News and updates, February 2008

Since June 16, 2000

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News and updates, February 2008	2008-03-02(Sun) 13:55

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News and updates, February 2008

Feb 29, 2008: By Sinkiti Sibata / PRIMO
(4·10²⁵¹⁰+17)/3 is prime.
Feb 28, 2008: By Hugo Platzer / GGNFS, Msieve
(4·10¹¹⁵+17)/3 = 1(3)₁₁₄9_<116> = 44273161259577833937371461_<26> · C90
C90 = P39 · P51
P39 = 319366236020566864959345447725369918009_<39>
P51 = 942994595128733071671702794426078062922265699564311_<51>

Number: pal/pal N=301160634434001859043915236810290858557068276203651269507515584105353054975494297092576799 ( 90 digits) SNFS difficulty: 115 digits. Divisors found: r1=319366236020566864959345447725369918009 (pp39) r2=942994595128733071671702794426078062922265699564311 (pp51) Version: GGNFS-0.77.0 Total time: 1.74 hours. Scaled time: 2.06 units (timescale=1.188). Factorization parameters were as follows: n: 301160634434001859043915236810290858557068276203651269507515584105353054975494297092576799 m: 100000000000000000000000 c5: 4 c0: 17 skew: 1.34 type: snfs Factor base limits: 450000/500000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [250000, 410001) Relations: rels:1114412, finalFF:123645 Initial matrix: 79657 x 123645 with sparse part having weight 5708692. Pruned matrix : 71040 x 71502 with weight 1969930. Total sieving time: 1.65 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.02 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,450000,500000,25,25,44,44,2.2,2.2,20000 total time: 1.74 hours. --------- CPU info (if available) ----------
(4·10¹⁰²+17)/3 = 1(3)₁₀₁9_<103> = 7 · 90997 · C97
C97 = P36 · P61
P36 = 908549692702934028385232905262450753_<36>
P61 = 2303906956496829188740684010099011404683762570088688116424697_<61>

Number: pal/pal N=2093213957341346156362036006419887207165908661562364431689794064377841865011771711992598395446841 ( 97 digits) SNFS difficulty: 102 digits. Divisors found: r1=908549692702934028385232905262450753 (pp36) r2=2303906956496829188740684010099011404683762570088688116424697 (pp61) Version: GGNFS-0.77.0 Total time: 1.06 hours. Scaled time: 1.30 units (timescale=1.226). Factorization parameters were as follows: n: 2093213957341346156362036006419887207165908661562364431689794064377841865011771711992598395446841 m: 200000000000000000000 c5: 25 c0: 34 skew: 1.06 type: snfs Factor base limits: 300000/350000 Large primes per side: 3 Large prime bits: 25/25 Sieved special-q in [175000, 255001) Relations: rels:834056, finalFF:65949 Initial matrix: 55703 x 65949 with sparse part having weight 1722162. Pruned matrix : 48155 x 48497 with weight 1039638. Total sieving time: 1.01 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,300000,350000,25,25,43,43,2.1,2.1,10000 total time: 1.06 hours. --------- CPU info (if available) ----------
(4·10¹⁰⁵+17)/3 = 1(3)₁₀₄9_<106> = 13 · 61 · 103 · 109 · 269 · 761 · 821 · 24439 · C86
C86 = P37 · P50
P37 = 1130021764079074147902253763132106677_<37>
P50 = 32266472809078491624666219453514850051247682267147_<50>

Mon Feb 25 19:02:32 2008 Mon Feb 25 19:02:32 2008 Mon Feb 25 19:02:32 2008 Msieve v. 1.33 Mon Feb 25 19:02:32 2008 random seeds: 489d45ae e59eb9a7 Mon Feb 25 19:02:32 2008 factoring 36461816524324356163353669314329958450145184317692851469585242129594363032425616440519 (86 digits) Mon Feb 25 19:02:33 2008 no P-1/P+1/ECM available, skipping Mon Feb 25 19:02:33 2008 commencing quadratic sieve (86-digit input) Mon Feb 25 19:02:33 2008 using multiplier of 5 Mon Feb 25 19:02:33 2008 using 64kb Pentium 4 sieve core Mon Feb 25 19:02:33 2008 sieve interval: 8 blocks of size 65536 Mon Feb 25 19:02:33 2008 processing polynomials in batches of 13 Mon Feb 25 19:02:33 2008 using a sieve bound of 1461401 (55581 primes) Mon Feb 25 19:02:33 2008 using large prime bound of 116912080 (26 bits) Mon Feb 25 19:02:33 2008 using double large prime bound of 332771997435520 (41-49 bits) Mon Feb 25 19:02:33 2008 using trial factoring cutoff of 49 bits Mon Feb 25 19:02:33 2008 polynomial 'A' values have 11 factors Mon Feb 25 19:55:41 2008 28010 relations (11626 full + 16384 combined from 433728 partial), need 55677 Mon Feb 25 19:55:41 2008 elapsed time 00:53:09 Tue Feb 26 14:33:17 2008 Tue Feb 26 14:33:17 2008 Tue Feb 26 14:33:17 2008 Msieve v. 1.33 Tue Feb 26 14:33:17 2008 random seeds: 1bd18fdc 512ff2e1 Tue Feb 26 14:33:17 2008 factoring 36461816524324356163353669314329958450145184317692851469585242129594363032425616440519 (86 digits) Tue Feb 26 14:33:18 2008 no P-1/P+1/ECM available, skipping Tue Feb 26 14:33:18 2008 commencing quadratic sieve (86-digit input) Tue Feb 26 14:33:19 2008 using multiplier of 5 Tue Feb 26 14:33:19 2008 using 64kb Pentium 4 sieve core Tue Feb 26 14:33:19 2008 sieve interval: 8 blocks of size 65536 Tue Feb 26 14:33:19 2008 processing polynomials in batches of 13 Tue Feb 26 14:33:19 2008 using a sieve bound of 1461401 (55581 primes) Tue Feb 26 14:33:19 2008 using large prime bound of 116912080 (26 bits) Tue Feb 26 14:33:19 2008 using double large prime bound of 332771997435520 (41-49 bits) Tue Feb 26 14:33:19 2008 using trial factoring cutoff of 49 bits Tue Feb 26 14:33:19 2008 polynomial 'A' values have 11 factors Tue Feb 26 14:33:19 2008 restarting with 11626 full and 433728 partial relations Tue Feb 26 14:52:43 2008 55935 relations (15723 full + 40212 combined from 587434 partial), need 55677 Tue Feb 26 14:52:43 2008 begin with 603157 relations Tue Feb 26 14:52:44 2008 reduce to 133993 relations in 11 passes Tue Feb 26 14:52:44 2008 attempting to read 133993 relations Tue Feb 26 14:52:47 2008 recovered 133993 relations Tue Feb 26 14:52:47 2008 recovered 114567 polynomials Tue Feb 26 14:52:47 2008 attempting to build 55935 cycles Tue Feb 26 14:52:47 2008 found 55935 cycles in 5 passes Tue Feb 26 14:52:47 2008 distribution of cycle lengths: Tue Feb 26 14:52:47 2008 length 1 : 15723 Tue Feb 26 14:52:47 2008 length 2 : 10989 Tue Feb 26 14:52:47 2008 length 3 : 9938 Tue Feb 26 14:52:47 2008 length 4 : 7222 Tue Feb 26 14:52:47 2008 length 5 : 4960 Tue Feb 26 14:52:47 2008 length 6 : 3120 Tue Feb 26 14:52:47 2008 length 7 : 1800 Tue Feb 26 14:52:47 2008 length 9+: 2183 Tue Feb 26 14:52:47 2008 largest cycle: 18 relations Tue Feb 26 14:52:47 2008 matrix is 55581 x 55935 (12.6 MB) with weight 3078328 (55.03/col) Tue Feb 26 14:52:47 2008 sparse part has weight 3078328 (55.03/col) Tue Feb 26 14:52:48 2008 filtering completed in 4 passes Tue Feb 26 14:52:48 2008 matrix is 51012 x 51076 (11.6 MB) with weight 2828283 (55.37/col) Tue Feb 26 14:52:48 2008 sparse part has weight 2828283 (55.37/col) Tue Feb 26 14:52:48 2008 saving the first 48 matrix rows for later Tue Feb 26 14:52:49 2008 matrix is 50964 x 51076 (6.8 MB) with weight 2143902 (41.97/col) Tue Feb 26 14:52:49 2008 sparse part has weight 1474804 (28.87/col) Tue Feb 26 14:52:49 2008 matrix includes 64 packed rows Tue Feb 26 14:52:49 2008 using block size 20430 for processor cache size 2048 kB Tue Feb 26 14:52:49 2008 commencing Lanczos iteration Tue Feb 26 14:52:49 2008 memory use: 7.0 MB Tue Feb 26 14:53:11 2008 lanczos halted after 807 iterations (dim = 50964) Tue Feb 26 14:53:11 2008 recovered 19 nontrivial dependencies Tue Feb 26 14:53:12 2008 prp37 factor: 1130021764079074147902253763132106677 Tue Feb 26 14:53:12 2008 prp50 factor: 32266472809078491624666219453514850051247682267147 Tue Feb 26 14:53:12 2008 elapsed time 00:19:55
(4·10¹⁰³+17)/3 = 1(3)₁₀₂9_<104> = 71 · 272825425082537387_<18> · C84
C84 = P34 · P51
P34 = 5999573294919686788638217605693019_<34>
P51 = 114729521955095979857325671845756990670861614334053_<51>

Mon Feb 25 16:51:57 2008 Mon Feb 25 16:51:57 2008 Mon Feb 25 16:51:57 2008 Msieve v. 1.33 Mon Feb 25 16:51:57 2008 random seeds: 865e6202 3cef8fa7 Mon Feb 25 16:51:57 2008 factoring 688328176060695733567653133817593886237944056362101592634801269296206820707236076007 (84 digits) Mon Feb 25 16:51:58 2008 no P-1/P+1/ECM available, skipping Mon Feb 25 16:51:58 2008 commencing quadratic sieve (84-digit input) Mon Feb 25 16:51:58 2008 using multiplier of 7 Mon Feb 25 16:51:58 2008 using 64kb Pentium 4 sieve core Mon Feb 25 16:51:58 2008 sieve interval: 6 blocks of size 65536 Mon Feb 25 16:51:58 2008 processing polynomials in batches of 17 Mon Feb 25 16:51:58 2008 using a sieve bound of 1408987 (53824 primes) Mon Feb 25 16:51:58 2008 using large prime bound of 119763895 (26 bits) Mon Feb 25 16:51:58 2008 using double large prime bound of 347525361371830 (41-49 bits) Mon Feb 25 16:51:58 2008 using trial factoring cutoff of 49 bits Mon Feb 25 16:51:58 2008 polynomial 'A' values have 11 factors Mon Feb 25 17:34:06 2008 54044 relations (16264 full + 37780 combined from 570002 partial), need 53920 Mon Feb 25 17:34:07 2008 begin with 586266 relations Mon Feb 25 17:34:07 2008 reduce to 124740 relations in 10 passes Mon Feb 25 17:34:07 2008 attempting to read 124740 relations Mon Feb 25 17:34:09 2008 recovered 124740 relations Mon Feb 25 17:34:09 2008 recovered 97661 polynomials Mon Feb 25 17:34:10 2008 attempting to build 54044 cycles Mon Feb 25 17:34:10 2008 found 54044 cycles in 5 passes Mon Feb 25 17:34:10 2008 distribution of cycle lengths: Mon Feb 25 17:34:10 2008 length 1 : 16264 Mon Feb 25 17:34:10 2008 length 2 : 11387 Mon Feb 25 17:34:10 2008 length 3 : 9603 Mon Feb 25 17:34:10 2008 length 4 : 6775 Mon Feb 25 17:34:10 2008 length 5 : 4392 Mon Feb 25 17:34:10 2008 length 6 : 2597 Mon Feb 25 17:34:10 2008 length 7 : 1454 Mon Feb 25 17:34:10 2008 length 9+: 1572 Mon Feb 25 17:34:10 2008 largest cycle: 16 relations Mon Feb 25 17:34:10 2008 matrix is 53824 x 54044 (11.5 MB) with weight 2806436 (51.93/col) Mon Feb 25 17:34:10 2008 sparse part has weight 2806436 (51.93/col) Mon Feb 25 17:34:10 2008 filtering completed in 3 passes Mon Feb 25 17:34:10 2008 matrix is 48513 x 48577 (10.4 MB) with weight 2532665 (52.14/col) Mon Feb 25 17:34:10 2008 sparse part has weight 2532665 (52.14/col) Mon Feb 25 17:34:11 2008 saving the first 48 matrix rows for later Mon Feb 25 17:34:11 2008 matrix is 48465 x 48577 (6.2 MB) with weight 1903865 (39.19/col) Mon Feb 25 17:34:11 2008 sparse part has weight 1328744 (27.35/col) Mon Feb 25 17:34:11 2008 matrix includes 64 packed rows Mon Feb 25 17:34:11 2008 commencing Lanczos iteration Mon Feb 25 17:34:11 2008 memory use: 8.0 MB Mon Feb 25 17:35:38 2008 lanczos halted after 768 iterations (dim = 48457) Mon Feb 25 17:35:38 2008 recovered 13 nontrivial dependencies Mon Feb 25 17:35:39 2008 prp34 factor: 5999573294919686788638217605693019 Mon Feb 25 17:35:39 2008 prp51 factor: 114729521955095979857325671845756990670861614334053 Mon Feb 25 17:35:39 2008 elapsed time 00:43:42
Feb 27, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, Msieve
(4·10¹⁴⁸+17)/3 = 1(3)₁₄₇9_<149> = 457 · 12401 · 545549 · C136
C136 = P33 · P103
P33 = 532912808365383321830732841180011_<33>
P103 = 8092373263092864819628133138996361186520651603049089855317300239501384692261426760504261399767313194493_<103>
(4·10¹⁵⁴+17)/3 = 1(3)₁₅₃9_<155> = 28097 · C150
C150 = P36 · P115
P36 = 415104467682959200738565774465754443_<36>
P115 = 1143197793410399407185698538514618525118222228412394584420498452315299754453223670868380083914065328519933881066609_<115>
(4·10¹⁵⁷+17)/3 = 1(3)₁₅₆9_<158> = 3989 · 13487875393271_<14> · 2257449223315382094947915963_<28> · C114
C114 = P29 · P37 · P48
P29 = 47215344192327994418258987129_<29>
P37 = 7609598281654676371263513938560727761_<37>
P48 = 305540140613631168561515299376375435879608838323_<48>

Wed Feb 27 19:01:59 2008 Wed Feb 27 19:01:59 2008 Wed Feb 27 19:01:59 2008 Msieve v. 1.32 Wed Feb 27 19:01:59 2008 random seeds: df8c8585 3390fcdc Wed Feb 27 19:01:59 2008 factoring 2325037728990015935986003917297505539985894435563542929797489279175271175442666784803 (85 digits) Wed Feb 27 19:02:00 2008 no P-1/P+1/ECM available, skipping Wed Feb 27 19:02:00 2008 commencing quadratic sieve (85-digit input) Wed Feb 27 19:02:00 2008 using multiplier of 3 Wed Feb 27 19:02:00 2008 using 32kb Intel Core sieve core Wed Feb 27 19:02:00 2008 sieve interval: 12 blocks of size 32768 Wed Feb 27 19:02:00 2008 processing polynomials in batches of 17 Wed Feb 27 19:02:00 2008 using a sieve bound of 1424231 (54412 primes) Wed Feb 27 19:02:00 2008 using large prime bound of 116786942 (26 bits) Wed Feb 27 19:02:00 2008 using double large prime bound of 332131201862394 (41-49 bits) Wed Feb 27 19:02:00 2008 using trial factoring cutoff of 49 bits Wed Feb 27 19:02:00 2008 polynomial 'A' values have 11 factors Wed Feb 27 19:33:30 2008 54805 relations (15971 full + 38834 combined from 576753 partial), need 54508 Wed Feb 27 19:33:31 2008 begin with 592724 relations Wed Feb 27 19:33:31 2008 reduce to 130102 relations in 10 passes Wed Feb 27 19:33:31 2008 attempting to read 130102 relations Wed Feb 27 19:33:32 2008 recovered 130102 relations Wed Feb 27 19:33:32 2008 recovered 110815 polynomials Wed Feb 27 19:33:32 2008 attempting to build 54805 cycles Wed Feb 27 19:33:32 2008 found 54805 cycles in 5 passes Wed Feb 27 19:33:32 2008 distribution of cycle lengths: Wed Feb 27 19:33:32 2008 length 1 : 15971 Wed Feb 27 19:33:32 2008 length 2 : 10733 Wed Feb 27 19:33:32 2008 length 3 : 9599 Wed Feb 27 19:33:32 2008 length 4 : 7051 Wed Feb 27 19:33:32 2008 length 5 : 4787 Wed Feb 27 19:33:32 2008 length 6 : 2900 Wed Feb 27 19:33:32 2008 length 7 : 1741 Wed Feb 27 19:33:32 2008 length 9+: 2023 Wed Feb 27 19:33:32 2008 largest cycle: 16 relations Wed Feb 27 19:33:32 2008 matrix is 54412 x 54805 with weight 2920282 (avg 53.28/col) Wed Feb 27 19:33:33 2008 filtering completed in 3 passes Wed Feb 27 19:33:33 2008 matrix is 49677 x 49741 with weight 2662605 (avg 53.53/col) Wed Feb 27 19:33:33 2008 saving the first 48 matrix rows for later Wed Feb 27 19:33:33 2008 matrix is 49629 x 49741 with weight 2029250 (avg 40.80/col) Wed Feb 27 19:33:33 2008 matrix includes 64 packed rows Wed Feb 27 19:33:33 2008 commencing Lanczos iteration Wed Feb 27 19:34:24 2008 lanczos halted after 786 iterations (dim = 49629) Wed Feb 27 19:34:24 2008 recovered 18 nontrivial dependencies Wed Feb 27 19:34:25 2008 prp37 factor: 7609598281654676371263513938560727761 Wed Feb 27 19:34:25 2008 prp48 factor: 305540140613631168561515299376375435879608838323 Wed Feb 27 19:34:25 2008 elapsed time 00:32:26
Feb 27, 2008: By Sinkiti Sibata / GGNFS
(4·10¹³⁷+17)/3 = 1(3)₁₃₆9_<138> = 6552669181_<10> · C128
C128 = P31 · P98
P31 = 1714801068361452362148879871541_<31>
P98 = 11866065698073971314555419688519586074878423197647649070453154014930648060685107891975630143616059_<98>

Number: 13339_137 N=20347942136304429029183631746254234306862886526261416848618003401892376616431131460981554065323923352408492867165444245144676919 ( 128 digits) SNFS difficulty: 137 digits. Divisors found: r1=1714801068361452362148879871541 (pp31) r2=11866065698073971314555419688519586074878423197647649070453154014930648060685107891975630143616059 (pp98) Version: GGNFS-0.77.1-20060513-k8 Total time: 10.83 hours. Scaled time: 21.50 units (timescale=1.986). Factorization parameters were as follows: name: 13339_137 n: 20347942136304429029183631746254234306862886526261416848618003401892376616431131460981554065323923352408492867165444245144676919 m: 2000000000000000000000000000 c5: 25 c0: 34 skew: 1.06 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, 1825001) Primes: RFBsize:78498, AFBsize:63478, largePrimes:1643983 encountered Relations: rels:1666339, finalFF:176380 Max relations in full relation-set: 28 Initial matrix: 142040 x 176380 with sparse part having weight 18465089. Pruned matrix : 133405 x 134179 with weight 12556937. Total sieving time: 10.51 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.19 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: 10.83 hours. --------- CPU info (if available) ----------
(4·10¹⁴⁰+17)/3 = 1(3)₁₃₉9_<141> = 139 · 149 · 419 · 2656035623_<10> · C124
C124 = P38 · P87
P38 = 26537771762988932797230520985691326549_<38>
P87 = 217984339902061538043658310872268089617507279115184973919874854501815077478362601957973_<87>

Number: 13339_140 N=5784818660226710392893078633225827009749351932038762240593991255227477040501870714437762806715702310280279904345671117125177 ( 124 digits) SNFS difficulty: 140 digits. Divisors found: r1=26537771762988932797230520985691326549 (pp38) r2=217984339902061538043658310872268089617507279115184973919874854501815077478362601957973 (pp87) Version: GGNFS-0.77.1-20060513-k8 Total time: 9.46 hours. Scaled time: 18.92 units (timescale=2.001). Factorization parameters were as follows: name: 13339_140 n: 5784818660226710392893078633225827009749351932038762240593991255227477040501870714437762806715702310280279904345671117125177 m: 10000000000000000000000000000 c5: 4 c0: 17 skew: 1.34 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, 1550001) Primes: RFBsize:100021, AFBsize:100163, largePrimes:2673595 encountered Relations: rels:2647843, finalFF:269918 Max relations in full relation-set: 28 Initial matrix: 200248 x 269918 with sparse part having weight 22264975. Pruned matrix : 177577 x 178642 with weight 12371339. Total sieving time: 9.05 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.26 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 9.46 hours. --------- CPU info (if available) ----------
(4·10¹⁴²+17)/3 = 1(3)₁₄₁9_<143> = 1459 · 356837938640928229_<18> · C122
C122 = P40 · P82
P40 = 4952433461126705550942268828114546821893_<40>
P82 = 5171229039310035816298410533513362321815097567656651449551330364234046974538947393_<82>

Number: 13339_142 N=25610167729429129154219135122692807752943626214310846468823181205165725036518490526562875573240011146514873716817667674949 ( 122 digits) SNFS difficulty: 142 digits. Divisors found: r1=4952433461126705550942268828114546821893 (pp40) r2=5171229039310035816298410533513362321815097567656651449551330364234046974538947393 (pp82) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 17.78 hours. Scaled time: 12.00 units (timescale=0.675). Factorization parameters were as follows: name: 13339_142 n: 25610167729429129154219135122692807752943626214310846468823181205165725036518490526562875573240011146514873716817667674949 m: 20000000000000000000000000000 c5: 25 c0: 34 skew: 1.06 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, 2350001) Primes: RFBsize:100021, AFBsize:99703, largePrimes:2800788 encountered Relations: rels:2789786, finalFF:244586 Max relations in full relation-set: 28 Initial matrix: 199788 x 244586 with sparse part having weight 26053579. Pruned matrix : 187306 x 188368 with weight 18253445. Total sieving time: 16.40 hours. Total relation processing time: 0.16 hours. Matrix solve time: 1.13 hours. Time per square root: 0.09 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: 17.78 hours. --------- CPU info (if available) ----------
(4·10¹⁴³+17)/3 = 1(3)₁₄₂9_<144> = 47 · 107 · 1019 · 3559 · C133
C133 = P53 · P81
P53 = 21530592730890687406724972323507960444311519390746899_<53>
P81 = 339546253576180671194251388956900458789709973584370940213518247026860941408782729_<81>

Number: 13339_143 N=7310632099048481632442417594674736817587577048810320179589357685324612306601759726202069186552803790311886326790976822657893721507371 ( 133 digits) SNFS difficulty: 143 digits. Divisors found: r1=21530592730890687406724972323507960444311519390746899 (pp53) r2=339546253576180671194251388956900458789709973584370940213518247026860941408782729 (pp81) Version: GGNFS-0.77.1-20060513-k8 Total time: 14.08 hours. Scaled time: 28.10 units (timescale=1.995). Factorization parameters were as follows: name: 13339_143 n: 7310632099048481632442417594674736817587577048810320179589357685324612306601759726202069186552803790311886326790976822657893721507371 m: 20000000000000000000000000000 c5: 125 c0: 17 skew: 0.67 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, 2150001) Primes: RFBsize:100021, AFBsize:100153, largePrimes:2776914 encountered Relations: rels:2762452, finalFF:254297 Max relations in full relation-set: 28 Initial matrix: 200239 x 254297 with sparse part having weight 25949347. Pruned matrix : 184883 x 185948 with weight 17064295. Total sieving time: 13.53 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.35 hours. Time per square root: 0.08 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: 14.08 hours. --------- CPU info (if available) ----------
Feb 26, 2008 (2nd): By Sinkiti Sibata / GGNFS
(4·10¹⁵⁰+11)/3 = 1(3)₁₄₉7_<151> = 67 · 97 · 181 · 51437 · 67069940098328863_<17> · C128
C123 = P45 · P78
P45 = 842567218953103748778820051250784569042311499_<45>
P78 = 389946940241801961370181471323403096587030785968251538514409936744648047951767_<78>

Number: 13337_150 N=328556508978807216467909242087984532386542899298545695789839803490270877924857370271680502884986361766553459019686141468733 ( 123 digits) SNFS difficulty: 150 digits. Divisors found: r1=842567218953103748778820051250784569042311499 (pp45) r2=389946940241801961370181471323403096587030785968251538514409936744648047951767 (pp78) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 23.88 hours. Scaled time: 16.09 units (timescale=0.674). Factorization parameters were as follows: name: 13337_150 n: 328556508978807216467909242087984532386542899298545695789839803490270877924857370271680502884986361766553459019686141468733 m: 1000000000000000000000000000000 c5: 4 c0: 11 skew: 1.22 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, 1800001) Primes: RFBsize:176302, AFBsize:175914, largePrimes:5199684 encountered Relations: rels:5061012, finalFF:454047 Max relations in full relation-set: 28 Initial matrix: 352280 x 454047 with sparse part having weight 34543199. Pruned matrix : 283186 x 285011 with weight 20367249. Total sieving time: 20.94 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.64 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 23.88 hours. --------- CPU info (if available) ----------
(4·10¹²⁸+17)/3 = 1(3)₁₂₇9_<129> = 30905143 · C121
C121 = P40 · P82
P40 = 2264647650843887046315670559789081872837_<40>
P82 = 1905054208279908717959032447092198327666493476216888547860932106950160593631866329_<82>

Number: 13339_128 N=4314276537511356389237006065085456272871260726194773903273423887193575947321561765086585534754954323729656689610960005373 ( 121 digits) SNFS difficulty: 128 digits. Divisors found: r1=2264647650843887046315670559789081872837 (pp40) r2=1905054208279908717959032447092198327666493476216888547860932106950160593631866329 (pp82) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.50 hours. Scaled time: 8.93 units (timescale=1.986). Factorization parameters were as follows: name:13339_128 n: 4314276537511356389237006065085456272871260726194773903273423887193575947321561765086585534754954323729656689610960005373 m: 20000000000000000000000000 c5: 125 c0: 17 skew: 0.67 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:64073, largePrimes:1650177 encountered Relations: rels:1772225, finalFF:282784 Max relations in full relation-set: 28 Initial matrix: 128089 x 282784 with sparse part having weight 20216596. Pruned matrix : 93487 x 94191 with weight 6406529. Total sieving time: 4.36 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.04 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) ----------
(4·10¹²¹+17)/3 = 1(3)₁₂₀9_<122> = 38737 · 198811 · C112
C112 = P49 · P64
P49 = 1066128263744179842966023845014133805371522028417_<49>
P64 = 1623913477852878066050128577369053541152591491514652526106580081_<64>

