parameters were as follows: name: 26669_133 n: 29014178612908736597074844178599916279879417120217498603765526981626610191279580281530698625258572423340334414729 m: 200000000000000000000000000 c5: 250 c0: 7 skew: 0.49 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1225001) Primes: RFBsize:78498, AFBsize:64168, largePrimes:1593511 encountered Relations: rels:1626248, finalFF:203055 Max relations in full relation-set: 28 Initial matrix: 142732 x 203055 with sparse part having weight 17060245. Pruned matrix : 124557 x 125334 with weight 8832672. Total sieving time: 6.72 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.08 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.92 hours. --------- CPU info (if available) ----------
(8·10¹⁰³+7)/3 = 2(6)₁₀₂9_<104> = 6641346161_<10> · C94
C94 = P44 · P50
P44 = 50628118279694776375171982905395943152916717_<44>
P50 = 79308699618830633011348707020263138933756280563537_<50>

Number: 26669_103 N=4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029 ( 94 digits) SNFS difficulty: 103 digits. Divisors found: r1=50628118279694776375171982905395943152916717 (pp44) r2=79308699618830633011348707020263138933756280563537 (pp50) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.18 hours. Scaled time: 2.36 units (timescale=1.995). Factorization parameters were as follows: name: 26669_103 n: 4015250224910941314607779057861800657715583674522859533065478269484027075195044432297987948029 m: 200000000000000000000 c5: 250 c0: 7 skew: 0.49 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 350001) Primes: RFBsize:37706, AFBsize:41542, largePrimes:1391765 encountered Relations: rels:1503988, finalFF:273193 Max relations in full relation-set: 28 Initial matrix: 79314 x 273193 with sparse part having weight 11183859. Pruned matrix : 40266 x 40726 with weight 1829275. Total sieving time: 1.13 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,103,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 1.18 hours. --------- CPU info (if available) ----------
(8·10¹⁰⁴+7)/3 = 2(6)₁₀₃9_<105> = 76561 · C100
C100 = P33 · P67
P33 = 733945223005884153559250475665329_<33>
P67 = 4745669469153279016048570235521763800475125498182552663288629329901_<67>

Number: 26669_104 N=3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429 ( 100 digits) SNFS difficulty: 105 digits. Divisors found: r1=733945223005884153559250475665329 (pp33) r2=4745669469153279016048570235521763800475125498182552663288629329901 (pp67) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.96 hours. Scaled time: 3.87 units (timescale=1.977). Factorization parameters were as follows: name: 26669_104 n: 3483061436849919236512933042497703356365077084503424284775103076849396777297405554612226416408702429 m: 1000000000000000000000 c5: 4 c0: 35 skew: 1.54 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 450001) Primes: RFBsize:49098, AFBsize:64193, largePrimes:2081424 encountered Relations: rels:2253638, finalFF:328853 Max relations in full relation-set: 28 Initial matrix: 113355 x 328853 with sparse part having weight 22829670. Pruned matrix : 62492 x 63122 with weight 3004338. Total sieving time: 1.88 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,105,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.96 hours. --------- CPU info (if available) ----------
(8·10¹³⁴+7)/3 = 2(6)₁₃₃9_<135> = 148654243 · 1262823917_<10> · C118
C118 = P41 · P77
P41 = 37620956682884538589371868827603031738343_<41>
P77 = 37758852612331776616795032844299692308607656131997210191374930427924942519293_<77>

Number: 26669_134 N=1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499 ( 118 digits) SNFS difficulty: 135 digits. Divisors found: r1=37620956682884538589371868827603031738343 (pp41) r2=37758852612331776616795032844299692308607656131997210191374930427924942519293 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.82 hours. Scaled time: 11.68 units (timescale=2.007). Factorization parameters were as follows: name: 26669_134 n: 1420524158523955469338558698249232537056327868898328355704847871904688048016727899141317771917491175737048611605351499 m: 1000000000000000000000000000 c5: 4 c0: 35 skew: 1.54 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:64193, largePrimes:1541556 encountered Relations: rels:1560889, finalFF:192289 Max relations in full relation-set: 28 Initial matrix: 142755 x 192289 with sparse part having weight 14621950. Pruned matrix : 126409 x 127186 with weight 7901050. Total sieving time: 5.64 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.82 hours. --------- CPU info (if available) ----------
(8·10¹⁴²+7)/3 = 2(6)₁₄₁9_<143> = 3064708476607_<13> · 4187678852923_<13> · C118
C118 = P40 · P78
P40 = 9788973638568650061780766529522450169529_<40>
P78 = 212260427653808834797575069001986356489959724932965465429439372027648665816401_<78>

Number: 26669_142 N=2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129 ( 118 digits) SNFS difficulty: 142 digits. Divisors found: r1=9788973638568650061780766529522450169529 (pp40) r2=212260427653808834797575069001986356489959724932965465429439372027648665816401 (pp78) Version: GGNFS-0.77.1-20060513-k8 Total time: 10.11 hours. Scaled time: 20.14 units (timescale=1.992). Factorization parameters were as follows: name: 26669_142 n: 2077811730814442779423909735030670832942412279493881032584070517296902178699768133028182972994685705973158369638645129 m: 20000000000000000000000000000 c5: 25 c0: 7 skew: 0.78 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 1750001) Primes: RFBsize:100021, AFBsize:99418, largePrimes:2798512 encountered Relations: rels:2847765, finalFF:330698 Max relations in full relation-set: 28 Initial matrix: 199503 x 330698 with sparse part having weight 30315932. Pruned matrix : 162985 x 164046 with weight 13847017. Total sieving time: 9.75 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.21 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 10.11 hours. --------- CPU info (if available) ----------
Oct 21, 2007 (2nd): By Jo Yeong Uk / GGNFS
(8·10¹³⁹+7)/3 = 2(6)₁₃₈9_<140> = 1768103158425827_<16> · 27452760668249467_<17> · C108
C108 = P40 · P69
P40 = 1241873230306512944129120625376444423573_<40>
P69 = 442382402449578672496474001239726150208458221956431612701743308645417_<69>

Number: 26669_139 N=549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941 ( 108 digits) SNFS difficulty: 140 digits. Divisors found: r1=1241873230306512944129120625376444423573 (pp40) r2=442382402449578672496474001239726150208458221956431612701743308645417 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.56 hours. Scaled time: 11.90 units (timescale=2.140). Factorization parameters were as follows: n: 549382863160814110758042194456932311882676877376245309068323886591250711707365842143014691420858830013214941 m: 10000000000000000000000000000 c5: 4 c0: 35 skew: 1.54 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1100001) Primes: RFBsize:114155, AFBsize:114442, largePrimes:3315311 encountered Relations: rels:3411950, finalFF:393858 Max relations in full relation-set: 28 Initial matrix: 228661 x 393858 with sparse part having weight 33230335. Pruned matrix : 169036 x 170243 with weight 12385404. Total sieving time: 5.40 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,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 5.56 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹⁴¹+7)/3 = 2(6)₁₄₀9_<142> = 29 · 73 · 1339806917806153_<16> · 92415619460291259403_<20> · C104
C104 = P39 · P65
P39 = 502212812269744236328154953897511547463_<39>
P65 = 20256877015611825323436706422598519488570631957881652952297498821_<65>

Number: 26669_141 N=10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123 ( 104 digits) SNFS difficulty: 142 digits. Divisors found: r1=502212812269744236328154953897511547463 (pp39) r2=20256877015611825323436706422598519488570631957881652952297498821 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.21 hours. Scaled time: 13.22 units (timescale=2.127). Factorization parameters were as follows: n: 10173263173812758517105524274113209930018018460702750505221307224574470950799246504255661100980128041123 m: 20000000000000000000000000000 c5: 5 c0: 14 skew: 1.23 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114392, largePrimes:3261056 encountered Relations: rels:3266559, finalFF:311634 Max relations in full relation-set: 28 Initial matrix: 228612 x 311634 with sparse part having weight 26294993. Pruned matrix : 196110 x 197317 with weight 13252279. Total sieving time: 6.01 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,142,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.21 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹⁵¹+7)/3 = 2(6)₁₅₀9_<152> = 83 · 191 · 222531925376261959597_<21> · 87151965549522581150273_<23> · C104
C104 = P37 · P68
P37 = 2151824979439633304570135127360335431_<37>
P68 = 40307031630293129082698941368209006104445744505208908458146567077043_<68>

Number: 26669_151 N=86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533 ( 104 digits) Divisors found: r1=2151824979439633304570135127360335431 (pp37) r2=40307031630293129082698941368209006104445744505208908458146567077043 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.74 hours. Scaled time: 12.28 units (timescale=2.138). Factorization parameters were as follows: name: 26669_151 n: 86733677509128161765261668212148242470942103656896529718188268435982587405152137619461718298337699610533 skew: 11778.21 # norm 6.95e+14 c5: 62160 c4: 1496130332 c3: -45556222412128 c2: -74626143902162469 c1: 113505084408824096690 c0: -1919290235623806504596725 # alpha -6.68 Y1: 4648483103 Y0: -67442740130436131592 # Murphy_E 2.11e-09 # M 56184838726415761082613399246235419642783909465629485767916514734753284656665661743230574578593360749961 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, 1620001) Primes: RFBsize:135072, AFBsize:135343, largePrimes:4346551 encountered Relations: rels:4257071, finalFF:317428 Max relations in full relation-set: 28 Initial matrix: 270499 x 317428 with sparse part having weight 25317400. Pruned matrix : 238627 x 240043 with weight 16192467. Polynomial selection time: 0.39 hours. Total sieving time: 5.00 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,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 5.74 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 21, 2007: By Yousuke Koide
10¹⁰⁷³+1 is divisible by 588831771788611721102815421599303_<33>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 20, 2007 (5th): By Jo Yeong Uk / GGNFS
(8·10¹³⁷+7)/3 = 2(6)₁₃₆9_<138> = 13 · 773 · 56401 · 23192382931_<11> · 887752643993_<12> · C107
C107 = P36 · P72
P36 = 225827415705440762247969188163076931_<36>
P72 = 101191741405873712462631199841067741763362688081142783407044807587961997_<72>

Number: 26669_137 N=22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207 ( 107 digits) SNFS difficulty: 137 digits. Divisors found: r1=225827415705440762247969188163076931 (pp36) r2=101191741405873712462631199841067741763362688081142783407044807587961997 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.05 hours. Scaled time: 6.48 units (timescale=2.122). Factorization parameters were as follows: n: 22851869452421705492448224919086710644084493570019228618031253647076457659430866698743479971878791015391207 m: 2000000000000000000000000000 c5: 25 c0: 7 skew: 0.78 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1250001) Primes: RFBsize:107126, AFBsize:106423, largePrimes:2289110 encountered Relations: rels:2432530, finalFF:305349 Max relations in full relation-set: 28 Initial matrix: 213613 x 305349 with sparse part having weight 22381011. Pruned matrix : 177541 x 178673 with weight 10158100. Total sieving time: 2.91 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.09 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.05 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 20, 2007 (4th): By Sinkiti Sibata / GGNFS
8·10¹⁶²-7 = 7(9)₁₆₁3_<163> = 494213 · 388509891553534266757079_<24> · C134
C134 = P59 · P76
P59 = 16147676136454049333700128338546853224145331776821755134693_<59>
P76 = 2580261432154997404112328929704725753375527855692727120431726388111826233063_<76>

Number: 79993_162 N=41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659 ( 134 digits) SNFS difficulty: 162 digits. Divisors found: r1=16147676136454049333700128338546853224145331776821755134693 (pp59) r2=2580261432154997404112328929704725753375527855692727120431726388111826233063 (pp76) Version: GGNFS-0.77.1-20060513-k8 Total time: 61.95 hours. Scaled time: 124.03 units (timescale=2.002). Factorization parameters were as follows: name: 79993_162 n: 41665225953822000619568717595040558356062958012654461159308411510245494930736049031230987938063485411773501288539791869984896374954659 m: 200000000000000000000000000000000 c5: 25 c0: -7 skew: 0.78 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:315706, largePrimes:5839925 encountered Relations: rels:6045274, finalFF:823077 Max relations in full relation-set: 28 Initial matrix: 631718 x 823077 with sparse part having weight 47717456. Pruned matrix : 473657 x 476879 with weight 31143738. Total sieving time: 59.04 hours. Total relation processing time: 0.22 hours. Matrix solve time: 2.51 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 61.95 hours. --------- CPU info (if available) ----------
(8·10¹¹¹+7)/3 = 2(6)₁₁₀9_<112> = 2145389 · 1377179399_<10> · C96
C96 = P35 · P62
P35 = 18106717789925267749261242702101927_<35>
P62 = 49846243240205443718855673321344571054539531011124970246880177_<62>

Number: 26669_111 N=902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079 ( 96 digits) SNFS difficulty: 112 digits. Divisors found: r1=18106717789925267749261242702101927 (pp35) r2=49846243240205443718855673321344571054539531011124970246880177 (pp62) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.44 hours. Scaled time: 2.88 units (timescale=2.004). Factorization parameters were as follows: name: 26669_111 n: 902551859238370029090835659332155419008692464984287175991403902356426578709847092352072009801079 m: 20000000000000000000000 c5: 5 c0: 14 skew: 1.23 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 450001) Primes: RFBsize:49098, AFBsize:63943, largePrimes:2241963 encountered Relations: rels:2551561, finalFF:441249 Max relations in full relation-set: 28 Initial matrix: 113106 x 441249 with sparse part having weight 35014615. Pruned matrix : 62074 x 62703 with weight 4765126. Total sieving time: 1.35 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.02 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,112,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.44 hours. --------- CPU info (if available) ----------
(8·10¹²³+7)/3 = 2(6)₁₂₂9_<124> = 1229019557_<10> · 379092951201193_<15> · C100
C100 = P49 · P52
P49 = 2898545393005568842248882069535618909163031509171_<49>
P52 = 1974622690311058776335153117537051940589078496100539_<52>

Number: 26669_123 N=5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169 ( 100 digits) SNFS difficulty: 123 digits. Divisors found: r1=2898545393005568842248882069535618909163031509171 (pp49) r2=1974622690311058776335153117537051940589078496100539 (pp52) Version: GGNFS-0.77.1-20060513-k8 Total time: 2.84 hours. Scaled time: 5.61 units (timescale=1.980). Factorization parameters were as follows: name: 26669_123 n: 5723533501925381515361880891681341029181435487375163222371432533464834744116374151471404911716543169 m: 2000000000000000000000000 c5: 250 c0: 7 skew: 0.49 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:64168, largePrimes:2114570 encountered Relations: rels:2123330, finalFF:147078 Max relations in full relation-set: 28 Initial matrix: 113332 x 147078 with sparse part having weight 13374411. Pruned matrix : 104524 x 105154 with weight 7551198. Total sieving time: 2.67 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,123,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.84 hours. --------- CPU info (if available) ----------
(8·10¹²⁸+7)/3 = 2(6)₁₂₇9_<129> = 419 · 16311689 · 7428034067_<10> · C109
C109 = P45 · P65
P45 = 351941064731415296526137239470932854807364819_<45>
P65 = 14924917745215309816252937894497602188907340265178654448165423583_<65>

Number: 26669_128 N=5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477 ( 109 digits) SNFS difficulty: 128 digits. Divisors found: r1=351941064731415296526137239470932854807364819 (pp45) r2=14924917745215309816252937894497602188907340265178654448165423583 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.50 hours. Scaled time: 8.89 units (timescale=1.977). Factorization parameters were as follows: name: 26669_128 n: 5252691442279870184066566890500076729558621086294228055364583650241045931829029287346821680267717975147126477 m: 20000000000000000000000000 c5: 250 c0: 7 skew: 0.49 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:64168, largePrimes:1486278 encountered Relations: rels:1489312, finalFF:175012 Max relations in full relation-set: 28 Initial matrix: 128185 x 175012 with sparse part having weight 12253287. Pruned matrix : 114089 x 114793 with weight 6318497. Total sieving time: 4.34 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.50 hours. --------- CPU info (if available) ----------
Oct 20, 2007 (3rd): By Jo Yeong Uk / GGNFS
6·10¹⁵⁷+7 = 6(0)₁₅₆7_<158> = 29575545858739133328361799_<26> · C133
C133 = P54 · P79
P54 = 909973554507637615273149646490856241896005712528152743_<54>
P79 = 2229408796486527839879415799102804165173602971152320543487096830961582839982551_<79>

Number: 60007_157 N=2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393 ( 133 digits) SNFS difficulty: 158 digits. Divisors found: r1=909973554507637615273149646490856241896005712528152743 (pp54) r2=2229408796486527839879415799102804165173602971152320543487096830961582839982551 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 31.18 hours. Scaled time: 66.81 units (timescale=2.143). Factorization parameters were as follows: n: 2028703046989440216492418523064717588124374356914471327996618052411940079032641598918868315472019544767523143015305980889826382787393 m: 20000000000000000000000000000000 c5: 75 c0: 28 skew: 0.82 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, 3800001) Primes: RFBsize:283146, AFBsize:283092, largePrimes:5685473 encountered Relations: rels:5694522, finalFF:634310 Max relations in full relation-set: 28 Initial matrix: 566304 x 634310 with sparse part having weight 42093593. Pruned matrix : 518113 x 521008 with weight 30976126. Total sieving time: 29.55 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.48 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 31.18 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹²⁰+7)/3 = 2(6)₁₁₉9_<121> = C121
C121 = P61 · P61
P61 = 1060471105842071452080239329331029536565351505210275149416401_<61>
P61 = 2514605680415204721631917533968366670395835407292136222935069_<61>

Number: 26669_120 N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 ( 121 digits) SNFS difficulty: 121 digits. Divisors found: r1=1060471105842071452080239329331029536565351505210275149416401 (pp61) r2=2514605680415204721631917533968366670395835407292136222935069 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.89 hours. Scaled time: 1.88 units (timescale=2.115). Factorization parameters were as follows: n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 m: 2000000000000000000000000 c5: 1 c0: 28 skew: 1.95 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [300000, 450001) Primes: RFBsize:49098, AFBsize:49156, largePrimes:1800198 encountered Relations: rels:1786914, finalFF:141902 Max relations in full relation-set: 28 Initial matrix: 98318 x 141902 with sparse part having weight 11624596. Pruned matrix : 86828 x 87383 with weight 5098835. Total sieving time: 0.84 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,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 0.89 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹²⁹+7)/3 = 2(6)₁₂₈9_<130> = C130
C130 = P34 · P97
P34 = 1638212584355948805449002823879881_<34>
P97 = 1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549_<97>

Number: 26669_129 N=2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 ( 130 digits) SNFS difficulty: 130 digits. Divisors found: r1=1638212584355948805449002823879881 (pp34) r2=1627790368681026216200316702373859265165289584295147399375933455475170245176591783551889658852549 (pp97) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.97 hours. Scaled time: 4.23 units (timescale=2.142). Factorization parameters were as follows: n: 2666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 m: 100000000000000000000000000 c5: 4 c0: 35 skew: 1.54 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 900001) Primes: RFBsize:78498, AFBsize:78746, largePrimes:1495528 encountered Relations: rels:1503818, finalFF:187166 Max relations in full relation-set: 28 Initial matrix: 157308 x 187166 with sparse part having weight 9227172. Pruned matrix : 142970 x 143820 with weight 5564851. 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,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(16·10¹⁵⁹-61)/9 = 1(7)₁₅₈1_<160> = 7 · 11 · 139 · 283 · 1123 · 5563 · 11321 · 1123247 · 11160628967_<11> · C126
C126 = P48 · P79
P48 = 188771796820566483431209728112718047569192774367_<48>
P79 = 3506798873133264834251861643109592173565728384191166286258478470759285819773297_<79>

Number: 17771_159 N=661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999 ( 126 digits) SNFS difficulty: 161 digits. Divisors found: r1=188771796820566483431209728112718047569192774367 (pp48) r2=3506798873133264834251861643109592173565728384191166286258478470759285819773297 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 29.47 hours. Scaled time: 63.21 units (timescale=2.145). Factorization parameters were as follows: n: 661984724369704169532858342692717943247722809774460911744787521251800997758672407790754400607584194600473401375243866412677999 m: 200000000000000000000000000000000 c5: 1 c0: -1220 skew: 4.14 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, 3700001) Primes: RFBsize:283146, AFBsize:282548, largePrimes:5712059 encountered Relations: rels:5803604, finalFF:708737 Max relations in full relation-set: 28 Initial matrix: 565758 x 708737 with sparse part having weight 44615649. Pruned matrix : 451837 x 454729 with weight 28540403. Total sieving time: 28.30 hours. Total relation processing time: 0.08 hours. Matrix solve time: 1.04 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 29.47 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹⁰⁶+7)/3 = 2(6)₁₀₅9_<107> = 38933 · C102
C102 = P31 · P72
P31 = 4246217137079532440315775172579_<31>
P72 = 161305309862279566253022081601447659781689908478972816016415808296252467_<72>

Number: 26669_106 N=684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393 ( 102 digits) SNFS difficulty: 107 digits. Divisors found: r1=4246217137079532440315775172579 (pp31) r2=161305309862279566253022081601447659781689908478972816016415808296252467 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.46 hours. Scaled time: 0.97 units (timescale=2.131). Factorization parameters were as follows: n: 684937371039135609037748610861394361253092920316098596734561083570920983912533497718302382725879502393 m: 2000000000000000000000 c5: 5 c0: 14 skew: 1.23 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:30719, largePrimes:1032267 encountered Relations: rels:965725, finalFF:100183 Max relations in full relation-set: 28 Initial matrix: 61541 x 100183 with sparse part having weight 4259001. Pruned matrix : 47943 x 48314 with weight 1440203. 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,107,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.46 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹¹⁴+7)/3 = 2(6)₁₁₃9_<115> = 19 · 59 · 131 · 1613 · 172841183 · C98
C98 = P38 · P61
P38 = 15049466556427553742046054404910545751_<38>
P61 = 4328018617649452918247261765466850080785970021940189130656211_<61>

Number: 26669_114 N=65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461 ( 98 digits) SNFS difficulty: 115 digits. Divisors found: r1=15049466556427553742046054404910545751 (pp38) r2=4328018617649452918247261765466850080785970021940189130656211 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.67 hours. Scaled time: 1.44 units (timescale=2.143). Factorization parameters were as follows: n: 65134371441911253580479783239297921264158773495625664468264260314515100006542227915558640767809461 m: 100000000000000000000000 c5: 4 c0: 35 skew: 1.54 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [300000, 390001) Primes: RFBsize:49098, AFBsize:49236, largePrimes:1810475 encountered Relations: rels:1862920, finalFF:208249 Max relations in full relation-set: 28 Initial matrix: 98398 x 208249 with sparse part having weight 15809065. Pruned matrix : 71479 x 72034 with weight 3436955. Total sieving time: 0.63 hours. Total relation processing time: 0.02 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 0.67 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹²¹+7)/3 = 2(6)₁₂₀9_<122> = 1201 · 130987 · 356098343 · C105
C105 = P34 · P72
P34 = 2613842632420286549810407132723579_<34>
P72 = 182116015280402325835265886158642537928794970041065896876634298939239171_<72>

Number: 26669_121 N=476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009 ( 105 digits) SNFS difficulty: 122 digits. Divisors found: r1=2613842632420286549810407132723579 (pp34) r2=182116015280402325835265886158642537928794970041065896876634298939239171 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.03 hours. Scaled time: 2.21 units (timescale=2.145). Factorization parameters were as follows: n: 476022604786419945107592660920030371584869577656015528481440710159671902378490644477488507224323312113009 m: 2000000000000000000000000 c5: 5 c0: 14 skew: 1.23 type: snfs Factor base limits: 600000/600000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [300000, 480001) Primes: RFBsize:49098, AFBsize:49101, largePrimes:1853503 encountered Relations: rels:1867932, finalFF:158603 Max relations in full relation-set: 28 Initial matrix: 98264 x 158603 with sparse part having weight 13988463. Pruned matrix : 85087 x 85642 with weight 5253077. Total sieving time: 0.97 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,122,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 1.03 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹²²+7)/3 = 2(6)₁₂₁9_<123> = 71 · C121
C121 = P32 · P89
P32 = 41145387625225226433684691675373_<32>
P89 = 91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343_<89>

Number: 26669_122 N=3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939 ( 121 digits) SNFS difficulty: 122 digits. Divisors found: r1=41145387625225226433684691675373 (pp32) r2=91282857238129608087362318513711416984201527885327331838828175050639169331657601989276343 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.01 hours. Scaled time: 2.16 units (timescale=2.140). Factorization parameters were as follows: n: 3755868544600938967136150234741784037558685446009389671361502347417840375586854460093896713615023474178403755868544600939 m: 2000000000000000000000000 c5: 25 c0: 7 skew: 0.78 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:63951, AFBsize:63568, largePrimes:1347942 encountered Relations: rels:1344158, finalFF:170026 Max relations in full relation-set: 28 Initial matrix: 127582 x 170026 with sparse part having weight 7333871. Pruned matrix : 103697 x 104398 with weight 3449577. Total sieving time: 0.96 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,122,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000 total time: 1.01 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
(8·10¹³⁶+7)/3 = 2(6)₁₃₅9_<137> = C137
C137 = P58 · P79
P58 = 5964796989232317289442216128587619639536748687234582636411_<58>
P79 = 4470674645726497105263584854203238916337233478995531171674915681021609495628279_<79>