Number: 13339_121 N=1731300056614061539047787291401292101287271622335940759125354484590113946145583400138478407257787884223968161777 ( 112 digits) SNFS difficulty: 121 digits. Divisors found: r1=1066128263744179842966023845014133805371522028417 (pp49) r2=1623913477852878066050128577369053541152591491514652526106580081 (pp64) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.64 hours. Scaled time: 1.78 units (timescale=0.675). Factorization parameters were as follows: name: 13339_121 n: 1731300056614061539047787291401292101287271622335940759125354484590113946145583400138478407257787884223968161777 m: 1000000000000000000000000 c5: 40 c0: 17 skew: 0.84 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 600001) Primes: RFBsize:49098, AFBsize:64053, largePrimes:2177636 encountered Relations: rels:2321030, finalFF:268528 Max relations in full relation-set: 28 Initial matrix: 113217 x 268528 with sparse part having weight 24912659. Pruned matrix : 83980 x 84610 with weight 5656348. Total sieving time: 2.40 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.12 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.64 hours. --------- CPU info (if available) ----------
(4·10¹³⁵+17)/3 = 1(3)₁₃₄9_<136> = 13 · 179 · 4441 · 449193700977237001_<18> · C111
C111 = P55 · P56
P55 = 4380977512855558196767027709308224937234411105284163883_<55>
P56 = 65562710303983445700242735959728821688792651648307630519_<56>

Number: 13339_135 N=287228759523614873835871623098592515574414650930219728909431025522262906433847741731199852827139960161808345277 ( 111 digits) SNFS difficulty: 135 digits. Divisors found: r1=4380977512855558196767027709308224937234411105284163883 (pp55) r2=65562710303983445700242735959728821688792651648307630519 (pp56) Version: GGNFS-0.77.1-20060513-k8 Total time: 5.81 hours. Scaled time: 11.63 units (timescale=2.001). Factorization parameters were as follows: name: 13339_135 n: 287228759523614873835871623098592515574414650930219728909431025522262906433847741731199852827139960161808345277 m: 1000000000000000000000000000 c5: 4 c0: 17 skew: 1.34 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:64243, largePrimes:1496217 encountered Relations: rels:1480212, finalFF:161368 Max relations in full relation-set: 28 Initial matrix: 142805 x 161368 with sparse part having weight 12113242. Pruned matrix : 136801 x 137579 with weight 8839142. Total sieving time: 5.58 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.12 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.81 hours. --------- CPU info (if available) ----------
(4·10¹²⁶+17)/3 = 1(3)₁₂₅9_<127> = 7 · 1451 · 484973620564064677_<18> · C105
C105 = P45 · P61
P45 = 236131606868916230324368736021180849580845243_<45>
P61 = 1146307265998928188707147607605206865081607528799744013788257_<61>

Number: 13339_126 N=270679376685841095843311932998986459968041182656991480680590979940930784945538563824171799516828487711451 ( 105 digits) SNFS difficulty: 126 digits. Divisors found: r1=236131606868916230324368736021180849580845243 (pp45) r2=1146307265998928188707147607605206865081607528799744013788257 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 3.58 hours. Scaled time: 2.42 units (timescale=0.675). Factorization parameters were as follows: name: 13339_126 n: 270679376685841095843311932998986459968041182656991480680590979940930784945538563824171799516828487711451 m: 10000000000000000000000000 c5: 40 c0: 17 skew: 0.84 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, 700001) Primes: RFBsize:49098, AFBsize:64053, largePrimes:2202658 encountered Relations: rels:2318750, finalFF:227942 Max relations in full relation-set: 28 Initial matrix: 113217 x 227942 with sparse part having weight 22222821. Pruned matrix : 92940 x 93570 with weight 6724861. Total sieving time: 3.29 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.16 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.58 hours. --------- CPU info (if available) ----------
(4·10¹³⁶+17)/3 = 1(3)₁₃₅9_<137> = 499 · 7487 · C130
C130 = P30 · P100
P30 = 956208466723298533771784872423_<30>
P100 = 3732310555325491082117959675188859828864096907351170143183605318022765214999058108875422540141456161_<100>

Number: 13339_136 N=3568866953442970710576578115047601101316653162966331576826240522539223855305999559780261292809562850379089508878404152590832348103 ( 130 digits) SNFS difficulty: 136 digits. Divisors found: r1=956208466723298533771784872423 (pp30) r2=3732310555325491082117959675188859828864096907351170143183605318022765214999058108875422540141456161 (pp100) Version: GGNFS-0.77.1-20060513-k8 Total time: 7.93 hours. Scaled time: 15.76 units (timescale=1.988). Factorization parameters were as follows: name: 13339_136 n: 3568866953442970710576578115047601101316653162966331576826240522539223855305999559780261292809562850379089508878404152590832348103 m: 1000000000000000000000000000 c5: 40 c0: 17 skew: 0.84 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:64053, largePrimes:1600737 encountered Relations: rels:1625919, finalFF:194313 Max relations in full relation-set: 28 Initial matrix: 142617 x 194313 with sparse part having weight 17340077. Pruned matrix : 127910 x 128687 with weight 9762916. Total sieving time: 7.66 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.13 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 7.93 hours. --------- CPU info (if available) ----------
Feb 26, 2008: By Jo Yeong Uk / Msieve, GGNFS, GMP-ECM
(4·10¹²⁹+17)/3 = 1(3)₁₂₈9_<130> = 13 · 13254286387148048113_<20> · 660386597469019359051247846799_<30> · C80
C80 = P33 · P47
P33 = 365060056289000062010732444238977_<33>
P47 = 32097888713326155328978718452411150896824316697_<47>

Mon Feb 25 23:07:08 2008 Mon Feb 25 23:07:08 2008 Mon Feb 25 23:07:08 2008 Msieve v. 1.32 Mon Feb 25 23:07:08 2008 random seeds: ed514adf 848fe788 Mon Feb 25 23:07:08 2008 factoring 11717657060444906039226517298146590277694612229277754702118211578659202199298969 (80 digits) Mon Feb 25 23:07:09 2008 no P-1/P+1/ECM available, skipping Mon Feb 25 23:07:09 2008 commencing quadratic sieve (79-digit input) Mon Feb 25 23:07:09 2008 using multiplier of 1 Mon Feb 25 23:07:09 2008 using 32kb Intel Core sieve core Mon Feb 25 23:07:09 2008 sieve interval: 12 blocks of size 32768 Mon Feb 25 23:07:09 2008 processing polynomials in batches of 17 Mon Feb 25 23:07:09 2008 using a sieve bound of 1182691 (45941 primes) Mon Feb 25 23:07:09 2008 using large prime bound of 118269100 (26 bits) Mon Feb 25 23:07:09 2008 using trial factoring cutoff of 27 bits Mon Feb 25 23:07:09 2008 polynomial 'A' values have 10 factors Mon Feb 25 23:17:56 2008 46269 relations (23525 full + 22744 combined from 251467 partial), need 46037 Mon Feb 25 23:17:56 2008 begin with 274992 relations Mon Feb 25 23:17:56 2008 reduce to 66226 relations in 2 passes Mon Feb 25 23:17:56 2008 attempting to read 66226 relations Mon Feb 25 23:17:57 2008 recovered 66226 relations Mon Feb 25 23:17:57 2008 recovered 55745 polynomials Mon Feb 25 23:17:57 2008 attempting to build 46269 cycles Mon Feb 25 23:17:57 2008 found 46269 cycles in 1 passes Mon Feb 25 23:17:57 2008 distribution of cycle lengths: Mon Feb 25 23:17:57 2008 length 1 : 23525 Mon Feb 25 23:17:57 2008 length 2 : 22744 Mon Feb 25 23:17:57 2008 largest cycle: 2 relations Mon Feb 25 23:17:57 2008 matrix is 45941 x 46269 with weight 1371427 (avg 29.64/col) Mon Feb 25 23:17:57 2008 filtering completed in 4 passes Mon Feb 25 23:17:57 2008 matrix is 39547 x 39611 with weight 1149437 (avg 29.02/col) Mon Feb 25 23:17:57 2008 saving the first 48 matrix rows for later Mon Feb 25 23:17:57 2008 matrix is 39499 x 39611 with weight 837611 (avg 21.15/col) Mon Feb 25 23:17:57 2008 matrix includes 64 packed rows Mon Feb 25 23:17:57 2008 commencing Lanczos iteration Mon Feb 25 23:18:17 2008 lanczos halted after 626 iterations (dim = 39493) Mon Feb 25 23:18:17 2008 recovered 14 nontrivial dependencies Mon Feb 25 23:18:17 2008 prp33 factor: 365060056289000062010732444238977 Mon Feb 25 23:18:17 2008 prp47 factor: 32097888713326155328978718452411150896824316697 Mon Feb 25 23:18:17 2008 elapsed time 00:11:09
(4·10¹²⁴+17)/3 = 1(3)₁₂₃9_<125> = 92152271 · 413087444597_<12> · 23123862157206241782847_<23> · C83
C83 = P41 · P42
P41 = 33682194968730310840375233374150796019583_<41>
P42 = 449707304395848847455968925235148050890497_<42>

Tue Feb 26 00:09:56 2008 Tue Feb 26 00:09:56 2008 Tue Feb 26 00:09:56 2008 Msieve v. 1.32 Tue Feb 26 00:09:56 2008 random seeds: 65ed768f 19de7d2d Tue Feb 26 00:09:56 2008 factoring 15147129105523130449266249388626985891346493244029314228392643742208865666200602751 (83 digits) Tue Feb 26 00:09:57 2008 no P-1/P+1/ECM available, skipping Tue Feb 26 00:09:57 2008 commencing quadratic sieve (82-digit input) Tue Feb 26 00:09:57 2008 using multiplier of 31 Tue Feb 26 00:09:57 2008 using 32kb Intel Core sieve core Tue Feb 26 00:09:57 2008 sieve interval: 12 blocks of size 32768 Tue Feb 26 00:09:57 2008 processing polynomials in batches of 17 Tue Feb 26 00:09:57 2008 using a sieve bound of 1350541 (52059 primes) Tue Feb 26 00:09:57 2008 using large prime bound of 124249772 (26 bits) Tue Feb 26 00:09:57 2008 using trial factoring cutoff of 27 bits Tue Feb 26 00:09:57 2008 polynomial 'A' values have 11 factors Tue Feb 26 00:26:53 2008 52429 relations (27593 full + 24836 combined from 269723 partial), need 52155 Tue Feb 26 00:26:54 2008 begin with 297316 relations Tue Feb 26 00:26:54 2008 reduce to 74133 relations in 2 passes Tue Feb 26 00:26:54 2008 attempting to read 74133 relations Tue Feb 26 00:26:54 2008 recovered 74133 relations Tue Feb 26 00:26:54 2008 recovered 65067 polynomials Tue Feb 26 00:26:54 2008 attempting to build 52429 cycles Tue Feb 26 00:26:54 2008 found 52429 cycles in 1 passes Tue Feb 26 00:26:54 2008 distribution of cycle lengths: Tue Feb 26 00:26:54 2008 length 1 : 27593 Tue Feb 26 00:26:54 2008 length 2 : 24836 Tue Feb 26 00:26:54 2008 largest cycle: 2 relations Tue Feb 26 00:26:54 2008 matrix is 52059 x 52429 with weight 1691215 (avg 32.26/col) Tue Feb 26 00:26:54 2008 filtering completed in 4 passes Tue Feb 26 00:26:54 2008 matrix is 44234 x 44298 with weight 1396136 (avg 31.52/col) Tue Feb 26 00:26:55 2008 saving the first 48 matrix rows for later Tue Feb 26 00:26:55 2008 matrix is 44186 x 44298 with weight 1030375 (avg 23.26/col) Tue Feb 26 00:26:55 2008 matrix includes 64 packed rows Tue Feb 26 00:26:55 2008 commencing Lanczos iteration Tue Feb 26 00:27:21 2008 lanczos halted after 700 iterations (dim = 44175) Tue Feb 26 00:27:21 2008 recovered 13 nontrivial dependencies Tue Feb 26 00:27:21 2008 prp41 factor: 33682194968730310840375233374150796019583 Tue Feb 26 00:27:21 2008 prp42 factor: 449707304395848847455968925235148050890497 Tue Feb 26 00:27:21 2008 elapsed time 00:17:25
(4·10¹¹⁷+17)/3 = 1(3)₁₁₆9_<118> = 13 · 5237 · 7919 · C109
C109 = P33 · P37 · P40
P33 = 723106245094697489786689511373211_<33>
P37 = 1124531409652827761547009490788252799_<37>
P40 = 3041366547432398229574496599264058102209_<40>

Number: 13339_117 N=2473104498593961880619564636823302910234312758577257036607839368934660595840602892623273796477189635668904101 ( 109 digits) SNFS difficulty: 117 digits. Divisors found: r1=723106245094697489786689511373211 (pp33) r2=1124531409652827761547009490788252799 (pp37) r3=3041366547432398229574496599264058102209 (pp40) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.96 hours. Scaled time: 1.78 units (timescale=1.856). Factorization parameters were as follows: n: 2473104498593961880619564636823302910234312758577257036607839368934660595840602892623273796477189635668904101 m: 200000000000000000000000 c5: 25 c0: 34 skew: 1.06 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:48661, largePrimes:1872252 encountered Relations: rels:1911209, finalFF:182604 Max relations in full relation-set: 28 Initial matrix: 97823 x 182604 with sparse part having weight 15576316. Pruned matrix : 79563 x 80116 with weight 4540075. Total sieving time: 0.91 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,117,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 0.96 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406455) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110) Calibrating delay using timer specific routine.. 4810.31 BogoMIPS (lpj=2405155) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
(4·10¹²⁰+17)/3 = 1(3)₁₁₉9_<121> = 7 · 1163 · 3631 · 1113317 · C107
C107 = P42 · P66
P42 = 217864194199759946513098280992116925864009_<42>
P66 = 185964493728313965614110121580783555616158402525331494591164931853_<66>

Number: 13339_120 N=40515004575885434417965215165127114851969961825105124857145999259505190381310511895041336508050733630378677 ( 107 digits) SNFS difficulty: 120 digits. Divisors found: r1=217864194199759946513098280992116925864009 (pp42) r2=185964493728313965614110121580783555616158402525331494591164931853 (pp66) Version: GGNFS-0.77.1-20050930-nocona Total time: 0.80 hours. Scaled time: 1.48 units (timescale=1.858). Factorization parameters were as follows: n: 40515004575885434417965215165127114851969961825105124857145999259505190381310511895041336508050733630378677 m: 1000000000000000000000000 c5: 4 c0: 17 skew: 1.34 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:49461, largePrimes:1837125 encountered Relations: rels:1852045, finalFF:164665 Max relations in full relation-set: 28 Initial matrix: 98623 x 164665 with sparse part having weight 13791456. Pruned matrix : 83260 x 83817 with weight 4715712. Total sieving time: 0.74 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,120,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 0.80 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406459) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405113) Calibrating delay using timer specific routine.. 4809.97 BogoMIPS (lpj=2404989) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(4·10¹⁹⁷+17)/3 = 1(3)₁₉₆9_<198> = C198
C198 = P44 · C154
P44 = 30911517865801875999507572028613382077670753_<44>
C154 = [4313386806567757392671601783903255857588579313081814644131577195810056098206845332856572255132864229461765584994838840653666401244846784162380204100450363_<154>]
Feb 25, 2008 (2nd): By Jo Yeong Uk / GGNFS
(4·10¹⁴⁶+11)/3 = 1(3)₁₄₅7_<147> = 137 · 15868498319799913439_<20> · C125
C125 = P34 · P34 · P58
P34 = 3373815312296460190139766384592183_<34>
P34 = 6790688513659658695196059113391453_<34>
P58 = 2676992930436323638563724011958164341185215909432586996541_<58>

Number: 13337_146 N=61331323866859234793535149039669162933374982327254070525498118062757055024749503269364810023134339956117348152633622026641359 ( 125 digits) SNFS difficulty: 147 digits. Divisors found: r1=3373815312296460190139766384592183 (pp34) r2=6790688513659658695196059113391453 (pp34) r3=2676992930436323638563724011958164341185215909432586996541 (pp58) Version: GGNFS-0.77.1-20050930-nocona Total time: 9.35 hours. Scaled time: 17.36 units (timescale=1.857). Factorization parameters were as follows: n: 61331323866859234793535149039669162933374982327254070525498118062757055024749503269364810023134339956117348152633622026641359 m: 200000000000000000000000000000 c5: 5 c0: 44 skew: 1.54 type: snfs Factor base limits: 1800000/1800000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [900000, 1500001) Primes: RFBsize:135072, AFBsize:135714, largePrimes:3758274 encountered Relations: rels:3890188, finalFF:425896 Max relations in full relation-set: 28 Initial matrix: 270852 x 425896 with sparse part having weight 38438323. Pruned matrix : 214967 x 216385 with weight 17402299. Total sieving time: 9.07 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.20 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,1800000,1800000,26,26,48,48,2.3,2.3,75000 total time: 9.35 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406455) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110) Calibrating delay using timer specific routine.. 4810.31 BogoMIPS (lpj=2405155) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Feb 25, 2008: The factor table of 133...339 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.
Feb 24, 2008 (2nd): By Hugo Platzer / Msieve
(4·10¹⁴⁵+11)/3 = 1(3)₁₄₄7_<146> = 17 · 31 · 2003011 · 4749509160841_<13> · 149747426454337_<15> · C110
C110 = P42 · P69
P42 = 102626434436458488227945394792517443917521_<42>
P69 = 173052329411585166509799947374407788780786872404668069218460927279653_<69>

Sat Feb 23 16:13:24 2008 Sat Feb 23 16:13:24 2008 Sat Feb 23 16:13:24 2008 Msieve v. 1.33 Sat Feb 23 16:13:24 2008 random seeds: 175687d3 05d4ec8b Sat Feb 23 16:13:24 2008 factoring 17759743538434462005501867658007215151785228754151261903789786747070005048229801123394965288753029945833500213 (110 digits) Sat Feb 23 16:13:26 2008 no P-1/P+1/ECM available, skipping Sat Feb 23 16:13:26 2008 commencing number field sieve (110-digit input) Sat Feb 23 16:13:26 2008 R0: -100000000000000000000000000000 Sat Feb 23 16:13:26 2008 R1: 1 Sat Feb 23 16:13:26 2008 A0: 11 Sat Feb 23 16:13:26 2008 A1: 0 Sat Feb 23 16:13:26 2008 A2: 0 Sat Feb 23 16:13:26 2008 A3: 0 Sat Feb 23 16:13:26 2008 A4: 0 Sat Feb 23 16:13:26 2008 A5: 4 Sat Feb 23 16:13:26 2008 size score = 6.148189e-10, Murphy alpha = 0.264305, combined = 5.629699e-10 Sat Feb 23 16:13:31 2008 restarting with 2588237 relations Sat Feb 23 16:13:33 2008 added 11057 free relations Sat Feb 23 16:13:33 2008 Sat Feb 23 16:13:33 2008 commencing relation filtering Sat Feb 23 16:13:33 2008 commencing duplicate removal, pass 1 Sat Feb 23 16:14:06 2008 found 12443 hash collisions in 2599294 relations Sat Feb 23 16:14:06 2008 commencing duplicate removal, pass 2 Sat Feb 23 16:14:09 2008 found 0 duplicates and 2599294 unique relations Sat Feb 23 16:14:09 2008 memory use: 36.5 MB Sat Feb 23 16:14:10 2008 ignoring smallest 136043 rational and 135518 algebraic ideals Sat Feb 23 16:14:10 2008 filtering rational ideals above 1813985 Sat Feb 23 16:14:10 2008 filtering algebraic ideals above 1813985 Sat Feb 23 16:14:10 2008 need 461653 more relations than ideals Sat Feb 23 16:14:10 2008 commencing singleton removal, pass 1 Sat Feb 23 16:14:40 2008 relations with 0 large ideals: 83025 Sat Feb 23 16:14:40 2008 relations with 1 large ideals: 588085 Sat Feb 23 16:14:40 2008 relations with 2 large ideals: 1248703 Sat Feb 23 16:14:40 2008 relations with 3 large ideals: 577206 Sat Feb 23 16:14:40 2008 relations with 4 large ideals: 92848 Sat Feb 23 16:14:40 2008 relations with 5 large ideals: 5058 Sat Feb 23 16:14:40 2008 relations with 6 large ideals: 4369 Sat Feb 23 16:14:40 2008 relations with 7+ large ideals: 0 Sat Feb 23 16:14:40 2008 2599294 relations and about 2552882 large ideals Sat Feb 23 16:14:40 2008 commencing singleton removal, pass 2 Sat Feb 23 16:15:13 2008 found 1440752 singletons Sat Feb 23 16:15:13 2008 current dataset: 1158542 relations and about 817492 large ideals Sat Feb 23 16:15:13 2008 commencing singleton removal, pass 3 Sat Feb 23 16:15:29 2008 found 194821 singletons Sat Feb 23 16:15:29 2008 current dataset: 963721 relations and about 611281 large ideals Sat Feb 23 16:15:29 2008 commencing singleton removal, final pass Sat Feb 23 16:15:43 2008 memory use: 15.3 MB Sat Feb 23 16:15:43 2008 commencing in-memory singleton removal Sat Feb 23 16:15:44 2008 begin with 963721 relations and 623692 unique ideals Sat Feb 23 16:15:44 2008 reduce to 883576 relations and 542216 ideals in 10 passes Sat Feb 23 16:15:44 2008 max relations containing the same ideal: 28 Sat Feb 23 16:15:44 2008 dataset has 25.7% excess relations Sat Feb 23 16:15:46 2008 ignoring smallest 123430 rational and 122825 algebraic ideals Sat Feb 23 16:15:46 2008 filtering rational ideals above 1632586 Sat Feb 23 16:15:46 2008 filtering algebraic ideals above 1632586 Sat Feb 23 16:15:46 2008 need 307223 more relations than ideals Sat Feb 23 16:15:46 2008 commencing singleton removal, final pass Sat Feb 23 16:15:59 2008 memory use: 15.3 MB Sat Feb 23 16:15:59 2008 commencing in-memory singleton removal Sat Feb 23 16:15:59 2008 begin with 883577 relations and 567386 unique ideals Sat Feb 23 16:15:59 2008 reduce to 882237 relations and 566044 ideals in 7 passes Sat Feb 23 16:15:59 2008 max relations containing the same ideal: 28 Sat Feb 23 16:16:00 2008 dataset has 16.4% excess relations Sat Feb 23 16:16:01 2008 ignoring smallest 110719 rational and 110299 algebraic ideals Sat Feb 23 16:16:01 2008 filtering rational ideals above 1451187 Sat Feb 23 16:16:01 2008 filtering algebraic ideals above 1451187 Sat Feb 23 16:16:01 2008 need 293285 more relations than ideals Sat Feb 23 16:16:01 2008 commencing singleton removal, final pass Sat Feb 23 16:16:14 2008 memory use: 15.3 MB Sat Feb 23 16:16:14 2008 commencing in-memory singleton removal Sat Feb 23 16:16:14 2008 begin with 882238 relations and 591202 unique ideals Sat Feb 23 16:16:14 2008 reduce to 881380 relations and 590342 ideals in 6 passes Sat Feb 23 16:16:14 2008 max relations containing the same ideal: 28 Sat Feb 23 16:16:14 2008 dataset has 7.2% excess relations Sat Feb 23 16:16:15 2008 relations with 0 large ideals: 44235 Sat Feb 23 16:16:15 2008 relations with 1 large ideals: 181651 Sat Feb 23 16:16:15 2008 relations with 2 large ideals: 309586 Sat Feb 23 16:16:15 2008 relations with 3 large ideals: 241636 Sat Feb 23 16:16:15 2008 relations with 4 large ideals: 88087 Sat Feb 23 16:16:15 2008 relations with 5 large ideals: 12113 Sat Feb 23 16:16:15 2008 relations with 6 large ideals: 4072 Sat Feb 23 16:16:15 2008 relations with 7+ large ideals: 0 Sat Feb 23 16:16:15 2008 commencing 2-way merge Sat Feb 23 16:16:15 2008 reduce to 564943 relation sets and 273905 unique ideals Sat Feb 23 16:16:15 2008 commencing full merge Sat Feb 23 16:16:22 2008 memory use: 19.8 MB Sat Feb 23 16:16:22 2008 found 295769 cycles, need 232105 Sat Feb 23 16:16:22 2008 weight of 232105 cycles is about 12331805 (53.13/cycle) Sat Feb 23 16:16:22 2008 distribution of cycle lengths: Sat Feb 23 16:16:22 2008 1 relations: 45548 Sat Feb 23 16:16:22 2008 2 relations: 28579 Sat Feb 23 16:16:22 2008 3 relations: 26155 Sat Feb 23 16:16:22 2008 4 relations: 23813 Sat Feb 23 16:16:22 2008 5 relations: 22040 Sat Feb 23 16:16:22 2008 6 relations: 19736 Sat Feb 23 16:16:22 2008 7 relations: 17520 Sat Feb 23 16:16:22 2008 8 relations: 15457 Sat Feb 23 16:16:22 2008 9 relations: 13409 Sat Feb 23 16:16:22 2008 10+ relations: 19848 Sat Feb 23 16:16:22 2008 heaviest cycle: 13 relations Sat Feb 23 16:16:22 2008 matrix not dense enough, retrying Sat Feb 23 16:16:22 2008 dataset has 7.2% excess relations Sat Feb 23 16:16:24 2008 ignoring smallest 97887 rational and 97616 algebraic ideals Sat Feb 23 16:16:24 2008 filtering rational ideals above 1269789 Sat Feb 23 16:16:24 2008 filtering algebraic ideals above 1269789 Sat Feb 23 16:16:24 2008 need 293285 more relations than ideals Sat Feb 23 16:16:24 2008 commencing singleton removal, final pass Sat Feb 23 16:16:37 2008 memory use: 15.3 MB Sat Feb 23 16:16:37 2008 commencing in-memory singleton removal Sat Feb 23 16:16:37 2008 begin with 881381 relations and 615815 unique ideals Sat Feb 23 16:16:37 2008 reduce to 880876 relations and 615308 ideals in 7 passes Sat Feb 23 16:16:37 2008 max relations containing the same ideal: 31 Sat Feb 23 16:16:37 2008 dataset has -2.2% excess relations Sat Feb 23 16:16:38 2008 relations with 0 large ideals: 29853 Sat Feb 23 16:16:38 2008 relations with 1 large ideals: 135797 Sat Feb 23 16:16:38 2008 relations with 2 large ideals: 280412 Sat Feb 23 16:16:38 2008 relations with 3 large ideals: 275356 Sat Feb 23 16:16:38 2008 relations with 4 large ideals: 130074 Sat Feb 23 16:16:38 2008 relations with 5 large ideals: 24264 Sat Feb 23 16:16:38 2008 relations with 6 large ideals: 5118 Sat Feb 23 16:16:38 2008 relations with 7+ large ideals: 2 Sat Feb 23 16:16:38 2008 commencing 2-way merge Sat Feb 23 16:16:38 2008 reduce to 563895 relation sets and 298327 unique ideals Sat Feb 23 16:16:38 2008 commencing full merge Sat Feb 23 16:16:47 2008 memory use: 20.7 MB Sat Feb 23 16:16:47 2008 found 277379 cycles, need 216527 Sat Feb 23 16:16:47 2008 weight of 216527 cycles is about 13335440 (61.59/cycle) Sat Feb 23 16:16:47 2008 distribution of cycle lengths: Sat Feb 23 16:16:47 2008 1 relations: 32177 Sat Feb 23 16:16:47 2008 2 relations: 22556 Sat Feb 23 16:16:47 2008 3 relations: 22387 Sat Feb 23 16:16:47 2008 4 relations: 21245 Sat Feb 23 16:16:47 2008 5 relations: 20362 Sat Feb 23 16:16:47 2008 6 relations: 18654 Sat Feb 23 16:16:47 2008 7 relations: 17219 Sat Feb 23 16:16:47 2008 8 relations: 15456 Sat Feb 23 16:16:47 2008 9 relations: 13974 Sat Feb 23 16:16:47 2008 10+ relations: 32497 Sat Feb 23 16:16:47 2008 heaviest cycle: 15 relations Sat Feb 23 16:16:47 2008 commencing cycle optimization Sat Feb 23 16:16:48 2008 start with 1172495 relations Sat Feb 23 16:16:51 2008 pruned 41529 relations Sat Feb 23 16:16:51 2008 memory use: 29.2 MB Sat Feb 23 16:16:51 2008 distribution of cycle lengths: Sat Feb 23 16:16:51 2008 1 relations: 32177 Sat Feb 23 16:16:51 2008 2 relations: 23166 Sat Feb 23 16:16:51 2008 3 relations: 23482 Sat Feb 23 16:16:51 2008 4 relations: 22187 Sat Feb 23 16:16:51 2008 5 relations: 21489 Sat Feb 23 16:16:51 2008 6 relations: 19596 Sat Feb 23 16:16:51 2008 7 relations: 17994 Sat Feb 23 16:16:51 2008 8 relations: 16017 Sat Feb 23 16:16:51 2008 9 relations: 13859 Sat Feb 23 16:16:51 2008 10+ relations: 26560 Sat Feb 23 16:16:51 2008 heaviest cycle: 15 relations Sat Feb 23 16:16:51 2008 Sat Feb 23 16:16:51 2008 commencing linear algebra Sat Feb 23 16:16:52 2008 read 216527 cycles Sat Feb 23 16:16:52 2008 cycles contain 583896 unique relations Sat Feb 23 16:17:00 2008 read 583896 relations Sat Feb 23 16:17:01 2008 using 32 quadratic characters above 67093592 Sat Feb 23 16:17:16 2008 building initial matrix Sat Feb 23 16:17:28 2008 memory use: 71.2 MB Sat Feb 23 16:17:29 2008 read 216527 cycles Sat Feb 23 16:17:30 2008 matrix is 216207 x 216527 (53.4 MB) with weight 18522721 (85.54/col) Sat Feb 23 16:17:30 2008 sparse part has weight 12477653 (57.63/col) Sat Feb 23 16:17:34 2008 filtering completed in 3 passes Sat Feb 23 16:17:34 2008 matrix is 214854 x 215054 (53.1 MB) with weight 18423986 (85.67/col) Sat Feb 23 16:17:34 2008 sparse part has weight 12419321 (57.75/col) Sat Feb 23 16:17:37 2008 read 215054 cycles Sat Feb 23 16:17:38 2008 matrix is 214854 x 215054 (53.1 MB) with weight 18423986 (85.67/col) Sat Feb 23 16:17:38 2008 sparse part has weight 12419321 (57.75/col) Sat Feb 23 16:17:38 2008 saving the first 48 matrix rows for later Sat Feb 23 16:17:38 2008 matrix is 214806 x 215054 (50.4 MB) with weight 13723478 (63.81/col) Sat Feb 23 16:17:38 2008 sparse part has weight 11933368 (55.49/col) Sat Feb 23 16:17:38 2008 matrix includes 64 packed rows Sat Feb 23 16:17:38 2008 using block size 65536 for processor cache size 2048 kB Sat Feb 23 16:17:40 2008 commencing Lanczos iteration Sat Feb 23 16:17:40 2008 memory use: 50.1 MB Sat Feb 23 16:29:15 2008 lanczos halted after 3399 iterations (dim = 214804) Sat Feb 23 16:29:16 2008 recovered 50 nontrivial dependencies Sat Feb 23 16:29:16 2008 Sat Feb 23 16:29:16 2008 commencing square root phase Sat Feb 23 16:29:16 2008 reading relations for dependency 1 Sat Feb 23 16:29:16 2008 read 107635 cycles Sat Feb 23 16:29:17 2008 cycles contain 354348 unique relations Sat Feb 23 16:29:22 2008 read 354348 relations Sat Feb 23 16:29:25 2008 multiplying 564220 relations Sat Feb 23 16:30:31 2008 multiply complete, coefficients have about 12.42 million bits Sat Feb 23 16:30:32 2008 initial square root is modulo 13694671 Sat Feb 23 16:32:21 2008 reading relations for dependency 2 Sat Feb 23 16:32:21 2008 read 107185 cycles Sat Feb 23 16:32:21 2008 cycles contain 353436 unique relations Sat Feb 23 16:32:26 2008 read 353436 relations Sat Feb 23 16:32:29 2008 multiplying 562622 relations Sat Feb 23 16:33:36 2008 multiply complete, coefficients have about 12.39 million bits Sat Feb 23 16:33:36 2008 initial square root is modulo 13126801 Sat Feb 23 16:35:25 2008 prp42 factor: 102626434436458488227945394792517443917521 Sat Feb 23 16:35:25 2008 prp69 factor: 173052329411585166509799947374407788780786872404668069218460927279653 Sat Feb 23 16:35:25 2008 elapsed time 00:22:01
Feb 24, 2008: By matsui / GGNFS
8·10¹⁷⁶+9 = 8(0)₁₇₅9_<177> = 17 · 3217 · C173
C173 = P81 · P93
P81 = 103961611179868503438377681867481435196874462689578948106251372965474787726477889_<81>
P93 = 140707421063833161706485449146184930821888979205845979668829757316153913675077037413502917929_<93>

N=14628170198760262575655067746713233008466053502532501965660370458410283603649728464590685512625939402804951635612280348881859240432262429373365759110607251915376035400171881 ( 173 digits) SNFS difficulty: 177 digits. Divisors found: r1=103961611179868503438377681867481435196874462689578948106251372965474787726477889 (pp81) r2=140707421063833161706485449146184930821888979205845979668829757316153913675077037413502917929 (pp93) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 228.46 hours. Scaled time: 435.44 units (timescale=1.906). Factorization parameters were as follows: n: 14628170198760262575655067746713233008466053502532501965660370458410283603649728464590685512625939402804951635612280348881859240432262429373365759110607251915376035400171881 m: 200000000000000000000000000000000000 c5: 5 c0: 18 skew: 1.29 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 12000001) Primes: RFBsize:501962, AFBsize:501791, largePrimes:6541923 encountered Relations: rels:7040504, finalFF:1165775 Max relations in full relation-set: 28 Initial matrix: 1003819 x 1165775 with sparse part having weight 75529051. Pruned matrix : 866295 x 871378 with weight 56505835. Total sieving time: 204.60 hours. Total relation processing time: 0.16 hours. Matrix solve time: 23.41 hours. Time per square root: 0.29 hours. Prototype def-par.txt line would be: snfs,177,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 228.46 hours.
Feb 22, 2008: By Sinkiti Sibata / GGNFS
(7·10¹⁶²-1)/3 = 2(3)₁₆₂_<163> = 1376191 · 1156149411505234849191678643368749_<34> · C124
C124 = P59 · P65
P59 = 18483157127083474363681317601965029524109620367701902163793_<59>
P65 = 79342878811142759961839897023661739977240662042432474165513682759_<65>

Number: 23333_162 N=1466506895981493687124535379820325804475916309373929762311497311107375702506795513963671876299233601761427778500890258144887 ( 124 digits) SNFS difficulty: 162 digits. Divisors found: r1=18483157127083474363681317601965029524109620367701902163793 (pp59) r2=79342878811142759961839897023661739977240662042432474165513682759 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 85.52 hours. Scaled time: 57.30 units (timescale=0.670). Factorization parameters were as follows: name: 23333_162 n: 1466506895981493687124535379820325804475916309373929762311497311107375702506795513963671876299233601761427778500890258144887 m: 100000000000000000000000000000000 c5: 700 c0: -1 skew: 0.27 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [2250000, 4250001) Primes: RFBsize:315948, AFBsize:315791, largePrimes:5746913 encountered Relations: rels:5875322, finalFF:758492 Max relations in full relation-set: 28 Initial matrix: 631806 x 758492 with sparse part having weight 45680761. Pruned matrix : 528671 x 531894 with weight 30022387. Total sieving time: 73.60 hours. Total relation processing time: 0.33 hours. Matrix solve time: 11.37 hours. Time per square root: 0.22 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: 85.52 hours. --------- CPU info (if available) ----------
Feb 21, 2008: By Sinkiti Sibata / GGNFS
(4·10¹⁴⁴+11)/3 = 1(3)₁₄₃7_<145> = 33501037 · 19162171112298569164633600877_<29> · C109
C109 = P54 · P55
P54 = 447889331573911295153276557347209198287124299467688541_<54>
P55 = 4637298522548643845125317323631350351129872341828192293_<55>

Number: 13337_144 N=2076996535572998507838714029821161997717606507974074306074404130017920430096263222528986801630708133180614513 ( 109 digits) SNFS difficulty: 145 digits. Divisors found: r1=447889331573911295153276557347209198287124299467688541 (pp54) r2=4637298522548643845125317323631350351129872341828192293 (pp55) Version: GGNFS-0.77.1-20060513-k8 Total time: 15.65 hours. Scaled time: 31.27 units (timescale=1.998). Factorization parameters were as follows: name: 13337_144 n: 2076996535572998507838714029821161997717606507974074306074404130017920430096263222528986801630708133180614513 m: 100000000000000000000000000000 c5: 2 c0: 55 skew: 1.94 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, 2350001) Primes: RFBsize:100021, AFBsize:99789, largePrimes:2823314 encountered Relations: rels:2832613, finalFF:264170 Max relations in full relation-set: 28 Initial matrix: 199875 x 264170 with sparse part having weight 28900389. Pruned matrix : 182618 x 183681 with weight 18326210. Total sieving time: 15.05 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.42 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000 total time: 15.65 hours. --------- CPU info (if available) ----------
Feb 20, 2008 (3rd): By Jo Yeong Uk / GMP-ECM, GGNFS
(4·10¹⁵⁸+11)/3 = 1(3)₁₅₇7_<159> = 8233 · C155
C155 = P31 · C125
P31 = 1527862686242403797544393553027_<31>
C125 = [10599766456206583622902219875082963980035743593315729410558814794508496584089071087989307287849025249575541272349851000517307_<125>]
(4·10¹⁵⁷+11)/3 = 1(3)₁₅₆7_<158> = C158
C158 = P73 · P85
P73 = 4766737278377335686560797181373572835442956918758084311522740015959165729_<73>
P85 = 2797161361045722925353515065028853432915519784372454180355700451963746101938543639353_<85>

Number: 13337_157 N=13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 ( 158 digits) SNFS difficulty: 157 digits. Divisors found: r1=4766737278377335686560797181373572835442956918758084311522740015959165729 (pp73) r2=2797161361045722925353515065028853432915519784372454180355700451963746101938543639353 (pp85) Version: GGNFS-0.77.1-20050930-nocona Total time: 21.35 hours. Scaled time: 39.60 units (timescale=1.855). Factorization parameters were as follows: n: 13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 m: 20000000000000000000000000000000 c5: 25 c0: 22 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, 2800001) Primes: RFBsize:216816, AFBsize:216262, largePrimes:5564985 encountered Relations: rels:5470103, finalFF:504877 Max relations in full relation-set: 28 Initial matrix: 433141 x 504877 with sparse part having weight 39439439. Pruned matrix : 394545 x 396774 with weight 27271708. Total sieving time: 20.39 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.83 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: 21.35 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2435k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.91 BogoMIPS (lpj=2406455) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405110) Calibrating delay using timer specific routine.. 4810.31 BogoMIPS (lpj=2405155) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405117)
Feb 20, 2008 (2nd): By Robert Backstrom / GGNFS, GMP-ECM
(4·10¹⁴⁹+11)/3 = 1(3)₁₄₈7_<150> = 21313 · 758361679 · 1214454453872951_<16> · C121
C121 = P37 · P85
P37 = 2717076605390979007381323216479100539_<37>
P85 = 2499969194587184389860981086852270761643057631388490569409971104066011589674512322579_<85>

Number: n N=6792607812810966812696054335486176763506067853623183131083234129992086750249270424315302728986609775323759382373740770081 ( 121 digits) SNFS difficulty: 150 digits. Divisors found: r1=2717076605390979007381323216479100539 (pp37) r2=2499969194587184389860981086852270761643057631388490569409971104066011589674512322579 (pp85) Version: GGNFS-0.77.1-20051202-athlon Total time: 10.10 hours. Scaled time: 18.48 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_3_148_7 n: 6792607812810966812696054335486176763506067853623183131083234129992086750249270424315302728986609775323759382373740770081 skew: 1.94 deg: 5 c5: 2 c0: 55 m: 1000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 660001) Primes: RFBsize:183072, AFBsize:182867, largePrimes:6264948 encountered Relations: rels:5745258, finalFF:448309 Max relations in full relation-set: 48 Initial matrix: 366004 x 448309 with sparse part having weight 28960939. Pruned matrix : 296128 x 298022 with weight 15039151. Total sieving time: 9.34 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.60 hours. Total square root time: 0.04 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,150,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 10.10 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(4·10¹³⁸+11)/3 = 1(3)₁₃₇7_<139> = 137 · 229 · C134
C134 = P64 · P70
P64 = 4867627495557587497174692021304110944538390547912798179387518159_<64>
P70 = 8731027407103137131104076747312662661769083489277298849485078143666291_<70>

Number: n N=42499389071282100319807902761397804906554468279518481921822373803376576461713362870408737874393055599825752504807743388688787598678269 ( 134 digits) SNFS difficulty: 140 digits. Divisors found: r1=4867627495557587497174692021304110944538390547912798179387518159 (pp64) r2=8731027407103137131104076747312662661769083489277298849485078143666291 (pp70) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.89 hours. Scaled time: 7.11 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_3_137_7 n: 42499389071282100319807902761397804906554468279518481921822373803376576461713362870408737874393055599825752504807743388688787598678269 skew: 3.08 deg: 5 c5: 1 c0: 275 m: 10000000000000000000000000000 type: snfs rlim: 2200000 alim: 2200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 2200000/2200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 580001) Primes: RFBsize:162662, AFBsize:163221, largePrimes:5751332 encountered Relations: rels:5168007, finalFF:374032 Max relations in full relation-set: 48 Initial matrix: 325947 x 374032 with sparse part having weight 20090079. Pruned matrix : 280278 x 281971 with weight 11315150. Total sieving time: 3.20 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.44 hours. Total square root time: 0.14 hours, sqrts: 5. Prototype def-par.txt line would be: snfs,140,5,0,0,0,0,0,0,0,0,2200000,2200000,28,28,48,48,2.5,2.5,75000 total time: 3.89 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(8·10¹⁸⁶-17)/9 = (8)₁₈₅7_<186> = 122041 · C181
C181 = P30 · C152
P30 = 600760122234227247339021404369_<30>
C152 = [12123851911813520689442426339677939520762900296076844725658595042305449072115945719786865839939239072337205062999312826980398145833769450425203032477503_<152>]
Feb 20, 2008: By Sinkiti Sibata / GGNFS
(4·10¹³¹+11)/3 = 1(3)₁₃₀7_<132> = 356287746791328491_<18> · C114
C114 = P52 · P63
P52 = 1893443194224894718878463833501834090719818444796249_<52>
P63 = 197644880595999725041267819674714849507845501682832456060475843_<63>

Number: 13337_131 N=374229354037887632864664831865915772225602984855244535305283336279006481767188196074768411542491621513546121512907 ( 114 digits) SNFS difficulty: 131 digits. Divisors found: r1=1893443194224894718878463833501834090719818444796249 (pp52) r2=197644880595999725041267819674714849507845501682832456060475843 (pp63) Version: GGNFS-0.77.1-20060513-k8 Total time: 4.49 hours. Scaled time: 8.92 units (timescale=1.988). Factorization parameters were as follows: name: 13337_131 n: 374229354037887632864664831865915772225602984855244535305283336279006481767188196074768411542491621513546121512907 m: 100000000000000000000000000 c5: 40 c0: 11 skew: 0.77 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:64254, largePrimes:1531023 encountered Relations: rels:1559054, finalFF:197232 Max relations in full relation-set: 28 Initial matrix: 128271 x 197232 with sparse part having weight 14484832. Pruned matrix : 109223 x 109928 with weight 6425650. Total sieving time: 4.33 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.06 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.49 hours. --------- CPU info (if available) ----------
(4·10¹²⁷+11)/3 = 1(3)₁₂₆7_<128> = 29 · 131 · 18199825817_<11> · C114
C114 = P36 · P39 · P39
P36 = 227060322506798993332149127795092037_<36>
P39 = 913336927466122993434262778590061373449_<39>
P39 = 929886502764280214041355493551431541603_<39>

Number: 13337_127 N=192842259547018009597079694636074182400710045315079783185799547260078047160967977004619128485484268956703784377639 ( 114 digits) SNFS difficulty: 127 digits. Divisors found: r1=227060322506798993332149127795092037 (pp36) r2=913336927466122993434262778590061373449 (pp39) r3=929886502764280214041355493551431541603 (pp39) Version: GGNFS-0.77.1-20060513-k8 Total time: 3.12 hours. Scaled time: 6.21 units (timescale=1.992). Factorization parameters were as follows: name: 13337_127 n: 192842259547018009597079694636074182400710045315079783185799547260078047160967977004619128485484268956703784377639 m: 20000000000000000000000000 c5: 25 c0: 22 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, 750001) Primes: RFBsize:63951, AFBsize:63939, largePrimes:1400313 encountered Relations: rels:1394145, finalFF:169686 Max relations in full relation-set: 28 Initial matrix: 127954 x 169686 with sparse part having weight 8194603. Pruned matrix : 110799 x 111502 with weight 4097518. Total sieving time: 3.00 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.05 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: 3.12 hours. --------- CPU info (if available) ----------
(4·10¹⁵¹+11)/3 = 1(3)₁₅₀7_<152> = 633619426343_<12> · 442973859605351119_<18> · 3975218224563891047_<19> · C104
C104 = P46 · P58
P46 = 2337821818609044897355108471584512338289378161_<46>
P58 = 5111634251655468130247648332197620987017296367122312286583_<58>

Number: 13337_151 N=11950090082269470772012979307480787589555936665450276418632716974465848898807642129099590952613093513863 ( 104 digits) Divisors found: r1=2337821818609044897355108471584512338289378161 (pp46) r2=5111634251655468130247648332197620987017296367122312286583 (pp58) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 14.67 hours. Scaled time: 9.91 units (timescale=0.675). Factorization parameters were as follows: name: 13337_151 n: 11950090082269470772012979307480787589555936665450276418632716974465848898807642129099590952613093513863 skew: 6800.61 # norm 1.74e+14 c5: 29640 c4: -1232540113 c3: 2169770658470 c2: -20196984656031629 c1: -134467529912451149353 c0: 32693537318913341764250 # alpha -5.44 Y1: 26651928809 Y0: -52613891591132659327 # Murphy_E 2.20e-09 # M 1484081719694419706365100096805128173093244655510772422378879253150230070968344633840020539840777333680 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1950001) Primes: RFBsize:169511, AFBsize:170092, largePrimes:4530487 encountered Relations: rels:4761478, finalFF:578150 Max relations in full relation-set: 28 Initial matrix: 339686 x 578150 with sparse part having weight 44365745. Pruned matrix : 189798 x 191560 with weight 21055717. Polynomial selection time: 0.79 hours. Total sieving time: 12.20 hours. Total relation processing time: 0.22 hours. Matrix solve time: 1.27 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 14.67 hours. --------- CPU info (if available) ----------
(4·10¹⁴³+11)/3 = 1(3)₁₄₂7_<144> = 19 · 394478557247107_<15> · C128
C128 = P45 · P83
P45 = 540221890483900213100183282378870340497411947_<45>
P83 = 32929835114364724990528981056819343712336652054415144940805074403713200462062903587_<83>

Number: 13337_143 N=17789417778805232112908786998844581501787575892209776794081262433217844819211255327899323908514311530976008988829918089682953889 ( 128 digits) SNFS difficulty: 143 digits. Divisors found: r1=540221890483900213100183282378870340497411947 (pp45) r2=32929835114364724990528981056819343712336652054415144940805074403713200462062903587 (pp83) Version: GGNFS-0.77.1-20060513-k8 Total time: 13.31 hours. Scaled time: 26.61 units (timescale=1.999). Factorization parameters were as follows: name: 13337_143 n: 17789417778805232112908786998844581501787575892209776794081262433217844819211255327899323908514311530976008988829918089682953889 m: 20000000000000000000000000000 c5: 125 c0: 11 skew: 0.62 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, 2150001) Primes: RFBsize:100021, AFBsize:100439, largePrimes:2797871 encountered Relations: rels:2800510, finalFF:269837 Max relations in full relation-set: 28 Initial matrix: 200525 x 269837 with sparse part having weight 27631150. Pruned matrix : 181432 x 182498 with weight 16800760. Total sieving time: 12.78 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.35 hours. Time per square root: 0.08 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: 13.31 hours. --------- CPU info (if available) ----------
Feb 19, 2008 (3rd): By Sinkiti Sibata / GGNFS
(4·10¹²⁵+11)/3 = 1(3)₁₂₄7_<126> = 19 · 2225471936246839129_<19> · C106
C106 = P38 · P69
P38 = 15803345655438486511972481152450794613_<38>
P69 = 199532651776252834039911251067175851500401630254970536186458226795599_<69>

Number: 13337_125 N=3153283465566365633508056367141023771988625666319413811577363839922534166099217033045727316239036281308187 ( 106 digits) SNFS difficulty: 125 digits. Divisors found: r1=15803345655438486511972481152450794613 (pp38) r2=199532651776252834039911251067175851500401630254970536186458226795599 (pp69) Version: GGNFS-0.77.1-20060513-k8 Total time: 1.95 hours. Scaled time: 3.86 units (timescale=1.981). Factorization parameters were as follows: name: 13337_125 n: 3153283465566365633508056367141023771988625666319413811577363839922534166099217033045727316239036281308187 m: 10000000000000000000000000 c5: 4 c0: 11 skew: 1.22 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:63629, largePrimes:2080670 encountered Relations: rels:2108833, finalFF:178021 Max relations in full relation-set: 28 Initial matrix: 112791 x 178021 with sparse part having weight 15251272. Pruned matrix : 95760 x 96387 with weight 5778001. Total sieving time: 1.82 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.05 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.95 hours. --------- CPU info (if available) ----------
(4·10¹¹³+11)/3 = 1(3)₁₁₂7_<114> = 17 · 397 · C110
C110 = P39 · P71
P39 = 304155774352865478339206504203892550259_<39>
P71 = 64953602405091887197954344906663271278940558317913767517079385452861407_<71>

Number: 13337_113 N=19756013236528868474341877809058132068948486195485750975453153553612880920630216822245270904331505902108954413 ( 110 digits) SNFS difficulty: 113 digits. Divisors found: r1=304155774352865478339206504203892550259 (pp39) r2=64953602405091887197954344906663271278940558317913767517079385452861407 (pp71) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.86 hours. Scaled time: 1.26 units (timescale=0.675). Factorization parameters were as follows: name: 13337_113 n: 19756013236528868474341877809058132068948486195485750975453153553612880920630216822245270904331505902108954413 m: 20000000000000000000000 c5: 125 c0: 11 skew: 0.62 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:64204, largePrimes:2116619 encountered Relations: rels:2254082, finalFF:285131 Max relations in full relation-set: 28 Initial matrix: 113367 x 285131 with sparse part having weight 22834055. Pruned matrix : 74586 x 75216 with weight 4095384. Total sieving time: 1.68 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Time per square root: 0.04 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: 1.86 hours. --------- CPU info (if available) ----------
Feb 19, 2008 (2nd): By Jo Yeong Uk / GGNFS
(4·10¹³⁶+11)/3 = 1(3)₁₃₅7_<137> = C137 = P48 · P89
P48 = 645109945959932436794670252937099004445884900281_<48>
P89 = 20668311528654469407072421372850207222818010052176468364973643563797095494823416253615777_<89>

Number: 13337_136 N=13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 ( 137 digits) SNFS difficulty: 137 digits. Divisors found: r1=645109945959932436794670252937099004445884900281 (pp48) r2=20668311528654469407072421372850207222818010052176468364973643563797095494823416253615777 (pp89) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.28 hours. Scaled time: 6.10 units (timescale=1.857). Factorization parameters were as follows: n: 13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333337 m: 2000000000000000000000000000 c5: 5 c0: 44 skew: 1.54 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:107659, largePrimes:2240727 encountered Relations: rels:2306072, finalFF:241669 Max relations in full relation-set: 28 Initial matrix: 214851 x 241669 with sparse part having weight 17262603. Pruned matrix : 203670 x 204808 with weight 12258523. Total sieving time: 3.06 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.16 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: 3.28 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406452) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405111) Calibrating delay using timer specific routine.. 4809.73 BogoMIPS (lpj=2404867) Calibrating delay using timer specific routine.. 4714.04 BogoMIPS (lpj=2357021)
(4·10¹⁹²-13)/9 = (4)₁₉₁3_<192> = C192
C192 = P89 · P104
P89 = 35045847515642783523626070569435470884822385339002400825581256172358614490951464260070747_<89>
P104 = 12681800440011210614082687744739066189716084468441089520538508971989616998911936443662265342146313320769_<104>

Number: 44443_192 N=444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 ( 192 digits) SNFS difficulty: 192 digits. Divisors found: r1=35045847515642783523626070569435470884822385339002400825581256172358614490951464260070747 (pp89) r2=12681800440011210614082687744739066189716084468441089520538508971989616998911936443662265342146313320769 (pp104) Version: GGNFS-0.77.1-20050930-nocona Total time: 677.17 hours. Scaled time: 1257.51 units (timescale=1.857). Factorization parameters were as follows: n: 444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444443 m: 200000000000000000000000000000000000000 c5: 25 c0: -26 skew: 1.01 type: snfs Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 51/51 Sieved algebraic special-q in [8000000, 18400001) Primes: RFBsize:1031130, AFBsize:1032793, largePrimes:12950076 encountered Relations: rels:14092984, finalFF:2343105 Max relations in full relation-set: 28 Initial matrix: 2063987 x 2343105 with sparse part having weight 150351956. Pruned matrix : 1810027 x 1820410 with weight 111950679. Total sieving time: 646.41 hours. Total relation processing time: 0.41 hours. Matrix solve time: 30.15 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,16000000,16000000,28,28,51,51,2.6,2.6,100000 total time: 677.17 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406452) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405111) Calibrating delay using timer specific routine.. 4809.73 BogoMIPS (lpj=2404867) Calibrating delay using timer specific routine.. 4714.04 BogoMIPS (lpj=2357021)
Feb 19, 2008: By Robert Backstrom / GMP-ECM, GGNFS
(4·10¹⁰²+11)/3 = 1(3)₁₀₁7_<103> = 307266829 · C94
C94 = P43 · P52
P43 = 1646560534466985058328605054610083645298993_<43>
P52 = 2635392807135816561786044834867478808294813224484621_<52>