Number: 26669_136 N=26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 ( 137 digits) SNFS difficulty: 137 digits. Divisors found: r1=5964796989232317289442216128587619639536748687234582636411 (pp58) r2=4470674645726497105263584854203238916337233478995531171674915681021609495628279 (pp79) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.34 hours. Scaled time: 7.05 units (timescale=2.115). Factorization parameters were as follows: n: 26666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666669 m: 2000000000000000000000000000 c5: 5 c0: 14 skew: 1.23 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1300001) Primes: RFBsize:107126, AFBsize:107483, largePrimes:2282771 encountered Relations: rels:2388130, finalFF:269548 Max relations in full relation-set: 28 Initial matrix: 214674 x 269548 with sparse part having weight 20402502. Pruned matrix : 193656 x 194793 with weight 11687881. Total sieving time: 3.16 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,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.34 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 20, 2007 (2nd): By Sinkiti Sibata / PRIMO
(19·10²⁴⁵⁰-1)/9 is prime.
Oct 20, 2007: The factor table of 266...669 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.
Oct 19, 2007 (4th): By anonymous / GMP-ECM
(5·10¹⁹⁷+7)/3 = 1(6)₁₉₆9_<198> = 83 · C196
C196 = P32 · P165
P32 = 15064399083367851403807447165139_<32>
P165 = 133296530276542123994572514856391958946944378887295148756651456417065116602615650106241786028692598529148978098311741021285646641176103363192439421156437978817430437_<165>
Oct 19, 2007 (3rd): By Robert Backstrom / GGNFS, Msieve
(7·10¹⁶⁵-61)/9 = (7)₁₆₄1_<165> = 3 · 24320321 · C158
C158 = P43 · P56 · P60
P43 = 2761925283898534955675154755036172189749839_<43>
P56 = 31324884696363766525451707222706492435165921240617655521_<56>
P60 = 123214995686345230412614529840111656059539641564894743216343_<60>

Number: n N=10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817 ( 158 digits) SNFS difficulty: 165 digits. Divisors found: Fri Oct 19 11:07:36 2007 prp43 factor: 2761925283898534955675154755036172189749839 Fri Oct 19 11:07:36 2007 prp56 factor: 31324884696363766525451707222706492435165921240617655521 Fri Oct 19 11:07:36 2007 prp60 factor: 123214995686345230412614529840111656059539641564894743216343 Fri Oct 19 11:07:36 2007 elapsed time 01:47:49 (Msieve 1.28) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 68.73 hours. Scaled time: 89.90 units (timescale=1.308). Factorization parameters were as follows: name: KA_7_164_1 n: 10660190680018543310314829284500778557127566665722021483978737750182625437355833389668633866274185248593522234318340586839263316436459011345255650994872117817 skew: 1.54 deg: 5 c5: 7 c0: -61 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2700000) Primes: RFBsize:216816, AFBsize:217077, largePrimes:7393191 encountered Relations: rels:6842637, finalFF:458263 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 68.48 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 68.73 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 19, 2007 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁵⁷-7 = 7(9)₁₅₆3_<158> = 857 · 3270705001345087307_<19> · C137
C137 = P45 · P92
P45 = 578713235026034382304696193140789480917763057_<45>
P92 = 49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451_<92>

Number: 79993_157 N=28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707 ( 137 digits) SNFS difficulty: 157 digits. Divisors found: r1=578713235026034382304696193140789480917763057 (pp45) r2=49317877250812105191907662188584024853530218296906864974832385857053714133780682125502798451 (pp92) Version: GGNFS-0.77.1-20060513-k8 Total time: 32.59 hours. Scaled time: 64.80 units (timescale=1.988). Factorization parameters were as follows: name: 79993_157 n: 28540908288434340243572900615340141426849017077515115869543700976161255377143717419668797504442722574263007547983496570507801448444624707 m: 20000000000000000000000000000000 c5: 25 c0: -7 skew: 0.78 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, 2600001) Primes: RFBsize:216816, AFBsize:216906, largePrimes:5533011 encountered Relations: rels:5442369, finalFF:511459 Max relations in full relation-set: 28 Initial matrix: 433786 x 511459 with sparse part having weight 38990519. Pruned matrix : 385864 x 388096 with weight 26569740. Total sieving time: 30.52 hours. Total relation processing time: 0.14 hours. Matrix solve time: 1.78 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.59 hours. --------- CPU info (if available) ----------
Oct 19, 2007: By Yousuke Koide
10¹²⁴⁰+1 is divisible by 15595203791066837732161767737921_<32>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 17, 2007 (5th): By suberi / PRIMO
(49·10²³⁴⁰+23)/9 is prime.
(49·10²⁴⁵⁴+23)/9 is prime.
Oct 17, 2007 (4th): By Jo Yeong Uk / GGNFS
6·10¹⁴⁷+7 = 6(0)₁₄₆7_<148> = 31 · 74460874157397706814885857_<26> · C121
C121 = P34 · P87
P34 = 3757810852757300286714196049398151_<34>
P87 = 691713910870677076891814665811219671401933953308716939722566516154829814248796350852671_<87>

Number: 60007_147 N=2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321 ( 121 digits) SNFS difficulty: 148 digits. Divisors found: r1=3757810852757300286714196049398151 (pp34) r2=691713910870677076891814665811219671401933953308716939722566516154829814248796350852671 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 13.31 hours. Scaled time: 28.42 units (timescale=2.135). Factorization parameters were as follows: n: 2599330041273026231158261182959552205625966726296449796273234752243784692588394514029060595219631994321473925185220811321 m: 200000000000000000000000000000 c5: 75 c0: 28 skew: 0.82 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, 1800001) Primes: RFBsize:135072, AFBsize:134748, largePrimes:3940451 encountered Relations: rels:4092560, finalFF:408421 Max relations in full relation-set: 28 Initial matrix: 269886 x 408421 with sparse part having weight 41102101. Pruned matrix : 230332 x 231745 with weight 21474737. Total sieving time: 12.95 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.27 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 13.31 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
6·10¹⁴⁹+7 = 6(0)₁₄₈7_<150> = 25747 · 436150417 · 2488433141_<10> · 314768938357_<12> · C116
C116 = P45 · P72
P45 = 288204824127944521231161772400113432086544229_<45>
P72 = 236684181525452140035337569045008331845614114346156387833169766487401841_<72>

Number: 60007_149 N=68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589 ( 116 digits) SNFS difficulty: 150 digits. Divisors found: r1=288204824127944521231161772400113432086544229 (pp45) r2=236684181525452140035337569045008331845614114346156387833169766487401841 (pp72) Version: GGNFS-0.77.1-20050930-nocona Total time: 11.33 hours. Scaled time: 24.17 units (timescale=2.133). Factorization parameters were as follows: n: 68213522910409429827571176132944362685370905642562309751882399036574081305064117581575728647981845432390542542525589 m: 1000000000000000000000000000000 c5: 3 c0: 35 skew: 1.63 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, 1650001) Primes: RFBsize:135072, AFBsize:135283, largePrimes:3745970 encountered Relations: rels:3742941, finalFF:304925 Max relations in full relation-set: 28 Initial matrix: 270420 x 304925 with sparse part having weight 27971216. Pruned matrix : 258210 x 259626 with weight 21031729. Total sieving time: 10.95 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.30 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: 11.33 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 17, 2007 (3rd): By Robert Backstrom / GGNFS, Msieve
8·10¹⁶⁰-7 = 7(9)₁₅₉3_<161> = 179 · 2341 · C156
C156 = P74 · P83
P74 = 16454596943744503209146711864636020997566170732129357607128813577870908913_<74>
P83 = 11602412280012005744956049762841701654854199246869403531853864740606458920710587799_<83>

Number: n N=190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487 ( 156 digits) SNFS difficulty: 160 digits. Divisors found: Thu Oct 18 14:19:06 2007 prp74 factor: 16454596943744503209146711864636020997566170732129357607128813577870908913 Thu Oct 18 14:19:06 2007 prp83 factor: 11602412280012005744956049762841701654854199246869403531853864740606458920710587799 Thu Oct 18 14:19:06 2007 elapsed time 01:30:26 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 44.43 hours. Scaled time: 53.27 units (timescale=1.199). Factorization parameters were as follows: name: KA_7_9_159_3 n: 190913017642749242910564410472533582793009719859010736470829684110548182866033949107362321884120571116292278284360166953433928584212925288576958230618152487 type: snfs skew: 0.97 deg: 5 c5: 8 c0: -7 m: 100000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1900000) Primes: RFBsize:230209, AFBsize:229842, largePrimes:6910058 encountered Relations: rels:6394628, finalFF:542880 Max relations in full relation-set: 28 Initial matrix: 460116 x 542880 with sparse part having weight 33147572. Pruned matrix : 389747 x 392111 with weight 20148312. Total sieving time: 44.19 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 44.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Oct 17, 2007 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁵⁶-7 = 7(9)₁₅₅3_<157> = 181 · 909281 · C149
C149 = P41 · P49 · P61
P41 = 10904285406759073728471842840772332558593_<41>
P49 = 1088070887339914750056094304772577853777226365141_<49>
P61 = 4096933317053668078876000501612735226248308616390449901334401_<61>

Number: 79993_156 N=48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813 ( 149 digits) SNFS difficulty: 157 digits. Divisors found: r1=10904285406759073728471842840772332558593 (pp41) r2=1088070887339914750056094304772577853777226365141 (pp49) r3=4096933317053668078876000501612735226248308616390449901334401 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 40.39 hours. Scaled time: 80.67 units (timescale=1.997). Factorization parameters were as follows: name: 79993_156 n: 48608620467846913541870107667669010851819834748797120444766932935980545031569810354864742533717415158103700184799645686904547817062501954598199593813 m: 20000000000000000000000000000000 c5: 5 c0: -14 skew: 1.23 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:217381, largePrimes:5747043 encountered Relations: rels:5780210, finalFF:606107 Max relations in full relation-set: 28 Initial matrix: 434262 x 606107 with sparse part having weight 50764657. Pruned matrix : 345539 x 347774 with weight 31579083. Total sieving time: 38.37 hours. Total relation processing time: 0.18 hours. Matrix solve time: 1.68 hours. Time per square root: 0.17 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: 40.39 hours. --------- CPU info (if available) ----------
Oct 18, 2007: By Sinkiti Sibata / PRIMO
(8·10²³⁰⁸+7)/3 is prime.
Oct 17, 2007 (3rd): By Jo Yeong Uk / GGNFS
(4·10¹⁸⁸-31)/9 = (4)₁₈₇1_<188> = C188
C188 = P89 · P100
P89 = 13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861_<89>
P100 = 3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781_<100>

Number: 44441_188 N=44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 ( 188 digits) SNFS difficulty: 190 digits. Divisors found: r1=13495944323227175196168775505661471275310792953928331944840120875227820565323694150016861 (pp89) r2=3293170405864330551260159426012918407131606691963604942513292260623991525800017750997167920521516781 (pp100) Version: GGNFS-0.77.1-20050930-nocona Total time: 506.97 hours. Scaled time: 1079.34 units (timescale=2.129). Factorization parameters were as follows: n: 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 m: 100000000000000000000000000000000000000 c5: 1 c0: -775 skew: 3.78 type: snfs Factor base limits: 13000000/13000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 51/51 Sieved algebraic special-q in [6500000, 14600001) Primes: RFBsize:849252, AFBsize:849399, largePrimes:12866508 encountered Relations: rels:13641443, finalFF:1950967 Max relations in full relation-set: 28 Initial matrix: 1698715 x 1950967 with sparse part having weight 145829012. Pruned matrix : 1480381 x 1488938 with weight 111459556. Total sieving time: 484.73 hours. Total relation processing time: 0.40 hours. Matrix solve time: 21.67 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,190,5,0,0,0,0,0,0,0,0,13000000,13000000,28,28,51,51,2.6,2.6,100000 total time: 506.97 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
P89 is the largest factor found by GGNFS in our tables so far. Congratulations!
Oct 17, 2007 (2nd): By Robert Backstrom / GGNFS
8·10¹⁵⁸-7 = 7(9)₁₅₇3_<159> = 13 · 67 · C156
C156 = P75 · P82
P75 = 346176468096559273822741304052813207109273708583996031665987163333529663757_<75>
P82 = 2653226273941471985206044635089360508906271929143252016829426314360757542050928219_<82>

Number: n N=918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783 ( 156 digits) SNFS difficulty: 158 digits. Divisors found: r1=346176468096559273822741304052813207109273708583996031665987163333529663757 (pp75) r2=2653226273941471985206044635089360508906271929143252016829426314360757542050928219 (pp82) Version: GGNFS-0.77.1-20051202-athlon Total time: 41.09 hours. Scaled time: 53.30 units (timescale=1.297). Factorization parameters were as follows: name: KA_7_9_157_3 n: 918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783008036739380022962112514351320321469575200918484500574052812858783 skew: 0.49 deg: 5 c5: 250 c0: -7 m: 20000000000000000000000000000000 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, 1700001) Primes: RFBsize:216816, AFBsize:217701, largePrimes:7120715 encountered Relations: rels:6580353, finalFF:493138 Max relations in full relation-set: 48 Initial matrix: 434583 x 493138 with sparse part having weight 42370582. Pruned matrix : 389862 x 392098 with weight 27989624. Total sieving time: 36.05 hours. Total relation processing time: 0.22 hours. Matrix solve time: 4.66 hours. Total square root time: 0.16 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 41.09 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 17, 2007: By Sinkiti Sibata / GGNFS
8·10¹⁵⁵-7 = 7(9)₁₅₄3_<156> = 17 · 29 · 43 · 671189 · 25898947 · C139
C139 = P33 · P107
P33 = 152487428057225842444645257923753_<33>
P107 = 14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193_<107>

Number: 79993_155 N=2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329 ( 139 digits) SNFS difficulty: 155 digits. Divisors found: r1=152487428057225842444645257923753 (pp33) r2=14236841024808958548325101138045141061138828604047990755202358992513725161786539507007143495539941593140193 (pp107) Version: GGNFS-0.77.1-20060513-k8 Total time: 32.46 hours. Scaled time: 64.57 units (timescale=1.989). Factorization parameters were as follows: name: 79993_155 n: 2170939271532717501787887771947025467482753556964582820892856569651806507508303518706699363818037448964912725918478477349824220002633704329 m: 10000000000000000000000000000000 c5: 8 c0: -7 skew: 0.97 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, 2600001) Primes: RFBsize:216816, AFBsize:216531, largePrimes:5864311 encountered Relations: rels:6046107, finalFF:741412 Max relations in full relation-set: 28 Initial matrix: 433412 x 741412 with sparse part having weight 59974965. Pruned matrix : 286069 x 288300 with weight 35055031. Total sieving time: 30.74 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.41 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.46 hours. --------- CPU info (if available) ----------
Oct 16, 2007 (5th): By Sinkiti Sibata / PRIMO
(13·10²²¹⁵+23)/9 is prime.
Oct 16, 2007 (4th): By suberi / PRIMO
(32·10²⁴⁸⁸-41)/9 is prime.
6·10²⁷⁴⁹+7 is prime.
(55·10²⁶⁸⁴+17)/9 is prime.
Oct 16, 2007 (3rd): By Sinkiti Sibata / GGNFS, Msieve
8·10¹⁵⁴-7 = 7(9)₁₅₃3_<155> = 2356867 · 603555989507_<12> · C137
C137 = P33 · P105
P33 = 113351694760778508277044308809837_<33>
P105 = 496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581_<105>

Number: 79993_154 N=56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297 ( 137 digits) SNFS difficulty: 155 digits. Divisors found: r1=113351694760778508277044308809837 (pp33) r2=496145811653311910056803679142753059087314051602854121158090203147254006251607995277425635648201231426581 (pp105) Version: GGNFS-0.77.1-20060513-k8 Total time: 32.35 hours. Scaled time: 64.79 units (timescale=2.003). Factorization parameters were as follows: name: 79993_154 n: 56238968599364916192824354906296195040092106248699331349662875284930630365782995510575903116148472404164256027791590822905326605756077297 m: 10000000000000000000000000000000 c5: 4 c0: -35 skew: 1.54 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, 2600001) Primes: RFBsize:216816, AFBsize:216906, largePrimes:5878753 encountered Relations: rels:6079432, finalFF:757874 Max relations in full relation-set: 28 Initial matrix: 433786 x 757874 with sparse part having weight 61304584. Pruned matrix : 284596 x 286828 with weight 35456047. Total sieving time: 30.84 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.20 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 32.35 hours. --------- CPU info (if available) ----------
8·10¹⁵¹-7 = 7(9)₁₅₀3_<152> = 23 · 107 · 5569 · 6029 · 5676941659286357_<16> · 21788576409750498214905595223_<29> · C97
C97 = P31 · P67
P31 = 5423671886025109442120246388749_<31>
P67 = 1443175595670302296287530288340641513337370692964945259930652789367_<67>

Sun Oct 14 13:22:15 2007 Msieve v. 1.28 Sun Oct 14 13:22:15 2007 random seeds: bb320d00 c465a215 Sun Oct 14 13:22:15 2007 factoring 7827310904834559223584755757587750335344461821449169367211160089090463613553875031305565495631883 (97 digits) Sun Oct 14 13:22:16 2007 commencing quadratic sieve (97-digit input) Sun Oct 14 13:22:17 2007 using multiplier of 2 Sun Oct 14 13:22:17 2007 using 64kb Pentium 2 sieve core Sun Oct 14 13:22:17 2007 sieve interval: 18 blocks of size 65536 Sun Oct 14 13:22:17 2007 processing polynomials in batches of 6 Sun Oct 14 13:22:17 2007 using a sieve bound of 2395621 (88235 primes) Sun Oct 14 13:22:17 2007 using large prime bound of 359343150 (28 bits) Sun Oct 14 13:22:17 2007 using double large prime bound of 2511405435485700 (43-52 bits) Sun Oct 14 13:22:17 2007 using trial factoring cutoff of 52 bits Sun Oct 14 13:22:17 2007 polynomial 'A' values have 13 factors Tue Oct 16 05:45:50 2007 88486 relations (21837 full + 66649 combined from 1318373 partial), need 88331 Tue Oct 16 05:46:24 2007 begin with 1340210 relations Tue Oct 16 05:49:03 2007 reduce to 229420 relations in 11 passes Tue Oct 16 05:49:04 2007 attempting to read 229420 relations Tue Oct 16 05:49:50 2007 recovered 229420 relations Tue Oct 16 05:49:51 2007 recovered 215053 polynomials Tue Oct 16 05:51:40 2007 attempting to build 88486 cycles Tue Oct 16 05:51:49 2007 found 88486 cycles in 6 passes Tue Oct 16 05:51:55 2007 distribution of cycle lengths: Tue Oct 16 05:51:55 2007 length 1 : 21837 Tue Oct 16 05:51:55 2007 length 2 : 15474 Tue Oct 16 05:51:55 2007 length 3 : 15081 Tue Oct 16 05:51:55 2007 length 4 : 12029 Tue Oct 16 05:51:55 2007 length 5 : 8894 Tue Oct 16 05:51:55 2007 length 6 : 6072 Tue Oct 16 05:51:55 2007 length 7 : 3868 Tue Oct 16 05:51:55 2007 length 9+: 5231 Tue Oct 16 05:51:55 2007 largest cycle: 19 relations Tue Oct 16 05:52:26 2007 matrix is 88235 x 88486 with weight 5849695 (avg 66.11/col) Tue Oct 16 05:53:30 2007 filtering completed in 3 passes Tue Oct 16 05:53:30 2007 matrix is 83979 x 84043 with weight 5585692 (avg 66.46/col) Tue Oct 16 05:53:34 2007 saving the first 48 matrix rows for later Tue Oct 16 05:53:35 2007 matrix is 83931 x 84043 with weight 4343397 (avg 51.68/col) Tue Oct 16 05:53:35 2007 matrix includes 64 packed rows Tue Oct 16 05:53:35 2007 using block size 10922 for processor cache size 256 kB Tue Oct 16 05:53:38 2007 commencing Lanczos iteration Tue Oct 16 05:59:52 2007 lanczos halted after 1329 iterations Tue Oct 16 05:59:53 2007 recovered 18 nontrivial dependencies Tue Oct 16 06:24:18 2007 prp31 factor: 5423671886025109442120246388749 Tue Oct 16 06:24:18 2007 prp67 factor: 1443175595670302296287530288340641513337370692964945259930652789367 Tue Oct 16 06:24:18 2007 elapsed time 41:02:03
8·10¹⁵²-7 = 7(9)₁₅₁3_<153> = 13 · 18307 · 4639298979169_<13> · 238372349228810543_<18> · C118
C118 = P33 · P86
P33 = 132196018950577432404812799228403_<33>
P86 = 22993381145741293920904930229003616713749210764279783545611429634014833752788402278923_<86>

Number: 79993_152 N=3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969 ( 118 digits) SNFS difficulty: 152 digits. Divisors found: r1=132196018950577432404812799228403 (pp33) r2=22993381145741293920904930229003616713749210764279783545611429634014833752788402278923 (pp86) Version: GGNFS-0.77.1-20060513-k8 Total time: 21.25 hours. Scaled time: 42.02 units (timescale=1.978). Factorization parameters were as follows: name: 79993_152 n: 3039633449680265926335230629866243286215279582467641725078699207006615408808046094193646027979410320642927781189849969 m: 2000000000000000000000000000000 c5: 25 c0: -7 skew: 0.78 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:175903, largePrimes:5420804 encountered Relations: rels:5333741, finalFF:489141 Max relations in full relation-set: 28 Initial matrix: 352269 x 489141 with sparse part having weight 41279494. Pruned matrix : 285474 x 287299 with weight 22202017. Total sieving time: 20.13 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.86 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 21.25 hours. --------- CPU info (if available) ----------
Oct 16, 2007 (2nd): By Bryan Koen / GGNFS
(23·10¹⁷⁰+1)/3 = 7(6)₁₆₉7_<171> = 13 · 461 · 1289 · 10909069 · 3428780111_<10> · 5783988689_<10> · 1475103520971674381_<19> · C120
C120 = P50 · P71
P50 = 28622256358095202962667644344453285032065134088263_<50>
P71 = 10864963237661550249466184242559236733294008124794269198135353057048507_<71>

Number: 76667_170 N=310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341 ( 120 digits) SNFS difficulty: 171 digits. Divisors found: r1=28622256358095202962667644344453285032065134088263 (pp50) r2=10864963237661550249466184242559236733294008124794269198135353057048507 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 96.07 hours. Scaled time: 214.23 units (timescale=2.230). Factorization parameters were as follows: n: 310979763109628948369420398838169134459778745943966806045542931361213579741500676681882065931657868642085688329210373341 m: 10000000000000000000000000000000000 c5: 23 c0: 1 skew: 0.53 type: snfs Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 6700001) Primes: RFBsize:412849, AFBsize:412891, largePrimes:5994447 encountered Relations: rels:6291016, finalFF:958381 Max relations in full relation-set: 28 Initial matrix: 825805 x 958381 with sparse part having weight 51452736. Pruned matrix : 711926 x 716119 with weight 36381718. Total sieving time: 83.92 hours. Total relation processing time: 0.15 hours. Matrix solve time: 11.78 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 96.07 hours. --------- CPU info (if available) ----------
Oct 16, 2007: By Robert Backstrom / GGNFS, Msieve
6·10¹⁶⁴+7 = 6(0)₁₆₃7_<165> = 29 · 127031 · C159
C159 = P61 · P98
P61 = 1770843922137685855971883220866292296403759900031873711559753_<61>
P98 = 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981_<98>

Number: n N=162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693 ( 159 digits) SNFS difficulty: 165 digits. Divisors found: Tue Oct 16 01:56:00 2007 prp61 factor: 1770843922137685855971883220866292296403759900031873711559753 Tue Oct 16 01:56:00 2007 prp98 factor: 91973613665363851062774584215016713526677170996970636469854370682108828520625054063548519257625981 Tue Oct 16 01:56:00 2007 elapsed time 01:28:26 (Msieve 1.28) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 53.90 hours. Scaled time: 70.50 units (timescale=1.308). Factorization parameters were as follows: name: KA_6_0_163_7 n: 162870914756349183297370530516716120610255601470072876590807728442066408443879704628167058868877784108630556918091402614458213973835873350490879364499406742693 skew: 1.63 deg: 5 c5: 3 c0: 35 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2700001) Primes: RFBsize:216816, AFBsize:216606, largePrimes:7411428 encountered Relations: rels:6890615, finalFF:484135 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 53.63 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 53.90 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
6·10¹⁸⁵+7 = 6(0)₁₈₄7_<186> = 9109 · 486119 · 10533650783_<11> · 7198232528923_<13> · 6020878659975871147_<19> · 57715737637649789572192595701_<29> · C106
C106 = P44 · P63
P44 = 15856940822896359383771402356889784989979289_<44>
P63 = 324309472250677628769264887001027044666888119049640084725461111_<63>

Number: n N=5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079 ( 106 digits) Divisors found: Wed Oct 17 00:32:49 2007 prp44 factor: 15856940822896359383771402356889784989979289 Wed Oct 17 00:32:49 2007 prp63 factor: 324309472250677628769264887001027044666888119049640084725461111 Wed Oct 17 00:32:49 2007 elapsed time 00:52:18 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.70 hours. Scaled time: 12.65 units (timescale=1.454). Factorization parameters were as follows: name: n n: 5142556109783744147491364117529179269926062940937525300905943350583234457373321719669183987601774864930079 skew: 21313.42 # norm 5.43e+14 c5: 9000 c4: -76048988 c3: 12119061025586 c2: -340898511045832731 c1: -5046737451005388060230 c0: -9154601256957836199856000 # alpha -6.42 Y1: 5525266307 Y0: -224588401435796917287 # Murphy_E 1.76e-09 # M 241119437529606858479298978826451053129591147004948447723988093141534466268833497155997142159084665980338 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved special-q in [100000, 1300000) Primes: RFBsize:183072, AFBsize:182920, largePrimes:4087871 encountered Relations: rels:4028528, finalFF:410738 Max relations in full relation-set: 28 Initial matrix: 366075 x 410738 with sparse part having weight 23343007. Pruned matrix : 317878 x 319772 with weight 13914370. Total sieving time: 8.54 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 8.70 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Oct 15, 2007 (3rd): By Sinkiti Sibata / PRIMO
(86·10²¹⁰⁷+13)/9 is prime.
Oct 15, 2007 (2nd): By Sinkiti Sibata / GGNFS
8·10¹⁴⁶-7 = 7(9)₁₄₅3_<147> = 13 · 1046365087_<10> · 19154907071_<11> · C127
C127 = P52 · P76
P52 = 1580183000642280038370796123881094831961607470495009_<52>
P76 = 1943014132025684712297993803987711508705879519397502794606730636362479155677_<76>

Number: 79993_146 N=3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093 ( 127 digits) SNFS difficulty: 147 digits. Divisors found: r1=1580183000642280038370796123881094831961607470495009 (pp52) r2=1943014132025684712297993803987711508705879519397502794606730636362479155677 (pp76) Version: GGNFS-0.77.1-20060513-k8 Total time: 19.55 hours. Scaled time: 39.02 units (timescale=1.996). Factorization parameters were as follows: name: 79993_146 n: 3070317901434701737005636645958802200607040503016177760156771811800164613700248026172643912484812419742745714980450551562516093 m: 200000000000000000000000000000 c5: 5 c0: -14 skew: 1.23 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, 2850001) Primes: RFBsize:114155, AFBsize:114392, largePrimes:2881812 encountered Relations: rels:2895290, finalFF:293370 Max relations in full relation-set: 28 Initial matrix: 228612 x 293370 with sparse part having weight 30568649. Pruned matrix : 209081 x 210288 with weight 20114196. Total sieving time: 18.83 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.52 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 19.55 hours. --------- CPU info (if available) ----------
Oct 15, 2007: By Robert Backstrom / GGNFS, Msieve, GMP-ECM
6·10¹⁸⁸+7 = 6(0)₁₈₇7_<189> = 17 · 199 · 257 · 3463 · 16649 · 96059 · 61883693 · 90624285000529213_<17> · 454041790607190733_<18> · 517371257791985827755390629_<27> · C101
C101 = P49 · P53
P49 = 3525119596170058088736272803183372325772469391249_<49>
P53 = 26831479803562967544394299568098567920660248574603957_<53>

Number: n N=94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293 ( 101 digits) Divisors found: r1=3525119596170058088736272803183372325772469391249 (pp49) r2=26831479803562967544394299568098567920660248574603957 (pp53) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.98 hours. Scaled time: 9.14 units (timescale=1.309). Factorization parameters were as follows: name: n n: 94584175249780957684016168054931694295712083157601963382080588311931355733585636495867363625056572293 skew: 7737.01 # norm 9.79e+13 c5: 78000 c4: -297470066 c3: -15863340244548 c2: 7080761517578508 c1: 414301049080350364575 c0: -367453236957540790697550 # alpha -5.80 Y1: 14831016739 Y0: -16471952224750940243 # Murphy_E 2.86e-09 # M 1155531281704554954285740779202815785221773336456573589977276941683087980735395064780088119878136440 type: gnfs rlim: 1800000 alim: 1800000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:135072, AFBsize:135064, largePrimes:3586849 encountered Relations: rels:3583146, finalFF:407778 Max relations in full relation-set: 48 Initial matrix: 270216 x 407778 with sparse part having weight 25913894. Pruned matrix : 153604 x 155019 with weight 8586650. Total sieving time: 6.41 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.35 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000 total time: 6.98 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁴²-7 = 7(9)₁₄₁3_<143> = 2857 · C140
C140 = P66 · P75
P66 = 170295424162300840230361627660073534692518109605861209895558110069_<66>
P75 = 164428376204146486985826323441216525770957734599964780155385367813374589421_<75>

Number: n N=28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049 ( 140 digits) SNFS difficulty: 142 digits. Divisors found: r1=170295424162300840230361627660073534692518109605861209895558110069 (pp66) r2=164428376204146486985826323441216525770957734599964780155385367813374589421 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.72 hours. Scaled time: 9.22 units (timescale=1.194). Factorization parameters were as follows: name: KA_7_9_141_3 n: 28001400070003500175008750437521876093804690234511725586279313965698284914245712285614280714035701785089254462723136156807840392019600980049 type: snfs skew: 0.65 deg: 5 c5: 25 c0: -7 m: 20000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 850001) Primes: RFBsize:148933, AFBsize:148500, largePrimes:5611558 encountered Relations: rels:4989427, finalFF:361392 Max relations in full relation-set: 28 Initial matrix: 297497 x 361392 with sparse part having weight 17904087. Pruned matrix : 240103 x 241654 with weight 9277622. Total sieving time: 6.20 hours. Total relation processing time: 0.20 hours. Matrix solve time: 1.13 hours. Total square root time: 0.19 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 7.72 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
5·10¹⁶⁵-1 = 4(9)₁₆₅_<166> = 428440364567_<12> · C155
C155 = P67 · P88
P67 = 4418255297469253568147847349351285035723609901981851222353873612047_<67>
P88 = 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151_<88>

Number: n N=11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097 ( 155 digits) SNFS difficulty: 165 digits. Divisors found: Mon Oct 15 22:21:57 2007 prp67 factor: 4418255297469253568147847349351285035723609901981851222353873612047 Mon Oct 15 22:21:57 2007 prp88 factor: 2641367423527036890767831864312306241956122491114136519637229891724953923688971860336151 Mon Oct 15 22:21:57 2007 elapsed time 01:18:34 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 44.16 hours. Scaled time: 64.21 units (timescale=1.454). Factorization parameters were as follows: name: KA_4_9_165 n: 11670235611561044253628931909394969161619544523964876135974702959832102611543850287772225137109509941642444928668610984199652981246175861323416965983211097 skew: 0.72 deg: 5 c5: 5 c0: -1 m: 1000000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2400000) Primes: RFBsize:203362, AFBsize:203387, largePrimes:7325021 encountered Relations: rels:6796373, finalFF:457305 Max relations in full relation-set: 28 Initial matrix: 406814 x 457305 with sparse part having weight 40727776. Pruned matrix : 379736 x 381834 with weight 30695175. Total sieving time: 43.93 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 44.16 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
8·10¹⁶⁸-7 = 7(9)₁₆₇3_<169> = 889051 · 3504811485997_<13> · 212811322817407_<15> · 15345355832599422733596083704019_<32> · C105
C105 = P33 · P73
P33 = 350969010395558715534644431751677_<33>
P73 = 2240052427411472440287076912394101922396296096003376631991190413937458559_<73>
Oct 14, 2007 (2nd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
6·10¹⁴⁶+7 = 6(0)₁₄₅7_<147> = 4357 · C144
C144 = P62 · P83
P62 = 11418173072097254220419104341228272288444055633023768296587371_<62>
P83 = 12060548760877474653322042621937488929340653264886088872424357570501388208759630481_<83>

Number: n N=137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451 ( 144 digits) SNFS difficulty: 146 digits. Divisors found: r1=11418173072097254220419104341228272288444055633023768296587371 (pp62) r2=12060548760877474653322042621937488929340653264886088872424357570501388208759630481 (pp83) Version: GGNFS-0.77.1-20051202-athlon Total time: 14.29 hours. Scaled time: 17.06 units (timescale=1.194). Factorization parameters were as follows: name: KA_6_0_145_7 n: 137709433096167087445490016066100527886160201973835207711728253385356896947440899701629561624971310534771631856782189579986229056690383291255451 type: snfs skew: 0.65 deg: 5 c5: 60 c0: 7 m: 100000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1500001) Primes: RFBsize:148933, AFBsize:148615, largePrimes:6235655 encountered Relations: rels:5562121, finalFF:337505 Max relations in full relation-set: 28 Initial matrix: 297615 x 337505 with sparse part having weight 22977078. Pruned matrix : 271076 x 272628 with weight 15819578. Total sieving time: 11.99 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.85 hours. Total square root time: 0.22 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 14.29 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
6·10¹⁴⁸+7 = 6(0)₁₄₇7_<149> = 4549 · 787609 · 12956873023_<11> · C130
C130 = P40 · P90
P40 = 9540749344069170990484839035782631826167_<40>
P90 = 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347_<90>

Number: n N=1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949 ( 130 digits) SNFS difficulty: 149 digits. Divisors found: Sun Oct 14 07:28:32 2007 prp40 factor: 9540749344069170990484839035782631826167 Sun Oct 14 07:28:32 2007 prp90 factor: 135469633078895411887709169907086398273346654936908113597527218378494142638547322866052347 Sun Oct 14 07:28:32 2007 elapsed time 00:56:42 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 15.17 hours. Scaled time: 17.95 units (timescale=1.183). Factorization parameters were as follows: name: KA_6_0_147_7 n: 1292481812938762669912955974480348284084579994249280402316109378518340638209958112361129835839479159506743055281672649662826363949 skew: 0.52 deg: 5 c5: 375 c0: 14 m: 200000000000000000000000000000 type: snfs rlim: 1800000 alim: 1800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1850000) Primes: RFBsize:135072, AFBsize:135288, largePrimes:6951878 encountered Relations: rels:6272499, finalFF:315014 Max relations in full relation-set: 28 Initial matrix: 270426 x 315014 with sparse part having weight 39437700. Pruned matrix : 259998 x 261414 with weight 27086460. Total sieving time: 14.94 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1800000,1800000,28,28,48,48,2.5,2.5,100000 total time: 15.17 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
8·10¹⁵³-7 = 7(9)₁₅₂3_<154> = 73 · 246833 · 540901 · C141
C141 = P38 · P104
P38 = 45503821118476645834178831665898714663_<38>
P104 = 18038409980107755666629933064361219737535695629711907649346771548449394176944215804284623352754129419979_<104>
Oct 14, 2007: By Sinkiti Sibata / GGNFS, Msieve
8·10¹³⁷-7 = 7(9)₁₃₆3_<138> = 73 · 9964781 · C130
C130 = P48 · P82
P48 = 141316153943199860951746141560760739245162925887_<48>
P82 = 7782292667443130880016248231198064453618474981570509859512503079754219269452839403_<82>

Number: 79993_137 N=1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461 ( 130 digits) SNFS difficulty: 137 digits. Divisors found: r1=141316153943199860951746141560760739245162925887 (pp48) r2=7782292667443130880016248231198064453618474981570509859512503079754219269452839403 (pp82) Version: GGNFS-0.77.1-20060513-k8 Total time: 6.78 hours. Scaled time: 13.49 units (timescale=1.990). Factorization parameters were as follows: name: 79993_137 n: 1099763668623428964057555400254567520253691063597981621885075953108843075523576896430442484976881173696051081207012566599402325461 m: 2000000000000000000000000000 c5: 25 c0: -7 skew: 0.78 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1225001) Primes: RFBsize:78498, AFBsize:63568, largePrimes:1548308 encountered Relations: rels:1559004, finalFF:182026 Max relations in full relation-set: 28 Initial matrix: 142130 x 182026 with sparse part having weight 14809823. Pruned matrix : 129678 x 130452 with weight 8882231. Total sieving time: 6.56 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 6.78 hours. --------- CPU info (if available) ----------
8·10¹⁶⁵-7 = 7(9)₁₆₄3_<166> = 2381 · 5443 · 9170957 · 1193913161057723_<16> · 18720100338778545677_<20> · 221092714624829016465471979_<27> · C92
C92 = P38 · P54
P38 = 14107017695779960660551276385083916411_<38>
P54 = 965577295039246891714130651139286441420217189730013597_<54>

Sat Oct 13 14:10:21 2007 Msieve v. 1.28 Sat Oct 13 14:10:21 2007 random seeds: d891a068 1d65775f Sat Oct 13 14:10:21 2007 factoring 13621415987762003925737115669456429853506846533116955465249119119459261411157655645041440367 (92 digits) Sat Oct 13 14:10:22 2007 commencing quadratic sieve (91-digit input) Sat Oct 13 14:10:22 2007 using multiplier of 7 Sat Oct 13 14:10:22 2007 using 64kb Pentium 2 sieve core Sat Oct 13 14:10:22 2007 sieve interval: 18 blocks of size 65536 Sat Oct 13 14:10:22 2007 processing polynomials in batches of 6 Sat Oct 13 14:10:22 2007 using a sieve bound of 1753547 (65651 primes) Sat Oct 13 14:10:22 2007 using large prime bound of 177108247 (27 bits) Sat Oct 13 14:10:22 2007 using double large prime bound of 702796695147472 (42-50 bits) Sat Oct 13 14:10:22 2007 using trial factoring cutoff of 50 bits Sat Oct 13 14:10:22 2007 polynomial 'A' values have 12 factors Sun Oct 14 04:42:53 2007 66323 relations (17390 full + 48933 combined from 797713 partial), need 65747 Sun Oct 14 04:43:12 2007 begin with 815103 relations Sun Oct 14 04:43:18 2007 reduce to 165651 relations in 10 passes Sun Oct 14 04:43:18 2007 attempting to read 165651 relations Sun Oct 14 04:43:40 2007 recovered 165651 relations Sun Oct 14 04:43:40 2007 recovered 143802 polynomials Sun Oct 14 04:44:26 2007 attempting to build 66323 cycles Sun Oct 14 04:44:27 2007 found 66323 cycles in 5 passes Sun Oct 14 04:44:31 2007 distribution of cycle lengths: Sun Oct 14 04:44:31 2007 length 1 : 17390 Sun Oct 14 04:44:31 2007 length 2 : 12238 Sun Oct 14 04:44:31 2007 length 3 : 11622 Sun Oct 14 04:44:31 2007 length 4 : 8894 Sun Oct 14 04:44:31 2007 length 5 : 6300 Sun Oct 14 04:44:31 2007 length 6 : 4157 Sun Oct 14 04:44:31 2007 length 7 : 2532 Sun Oct 14 04:44:31 2007 length 9+: 3190 Sun Oct 14 04:44:32 2007 largest cycle: 19 relations Sun Oct 14 04:44:33 2007 matrix is 65651 x 66323 with weight 3988888 (avg 60.14/col) Sun Oct 14 04:44:40 2007 filtering completed in 4 passes Sun Oct 14 04:44:40 2007 matrix is 61409 x 61473 with weight 3690038 (avg 60.03/col) Sun Oct 14 04:44:44 2007 saving the first 48 matrix rows for later Sun Oct 14 04:44:44 2007 matrix is 61361 x 61473 with weight 2824181 (avg 45.94/col) Sun Oct 14 04:44:44 2007 matrix includes 64 packed rows Sun Oct 14 04:44:44 2007 using block size 10922 for processor cache size 256 kB Sun Oct 14 04:44:47 2007 commencing Lanczos iteration Sun Oct 14 04:49:15 2007 lanczos halted after 972 iterations Sun Oct 14 04:49:16 2007 recovered 17 nontrivial dependencies Sun Oct 14 04:50:10 2007 prp38 factor: 14107017695779960660551276385083916411 Sun Oct 14 04:50:10 2007 prp54 factor: 965577295039246891714130651139286441420217189730013597 Sun Oct 14 04:50:10 2007 elapsed time 14:39:49
8·10¹³¹-7 = 7(9)₁₃₀3_<132> = 149 · 281 · 376313501619021334931_<21> · C107
C107 = P44 · P64
P44 = 37274544353516647698335148848851846484864657_<44>
P64 = 1362182369130717145175925548652388406862572932354777517395196191_<64>

Number: 79993_131 N=50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487 ( 107 digits) SNFS difficulty: 132 digits. Divisors found: r1=37274544353516647698335148848851846484864657 (pp44) r2=1362182369130717145175925548652388406862572932354777517395196191 (pp64) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.40 hours. Scaled time: 8.79 units (timescale=1.999). Factorization parameters were as follows: name: 79993_131 n: 50774727135741302668281681978154025666220800077589563173122909846534600529922377074914069545651920596921487 m: 200000000000000000000000000 c5: 5 c0: -14 skew: 1.23 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63943, largePrimes:1469981 encountered Relations: rels:1455868, finalFF:158326 Max relations in full relation-set: 28 Initial matrix: 127959 x 158326 with sparse part having weight 11756685. Pruned matrix : 119410 x 120113 with weight 7188237. Total sieving time: 4.24 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.07 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.40 hours. --------- CPU info (if available) ----------
6·10¹⁵⁰+7 = 6(0)₁₄₉7_<151> = 13 · 1021 · 51377866217_<11> · 38690659722181_<14> · 13553397374370467_<17> · C107
C107 = P44 · P63
P44 = 75896163172818350563639937211446513525782697_<44>
P63 = 221071096062905112755419151133504653865878416206951105384644033_<63>

Number: 60007_150 N=16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001 ( 107 digits) Divisors found: r1=75896163172818350563639937211446513525782697 (pp44) r2=221071096062905112755419151133504653865878416206951105384644033 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 19.13 hours. Scaled time: 12.93 units (timescale=0.676). Factorization parameters were as follows: name: 60007_150 n: 16778447979584046870105927524867093522623211025234406911205125926978020882062201070003687860376291055697001 skew: 36403.92 # norm 2.09e+14 c5: 2100 c4: -112214840 c3: -13116197646990 c2: 123037965666033289 c1: 5760329507112287712094 c0: 1238462310613528311780792 # alpha -5.17 Y1: 120696764773 Y0: -380634342801918434537 # Murphy_E 1.56e-09 # M 13741135059811030920870521422422840200370178162132655706061264578222105542413703524686047496399343377873432 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2300001) Primes: RFBsize:183072, AFBsize:183420, largePrimes:4395571 encountered Relations: rels:4422833, finalFF:421465 Max relations in full relation-set: 28 Initial matrix: 366571 x 421465 with sparse part having weight 30675596. Pruned matrix : 323362 x 325258 with weight 19810409. Total sieving time: 15.47 hours. Total relation processing time: 0.20 hours. Matrix solve time: 3.20 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 19.13 hours. --------- CPU info (if available) ----------
8·10¹³⁴-7 = 7(9)₁₃₃3_<135> = 13 · 31 · 43 · 379 · 398471 · 16515812627621261_<17> · C107
C107 = P41 · P66
P41 = 48003731369287073342189922196135629754309_<41>
P66 = 385572109653783210030204978859579938448033879962204411809558451037_<66>

Number: 79993_134 N=18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433 ( 107 digits) SNFS difficulty: 135 digits. Divisors found: r1=48003731369287073342189922196135629754309 (pp41) r2=385572109653783210030204978859579938448033879962204411809558451037 (pp66) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.87 hours. Scaled time: 11.71 units (timescale=1.996). Factorization parameters were as follows: name: 79993_134 n: 18508899975309508283025996892062552559124843281306774880121900716696676128531676413045071788063922916268433 m: 1000000000000000000000000000 c5: 4 c0: -35 skew: 1.54 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:64193, largePrimes:1523402 encountered Relations: rels:1537466, finalFF:188576 Max relations in full relation-set: 28 Initial matrix: 142755 x 188576 with sparse part having weight 13498820. Pruned matrix : 126954 x 127731 with weight 7386006. Total sieving time: 5.68 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.10 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.87 hours. --------- CPU info (if available) ----------
8·10¹³⁶-7 = 7(9)₁₃₅3_<137> = 163 · 269 · 22407799279_<11> · 81876428270723_<14> · C108
C108 = P42 · P67
P42 = 110918576820312746668279691257635716599183_<42>
P67 = 8965772596523034939022478706473281787255547555025279231551238868629_<67>

Number: 79993_136 N=994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107 ( 108 digits) SNFS difficulty: 137 digits. Divisors found: r1=110918576820312746668279691257635716599183 (pp42) r2=8965772596523034939022478706473281787255547555025279231551238868629 (pp67) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.91 hours. Scaled time: 15.72 units (timescale=1.988). Factorization parameters were as follows: name: 79993_136 n: 994470736500895131291624755886395172525421692165650373010779297212968520824895570611922816043828312385730107 m: 2000000000000000000000000000 c5: 5 c0: -14 skew: 1.23 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1375001) Primes: RFBsize:78498, AFBsize:63943, largePrimes:1589559 encountered Relations: rels:1610836, finalFF:189841 Max relations in full relation-set: 28 Initial matrix: 142506 x 189841 with sparse part having weight 16890095. Pruned matrix : 128981 x 129757 with weight 9843551. Total sieving time: 7.67 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.13 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 7.91 hours. --------- CPU info (if available) ----------
Oct 13, 2007 (6th): By Robert Backstrom / Msieve, GGNFS
8·10¹¹⁰-7 = 7(9)₁₀₉3_<111> = 13 · 30197 · 69511273067394199277_<20> · C86
C86 = P43 · P43
P43 = 3412752588243064179197971634430268240789861_<43>
P43 = 8590585972779452282610598329176427275489929_<43>

Sat Oct 13 14:21:54 2007 Msieve v. 1.28 Sat Oct 13 14:21:54 2007 random seeds: 71c0a470 a1018f8f Sat Oct 13 14:21:54 2007 factoring 29317544513127637059005073107012633156477405810349541305000972214868654912800710809869 (86 digits) Sat Oct 13 14:21:54 2007 commencing quadratic sieve (85-digit input) Sat Oct 13 14:21:54 2007 using multiplier of 1 Sat Oct 13 14:21:54 2007 using 64kb Opteron sieve core Sat Oct 13 14:21:54 2007 sieve interval: 7 blocks of size 65536 Sat Oct 13 14:21:54 2007 processing polynomials in batches of 15 Sat Oct 13 14:21:54 2007 using a sieve bound of 1442579 (55333 primes) Sat Oct 13 14:21:54 2007 using large prime bound of 115406320 (26 bits) Sat Oct 13 14:21:54 2007 using double large prime bound of 325097179907280 (41-49 bits) Sat Oct 13 14:21:54 2007 using trial factoring cutoff of 49 bits Sat Oct 13 14:21:54 2007 polynomial 'A' values have 11 factors Sat Oct 13 14:54:41 2007 55598 relations (16566 full + 39032 combined from 566706 partial), need 55429 Sat Oct 13 14:54:42 2007 begin with 583272 relations Sat Oct 13 14:54:43 2007 reduce to 129047 relations in 9 passes Sat Oct 13 14:54:43 2007 attempting to read 129047 relations Sat Oct 13 14:54:44 2007 recovered 129047 relations Sat Oct 13 14:54:44 2007 recovered 103401 polynomials Sat Oct 13 14:54:45 2007 attempting to build 55598 cycles Sat Oct 13 14:54:45 2007 found 55598 cycles in 5 passes Sat Oct 13 14:54:45 2007 distribution of cycle lengths: Sat Oct 13 14:54:45 2007 length 1 : 16566 Sat Oct 13 14:54:46 2007 length 2 : 11426 Sat Oct 13 14:54:46 2007 length 3 : 9845 Sat Oct 13 14:54:46 2007 length 4 : 7055 Sat Oct 13 14:54:46 2007 length 5 : 4727 Sat Oct 13 14:54:46 2007 length 6 : 2766 Sat Oct 13 14:54:46 2007 length 7 : 1568 Sat Oct 13 14:54:46 2007 length 9+: 1645 Sat Oct 13 14:54:46 2007 largest cycle: 19 relations Sat Oct 13 14:54:46 2007 matrix is 55333 x 55598 with weight 2843187 (avg 51.14/col) Sat Oct 13 14:54:47 2007 filtering completed in 3 passes Sat Oct 13 14:54:47 2007 matrix is 49684 x 49748 with weight 2566866 (avg 51.60/col) Sat Oct 13 14:54:48 2007 saving the first 48 matrix rows for later Sat Oct 13 14:54:48 2007 matrix is 49636 x 49748 with weight 1895227 (avg 38.10/col) Sat Oct 13 14:54:48 2007 matrix includes 64 packed rows Sat Oct 13 14:54:48 2007 commencing Lanczos iteration Sat Oct 13 14:56:13 2007 lanczos halted after 786 iterations Sat Oct 13 14:56:13 2007 recovered 16 nontrivial dependencies Sat Oct 13 14:56:14 2007 prp43 factor: 3412752588243064179197971634430268240789861 Sat Oct 13 14:56:14 2007 prp43 factor: 8590585972779452282610598329176427275489929 Sat Oct 13 14:56:14 2007 elapsed time 00:34:20
8·10¹⁰³-7 = 7(9)₁₀₂3_<104> = 281 · 9903493 · 76751663 · C87
C87 = P35 · P53
P35 = 11645958539351398837968999925860551_<35>
P53 = 32161199219947116795810535309580815458905862060506117_<53>

Sat Oct 13 14:18:15 2007 Msieve v. 1.28 Sat Oct 13 14:18:15 2007 random seeds: fd6310c0 0e9f8101 Sat Oct 13 14:18:15 2007 factoring 374547992691324672010178946818039861713393421705423703090741037387853600337071824490467 (87 digits) Sat Oct 13 14:18:15 2007 commencing quadratic sieve (87-digit input) Sat Oct 13 14:18:15 2007 using multiplier of 7 Sat Oct 13 14:18:15 2007 using 64kb Athlon XP sieve core Sat Oct 13 14:18:15 2007 sieve interval: 10 blocks of size 65536 Sat Oct 13 14:18:15 2007 processing polynomials in batches of 11 Sat Oct 13 14:18:15 2007 using a sieve bound of 1483429 (56667 primes) Sat Oct 13 14:18:15 2007 using large prime bound of 118674320 (26 bits) Sat Oct 13 14:18:15 2007 using double large prime bound of 341855144981120 (42-49 bits) Sat Oct 13 14:18:15 2007 using trial factoring cutoff of 49 bits Sat Oct 13 14:18:15 2007 polynomial 'A' values have 11 factors Sat Oct 13 15:27:24 2007 56771 relations (15604 full + 41167 combined from 595942 partial), need 56763 Sat Oct 13 15:27:25 2007 begin with 611546 relations Sat Oct 13 15:27:25 2007 reduce to 136916 relations in 9 passes Sat Oct 13 15:27:25 2007 attempting to read 136916 relations Sat Oct 13 15:27:27 2007 recovered 136916 relations Sat Oct 13 15:27:27 2007 recovered 116979 polynomials Sat Oct 13 15:27:28 2007 attempting to build 56771 cycles Sat Oct 13 15:27:28 2007 found 56771 cycles in 6 passes Sat Oct 13 15:27:28 2007 distribution of cycle lengths: Sat Oct 13 15:27:28 2007 length 1 : 15604 Sat Oct 13 15:27:28 2007 length 2 : 10981 Sat Oct 13 15:27:28 2007 length 3 : 9938 Sat Oct 13 15:27:28 2007 length 4 : 7431 Sat Oct 13 15:27:28 2007 length 5 : 5307 Sat Oct 13 15:27:28 2007 length 6 : 3290 Sat Oct 13 15:27:28 2007 length 7 : 1927 Sat Oct 13 15:27:28 2007 length 9+: 2293 Sat Oct 13 15:27:28 2007 largest cycle: 20 relations Sat Oct 13 15:27:29 2007 matrix is 56667 x 56771 with weight 3278330 (avg 57.75/col) Sat Oct 13 15:27:30 2007 filtering completed in 4 passes Sat Oct 13 15:27:30 2007 matrix is 52445 x 52509 with weight 3068265 (avg 58.43/col) Sat Oct 13 15:27:31 2007 saving the first 48 matrix rows for later Sat Oct 13 15:27:31 2007 matrix is 52397 x 52509 with weight 2467820 (avg 47.00/col) Sat Oct 13 15:27:31 2007 matrix includes 64 packed rows Sat Oct 13 15:27:31 2007 using block size 10922 for processor cache size 256 kB Sat Oct 13 15:27:32 2007 commencing Lanczos iteration Sat Oct 13 15:28:04 2007 lanczos halted after 830 iterations Sat Oct 13 15:28:04 2007 recovered 18 nontrivial dependencies Sat Oct 13 15:28:05 2007 prp35 factor: 11645958539351398837968999925860551 Sat Oct 13 15:28:05 2007 prp53 factor: 32161199219947116795810535309580815458905862060506117 Sat Oct 13 15:28:05 2007 elapsed time 01:09:50
8·10¹¹⁹-7 = 7(9)₁₁₈3_<120> = 31 · C119
C119 = P41 · P78
P41 = 65850038351296212647890397578950381287521_<41>
P78 = 391897290556327270259798161999635360467060860906617319029511693859070848809543_<78>