Number: n N=4339333789047998192259579485338241093812743885000789764173773971980988983790805916551875286653 ( 94 digits) SNFS difficulty: 102 digits. Divisors found: r1=1646560534466985058328605054610083645298993 (pp43) r2=2635392807135816561786044834867478808294813224484621 (pp52) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.43 hours. Scaled time: 0.79 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_3_101_7 n: 4339333789047998192259579485338241093812743885000789764173773971980988983790805916551875286653 skew: 1.00 deg: 5 c5: 25 c0: 22 m: 200000000000000000000 type: snfs rlim: 500000 alim: 500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 500000/500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 140001) Primes: RFBsize:41538, AFBsize:41568, largePrimes:3448580 encountered Relations: rels:2920109, finalFF:148659 Max relations in full relation-set: 48 Initial matrix: 83170 x 148659 with sparse part having weight 9271658. Pruned matrix : 58314 x 58793 with weight 1969435. Total sieving time: 0.38 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.01 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,102,5,0,0,0,0,0,0,0,0,500000,500000,28,28,48,48,2.5,2.5,20000 total time: 0.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(4·10¹¹⁵+11)/3 = 1(3)₁₁₄7_<116> = 31 · 275416674221551_<15> · C100
C100 = P46 · P54
P46 = 1805025368704280366962983811597818948051327631_<46>
P54 = 865174086391486453505012758489951524756223702524904967_<54>

Number: n N=1561661174282181750855560882405506568818194843939868509965372037918767188901167683328566806456243177 ( 100 digits) SNFS difficulty: 115 digits. Divisors found: r1=1805025368704280366962983811597818948051327631 (pp46) r2=865174086391486453505012758489951524756223702524904967 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.77 hours. Scaled time: 1.42 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_3_114_7 n: 1561661174282181750855560882405506568818194843939868509965372037918767188901167683328566806456243177 skew: 1.00 deg: 5 c5: 4 c0: 11 m: 100000000000000000000000 type: snfs rlim: 800000 alim: 800000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 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, 160001) Primes: RFBsize:63951, AFBsize:63629, largePrimes:4202404 encountered Relations: rels:3652012, finalFF:223982 Max relations in full relation-set: 48 Initial matrix: 127644 x 223982 with sparse part having weight 12430380. Pruned matrix : 80889 x 81591 with weight 2898267. Total sieving time: 0.70 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,115,5,0,0,0,0,0,0,0,0,800000,800000,28,28,48,48,2.5,2.5,50000 total time: 0.77 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(4·10¹²²+11)/3 = 1(3)₁₂₁7_<123> = 137 · 311 · 75767110971407101_<17> · C101
C101 = P34 · P67
P34 = 5272921641050465131362660361244101_<34>
P67 = 7832956869217103170630125848353003163038606291478854203546482793191_<67>
(4·10¹³⁹+11)/3 = 1(3)₁₃₈7_<140> = 4311337 · 21247651 · 149032782893_<12> · 175317660870361_<15> · C100
C100 = P36 · P65
P36 = 337617990811478180020888640562676309_<36>
P65 = 16499955819490232143991256389127069993152179641301496930299925443_<65>
(4·10¹¹⁶+11)/3 = 1(3)₁₁₅7_<117> = 120383704907_<12> · C106
C106 = P35 · P71
P35 = 28802954401798198620925160019003859_<35>
P71 = 38453333520441584543202578333588710413505012991763189928723152862992649_<71>
(4·10¹²⁹+11)/3 = 1(3)₁₂₈7_<130> = 7 · 17 · C128
C128 = P31 · P97
P31 = 1623689600151579293848901161081_<31>
P97 = 6900630386294950804431484242986375136955298070601334173121463514139852321236962540139980145351783_<97>
(4·10¹²⁴+11)/3 = 1(3)₁₂₃7_<125> = 157 · 257 · 863 · 3114563 · 734742979 · C102
C102 = P40 · P62
P40 = 2203938796192403342392271268196078673989_<40>
P62 = 75921201152552818087132501075621030841933093815300464956718367_<62>

Number: n N=167325680673638563081548947403636743907474465909076656035498500293151015645904444990307855678281455963 ( 102 digits) SNFS difficulty: 125 digits. Divisors found: r1=2203938796192403342392271268196078673989 (pp40) r2=75921201152552818087132501075621030841933093815300464956718367 (pp62) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.44 hours. Scaled time: 2.63 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_3_123_7 n: 167325680673638563081548947403636743907474465909076656035498500293151015645904444990307855678281455963 skew: 1.94 deg: 5 c5: 2 c0: 55 m: 10000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 240001) Primes: RFBsize:114155, AFBsize:113953, largePrimes:4515312 encountered Relations: rels:3995223, finalFF:291897 Max relations in full relation-set: 48 Initial matrix: 228173 x 291897 with sparse part having weight 12613705. Pruned matrix : 166879 x 168083 with weight 5210343. Total sieving time: 1.28 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.08 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000 total time: 1.44 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(4·10¹³⁰+11)/3 = 1(3)₁₂₉7_<131> = 23 · 31 · 137 · C126
C126 = P33 · P93
P33 = 586747933411274964170925848158487_<33>
P93 = 232636079856833912272452423645428068658508651978665240250136011794304923321522084851723290271_<93>
(4·10¹³⁴+11)/3 = 1(3)₁₃₃7_<135> = 50604613 · C127
C127 = P40 · P87
P40 = 3820162630866551606713037132751079542817_<40>
P87 = 689710403238257935905626272855854844006021482308071303691508206972486304337202234301797_<87>

Number: n N=2634805908570693611140417837664983888590025050351305588155240577244081153892696172448415588779096746245907133670468605961542149 ( 127 digits) SNFS difficulty: 135 digits. Divisors found: r1=3820162630866551606713037132751079542817 (pp40) r2=689710403238257935905626272855854844006021482308071303691508206972486304337202234301797 (pp87) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.69 hours. Scaled time: 4.92 units (timescale=1.828). Factorization parameters were as follows: name: KA_1_3_133_7 n: 2634805908570693611140417837664983888590025050351305588155240577244081153892696172448415588779096746245907133670468605961542149 skew: 1.94 deg: 5 c5: 2 c0: 55 m: 1000000000000000000000000000 type: snfs rlim: 2000000 alim: 2000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 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, 420001) Primes: RFBsize:148933, AFBsize:148701, largePrimes:5227610 encountered Relations: rels:4670599, finalFF:342239 Max relations in full relation-set: 48 Initial matrix: 297699 x 342239 with sparse part having weight 16564263. Pruned matrix : 253523 x 255075 with weight 9103303. Total sieving time: 2.32 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.25 hours. Total square root time: 0.05 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,135,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000 total time: 2.69 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Feb 18, 2008 (3rd): By Robert Backstrom / GMP-ECM
(4·10¹⁵⁶+11)/3 = 1(3)₁₅₅7_<157> = 71 · 2161 · 14831 · 658453 · 394839461087_<12> · 126692824237732751_<18> · 1333267352305266238694551_<25> · C89
C89 = P31 · P58
P31 = 3843061199517217692568521094769_<31>
P58 = 3471868696924966252462632988741475891496853178404981998763_<58>
Feb 18, 2008 (2nd): The factor table of 133...337 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.
Feb 18, 2008: By Robert Backstrom / GMP-ECM
(79·10¹⁸³-7)/9 = 8(7)₁₈₃_<184> = 1913 · C181
C181 = P32 · P37 · P114
P32 = 12153807173571949007375230348211_<32>
P37 = 2375716400628936749079408376044022391_<37>
P114 = 158914188404109477281052206971033581029810208002769801689981446299251940791541808338262878938295863778304036304629_<114>
Feb 17, 2008 (2nd): By Sinkiti Sibata / GGNFS
(11·10¹⁴⁹+61)/9 = 1(2)₁₄₈9_<150> = 3² · 43 · C147
C147 = P31 · P55 · P61
P31 = 6242261523111451604167188855731_<31>
P55 = 5345904564855449996407866180568566463290283484418398029_<55>
P61 = 9464028719153806681139681352642106781803923220341415398103633_<61>

Number: 12229_149 N=315819695664656904966982486362331323571633649153028997990238300315819695664656904966982486362331323571633649153028997990238300315819695664656904967 ( 147 digits) SNFS difficulty: 151 digits. Divisors found: r1=6242261523111451604167188855731 (pp31) r2=5345904564855449996407866180568566463290283484418398029 (pp55) r3=9464028719153806681139681352642106781803923220341415398103633 (pp61) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 37.15 hours. Scaled time: 25.08 units (timescale=0.675). Factorization parameters were as follows: name: 12229_149 n: 315819695664656904966982486362331323571633649153028997990238300315819695664656904966982486362331323571633649153028997990238300315819695664656904967 m: 1000000000000000000000000000000 c5: 11 c0: 610 skew: 2.23 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, 2200001) Primes: RFBsize:176302, AFBsize:175370, largePrimes:5628786 encountered Relations: rels:5580248, finalFF:504483 Max relations in full relation-set: 28 Initial matrix: 351737 x 504483 with sparse part having weight 45930839. Pruned matrix : 290346 x 292168 with weight 24671675. Total sieving time: 33.54 hours. Total relation processing time: 0.23 hours. Matrix solve time: 3.22 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 37.15 hours. --------- CPU info (if available) ----------
Feb 17, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(71·10¹⁸⁴-17)/9 = 7(8)₁₈₃7_<185> = 584027 · 67972403356899191_<17> · 12252647954833593078177200604809_<32> · C132
C132 = P31 · P37 · P65
P31 = 2689572403442632769337374190077_<31>
P37 = 1925866741774738582164323933510316983_<37>
P65 = 31312003673636456198021235073960417940459037776283793591711449889_<65>

Number: n N=60302746493384886847709617108784565070134687576182721026645805344525114269394313542409814350910164887 ( 101 digits) Divisors found: Sun Feb 17 10:05:35 2008 prp37 factor: 1925866741774738582164323933510316983 Sun Feb 17 10:05:35 2008 prp65 factor: 31312003673636456198021235073960417940459037776283793591711449889 Sun Feb 17 10:05:35 2008 elapsed time 00:11:39 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-k8 Total time: 5.51 hours. Scaled time: 4.60 units (timescale=0.835). Factorization parameters were as follows: name: KA_7_8_183 n: 60302746493384886847709617108784565070134687576182721026645805344525114269394313542409814350910164887 skew: 1591.76 # norm 2.54e+13 c5: 490680 c4: -2420530822 c3: 1607362527322 c2: 7712572522997431 c1: -1015553300418810242 c0: -2676058812104523333649 # alpha -5.19 Y1: 13671193657 Y0: -10420973927095743510 # Murphy_E 3.29e-09 # M 13575008737661884978698488583945020638176130417697145616183711579278417102206895065551839353226346846 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, 800001) Primes: RFBsize:135072, AFBsize:136018, largePrimes:3464132 encountered Relations: rels:3423937, finalFF:377196 Max relations in full relation-set: 28 Initial matrix: 271178 x 377196 with sparse part having weight 20957178. Pruned matrix : 173729 x 175148 with weight 7500817. Polynomial selection time: 0.55 hours. Total sieving time: 4.69 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.14 hours. Time per square root: 0.00 hours. 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: 5.51 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(46·10¹⁶³-1)/9 = 5(1)₁₆₃_<164> = 3 · 199 · 1481 · 33637 · 65609 · 348944548907_<12> · 3094508928368237_<16> · C122
C122 = P50 · P72
P50 = 42383839285525795753607722140791837846064285912043_<50>
P72 = 572343567840351351004052047916227199387688191587467882881579520189050963_<72>

Number: n N=24258117795449882016463515363358612414330257454310490695425839412626146864798222116552055288007645093745929170939062447409 ( 122 digits) SNFS difficulty: 164 digits. Divisors found: Sun Feb 17 11:29:09 2008 prp50 factor: 42383839285525795753607722140791837846064285912043 Sun Feb 17 11:29:09 2008 prp72 factor: 572343567840351351004052047916227199387688191587467882881579520189050963 Sun Feb 17 11:29:09 2008 elapsed time 01:33:30 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 64.27 hours. Scaled time: 93.38 units (timescale=1.453). Factorization parameters were as follows: name: KA_5_1_163 n: 24258117795449882016463515363358612414330257454310490695425839412626146864798222116552055288007645093745929170939062447409 skew: 0.23 deg: 5 c5: 2875 c0: -2 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, 3200001) Primes: RFBsize:216816, AFBsize:217086, largePrimes:7722673 encountered Relations: rels:7223944, finalFF:486300 Max relations in full relation-set: 28 Initial matrix: 433968 x 486300 with sparse part having weight 47481030. Pruned matrix : Total sieving time: 64.00 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,164,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.5,2.5,100000 total time: 64.27 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Feb 16, 2008 (2nd): By matsui / GGNFS
3·10¹⁷⁹-1 = 2(9)₁₇₉_<180> = 7 · 83 · 269 · 8731 · 81853 · 116981 · 341557 · 12603850771_<11> · 40741126949_<11> · 135924365039_<12> · C123
C123 = P59 · P65
P59 = 65229101266939367735801851025243606155752420471073669310383_<59>
P65 = 14765247618055126790247356701740302955486828755600519733418471207_<65>

N=963123832109553152595040489985247676605852097732313677970697180432654991239607824625799134317843703968468200269973831642281 ( 123 digits) Divisors found: r1=65229101266939367735801851025243606155752420471073669310383 (pp59) r2=14765247618055126790247356701740302955486828755600519733418471207 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 105.78 hours. Scaled time: 136.98 units (timescale=1.295). Factorization parameters were as follows: name: 3000 n: 963123832109553152595040489985247676605852097732313677970697180432654991239607824625799134317843703968468200269973831642281 skew: 96096.19 # norm 9.91e+16 c5: 66240 c4: -32279355888 c3: -2129454685216800 c2: 294388916535552239654 c1: 12148253690490472323530277 c0: 57066639980311126901329358611 # alpha -6.31 Y1: 16016640817309 Y0: -429055962076730058362034 # Murphy_E 1.89e-10 # M 61974167399733499335733838603131508133502921043676458000972502662641628379410764569675900458759902446519498408010415736179 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5920001) Primes: RFBsize:348513, AFBsize:348802, largePrimes:7933036 encountered Relations: rels:8259254, finalFF:863393 Max relations in full relation-set: 28 Initial matrix: 697393 x 863393 with sparse part having weight 88990510. Pruned matrix : 565520 x 569070 with weight 62336262. Total sieving time: 91.13 hours. Total relation processing time: 0.34 hours. Matrix solve time: 13.66 hours. Time per square root: 0.65 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,e StepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 105.78 hours.
Feb 16, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(2·10¹⁷⁹-17)/3 = (6)₁₇₈1_<179> = 7 · 1303 · 2113 · 29119157 · 5793684977_<10> · 336644628636372600585073_<24> · C131
C131 = P30 · P40 · P63
P30 = 117733382538191803231594866287_<30>
P40 = 2026710201705934049640343657007900267053_<40>
P63 = 255252584468709657651315972742139518142414624901650982711938171_<63>

Number: n N=517323016954539519104299878861340926635621421290927921190677439277366154322066511600055544722124380063 ( 102 digits) Divisors found: Sat Feb 16 09:01:49 2008 prp40 factor: 2026710201705934049640343657007900267053 Sat Feb 16 09:01:49 2008 prp63 factor: 255252584468709657651315972742139518142414624901650982711938171 Sat Feb 16 09:01:49 2008 elapsed time 00:44:05 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 6.88 hours. Scaled time: 8.90 units (timescale=1.293). Factorization parameters were as follows: name: KA_6_178_1 n: 517323016954539519104299878861340926635621421290927921190677439277366154322066511600055544722124380063 skew: 15433.97 # norm 1.78e+14 c5: 11340 c4: -210213358 c3: 822174645868 c2: 75764522101157211 c1: 818325393752775442490 c0: -2819299342594052083394120 # alpha -6.47 Y1: 26670758489 Y0: -34027575905630961057 # Murphy_E 2.65e-09 # M 40674032749483108661264023893591174142795240211848184405971828080856584641743182758663277192319315897 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved special-q in [100000, 800000) Primes: RFBsize:169511, AFBsize:169673, largePrimes:3882109 encountered Relations: rels:3787702, finalFF:401409 Max relations in full relation-set: 28 Initial matrix: 339268 x 401409 with sparse part having weight 19928409. Pruned matrix : 268583 x 270343 with weight 9451561. Total sieving time: 6.19 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.52 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,101,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 6.88 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(2·10¹⁷⁶+43)/9 = (2)₁₇₅7_<176> = 3 · 48971055909467_<14> · 228716882727738050432210325227_<30> C132
C132 = P36 · P97
P36 = 404075342846215616011831753904136079_<36>
P97 = 1636689099026739176899658261871273953653786966383885960693665967442392548030342512207866446134919_<97>
(4·10¹⁸⁶+23)/9 = (4)₁₈₅7_<186> = 3² · 31 · 47 · 179 · 12743 · 18541 · 1519769856019001_<16> · 2375090177092212015679433_<25> · C132
C132 = P30 · P103
P30 = 118270750950320247085810333307_<30>
P103 = 1877250672708337815991348552500624443658145975176294067599617799874145110659688921540769920338722450837_<103>
Feb 15, 2008 (4th): By Sinkiti Sibata / GGNFS
(11·10¹⁵⁸+61)/9 = 1(2)₁₅₇9_<159> = 3² · 29 · 2417 · 850637 · 20357861 · 34953302776819747_<17> · C123
C123 = P35 · P37 · P52
P35 = 11920843112330238846091327134150343_<35>
P37 = 5533180785858157565411447744926232573_<37>
P52 = 4852734739010638529320321809660405214270996767425057_<52>

Number: 12229_158 N=320087257170379743745512038306524681451620506378742376663804041998523402739301653903245691152522955108248039967344338259723 ( 123 digits) SNFS difficulty: 159 digits. Divisors found: r1=11920843112330238846091327134150343 (pp35) r2=5533180785858157565411447744926232573 (pp37) r3=4852734739010638529320321809660405214270996767425057 (pp52) Version: GGNFS-0.77.1-20060513-k8 Total time: 65.85 hours. Scaled time: 131.77 units (timescale=2.001). Factorization parameters were as follows: name: 12229_158 n: 320087257170379743745512038306524681451620506378742376663804041998523402739301653903245691152522955108248039967344338259723 m: 10000000000000000000000000000000 c5: 11000 c0: 61 skew: 0.35 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:284229, largePrimes:5875710 encountered Relations: rels:6004080, finalFF:729809 Max relations in full relation-set: 28 Initial matrix: 567442 x 729809 with sparse part having weight 53653069. Pruned matrix : 449842 x 452743 with weight 37603921. Total sieving time: 62.66 hours. Total relation processing time: 0.25 hours. Matrix solve time: 2.73 hours. Time per square root: 0.21 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 65.85 hours. --------- CPU info (if available) ----------
(11·10¹⁴⁸+61)/9 = 1(2)₁₄₇9_<149> = 7² · 1633007 · 73216302241_<11> · 2824656770917_<13> · C117
C117 = P53 · P65
P53 = 11902378768854297574550472754083771786485974613585009_<53>
P65 = 62052432086827128788540349410927173560773558990532128882788082911_<65>

Number: 12229_148 N=738571550226024392405858563209788417084723191785980144725541056915264197135700547827962950228341820185276112038681199 ( 117 digits) SNFS difficulty: 149 digits. Divisors found: r1=11902378768854297574550472754083771786485974613585009 (pp53) r2=62052432086827128788540349410927173560773558990532128882788082911 (pp65) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 49.88 hours. Scaled time: 33.72 units (timescale=0.676). Factorization parameters were as follows: name: 12229_148 n: 738571550226024392405858563209788417084723191785980144725541056915264197135700547827962950228341820185276112038681199 m: 100000000000000000000000000000 c5: 11000 c0: 61 skew: 0.35 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, 5750001) Primes: RFBsize:114155, AFBsize:114409, largePrimes:3268022 encountered Relations: rels:3436305, finalFF:267502 Max relations in full relation-set: 28 Initial matrix: 228631 x 267502 with sparse part having weight 36416837. Pruned matrix : 219053 x 220260 with weight 28994291. Total sieving time: 47.18 hours. Total relation processing time: 0.37 hours. Matrix solve time: 2.20 hours. Time per square root: 0.13 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: 49.88 hours. --------- CPU info (if available) ----------
Feb 15, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
(65·10¹⁶²+43)/9 = 7(2)₁₆₁7_<163> = 3 · 677 · 10193 · 1573237 · 10037269604188014489625787_<26> · C125
C125 = P54 · P72
P54 = 137954707191964580423759095965459263169617010356229781_<54>
P72 = 160144723690182851686046435792735566441355086416901397233226149694716271_<72>

Number: n N=22092718465017248771037776619885496253769731032787367896536812757589874812967027353750731118374142593784616914591704075466651 ( 125 digits) SNFS difficulty: 163 digits. Divisors found: Fri Feb 15 11:54:20 2008 prp54 factor: 137954707191964580423759095965459263169617010356229781 Fri Feb 15 11:54:20 2008 prp72 factor: 160144723690182851686046435792735566441355086416901397233226149694716271 Fri Feb 15 11:54:20 2008 elapsed time 00:55:13 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 35.21 hours. Scaled time: 64.41 units (timescale=1.829). Factorization parameters were as follows: name: KA_7_2_161_7 n: 22092718465017248771037776619885496253769731032787367896536812757589874812967027353750731118374142593784616914591704075466651 skew: 0.37 deg: 5 c5: 6500 c0: 43 m: 100000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2300001) Primes: RFBsize:230209, AFBsize:230052, largePrimes:7364839 encountered Relations: rels:6841139, finalFF:523751 Max relations in full relation-set: 28 Initial matrix: 460328 x 523751 with sparse part having weight 47945873. Pruned matrix : Total sieving time: 35.04 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 35.21 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Feb 15, 2008 (2nd): By Jo Yeong Uk / GGNFS
(11·10¹⁶⁹+43)/9 = 1(2)₁₆₈7_<170> = C170
C170 = P48 · P122
P48 = 227030126709317368877348740835730359515559877331_<48>
P122 = 53835243803881555060152528124341137855983903787606163934998794151883156545332025716371870291431461909592002513314902039617_<122>

Number: 12227_169 N=12222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 ( 170 digits) SNFS difficulty: 171 digits. Divisors found: r1=227030126709317368877348740835730359515559877331 (pp48) r2=53835243803881555060152528124341137855983903787606163934998794151883156545332025716371870291431461909592002513314902039617 (pp122) Version: GGNFS-0.77.1-20050930-nocona Total time: 97.15 hours. Scaled time: 180.60 units (timescale=1.859). Factorization parameters were as follows: n: 12222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 m: 10000000000000000000000000000000000 c5: 11 c0: 430 skew: 2.08 type: snfs Factor base limits: 8000000/8000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 49/49 Sieved algebraic special-q in [4000000, 8500001) Primes: RFBsize:539777, AFBsize:539881, largePrimes:9820148 encountered Relations: rels:9752653, finalFF:1218038 Max relations in full relation-set: 28 Initial matrix: 1079723 x 1218038 with sparse part having weight 64331651. Pruned matrix : 958872 x 964334 with weight 46529221. Total sieving time: 91.68 hours. Total relation processing time: 0.17 hours. Matrix solve time: 5.20 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: snfs,171,5,0,0,0,0,0,0,0,0,8000000,8000000,28,28,49,49,2.6,2.6,100000 total time: 97.15 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406452) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405111) Calibrating delay using timer specific routine.. 4809.73 BogoMIPS (lpj=2404867) Calibrating delay using timer specific routine.. 4714.04 BogoMIPS (lpj=2357021)
Feb 15, 2008: By Robert Backstrom / GMP-ECM, Msieve
2·10¹⁷⁴+9 = 2(0)₁₇₃9_<175> = 11 · 449 · 773713 · 2243296177_<10> · 74158382575383580813200721_<26> · C130
C130 = P34 · P46 · P50
P34 = 6474833169609810754024951641805051_<34>
P46 = 6504635362555600808299400218239308558804216297_<46>
P50 = 74698635967538385695610601830647283165089131842313_<50>

Thu Feb 14 23:19:07 2008 Thu Feb 14 23:19:07 2008 Thu Feb 14 23:19:07 2008 Msieve v. 1.33 Thu Feb 14 23:19:07 2008 random seeds: a04a6710 79a96968 Thu Feb 14 23:19:07 2008 factoring 485887389049117890210490665624086802374006262683353795179735136350962989087028228699823748774961 (96 digits) Thu Feb 14 23:19:08 2008 no P-1/P+1/ECM available, skipping Thu Feb 14 23:19:08 2008 commencing quadratic sieve (96-digit input) Thu Feb 14 23:19:08 2008 using multiplier of 1 Thu Feb 14 23:19:08 2008 using 64kb Opteron sieve core Thu Feb 14 23:19:08 2008 sieve interval: 18 blocks of size 65536 Thu Feb 14 23:19:08 2008 processing polynomials in batches of 6 Thu Feb 14 23:19:08 2008 using a sieve bound of 2263381 (83529 primes) Thu Feb 14 23:19:08 2008 using large prime bound of 339507150 (28 bits) Thu Feb 14 23:19:08 2008 using double large prime bound of 2267399519796450 (43-52 bits) Thu Feb 14 23:19:08 2008 using trial factoring cutoff of 52 bits Thu Feb 14 23:19:08 2008 polynomial 'A' values have 12 factors Fri Feb 15 02:20:26 2008 83856 relations (20273 full + 63583 combined from 1263041 partial), need 83625 Fri Feb 15 02:20:27 2008 begin with 1283314 relations Fri Feb 15 02:20:28 2008 reduce to 220570 relations in 12 passes Fri Feb 15 02:20:28 2008 attempting to read 220570 relations Fri Feb 15 02:20:29 2008 recovered 220570 relations Fri Feb 15 02:20:29 2008 recovered 205365 polynomials Fri Feb 15 02:20:30 2008 attempting to build 83856 cycles Fri Feb 15 02:20:30 2008 found 83856 cycles in 5 passes Fri Feb 15 02:20:30 2008 distribution of cycle lengths: Fri Feb 15 02:20:30 2008 length 1 : 20273 Fri Feb 15 02:20:30 2008 length 2 : 14503 Fri Feb 15 02:20:30 2008 length 3 : 13852 Fri Feb 15 02:20:30 2008 length 4 : 11290 Fri Feb 15 02:20:30 2008 length 5 : 8508 Fri Feb 15 02:20:30 2008 length 6 : 6030 Fri Feb 15 02:20:30 2008 length 7 : 3857 Fri Feb 15 02:20:30 2008 length 9+: 5543 Fri Feb 15 02:20:30 2008 largest cycle: 20 relations Fri Feb 15 02:20:30 2008 matrix is 83529 x 83856 (22.9 MB) with weight 5672561 (67.65/col) Fri Feb 15 02:20:30 2008 sparse part has weight 5672561 (67.65/col) Fri Feb 15 02:20:31 2008 filtering completed in 3 passes Fri Feb 15 02:20:31 2008 matrix is 79794 x 79858 (21.9 MB) with weight 5427260 (67.96/col) Fri Feb 15 02:20:31 2008 sparse part has weight 5427260 (67.96/col) Fri Feb 15 02:20:31 2008 saving the first 48 matrix rows for later Fri Feb 15 02:20:31 2008 matrix is 79746 x 79858 (15.2 MB) with weight 4438378 (55.58/col) Fri Feb 15 02:20:31 2008 sparse part has weight 3514587 (44.01/col) Fri Feb 15 02:20:31 2008 matrix includes 64 packed rows Fri Feb 15 02:20:31 2008 using block size 31943 for processor cache size 1024 kB Fri Feb 15 02:20:32 2008 commencing Lanczos iteration Fri Feb 15 02:20:32 2008 memory use: 13.9 MB Fri Feb 15 02:21:17 2008 lanczos halted after 1263 iterations (dim = 79745) Fri Feb 15 02:21:17 2008 recovered 16 nontrivial dependencies Fri Feb 15 02:21:18 2008 prp46 factor: 6504635362555600808299400218239308558804216297 Fri Feb 15 02:21:18 2008 prp50 factor: 74698635967538385695610601830647283165089131842313 Fri Feb 15 02:21:18 2008 elapsed time 03:02:11
Feb 14, 2008 (2nd): By Robert Backstrom / GMP-ECM, Msieve
(4·10¹⁷³+23)/9 = (4)₁₇₂7_<173> = 13 · 547 · 3457 · 7742677 · 92344480022803_<14> · 17066676439984957_<17> · C129
C129 = P32 · P98
P32 = 11547865405892626687884211439681_<32>
P98 = 12830236827967471491637490179825912863260274126012053520529623406724702467484496830797955662017043_<98>
(71·10¹⁶⁸-17)/9 = 7(8)₁₆₇7_<169> = 3³ · 61 · 692912981 · 1573653452257_<13> · 170069809907779157_<18> · C128
C128 = P32 · P42 · P55
P32 = 81536190423163571092923033457303_<32>
P42 = 115590451395574759743903097570647982150751_<42>
P55 = 2740531773173258744191221418003242079036846153092673753_<55>