Number: n N=25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903 ( 119 digits) SNFS difficulty: 120 digits. Divisors found: r1=65850038351296212647890397578950381287521 (pp41) r2=391897290556327270259798161999635360467060860906617319029511693859070848809543 (pp78) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.48 hours. Scaled time: 1.94 units (timescale=1.313). Factorization parameters were as follows: name: KA_7_9_118_3 n: 25806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903 skew: 1.54 deg: 5 c5: 4 c0: -35 m: 1000000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 800000/800000 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:63951, AFBsize:64193, largePrimes:4027991 encountered Relations: rels:3391987, finalFF:155362 Max relations in full relation-set: 48 Initial matrix: 128208 x 155362 with sparse part having weight 9403022. Pruned matrix : 112183 x 112888 with weight 4664374. Total sieving time: 1.28 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.12 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 1.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 13, 2007 (5th): By Sinkiti Sibata / GGNFS
6·10¹³⁴+7 = 6(0)₁₃₃7_<135> = 193 · 863 · 23603 · 100586824269101_<15> · C112
C112 = P35 · P77
P35 = 16080745011300179212403283434151191_<35>
P77 = 94355816472667095064977591820097467102390568492729306979142286831385089101801_<77>

Number: 60007_134 N=1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991 ( 112 digits) SNFS difficulty: 135 digits. Divisors found: r1=16080745011300179212403283434151191 (pp35) r2=94355816472667095064977591820097467102390568492729306979142286831385089101801 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.83 hours. Scaled time: 11.61 units (timescale=1.992). Factorization parameters were as follows: name: 60007_134 n: 1517311825029996661504435096321997519435645891033130360977335775340869413282472959239396871158506225871024394991 m: 1000000000000000000000000000 c5: 3 c0: 35 skew: 1.63 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1075001) Primes: RFBsize:78498, AFBsize:63993, largePrimes:1532434 encountered Relations: rels:1543630, finalFF:184907 Max relations in full relation-set: 28 Initial matrix: 142556 x 184907 with sparse part having weight 13770867. Pruned matrix : 128299 x 129075 with weight 7860258. Total sieving time: 5.62 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.11 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.83 hours. --------- CPU info (if available) ----------
8·10¹⁰²-7 = 7(9)₁₀₁3_<103> = 2599231 · C97
C97 = P36 · P62
P36 = 123290814675728514277867589716453613_<36>
P62 = 24964012229434350382875423100742889170251821341837628816240131_<62>

Number: 79993_102 N=3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303 ( 97 digits) SNFS difficulty: 102 digits. Divisors found: r1=123290814675728514277867589716453613 (pp36) r2=24964012229434350382875423100742889170251821341837628816240131 (pp62) Version: GGNFS-0.77.1-20060513-k8 Total time: 0.89 hours. Scaled time: 1.79 units (timescale=1.999). Factorization parameters were as follows: name: 79993_102 n: 3077833405341810712476113127305730040923642415776050685760519168938813056630980470762313930543303 m: 200000000000000000000 c5: 25 c0: -7 skew: 0.78 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [250000, 310001) Primes: RFBsize:37706, AFBsize:41317, largePrimes:1576393 encountered Relations: rels:1849951, finalFF:427438 Max relations in full relation-set: 28 Initial matrix: 79087 x 427438 with sparse part having weight 15779526. Pruned matrix : 37970 x 38429 with weight 2534723. Total sieving time: 0.84 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 0.89 hours. --------- CPU info (if available) ----------
8·10¹¹³-7 = 7(9)₁₁₂3_<114> = 43 · 73 · 947 · 138185209 · C100
C100 = P34 · P67
P34 = 1766907794190056087078782907983423_<34>
P67 = 1102232585621228023273179280338960623464028098584925315433259382103_<67>

Number: 79993_113 N=1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569 ( 100 digits) SNFS difficulty: 113 digits. Divisors found: r1=1766907794190056087078782907983423 (pp34) r2=1102232585621228023273179280338960623464028098584925315433259382103 (pp67) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.01 hours. Scaled time: 7.94 units (timescale=1.983). Factorization parameters were as follows: name: 79993_113 n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569 m: 20000000000000000000000 c5: 250 c0: -7 skew: 0.49 type: snfs n: 1947543346544406138446494012197593494161099060936009527105845848444968706122941158047420354746878569 m: 20000000000000000000000 c5: 250 c0: -7 skew: 0.49 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64168, largePrimes:2727503 encountered Relations: rels:3846323, finalFF:1205129 Max relations in full relation-set: 28 Initial matrix: 113332 x 1205129 with sparse part having weight 90876931. Pruned matrix : 49293 x 49923 with weight 10051860. Total sieving time: 3.88 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.02 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,113,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 4.01 hours. --------- CPU info (if available) ----------
8·10¹²⁸-7 = 7(9)₁₂₇3_<129> = 13 · 4458931 · 28353751 · 344697087446640263047_<21> · C94
C94 = P39 · P55
P39 = 212705206095827642161365792695450030873_<39>
P55 = 6638800655743115255251905310435410068403132728886029351_<55>

Number: 79993_128 N=1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423 ( 94 digits) SNFS difficulty: 128 digits. Divisors found: r1=212705206095827642161365792695450030873 (pp39) r2=6638800655743115255251905310435410068403132728886029351 (pp55) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 5.28 hours. Scaled time: 3.57 units (timescale=0.676). Factorization parameters were as follows: name: 79993_128 n: 1412107461708955027069290923954737312907713787250726572515699054670309444073066843051334153423 m: 20000000000000000000000000 c5: 250 c0: -7 skew: 0.49 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:64168, largePrimes:1487851 encountered Relations: rels:1489577, finalFF:174328 Max relations in full relation-set: 28 Initial matrix: 128185 x 174328 with sparse part having weight 12264098. Pruned matrix : 114449 x 115153 with weight 6368258. Total sieving time: 4.96 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.20 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.28 hours. --------- CPU info (if available) ----------
8·10¹¹⁴-7 = 7(9)₁₁₃3_<115> = 230904677 · C107
C107 = P48 · P59
P48 = 587132704218609332602624273840988912804671457773_<48>
P59 = 59009370997911180303851532975515874983963222792974758349433_<59>

Number: 79993_114 N=34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709 ( 107 digits) SNFS difficulty: 115 digits. Divisors found: r1=587132704218609332602624273840988912804671457773 (pp48) r2=59009370997911180303851532975515874983963222792974758349433 (pp59) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.32 hours. Scaled time: 6.61 units (timescale=1.994). Factorization parameters were as follows: name: 79993_114 n: 34646331568242768854785908039446078435215064959468101202644760634276801591160494336803753871126655437992709 m: 100000000000000000000000 c5: 4 c0: -35 skew: 1.54 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:64193, largePrimes:2486912 encountered Relations: rels:3148089, finalFF:767372 Max relations in full relation-set: 28 Initial matrix: 113355 x 767372 with sparse part having weight 60310023. Pruned matrix : 62081 x 62711 with weight 6647029. Total sieving time: 3.20 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.02 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.32 hours. --------- CPU info (if available) ----------
Oct 13, 2007 (4th): The factor table of 799...993 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.
Oct 13, 2007 (3rd): By Robert Backstrom / GGNFS
6·10¹⁴⁴+7 = 6(0)₁₄₃7_<145> = 13 · 61 · 6217 · C139
C139 = P47 · P92
P47 = 17996214744046724344420417956846958165765495333_<47>
P92 = 67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259_<92>

Number: n N=1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247 ( 139 digits) SNFS difficulty: 145 digits. Divisors found: r1=17996214744046724344420417956846958165765495333 (pp47) r2=67626362611447967176376164281940047499923797596474846813424537050089499416597128887441863259 (pp92) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.95 hours. Scaled time: 11.51 units (timescale=1.449). Factorization parameters were as follows: name: KA_6_0_143_7 n: 1217018543914390047546886146495361840910930266662961521321860634744135035509558565062115612299270539368420113178667855558559788368588670247 skew: 1.63 deg: 5 c5: 3 c0: 35 m: 100000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 900001) Primes: RFBsize:148933, AFBsize:148840, largePrimes:6333809 encountered Relations: rels:5693227, finalFF:347656 Max relations in full relation-set: 28 Initial matrix: 297838 x 347656 with sparse part having weight 22955213. Pruned matrix : 259683 x 261236 with weight 14197561. Total sieving time: 6.15 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.51 hours. Total square root time: 0.13 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,100000 total time: 7.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Oct 13, 2007 (2nd): By Sinkiti Sibata / GGNFS
6·10¹³²+7 = 6(0)₁₃₁7_<133> = 13 · 31 · 59 · 2090009 · 148913261947_<12> · C111
C111 = P55 · P57
P55 = 1983329501828473727548585254782922572449329984672734213_<55>
P57 = 408806495210391060163003461145989705978462625906890077609_<57>

Number: 60007_132 N=810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717 ( 111 digits) SNFS difficulty: 132 digits. Divisors found: r1=1983329501828473727548585254782922572449329984672734213 (pp55) r2=408806495210391060163003461145989705978462625906890077609 (pp57) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 7.78 hours. Scaled time: 5.26 units (timescale=0.676). Factorization parameters were as follows: name: 60007_132 n: 810797982489869232300976179328579352721883380713949594003733868807533449400899968769781243999195835893799536717 m: 100000000000000000000000000 c5: 600 c0: 7 skew: 0.41 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1250001) Primes: RFBsize:63951, AFBsize:63523, largePrimes:1533110 encountered Relations: rels:1528629, finalFF:158241 Max relations in full relation-set: 28 Initial matrix: 127540 x 158241 with sparse part having weight 14199593. Pruned matrix : 119830 x 120531 with weight 9182188. Total sieving time: 7.35 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.29 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 7.78 hours. --------- CPU info (if available) ----------
6·10¹⁶⁷-7 = 5(9)₁₆₆3_<168> = 86004929922823687_<17> · 117124643630091042473553137641_<30> · C122
C122 = P55 · P68
P55 = 1422924018199617086667469983408773956446337923324187259_<55>
P68 = 41859873490837916408900575837828799444368507615420908476733092182981_<68>

Number: 59993_167 N=59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079 ( 122 digits) SNFS difficulty: 167 digits. Divisors found: r1=1422924018199617086667469983408773956446337923324187259 (pp55) r2=41859873490837916408900575837828799444368507615420908476733092182981 (pp68) Version: GGNFS-0.77.1-20060513-k8 Total time: 154.80 hours. Scaled time: 308.82 units (timescale=1.995). Factorization parameters were as follows: name: 59993_167 n: 59563419388910720197810859969956349938363680093704772757910598946408447555545711050233081537114891883517241917857936839079 m: 1000000000000000000000000000000000 c5: 600 c0: -7 skew: 0.41 type: snfs Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2750000, 7450001) Primes: RFBsize:380800, AFBsize:380567, largePrimes:6136257 encountered Relations: rels:6361592, finalFF:867619 Max relations in full relation-set: 28 Initial matrix: 761433 x 867619 with sparse part having weight 66909828. Pruned matrix : 680057 x 683928 with weight 51296332. Total sieving time: 147.94 hours. Total relation processing time: 0.30 hours. Matrix solve time: 6.30 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000 total time: 154.80 hours. --------- CPU info (if available) ----------
Oct 13, 2007: By Jo Yeong Uk / GMP-ECM, GGNFS
6·10¹⁹³+7 = 6(0)₁₉₂7_<194> = C194
C194 = P37 · C157
P37 = 9431867921209970677263227064224760463_<37>
C157 = [6361412235753920282712594389572541485300199982510262458997768914548898435588007324833733189857362507423842664895526461468007039663923961796686299905053607689_<157>]
6·10¹⁴⁰+7 = 6(0)₁₃₉7_<141> = 17 · 25765322537_<11> · 29151135776457323_<17> · C113
C113 = P52 · P61
P52 = 6123908191785128062611453979386707666992816396823857_<52>
P61 = 7673307351852464227438937019759901799643665911557369118867853_<61>

Number: 60007_140 N=46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021 ( 113 digits) SNFS difficulty: 140 digits. Divisors found: r1=6123908191785128062611453979386707666992816396823857 (pp52) r2=7673307351852464227438937019759901799643665911557369118867853 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 6.19 hours. Scaled time: 13.10 units (timescale=2.117). Factorization parameters were as follows: n: 46990629750094353640929945031801720386834025557110371526615491443551271997160943220584424618795094865880900769021 m: 10000000000000000000000000000 c5: 6 c0: 7 skew: 1.03 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1150001) Primes: RFBsize:114155, AFBsize:114412, largePrimes:3206977 encountered Relations: rels:3155190, finalFF:262058 Max relations in full relation-set: 28 Initial matrix: 228633 x 262058 with sparse part having weight 22384343. Pruned matrix : 214081 x 215288 with weight 15710541. Total sieving time: 5.95 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.17 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 6.19 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
6·10¹⁸³+7 = 6(0)₁₈₂7_<184> = C184
C184 = P37 · P148
P37 = 4646109535270935651861373920553944113_<37>
P148 = 1291403044730436574664225203953221354301912479271324672689780038042977651172600578097674193944368819808698887156719580132180993397271065994090189239_<148>
6·10¹⁶⁰+7 = 6(0)₁₅₉7_<161> = 4229 · 482513 · 19099104039013_<14> · C139
C139 = P34 · P105
P34 = 2891475901086594031773677024975431_<34>
P105 = 532441594081401683367165802963920698884830621397625778059323292338660459693626121501287829706854904467897_<105>
Oct 12, 2007 (3rd): By Jo Yeong Uk / GGNFS
6·10¹⁵²+7 = 6(0)₁₅₁7_<153> = C153
C153 = P43 · P111
P43 = 1840685266806508095129806305318544351784701_<43>
P111 = 325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107_<111>

Number: 60007_152 N=600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 ( 153 digits) SNFS difficulty: 153 digits. Divisors found: r1=1840685266806508095129806305318544351784701 (pp43) r2=325965557947322722135583311765356705447166321685192963549916970963466614546316438202055770474848508291355137107 (pp111) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.05 hours. Scaled time: 42.60 units (timescale=2.125). Factorization parameters were as follows: n: 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 m: 2000000000000000000000000000000 c5: 75 c0: 28 skew: 0.82 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, 2500001) Primes: RFBsize:176302, AFBsize:175743, largePrimes:5716294 encountered Relations: rels:5680786, finalFF:487419 Max relations in full relation-set: 28 Initial matrix: 352111 x 487419 with sparse part having weight 48790712. Pruned matrix : 305178 x 307002 with weight 29072127. Total sieving time: 19.36 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.56 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 20.05 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 12, 2007 (2nd): By Robert Backstrom / GGNFS, Msieve
(89·10¹⁶³+1)/9 = 9(8)₁₆₂9_<164> = 3² · 11 · 191 · 44453 · 169823791 · C147
C147 = P71 · P77
P71 = 53555495404586983124284868689499027110767249977749056417262621184569457_<71>
P77 = 12935263718227109600388586097547759844207588321745878007455274683392359947511_<77>

Number: n N=692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527 ( 147 digits) SNFS difficulty: 164 digits. Divisors found: Fri Oct 12 07:40:24 2007 prp71 factor: 53555495404586983124284868689499027110767249977749056417262621184569457 Fri Oct 12 07:40:24 2007 prp77 factor: 12935263718227109600388586097547759844207588321745878007455274683392359947511 Fri Oct 12 07:40:24 2007 elapsed time 01:36:36 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.85 hours. Scaled time: 58.50 units (timescale=1.432). Factorization parameters were as follows: name: KA_9_8_162_9 n: 692754456618632700742588855519739501284878125239435320459568642724351039203120317771928341708484604722354579869380134021593082789437079791653771527 skew: 0.10 deg: 5 c5: 89000 c0: 1 m: 100000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100001) Primes: RFBsize:203362, AFBsize:202807, largePrimes:7209972 encountered Relations: rels:6664266, finalFF:448066 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 40.59 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,164,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 40.85 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
6·10¹⁴⁵+7 = 6(0)₁₄₄7_<146> = 163 · C144
C144 = P64 · P80
P64 = 3919572055477532086753025839329335485817252963822084748594102007_<64>
P80 = 93912844131744392068992466757974562467028071947951869170587151041083038337579227_<80>

Number: n N=368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589 ( 144 digits) SNFS difficulty: 145 digits. Divisors found: r1=3919572055477532086753025839329335485817252963822084748594102007 (pp64) r2=93912844131744392068992466757974562467028071947951869170587151041083038337579227 (pp80) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.95 hours. Scaled time: 14.29 units (timescale=1.196). Factorization parameters were as follows: name: KA_6_0_144_7 n: 368098159509202453987730061349693251533742331288343558282208588957055214723926380368098159509202453987730061349693251533742331288343558282208589 type: snfs skew: 1.03 deg: 5 c5: 6 c0: 7 m: 100000000000000000000000000000 rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:148933, AFBsize:149160, largePrimes:6126432 encountered Relations: rels:5452417, finalFF:336584 Max relations in full relation-set: 28 Initial matrix: 298159 x 336584 with sparse part having weight 21730162. Pruned matrix : 270315 x 271869 with weight 14890622. Total sieving time: 9.92 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.75 hours. Total square root time: 0.07 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.3,2.3,100000 total time: 11.95 hours. --------- CPU info (if available) ----------
6·10¹³⁸+7 = 6(0)₁₃₇7_<139> = 13 · C138
C138 = P52 · P86
P52 = 8786475728072227386487041599685529123701731718444931_<52>
P86 = 52528280487235138475680678891847720293425922478509734700005290994634833797311729822369_<86>

Number: n N=461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539 ( 138 digits) SNFS difficulty: 138 digits. Divisors found: r1=8786475728072227386487041599685529123701731718444931 (pp52) r2=52528280487235138475680678891847720293425922478509734700005290994634833797311729822369 (pp86) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.79 hours. Scaled time: 8.84 units (timescale=1.302). Factorization parameters were as follows: name: KA_6_0_137_3 n: 461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461539 skew: 0.26 deg: 5 c5: 6000 c0: 7 m: 1000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 750001) Primes: RFBsize:114155, AFBsize:114432, largePrimes:6211466 encountered Relations: rels:5545647, finalFF:312486 Max relations in full relation-set: 48 Initial matrix: 228654 x 312486 with sparse part having weight 29654727. Pruned matrix : 190499 x 191706 with weight 12900013. Total sieving time: 5.71 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.83 hours. Total square root time: 0.08 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,75000 total time: 6.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(25·10¹⁶⁴-7)/9 = 2(7)₁₆₄_<165> = 109 · 233 · 98429 · 3605093 · C149
C149 = P69 · P81
P69 = 202665523211650989063300380086943340369476928178393708116016987186139_<69>
P81 = 152088249235178053009249905689353519859990659090201830262384603581442406000454727_<81>

Number: n N=30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053 ( 149 digits) SNFS difficulty: 165 digits. Divisors found: r1=202665523211650989063300380086943340369476928178393708116016987186139 (pp69) r2=152088249235178053009249905689353519859990659090201830262384603581442406000454727 (pp81) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 63.84 hours. Scaled time: 83.38 units (timescale=1.306). Factorization parameters were as follows: name: KA_2_7_164 n: 30823044605591338486772528468080215864221880056493623390494021588481356096730350429012600680064293390882554678466909555819589219907302066966191429053 skew: 1.23 deg: 5 c5: 5 c0: -14 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 2800001) Primes: RFBsize:216816, AFBsize:217381, largePrimes:7523615 encountered Relations: rels:7019729, finalFF:495769 Max relations in full relation-set: 28 Initial matrix: 434262 x 495769 with sparse part having weight 44468095. Pruned matrix : 406710 x 408945 with weight 32940913. Total sieving time: 58.95 hours. Total relation processing time: 0.28 hours. Matrix solve time: 4.48 hours. Total square root time: 0.14 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 63.84 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 12, 2007: By Sinkiti Sibata / GGNFS
6·10¹¹⁴+7 = 6(0)₁₁₃7_<115> = 13 · 23 · 294199 · 314707 · 2354837 · C95
C95 = P32 · P64
P32 = 13963735493801662655038504422019_<32>
P64 = 6591283660858015718799436869882276779748116589270476529805242367_<64>

Number: 60007_114 N=92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973 ( 95 digits) SNFS difficulty: 115 digits. Divisors found: r1=13963735493801662655038504422019 (pp32) r2=6591283660858015718799436869882276779748116589270476529805242367 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.60 hours. Scaled time: 1.08 units (timescale=0.676). Factorization parameters were as follows: name: 60007_114 n: 92038941604838034885826953995277077283508823907453477048445035739217774475488560068977546478973 m: 100000000000000000000000 c5: 3 c0: 35 skew: 1.63 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 500001) Primes: RFBsize:49098, AFBsize:63993, largePrimes:2069865 encountered Relations: rels:2160911, finalFF:246690 Max relations in full relation-set: 28 Initial matrix: 113156 x 246690 with sparse part having weight 18938825. Pruned matrix : 79136 x 79765 with weight 3921681. Total sieving time: 1.41 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.60 hours. --------- CPU info (if available) ----------
6·10¹¹⁶+7 = 6(0)₁₁₅7_<117> = 1433 · C114
C114 = P46 · P68
P46 = 4260569836341526184189932091009434032922764443_<46>
P68 = 98273714505283129560284285927238795172266087521311216860992588389453_<68>

Number: 60007_116 N=418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679 ( 114 digits) SNFS difficulty: 116 digits. Divisors found: r1=4260569836341526184189932091009434032922764443 (pp46) r2=98273714505283129560284285927238795172266087521311216860992588389453 (pp68) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.17 hours. Scaled time: 1.47 units (timescale=0.676). Factorization parameters were as follows: name: 60007_116 n: 418702023726448011165387299371946964410327983251919050942079553384508025122121423586880669923237962316817864619679 m: 100000000000000000000000 c5: 60 c0: 7 skew: 0.65 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63883, largePrimes:2216313 encountered Relations: rels:2423409, finalFF:333688 Max relations in full relation-set: 28 Initial matrix: 113048 x 333688 with sparse part having weight 30159400. Pruned matrix : 73820 x 74449 with weight 5302920. Total sieving time: 1.96 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.17 hours. --------- CPU info (if available) ----------
6·10¹¹⁷+7 = 6(0)₁₁₆7_<118> = 31 · 2602909783189_<13> · C104
C104 = P39 · P65
P39 = 761007481197519851161967935908199514911_<39>
P65 = 97710562768479463816800500502385687103003804418987111582005841643_<65>

Number: 60007_117 N=74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773 ( 104 digits) SNFS difficulty: 117 digits. Divisors found: r1=761007481197519851161967935908199514911 (pp39) r2=97710562768479463816800500502385687103003804418987111582005841643 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.20 hours. Scaled time: 1.49 units (timescale=0.676). Factorization parameters were as follows: name: 60007_117 n: 74358469258832718774436183724553279940996020408249446899718017650687200724318637458592452381540883238773 m: 100000000000000000000000 c5: 600 c0: 7 skew: 0.41 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 550001) Primes: RFBsize:49098, AFBsize:63523, largePrimes:1980594 encountered Relations: rels:1938172, finalFF:128803 Max relations in full relation-set: 28 Initial matrix: 112687 x 128803 with sparse part having weight 10218920. Pruned matrix : 106545 x 107172 with weight 7132342. Total sieving time: 1.89 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.20 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,117,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.20 hours. --------- CPU info (if available) ----------
6·10¹²⁷+7 = 6(0)₁₂₆7_<128> = 197 · 9720031 · 266168660299_<12> · C108
C108 = P43 · P65
P43 = 3583617409332378966987419272264607655669797_<43>
P65 = 32850260496263134596383389203484134247046587543608521946389524867_<65>

Number: 60007_127 N=117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999 ( 108 digits) SNFS difficulty: 127 digits. Divisors found: r1=3583617409332378966987419272264607655669797 (pp43) r2=32850260496263134596383389203484134247046587543608521946389524867 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 5.28 hours. Scaled time: 3.57 units (timescale=0.676). Factorization parameters were as follows: name: 60007_127 n: 117722765415512284233525269842016058687696108332067481812522215595485313176760239621795561889746921472341999 m: 10000000000000000000000000 c5: 600 c0: 7 skew: 0.41 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:63523, largePrimes:1506649 encountered Relations: rels:1516333, finalFF:181202 Max relations in full relation-set: 28 Initial matrix: 127540 x 181202 with sparse part having weight 12751877. Pruned matrix : 111515 x 112216 with weight 6223089. Total sieving time: 4.97 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.19 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.28 hours. --------- CPU info (if available) ----------
Oct 11, 2007 (4th): By Sinkiti Sibata / Msieve
6·10¹⁵⁵+7 = 6(0)₁₅₄7_<156> = 30253 · 8290186057_<10> · 93174093649657_<14> · 47369174977499761_<17> · 7846580404504329797862521_<25> · C86
C86 = P41 · P46
P41 = 11519704348754539604022205034624081555611_<41>
P46 = 5996609457515185443760101854342559834794121041_<46>

Thu Oct 11 07:46:13 2007 Msieve v. 1.28 Thu Oct 11 07:46:13 2007 random seeds: a4efa528 11c3b45d Thu Oct 11 07:46:13 2007 factoring 69079168045520282358058872569745380341436008514853935086936756082097682617184706711051 (86 digits) Thu Oct 11 07:46:14 2007 commencing quadratic sieve (86-digit input) Thu Oct 11 07:46:14 2007 using multiplier of 11 Thu Oct 11 07:46:14 2007 using 64kb Pentium 2 sieve core Thu Oct 11 07:46:14 2007 sieve interval: 9 blocks of size 65536 Thu Oct 11 07:46:14 2007 processing polynomials in batches of 12 Thu Oct 11 07:46:14 2007 using a sieve bound of 1470947 (55891 primes) Thu Oct 11 07:46:14 2007 using large prime bound of 117675760 (26 bits) Thu Oct 11 07:46:14 2007 using double large prime bound of 336694943593840 (41-49 bits) Thu Oct 11 07:46:14 2007 using trial factoring cutoff of 49 bits Thu Oct 11 07:46:14 2007 polynomial 'A' values have 11 factors Thu Oct 11 13:23:21 2007 56030 relations (15871 full + 40159 combined from 586780 partial), need 55987 Thu Oct 11 13:23:28 2007 begin with 602651 relations Thu Oct 11 13:23:29 2007 reduce to 133601 relations in 10 passes Thu Oct 11 13:23:29 2007 attempting to read 133601 relations Thu Oct 11 13:23:38 2007 recovered 133601 relations Thu Oct 11 13:23:38 2007 recovered 112180 polynomials Thu Oct 11 13:23:39 2007 attempting to build 56030 cycles Thu Oct 11 13:23:39 2007 found 56030 cycles in 6 passes Thu Oct 11 13:23:42 2007 distribution of cycle lengths: Thu Oct 11 13:23:42 2007 length 1 : 15871 Thu Oct 11 13:23:42 2007 length 2 : 11072 Thu Oct 11 13:23:42 2007 length 3 : 9884 Thu Oct 11 13:23:42 2007 length 4 : 7361 Thu Oct 11 13:23:42 2007 length 5 : 4850 Thu Oct 11 13:23:42 2007 length 6 : 3171 Thu Oct 11 13:23:42 2007 length 7 : 1783 Thu Oct 11 13:23:42 2007 length 9+: 2038 Thu Oct 11 13:23:42 2007 largest cycle: 20 relations Thu Oct 11 13:23:42 2007 matrix is 55891 x 56030 with weight 3116041 (avg 55.61/col) Thu Oct 11 13:23:47 2007 filtering completed in 3 passes Thu Oct 11 13:23:47 2007 matrix is 51400 x 51464 with weight 2897239 (avg 56.30/col) Thu Oct 11 13:23:49 2007 saving the first 48 matrix rows for later Thu Oct 11 13:23:49 2007 matrix is 51352 x 51464 with weight 2270531 (avg 44.12/col) Thu Oct 11 13:23:49 2007 matrix includes 64 packed rows Thu Oct 11 13:23:49 2007 using block size 5461 for processor cache size 128 kB Thu Oct 11 13:23:51 2007 commencing Lanczos iteration Thu Oct 11 13:26:11 2007 lanczos halted after 814 iterations Thu Oct 11 13:26:12 2007 recovered 16 nontrivial dependencies Thu Oct 11 13:26:13 2007 prp41 factor: 11519704348754539604022205034624081555611 Thu Oct 11 13:26:13 2007 prp46 factor: 5996609457515185443760101854342559834794121041 Thu Oct 11 13:26:13 2007 elapsed time 05:40:00
6·10¹⁰⁴+7 = 6(0)₁₀₃7_<105> = 8629566092175419113_<19> · C86
C86 = P39 · P48
P39 = 312703414298744945585964596618843105759_<39>
P48 = 222346177668355476515021026054869613681073668721_<48>

Thu Oct 11 08:00:35 2007 Msieve v. 1.26 Thu Oct 11 08:00:35 2007 random seeds: 35251e1c b1bd4346 Thu Oct 11 08:00:35 2007 factoring 69528408913170114020623970508248965547977728760224458789292141359530747384979933264239 (86 digits) Thu Oct 11 08:00:36 2007 commencing quadratic sieve (86-digit input) Thu Oct 11 08:00:36 2007 using multiplier of 31 Thu Oct 11 08:00:36 2007 using 64kb Pentium 2 sieve core Thu Oct 11 08:00:36 2007 sieve interval: 9 blocks of size 65536 Thu Oct 11 08:00:36 2007 processing polynomials in batches of 12 Thu Oct 11 08:00:36 2007 using a sieve bound of 1470947 (55662 primes) Thu Oct 11 08:00:36 2007 using large prime bound of 117675760 (26 bits) Thu Oct 11 08:00:36 2007 using double large prime bound of 336694943593840 (41-49 bits) Thu Oct 11 08:00:36 2007 using trial factoring cutoff of 49 bits Thu Oct 11 08:00:36 2007 polynomial 'A' values have 11 factors Thu Oct 11 13:29:42 2007 55839 relations (15809 full + 40030 combined from 583377 partial), need 55758 Thu Oct 11 13:29:51 2007 begin with 599186 relations Thu Oct 11 13:29:54 2007 reduce to 132538 relations in 10 passes Thu Oct 11 13:29:54 2007 attempting to read 132538 relations Thu Oct 11 13:30:03 2007 recovered 132538 relations Thu Oct 11 13:30:03 2007 recovered 110467 polynomials Thu Oct 11 13:30:16 2007 attempting to build 55839 cycles Thu Oct 11 13:30:16 2007 found 55838 cycles in 5 passes Thu Oct 11 13:30:18 2007 distribution of cycle lengths: Thu Oct 11 13:30:18 2007 length 1 : 15809 Thu Oct 11 13:30:18 2007 length 2 : 11217 Thu Oct 11 13:30:18 2007 length 3 : 9985 Thu Oct 11 13:30:18 2007 length 4 : 7192 Thu Oct 11 13:30:18 2007 length 5 : 4922 Thu Oct 11 13:30:18 2007 length 6 : 3106 Thu Oct 11 13:30:18 2007 length 7 : 1762 Thu Oct 11 13:30:18 2007 length 9+: 1845 Thu Oct 11 13:30:18 2007 largest cycle: 18 relations Thu Oct 11 13:30:19 2007 matrix is 55662 x 55838 with weight 3139688 (avg 56.23/col) Thu Oct 11 13:30:22 2007 filtering completed in 3 passes Thu Oct 11 13:30:22 2007 matrix is 50880 x 50944 with weight 2899893 (avg 56.92/col) Thu Oct 11 13:30:24 2007 saving the first 48 matrix rows for later Thu Oct 11 13:30:24 2007 matrix is 50832 x 50944 with weight 2295297 (avg 45.06/col) Thu Oct 11 13:30:24 2007 matrix includes 64 packed rows Thu Oct 11 13:30:24 2007 using block size 10922 for processor cache size 256 kB Thu Oct 11 13:30:25 2007 commencing Lanczos iteration Thu Oct 11 13:33:05 2007 lanczos halted after 805 iterations Thu Oct 11 13:33:06 2007 recovered 17 nontrivial dependencies Thu Oct 11 13:33:21 2007 prp39 factor: 312703414298744945585964596618843105759 Thu Oct 11 13:33:21 2007 prp48 factor: 222346177668355476515021026054869613681073668721 Thu Oct 11 13:33:21 2007 elapsed time 05:32:46
Oct 11, 2007 (3rd): By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(4·10¹⁶²+23)/9 = (4)₁₆₁7_<162> = 3 · 191537 · 36201871247_<11> · C146
C146 = P68 · P79
P68 = 14267717847005813507700165288034158445726684150241889062913896709923_<68>
P79 = 1497469599792136047698907928447361359099204601762726546842329109356470216353817_<79>

Number: n N=21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091 ( 146 digits) SNFS difficulty: 162 digits. Divisors found: Thu Oct 11 07:49:06 2007 prp68 factor: 14267717847005813507700165288034158445726684150241889062913896709923 Thu Oct 11 07:49:06 2007 prp79 factor: 1497469599792136047698907928447361359099204601762726546842329109356470216353817 Thu Oct 11 07:49:06 2007 elapsed time 02:07:31 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 67.17 hours. Scaled time: 80.33 units (timescale=1.196). Factorization parameters were as follows: name: KA_4_161_7 n: 21365473734302912529054906948237323508436428295729914712019667578602171034133803699777503768069330971332086852316622127836560860767947345582826091 type: snfs skew: 1.13 deg: 5 c5: 25 c0: 46 m: 200000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2900000) Primes: RFBsize:230209, AFBsize:229862, largePrimes:7394863 encountered Relations: rels:6833492, finalFF:510861 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 66.85 hours. Total relation processing time: 0.31 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 67.17 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
6·10¹⁰⁶+7 = 6(0)₁₀₅7_<107> = C107
C107 = P33 · P74
P33 = 660354883413107731466749453206421_<33>
P74 = 90860235166103760559298389079671871752970399872818769276787670766575373867_<74>

Number: n N=60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 ( 107 digits) SNFS difficulty: 106 digits. Divisors found: r1=660354883413107731466749453206421 (pp33) r2=90860235166103760559298389079671871752970399872818769276787670766575373867 (pp74) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.81 hours. Scaled time: 0.97 units (timescale=1.196). Factorization parameters were as follows: name: KA_6_0_105_7 n: 60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007 type: snfs skew: 0.65 deg: 5 c5: 60 c0: 7 m: 1000000000000000000000 rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 200001) Primes: RFBsize:41538, AFBsize:41547, largePrimes:2680462 encountered Relations: rels:2220524, finalFF:111084 Max relations in full relation-set: 28 Initial matrix: 83152 x 111084 with sparse part having weight 5499964. Pruned matrix : 67479 x 67958 with weight 2313666. Total sieving time: 0.68 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.04 hours. Total square root time: 0.04 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,106,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.4,2.4,50000 total time: 0.81 hours. --------- CPU info (if available) ----------
6·10¹¹²+7 = 6(0)₁₁₁7_<113> = 43 · C112
C112 = P29 · P32 · P52
P29 = 42037675529382231904791550999_<29>
P32 = 14936485810428385363892834492251_<32>
P52 = 2222264100043128899370105966054617650050692155163401_<52>

N = 6*10^112+7 : c112 prp29 factor: 42037675529382231904791550999 prp32 factor: 14936485810428385363892834492251 prp52 factor: 2222264100043128899370105966054617650050692155163401 GMP-ECM 6.0.1 [powered by GMP 4.1.4] [ECM] Input number is 1395348837209302325581395348837209302325581395348837209302325581395348837209302325581395348837209302325581395349 (112 digits) Using B1=87500, B2=26096911, polynomial x^2, sigma=730686625 Step 1 took 1203ms Step 2 took 953ms ********** Factor found in step 2: 42037675529382231904791550999 Found probable prime factor of 29 digits: 42037675529382231904791550999 Composite cofactor 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 has 83 digits Thu Oct 11 14:51:32 2007 Thu Oct 11 14:51:32 2007 Thu Oct 11 14:51:32 2007 Msieve v. 1.28 Thu Oct 11 14:51:32 2007 random seeds: 409cfc00 e37a735e Thu Oct 11 14:51:32 2007 factoring 33192816197318600608605463828793223988644935250050070386447688396465987039773305651 (83 digits) Thu Oct 11 14:51:32 2007 commencing quadratic sieve (83-digit input) Thu Oct 11 14:51:33 2007 using multiplier of 1 Thu Oct 11 14:51:33 2007 using 64kb Athlon XP sieve core Thu Oct 11 14:51:33 2007 sieve interval: 6 blocks of size 65536 Thu Oct 11 14:51:33 2007 processing polynomials in batches of 17 Thu Oct 11 14:51:33 2007 using a sieve bound of 1369321 (52647 primes) Thu Oct 11 14:51:33 2007 using large prime bound of 121869569 (26 bits) Thu Oct 11 14:51:33 2007 using trial factoring cutoff of 27 bits Thu Oct 11 14:51:33 2007 polynomial 'A' values have 10 factors Thu Oct 11 15:25:57 2007 52751 relations (26020 full + 26731 combined from 283185 partial), need 52743 Thu Oct 11 15:25:58 2007 begin with 309205 relations Thu Oct 11 15:25:58 2007 reduce to 76065 relations in 2 passes Thu Oct 11 15:25:58 2007 attempting to read 76065 relations Thu Oct 11 15:25:59 2007 recovered 76065 relations Thu Oct 11 15:25:59 2007 recovered 69714 polynomials Thu Oct 11 15:25:59 2007 attempting to build 52751 cycles Thu Oct 11 15:25:59 2007 found 52751 cycles in 1 passes Thu Oct 11 15:25:59 2007 distribution of cycle lengths: Thu Oct 11 15:25:59 2007 length 1 : 26020 Thu Oct 11 15:25:59 2007 length 2 : 26731 Thu Oct 11 15:25:59 2007 largest cycle: 2 relations Thu Oct 11 15:25:59 2007 matrix is 52647 x 52751 with weight 1646722 (avg 31.22/col) Thu Oct 11 15:26:00 2007 filtering completed in 4 passes Thu Oct 11 15:26:00 2007 matrix is 46089 x 46153 with weight 1415834 (avg 30.68/col) Thu Oct 11 15:26:00 2007 saving the first 48 matrix rows for later Thu Oct 11 15:26:01 2007 matrix is 46041 x 46153 with weight 1132687 (avg 24.54/col) Thu Oct 11 15:26:01 2007 matrix includes 64 packed rows Thu Oct 11 15:26:01 2007 commencing Lanczos iteration Thu Oct 11 15:27:17 2007 lanczos halted after 730 iterations Thu Oct 11 15:27:18 2007 recovered 10 nontrivial dependencies Thu Oct 11 15:27:18 2007 prp32 factor: 14936485810428385363892834492251 Thu Oct 11 15:27:18 2007 prp52 factor: 2222264100043128899370105966054617650050692155163401 Thu Oct 11 15:27:18 2007 elapsed time 00:35:46
(55·10¹⁶⁴-1)/9 = 6(1)₁₆₄_<165> = 13 · 863 · 19751 · C157
C157 = P46 · P112
P46 = 2039347963490980778560349082035680167389362879_<46>
P112 = 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861_<112>

Number: n N=2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819 ( 157 digits) SNFS difficulty: 166 digits. Divisors found: Thu Oct 11 23:37:55 2007 prp46 factor: 2039347963490980778560349082035680167389362879 Thu Oct 11 23:37:55 2007 prp112 factor: 1352339114250697693044223701395926133298449563024538791688249501380572686573552852589778414243811182815085121861 Thu Oct 11 23:37:55 2007 elapsed time 01:27:35 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 46.45 hours. Scaled time: 61.40 units (timescale=1.322). Factorization parameters were as follows: name: KA_6_1_164 n: 2757890018596357122830957296003083613878567247312881325398578877625921784561272606907739980779742968471198081644196023138538802706004178942492698464864797819 skew: 0.71 deg: 5 c5: 11 c0: -2 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 special-q in [100000, 2200000) Primes: RFBsize:250150, AFBsize:250187, largePrimes:7389826 encountered Relations: rels:6945502, finalFF:606876 Max relations in full relation-set: 28 Initial matrix: 500404 x 606876 with sparse part having weight 45655180. Pruned matrix : 414282 x 416848 with weight 26923583. Total sieving time: 46.18 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 46.45 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 11, 2007 (2nd): By Yousuke Koide
10¹⁰⁰⁹+1 is divisible by 873234964696345278371172272680705837_<36>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 11, 2007: The factor table of 600...007 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.
Oct 10, 2007 (2nd): By Sinkiti Sibata / PRIMO
(28·10²²⁰⁷+53)/9 is prime.
Oct 10, 2007: By Jo Yeong Uk / GGNFS
(8·10¹⁵⁹-53)/9 = (8)₁₅₈3_<159> = 480451 · 4208429 · 104033087 · 13728238483_<11> · C129
C129 = P42 · P87
P42 = 316712295015730221860570435349138324870013_<42>
P87 = 971912454296354051931961805793739631984439234627451326067513307017004518364331228609949_<87>

Number: 88883_159 N=307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337 ( 129 digits) SNFS difficulty: 160 digits. Divisors found: r1=316712295015730221860570435349138324870013 (pp42) r2=971912454296354051931961805793739631984439234627451326067513307017004518364331228609949 (pp87) Version: GGNFS-0.77.1-20050930-nocona Total time: 36.09 hours. Scaled time: 76.93 units (timescale=2.132). Factorization parameters were as follows: n: 307816623954569300455053980011477723245374843831649497265306543156045707790951139583730144537538886277612234831260348782103559337 m: 100000000000000000000000000000000 c5: 4 c0: -265 skew: 2.31 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, 4100001) Primes: RFBsize:283146, AFBsize:282842, largePrimes:5712676 encountered Relations: rels:5728756, finalFF:637907 Max relations in full relation-set: 28 Initial matrix: 566052 x 637907 with sparse part having weight 44270840. Pruned matrix : 519131 x 522025 with weight 33004800. Total sieving time: 34.34 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.60 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: 36.09 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 9, 2007 (5th): By Sinkiti Sibata / GGNFS
6·10¹⁶³-7 = 5(9)₁₆₂3_<164> = 30339296027748931253_<20> · C145
C145 = P50 · P96
P50 = 15909833358959093262353180001154624082529476187767_<50>
P96 = 124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843_<96>

Number: 59993_163 N=1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581 ( 145 digits) SNFS difficulty: 164 digits. Divisors found: r1=15909833358959093262353180001154624082529476187767 (pp50) r2=124302573471643865966793637908816400185876720580733444177989495780776161055978026073936417281843 (pp96) Version: GGNFS-0.77.1-20060513-k8 Total time: 95.21 hours. Scaled time: 190.23 units (timescale=1.998). Factorization parameters were as follows: name: 59993_163 n: 1977633230023623206564389103658481345270454210925237336059189627833971133619728015943405220774679827442341511985530665001766489444666368027814581 m: 200000000000000000000000000000000 c5: 375 c0: -14 skew: 0.52 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, 5350001) Primes: RFBsize:315948, AFBsize:315866, largePrimes:5944123 encountered Relations: rels:6092944, finalFF:763528 Max relations in full relation-set: 28 Initial matrix: 631880 x 763528 with sparse part having weight 59643557. Pruned matrix : 535995 x 539218 with weight 43398744. Total sieving time: 90.70 hours. Total relation processing time: 0.26 hours. Matrix solve time: 4.03 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: 95.21 hours. --------- CPU info (if available) ----------
Oct 9, 2007 (4th): By Sinkiti Sibata / PRIMO
(8·10²⁰⁷³-11)/3 is prime.
Oct 9, 2007 (3rd): By suberi / PRIMO
5·10²⁷³³+9 is prime.
Oct 9, 2007 (2nd): By Jo Yeong Uk / GGNFS
(8·10¹⁵⁹-17)/9 = (8)₁₅₈7_<159> = 229 · 800509 · 4884721 · 262148354051_<12> · C133
C133 = P41 · P93
P41 = 31689588497279916590736503849012575753313_<41>
P93 = 119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029_<93>

Number: 88887_159 N=3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077 ( 133 digits) SNFS difficulty: 160 digits. Divisors found: r1=31689588497279916590736503849012575753313 (pp41) r2=119492948637304780639682337876688171145045603197808488844094715899024113564434226339292816029 (pp93) Version: GGNFS-0.77.1-20050930-nocona Total time: 31.11 hours. Scaled time: 66.71 units (timescale=2.144). Factorization parameters were as follows: n: 3786682370642793460441992233699759761247607307411975413165317553691947475895090384189590618511490509963186182014264349114253796254077 m: 100000000000000000000000000000000 c5: 4 c0: -85 skew: 1.84 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, 3800001) Primes: RFBsize:283146, AFBsize:283447, largePrimes:5649191 encountered Relations: rels:5661375, finalFF:639116 Max relations in full relation-set: 28 Initial matrix: 566657 x 639116 with sparse part having weight 40954229. Pruned matrix : 512428 x 515325 with weight 29660434. Total sieving time: 29.57 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.40 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: 31.11 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: 8167512k/8912896k available (2114k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.35 BogoMIPS (lpj=2407679) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405127) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405115) Calibrating delay using timer specific routine.. 4810.25 BogoMIPS (lpj=2405125) Total of 4 processors activated (19246.09 BogoMIPS).
Oct 9, 2007: By Robert Backstrom / GGNFS, Msieve
4·10¹⁶²+3 = 4(0)₁₆₁3_<163> = 7 · 16111 · 898857769272037_<15> · C143
C143 = P47 · P96
P47 = 52633384675921297349532423419308829377260438229_<47>
P96 = 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643_<96>

Number: n N=39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247 ( 143 digits) SNFS difficulty: 162 digits. Divisors found: Tue Oct 09 03:46:58 2007 prp47 factor: 52633384675921297349532423419308829377260438229 Tue Oct 09 03:46:58 2007 prp96 factor: 749699425654555588156813979006319175064153379838686656191939648186729452596767342041598941114643 Tue Oct 09 03:46:58 2007 elapsed time 01:16:25 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.15 hours. Scaled time: 52.53 units (timescale=1.453). Factorization parameters were as follows: name: KA_4_0_161_3 n: 39459218261793484031429986564259843918054327571537121376310544925094790528770124732699157255927616425625128819829539343779063155819583908887247 skew: 0.75 deg: 5 c5: 25 c0: 6 m: 200000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1900000) Primes: RFBsize:203362, AFBsize:202562, largePrimes:7139160 encountered Relations: rels:6577562, finalFF:434257 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 35.92 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 36.15 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Oct 8, 2007 (4th): By Bryan Koen / GMP-ECM
(23·10¹⁷³+1)/3 = 7(6)₁₇₂7_<174> = 11 · 19 · 41 · C170
C170 = P30 · P141
P30 = 357911945978650040346202809163_<30>
P141 = 249977110919930838083661846538618118461822803550100409862996457896163981755684629971850878837293997356705743192000800069352481784564014480361_<141>
Oct 8, 2007 (3rd): By Sinkiti Sibata / PRIMO
(31·10²¹⁷⁷+23)/9 is prime.
Oct 8, 2007 (2nd): By Robert Backstrom / GGNFS, Msieve
(73·10¹⁵⁹-1)/9 = 8(1)₁₅₉_<160> = 2657 · 105091757 · 340002075499_<12> · C137
C137 = P68 · P69
P68 = 85748085121300963152030695599342054561573492952495448497507158243159_<68>
P69 = 996355092269813964638397829269428609707014906515819237429532829639679_<69>

Number: n N=85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961 ( 137 digits) SNFS difficulty: 161 digits. Divisors found: Mon Oct 08 11:11:00 2007 prp68 factor: 85748085121300963152030695599342054561573492952495448497507158243159 Mon Oct 08 11:11:00 2007 prp69 factor: 996355092269813964638397829269428609707014906515819237429532829639679 Mon Oct 08 11:11:01 2007 elapsed time 01:25:31 (Msieve 1.28) Version: GGNFS-0.77.1-20051202-athlon Total time: 45.89 hours. Scaled time: 60.85 units (timescale=1.326). Factorization parameters were as follows: name: KA_8_1_159 n: 85435541262993683107759178811222508432637694938946198668249661730703724787996850375797180518678700584591827296195920977054636644636705961 skew: 0.67 deg: 5 c5: 73 c0: -10 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 special-q in [100000, 2100000) Primes: RFBsize:250150, AFBsize:250101, largePrimes:7499050 encountered Relations: rels:7084336, finalFF:634136 Max relations in full relation-set: 28 Initial matrix: 500316 x 634136 with sparse part having weight 48027068. Pruned matrix : 392586 x 395151 with weight 27479275. Total sieving time: 45.64 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 45.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
6·10¹⁶⁴-7 = 5(9)₁₆₃3_<165> = 17 · 302404974167609_<15> · C150
C150 = P51 · P99
P51 = 604857162810389628774661784293336029351376392407791_<51>
P99 = 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991_<99>

Number: n N=116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881 ( 150 digits) SNFS difficulty: 165 digits. Divisors found: Mon Oct 08 17:31:28 2007 prp51 factor: 604857162810389628774661784293336029351376392407791 Mon Oct 08 17:31:28 2007 prp99 factor: 192957014318376632131120220747611805227589329088927241976832631934622388748514730334494973730320991 Mon Oct 08 17:31:28 2007 elapsed time 01:42:50 (Msieve 1.28) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 53.19 hours. Scaled time: 63.34 units (timescale=1.191). Factorization parameters were as follows: name: KA_5_9_163_3 n: 116711432224977017360883726082633787948846053120532190717761735193932640441906310777526105200497999505680676600497638929152987804613749651905799240881 skew: 1.63 deg: 5 c5: 3 c0: -35 m: 1000000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2600000) Primes: RFBsize:216816, AFBsize:216606, largePrimes:7376363 encountered Relations: rels:6846162, finalFF:475104 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 52.94 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 53.19 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 8, 2007: By Jo Yeong Uk / GGNFS
(5·10¹⁵⁹-41)/9 = (5)₁₅₈1_<159> = 203232471011_<12> · 30634761442301959_<17> · C131
C131 = P66 · P66
P66 = 140302918730839359783997803266247889954113331203299846460516096197_<66>
P66 = 635994249340914371879827621457572197377938193794948288296614712167_<66>