Thu Feb 14 11:42:36 2008 Thu Feb 14 11:42:36 2008 Thu Feb 14 11:42:36 2008 Msieve v. 1.33 Thu Feb 14 11:42:36 2008 random seeds: ab969178 270d785b Thu Feb 14 11:42:36 2008 factoring 316779304725011877124301481980306957487837556226816564915372139752044167430993971558690106938503 (96 digits) Thu Feb 14 11:42:37 2008 searching for 15-digit factors Thu Feb 14 11:42:38 2008 commencing quadratic sieve (96-digit input) Thu Feb 14 11:42:38 2008 using multiplier of 5 Thu Feb 14 11:42:38 2008 using 64kb Opteron sieve core Thu Feb 14 11:42:38 2008 sieve interval: 18 blocks of size 65536 Thu Feb 14 11:42:38 2008 processing polynomials in batches of 6 Thu Feb 14 11:42:38 2008 using a sieve bound of 2265611 (83426 primes) Thu Feb 14 11:42:38 2008 using large prime bound of 339841650 (28 bits) Thu Feb 14 11:42:38 2008 using double large prime bound of 2271422065653900 (43-52 bits) Thu Feb 14 11:42:38 2008 using trial factoring cutoff of 52 bits Thu Feb 14 11:42:38 2008 polynomial 'A' values have 12 factors Thu Feb 14 16:54:45 2008 83627 relations (20300 full + 63327 combined from 1266567 partial), need 83522 Thu Feb 14 16:54:46 2008 begin with 1286866 relations Thu Feb 14 16:54:47 2008 reduce to 219798 relations in 11 passes Thu Feb 14 16:54:47 2008 attempting to read 219798 relations Thu Feb 14 16:54:50 2008 recovered 219798 relations Thu Feb 14 16:54:50 2008 recovered 206527 polynomials Thu Feb 14 16:54:50 2008 attempting to build 83627 cycles Thu Feb 14 16:54:50 2008 found 83627 cycles in 5 passes Thu Feb 14 16:54:51 2008 distribution of cycle lengths: Thu Feb 14 16:54:51 2008 length 1 : 20300 Thu Feb 14 16:54:51 2008 length 2 : 14221 Thu Feb 14 16:54:51 2008 length 3 : 14186 Thu Feb 14 16:54:51 2008 length 4 : 11367 Thu Feb 14 16:54:51 2008 length 5 : 8506 Thu Feb 14 16:54:51 2008 length 6 : 5896 Thu Feb 14 16:54:51 2008 length 7 : 3790 Thu Feb 14 16:54:51 2008 length 9+: 5361 Thu Feb 14 16:54:51 2008 largest cycle: 19 relations Thu Feb 14 16:54:51 2008 matrix is 83426 x 83627 (23.6 MB) with weight 5854011 (70.00/col) Thu Feb 14 16:54:51 2008 sparse part has weight 5854011 (70.00/col) Thu Feb 14 16:54:53 2008 filtering completed in 3 passes Thu Feb 14 16:54:53 2008 matrix is 79580 x 79644 (22.7 MB) with weight 5620651 (70.57/col) Thu Feb 14 16:54:53 2008 sparse part has weight 5620651 (70.57/col) Thu Feb 14 16:54:54 2008 saving the first 48 matrix rows for later Thu Feb 14 16:54:54 2008 matrix is 79532 x 79644 (17.0 MB) with weight 4764049 (59.82/col) Thu Feb 14 16:54:54 2008 sparse part has weight 3989892 (50.10/col) Thu Feb 14 16:54:54 2008 matrix includes 64 packed rows Thu Feb 14 16:54:54 2008 using block size 21845 for processor cache size 512 kB Thu Feb 14 16:54:55 2008 commencing Lanczos iteration Thu Feb 14 16:54:55 2008 memory use: 14.8 MB Thu Feb 14 16:56:09 2008 lanczos halted after 1258 iterations (dim = 79530) Thu Feb 14 16:56:09 2008 recovered 17 nontrivial dependencies Thu Feb 14 16:56:10 2008 prp42 factor: 115590451395574759743903097570647982150751 Thu Feb 14 16:56:10 2008 prp55 factor: 2740531773173258744191221418003242079036846153092673753 Thu Feb 14 16:56:10 2008 elapsed time 05:13:34
Feb 14, 2008: By Sinkiti Sibata / GGNFS
(11·10¹⁵⁷+61)/9 = 1(2)₁₅₆9_<158> = 1499470118834882516029_<22> · C136
C136 = P60 · P77
P60 = 298230907234615127467511105889531439850968018155959379903529_<60>
P77 = 27331263575954269106179281929739251896488872337195589729335803802039679866769_<77>

Number: 12229_157 N=8151027532125232953778580806805926102268082591328572421015894830608242951223091720643534080488498064269911620158916872675205886792927801 ( 136 digits) SNFS difficulty: 158 digits. Divisors found: r1=298230907234615127467511105889531439850968018155959379903529 (pp60) r2=27331263575954269106179281929739251896488872337195589729335803802039679866769 (pp77) Version: GGNFS-0.77.1-20060513-k8 Total time: 59.82 hours. Scaled time: 119.89 units (timescale=2.004). Factorization parameters were as follows: name: 12229_157 n: 8151027532125232953778580806805926102268082591328572421015894830608242951223091720643534080488498064269911620158916872675205886792927801 m: 10000000000000000000000000000000 c5: 1100 c0: 61 skew: 0.56 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:282319, largePrimes:5908492 encountered Relations: rels:6075893, finalFF:766526 Max relations in full relation-set: 28 Initial matrix: 565532 x 766526 with sparse part having weight 52202300. Pruned matrix : 420115 x 423006 with weight 36980807. Total sieving time: 56.81 hours. Total relation processing time: 0.25 hours. Matrix solve time: 2.56 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: 59.82 hours. --------- CPU info (if available) ----------
Feb 13, 2008 (2nd): By Sinkiti Sibata / GGNFS
(11·10¹³⁷+61)/9 = 1(2)₁₃₆9_<138> = 3 · C137
C137 = P37 · P46 · P55
P37 = 2608315158960413241863591725014062287_<37>
P46 = 3302992739511359700540576991511204918126169779_<46>
P55 = 4728912045866904847657086157801846080638041217325830291_<55>

Number: 12229_137 N=40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 ( 137 digits) SNFS difficulty: 138 digits. Divisors found: r1=2608315158960413241863591725014062287 (pp37) r2=3302992739511359700540576991511204918126169779 (pp46) r3=4728912045866904847657086157801846080638041217325830291 (pp55) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 16.64 hours. Scaled time: 11.25 units (timescale=0.676). Factorization parameters were as follows: name: 12229_137 n: 40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 m: 1000000000000000000000000000 c5: 1100 c0: 61 skew: 0.56 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, 2200001) Primes: RFBsize:78498, AFBsize:63770, largePrimes:1670073 encountered Relations: rels:1697648, finalFF:166498 Max relations in full relation-set: 28 Initial matrix: 142335 x 166498 with sparse part having weight 18460835. Pruned matrix : 136551 x 137326 with weight 13956169. Total sieving time: 15.90 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.54 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 16.64 hours. --------- CPU info (if available) ----------
Feb 13, 2008: By Robert Backstrom / GGNFS, GMP-ECM
(11·10¹³¹+61)/9 = 1(2)₁₃₀9_<132> = 3² · 23 · 128341229 · 587699374274461_<15> · C106
C106 = P47 · P60
P47 = 27843156313687337057580167590404968827671407657_<47>
P60 = 281151200709441301666481826274926616585678854755382437224859_<60>

Number: n N=7828136829133856296228799392803241434599084869328918335227018985215989728730754311284916914786485163345363 ( 106 digits) SNFS difficulty: 132 digits. Divisors found: r1=27843156313687337057580167590404968827671407657 (pp47) r2=281151200709441301666481826274926616585678854755382437224859 (pp60) Version: GGNFS-0.77.1-20051202-athlon Total time: 5.23 hours. Scaled time: 9.15 units (timescale=1.749). Factorization parameters were as follows: name: KA_1_2_130_9 n: 7828136829133856296228799392803241434599084869328918335227018985215989728730754311284916914786485163345363 type: snfs skew: 0.89 deg: 5 c5: 110 c0: 61 m: 100000000000000000000000000 rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 100000) Primes: RFBsize:114155, AFBsize:114754, largePrimes:4459635 encountered Relations: rels:3776537, finalFF:262915 Max relations in full relation-set: 28 Initial matrix: 228976 x 262915 with sparse part having weight 9371341. Pruned matrix : 190800 x 192008 with weight 5465175. Total sieving time: 4.71 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.38 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.2,2.2,50000 total time: 5.23 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(11·10¹⁴⁶+61)/9 = 1(2)₁₄₅9_<147> = 3 · C146
C146 = P71 · P75
P71 = 62188614383244022472029465985668051260768030696286619714122612487056057_<71>
P75 = 655115749800623400328076022959829614473983866531716207736106837240179182399_<75>

Number: n N=40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 ( 146 digits) SNFS difficulty: 147 digits. Divisors found: r1=62188614383244022472029465985668051260768030696286619714122612487056057 (pp71) r2=655115749800623400328076022959829614473983866531716207736106837240179182399 (pp75) Version: GGNFS-0.77.1-20051202-athlon Total time: 8.95 hours. Scaled time: 16.36 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_2_145_9 n: 40740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740743 skew: 0.89 deg: 5 c5: 110 c0: 61 m: 100000000000000000000000000000 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 algebraic special-q in [100000, 1500001) Primes: RFBsize:183072, AFBsize:183928, largePrimes:6812996 encountered Relations: rels:6186693, finalFF:411405 Max relations in full relation-set: 48 Initial matrix: 367067 x 411405 with sparse part having weight 33106963. Pruned matrix : 334890 x 336789 with weight 21893831. Total sieving time: 7.91 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.80 hours. Total square root time: 0.09 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,147,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 8.95 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(11·10¹⁴⁴+61)/9 = 1(2)₁₄₃9_<145> = C145
C145 = P45 · P100
P45 = 611795764847397761032073514896073448555427693_<45>
P100 = 1997761822570127057468384244424067756878599815628503448366355433606752749308486975935581518284356553_<100>

Number: n N=1222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 ( 145 digits) SNFS difficulty: 146 digits. Divisors found: r1=611795764847397761032073514896073448555427693 (pp45) r2=1997761822570127057468384244424067756878599815628503448366355433606752749308486975935581518284356553 (pp100) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 12.91 hours. Scaled time: 16.84 units (timescale=1.305). Factorization parameters were as follows: name: KA_1_2_143_9 n: 1222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222229 skew: 2.23 deg: 5 c5: 11 c0: 610 m: 100000000000000000000000000000 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, 1250001) Primes: RFBsize:203362, AFBsize:202469, largePrimes:6738611 encountered Relations: rels:6158473, finalFF:455293 Max relations in full relation-set: 28 Initial matrix: 405896 x 455293 with sparse part having weight 25724138. Pruned matrix : 361436 x 363529 with weight 16686234. Total sieving time: 10.51 hours. Total relation processing time: 0.21 hours. Matrix solve time: 1.88 hours. Total square root time: 0.30 hours, sqrts: 3. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2800000,2800000,28,28,48,48,2.5,2.5,100000 total time: 12.91 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
7·10¹⁶⁹+3 = 7(0)₁₆₈3_<170> = 61 · 73 · 1670391467493499_<16> · 32397946134897073854757_<23> · C129
C129 = P37 · P92
P37 = 5175216009374760485968852867656086119_<37>
P92 = 56128200837449627643617345573916608964872045642509134587009683630669439311948801876882681303_<92>
Feb 12, 2008 (4th): By Tyler Cadigan / GGNFS, Msieve
(16·10¹⁹⁰-61)/9 = 1(7)₁₈₉1_<191> = 13 · 109 · 8353 · 1219891 · 61566587 · 195452790030217399_<18> · 780043984544746420521955762987_<30> · C123
C123 = P59 · P64
P59 = 34094621548106215029203735244490780734764543703560567350309_<59>
P64 = 3847265829146448766592546059775321362358930468529413258124622339_<64>

Number: 17771_190 N=131171072439709236017541566171110987272288625359372833448549849838030010503222808824551261610337811526472955528084539952751 ( 123 digits) Divisors found: r1=34094621548106215029203735244490780734764543703560567350309 r2=3847265829146448766592546059775321362358930468529413258124622339 Version: Total time: 66.45 hours. Scaled time: 171.78 units (timescale=2.585). Factorization parameters were as follows: name: 17771_190 n: 131171072439709236017541566171110987272288625359372833448549849838030010503222808824551261610337811526472955528084539952751 skew: 47294.61 # norm 4.29e+016 c5: 61560 c4: -17874778431 c3: -663111392301151 c2: -9801637011659482709 c1: 576431364686994339439656 c0: 1878564961861044229586185155 # alpha -5.56 Y1: 20572302513413 Y0: -292219818845037446106556 # Murphy_E 2.11e-010 # M 45786454644921295568793144589561397825475712419937552306625156200432901874416142023443502841645551053254909538820787308731 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 5440001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 752592 x 752840 Polynomial selection time: 8.04 hours. Total sieving time: 58.42 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000 total time: 66.45 hours. --------- CPU info (if available) ----------
Feb 12, 2008 (3rd): By Jo Yeong Uk / GMP-ECM
(11·10¹⁶⁰+61)/9 = 1(2)₁₅₉9_<161> = 7 · 316317381526758701_<18> · C142
C142 = P34 · P109
P34 = 1483611984731557267694074530155063_<34>
P109 = 3720563711585825353249049668598930117813079072610125563407773914202785970215359546760420442923601907083314569_<109>
Feb 12, 2008 (2nd): By Sinkiti Sibata / GGNFS
(11·10¹¹³+61)/9 = 1(2)₁₁₂9_<114> = 3³ · 32797 · C108
C108 = P53 · P55
P53 = 89185329511743931743340432259475771218472031894737047_<53>
P55 = 1547600532511926130818633628615142423602309348889997853_<55>

Number: 12229_113 N=138023263444626509676497310867663169533598061952620126978892855175577511292498774416158458736878849829560091 ( 108 digits) SNFS difficulty: 114 digits. Divisors found: r1=89185329511743931743340432259475771218472031894737047 (pp53) r2=1547600532511926130818633628615142423602309348889997853 (pp55) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.44 hours. Scaled time: 1.65 units (timescale=0.676). Factorization parameters were as follows: name:12229_113 n: 138023263444626509676497310867663169533598061952620126978892855175577511292498774416158458736878849829560091 m: 10000000000000000000000 c5: 11000 c0: 61 skew: 0.35 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:63930, largePrimes:2203646 encountered Relations: rels:2410372, finalFF:336430 Max relations in full relation-set: 28 Initial matrix: 113095 x 336430 with sparse part having weight 29283357. Pruned matrix : 73057 x 73686 with weight 5021225. Total sieving time: 2.24 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,114,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 2.44 hours. --------- CPU info (if available) ----------
(11·10¹¹⁵+61)/9 = 1(2)₁₁₄9_<116> = 223 · 617 · C110
C110 = P34 · P77
P34 = 7212822845172862724558959691868961_<34>
P77 = 12315580379654942378938247217218906466558770709724027914022290754605779304179_<77>

Number: 12229_115 N=88830099513937846386916456906499859890706675743487744272679333838857354203561440953421533546687081438627688019 ( 110 digits) SNFS difficulty: 116 digits. Divisors found: r1=7212822845172862724558959691868961 (pp34) r2=12315580379654942378938247217218906466558770709724027914022290754605779304179 (pp77) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 1.61 hours. Scaled time: 1.09 units (timescale=0.675). Factorization parameters were as follows: name: 12229_115 n: 88830099513937846386916456906499859890706675743487744272679333838857354203561440953421533546687081438627688019 m: 100000000000000000000000 c5: 11 c0: 61 skew: 1.41 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, 500001) Primes: RFBsize:49098, AFBsize:64130, largePrimes:1981292 encountered Relations: rels:1990054, finalFF:180327 Max relations in full relation-set: 28 Initial matrix: 113295 x 180327 with sparse part having weight 13872256. Pruned matrix : 90740 x 91370 with weight 4669829. Total sieving time: 1.41 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.11 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: 1.61 hours. --------- CPU info (if available) ----------
(11·10¹³⁵+61)/9 = 1(2)₁₃₄9_<136> = 449 · C133
C133 = P41 · P92
P41 = 44733788040439743106075919870152803049769_<41>
P92 = 60851061573677909538404481871209053051577251320251971454994510548611542213319025413140789709_<92>

Number: 12229_135 N=2722098490472655283345706508290027220984904726552833457065082900272209849047265528334570650829002722098490472655283345706508290027221 ( 133 digits) SNFS difficulty: 136 digits. Divisors found: r1=44733788040439743106075919870152803049769 (pp41) r2=60851061573677909538404481871209053051577251320251971454994510548611542213319025413140789709 (pp92) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 8.34 hours. Scaled time: 5.63 units (timescale=0.675). Factorization parameters were as follows: name: 12229_135 n: 2722098490472655283345706508290027220984904726552833457065082900272209849047265528334570650829002722098490472655283345706508290027221 m: 1000000000000000000000000000 c5: 11 c0: 61 skew: 1.41 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:64130, largePrimes:1529572 encountered Relations: rels:1534791, finalFF:178563 Max relations in full relation-set: 28 Initial matrix: 142695 x 178563 with sparse part having weight 14130024. Pruned matrix : 131056 x 131833 with weight 8673274. Total sieving time: 7.84 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.35 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 8.34 hours. --------- CPU info (if available) ----------
Feb 12, 2008: By Robert Backstrom / GMP-ECM, Msieve, GGNFS
(11·10¹¹²+61)/9 = 1(2)₁₁₁9_<113> = 7 · 22171 · 289088113781_<12> · C96
C96 = P41 · P56
P41 = 23364777919548735601339497408589195152559_<41>
P56 = 11659366680299595782072792886752985694167830402696085083_<56>
(11·10¹⁰⁷+61)/9 = 1(2)₁₀₆9_<108> = 3 · 43 · 967491665150369_<15> · C90
C90 = P43 · P48
P43 = 8254078063236444636671476566658758452630059_<43>
P48 = 118643694302743846510055142733530124877331720031_<48>

Tue Feb 12 09:14:45 2008 Tue Feb 12 09:14:45 2008 Tue Feb 12 09:14:45 2008 Msieve v. 1.33 Tue Feb 12 09:14:45 2008 random seeds: fbd5dde8 054b1945 Tue Feb 12 09:14:45 2008 factoring 979294314485608729379659265652592455768584086435122697907223765060392284274205698203011829 (90 digits) Tue Feb 12 09:14:46 2008 searching for 15-digit factors Tue Feb 12 09:14:46 2008 commencing quadratic sieve (90-digit input) Tue Feb 12 09:14:46 2008 using multiplier of 5 Tue Feb 12 09:14:46 2008 using 64kb Opteron sieve core Tue Feb 12 09:14:46 2008 sieve interval: 18 blocks of size 65536 Tue Feb 12 09:14:46 2008 processing polynomials in batches of 6 Tue Feb 12 09:14:46 2008 using a sieve bound of 1616231 (61176 primes) Tue Feb 12 09:14:46 2008 using large prime bound of 135763404 (27 bits) Tue Feb 12 09:14:46 2008 using double large prime bound of 435520718464356 (42-49 bits) Tue Feb 12 09:14:46 2008 using trial factoring cutoff of 49 bits Tue Feb 12 09:14:46 2008 polynomial 'A' values have 12 factors Tue Feb 12 10:14:53 2008 61405 relations (16554 full + 44851 combined from 665810 partial), need 61272 Tue Feb 12 10:14:53 2008 begin with 682363 relations Tue Feb 12 10:14:54 2008 reduce to 149843 relations in 12 passes Tue Feb 12 10:14:54 2008 attempting to read 149843 relations Tue Feb 12 10:14:55 2008 recovered 149843 relations Tue Feb 12 10:14:55 2008 recovered 130637 polynomials Tue Feb 12 10:14:55 2008 attempting to build 61405 cycles Tue Feb 12 10:14:55 2008 found 61405 cycles in 6 passes Tue Feb 12 10:14:56 2008 distribution of cycle lengths: Tue Feb 12 10:14:56 2008 length 1 : 16554 Tue Feb 12 10:14:56 2008 length 2 : 11742 Tue Feb 12 10:14:56 2008 length 3 : 10834 Tue Feb 12 10:14:56 2008 length 4 : 8104 Tue Feb 12 10:14:56 2008 length 5 : 5795 Tue Feb 12 10:14:56 2008 length 6 : 3613 Tue Feb 12 10:14:56 2008 length 7 : 2201 Tue Feb 12 10:14:56 2008 length 9+: 2562 Tue Feb 12 10:14:56 2008 largest cycle: 21 relations Tue Feb 12 10:14:56 2008 matrix is 61176 x 61405 (15.1 MB) with weight 3715538 (60.51/col) Tue Feb 12 10:14:56 2008 sparse part has weight 3715538 (60.51/col) Tue Feb 12 10:14:56 2008 filtering completed in 3 passes Tue Feb 12 10:14:56 2008 matrix is 57197 x 57261 (14.2 MB) with weight 3488523 (60.92/col) Tue Feb 12 10:14:56 2008 sparse part has weight 3488523 (60.92/col) Tue Feb 12 10:14:57 2008 saving the first 48 matrix rows for later Tue Feb 12 10:14:57 2008 matrix is 57149 x 57261 (9.3 MB) with weight 2781100 (48.57/col) Tue Feb 12 10:14:57 2008 sparse part has weight 2101395 (36.70/col) Tue Feb 12 10:14:57 2008 matrix includes 64 packed rows Tue Feb 12 10:14:57 2008 using block size 22904 for processor cache size 1024 kB Tue Feb 12 10:14:57 2008 commencing Lanczos iteration Tue Feb 12 10:14:57 2008 memory use: 8.9 MB Tue Feb 12 10:15:16 2008 lanczos halted after 905 iterations (dim = 57147) Tue Feb 12 10:15:16 2008 recovered 16 nontrivial dependencies Tue Feb 12 10:15:16 2008 prp43 factor: 8254078063236444636671476566658758452630059 Tue Feb 12 10:15:16 2008 prp48 factor: 118643694302743846510055142733530124877331720031 Tue Feb 12 10:15:16 2008 elapsed time 01:00:31
(11·10¹²³+61)/9 = 1(2)₁₂₂9_<124> = 70607 · 133813186965299890511_<21> · C99
C99 = P47 · P53
P47 = 10137105138517733202360425644260487744453606741_<47>
P53 = 12761142295089496212129634669299067935927677632288097_<53>

Number: n N=129361041132907711288024614211894650311321702762232554416003033514132326809107206608063968053261877 ( 99 digits) SNFS difficulty: 124 digits. Divisors found: Tue Feb 12 11:48:55 2008 prp47 factor: 10137105138517733202360425644260487744453606741 Tue Feb 12 11:48:55 2008 prp53 factor: 12761142295089496212129634669299067935927677632288097 Tue Feb 12 11:48:55 2008 elapsed time 00:09:53 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 2.11 hours. Scaled time: 1.77 units (timescale=0.838). Factorization parameters were as follows: name: KA_1_2_122_9 n: 129361041132907711288024614211894650311321702762232554416003033514132326809107206608063968053261877 type: snfs deg: 5 c5: 11000 c0: 61 skew: 0.24 m: 1000000000000000000000000 rlim: 700000 alim: 700000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved special-q in [100000, 350001) Primes: RFBsize:56543, AFBsize:56425, largePrimes:2054212 encountered Relations: rels:2103983, finalFF:203790 Max relations in full relation-set: 28 Initial matrix: 113035 x 203790 with sparse part having weight 17909229. Pruned matrix : Total sieving time: 2.05 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,124,5,0,0,0,0,0,0,0,0,700000,700000,25,25,46,46,2.5,2.5,50000 total time: 2.11 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
(11·10¹¹⁹+61)/9 = 1(2)₁₁₈9_<120> = 3 · 761 · 457061314137360899_<18> · C99
C99 = P42 · P57
P42 = 297331187884013676219113574010340108544431_<42>
P57 = 393939323086765551889841121296691017236081365848804304827_<57>

Tue Feb 12 15:42:39 2008 Tue Feb 12 15:42:39 2008 Tue Feb 12 15:42:39 2008 Msieve v. 1.33 Tue Feb 12 15:42:39 2008 random seeds: ac273248 99b8daf8 Tue Feb 12 15:42:39 2008 factoring 117130446887612254743317289337618603555793615683610795182304459859203598933750583971206477797268437 (99 digits) Tue Feb 12 15:42:40 2008 searching for 15-digit factors Tue Feb 12 15:42:41 2008 commencing quadratic sieve (99-digit input) Tue Feb 12 15:42:41 2008 using multiplier of 1 Tue Feb 12 15:42:41 2008 using 64kb Opteron sieve core Tue Feb 12 15:42:41 2008 sieve interval: 18 blocks of size 65536 Tue Feb 12 15:42:41 2008 processing polynomials in batches of 6 Tue Feb 12 15:42:41 2008 using a sieve bound of 2542919 (92845 primes) Tue Feb 12 15:42:41 2008 using large prime bound of 381437850 (28 bits) Tue Feb 12 15:42:41 2008 using double large prime bound of 2796164870269350 (43-52 bits) Tue Feb 12 15:42:41 2008 using trial factoring cutoff of 52 bits Tue Feb 12 15:42:41 2008 polynomial 'A' values have 13 factors Wed Feb 13 00:08:09 2008 93124 relations (21863 full + 71261 combined from 1412845 partial), need 92941 Wed Feb 13 00:08:11 2008 begin with 1434707 relations Wed Feb 13 00:08:12 2008 reduce to 247553 relations in 11 passes Wed Feb 13 00:08:12 2008 attempting to read 247553 relations Wed Feb 13 00:08:16 2008 recovered 247553 relations Wed Feb 13 00:08:16 2008 recovered 237150 polynomials Wed Feb 13 00:08:16 2008 attempting to build 93124 cycles Wed Feb 13 00:08:16 2008 found 93123 cycles in 5 passes Wed Feb 13 00:08:17 2008 distribution of cycle lengths: Wed Feb 13 00:08:17 2008 length 1 : 21863 Wed Feb 13 00:08:17 2008 length 2 : 15753 Wed Feb 13 00:08:17 2008 length 3 : 15456 Wed Feb 13 00:08:17 2008 length 4 : 12692 Wed Feb 13 00:08:17 2008 length 5 : 9820 Wed Feb 13 00:08:17 2008 length 6 : 6695 Wed Feb 13 00:08:17 2008 length 7 : 4456 Wed Feb 13 00:08:17 2008 length 9+: 6388 Wed Feb 13 00:08:17 2008 largest cycle: 21 relations Wed Feb 13 00:08:18 2008 matrix is 92845 x 93123 (25.1 MB) with weight 6203991 (66.62/col) Wed Feb 13 00:08:18 2008 sparse part has weight 6203991 (66.62/col) Wed Feb 13 00:08:20 2008 filtering completed in 3 passes Wed Feb 13 00:08:20 2008 matrix is 89183 x 89247 (24.1 MB) with weight 5972500 (66.92/col) Wed Feb 13 00:08:20 2008 sparse part has weight 5972500 (66.92/col) Wed Feb 13 00:08:21 2008 saving the first 48 matrix rows for later Wed Feb 13 00:08:21 2008 matrix is 89135 x 89247 (14.6 MB) with weight 4655973 (52.17/col) Wed Feb 13 00:08:21 2008 sparse part has weight 3297383 (36.95/col) Wed Feb 13 00:08:21 2008 matrix includes 64 packed rows Wed Feb 13 00:08:21 2008 using block size 21845 for processor cache size 512 kB Wed Feb 13 00:08:22 2008 commencing Lanczos iteration Wed Feb 13 00:08:22 2008 memory use: 14.5 MB Wed Feb 13 00:09:40 2008 lanczos halted after 1411 iterations (dim = 89133) Wed Feb 13 00:09:40 2008 recovered 15 nontrivial dependencies Wed Feb 13 00:09:41 2008 prp42 factor: 297331187884013676219113574010340108544431 Wed Feb 13 00:09:41 2008 prp57 factor: 393939323086765551889841121296691017236081365848804304827 Wed Feb 13 00:09:41 2008 elapsed time 08:27:02
Feb 11, 2008 (4th): By Robert Backstrom / GMP-ECM
(11·10¹³⁴+61)/9 = 1(2)₁₃₃9_<135> = 3 · 887 · 35863 · 6443166705211_<13> · 5420992073158442273512673551_<28> · C86
C86 = P29 · P57
P29 = 72262687717088370908767938209_<29>
P57 = 507418660021790002190944224034674082883979558173581771547_<57>
(11·10¹¹⁷+61)/9 = 1(2)₁₁₆9_<118> = 199 · 6247 · 1710937 · 158006612980033_<15> · C91
C91 = P33 · P59
P33 = 263003561317130722985502794515043_<33>
P59 = 13827850710715765070628800684573938236616215726252446506831_<59>
(11·10¹⁰⁹+61)/9 = 1(2)₁₀₈9_<110> = 19 · 23 · 19389658353125041_<17> · C91
C91 = P32 · P59
P32 = 25963864742768432702463389177291_<32>
P59 = 55555779286126867906535634003991867240948718030556740625907_<59>
(11·10¹⁴⁷+61)/9 = 1(2)₁₄₆9_<148> = 227 · 50647 · 32830739197093_<14> · 3144183907883242907077468873230638509_<37> · C91
C91 = P35 · P56
P35 = 48362529052411789499072324359991381_<35>
P56 = 21294771654514384272421899428463822955945910176527190253_<56>
Feb 11, 2008 (3rd): By Sinkiti Sibata / GGNFS
(11·10¹⁶⁶+7)/9 = 1(2)₁₆₅3_<167> = 32443 · 121369 · 67617421 · C149
C149 = P42 · P108
P42 = 101989684325869449705527286805060691736463_<42>
P108 = 450097442915430795779994542402496558803504752094572069564062884789059603979985386323743477433742726962278103_<108>

Number: 12223_166 N=45905296118825831622186591617833147208955244311512453516285503045623177834727084405817833581225020542229541491682063403005260492580868462169391569689 ( 149 digits) SNFS difficulty: 167 digits. Divisors found: r1=101989684325869449705527286805060691736463 (pp42) r2=450097442915430795779994542402496558803504752094572069564062884789059603979985386323743477433742726962278103 (pp108) Version: GGNFS-0.77.1-20060513-k8 Total time: 143.84 hours. Scaled time: 286.53 units (timescale=1.992). Factorization parameters were as follows: name: 12223_166 n: 45905296118825831622186591617833147208955244311512453516285503045623177834727084405817833581225020542229541491682063403005260492580868462169391569689 m: 1000000000000000000000000000000000 c5: 110 c0: 7 skew: 0.58 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, 7050001) Primes: RFBsize:380800, AFBsize:381423, largePrimes:6105750 encountered Relations: rels:6346470, finalFF:883846 Max relations in full relation-set: 28 Initial matrix: 762290 x 883846 with sparse part having weight 64492068. Pruned matrix : 667219 x 671094 with weight 48020573. Total sieving time: 137.22 hours. Total relation processing time: 0.36 hours. Matrix solve time: 5.98 hours. Time per square root: 0.28 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: 143.84 hours. --------- CPU info (if available) ----------
Feb 11, 2008 (2nd): By Robert Backstrom / GMP-ECM, Msieve
9·10¹⁶⁸-7 = 8(9)₁₆₇3_<169> = 11369 · 646974011 · 57572701889099_<14> · 5558386317692349989_<19> · C124
C124 = P44 · P80
P44 = 49210457799346902131698308801292711620150749_<44>
P80 = 77698147296321048398209905863232249781232086869460260825621557916054516169171993_<80>
(43·10¹⁶⁹-7)/9 = 4(7)₁₆₉_<170> = 367 · 4950421240482181291_<19> · 2775699859016352530477357_<25> · C124
C124 = P34 · P91
P34 = 3156831836580797731306525780758247_<34>
P91 = 3001191966934602598099805375944976471798484695463390773319663402408270737672035770264235879_<91>
(88·10¹⁷⁴-7)/9 = 9(7)₁₇₄_<175> = 3 · 17 · 95379796597_<11> · 54666930292056143_<17> · 511970441008370800237_<21> · C125
C125 = P30 · P30 · P33 · P34
P30 = 173757058143498816926924955673_<30>
P30 = 465925434517972487069313694967_<30>
P33 = 412578114115540514069896286025893_<33>
P34 = 2150200504074416197658991311110927_<34>
4·10¹⁷³+9 = 4(0)₁₇₂9_<174> = 241 · 2609 · 49277 · 37490161253921_<14> · 817315416761140501205161_<24> · C126
C126 = P39 · P88
P39 = 192750975747012200555324918025716343881_<39>
P88 = 2185853367735352411488999932909611191071596551799121040574783002059359617054726183998413_<88>
(5·10¹⁶⁹-23)/9 = (5)₁₆₈3_<169> = 3 · 6774331 · 306184391 · 557012815014644105825820881_<27> · C127
C127 = P31 · P35 · P62
P31 = 2087471764369186746744924457169_<31>
P35 = 76293479821546473110280044511336659_<35>
P62 = 10064299668743025389207488369674286100888124822116938935677981_<62>
(13·10¹⁷⁵-1)/3 = 4(3)₁₇₅_<176> = 53 · 1006333 · 5346101863_<10> · 77007123278857_<14> · 204401323997546371_<18> · C127
C127 = P32 · P96
P32 = 28651730387084497770902398579711_<32>
P96 = 336978213701637697571422651263830961732419798315444065386385634383590453793058262972127890968327_<96>
4·10¹⁷⁶+3 = 4(0)₁₇₅3_<177> = 13² · 14479 · 1727839 · 30175961085952909008534878737421283007_<38> · C127
C127 = P34 · P93
P34 = 3661730251935283360279392267311779_<34>
P93 = 856217277330621580192849824402420828954681540263284216581477838361242201893253167019116379159_<93>
Feb 11, 2008: The factor table of 122...229 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.
Feb 10, 2008 (3rd): By Tyler Cadigan / GGNFS, Msieve
(64·10¹⁸¹-1)/9 = 7(1)₁₈₁_<182> = 2027 · 4241 · 706523 · 1094470049_<10> · C161
C161 = P72 · P89
P72 = 902771192272967778558243776478070514120292619368690645567010419017401517_<72>
P89 = 11849705735852950447627236292576531232583382440257054318850407174201209353635326074829147_<89>

Number: 71111_181 N=10697572975239793063606032978084292467067822049528412583082347469153753461107302080860461265886162919093566187463970134567420022290339189108159132374275673615999 ( 161 digits) SNFS difficulty: 182 digits. Divisors found: r1=902771192272967778558243776478070514120292619368690645567010419017401517 r2=11849705735852950447627236292576531232583382440257054318850407174201209353635326074829147 Version: Total time: 306.07 hours. Scaled time: 790.28 units (timescale=2.582). Factorization parameters were as follows: n: 10697572975239793063606032978084292467067822049528412583082347469153753461107302080860461265886162919093566187463970134567420022290339189108159132374275673615999 m: 2000000000000000000000000000000000000 c5: 20 c4: 0 c3: 0 c2: 0 c1: 0 c0: -1 skew: 0.55 type: snfs Y1: 1 Y0: -2000000000000000000000000000000000000 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 8900001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 860542 x 860790 Total sieving time: 306.07 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,182,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 306.07 hours. --------- CPU info (if available) ----------
Feb 10, 2008 (2nd): By JMB / GMP-ECM
(2·10¹⁷⁴+61)/9 = (2)₁₇₃9_<174> = 7 · 31 · 2039 · 2287 · 1601389 · 1020612252807407600156466188953_<31> · C127
C127 = P31 · P97
P31 = 1020612252807407600156466188953_<31>
P97 = 9267549867506020078240059593658577219817808702660486443916526167862619471929169641286722869220679_<97>
(2·10¹⁷⁸+61)/9 = (2)₁₇₇9_<178> = 3 · 2027 · 20297 · 2066378869_<10> · 3247837269569_<13> · C148
C148 = P27 · C122
P27 = 163433233996276243474084319_<27>
C122 = [16414816924183620628070288142730847259538958407278070871366182577042951560674699400450759287353464473072300307093265371783_<122>]
Feb 10, 2008: By Robert Backstrom / GMP-ECM, Msieve
(43·10¹⁶⁷-7)/9 = 4(7)₁₆₇_<168> = 3 · 113 · 491 · 993431 · 3245863392116255245078685507_<28> · C129
C129 = P29 · P101
P29 = 27530433290624738915011972223_<29>
P101 = 32334322329331329096070235876248176740375231051072784305900774570153124823803731961300200455222281203_<101>
5·10¹⁶⁸-3 = 4(9)₁₆₇7_<169> = 2957 · 5297 · 38287 · 66179 · 1421954227_<10> · 1694194073272983839_<19> · C125
C125 = P34 · P91
P34 = 8731823085626565428330649512690831_<34>
P91 = 5989126214432165607435098739078535035401301616100708973660232195133893598575906722810990487_<91>
2·10¹⁶⁷-3 = 1(9)₁₆₆7_<168> = 7 · 77550151291532631003351523_<26> · C141
C141 = P37 · P105
P37 = 1416288347210403639057173330195587867_<37>
P105 = 260134302671767920102022631505867541342722247157905131978577734973578865145671722044817281277952599937931_<105>
(82·10¹⁶⁹-1)/9 = 9(1)₁₆₉_<170> = 7 · 13 · 1193432857_<10> · 478477940789_<12> · 17915037325037174830484621_<26> · C122
C122 = P32 · P91
P32 = 32484371140271987256060780720151_<32>
P91 = 3012852418652154785011905762729241593097128731869132200674495589633594003211540806300169387_<91>
9·10¹⁷³-7 = 8(9)₁₇₂3_<174> = 317 · 31815104256736732410487_<23> · 1143831950766122847147685783_<28> · C122
C122 = P35 · P88
P35 = 32933203402548031161720747926069273_<35>
P88 = 2368938010738226751172660755825073523676287922290421869222162020029734816560986221793413_<88>
(10¹⁷³+71)/9 = (1)₁₇₂9_<173> = 23² · 107 · 424722629 · 3163656490366535907132680457817794161_<37> · C123
C123 = P36 · P40 · P47
P36 = 187679214118451681266132692899356843_<36>
P40 = 9195777497317241672839400152874797906417_<40>
P47 = 84648387182546183617852698023055943681186500107_<47>
Feb 9, 2008 (2nd): By JMB / GMP-ECM
(2·10¹⁶⁸+61)/9 = (2)₁₆₇9_<168> = 7 · 14455081350043_<14> · C154
C154 = P39 · P116
P39 = 124665318009842949761185556866477754527_<39>
P116 = 17616647193806251861229772487131487378494707726207548488604765361306707918929630500734870981346369090407284002821927_<116>
(2·10¹⁶⁹+61)/9 = (2)₁₆₈9_<169> = 3 · 397 · 2174019307913_<13> · C153
C153 = P33 · P121
P33 = 155563984348954661900854974395441_<33>
P121 = 5517003634007995443119710663047195342439310806021769462472359559639148189247375617671640931735072033807669397978259390843_<121>
Feb 9, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(28·10¹⁶⁶+17)/9 = 3(1)₁₆₅3_<167> = 3² · 3098612050986082314588917513_<28> · C139
C139 = P35 · P104
P35 = 15690324817273401715948623986515369_<35>
P104 = 71100699358036734069101432325185455650755867126782812613471077612512751318328514905837455085857243459281_<104>
7·10¹⁶⁷+1 = 7(0)₁₆₆1_<168> = 94126111912362384454419640507_<29> · C139
C139 = P35 · P105
P35 = 45944168788570289296719424358942927_<35>
P105 = 161866703314530544206931137643404221120769747950795429104385791774237543764981165611916824698958062426909_<105>
8·10¹⁶⁷-9 = 7(9)₁₆₆1_<168> = 2371 · 3152099 · 68098319 · 39805790809_<11> · C140
C140 = P33 · P108
P33 = 328122692405400099376586451015551_<33>
P108 = 120348219501465859000916415860703533989146155732677824787903392809000729377628019185401396804542816303837799_<108>
(46·10¹⁹⁹-1)/9 = 5(1)₁₉₉_<200> = 3 · 55921 · 341701 · 476351 · 614051 · 58174269328757521_<17> · 582857153092184281963_<21> · C140
C140 = P33 · P108
P33 = 152159122038178839896993789376937_<33>
P108 = 590813353794208480835899546789264311537044346698701181714273385252084401898654909485599983690398143316984447_<108>
(34·10¹⁶⁶-43)/9 = 3(7)₁₆₅3_<167> = 3³ · 334306839006823133579471153_<27> · C139
C139 = P31 · P48 · P61
P31 = 6442347110462974423706047241203_<31>
P48 = 482409865451456968711095592247299291866460859567_<48>
P61 = 1346688281084137187308096903842451133318456201425034896421683_<61>

Number: n N=649655712482852483347779169077738335847188574070186547360431816947990739875046547488854069593255264676791261 ( 108 digits) Divisors found: Sat Feb 9 22:44:45 2008 prp48 factor: 482409865451456968711095592247299291866460859567 Sat Feb 9 22:44:45 2008 prp61 factor: 1346688281084137187308096903842451133318456201425034896421683 Sat Feb 9 22:44:45 2008 elapsed time 00:20:13 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 7.97 hours. Scaled time: 6.67 units (timescale=0.837). Factorization parameters were as follows: name: n n: 649655712482852483347779169077738335847188574070186547360431816947990739875046547488854069593255264676791261 skew: 14944.95 # norm 2.97e+15 c5: 485280 c4: -211392396 c3: -172714567923928 c2: -549425193124079357 c1: -877342288911281723800 c0: 100702957185654776225441700 # alpha -8.28 Y1: 195526208023 Y0: -266279787393641041081 # Murphy_E 1.54e-09 # M 53391717093376356172982235894071299555959712989798205258165735547349383107399703860337342131677000333041742 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, 1150651) Primes: RFBsize:183072, AFBsize:183595, largePrimes:4066133 encountered Relations: rels:3988898, finalFF:410603 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 7.83 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 7.97 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6029.31 BogoMIPS (lpj=3014656) Total of 2 processors activated (11993.08 BogoMIPS).
Feb 8, 2008 (3rd): By matsui / GGNFS
4·10¹⁷⁵+1 = 4(0)₁₇₄1_<176> = 16811 · C172
C172 = P47 · P51 · P75
P47 = 33374333358396914109100082498630504183786129383_<47>
P51 = 105371111708302205780401868932937382113312422601077_<51>
P75 = 676600448832315856534571187702619060715236193076202145589311912099919790801_<75>

N=2379394444113972993873059306406519540776872286003212182499553863541728630063648801380048777586104336446374397715781333650585925881863065849741240854202605436916304800428291 ( 172 digits) SNFS difficulty: 175 digits. Divisors found: r1=33374333358396914109100082498630504183786129383 (pp47) r2=105371111708302205780401868932937382113312422601077 (pp51) r3=676600448832315856534571187702619060715236193076202145589311912099919790801 (pp75) Version: GGNFS-0.77.1-20060513-prescott Total time: 193.78 hours. Scaled time: 329.61 units (timescale=1.701). Factorization parameters were as follows: n: 2379394444113972993873059306406519540776872286003212182499553863541728630063648801380048777586104336446374397715781333650585925881863065849741240854202605436916304800428291 m: 100000000000000000000000000000000000 c5: 4 c0: 1 skew: 0.76 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10400001) Primes: RFBsize:501962, AFBsize:501936, large Primes:6393125 encountered Relations: rels:6843406, finalFF:1132531 Max relations in full relation-set: 28 Initial matrix: 1003962 x 1132531 with sparse part having weight 66657298. Pruned matrix : 892499 x 897582 with weight 50296953. Total sieving time: 176.54 hours. Total relation processing time: 0.16 hours. Matrix solve time: 16.83 hours. Time per square root: 0.25 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 193.78 hours.
Feb 8, 2008 (2nd): By Sinkiti Sibata / GGNFS
(11·10¹⁶¹+7)/9 = 1(2)₁₆₀3_<162> = 3² · 23 · 409 · 10077835316092177735308344255341_<32> · C126
C126 = P39 · P87
P39 = 260689377498163087443735013320304256953_<39>
P87 = 549497764648131597130953367858390114380546441669938042117834896217907773886247268939477_<87>

Number: 12223_161 N=143248230202753553250627324007667704007774209136426780649557690599037990179649906991462317956463890376489091431485736813433581 ( 126 digits) SNFS difficulty: 162 digits. Divisors found: r1=260689377498163087443735013320304256953 (pp39) r2=549497764648131597130953367858390114380546441669938042117834896217907773886247268939477 (pp87) Version: GGNFS-0.77.1-20060513-k8 Total time: 78.87 hours. Scaled time: 157.58 units (timescale=1.998). Factorization parameters were as follows: name: 12223_161 n: 143248230202753553250627324007667704007774209136426780649557690599037990179649906991462317956463890376489091431485736813433581 m: 100000000000000000000000000000000 c5: 110 c0: 7 skew: 0.58 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, 4750001) Primes: RFBsize:315948, AFBsize:316567, largePrimes:5881541 encountered Relations: rels:6019866, finalFF:761148 Max relations in full relation-set: 28 Initial matrix: 632582 x 761148 with sparse part having weight 52817466. Pruned matrix : 536094 x 539320 with weight 37129453. Total sieving time: 74.82 hours. Total relation processing time: 0.30 hours. Matrix solve time: 3.51 hours. Time per square root: 0.24 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: 78.87 hours. --------- CPU info (if available) ----------
(11·10¹⁵⁹+7)/9 = 1(2)₁₅₈3_<160> = 19 · 1574569 · 140094047 · 1752430422887_<13> · 3867814284039329713_<19> · C113
C113 = P51 · P63
P51 = 411917824030997137139094198484004214186454078374563_<51>
P63 = 104447539825442495437964036453728510925486296174666075535780023_<63>

Number: 12223_159 N=43023803330287187273746316838635004481199686462719115124977818948619389370183740498431606534990591450192166754949 ( 113 digits) SNFS difficulty: 161 digits. Divisors found: r1=411917824030997137139094198484004214186454078374563 (pp51) r2=104447539825442495437964036453728510925486296174666075535780023 (pp63) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 82.36 hours. Scaled time: 55.59 units (timescale=0.675). Factorization parameters were as follows: name: 12223_159 n: 43023803330287187273746316838635004481199686462719115124977818948619389370183740498431606534990591450192166754949 m: 100000000000000000000000000000000 c5: 11 c0: 70 skew: 1.45 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:282983, largePrimes:5738850 encountered Relations: rels:5793505, finalFF:674155 Max relations in full relation-set: 28 Initial matrix: 566194 x 674155 with sparse part having weight 43837589. Pruned matrix : 489774 x 492668 with weight 30368801. Total sieving time: 71.12 hours. Total relation processing time: 0.32 hours. Matrix solve time: 10.68 hours. Time per square root: 0.23 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: 82.36 hours. --------- CPU info (if available) ----------
Feb 7, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(2·10¹⁶⁷+61)/9 = (2)₁₆₆9_<167> = 2111 · 1832969 · 283308492690325304249221_<24> · C134
C134 = P37 · P97
P37 = 5293786095595604399312089576073126581_<37>
P97 = 3829289055393909099323406022568046034410055633038604578659954318885645966267504426432067768012731_<97>
3·10¹⁶⁷+7 = 3(0)₁₆₆7_<168> = 73 · 2820908683_<10> · 47840528956935069857729_<23> · C134
C134 = P40 · P95
P40 = 1357442863346680718028321638854705863851_<40>
P95 = 22433231368448594492739585313305402233259675370737675880559365524717784659590253895181940293287_<95>
9·10¹⁹⁶-7 = 8(9)₁₉₅3_<197> = 731413 · 15089069 · 101668669 · 13688355513133121_<17> · 20476877778258297685878989_<26> · C135
C135 = P32 · P104
P32 = 23222917624869682986808856353387_<32>
P104 = 12322489474660531695741954992123566822217378113251020935855509359836204616518712285683147287205008714067_<104>
(11·10¹⁶⁷+43)/9 = 1(2)₁₆₆7_<168> = 7² · 19 · C165
C165 = P75 · P90
P75 = 541971448192550699513304798616393006342507476379452171739705124200789773013_<75>
P90 = 242227856921645093713988883275176251092372232052137498460161900833598670237188488521812109_<90>

Number: n N=131280582408401957274137725265544814416994868122687671559852010979830528702709153836973385845566296694116242988423439551259100131280582408401957274137725265544814417 ( 165 digits) SNFS difficulty: 168 digits. Divisors found: Thu Feb 07 23:20:45 2008 prp75 factor: 541971448192550699513304798616393006342507476379452171739705124200789773013 Thu Feb 07 23:20:45 2008 prp90 factor: 242227856921645093713988883275176251092372232052137498460161900833598670237188488521812109 Thu Feb 07 23:20:45 2008 elapsed time 01:25:46 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 74.38 hours. Scaled time: 136.04 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_2_166_7 n: 131280582408401957274137725265544814416994868122687671559852010979830528702709153836973385845566296694116242988423439551259100131280582408401957274137725265544814417 skew: 0.55 deg: 5 c5: 1100 c0: 43 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, 5131969) Primes: RFBsize:250150, AFBsize:250467, largePrimes:8087111 encountered Relations: rels:7536817, finalFF:549247 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 74.14 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,168,5,0,0,0,0,0,0,0,0,3500000,3500000,28,28,48,48,2.5,2.5,100000 total time: 74.38 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(37·10¹⁹⁴-1)/9 = 4(1)₁₉₄_<195> = 3² · 137 · 937 · 1471 · 206291 · 756005167 · 3310998276737_<13> · 86160185894982385604741_<23> · C136
C136 = P33 · P104
P33 = 227665057537224694948644929138647_<33>
P104 = 23882339520004120338160997543040692573102301514832723172916776549468348272189791118195375411520469002007_<104>
Feb 6, 2008 (3rd): By Robert Backstrom / GGNFS, Msieve
3·10¹⁶⁵-1 = 2(9)₁₆₅_<166> = 17 · 563 · 10366352216620195513339_<23> · C140
C140 = P59 · P81
P59 = 32537822232223537739373298666992795881162109492993066147359_<59>
P81 = 929286216648341931114487283109312466413415118752186358498797622230367374713700369_<81>

Number: n N=30236949720159319152255112676945296055617775960741404375126742070045530650217672185324750510281942081046922358241732522840944089077526675471 ( 140 digits) SNFS difficulty: 165 digits. Divisors found: Wed Feb 06 19:22:09 2008 prp59 factor: 32537822232223537739373298666992795881162109492993066147359 Wed Feb 06 19:22:09 2008 prp81 factor: 929286216648341931114487283109312466413415118752186358498797622230367374713700369 Wed Feb 06 19:22:09 2008 elapsed time 01:17:35 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 48.16 hours. Scaled time: 63.14 units (timescale=1.311). Factorization parameters were as follows: name: KA_2_9_165 n: 30236949720159319152255112676945296055617775960741404375126742070045530650217672185324750510281942081046922358241732522840944089077526675471 skew: 0.80 deg: 5 c5: 3 c0: -1 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100001) Primes: RFBsize:230209, AFBsize:230192, largePrimes:7367519 encountered Relations: rels:6892734, finalFF:544123 Max relations in full relation-set: 28 Initial matrix: 460466 x 544123 with sparse part having weight 41822415. Pruned matrix : Total sieving time: 47.92 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,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 48.16 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
Feb 6, 2008 (2nd): By Jo Yeong Uk / GGNFS
(11·10¹⁹⁵+7)/9 = 1(2)₁₉₄3_<196> = 19 · 1381 · 2084369471_<10> · 579482349518918778349_<21> · 5743319303613011520138439_<25> · 19053471272924412355461223_<26> · C111
C111 = P52 · P59
P52 = 4691572442730948975926971646226019258011380478343997_<52>
P59 = 75116005013147098086271597306014879649488629658821732388887_<59>

Number: 12223_195 N=352412179127720740013907904143564416698937087894671770725472299693443506152847629222680315553965315424565961339 ( 111 digits) Divisors found: r1=4691572442730948975926971646226019258011380478343997 (pp52) r2=75116005013147098086271597306014879649488629658821732388887 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 20.99 hours. Scaled time: 38.89 units (timescale=1.853). Factorization parameters were as follows: name: 12223_195 n: 352412179127720740013907904143564416698937087894671770725472299693443506152847629222680315553965315424565961339 skew: 34427.94 # norm 1.21e+15 c5: 2940 c4: -1952990832 c3: -13969156205551 c2: 2547772263330774383 c1: -2753925105065485237741 c0: -55382786679887219119766175 # alpha -5.69 Y1: 32531887111 Y0: -2604602399830499331596 # Murphy_E 8.81e-10 # M 309779091830781573053660742294457742119204166492528584961833291120202055958849242113189450704981453714341382827 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, 2040001) Primes: RFBsize:176302, AFBsize:175883, largePrimes:7508048 encountered Relations: rels:7241972, finalFF:409200 Max relations in full relation-set: 28 Initial matrix: 352265 x 409200 with sparse part having weight 39556757. Pruned matrix : 313974 x 315799 with weight 27717209. Total sieving time: 20.26 hours. Total relation processing time: 0.13 hours. Matrix solve time: 0.49 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 20.99 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Feb 6, 2008: By Sinkiti Sibata / GGNFS
(11·10¹⁵⁵+7)/9 = 1(2)₁₅₄3_<156> = 3 · 1979 · 2333 · 832109 · 4940333 · 484929907573939_<15> · C121
C121 = P55 · P67
P55 = 4264116202467938770951293907576359430192576324566865877_<55>
P67 = 1038063556762454948769332965821742017541903031000047864051013665693_<67>