Number: 55551_159 N=89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899 ( 131 digits) SNFS difficulty: 160 digits. Divisors found: r1=140302918730839359783997803266247889954113331203299846460516096197 (pp66) r2=635994249340914371879827621457572197377938193794948288296614712167 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 27.76 hours. Scaled time: 59.39 units (timescale=2.139). Factorization parameters were as follows: n: 89231849478559493177495087019280828859221907790013794337807829144866668300309536154113542379040143520122806007729736339743638328899 m: 100000000000000000000000000000000 c5: 1 c0: -82 skew: 2.41 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:282833, largePrimes:5618340 encountered Relations: rels:5637592, finalFF:646613 Max relations in full relation-set: 28 Initial matrix: 566045 x 646613 with sparse part having weight 40570327. Pruned matrix : 501999 x 504893 with weight 27943297. Total sieving time: 26.39 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.23 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: 27.76 hours. --------- CPU info (if available) ----------
Oct 7, 2007 (5th): By Sinkiti Sibata / PRIMO
(17·10²⁰⁶⁸-53)/9 is prime.
Oct 7, 2007 (4th): By Yousuke Koide
10¹⁰⁰⁷+1 is divisible by 80130271534233515728987750894609_<32>
10¹⁰⁵⁴+1 is divisible by 111276132074930025328712302045364981_<36>
10¹⁶⁰⁵+1 is divisible by 4298338634928851216299618775086771_<34>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Oct 7, 2007 (3rd): By Sinkiti Sibata / GGNFS
6·10¹⁶¹-7 = 5(9)₁₆₀3_<162> = 59 · 4889 · 22063 · 61949 · 56338169 · 5137570679_<10> · C130
C130 = P32 · P99
P32 = 25632208522320555148392302355173_<32>
P99 = 205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443_<99>

Number: 59993_161 N=5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639 ( 130 digits) SNFS difficulty: 161 digits. Divisors found: r1=25632208522320555148392302355173 (pp32) r2=205132168410612051871480238620927190554253620898540807301677670565578241342961193951890988344739443 (pp99) Version: GGNFS-0.77.1-20060513-k8 Total time: 67.83 hours. Scaled time: 134.98 units (timescale=1.990). Factorization parameters were as follows: name: 59993_161 n: 5257990515336585603900960324981397066212063936330995720178877708548412575128763722465208456773985220196118351156898540333928188639 m: 100000000000000000000000000000000 c5: 60 c0: -7 skew: 0.65 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, 4350001) Primes: RFBsize:315948, AFBsize:316366, largePrimes:5776158 encountered Relations: rels:5879966, finalFF:735887 Max relations in full relation-set: 28 Initial matrix: 632381 x 735887 with sparse part having weight 44476895. Pruned matrix : 553498 x 556723 with weight 31162467. Total sieving time: 64.08 hours. Total relation processing time: 0.18 hours. Matrix solve time: 3.36 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: 67.83 hours. --------- CPU info (if available) ----------
Oct 7, 2007 (2nd): By Jo Yeong Uk / GMP-ECM
10¹⁹²+9 = 1(0)₁₉₁9_<193> = C193
C193 = P48 · P145
P48 = 325208379747671632800443572929049811907718391209_<48>
P145 = 3074951515012920315894112276452006313835272802228418099697777887803931547784516799444634005241238767287033369894773351997005678938044816110863201_<145>
Oct 7, 2007: By suberi / PRIMO
(13·10²⁰⁷⁹-7)/3 is prime.
(13·10²¹²⁰-7)/3 is prime.
(13·10²²⁶⁰-7)/3 is prime.
(13·10²⁴²³-7)/3 is prime.
Oct 6, 2007 (4th): By Jo Yeong Uk / GGNFS
(4·10¹⁵⁹+41)/9 = (4)₁₅₈9_<159> = 3709 · 3456197 · 40995079027450649_<17> · C132
C132 = P48 · P85
P48 = 218551920024031168927773697661809538745109102567_<48>
P85 = 3869686706115428835860198962763376764473465747888783930870949253002451781545174371711_<85>

Number: 44449_159 N=845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137 ( 132 digits) SNFS difficulty: 160 digits. Divisors found: r1=218551920024031168927773697661809538745109102567 (pp48) r2=3869686706115428835860198962763376764473465747888783930870949253002451781545174371711 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 27.95 hours. Scaled time: 59.92 units (timescale=2.144). Factorization parameters were as follows: n: 845727459512995808632831376766004857195411667709864917200855795181161872981252627569069291871505578807711339836312388193111282282137 m: 100000000000000000000000000000000 c5: 2 c0: 205 skew: 2.52 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:283793, largePrimes:5629726 encountered Relations: rels:5660465, finalFF:657003 Max relations in full relation-set: 28 Initial matrix: 567004 x 657003 with sparse part having weight 41479342. Pruned matrix : 495662 x 498561 with weight 28049677. Total sieving time: 26.61 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.20 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: 27.95 hours. --------- CPU info (if available) ----------
Oct 6, 2007 (3rd): By Robert Backstrom / GGNFS, Msieve
2·10¹⁶¹+3 = 2(0)₁₆₀3_<162> = 1645747984609139286241_<22> · C141
C141 = P44 · P97
P44 = 23143371269685496536153160328427093498540901_<44>
P97 = 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383_<97>

Number: n N=121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083 ( 141 digits) SNFS difficulty: 161 digits. Divisors found: Sat Oct 06 11:57:55 2007 prp44 factor: 23143371269685496536153160328427093498540901 Sat Oct 06 11:57:55 2007 prp97 factor: 5250976096680145607463471043357442149484478476541758912748098433643075952275139383190561991897383 Sat Oct 06 11:57:55 2007 elapsed time 01:40:44 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 43.82 hours. Scaled time: 63.63 units (timescale=1.452). Factorization parameters were as follows: name: KA_2_0_160_3 n: 121525289333712574060203929849274253650679147008067862136662858454750139437642287196603579159652285468795971038414619211834083134495020362083 skew: 0.68 deg: 5 c5: 20 c0: 3 m: 100000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300000) Primes: RFBsize:203362, AFBsize:203062, largePrimes:7438144 encountered Relations: rels:6924431, finalFF:458969 Max relations in full relation-set: 28 Initial matrix: 406490 x 458969 with sparse part having weight 41917861. Pruned matrix : 379962 x 382058 with weight 31649775. Total sieving time: 43.56 hours. Total relation processing time: 0.26 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 43.82 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
2·10¹⁶⁰-9 = 1(9)₁₅₉1_<161> = 158642813009799873789292199_<27> · C135
C135 = P48 · P87
P48 = 514829968216555250825419476063055331353216130401_<48>
P87 = 244875747315362559771904473968778705005860870814895857896156971504755878896463497536209_<87>

Number: n N=126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809 ( 135 digits) SNFS difficulty: 160 digits. Divisors found: r1=514829968216555250825419476063055331353216130401 (pp48) r2=244875747315362559771904473968778705005860870814895857896156971504755878896463497536209 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 39.32 hours. Scaled time: 46.99 units (timescale=1.195). Factorization parameters were as follows: name: KA_1_9_159_1 n: 126069373207373321436708046654043582257956838503880528523913166513739523221993375991519276144852178818516438085011957703665140363189809 type: snfs skew: 1.35 deg: 5 c5: 2 c0: -9 m: 100000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 1600001) Primes: RFBsize:230209, AFBsize:230337, largePrimes:6544960 encountered Relations: rels:6024747, finalFF:519640 Max relations in full relation-set: 28 Initial matrix: 460611 x 519640 with sparse part having weight 28682777. Pruned matrix : 405415 x 407782 with weight 18445497. Total sieving time: 35.33 hours. Total relation processing time: 0.22 hours. Matrix solve time: 3.68 hours. Total square root time: 0.09 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 39.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Oct 6, 2007 (2nd): By Sinkiti Sibata / GGNFS
6·10¹⁶⁰-7 = 5(9)₁₅₉3_<161> = 110893837864780114169227_<24> · 53482456690377432712639319435401_<32> · C107
C107 = P51 · P56
P51 = 125543951754463483312651367167081146619879782542807_<51>
P56 = 80581749745901679359607613279455998414547734638470247237_<56>

Number: 59993_160 N=10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259 ( 107 digits) Divisors found: r1=125543951754463483312651367167081146619879782542807 (pp51) r2=80581749745901679359607613279455998414547734638470247237 (pp56) Version: GGNFS-0.77.1-20060513-k8 Total time: 16.09 hours. Scaled time: 31.66 units (timescale=1.968). Factorization parameters were as follows: name: 59993_160 n: 10116551302389730489061629792753496443305947169260756466085450095805957750759395081955491468661781825974259 skew: 8717.48 # norm 7.18e+14 c5: 34200 c4: 3446830450 c3: -49450344917839 c2: -282207816974048745 c1: 293743109705688382953 c0: -105852972657943776101076 # alpha -6.04 Y1: 1982489113 Y0: -196879813041941649923 # Murphy_E 1.63e-09 # M 8200850302644055184453131829831345367830490194178486463399401491964831823878780279463907218481306105711361 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2300001) Primes: RFBsize:183072, AFBsize:182207, largePrimes:4770558 encountered Relations: rels:5287342, finalFF:797494 Max relations in full relation-set: 28 Initial matrix: 365359 x 797494 with sparse part having weight 66842766. Pruned matrix : 198399 x 200289 with weight 27225588. Total sieving time: 15.17 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.58 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 16.09 hours. --------- CPU info (if available) ----------
6·10¹⁴⁸-7 = 5(9)₁₄₇3_<149> = 17 · 5261 · 7069 · 20877877 · 4124979457_<10> · C124
C124 = P46 · P78
P46 = 2202754157836179317307651152968047629805882079_<46>
P78 = 500267040879752050179524392513061490125276212618093746534715313369595549802451_<78>

Number: 59993_148 N=1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629 ( 124 digits) SNFS difficulty: 149 digits. Divisors found: r1=2202754157836179317307651152968047629805882079 (pp46) r2=500267040879752050179524392513061490125276212618093746534715313369595549802451 (pp78) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 38.13 hours. Scaled time: 25.82 units (timescale=0.677). Factorization parameters were as follows: name: 59993_148 n: 1101965304326275718376569832258079442992217073921951287705392731002575698336321117095630581548488817660192266002626251175629 m: 200000000000000000000000000000 c5: 375 c0: -14 skew: 0.52 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, 4550001) Primes: RFBsize:114155, AFBsize:114432, largePrimes:3074783 encountered Relations: rels:3142613, finalFF:260671 Max relations in full relation-set: 28 Initial matrix: 228653 x 260671 with sparse part having weight 33256669. Pruned matrix : 220290 x 221497 with weight 26947508. Total sieving time: 35.67 hours. Total relation processing time: 0.28 hours. Matrix solve time: 2.06 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 38.13 hours. --------- CPU info (if available) ----------
Oct 6, 2007: By Bryan Koen / GGNFS
(61·10¹⁶⁹-7)/9 = 6(7)₁₆₉_<170> = 679517 · 2099650316119_<13> · 462133680259364512974037301324911_<33> · C120
C120 = P38 · P82
P38 = 56540095809527061398275309610361450221_<38>
P82 = 1818092044741429958746153841013907596909769895723120119363711217697392274661650529_<82>

Number: 67777_169 N=102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909 ( 120 digits) Divisors found: r1=56540095809527061398275309610361450221 (pp38) r2=1818092044741429958746153841013907596909769895723120119363711217697392274661650529 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 57.70 hours. Scaled time: 129.60 units (timescale=2.246). Factorization parameters were as follows: name: 67777_169 n: 102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909 skew: 105558.47 # norm 5.86e+015 c5: 3420 c4: -855817826 c3: -172975041238792 c2: 10097144255620342185 c1: 454824918396171751978112 c0: 4817673992078805183239899869 # alpha -4.79 Y1: 1203809206333 Y0: -124620494456053891335838 # Murphy_E 3.13e-010 # M 19860790920966959294374370574608201829699352757127470678651745225926909610626249915480516469649586859101696560082650191 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, 4350001) Primes: RFBsize:315948, AFBsize:316478, largePrimes:7651281 encountered Relations: rels:7683310, finalFF:711142 Max relations in full relation-set: 28 Initial matrix: 632504 x 711142 with sparse part having weight 59334766. Pruned matrix : 568876 x 572102 with weight 42656010. Total sieving time: 48.21 hours. Total relation processing time: 0.50 hours. Matrix solve time: 8.60 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 57.70 hours. --------- CPU info (if available) ----------
Oct 5, 2007 (4th): By Jo Yeong Uk / PRIMO
(55·10²⁰¹⁵+17)/9 is prime.
Oct 5, 2007 (3rd): By Robert Backstrom / GGNFS, Msieve
6·10¹⁵¹-7 = 5(9)₁₅₀3_<152> = 38049083 · C145
C145 = P45 · P100
P45 = 163890451242523530323685961374784914589069397_<45>
P100 = 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143_<100>

Number: n N=1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771 ( 145 digits) SNFS difficulty: 151 digits. Divisors found: Fri Oct 05 09:28:44 2007 prp45 factor: 163890451242523530323685961374784914589069397 Fri Oct 05 09:28:44 2007 prp100 factor: 9621735296463067319406359609200658570446718765888423723850749029550679811036943776234172558145948143 Fri Oct 05 09:28:44 2007 elapsed time 00:54:09 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 19.99 hours. Scaled time: 26.51 units (timescale=1.326). Factorization parameters were as follows: name: KA_5_9_150_3 n: 1576910539473448019759109569079496607053578663117847018809888269843454571559582658010444036193986593579666558586970413978176556843695812590279771 skew: 0.65 deg: 5 c5: 60 c0: -7 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 special-q in [100000, 900000) Primes: RFBsize:216816, AFBsize:216901, largePrimes:6806958 encountered Relations: rels:6383461, finalFF:576223 Max relations in full relation-set: 28 Initial matrix: 433784 x 576223 with sparse part having weight 36816750. Pruned matrix : 309229 x 311461 with weight 17215851. Total sieving time: 19.80 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 19.99 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 5, 2007 (2nd): By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM
6·10¹⁵⁹-7 = 5(9)₁₅₈3_<160> = 13 · 46099251251888935727327_<23> · 24879066220185916328457524320554279793687_<41> · C96
C96 = P41 · P56
P41 = 17014311483120697384989356382969398497597_<41>
P56 = 23651874787979709585009977994193399030605069949949286937_<56>

Thu Oct 4 21:37:14 2007 Thu Oct 4 21:37:14 2007 Thu Oct 4 21:37:14 2007 Msieve v. 1.28 Thu Oct 4 21:37:14 2007 random seeds: 1a77d3d5 9d0329b9 Thu Oct 4 21:37:14 2007 factoring 402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389 (96 digits) Thu Oct 4 21:37:14 2007 commencing quadratic sieve (96-digit input) Thu Oct 4 21:37:14 2007 using multiplier of 1 Thu Oct 4 21:37:14 2007 using 32kb Intel Core sieve core Thu Oct 4 21:37:14 2007 sieve interval: 36 blocks of size 32768 Thu Oct 4 21:37:14 2007 processing polynomials in batches of 6 Thu Oct 4 21:37:14 2007 using a sieve bound of 2248781 (83529 primes) Thu Oct 4 21:37:14 2007 using large prime bound of 337317150 (28 bits) Thu Oct 4 21:37:14 2007 using double large prime bound of 2241140878991550 (43-51 bits) Thu Oct 4 21:37:14 2007 using trial factoring cutoff of 51 bits Thu Oct 4 21:37:14 2007 polynomial 'A' values have 12 factors Fri Oct 5 02:05:05 2007 83793 relations (19127 full + 64666 combined from 1276886 partial), need 83625 Fri Oct 5 02:05:06 2007 begin with 1296013 relations Fri Oct 5 02:05:07 2007 reduce to 225145 relations in 12 passes Fri Oct 5 02:05:07 2007 attempting to read 225145 relations Fri Oct 5 02:05:08 2007 recovered 225145 relations Fri Oct 5 02:05:08 2007 recovered 213597 polynomials Fri Oct 5 02:05:09 2007 attempting to build 83793 cycles Fri Oct 5 02:05:09 2007 found 83793 cycles in 6 passes Fri Oct 5 02:05:09 2007 distribution of cycle lengths: Fri Oct 5 02:05:09 2007 length 1 : 19127 Fri Oct 5 02:05:09 2007 length 2 : 13665 Fri Oct 5 02:05:09 2007 length 3 : 13753 Fri Oct 5 02:05:09 2007 length 4 : 11694 Fri Oct 5 02:05:09 2007 length 5 : 8929 Fri Oct 5 02:05:09 2007 length 6 : 6357 Fri Oct 5 02:05:09 2007 length 7 : 4300 Fri Oct 5 02:05:09 2007 length 9+: 5968 Fri Oct 5 02:05:09 2007 largest cycle: 20 relations Fri Oct 5 02:05:09 2007 matrix is 83529 x 83793 with weight 5817253 (avg 69.42/col) Fri Oct 5 02:05:10 2007 filtering completed in 4 passes Fri Oct 5 02:05:10 2007 matrix is 80599 x 80663 with weight 5617583 (avg 69.64/col) Fri Oct 5 02:05:11 2007 saving the first 48 matrix rows for later Fri Oct 5 02:05:11 2007 matrix is 80551 x 80663 with weight 4705622 (avg 58.34/col) Fri Oct 5 02:05:11 2007 matrix includes 64 packed rows Fri Oct 5 02:05:11 2007 using block size 32265 for processor cache size 4096 kB Fri Oct 5 02:05:14 2007 commencing Lanczos iteration Fri Oct 5 02:05:49 2007 lanczos halted after 1276 iterations Fri Oct 5 02:05:49 2007 recovered 17 nontrivial dependencies Fri Oct 5 02:05:50 2007 prp41 factor: 17014311483120697384989356382969398497597 Fri Oct 5 02:05:50 2007 prp56 factor: 23651874787979709585009977994193399030605069949949286937 Fri Oct 5 02:05:50 2007 elapsed time 04:28:36
(5·10¹⁶¹-23)/9 = (5)₁₆₀3_<161> = 181 · 9377 · 59980747 · 1556391950309252260727_<22> · C126
C126 = P30 · P97
P30 = 204200339305081254682089876323_<30>
P97 = 1717108343637436044836379289726170911481645229487158423846189656851215623920488863042590355402187_<97>
6·10¹⁸⁵-7 = 5(9)₁₈₄3_<186> = 1259 · 105094819 · 18234595094684519_<17> · 496645177774564607081_<21> · 91097916289552225379407273_<26> · C112
C112 = P43 · P70
P43 = 1567828725851495950483147060696472797473131_<43>
P70 = 3505861909643653215337674382799814173297028903124851463841838321295469_<70>

Number: 59993_185 N=5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439 ( 112 digits) Divisors found: r1=1567828725851495950483147060696472797473131 (pp43) r2=3505861909643653215337674382799814173297028903124851463841838321295469 (pp70) Version: GGNFS-0.77.1-20050930-nocona Total time: 17.45 hours. Scaled time: 37.14 units (timescale=2.129). Factorization parameters were as follows: name: 59993_185 n: 5496591010807901243959700004966756355343953965432332097077840850790392390952200017975624837864532764649639543439 skew: 31918.14 # norm 4.35e+15 c5: 49500 c4: 1148015948 c3: -102222124732255 c2: -6099585714717477637 c1: 33741417547897847981555 c0: 598316031826581667570223049 # alpha -6.53 Y1: 598253464301 Y0: -2565057913790794214018 # Murphy_E 7.81e-10 # M 3628664822376311219602672466853507363069765951502221673628741042021637214537904922189021557595578069943077896990 type: gnfs rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 70000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1400000, 2240001) Primes: RFBsize:203362, AFBsize:203437, largePrimes:7582629 encountered Relations: rels:7467623, finalFF:565840 Max relations in full relation-set: 28 Initial matrix: 406880 x 565840 with sparse part having weight 52660477. Pruned matrix : 291699 x 293797 with weight 29738311. Polynomial selection time: 0.94 hours. Total sieving time: 15.79 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.47 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2800000,2800000,27,27,50,50,2.6,2.6,70000 total time: 17.45 hours. --------- CPU info (if available) ---------- 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 Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
Oct 5, 2007: By Sinkiti Sibata / GGNFS
6·10¹⁴²-7 = 5(9)₁₄₁3_<143> = 353 · 85223 · 1064743 · 17170804432778660568577_<23> · C108
C108 = P32 · P76
P32 = 42191759522915775604583057626823_<32>
P76 = 2585572109501371476246882696300039865583164290410873961325438433783561473999_<76>

Number: 59993_142 N=109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177 ( 108 digits) SNFS difficulty: 142 digits. Divisors found: r1=42191759522915775604583057626823 (pp32) r2=2585572109501371476246882696300039865583164290410873961325438433783561473999 (pp76) Version: GGNFS-0.77.1-20060513-k8 Total time: 17.01 hours. Scaled time: 34.09 units (timescale=2.004). Factorization parameters were as follows: name: 59993_142 n: 109089836673239920516770319965068209364823641145718230527163887975622905277416393899382401902254788759475177 m: 10000000000000000000000000000 c5: 600 c0: -7 skew: 0.41 type: snfs Factor base limits: 1300000/1300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [650000, 2550001) Primes: RFBsize:100021, AFBsize:99733, largePrimes:2907987 encountered Relations: rels:2943976, finalFF:268434 Max relations in full relation-set: 28 Initial matrix: 199820 x 268434 with sparse part having weight 31091401. Pruned matrix : 182446 x 183509 with weight 19802614. Total sieving time: 16.40 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.42 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,142,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 17.01 hours. --------- CPU info (if available) ----------
6·10¹⁵²-7 = 5(9)₁₅₁3_<153> = 19 · 79 · 317 · 683 · 194723 · C139
C139 = P61 · P79
P61 = 2422519199645591483038400362598333261141854085321449290981587_<61>
P79 = 3913867442685506786621678329983313608259562954908441460080566565534765765237163_<79>

Number: 59993_152 N=9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681 ( 139 digits) SNFS difficulty: 152 digits. Divisors found: r1=2422519199645591483038400362598333261141854085321449290981587 (pp61) r2=3913867442685506786621678329983313608259562954908441460080566565534765765237163 (pp79) Version: GGNFS-0.77.1-20060513-k8 Total time: 30.48 hours. Scaled time: 59.79 units (timescale=1.962). Factorization parameters were as follows: name: 59993_152 n: 9481419024773431796374859861929423222068324195372690108617292629460624268055670298332904077189122625243218702260577584276221851166121117681 m: 1000000000000000000000000000000 c5: 600 c0: -7 skew: 0.41 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, 2300001) Primes: RFBsize:176302, AFBsize:175743, largePrimes:5726784 encountered Relations: rels:5711566, finalFF:522112 Max relations in full relation-set: 28 Initial matrix: 352111 x 522112 with sparse part having weight 50262752. Pruned matrix : 292470 x 294294 with weight 27860308. Total sieving time: 28.94 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.25 hours. Time per square root: 0.14 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 30.48 hours. --------- CPU info (if available) ----------
Oct 4, 2007 (10th): By Jo Yeong Uk / GGNFS
6·10¹⁴⁵-7 = 5(9)₁₄₄3_<146> = 1766550377_<10> · 157012037513_<12> · 4348276733443_<13> · C113
C113 = P36 · P78
P36 = 208622310195879907337278472254444759_<36>
P78 = 238459345830976112102219160803088310324167412809493635059788300420093626611189_<78>

Number: 59993_145 N=49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451 ( 113 digits) SNFS difficulty: 145 digits. Divisors found: r1=208622310195879907337278472254444759 (pp36) r2=238459345830976112102219160803088310324167412809493635059788300420093626611189 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.31 hours. Scaled time: 21.94 units (timescale=2.128). Factorization parameters were as follows: n: 49747939615056500626663559867471926285149195969519260672945306537946404080535869032470347651193685603727971808451 m: 100000000000000000000000000000 c5: 6 c0: -7 skew: 1.03 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved algebraic special-q in [750000, 1450001) Primes: RFBsize:114155, AFBsize:114412, largePrimes:3499162 encountered Relations: rels:3558668, finalFF:328093 Max relations in full relation-set: 28 Initial matrix: 228633 x 328093 with sparse part having weight 33496163. Pruned matrix : 202020 x 203227 with weight 17855809. Total sieving time: 10.03 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.20 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,47,47,2.3,2.3,50000 total time: 10.31 hours. --------- CPU info (if available) ---------- 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 Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
Oct 4, 2007 (9th): By Robert Backstrom / GGNFS, Msieve
(17·10¹⁶¹-71)/9 = 1(8)₁₆₀1_<162> = 7 · 11 · 523 · 12553 · 892039002817_<12> · C141
C141 = P70 · P71
P70 = 5517382888130356012700422947230695246102802588279510829603153154612691_<70>
P71 = 75918829205014441614543498027493064480460216213141344861042989326442621_<71>

Number: n N=418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111 ( 141 digits) SNFS difficulty: 162 digits. Divisors found: Thu Oct 04 19:17:06 2007 prp70 factor: 5517382888130356012700422947230695246102802588279510829603153154612691 Thu Oct 04 19:17:06 2007 prp71 factor: 75918829205014441614543498027493064480460216213141344861042989326442621 Thu Oct 04 19:17:06 2007 elapsed time 01:24:27 (Msieve 1.26) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 56.52 hours. Scaled time: 73.71 units (timescale=1.304). Factorization parameters were as follows: name: KA_1_8_160_1 n: 418873249142637799821007491061910714467071107673848593381389819578321584166718844538758955967710943384855248756160831082732301629584089903111 skew: 0.84 deg: 5 c5: 170 c0: -71 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300000) Primes: RFBsize:216816, AFBsize:216842, largePrimes:7378545 encountered Relations: rels:6867652, finalFF:491420 Max relations in full relation-set: 28 Initial matrix: 433725 x 491420 with sparse part having weight 41722542. Pruned matrix : 394644 x 396876 with weight 30589920. Total sieving time: 55.53 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.74 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 56.52 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 4, 2007 (8th): By Sinkiti Sibata / GGNFS
6·10¹³²-7 = 5(9)₁₃₁3_<133> = 17 · 31397 · 60607 · 17658261422573_<14> · C110
C110 = P45 · P65
P45 = 157220545256202605499721340161299887750890477_<45>
P65 = 66808873437291415726408144788722762650560407722248850407211168531_<65>