Number: 12223_155 N=4426423631582280997263144548425906821817226170288044990471077946959857011196243187970733067231824314700177486874047257761 ( 121 digits) SNFS difficulty: 156 digits. Divisors found: r1=4264116202467938770951293907576359430192576324566865877 (pp55) r2=1038063556762454948769332965821742017541903031000047864051013665693 (pp67) Version: GGNFS-0.77.1-20060513-k8 Total time: 27.06 hours. Scaled time: 54.16 units (timescale=2.002). Factorization parameters were as follows: name: 12223_155 n: 4426423631582280997263144548425906821817226170288044990471077946959857011196243187970733067231824314700177486874047257761 m: 10000000000000000000000000000000 c5: 11 c0: 7 skew: 0.91 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:216272, largePrimes:5579968 encountered Relations: rels:5574910, finalFF:586449 Max relations in full relation-set: 28 Initial matrix: 433153 x 586449 with sparse part having weight 43927938. Pruned matrix : 323992 x 326221 with weight 27346196. Total sieving time: 25.55 hours. Total relation processing time: 0.13 hours. Matrix solve time: 1.23 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 27.06 hours. --------- CPU info (if available) ----------
Feb 5, 2008 (3rd): By Jo Yeong Uk / GGNFS
(11·10¹⁷²+7)/9 = 1(2)₁₇₁3_<173> = 41 · 47 · 112217052089437_<15> · 98927200774175682049_<20> · 2356137621413028954776819_<25> · C111
C111 = P36 · P76
P36 = 111487462047472904549551202867568979_<36>
P76 = 2175039767542759059001773194327055783343681329625388358095052729519501204773_<76>

Number: 12223_172 N=242489663535667639241651384176198619583752763717021557825727032888978929081904591019907021815847107960181536767 ( 111 digits) Divisors found: r1=111487462047472904549551202867568979 (pp36) r2=2175039767542759059001773194327055783343681329625388358095052729519501204773 (pp76) Version: GGNFS-0.77.1-20050930-nocona Total time: 16.82 hours. Scaled time: 31.26 units (timescale=1.858). Factorization parameters were as follows: name: 12223_172 n: 242489663535667639241651384176198619583752763717021557825727032888978929081904591019907021815847107960181536767 skew: 32353.91 # norm 3.37e+15 c5: 40320 c4: -2363866290 c3: 72861550321301 c2: 4433137019570566225 c1: -78112732505301434752569 c0: -447267567058045530535974555 # alpha -6.74 Y1: 109208032219 Y0: -1431643645502336882936 # Murphy_E 9.03e-10 # M 13490647646898210578774861483495916783026841972197418764250733041946106194943433052920323966293034641219362176 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, 2040001) Primes: RFBsize:176302, AFBsize:176469, largePrimes:7677263 encountered Relations: rels:7584793, finalFF:522842 Max relations in full relation-set: 28 Initial matrix: 352854 x 522842 with sparse part having weight 54628482. Pruned matrix : 258861 x 260689 with weight 29452672. Polynomial selection time: 0.86 hours. Total sieving time: 15.33 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.39 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2400000,2400000,27,27,50,50,2.6,2.6,60000 total time: 16.82 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Feb 5, 2008 (2nd): By Sinkiti Sibata / GGNFS
(11·10¹⁵²+7)/9 = 1(2)₁₅₁3_<153> = 3² · 41 · 3209 · 1679541668501_<13> · 4449251166733119007_<19> · C116
C116 = P55 · P61
P55 = 8511935397927024191899434347488658797919067426392222579_<55>
P61 = 1622736735024800828915830534770168951277226403012313894450871_<61>

Number: 12223_152 N=13812630256374128058975491572338375909272705190772233288419791120726713032137426286286429659495567817867100412416309 ( 116 digits) SNFS difficulty: 153 digits. Divisors found: r1=8511935397927024191899434347488658797919067426392222579 (pp55) r2=1622736735024800828915830534770168951277226403012313894450871 (pp61) Version: GGNFS-0.77.1-20060513-k8 Total time: 33.22 hours. Scaled time: 66.25 units (timescale=1.994). Factorization parameters were as follows: name: 12223_152 n: 13812630256374128058975491572338375909272705190772233288419791120726713032137426286286429659495567817867100412416309 m: 1000000000000000000000000000000 c5: 1100 c0: 7 skew: 0.36 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:175784, largePrimes:5725226 encountered Relations: rels:5716673, finalFF:530496 Max relations in full relation-set: 28 Initial matrix: 352153 x 530496 with sparse part having weight 50516089. Pruned matrix : 288883 x 290707 with weight 27675748. Total sieving time: 31.64 hours. Total relation processing time: 0.15 hours. Matrix solve time: 1.29 hours. Time per square root: 0.14 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: 33.22 hours. --------- CPU info (if available) ----------
Feb 5, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(11·10¹⁶³+43)/9 = 1(2)₁₆₂7_<164> = 113 · 3451661 · 294424687 · C147
C147 = P34 · P44 · P69
P34 = 3212438113559117047787995708543127_<34>
P44 = 85399350297534323459073364282519538599251337_<44>
P69 = 387953825000560041646082303950754107610352645432704733536989058413903_<69>

Number: n N=33131004600491156047449733045194672547442039666553616380896628350782674308658517596250464372112320545716472138311 ( 113 digits) Divisors found: r1=85399350297534323459073364282519538599251337 (pp44) r2=387953825000560041646082303950754107610352645432704733536989058413903 (pp69) Version: GGNFS-0.77.1-20051202-athlon Total time: 23.43 hours. Scaled time: 42.84 units (timescale=1.828). Factorization parameters were as follows: name: KA_1_2_162_7 n: 33131004600491156047449733045194672547442039666553616380896628350782674308658517596250464372112320545716472138311 skew: 28302.88 # norm 4.59e+15 c5: 67860 c4: -3555859626 c3: -286213861045720 c2: 2436750071245123937 c1: 62076746826681929023734 c0: -171681952438916685211104945 # alpha -6.04 Y1: 1026639632953 Y0: -3449256605174613017842 # Murphy_E 7.06e-10 # M 14313394424989021120980462687781058952527077536141995833789940857339061995942088651721890218689067737197530374193 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved algebraic special-q in [100000, 1400001) Primes: RFBsize:250150, AFBsize:250126, largePrimes:9402281 encountered Relations: rels:8572818, finalFF:572608 Max relations in full relation-set: 48 Initial matrix: 500360 x 572608 with sparse part having weight 42902050. Pruned matrix : 432356 x 434921 with weight 24320488. Total sieving time: 21.70 hours. Total relation processing time: 0.25 hours. Matrix solve time: 1.33 hours. Total square root time: 0.15 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,28,28,50,50,2.6,2.6,100000 total time: 23.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(61·10¹⁸⁸-7)/9 = 6(7)₁₈₈_<189> = 761 · 14923 · 34667944967_<11> · 9342443007080306141_<19> · 8519617172494291276031_<22> · C131
C131 = P39 · P42 · P51
P39 = 824978914747918693560935356005485199233_<39>
P42 = 240133410788291625341200280280267296905327_<42>
P51 = 109179840536766784953562310705149908464858846735857_<51>

Tue Feb 05 09:17:00 2008 Tue Feb 05 09:17:00 2008 Tue Feb 05 09:17:00 2008 Msieve v. 1.33 Tue Feb 05 09:17:00 2008 random seeds: 9b5e2ca0 656e7f58 Tue Feb 05 09:17:00 2008 factoring 90071066358372683019711240485258915593667540152249648664868090325489848213660787369997681 (89 digits) Tue Feb 05 09:17:00 2008 searching for 15-digit factors Tue Feb 05 09:17:01 2008 commencing quadratic sieve (89-digit input) Tue Feb 05 09:17:01 2008 using multiplier of 1 Tue Feb 05 09:17:01 2008 using 64kb Opteron sieve core Tue Feb 05 09:17:01 2008 sieve interval: 17 blocks of size 65536 Tue Feb 05 09:17:01 2008 processing polynomials in batches of 6 Tue Feb 05 09:17:01 2008 using a sieve bound of 1555153 (59333 primes) Tue Feb 05 09:17:01 2008 using large prime bound of 124412240 (26 bits) Tue Feb 05 09:17:01 2008 using double large prime bound of 372180460082400 (42-49 bits) Tue Feb 05 09:17:01 2008 using trial factoring cutoff of 49 bits Tue Feb 05 09:17:01 2008 polynomial 'A' values have 11 factors Tue Feb 05 09:59:23 2008 59447 relations (16301 full + 43146 combined from 623387 partial), need 59429 Tue Feb 05 09:59:24 2008 begin with 639687 relations Tue Feb 05 09:59:25 2008 reduce to 143634 relations in 10 passes Tue Feb 05 09:59:25 2008 attempting to read 143634 relations Tue Feb 05 09:59:26 2008 recovered 143634 relations Tue Feb 05 09:59:26 2008 recovered 118660 polynomials Tue Feb 05 09:59:26 2008 attempting to build 59447 cycles Tue Feb 05 09:59:26 2008 found 59447 cycles in 6 passes Tue Feb 05 09:59:26 2008 distribution of cycle lengths: Tue Feb 05 09:59:26 2008 length 1 : 16301 Tue Feb 05 09:59:26 2008 length 2 : 11449 Tue Feb 05 09:59:26 2008 length 3 : 10574 Tue Feb 05 09:59:26 2008 length 4 : 7994 Tue Feb 05 09:59:26 2008 length 5 : 5383 Tue Feb 05 09:59:26 2008 length 6 : 3363 Tue Feb 05 09:59:26 2008 length 7 : 1997 Tue Feb 05 09:59:26 2008 length 9+: 2386 Tue Feb 05 09:59:26 2008 largest cycle: 17 relations Tue Feb 05 09:59:26 2008 matrix is 59333 x 59447 (14.4 MB) with weight 3545673 (59.64/col) Tue Feb 05 09:59:26 2008 sparse part has weight 3545673 (59.64/col) Tue Feb 05 09:59:27 2008 filtering completed in 3 passes Tue Feb 05 09:59:27 2008 matrix is 55126 x 55189 (13.6 MB) with weight 3334863 (60.43/col) Tue Feb 05 09:59:27 2008 sparse part has weight 3334863 (60.43/col) Tue Feb 05 09:59:27 2008 saving the first 48 matrix rows for later Tue Feb 05 09:59:27 2008 matrix is 55078 x 55189 (10.1 MB) with weight 2797379 (50.69/col) Tue Feb 05 09:59:27 2008 sparse part has weight 2327254 (42.17/col) Tue Feb 05 09:59:27 2008 matrix includes 64 packed rows Tue Feb 05 09:59:27 2008 using block size 22075 for processor cache size 1024 kB Tue Feb 05 09:59:28 2008 commencing Lanczos iteration Tue Feb 05 09:59:28 2008 memory use: 9.1 MB Tue Feb 05 09:59:47 2008 lanczos halted after 872 iterations (dim = 55078) Tue Feb 05 09:59:48 2008 recovered 17 nontrivial dependencies Tue Feb 05 09:59:49 2008 prp39 factor: 824978914747918693560935356005485199233 Tue Feb 05 09:59:49 2008 prp51 factor: 109179840536766784953562310705149908464858846735857 Tue Feb 05 09:59:49 2008 elapsed time 00:42:49
(11·10¹⁶²+43)/9 = 1(2)₁₆₁7_<163> = 3 · 29 · 326742809 · C152
C152 = P51 · P102
P51 = 318837544764593718793341618330869638110392459849809_<51>
P102 = 134851390385127161706957990388292357099558851675798087663094956194342092914353779808237658244386936541_<102>

Number: n N=42995686218485684425354382121193634172142999966913173892702721973494978030934860093628100416097942649000816546309174279218259378307775145242162473970669 ( 152 digits) SNFS difficulty: 163 digits. Divisors found: Tue Feb 5 10:34:00 2008 prp51 factor: 318837544764593718793341618330869638110392459849809 Tue Feb 5 10:34:00 2008 prp102 factor: 134851390385127161706957990388292357099558851675798087663094956194342092914353779808237658244386936541 Tue Feb 5 10:34:00 2008 elapsed time 01:01:47 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 50.89 hours. Scaled time: 42.55 units (timescale=0.836). Factorization parameters were as follows: name: KA_1_2_161_7 n: 42995686218485684425354382121193634172142999966913173892702721973494978030934860093628100416097942649000816546309174279218259378307775145242162473970669 type: snfs deg: 5 c5: 1100 c0: 43 skew: 0.52 m: 100000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3200191) Primes: RFBsize:216816, AFBsize:216802, largePrimes:5671714 encountered Relations: rels:5520680, finalFF:479300 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 50.71 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 50.89 hours. --------- CPU info (if available) ---------- CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Total of 2 processors activated (12009.47 BogoMIPS).
(5·10¹⁸⁹-17)/3 = 1(6)₁₈₈1_<190> = 11 · 139 · 308923723 · 4624276074181_<13> · 26156789250217_<14> · 2912928289309013648987_<22> · C131
C131 = P41 · P43 · P48
P41 = 20868712662673929425351208727898548430827_<41>
P43 = 1186280973757452857825332756781618820498731_<43>
P48 = 404528197374300908699982328463045462331168395041_<48>

Tue Feb 05 13:28:32 2008 Tue Feb 05 13:28:32 2008 Tue Feb 05 13:28:32 2008 Msieve v. 1.33 Tue Feb 05 13:28:32 2008 random seeds: 9aae636c ffa3d539 Tue Feb 05 13:28:32 2008 factoring 479884103893532766339493695699275521182139215549108179534976372846630679623126216447192971 (90 digits) Tue Feb 05 13:28:32 2008 searching for 15-digit factors Tue Feb 05 13:28:33 2008 commencing quadratic sieve (90-digit input) Tue Feb 05 13:28:33 2008 using multiplier of 41 Tue Feb 05 13:28:33 2008 using 64kb Opteron sieve core Tue Feb 05 13:28:33 2008 sieve interval: 18 blocks of size 65536 Tue Feb 05 13:28:33 2008 processing polynomials in batches of 6 Tue Feb 05 13:28:33 2008 using a sieve bound of 1582247 (60000 primes) Tue Feb 05 13:28:33 2008 using large prime bound of 126579760 (26 bits) Tue Feb 05 13:28:33 2008 using double large prime bound of 383933120608320 (42-49 bits) Tue Feb 05 13:28:33 2008 using trial factoring cutoff of 49 bits Tue Feb 05 13:28:33 2008 polynomial 'A' values have 12 factors Tue Feb 05 14:42:32 2008 60432 relations (16460 full + 43972 combined from 631008 partial), need 60096 Tue Feb 05 14:42:33 2008 begin with 647467 relations Tue Feb 05 14:42:34 2008 reduce to 144826 relations in 10 passes Tue Feb 05 14:42:34 2008 attempting to read 144826 relations Tue Feb 05 14:42:36 2008 recovered 144826 relations Tue Feb 05 14:42:36 2008 recovered 123295 polynomials Tue Feb 05 14:42:36 2008 attempting to build 60432 cycles Tue Feb 05 14:42:36 2008 found 60432 cycles in 5 passes Tue Feb 05 14:42:37 2008 distribution of cycle lengths: Tue Feb 05 14:42:37 2008 length 1 : 16460 Tue Feb 05 14:42:37 2008 length 2 : 11957 Tue Feb 05 14:42:37 2008 length 3 : 10793 Tue Feb 05 14:42:37 2008 length 4 : 8024 Tue Feb 05 14:42:37 2008 length 5 : 5471 Tue Feb 05 14:42:37 2008 length 6 : 3456 Tue Feb 05 14:42:37 2008 length 7 : 2003 Tue Feb 05 14:42:37 2008 length 9+: 2268 Tue Feb 05 14:42:37 2008 largest cycle: 18 relations Tue Feb 05 14:42:37 2008 matrix is 60000 x 60432 (14.8 MB) with weight 3642461 (60.27/col) Tue Feb 05 14:42:37 2008 sparse part has weight 3642461 (60.27/col) Tue Feb 05 14:42:38 2008 filtering completed in 3 passes Tue Feb 05 14:42:38 2008 matrix is 55611 x 55675 (13.7 MB) with weight 3372205 (60.57/col) Tue Feb 05 14:42:38 2008 sparse part has weight 3372205 (60.57/col) Tue Feb 05 14:42:39 2008 saving the first 48 matrix rows for later Tue Feb 05 14:42:39 2008 matrix is 55563 x 55675 (8.7 MB) with weight 2632003 (47.27/col) Tue Feb 05 14:42:39 2008 sparse part has weight 1939874 (34.84/col) Tue Feb 05 14:42:39 2008 matrix includes 64 packed rows Tue Feb 05 14:42:39 2008 using block size 21845 for processor cache size 512 kB Tue Feb 05 14:42:39 2008 commencing Lanczos iteration Tue Feb 05 14:42:39 2008 memory use: 8.4 MB Tue Feb 05 14:43:05 2008 lanczos halted after 880 iterations (dim = 55562) Tue Feb 05 14:43:06 2008 recovered 18 nontrivial dependencies Tue Feb 05 14:43:06 2008 prp43 factor: 1186280973757452857825332756781618820498731 Tue Feb 05 14:43:06 2008 prp48 factor: 404528197374300908699982328463045462331168395041 Tue Feb 05 14:43:06 2008 elapsed time 01:14:34
(2·10¹⁶³+1)/3 = (6)₁₆₂7_<163> = 7 · 61 · 167 · 34963 · 12614592942079272049_<20> · C135
C135 = P65 · P71
P65 = 10377754436587567376693516896966925177426777542616355517332761623_<65>
P71 = 20425799928742290584344313773322626491010687290873847923471967649372363_<71>

Number: n N=211973935831355323693477966455996075420736602698565413687534168539153599729601192528535499470177455623893501702677635272385313443225149 ( 135 digits) SNFS difficulty: 163 digits. Divisors found: Tue Feb 05 14:44:10 2008 prp65 factor: 10377754436587567376693516896966925177426777542616355517332761623 Tue Feb 05 14:44:10 2008 prp71 factor: 20425799928742290584344313773322626491010687290873847923471967649372363 Tue Feb 05 14:44:10 2008 elapsed time 01:07:48 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 41.47 hours. Scaled time: 72.75 units (timescale=1.754). Factorization parameters were as follows: name: KA_6_162_7 n: 211973935831355323693477966455996075420736602698565413687534168539153599729601192528535499470177455623893501702677635272385313443225149 type: snfs skew: 0.44 deg: 5 c5: 125 c0: 2 m: 200000000000000000000000000000000 rlim: 3000000 alim: 3000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2099990) Primes: RFBsize:216816, AFBsize:216926, largePrimes:6940658 encountered Relations: rels:6381595, finalFF:492593 Max relations in full relation-set: 28 Initial matrix: 433807 x 492593 with sparse part having weight 32470962. Pruned matrix : Total sieving time: 41.26 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,28,28,48,48,2.3,2.3,100000 total time: 41.47 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
9·10¹⁹⁹-1 = 8(9)₁₉₉_<200> = 311 · 18816601 · 7199849885356048147_<19> · 8780607192536057363_<19> · 6189868364159015753089_<22> · C131
C131 = P39 · P92
P39 = 653013029588688183402047290771742842951_<39>
P92 = 60185198005340312093913851920027593244762401225251579516624254991791230274129125334702673471_<92>
(11·10¹⁶⁵+7)/9 = 1(2)₁₆₄3_<166> = 2323037 · 3024071 · 801547104685055220907_<21> · 2244551866593860631050339_<25> · C107
C107 = P50 · P58
P50 = 22667491190849706134196427735425561647719849624523_<50>
P58 = 4266187260102382245262999179515923658804140846831092944231_<58>

Number: n N=96703762136885993527051098298870383339158901947010897471096334946417565075450884442730993018763399928976813 ( 107 digits) Divisors found: Tue Feb 5 21:58:19 2008 prp50 factor: 22667491190849706134196427735425561647719849624523 Tue Feb 5 21:58:19 2008 prp58 factor: 4266187260102382245262999179515923658804140846831092944231 Tue Feb 5 21:58:19 2008 elapsed time 00:31:25 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 10.14 hours. Scaled time: 8.49 units (timescale=0.837). Factorization parameters were as follows: name: KA_1_2_164_3 n: 96703762136885993527051098298870383339158901947010897471096334946417565075450884442730993018763399928976813 skew: 5982.01 # norm 2.22e+14 c5: 408000 c4: 39585968 c3: -38249412823790 c2: -4391565209106421 c1: 696703255789243605102 c0: 645439348323787340602296 # alpha -4.96 Y1: 248694786263 Y0: -188346099305469065669 # Murphy_E 1.38e-09 # M 51061564494728018280537336885306695758903469801669314827242486514533346876854629373845711032256659328639940 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 49/49 Sieved special-q in [100000, 1600000) Primes: RFBsize:183072, AFBsize:183292, largePrimes:7923702 encountered Relations: rels:7188725, finalFF:454354 Max relations in full relation-set: 28 Initial matrix: 366442 x 454354 with sparse part having weight 31541384. Pruned matrix : 317266 x 319162 with weight 16959885. Total sieving time: 9.92 hours. Total relation processing time: 0.22 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,28,28,49,49,2.6,2.6,150000 total time: 10.14 hours. --------- CPU info (if available) ---------- CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Total of 2 processors activated (12009.47 BogoMIPS).
Feb 4, 2008 (2nd): By Jo Yeong Uk / GMP-ECM, GGNFS
(11·10¹⁴⁴+7)/9 = 1(2)₁₄₃3_<145> = 59 · 1669 · 51429901 · 2361395713_<10> · 65397750107_<11> · C112
C112 = P34 · P78
P34 = 4258603296735103039935301521943217_<34>
P78 = 366967307314766659198303919155557622909193203642497744426932236576610478647479_<78>
(11·10¹⁵⁶+7)/9 = 1(2)₁₅₅3_<157> = 12721 · 2742200326538945243417_<22> · 9541792824687531700463092793_<28> · C103
C103 = P41 · P63
P41 = 20014512109901815744898373231694000857379_<41>
P63 = 183465645941118388677264534427318636676528636593091062790132837_<63>

Number: 12223_156 N=3671975392439472899341330402417834604335376052564536472613853563638553912495032350819060859819301654223 ( 103 digits) Divisors found: r1=20014512109901815744898373231694000857379 (pp41) r2=183465645941118388677264534427318636676528636593091062790132837 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.31 hours. Scaled time: 9.87 units (timescale=1.858). Factorization parameters were as follows: name: 12223_156 n: 3671975392439472899341330402417834604335376052564536472613853563638553912495032350819060859819301654223 skew: 19530.82 # norm 1.35e+14 c5: 6720 c4: -442157698 c3: -8623263312341 c2: 181075102603430862 c1: 1613496398437236320040 c0: 174910907146950939185280 # alpha -6.11 Y1: 48802931441 Y0: -55912780045085853073 # Murphy_E 2.56e-09 # M 144302031692213904811710240983196039277303241981002758121166447200177541282832116968539726573935138066 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, 1560001) Primes: RFBsize:135072, AFBsize:134658, largePrimes:4325792 encountered Relations: rels:4231829, finalFF:317982 Max relations in full relation-set: 28 Initial matrix: 269812 x 317982 with sparse part having weight 25295169. Pruned matrix : 235496 x 236909 with weight 15884839. Polynomial selection time: 0.35 hours. Total sieving time: 4.63 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.19 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 5.31 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹⁷⁵+43)/9 = 1(2)₁₇₄7_<176> = 431 · 563 · 16290121 · 38995664297_<11> · 593004715928370319507_<21> · 34213955179215476404658449_<26> · C106
C106 = P47 · P59
P47 = 47531082292491978658661669522302345299666587893_<47>
P59 = 82221376817115875746030616826703371178580921798546057059393_<59>

Number: 12227_175 N=3908071027696326886864028499843206919992522378639674173594528479164089521830871500698729823982185555728949 ( 106 digits) Divisors found: r1=47531082292491978658661669522302345299666587893 (pp47) r2=82221376817115875746030616826703371178580921798546057059393 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 10.32 hours. Scaled time: 19.18 units (timescale=1.858). Factorization parameters were as follows: name: 12227_175 n: 3908071027696326886864028499843206919992522378639674173594528479164089521830871500698729823982185555728949 skew: 8608.29 # norm 1.20e+14 c5: 25260 c4: -60371188 c3: 5757318952065 c2: 46830095000041631 c1: -261301190147423580723 c0: 3535830573716278227215 # alpha -5.17 Y1: 25621186877 Y0: -172944140038548492006 # Murphy_E 1.75e-09 # M 2075970695538704841661361494941305006763486824834160907225439575126500475951541082025147569146320170113636 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:135115, largePrimes:4655871 encountered Relations: rels:4809611, finalFF:441492 Max relations in full relation-set: 28 Initial matrix: 270272 x 441492 with sparse part having weight 44629901. Pruned matrix : 194914 x 196329 with weight 18507439. Polynomial selection time: 0.49 hours. Total sieving time: 9.52 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.16 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 10.32 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Feb 4, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(8·10¹⁶⁷-71)/9 = (8)₁₆₆1_<167> = 3 · 13 · 7480258613071537_<16> · C150
C150 = P34 · P117
P34 = 2269232521002778040596096495435919_<34>
P117 = 134272556782880983389435035962509777764315564283238280173555744073973109616249276693619292540182473602203459354521593_<117>
(11·10¹⁵⁹+43)/9 = 1(2)₁₅₈7_<160> = 3⁶ · 607 · 1523 · 9672317 · C144
C144 = P41 · P103
P41 = 25040024464232789848294795392827328171553_<41>
P103 = 7488050807888404363384367482738346838595043907027771100444640147357671594913324944576167521340548615683_<103>

Number: n N=187500975418943751652660969335071540461164444315032750609349244011086201230476532801845590733194291631585853137616657120810227526386921690265699 ( 144 digits) SNFS difficulty: 161 digits. Divisors found: Tue Feb 05 00:24:40 2008 prp41 factor: 25040024464232789848294795392827328171553 Tue Feb 05 00:24:40 2008 prp103 factor: 7488050807888404363384367482738346838595043907027771100444640147357671594913324944576167521340548615683 Tue Feb 05 00:24:40 2008 elapsed time 01:23:19 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.04 hours. Scaled time: 57.97 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_2_158_7 n: 187500975418943751652660969335071540461164444315032750609349244011086201230476532801845590733194291631585853137616657120810227526386921690265699 skew: 2.08 deg: 5 c5: 11 c0: 430 m: 100000000000000000000000000000000 type: snfs rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2000001) Primes: RFBsize:183072, AFBsize:182932, largePrimes:7315120 encountered Relations: rels:6778458, finalFF:413850 Max relations in full relation-set: 28 Initial matrix: 366069 x 413850 with sparse part having weight 39217428. Pruned matrix : Total sieving time: 39.82 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,161,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 40.04 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
Feb 3, 2008 (4th): By Kurt Beschorner
10⁸¹³+1 is divisible by 21765743514521277143440823504372166157_<38>
By Yousuke Koide
10¹¹³³+1 is divisible by 5571170781540045423292640754334163561_<37>
(10¹³²⁷-1)/9 is divisible by 32902513329012026560826807111_<29>
Feb 3, 2008 (3rd): By Jo Yeong Uk / GGNFS
(11·10¹³⁶+7)/9 = 1(2)₁₃₅3_<137> = 95561 · 155465684301056887579729_<24> · C108
C108 = P44 · P65
P44 = 14334185432356752323140436045325276938680249_<44>
P65 = 57393396768433653752614517111796708118174950424989467951382669983_<65>