Number: 59993_132 N=10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287 ( 110 digits) SNFS difficulty: 132 digits. Divisors found: r1=157220545256202605499721340161299887750890477 (pp45) r2=66808873437291415726408144788722762650560407722248850407211168531 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 8.23 hours. Scaled time: 5.57 units (timescale=0.677). Factorization parameters were as follows: name: 59993_132 n: 10503727509763587149462644038115572609411003558019047308296016303974338616397089884714139804160694574969979287 m: 100000000000000000000000000 c5: 600 c0: -7 skew: 0.41 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1300001) Primes: RFBsize:63951, AFBsize:63523, largePrimes:1546399 encountered Relations: rels:1543966, finalFF:157068 Max relations in full relation-set: 28 Initial matrix: 127540 x 157068 with sparse part having weight 14736218. Pruned matrix : 120366 x 121067 with weight 9730311. Total sieving time: 7.77 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.30 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 8.23 hours. --------- CPU info (if available) ----------
Oct 4, 2007 (7th): By Jo Yeong Uk / GMP-ECM
6·10¹⁵⁹-7 = 5(9)₁₅₈3_<160> = 13 · 46099251251888935727327_<23> · C137
C137 = P41 · C96
P41 = 24879066220185916328457524320554279793687_<41>
C96 = [402420364802456082600245272138853200856277707189366407172983739323623291446802112677069257990389_<96>]
Oct 4, 2007 (6th): By Sinkiti Sibata / GGNFS
6·10¹³⁵-7 = 5(9)₁₃₄3_<136> = 13 · 414413481743_<12> · 36564792200396563_<17> · C107
C107 = P43 · P65
P43 = 1126059761985818701739729351936313997694323_<43>
P65 = 27048891575232108774848633209666793723302095208678124558846257723_<65>

Number: 59993_135 N=30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529 ( 107 digits) SNFS difficulty: 135 digits. Divisors found: r1=1126059761985818701739729351936313997694323 (pp43) r2=27048891575232108774848633209666793723302095208678124558846257723 (pp65) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.79 hours. Scaled time: 15.48 units (timescale=1.986). Factorization parameters were as follows: name: 59993_135 n: 30458668409186085102726075004708104994463090774955003534458454777954452719667825900945750528186059032006529 m: 1000000000000000000000000000 c5: 6 c0: -7 skew: 1.03 type: snfs Factor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved algebraic special-q in [400000, 1375001) Primes: RFBsize:78498, AFBsize:63888, largePrimes:1589402 encountered Relations: rels:1605693, finalFF:183280 Max relations in full relation-set: 28 Initial matrix: 142452 x 183280 with sparse part having weight 16657071. Pruned matrix : 130634 x 131410 with weight 10249543. Total sieving time: 7.56 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 7.79 hours. --------- CPU info (if available) ----------
Oct 4, 2007 (5th): By Robert Backstrom / GGNFS, Msieve
(73·10¹⁵⁸-1)/9 = 8(1)₁₅₈_<159> = 26530558669965200379377507_<26> · C134
C134 = P54 · P81
P54 = 212107814191998704725420221052699981457889085100997601_<54>
P81 = 144137600146936537044461384043301075248536512091523845543692062426638973343118573_<81>

Number: n N=30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373 ( 134 digits) SNFS difficulty: 159 digits. Divisors found: Thu Oct 04 16:13:30 2007 prp54 factor: 212107814191998704725420221052699981457889085100997601 Thu Oct 04 16:13:30 2007 prp81 factor: 144137600146936537044461384043301075248536512091523845543692062426638973343118573 Thu Oct 04 16:13:30 2007 elapsed time 01:50:08 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 50.48 hours. Scaled time: 60.38 units (timescale=1.196). Factorization parameters were as follows: name: KA_8_1_158 n: 30572711310047020199673079420220032560072723217483618025140594148989783940701088253778438397676150664410526395099842238233630731543373 type: snfs skew: 0.11 deg: 5 c5: 73000 c0: -1 m: 10000000000000000000000000000000 rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100000) Primes: RFBsize:230209, AFBsize:230497, largePrimes:7060727 encountered Relations: rels:6539168, finalFF:541829 Max relations in full relation-set: 28 Initial matrix: 460773 x 541829 with sparse part having weight 34927383. Pruned matrix : 393656 x 396023 with weight 22051476. Total sieving time: 50.21 hours. Total relation processing time: 0.27 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.3,2.3,100000 total time: 50.48 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
Oct 4, 2007 (4th): By Jo Yeong Uk / PRIMO
(38·10²⁰⁴³+61)/9 is prime.
Oct 4, 2007 (3rd): By Jo Yeong Uk / GGNFS, GMP-ECM
6·10¹³¹-7 = 5(9)₁₃₀3_<132> = 53 · 169607 · C125
C125 = P59 · P67
P59 = 12872498163753083570298872692434111691304047437203023579603_<59>
P67 = 5185238891853061753866196726218370889062130742679403097113868915761_<67>

Number: 59993_131 N=66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883 ( 125 digits) SNFS difficulty: 131 digits. Divisors found: r1=12872498163753083570298872692434111691304047437203023579603 (pp59) r2=5185238891853061753866196726218370889062130742679403097113868915761 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.84 hours. Scaled time: 6.06 units (timescale=2.135). Factorization parameters were as follows: n: 66746978113999611310097449475596804199185887107943546740850741408746145779182529734944412560401843507037523259931310684822883 m: 100000000000000000000000000 c5: 60 c0: -7 skew: 0.65 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 1100001) Primes: RFBsize:78498, AFBsize:78436, largePrimes:1617139 encountered Relations: rels:1662134, finalFF:216620 Max relations in full relation-set: 28 Initial matrix: 157001 x 216620 with sparse part having weight 13625699. Pruned matrix : 135783 x 136632 with weight 6867620. Total sieving time: 2.75 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,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 2.84 hours. --------- CPU info (if available) ---------- 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 Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
(86·10¹⁵⁸+31)/9 = 9(5)₁₅₇9_<159> = 7² · 1657 · 48530561 · 369122094120620012071_<21> · C126
C126 = P49 · P78
P49 = 3016236812826278990601156748919149544847529142617_<49>
P78 = 217814388128186210847141219564082430746842862444289701637257172552121621783169_<78>

Number: 95559_158 N=656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273 ( 126 digits) SNFS difficulty: 161 digits. Divisors found: r1=3016236812826278990601156748919149544847529142617 (pp49) r2=217814388128186210847141219564082430746842862444289701637257172552121621783169 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 36.34 hours. Scaled time: 76.82 units (timescale=2.114). Factorization parameters were as follows: n: 656979775835466476708907333677417137270421517155228763448205475015038680910810608163311078289165054665585517079132773251213273 m: 100000000000000000000000000000000 c5: 43 c0: 1550 skew: 2.05 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, 4100001) Primes: RFBsize:283146, AFBsize:282493, largePrimes:5699146 encountered Relations: rels:5718310, finalFF:642706 Max relations in full relation-set: 28 Initial matrix: 565705 x 642706 with sparse part having weight 43053754. Pruned matrix : 513370 x 516262 with weight 31561464. Total sieving time: 34.80 hours. Total relation processing time: 0.10 hours. Matrix solve time: 1.38 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 36.34 hours. --------- CPU info (if available) ---------- 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 Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
6·10¹⁴¹-7 = 5(9)₁₄₀3_<142> = 13 · 1447583 · 84331879 · C127
C127 = P37 · P90
P37 = 6476031936152650611823116269070611627_<37>
P90 = 583799427952449996104077409330623614593075799711097271574870756751412606331718775669681999_<90>
Oct 4, 2007 (2nd): By Sinkiti Sibata / Msieve, GGNFS
6·10¹²⁷-7 = 5(9)₁₂₆3_<128> = 343127 · 582525896334758811474813322548179_<33> · C90
C90 = P42 · P48
P42 = 538379064288744086953750328027856177081161_<42>
P48 = 557561730154771569560097260837268094018249256461_<48>

Wed Oct 03 15:19:24 2007 Msieve v. 1.26 Wed Oct 03 15:19:24 2007 random seeds: ee28c423 6aa74c56 Wed Oct 03 15:19:24 2007 factoring 300179562563939145447468893460840371948057004209201877467016267991673377504711137500631221 (90 digits) Wed Oct 03 15:19:25 2007 commencing quadratic sieve (90-digit input) Wed Oct 03 15:19:26 2007 using multiplier of 5 Wed Oct 03 15:19:26 2007 using 64kb Pentium 2 sieve core Wed Oct 03 15:19:26 2007 sieve interval: 18 blocks of size 65536 Wed Oct 03 15:19:26 2007 processing polynomials in batches of 6 Wed Oct 03 15:19:26 2007 using a sieve bound of 1579619 (60000 primes) Wed Oct 03 15:19:26 2007 using large prime bound of 126369520 (26 bits) Wed Oct 03 15:19:26 2007 using double large prime bound of 382786039401520 (42-49 bits) Wed Oct 03 15:19:26 2007 using trial factoring cutoff of 49 bits Wed Oct 03 15:19:26 2007 polynomial 'A' values have 12 factors Thu Oct 04 01:00:41 2007 60563 relations (16228 full + 44335 combined from 633835 partial), need 60096 Thu Oct 04 01:00:52 2007 begin with 650063 relations Thu Oct 04 01:01:24 2007 reduce to 146669 relations in 10 passes Thu Oct 04 01:01:24 2007 attempting to read 146669 relations Thu Oct 04 01:01:38 2007 recovered 146669 relations Thu Oct 04 01:01:38 2007 recovered 124245 polynomials Thu Oct 04 01:02:13 2007 attempting to build 60563 cycles Thu Oct 04 01:02:14 2007 found 60563 cycles in 6 passes Thu Oct 04 01:02:17 2007 distribution of cycle lengths: Thu Oct 04 01:02:17 2007 length 1 : 16228 Thu Oct 04 01:02:17 2007 length 2 : 11907 Thu Oct 04 01:02:17 2007 length 3 : 10599 Thu Oct 04 01:02:17 2007 length 4 : 8065 Thu Oct 04 01:02:17 2007 length 5 : 5670 Thu Oct 04 01:02:17 2007 length 6 : 3510 Thu Oct 04 01:02:18 2007 length 7 : 2163 Thu Oct 04 01:02:18 2007 length 9+: 2421 Thu Oct 04 01:02:18 2007 largest cycle: 19 relations Thu Oct 04 01:02:20 2007 matrix is 60000 x 60563 with weight 3581602 (avg 59.14/col) Thu Oct 04 01:02:25 2007 filtering completed in 3 passes Thu Oct 04 01:02:25 2007 matrix is 55899 x 55963 with weight 3306276 (avg 59.08/col) Thu Oct 04 01:02:28 2007 saving the first 48 matrix rows for later Thu Oct 04 01:02:28 2007 matrix is 55851 x 55963 with weight 2583325 (avg 46.16/col) Thu Oct 04 01:02:28 2007 matrix includes 64 packed rows Thu Oct 04 01:02:28 2007 using block size 10922 for processor cache size 256 kB Thu Oct 04 01:02:29 2007 commencing Lanczos iteration Thu Oct 04 01:06:36 2007 lanczos halted after 885 iterations Thu Oct 04 01:06:37 2007 recovered 17 nontrivial dependencies Thu Oct 04 01:07:05 2007 prp42 factor: 538379064288744086953750328027856177081161 Thu Oct 04 01:07:05 2007 prp48 factor: 557561730154771569560097260837268094018249256461 Thu Oct 04 01:07:05 2007 elapsed time 09:47:41
6·10¹²³-7 = 5(9)₁₂₂3_<124> = 13² · 1660493 · C116
C116 = P45 · P71
P45 = 419726743015322283340796841866026105998611897_<45>
P71 = 50940224585810878707118381444742680923300871417714179798205170107648957_<71>

Number: 59993_123 N=21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429 ( 116 digits) SNFS difficulty: 124 digits. Divisors found: r1=419726743015322283340796841866026105998611897 (pp45) r2=50940224585810878707118381444742680923300871417714179798205170107648957 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 3.06 hours. Scaled time: 2.07 units (timescale=0.677). Factorization parameters were as follows: name: 59993_123 n: 21380974553871444688254468890053067115588260258501612679604952428097769224215962068469171433819236054429504159841429 m: 2000000000000000000000000 c5: 375 c0: -14 skew: 0.52 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:64283, largePrimes:2107214 encountered Relations: rels:2116210, finalFF:152007 Max relations in full relation-set: 28 Initial matrix: 113447 x 152007 with sparse part having weight 13697410. Pruned matrix : 103414 x 104045 with weight 7180122. Total sieving time: 2.74 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.20 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.06 hours. --------- CPU info (if available) ----------
6·10¹²⁸-7 = 5(9)₁₂₇3_<129> = 47 · 157 · 8893 · C121
C121 = P35 · P42 · P46
P35 = 45062760365254252417196977668457049_<35>
P42 = 107331866482129355939909099089742932497167_<42>
P46 = 1890422922086710862023492300837255153472513593_<46>

Number: 59993_128 N=9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519 ( 121 digits) SNFS difficulty: 129 digits. Divisors found: r1=45062760365254252417196977668457049 (pp35) r2=107331866482129355939909099089742932497167 (pp42) r3=1890422922086710862023492300837255153472513593 (pp46) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 5.27 hours. Scaled time: 3.57 units (timescale=0.677). Factorization parameters were as follows: name: 59993_128 n: 9143352172651724671661080561054985575066639417445336126160095189610799042575211729177505031243824903769647139905342227519 m: 20000000000000000000000000 c5: 375 c0: -14 skew: 0.52 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:64283, largePrimes:1484571 encountered Relations: rels:1488026, finalFF:176006 Max relations in full relation-set: 28 Initial matrix: 128300 x 176006 with sparse part having weight 12189392. Pruned matrix : 113811 x 114516 with weight 6184426. Total sieving time: 4.96 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.20 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.27 hours. --------- CPU info (if available) ----------
(37·10¹⁶¹-1)/9 = 4(1)₁₆₁_<162> = 3 · 41 · 1307 · 2075820356295079_<16> · 1262790142328673659357_<22> · C120
C120 = P38 · P83
P38 = 37343365815058483964552266720070550859_<38>
P83 = 26124266598228484286956693574306899716358742145356317706463821362063741663610307863_<83>

Number: 41111_161 N=975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317 ( 120 digits) SNFS difficulty: 162 digits. Divisors found: r1=37343365815058483964552266720070550859 (pp38) r2=26124266598228484286956693574306899716358742145356317706463821362063741663610307863 (pp83) Version: GGNFS-0.77.1-20060513-k8 Total time: 73.17 hours. Scaled time: 146.20 units (timescale=1.998). Factorization parameters were as follows: name: 41111_161 n: 975568044227759770362488001375467674400042183142302355527744077810832923409238855463500596189094164000811015620989104317 m: 100000000000000000000000000000000 c5: 370 c0: -1 skew: 0.31 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:315496, largePrimes:5801398 encountered Relations: rels:5906549, finalFF:737188 Max relations in full relation-set: 28 Initial matrix: 631511 x 737188 with sparse part having weight 47432370. Pruned matrix : 551065 x 554286 with weight 33711664. Total sieving time: 69.23 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.52 hours. Time per square root: 0.23 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 73.17 hours. --------- CPU info (if available) ----------
Oct 4, 2007: By Robert Backstrom / Msieve, GGNFS
6·10¹⁵⁵-7 = 5(9)₁₅₄3_<156> = 9151759 · 44509450084691841113_<20> · 1276610766484719268151_<22> · 1340426558177838497399939_<25> · C84
C84 = P36 · P49
P36 = 217264834889735630458321389261532721_<36>
P49 = 3961899731258636703690742682913482426977474823891_<49>

Wed Oct 03 15:36:33 2007 Msieve v. 1.26 Wed Oct 03 15:36:33 2007 random seeds: 965c87cc d2ef83b1 Wed Oct 03 15:36:33 2007 factoring 860781490961595669697733605784670171336258336753794416470408536041356301000209037411 (84 digits) Wed Oct 03 15:36:34 2007 commencing quadratic sieve (84-digit input) Wed Oct 03 15:36:34 2007 using multiplier of 1 Wed Oct 03 15:36:34 2007 using 64kb Opteron sieve core Wed Oct 03 15:36:34 2007 sieve interval: 6 blocks of size 65536 Wed Oct 03 15:36:34 2007 processing polynomials in batches of 17 Wed Oct 03 15:36:34 2007 using a sieve bound of 1409117 (53799 primes) Wed Oct 03 15:36:34 2007 using large prime bound of 119774945 (26 bits) Wed Oct 03 15:36:34 2007 using trial factoring cutoff of 27 bits Wed Oct 03 15:36:34 2007 polynomial 'A' values have 11 factors Wed Oct 03 16:07:49 2007 54021 relations (27210 full + 26811 combined from 284568 partial), need 53895 Wed Oct 03 16:07:50 2007 begin with 311778 relations Wed Oct 03 16:07:50 2007 reduce to 77387 relations in 2 passes Wed Oct 03 16:07:50 2007 attempting to read 77387 relations Wed Oct 03 16:07:51 2007 recovered 77387 relations Wed Oct 03 16:07:51 2007 recovered 71517 polynomials Wed Oct 03 16:07:51 2007 attempting to build 54021 cycles Wed Oct 03 16:07:51 2007 found 54021 cycles in 1 passes Wed Oct 03 16:07:51 2007 distribution of cycle lengths: Wed Oct 03 16:07:51 2007 length 1 : 27210 Wed Oct 03 16:07:51 2007 length 2 : 26811 Wed Oct 03 16:07:51 2007 largest cycle: 2 relations Wed Oct 03 16:07:51 2007 matrix is 53799 x 54021 with weight 1755888 (avg 32.50/col) Wed Oct 03 16:07:51 2007 filtering completed in 4 passes Wed Oct 03 16:07:51 2007 matrix is 46702 x 46766 with weight 1491481 (avg 31.89/col) Wed Oct 03 16:07:52 2007 saving the first 48 matrix rows for later Wed Oct 03 16:07:52 2007 matrix is 46654 x 46766 with weight 1088600 (avg 23.28/col) Wed Oct 03 16:07:52 2007 matrix includes 64 packed rows Wed Oct 03 16:07:52 2007 commencing Lanczos iteration Wed Oct 03 16:08:46 2007 lanczos halted after 739 iterations Wed Oct 03 16:08:47 2007 recovered 6 nontrivial dependencies Wed Oct 03 16:08:47 2007 prp36 factor: 217264834889735630458321389261532721 Wed Oct 03 16:08:47 2007 prp49 factor: 3961899731258636703690742682913482426977474823891 Wed Oct 03 16:08:47 2007 elapsed time 00:32:14
(31·10¹⁵⁸-13)/9 = 3(4)₁₅₇3_<159> = 7 · 127 · 78148787 · 4740691519332947_<16> · C133
C133 = P41 · P92
P41 = 58339351804238222158586791687727596860143_<41>
P92 = 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581_<92>

Number: n N=1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083 ( 133 digits) SNFS difficulty: 159 digits. Divisors found: Thu Oct 04 02:14:25 2007 prp41 factor: 58339351804238222158586791687727596860143 Thu Oct 04 02:14:25 2007 prp92 factor: 17926350607259622695271137524190494788700231091726771361636249626207975716925845807554474581 Thu Oct 04 02:14:25 2007 elapsed time 01:06:27 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 42.50 hours. Scaled time: 61.62 units (timescale=1.450). Factorization parameters were as follows: name: KA_3_4_157_3 n: 1045811674643038618720970610503378607430945162952929917680418191298320275906164719144573731068294405811697968071724804081565705525083 skew: 0.21 deg: 5 c5: 31000 c0: -13 m: 10000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1800000) Primes: RFBsize:183072, AFBsize:182522, largePrimes:7262660 encountered Relations: rels:6751741, finalFF:444988 Max relations in full relation-set: 28 Initial matrix: 365661 x 444988 with sparse part having weight 40908464. Pruned matrix : 320686 x 322578 with weight 26986987. Total sieving time: 42.25 hours. Total relation processing time: 0.25 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 42.50 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(82·10¹⁶⁰-1)/9 = 9(1)₁₆₀_<161> = 1183282325293_<13> · 1398206145473_<13> · C137
C137 = P59 · P79
P59 = 22056688036771319510990392077888123590637483193298813665679_<59>
P79 = 2496729301249539633152615904948407043950273202114296465618776682890249002888781_<79>

Number: n N=55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299 ( 137 digits) SNFS difficulty: 161 digits. Divisors found: Thu Oct 04 02:36:45 2007 prp59 factor: 22056688036771319510990392077888123590637483193298813665679 Thu Oct 04 02:36:45 2007 prp79 factor: 2496729301249539633152615904948407043950273202114296465618776682890249002888781 Thu Oct 04 02:36:45 2007 elapsed time 01:27:51 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 36.40 hours. Scaled time: 48.16 units (timescale=1.323). Factorization parameters were as follows: name: KA_9_1_160 n: 55069579309927136700780310410936392743026521929117229883721627958613372143091384300827504395420854995614166408956523800756004310953847299 skew: 0.41 deg: 5 c5: 82 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 special-q in [100000, 1700000) Primes: RFBsize:250150, AFBsize:250142, largePrimes:7161867 encountered Relations: rels:6671064, finalFF:562452 Max relations in full relation-set: 28 Initial matrix: 500360 x 562452 with sparse part having weight 39726103. Pruned matrix : 448099 x 450664 with weight 25765807. Total sieving time: 36.16 hours. Total relation processing time: 0.24 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 36.40 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
6·10¹³³-7 = 5(9)₁₃₂3_<134> = 419 · C132
C132 = P39 · P40 · P53
P39 = 803784771613572434432727851402219930947_<39>
P40 = 8211994164161688590117664996602372379877_<40>
P53 = 21694458850171435203820744840123411555745339465862013_<53>

Number: n N=143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747 ( 132 digits) SNFS difficulty: 134 digits. Divisors found: r1=803784771613572434432727851402219930947 (pp39) r2=8211994164161688590117664996602372379877 (pp40) r3=21694458850171435203820744840123411555745339465862013 (pp53) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.50 hours. Scaled time: 6.52 units (timescale=1.449). Factorization parameters were as follows: name: KA_5_9_132_3 n: 143198090692124105011933174224343675417661097852028639618138424821002386634844868735083532219570405727923627684964200477326968973747 skew: 0.52 deg: 5 c5: 375 c0: -14 m: 200000000000000000000000000 type: snfs rlim: 1200000 alim: 1200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 550001) Primes: RFBsize:92938, AFBsize:93099, largePrimes:5807271 encountered Relations: rels:5166926, finalFF:262402 Max relations in full relation-set: 28 Initial matrix: 186103 x 262402 with sparse part having weight 21646923. Pruned matrix : 153360 x 154354 with weight 9710538. Total sieving time: 3.84 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.40 hours. Total square root time: 0.12 hours, sqrts: 4. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,1200000,1200000,28,28,48,48,2.5,2.5,75000 total time: 4.50 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
6·10¹⁴⁰-7 = 5(9)₁₃₉3_<141> = 118447393 · C133
C133 = P39 · P95
P39 = 488302592269751645844131141513207371459_<39>
P95 = 10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739_<95>

Number: n N=5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201 ( 133 digits) SNFS difficulty: 140 digits. Divisors found: r1=488302592269751645844131141513207371459 (pp39) r2=10373772369705551105830529941865993946904275182321723727108870993322153016866124697921503890739 (pp95) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.15 hours. Scaled time: 9.46 units (timescale=1.322). Factorization parameters were as follows: name: KA_5_9_139_3 n: 5065539939743545052105958972013845842938898621432723301896564325396338609157906919910005955133178828173955673300466815677403723018201 skew: 1.03 deg: 5 c5: 6 c0: -7 m: 10000000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 850001) Primes: RFBsize:114155, AFBsize:114412, largePrimes:6395094 encountered Relations: rels:5722594, finalFF:311875 Max relations in full relation-set: 48 Initial matrix: 228633 x 311875 with sparse part having weight 33205990. Pruned matrix : 195644 x 196851 with weight 15042093. Total sieving time: 5.86 hours. Total relation processing time: 0.23 hours. Matrix solve time: 1.01 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,100000 total time: 7.15 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 3, 2007 (5th): By suberi / PRIMO
(13·10²⁵⁶³+41)/9 is prime.
(13·10²⁶⁴¹+41)/9 is prime.
Oct 3, 2007 (4th): By Robert Backstrom / GMP-ECM, Msieve
6·10¹²⁵-7 = 5(9)₁₂₄3_<126> = 23 · 3623 · 10966621 · C114
C114 = P38 · P77
P38 = 50636596327829583320839536142290785563_<38>
P77 = 12966349985343467300064590701602747532440337222241547532187032604088384653879_<77>
6·10¹⁵⁷-7 = 5(9)₁₅₆3_<158> = 53 · 97 · 739 · 1091 · 519487 · 709369890512947561_<18> · 1398747574182377711176049107_<28> · C98
C98 = P35 · P64
P35 = 22320341571287862440791180961911537_<35>
P64 = 1258191770139023959637271001787399781177095229292345787867966729_<64>

Wed Oct 03 16:19:38 2007 Msieve v. 1.26 Wed Oct 03 16:19:38 2007 random seeds: b8709f30 80cbbce4 Wed Oct 03 16:19:38 2007 factoring 28083270071686319089592401973395533416884243987372294079591744321397845903861895820202049357252473 (98 digits) Wed Oct 03 16:19:38 2007 commencing quadratic sieve (98-digit input) Wed Oct 03 16:19:38 2007 using multiplier of 1 Wed Oct 03 16:19:38 2007 using 64kb Opteron sieve core Wed Oct 03 16:19:38 2007 sieve interval: 18 blocks of size 65536 Wed Oct 03 16:19:38 2007 processing polynomials in batches of 6 Wed Oct 03 16:19:38 2007 using a sieve bound of 2473301 (90543 primes) Wed Oct 03 16:19:38 2007 using large prime bound of 370995150 (28 bits) Wed Oct 03 16:19:38 2007 using double large prime bound of 2659884601469100 (43-52 bits) Wed Oct 03 16:19:38 2007 using trial factoring cutoff of 52 bits Wed Oct 03 16:19:38 2007 polynomial 'A' values have 13 factors Wed Oct 03 23:18:45 2007 90718 relations (21893 full + 68825 combined from 1364772 partial), need 90639 Wed Oct 03 23:18:47 2007 begin with 1386665 relations Wed Oct 03 23:18:48 2007 reduce to 237587 relations in 12 passes Wed Oct 03 23:18:48 2007 attempting to read 237587 relations Wed Oct 03 23:18:52 2007 recovered 237587 relations Wed Oct 03 23:18:52 2007 recovered 225257 polynomials Wed Oct 03 23:18:52 2007 attempting to build 90718 cycles Wed Oct 03 23:18:53 2007 found 90718 cycles in 6 passes Wed Oct 03 23:18:53 2007 distribution of cycle lengths: Wed Oct 03 23:18:53 2007 length 1 : 21893 Wed Oct 03 23:18:53 2007 length 2 : 15660 Wed Oct 03 23:18:53 2007 length 3 : 15243 Wed Oct 03 23:18:53 2007 length 4 : 12310 Wed Oct 03 23:18:53 2007 length 5 : 9641 Wed Oct 03 23:18:53 2007 length 6 : 6118 Wed Oct 03 23:18:53 2007 length 7 : 4176 Wed Oct 03 23:18:53 2007 length 9+: 5677 Wed Oct 03 23:18:53 2007 largest cycle: 19 relations Wed Oct 03 23:18:53 2007 matrix is 90543 x 90718 with weight 6047781 (avg 66.67/col) Wed Oct 03 23:18:54 2007 filtering completed in 3 passes Wed Oct 03 23:18:54 2007 matrix is 86539 x 86603 with weight 5807038 (avg 67.05/col) Wed Oct 03 23:18:55 2007 saving the first 48 matrix rows for later Wed Oct 03 23:18:55 2007 matrix is 86491 x 86603 with weight 4591383 (avg 53.02/col) Wed Oct 03 23:18:55 2007 matrix includes 64 packed rows Wed Oct 03 23:18:55 2007 using block size 21845 for processor cache size 512 kB Wed Oct 03 23:18:55 2007 commencing Lanczos iteration Wed Oct 03 23:20:21 2007 lanczos halted after 1370 iterations Wed Oct 03 23:20:21 2007 recovered 17 nontrivial dependencies Wed Oct 03 23:20:22 2007 prp35 factor: 22320341571287862440791180961911537 Wed Oct 03 23:20:22 2007 prp64 factor: 1258191770139023959637271001787399781177095229292345787867966729 Wed Oct 03 23:20:22 2007 elapsed time 07:00:44
Oct 3, 2007 (3rd): By Sinkiti Sibata / Msieve v. 1.26, GGNFS
6·10¹⁵³-7 = 5(9)₁₅₂3_<154> = 13 · 139747 · 41191413729044567_<17> · 28576336929599376517741_<23> · 1025244729230700913218569_<25> · C85
C85 = P42 · P43
P42 = 356746994819799697074718391780142365509993_<42>
P43 = 7671217220429161293573234558957602035904237_<43>

Wed Oct 03 14:47:30 2007 Msieve v. 1.26 Wed Oct 03 14:47:30 2007 random seeds: 460178a0 145787d5 Wed Oct 03 14:47:30 2007 factoring 2736683689998000234925592599907106848522357423838373040075488018168277701797414540341 (85 digits) Wed Oct 03 14:47:30 2007 commencing quadratic sieve (85-digit input) Wed Oct 03 14:47:31 2007 using multiplier of 21 Wed Oct 03 14:47:31 2007 using 64kb Pentium 2 sieve core Wed Oct 03 14:47:31 2007 sieve interval: 6 blocks of size 65536 Wed Oct 03 14:47:31 2007 processing polynomials in batches of 17 Wed Oct 03 14:47:31 2007 using a sieve bound of 1425547 (54412 primes) Wed Oct 03 14:47:31 2007 using large prime bound of 116894854 (26 bits) Wed Oct 03 14:47:31 2007 using double large prime bound of 332683806537686 (41-49 bits) Wed Oct 03 14:47:31 2007 using trial factoring cutoff of 49 bits Wed Oct 03 14:47:31 2007 polynomial 'A' values have 11 factors Wed Oct 03 19:20:05 2007 54584 relations (15772 full + 38812 combined from 574026 partial), need 54508 Wed Oct 03 19:20:07 2007 begin with 589798 relations Wed Oct 03 19:20:09 2007 reduce to 128585 relations in 11 passes Wed Oct 03 19:20:09 2007 attempting to read 128585 relations Wed Oct 03 19:20:14 2007 recovered 128585 relations Wed Oct 03 19:20:14 2007 recovered 109292 polynomials Wed Oct 03 19:20:15 2007 attempting to build 54584 cycles Wed Oct 03 19:20:15 2007 found 54584 cycles in 5 passes Wed Oct 03 19:20:19 2007 distribution of cycle lengths: Wed Oct 03 19:20:19 2007 length 1 : 15772 Wed Oct 03 19:20:19 2007 length 2 : 11077 Wed Oct 03 19:20:19 2007 length 3 : 9717 Wed Oct 03 19:20:19 2007 length 4 : 6987 Wed Oct 03 19:20:19 2007 length 5 : 4720 Wed Oct 03 19:20:19 2007 length 6 : 2838 Wed Oct 03 19:20:19 2007 length 7 : 1656 Wed Oct 03 19:20:19 2007 length 9+: 1817 Wed Oct 03 19:20:19 2007 largest cycle: 17 relations Wed Oct 03 19:20:20 2007 matrix is 54412 x 54584 with weight 2905977 (avg 53.24/col) Wed Oct 03 19:20:22 2007 filtering completed in 3 passes Wed Oct 03 19:20:22 2007 matrix is 49748 x 49812 with weight 2673600 (avg 53.67/col) Wed Oct 03 19:20:24 2007 saving the first 48 matrix rows for later Wed Oct 03 19:20:24 2007 matrix is 49700 x 49812 with weight 1993341 (avg 40.02/col) Wed Oct 03 19:20:24 2007 matrix includes 64 packed rows Wed Oct 03 19:20:24 2007 commencing Lanczos iteration Wed Oct 03 19:25:55 2007 lanczos halted after 787 iterations Wed Oct 03 19:25:56 2007 recovered 19 nontrivial dependencies Wed Oct 03 19:25:59 2007 prp42 factor: 356746994819799697074718391780142365509993 Wed Oct 03 19:25:59 2007 prp43 factor: 7671217220429161293573234558957602035904237 Wed Oct 03 19:25:59 2007 elapsed time 04:38:29
8·10¹⁶⁰-3 = 7(9)₁₅₉7_<161> = 43² · 431 · 48859 · 4647456722639_<13> · 626627965062020591_<18> · C120
C120 = P47 · P74
P47 = 14692417462058974457446490078935236626410262041_<47>
P74 = 48018970537507694295810504240418883922125431142142818767721221650978656473_<74>

Number: 79997_160 N=705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393 ( 120 digits) SNFS difficulty: 160 digits. Divisors found: r1=14692417462058974457446490078935236626410262041 (pp47) r2=48018970537507694295810504240418883922125431142142818767721221650978656473 (pp74) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 60.89 hours. Scaled time: 41.22 units (timescale=0.677). Factorization parameters were as follows: name: 79997_160 n: 705514761235373466365712554295053490555390684232165126019501416207453667149193594120119006252562816485365473350050841393 m: 100000000000000000000000000000000 c5: 8 c0: -3 skew: 0.82 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, 3500001) Primes: RFBsize:283146, AFBsize:283367, largePrimes:5694153 encountered Relations: rels:5794190, finalFF:713570 Max relations in full relation-set: 28 Initial matrix: 566578 x 713570 with sparse part having weight 44691099. Pruned matrix : 447630 x 450526 with weight 27726964. Total sieving time: 52.59 hours. Total relation processing time: 0.28 hours. Matrix solve time: 7.83 hours. Time per square root: 0.19 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: 60.89 hours. --------- CPU info (if available) ----------
Oct 3, 2007 (2nd): By Jo Yeong Uk / GGNFS
6·10¹¹¹-7 = 5(9)₁₁₀3_<112> = 13 · 2423 · C108
C108 = P51 · P57
P51 = 360964079692659801539218828060656161476910423250161_<51>
P57 = 527704135252280213728502010679882140961843051369612566587_<57>

Number: 59993_111 N=190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507 ( 108 digits) SNFS difficulty: 111 digits. Divisors found: r1=360964079692659801539218828060656161476910423250161 (pp51) r2=527704135252280213728502010679882140961843051369612566587 (pp57) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.71 hours. Scaled time: 1.53 units (timescale=2.145). Factorization parameters were as follows: n: 190482237531350201593701387345630020000634940791771167338645671291152100066668783135972570557795485570970507 m: 10000000000000000000000 c5: 60 c0: -7 skew: 0.65 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:30694, largePrimes:1074870 encountered Relations: rels:1007128, finalFF:101389 Max relations in full relation-set: 28 Initial matrix: 61518 x 101389 with sparse part having weight 4955758. Pruned matrix : 50735 x 51106 with weight 1760939. Total sieving time: 0.68 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,111,5,0,0,0,0,0,0,0,0,360000,360000,25,25,44,44,2.2,2.2,20000 total time: 0.71 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
6·10¹²²-7 = 5(9)₁₂₁3_<123> = 29 · C122
C122 = P38 · P84
P38 = 68004493287578401111324018574258290351_<38>
P84 = 304239531422152873078652750157120871113171209374964566110469309352350285844274312067_<84>

Number: 59993_122 N=20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517 ( 122 digits) SNFS difficulty: 123 digits. Divisors found: r1=68004493287578401111324018574258290351 (pp38) r2=304239531422152873078652750157120871113171209374964566110469309352350285844274312067 (pp84) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.52 hours. Scaled time: 3.26 units (timescale=2.144). Factorization parameters were as follows: n: 20689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517 m: 2000000000000000000000000 c5: 75 c0: -28 skew: 0.82 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved algebraic special-q in [400000, 720001) Primes: RFBsize:63951, AFBsize:63523, largePrimes:1389910 encountered Relations: rels:1372098, finalFF:158574 Max relations in full relation-set: 28 Initial matrix: 127540 x 158574 with sparse part having weight 7799698. Pruned matrix : 114540 x 115241 with weight 4337757. Total sieving time: 1.46 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,123,5,0,0,0,0,0,0,0,0,800000,800000,25,25,45,45,2.2,2.2,40000 total time: 1.52 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
6·10¹³⁷-7 = 5(9)₁₃₆3_<138> = C138
C138 = P44 · P95
P44 = 11930304707794017951010060929038611787637529_<44>
P95 = 50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017_<95>

Number: 59993_137 N=599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 ( 138 digits) SNFS difficulty: 138 digits. Divisors found: r1=11930304707794017951010060929038611787637529 (pp44) r2=50292093512751817677191069598755399434481984540235534607565516222232375080068547729293970178017 (pp95) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.81 hours. Scaled time: 10.24 units (timescale=2.129). Factorization parameters were as follows: n: 599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999993 m: 2000000000000000000000000000 c5: 75 c0: -28 skew: 0.82 type: snfs Factor base limits: 1400000/1400000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 47/47 Sieved algebraic special-q in [700000, 1600001) Primes: RFBsize:107126, AFBsize:106878, largePrimes:2399412 encountered Relations: rels:2552130, finalFF:267534 Max relations in full relation-set: 28 Initial matrix: 214070 x 267534 with sparse part having weight 24798377. Pruned matrix : 197717 x 198851 with weight 15730218. Total sieving time: 4.58 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.16 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 4.81 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
6·10¹³⁰-7 = 5(9)₁₂₉3_<131> = 3581 · 11927683 · 77492399487775327777_<20> · C101
C101 = P41 · P60
P41 = 41741913374238084153759348799228096820219_<41>
P60 = 434269551129510598310111242531747787622152307167204480286557_<60>

Number: 59993_130 N=18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983 ( 101 digits) SNFS difficulty: 130 digits. Divisors found: r1=41741913374238084153759348799228096820219 (pp41) r2=434269551129510598310111242531747787622152307167204480286557 (pp60) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.61 hours. Scaled time: 5.60 units (timescale=2.145). Factorization parameters were as follows: n: 18127241984317287948259696060358425132269108005734409737154495900535745003233991139307777121631495983 m: 100000000000000000000000000 c5: 6 c0: -7 skew: 1.03 type: snfs Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [500000, 1050001) Primes: RFBsize:78498, AFBsize:78516, largePrimes:1562106 encountered Relations: rels:1575211, finalFF:190100 Max relations in full relation-set: 28 Initial matrix: 157080 x 190100 with sparse part having weight 11252053. Pruned matrix : 145006 x 145855 with weight 6877487. Total sieving time: 2.51 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.06 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,130,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 2.61 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
Oct 3, 2007: The factor table of 599...993 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.
Oct 2, 2007 (3rd): By Jo Yeong Uk / GGNFS
4·10¹⁵⁸+7 = 4(0)₁₅₇7_<159> = 11 · 37 · 12007 · 64184521 · 801992267819_<12> · C133
C133 = P47 · P86
P47 = 40168232933255472863199410867005086259141899511_<47>
P86 = 39586568659768781756154959633375249919813838935426658359620291935490219828230564916987_<86>

Number: 40007_158 N=1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357 ( 133 digits) SNFS difficulty: 160 digits. Divisors found: r1=40168232933255472863199410867005086259141899511 (pp47) r2=39586568659768781756154959633375249919813838935426658359620291935490219828230564916987 (pp86) Version: GGNFS-0.77.1-20050930-nocona Total time: 24.50 hours. Scaled time: 52.33 units (timescale=2.136). Factorization parameters were as follows: n: 1590122510953903345542624420568097263521630484531474875782839648114082015795534996005269615326322770371113782601521530538607210893357 m: 100000000000000000000000000000000 c5: 1 c0: 175 skew: 2.81 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:283052, largePrimes:5731305 encountered Relations: rels:5871089, finalFF:749665 Max relations in full relation-set: 28 Initial matrix: 566262 x 749665 with sparse part having weight 45967150. Pruned matrix : 415205 x 418100 with weight 27576167. Total sieving time: 23.50 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.87 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: 24.50 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: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
Oct 2, 2007 (2nd): By Sinkiti Sibata / GGNFS
(5·10¹⁶¹+7)/3 = 1(6)₁₆₀9_<162> = 570049 · 111524293 · 148946655411315836615893811933_<30> · C119
C119 = P59 · P60
P59 = 19431998449239836919883891499392364284154878753810288198627_<59>
P60 = 905771934729220258028194158863173230204066471520265077490687_<60>

Number: 16669_161 N=17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749 ( 119 digits) SNFS difficulty: 161 digits. Divisors found: r1=19431998449239836919883891499392364284154878753810288198627 (pp59) r2=905771934729220258028194158863173230204066471520265077490687 (pp60) Version: GGNFS-0.77.1-20060513-k8 Total time: 73.18 hours. Scaled time: 146.44 units (timescale=2.001). Factorization parameters were as follows: name: 16669_161 n: 17600958831023174839925978092753242124486597026417452012549969280102392991960434543098921399672637559438776334598686749 m: 100000000000000000000000000000000 c5: 50 c0: 7 skew: 0.67 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:316881, largePrimes:5795306 encountered Relations: rels:5901400, finalFF:737692 Max relations in full relation-set: 28 Initial matrix: 632894 x 737692 with sparse part having weight 45414630. Pruned matrix : 553191 x 556419 with weight 32190862. Total sieving time: 69.32 hours. Total relation processing time: 0.19 hours. Matrix solve time: 3.47 hours. Time per square root: 0.20 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: 73.18 hours. --------- CPU info (if available) ----------
Oct 2, 2007: By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶¹-7)/3 = 1(3)₁₆₀1_<162> = 11 · 11124606089_<11> · 100299923063_<12> · C140
C140 = P45 · P95
P45 = 866216913035861859660556067350054626872174933_<45>
P95 = 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091_<95>

Number: n N=10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903 ( 140 digits) SNFS difficulty: 161 digits. Divisors found: prp45 factor: 866216913035861859660556067350054626872174933 prp95 factor: 12541057250108172132778787912475915358164724857304431753382275697071209996577378790384734808091 elapsed time 02:26:08 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.30 hours. Scaled time: 48.24 units (timescale=1.197). Factorization parameters were as follows: name: KA_1_3_160_1 n: 10863275897394715416026646238743388383563411275697039333548489540819916417179198180218113482105248693668875830361857053271903904435535782903 type: snfs skew: 0.71 deg: 5 c5: 40 c0: -7 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 special-q in [100000, 1700000) Primes: RFBsize:250150, AFBsize:249831, largePrimes:6771115 encountered Relations: rels:6304352, finalFF:590349 Max relations in full relation-set: 28 Initial matrix: 500047 x 590349 with sparse part having weight 31375036. Pruned matrix : 415114 x 417678 with weight 17906321. Total sieving time: 40.07 hours. Total relation processing time: 0.23 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.3,2.3,100000 total time: 40.30 hours. --------- CPU info (if available) ---------- Cygwin on AMD XP 2700+
5·10¹⁶¹-1 = 4(9)₁₆₁_<162> = 23 · 5039 · 5503 · 121219311137_<12> · C142
C142 = P69 · P74
P69 = 205172085665013628136788854347422145538579372307983152097920947502671_<69>
P74 = 31521596990625887572504276079879084677165618298704568194646451128941172807_<74>

Number: n N=6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497 ( 142 digits) SNFS difficulty: 161 digits. Divisors found: Tue Oct 02 05:21:23 2007 prp69 factor: 205172085665013628136788854347422145538579372307983152097920947502671 Tue Oct 02 05:21:23 2007 prp74 factor: 31521596990625887572504276079879084677165618298704568194646451128941172807 Tue Oct 02 05:21:23 2007 elapsed time 01:18:32 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 29.84 hours. Scaled time: 43.39 units (timescale=1.454). Factorization parameters were as follows: name: KA_4_9_161 n: 6467351798058730387628097619584464793561004208531537922182496075642274563849187638841619505437822847268801141316782851382812647988076505067497 skew: 0.46 deg: 5 c5: 50 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 2800000 alim: 2800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1600000) Primes: RFBsize:203362, AFBsize:203587, largePrimes:7032000 encountered Relations: rels:6494307, finalFF:456833 Max relations in full relation-set: 28 Initial matrix: 407014 x 456833 with sparse part having weight 35481673. Pruned matrix : 369264 x 371363 with weight 25332214. Total sieving time: 29.63 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 29.84 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(28·10¹⁶⁰-1)/9 = 3(1)₁₆₀_<161> = 53 · 113 · 367 · 10608547 · 331545143 · C139
C139 = P51 · P88
P51 = 633091035242735539801967600647466189684568802167457_<51>
P88 = 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001_<88>

Number: n N=4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457 ( 139 digits) SNFS difficulty: 161 digits. Divisors found: Tue Oct 02 06:04:18 2007 prp51 factor: 633091035242735539801967600647466189684568802167457 Tue Oct 02 06:04:18 2007 prp88 factor: 6356680828325396531036158080960100862662205508268214943170736874990151494680541613194001 Tue Oct 02 06:04:18 2007 elapsed time 01:22:53 (Msieve 1.26) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 34.41 hours. Scaled time: 44.59 units (timescale=1.296). Factorization parameters were as follows: name: KA_3_1_160 n: 4024357646312174958831474608222302299118450594684435034315875112537932079099180653597254994891579763036098222505425488832273115077429825457 skew: 0.51 deg: 5 c5: 28 c0: -1 m: 100000000000000000000000000000000 type: snfs rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1700000) Primes: RFBsize:216816, AFBsize:216531, largePrimes:7070916 encountered Relations: rels:6546532, finalFF:488128 Max relations in full relation-set: 28 Initial matrix: 433413 x 488128 with sparse part having weight 35567073. Pruned matrix : 391277 x 393508 with weight 24641110. Total sieving time: 33.14 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.06 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 34.41 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁶¹-3 = 6(9)₁₆₀7_<162> = 11759927 · 890858477521139_<15> · C140
C140 = P52 · P89
P52 = 5434034586523956104106766412088428719802308238404951_<52>
P89 = 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399_<89>

Number: n N=66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449 ( 140 digits) SNFS difficulty: 161 digits. Divisors found: Tue Oct 02 11:41:36 2007 prp52 factor: 5434034586523956104106766412088428719802308238404951 Tue Oct 02 11:41:36 2007 prp89 factor: 12295955952110120403085408303775786006169912054674465432621806697568821168788407881446399 Tue Oct 02 11:41:36 2007 elapsed time 02:02:16 (Msieve 1.26) Version: GGNFS-0.77.1-20051202-athlon Total time: 53.37 hours. Scaled time: 70.61 units (timescale=1.323). Factorization parameters were as follows: name: KA_6_9_160_7 n: 66816649918141495127926394200224912688873813650781970983701894207994243406438544537584681883365367975168764122211116754043488833134562721449 skew: 0.53 deg: 5 c5: 70 c0: -3 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 special-q in [100000, 2500000) Primes: RFBsize:250150, AFBsize:249361, largePrimes:7482224 encountered Relations: rels:6975734, finalFF:559949 Max relations in full relation-set: 28 Initial matrix: 499578 x 559949 with sparse part having weight 47483613. Pruned matrix : 454399 x 456960 with weight 33007219. Total sieving time: 53.09 hours. Total relation processing time: 0.29 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. 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: 53.37 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Oct 1, 2007 (3rd): By Jo Yeong Uk / GGNFS
2·10¹⁵⁸-7 = 1(9)₁₅₇3_<159> = 953 · 25057 · 2414090848213589432916932990633_<31> · C121
C121 = P53 · P69
P53 = 31571248495465350553236417278124057355578453451578557_<53>
P69 = 109891134207565565423460471928953710097707635400211726467910976480493_<69>

Number: 19993_158 N=3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601 ( 121 digits) SNFS difficulty: 160 digits. Divisors found: r1=31571248495465350553236417278124057355578453451578557 (pp53) r2=109891134207565565423460471928953710097707635400211726467910976480493 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 34.21 hours. Scaled time: 72.22 units (timescale=2.111). Factorization parameters were as follows: n: 3469400305515585275088518477571852718127951025814114467282749380810057951257353312433363378995962611612031180850967588601 m: 100000000000000000000000000000000 c5: 1 c0: -350 skew: 3.23 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, 4000001) Primes: RFBsize:283146, AFBsize:283727, largePrimes:5808005 encountered Relations: rels:5905005, finalFF:708062 Max relations in full relation-set: 28 Initial matrix: 566937 x 708062 with sparse part having weight 48034519. Pruned matrix : 464821 x 467719 with weight 33043298. Total sieving time: 32.81 hours. Total relation processing time: 0.09 hours. Matrix solve time: 1.26 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: 34.21 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Intel(R) Core(TM)2 Quad CPU @ 2.40GHz stepping 07 Memory: 8167512k/8912896k available (2115k kernel code, 0k reserved, 1306k data, 208k init) Calibrating delay using timer specific routine.. 4815.34 BogoMIPS (lpj=2407674) Calibrating delay using timer specific routine.. 4684.13 BogoMIPS (lpj=2342066) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405119) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405124) Total of 4 processors activated (19119.96 BogoMIPS).
Oct 2, 2007 (2nd): By Jo Yeong Uk / PRIMO
4·10²⁰³⁸+9 is prime!
Oct 1, 2007: By Sinkiti Sibata / GGNFS
(5·10¹⁵⁹+7)/3 = 1(6)₁₅₈9_<160> = 61 · 139 · 22354882834663_<14> · C142
C142 = P50 · P93
P50 = 20633650419206281386733031458970921470010125270621_<50>
P93 = 426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857_<93>

Number: 16669_159 N=8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197 ( 142 digits) SNFS difficulty: 160 digits. Divisors found: r1=20633650419206281386733031458970921470010125270621 (pp50) r2=426143283646225856200448242499018567906598044643963243984154881765936470251951711802769440857 (pp93) Version: GGNFS-0.77.1-20060513-k8 Total time: 40.03 hours. Scaled time: 77.81 units (timescale=1.944). Factorization parameters were as follows: name: 16669_159 n: 8792891543248889413056523663055605397019366650336981625335329343284007000558823348485757194490519250667301471004607262229383740155945979162197 m: 100000000000000000000000000000000 c5: 1 c0: 14 skew: 1.7 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:283092, largePrimes:5781861 encountered Relations: rels:5963802, finalFF:786585 Max relations in full relation-set: 28 Initial matrix: 566302 x 786585 with sparse part having weight 46911389. Pruned matrix : 388163 x 391058 with weight 28940900. Total sieving time: 37.70 hours. Total relation processing time: 0.15 hours. Matrix solve time: 2.02 hours. Time per square root: 0.16 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: 40.03 hours. --------- CPU info (if available) ----------
(5·10¹⁵⁴+7)/3 = 1(6)₁₅₃9_<155> = 17² · 211 · 89227 · 3642209 · 34988803 · C131
C131 = P64 · P67
P64 = 3039500772684756067905656547847651710767202885317667360748022141_<64>
P67 = 7908169219491322981400916567456394408788268380654149703529298881099_<67>

Number: 16669_154 N=24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959 ( 131 digits) SNFS difficulty: 155 digits. Divisors found: r1=3039500772684756067905656547847651710767202885317667360748022141 (pp64) r2=7908169219491322981400916567456394408788268380654149703529298881099 (pp67) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 35.56 hours. Scaled time: 24.07 units (timescale=0.677). Factorization parameters were as follows: name: 16669_154 n: 24036886453165680508340850848781676496510660976142667106365241496273418489191071703314462061843335352040879870593174633908578412959 m: 10000000000000000000000000000000 c5: 1 c0: 14 skew: 1.7 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, 2400001) Primes: RFBsize:216816, AFBsize:216671, largePrimes:5670953 encountered Relations: rels:5752856, finalFF:662121 Max relations in full relation-set: 28 Initial matrix: 433551 x 662121 with sparse part having weight 48626390. Pruned matrix : 281115 x 283346 with weight 30459459. Total sieving time: 31.66 hours. Total relation processing time: 0.21 hours. Matrix solve time: 3.54 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 35.56 hours. --------- CPU info (if available) ----------

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