Number: 12223_136 N=822687591871552784709318643813197336735469821034016549030837174471470985203346819632076285577794861927265767 ( 108 digits) SNFS difficulty: 137 digits. Divisors found: r1=14334185432356752323140436045325276938680249 (pp44) r2=57393396768433653752614517111796708118174950424989467951382669983 (pp65) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.35 hours. Scaled time: 8.07 units (timescale=1.857). Factorization parameters were as follows: n: 822687591871552784709318643813197336735469821034016549030837174471470985203346819632076285577794861927265767 m: 1000000000000000000000000000 c5: 110 c0: 7 skew: 0.58 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, 1500001) Primes: RFBsize:107126, AFBsize:107674, largePrimes:2376958 encountered Relations: rels:2529390, finalFF:284184 Max relations in full relation-set: 28 Initial matrix: 214867 x 284184 with sparse part having weight 25136993. Pruned matrix : 193207 x 194345 with weight 14316828. Total sieving time: 4.15 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,137,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 4.35 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹³⁸+7)/9 = 1(2)₁₃₇3_<139> = 623766815165969_<15> · 23752250570612018894611_<23> · C101
C101 = P39 · P63
P39 = 160798003756692938654694712820528450413_<39>
P63 = 513029679588668744253094982652790979172390866713850617213539769_<63>

Number: 12223_138 N=82494148345793731369441602124244699834884418764952216407190783233269739489161851992590938580119974597 ( 101 digits) Divisors found: r1=160798003756692938654694712820528450413 (pp39) r2=513029679588668744253094982652790979172390866713850617213539769 (pp63) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.18 hours. Scaled time: 7.76 units (timescale=1.859). Factorization parameters were as follows: name: 12223_138 n: 82494148345793731369441602124244699834884418764952216407190783233269739489161851992590938580119974597 skew: 4243.25 # norm 1.19e+14 c5: 193680 c4: -67658172 c3: -9221234168102 c2: -47361928099406800 c1: 41132723755137780999 c0: 104857604310820431424095 # alpha -5.94 Y1: 43351291357 Y0: -13361886298864081646 # Murphy_E 2.87e-09 # M 71500888182725105628880026829625266678105175754627294008919100390854775685964105360002187732656023157 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved algebraic special-q in [750000, 1350001) Primes: RFBsize:114155, AFBsize:113911, largePrimes:3839474 encountered Relations: rels:3720898, finalFF:269923 Max relations in full relation-set: 28 Initial matrix: 228148 x 269923 with sparse part having weight 21108901. Pruned matrix : 202141 x 203345 with weight 13187397. Polynomial selection time: 0.28 hours. Total sieving time: 3.64 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.13 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,48,48,2.5,2.5,50000 total time: 4.18 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹⁴²+7)/9 = 1(2)₁₄₁3_<143> = 41 · 154061 · 852989 · 641716583188361789950959757_<27> · C103
C103 = P51 · P53
P51 = 213109970184769549110217954567545220770332311910759_<51>
P53 = 16587584380176701656934488951246590820083044778169789_<53>

Number: 12223_142 N=3534979612696805971561202559424469132527119933396271700242344599515181935142280999950609689873517859851 ( 103 digits) Divisors found: r1=213109970184769549110217954567545220770332311910759 (pp51) r2=16587584380176701656934488951246590820083044778169789 (pp53) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.53 hours. Scaled time: 10.28 units (timescale=1.858). Factorization parameters were as follows: name: 12223_142 n: 3534979612696805971561202559424469132527119933396271700242344599515181935142280999950609689873517859851 skew: 2679.82 # norm 5.30e+13 c5: 264600 c4: 1519439634 c3: 5152788085665 c2: -11953194132301114 c1: -25402458644324276290 c0: 28335371836441837330020 # alpha -5.47 Y1: 61721076197 Y0: -26616948120759083489 # Murphy_E 2.59e-09 # M 1548383572242134576146617681526396291714054299406984080533713325745441083028013889105891537464365554166 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:134902, largePrimes:4460724 encountered Relations: rels:4495194, finalFF:394216 Max relations in full relation-set: 28 Initial matrix: 270054 x 394216 with sparse part having weight 33311263. Pruned matrix : 199211 x 200625 with weight 15737659. Polynomial selection time: 0.35 hours. Total sieving time: 4.89 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.15 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,49,49,2.6,2.6,60000 total time: 5.53 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Feb 3, 2008 (2nd): By Sinkiti Sibata / Msieve
(11·10¹²⁵+43)/9 = 1(2)₁₂₄7_<126> = 7³ · 47 · 503 · 9791 · 319485419022834938413_<21> · C94
C94 = P41 · P54
P41 = 26911423347030094859147806513779908366419_<41>
P54 = 179050464360592207024627576920634186756605854426645477_<54>

Sat Feb 02 08:18:48 2008 Msieve v. 1.30 Sat Feb 02 08:18:49 2008 random seeds: 9e0bea2a 4bbaab61 Sat Feb 02 08:18:49 2008 factoring 4818502846890221045374101350076711059884336292143407476048410706538319861125528494833125036863 (94 digits) Sat Feb 02 08:18:49 2008 commencing quadratic sieve (94-digit input) Sat Feb 02 08:18:50 2008 using multiplier of 2 Sat Feb 02 08:18:50 2008 using 64kb Pentium 2 sieve core Sat Feb 02 08:18:50 2008 sieve interval: 18 blocks of size 65536 Sat Feb 02 08:18:50 2008 processing polynomials in batches of 6 Sat Feb 02 08:18:50 2008 using a sieve bound of 2057791 (76471 primes) Sat Feb 02 08:18:50 2008 using large prime bound of 283975158 (28 bits) Sat Feb 02 08:18:50 2008 using double large prime bound of 1644010566805608 (42-51 bits) Sat Feb 02 08:18:50 2008 using trial factoring cutoff of 51 bits Sat Feb 02 08:18:50 2008 polynomial 'A' values have 12 factors Sun Feb 03 06:22:02 2008 76863 relations (18980 full + 57883 combined from 1103923 partial), need 76567 Sun Feb 03 06:22:22 2008 begin with 1122903 relations Sun Feb 03 06:23:45 2008 reduce to 199427 relations in 10 passes Sun Feb 03 06:23:46 2008 attempting to read 199427 relations Sun Feb 03 06:24:11 2008 recovered 199427 relations Sun Feb 03 06:24:11 2008 recovered 181755 polynomials Sun Feb 03 06:24:36 2008 attempting to build 76863 cycles Sun Feb 03 06:24:36 2008 found 76863 cycles in 6 passes Sun Feb 03 06:24:41 2008 distribution of cycle lengths: Sun Feb 03 06:24:41 2008 length 1 : 18980 Sun Feb 03 06:24:41 2008 length 2 : 13444 Sun Feb 03 06:24:41 2008 length 3 : 13097 Sun Feb 03 06:24:41 2008 length 4 : 10345 Sun Feb 03 06:24:41 2008 length 5 : 7787 Sun Feb 03 06:24:41 2008 length 6 : 5269 Sun Feb 03 06:24:42 2008 length 7 : 3401 Sun Feb 03 06:24:42 2008 length 9+: 4540 Sun Feb 03 06:24:42 2008 largest cycle: 20 relations Sun Feb 03 06:24:43 2008 matrix is 76471 x 76863 with weight 4943542 (avg 64.32/col) Sun Feb 03 06:24:48 2008 filtering completed in 3 passes Sun Feb 03 06:24:48 2008 matrix is 72682 x 72746 with weight 4694355 (avg 64.53/col) Sun Feb 03 06:24:51 2008 saving the first 48 matrix rows for later Sun Feb 03 06:24:52 2008 matrix is 72634 x 72746 with weight 3670006 (avg 50.45/col) Sun Feb 03 06:24:52 2008 matrix includes 64 packed rows Sun Feb 03 06:24:52 2008 using block size 10922 for processor cache size 256 kB Sun Feb 03 06:24:55 2008 commencing Lanczos iteration Sun Feb 03 06:29:16 2008 lanczos halted after 1149 iterations (dim = 72632) Sun Feb 03 06:29:17 2008 recovered 16 nontrivial dependencies Sun Feb 03 06:32:11 2008 prp41 factor: 26911423347030094859147806513779908366419 Sun Feb 03 06:32:11 2008 prp54 factor: 179050464360592207024627576920634186756605854426645477 Sun Feb 03 06:32:11 2008 elapsed time 22:13:22
Feb 3, 2008: By Robert Backstrom / GGNFS, Msieve
(11·10¹³²+43)/9 = 1(2)₁₃₁7_<133> = 3³ · 83 · C129
C129 = P57 · P73
P57 = 111112771172331750872514090492110122437339906630826550009_<57>
P73 = 4908449645869942293694487080630525727438428859396006401801847501095827883_<73>

Number: n N=545391442312459715404829193316475779661857305766274976449005900143785016609648470424909514601616341910853289702017948336556100947 ( 129 digits) SNFS difficulty: 133 digits. Divisors found: r1=111112771172331750872514090492110122437339906630826550009 (pp57) r2=4908449645869942293694487080630525727438428859396006401801847501095827883 (pp73) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 5.51 hours. Scaled time: 7.21 units (timescale=1.309). Factorization parameters were as follows: name: KA_1_2_131_7 n: 545391442312459715404829193316475779661857305766274976449005900143785016609648470424909514601616341910853289702017948336556100947 skew: 0.52 deg: 5 c5: 1100 c0: 43 m: 100000000000000000000000000 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, 500001) Primes: RFBsize:148933, AFBsize:148846, largePrimes:5439382 encountered Relations: rels:4852705, finalFF:336542 Max relations in full relation-set: 28 Initial matrix: 297846 x 336542 with sparse part having weight 16711281. Pruned matrix : 259856 x 261409 with weight 10061932. Total sieving time: 4.37 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.95 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,133,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,50000 total time: 5.51 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(11·10¹³⁷+43)/9 = 1(2)₁₃₆7_<138> = 7 · C137
C137 = P39 · P98
P39 = 826947682191349154287338776865934602857_<39>
P98 = 21114174253501663398552547882800994034080029605303708859438928706621453258063526161207848053837773_<98>

Number: n N=17460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461 ( 137 digits) SNFS difficulty: 138 digits. Divisors found: r1=826947682191349154287338776865934602857 (pp39) r2=21114174253501663398552547882800994034080029605303708859438928706621453258063526161207848053837773 (pp98) Version: GGNFS-0.77.1-20051202-athlon Total time: 7.20 hours. Scaled time: 12.62 units (timescale=1.753). Factorization parameters were as follows: name: KA_1_2_136_7 n: 17460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317460317461 type: snfs skew: 0.52 deg: 5 c5: 1100 c0: 43 m: 1000000000000000000000000000 rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1000000) Primes: RFBsize:114155, AFBsize:114198, largePrimes:5398021 encountered Relations: rels:4770513, finalFF:299953 Max relations in full relation-set: 28 Initial matrix: 228420 x 299953 with sparse part having weight 19344439. Pruned matrix : 185538 x 186744 with weight 9834435. Total sieving time: 6.31 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.67 hours. Total square root time: 0.07 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.3,2.3,75000 total time: 7.20 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(11·10¹³³+43)/9 = 1(2)₁₃₂7_<134> = 1321 · 1410916038767_<13> · 3759336512783_<13> · C106
C106 = P37 · P69
P37 = 3516588143890561652644886771677592087_<37>
P69 = 496036320496666194477662303711920463713480656308118096409742336798941_<69>

Number: n N=1744355443597675135882479103597911072800396043417938417736429887625152088132861173319540054833362331579867 ( 106 digits) SNFS difficulty: 134 digits. Divisors found: r1=3516588143890561652644886771677592087 (pp37) r2=496036320496666194477662303711920463713480656308118096409742336798941 (pp69) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 5.91 hours. Scaled time: 7.74 units (timescale=1.309). Factorization parameters were as follows: name: KA_1_2_132_7 n: 1744355443597675135882479103597911072800396043417938417736429887625152088132861173319540054833362331579867 skew: 0.33 deg: 5 c5: 11000 c0: 43 m: 100000000000000000000000000 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, 550001) Primes: RFBsize:148933, AFBsize:149056, largePrimes:5686122 encountered Relations: rels:5129599, finalFF:373496 Max relations in full relation-set: 28 Initial matrix: 298056 x 373496 with sparse part having weight 20625775. Pruned matrix : 230995 x 232549 with weight 9849788. Total sieving time: 5.01 hours. Total relation processing time: 0.15 hours. Matrix solve time: 0.68 hours. Total square root time: 0.06 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,134,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000 total time: 5.91 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(11·10¹⁴⁸+43)/9 = 1(2)₁₄₇7_<149> = 2237 · C145
C145 = P46 · P99
P46 = 5708590448834065059889081709749195794968604751_<46>
P99 = 957095567805688585006539301709267550428734463658167833478066966464619925304020149513216150426243521_<99>

Number: n N=5463666616996970148512392589281279491382307654100233447573635325088163711319723836487359062236129737247305418963890130631301842745740823523568271 ( 145 digits) SNFS difficulty: 149 digits. Divisors found: r1=5708590448834065059889081709749195794968604751 (pp46) r2=957095567805688585006539301709267550428734463658167833478066966464619925304020149513216150426243521 (pp99) Version: GGNFS-0.77.1-20051202-athlon Total time: 11.16 hours. Scaled time: 20.27 units (timescale=1.817). Factorization parameters were as follows: name: KA_1_2_147_7 n: 5463666616996970148512392589281279491382307654100233447573635325088163711319723836487359062236129737247305418963890130631301842745740823523568271 skew: 0.33 deg: 5 c5: 11000 c0: 43 m: 100000000000000000000000000000 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 algebraic special-q in [100000, 1900001) Primes: RFBsize:183072, AFBsize:183037, largePrimes:7044436 encountered Relations: rels:6450847, finalFF:440285 Max relations in full relation-set: 48 Initial matrix: 366176 x 440285 with sparse part having weight 39436571. Pruned matrix : 321112 x 323006 with weight 23568462. Total sieving time: 10.11 hours. Total relation processing time: 0.16 hours. Matrix solve time: 0.84 hours. Total square root time: 0.05 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.5,2.5,100000 total time: 11.16 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(11·10¹⁴²+43)/9 = 1(2)₁₄₁7_<143> = 199 · 2711 · 25447 · C132
C132 = P55 · P78
P55 = 3068600121073799335852157386784751919947571513958188339_<55>
P78 = 290128701364190538984568387515170669387068553760927649832295688847493293426071_<78>

Number: n N=890288968133139258467427941637942626811916485305684466174890492674520641988294022763275638082211998002722782842984474256989590786069 ( 132 digits) SNFS difficulty: 143 digits. Divisors found: Sun Feb 3 19:04:45 2008 prp55 factor: 3068600121073799335852157386784751919947571513958188339 Sun Feb 3 19:04:45 2008 prp78 factor: 290128701364190538984568387515170669387068553760927649832295688847493293426071 Sun Feb 3 19:04:45 2008 elapsed time 00:16:14 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-k8 Total time: 10.62 hours. Scaled time: 8.91 units (timescale=0.839). Factorization parameters were as follows: name: KA_1_2_141_7 n: 890288968133139258467427941637942626811916485305684466174890492674520641988294022763275638082211998002722782842984474256989590786069 type: snfs deg: 5 c5: 1100 c0: 43 skew: 0.52 m: 10000000000000000000000000000 rlim: 2000000 alim: 2000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 1700001) Primes: RFBsize:148933, AFBsize:148846, largePrimes:2743285 encountered Relations: rels:2743528, finalFF:343108 Max relations in full relation-set: 28 Initial matrix: 297846 x 343108 with sparse part having weight 16612589. Pruned matrix : 264132 x 265685 with weight 10944419. Total sieving time: 10.12 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.39 hours. Total time per square root: 0.00 hours, sqrts: 32. Prototype def-par.txt line would be: snfs,143,5,0,0,0,0,0,0,0,0,2000000,2000000,26,26,45,45,2.5,2.5,100000 total time: 10.62 hours. --------- CPU info (if available) ---------- CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Total of 2 processors activated (12009.47 BogoMIPS).
Feb 2, 2008 (3rd): By Sinkiti Sibata / Msieve, GGNFS
(11·10¹¹⁰+7)/9 = 1(2)₁₀₉3_<111> = 3 · 8874935947_<10> · C100
C100 = P36 · P65
P36 = 192974421658293224031417306264104681_<36>
P65 = 23788329512941257985749836483187483343956508948136539261231691863_<65>

Fri Feb 1 13:49:44 2008 Msieve v. 1.33 Fri Feb 1 13:49:44 2008 random seeds: a1488afa bb05cf89 Fri Feb 1 13:49:44 2008 factoring 4590539129976747396207516622062302388438943934694827013914981750655415827841212558189152724567910703 (100 digits) Fri Feb 1 13:49:45 2008 searching for 15-digit factors Fri Feb 1 13:49:47 2008 commencing quadratic sieve (100-digit input) Fri Feb 1 13:49:48 2008 using multiplier of 23 Fri Feb 1 13:49:48 2008 using 64kb Pentium 4 sieve core Fri Feb 1 13:49:48 2008 sieve interval: 18 blocks of size 65536 Fri Feb 1 13:49:48 2008 processing polynomials in batches of 6 Fri Feb 1 13:49:48 2008 using a sieve bound of 2751493 (99912 primes) Fri Feb 1 13:49:48 2008 using large prime bound of 412723950 (28 bits) Fri Feb 1 13:49:48 2008 using double large prime bound of 3222459040502850 (43-52 bits) Fri Feb 1 13:49:48 2008 using trial factoring cutoff of 52 bits Fri Feb 1 13:49:48 2008 polynomial 'A' values have 13 factors Sat Feb 2 10:18:44 2008 100088 relations (23581 full + 76507 combined from 1507071 partial), need 100008 Sat Feb 2 10:18:50 2008 begin with 1530652 relations Sat Feb 2 10:18:52 2008 reduce to 264655 relations in 12 passes Sat Feb 2 10:18:52 2008 attempting to read 264655 relations Sat Feb 2 10:19:02 2008 recovered 264655 relations Sat Feb 2 10:19:02 2008 recovered 256120 polynomials Sat Feb 2 10:19:02 2008 attempting to build 100088 cycles Sat Feb 2 10:19:03 2008 found 100088 cycles in 6 passes Sat Feb 2 10:19:03 2008 distribution of cycle lengths: Sat Feb 2 10:19:03 2008 length 1 : 23581 Sat Feb 2 10:19:03 2008 length 2 : 16969 Sat Feb 2 10:19:03 2008 length 3 : 16869 Sat Feb 2 10:19:03 2008 length 4 : 13612 Sat Feb 2 10:19:03 2008 length 5 : 10500 Sat Feb 2 10:19:03 2008 length 6 : 7350 Sat Feb 2 10:19:03 2008 length 7 : 4635 Sat Feb 2 10:19:03 2008 length 9+: 6572 Sat Feb 2 10:19:03 2008 largest cycle: 20 relations Sat Feb 2 10:19:03 2008 matrix is 99912 x 100088 (28.1 MB) with weight 6958780 (69.53/col) Sat Feb 2 10:19:03 2008 sparse part has weight 6958780 (69.53/col) Sat Feb 2 10:19:06 2008 filtering completed in 4 passes Sat Feb 2 10:19:06 2008 matrix is 96049 x 96113 (27.1 MB) with weight 6726665 (69.99/col) Sat Feb 2 10:19:06 2008 sparse part has weight 6726665 (69.99/col) Sat Feb 2 10:19:07 2008 saving the first 48 matrix rows for later Sat Feb 2 10:19:07 2008 matrix is 96001 x 96113 (17.4 MB) with weight 5308583 (55.23/col) Sat Feb 2 10:19:07 2008 sparse part has weight 3978156 (41.39/col) Sat Feb 2 10:19:07 2008 matrix includes 64 packed rows Sat Feb 2 10:19:07 2008 using block size 21845 for processor cache size 512 kB Sat Feb 2 10:19:08 2008 commencing Lanczos iteration Sat Feb 2 10:19:08 2008 memory use: 16.5 MB Sat Feb 2 10:20:46 2008 lanczos halted after 1520 iterations (dim = 95999) Sat Feb 2 10:20:47 2008 recovered 16 nontrivial dependencies Sat Feb 2 10:20:50 2008 prp36 factor: 192974421658293224031417306264104681 Sat Feb 2 10:20:50 2008 prp65 factor: 23788329512941257985749836483187483343956508948136539261231691863 Sat Feb 2 10:20:50 2008 elapsed time 20:31:06
(11·10¹¹²+43)/9 = 1(2)₁₁₁7_<113> = 1392541 · 171740189 · C98
C98 = P42 · P57
P42 = 143286201861700132912700962874088411962741_<42>
P57 = 356669421688691816769551532579943147017949354032325568303_<57>

Number: 12227_112 N=51105806753981743159739057597763445623761010676640079468814415944058025931144285169076386486598523 ( 98 digits) SNFS difficulty: 113 digits. Divisors found: r1=143286201861700132912700962874088411962741 (pp42) r2=356669421688691816769551532579943147017949354032325568303 (pp57) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2.46 hours. Scaled time: 1.66 units (timescale=0.676). Factorization parameters were as follows: name: 12227_112 n: 51105806753981743159739057597763445623761010676640079468814415944058025931144285169076386486598523 m: 10000000000000000000000 c5: 1100 c0: 43 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, 550001) Primes: RFBsize:49098, AFBsize:63799, largePrimes:2296912 encountered Relations: rels:2612701, finalFF:434420 Max relations in full relation-set: 28 Initial matrix: 112964 x 434420 with sparse part having weight 37514997. Pruned matrix : 67377 x 68005 with weight 5864456. Total sieving time: 2.26 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.09 hours. Time per square root: 0.04 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: 2.46 hours. --------- CPU info (if available) ----------
(11·10¹³⁸+43)/9 = 1(2)₁₃₇7_<139> = 3 · 353 · 3772770559_<10> · 5375963324383_<13> · 1780869062599870907_<19> · C95
C95 = P37 · P58
P37 = 7463409413579206909424210728917778139_<37>
P58 = 4281227127600524118339409264146075718886687783760343681913_<58>

Sat Feb 2 14:26:10 2008 Msieve v. 1.33 Sat Feb 2 14:26:10 2008 random seeds: 518df1e8 4f66404b Sat Feb 2 14:26:10 2008 factoring 31952550845804420141668463672712528275349504043112878808043841079538101373805116809050521099907 (95 digits) Sat Feb 2 14:26:11 2008 searching for 15-digit factors Sat Feb 2 14:26:13 2008 commencing quadratic sieve (95-digit input) Sat Feb 2 14:26:14 2008 using multiplier of 3 Sat Feb 2 14:26:14 2008 using 64kb Pentium 4 sieve core Sat Feb 2 14:26:14 2008 sieve interval: 18 blocks of size 65536 Sat Feb 2 14:26:14 2008 processing polynomials in batches of 6 Sat Feb 2 14:26:14 2008 using a sieve bound of 2119673 (78824 primes) Sat Feb 2 14:26:14 2008 using large prime bound of 309472258 (28 bits) Sat Feb 2 14:26:14 2008 using double large prime bound of 1919194993237322 (43-51 bits) Sat Feb 2 14:26:14 2008 using trial factoring cutoff of 51 bits Sat Feb 2 14:26:14 2008 polynomial 'A' values have 12 factors Sat Feb 2 20:59:00 2008 79041 relations (18875 full + 60166 combined from 1164620 partial), need 78920 Sat Feb 2 20:59:05 2008 begin with 1183495 relations Sat Feb 2 20:59:06 2008 reduce to 207464 relations in 11 passes Sat Feb 2 20:59:06 2008 attempting to read 207464 relations Sat Feb 2 20:59:13 2008 recovered 207464 relations Sat Feb 2 20:59:13 2008 recovered 192697 polynomials Sat Feb 2 20:59:13 2008 attempting to build 79041 cycles Sat Feb 2 20:59:13 2008 found 79041 cycles in 5 passes Sat Feb 2 20:59:13 2008 distribution of cycle lengths: Sat Feb 2 20:59:13 2008 length 1 : 18875 Sat Feb 2 20:59:13 2008 length 2 : 13735 Sat Feb 2 20:59:13 2008 length 3 : 13435 Sat Feb 2 20:59:13 2008 length 4 : 10830 Sat Feb 2 20:59:13 2008 length 5 : 8231 Sat Feb 2 20:59:13 2008 length 6 : 5366 Sat Feb 2 20:59:13 2008 length 7 : 3632 Sat Feb 2 20:59:13 2008 length 9+: 4937 Sat Feb 2 20:59:13 2008 largest cycle: 19 relations Sat Feb 2 20:59:14 2008 matrix is 78824 x 79041 (21.5 MB) with weight 5328815 (67.42/col) Sat Feb 2 20:59:14 2008 sparse part has weight 5328815 (67.42/col) Sat Feb 2 20:59:15 2008 filtering completed in 3 passes Sat Feb 2 20:59:15 2008 matrix is 75388 x 75452 (20.7 MB) with weight 5113466 (67.77/col) Sat Feb 2 20:59:15 2008 sparse part has weight 5113466 (67.77/col) Sat Feb 2 20:59:16 2008 saving the first 48 matrix rows for later Sat Feb 2 20:59:16 2008 matrix is 75340 x 75452 (14.2 MB) with weight 4180469 (55.41/col) Sat Feb 2 20:59:16 2008 sparse part has weight 3274785 (43.40/col) Sat Feb 2 20:59:16 2008 matrix includes 64 packed rows Sat Feb 2 20:59:16 2008 using block size 21845 for processor cache size 512 kB Sat Feb 2 20:59:17 2008 commencing Lanczos iteration Sat Feb 2 20:59:17 2008 memory use: 13.0 MB Sat Feb 2 21:00:18 2008 lanczos halted after 1193 iterations (dim = 75337) Sat Feb 2 21:00:18 2008 recovered 16 nontrivial dependencies Sat Feb 2 21:00:22 2008 prp37 factor: 7463409413579206909424210728917778139 Sat Feb 2 21:00:22 2008 prp58 factor: 4281227127600524118339409264146075718886687783760343681913 Sat Feb 2 21:00:22 2008 elapsed time 06:34:12
Feb 2, 2008 (2nd): By Jo Yeong Uk / GGNFS
(11·10¹³⁵+7)/9 = 1(2)₁₃₄3_<136> = 131 · 318423851 · 8863447521283_<13> · C112
C112 = P45 · P68
P45 = 146507265503071162570097163593367631761112907_<45>
P68 = 22563758847479551553339931144774084951879508530066949268898335852143_<68>

Number: 12223_135 N=3305754608214957636859188617439640563208150384163881738373873556942454204082790415027851957410195271119880909701 ( 112 digits) SNFS difficulty: 136 digits. Divisors found: r1=146507265503071162570097163593367631761112907 (pp45) r2=22563758847479551553339931144774084951879508530066949268898335852143 (pp68) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.57 hours. Scaled time: 4.77 units (timescale=1.857). Factorization parameters were as follows: n: 3305754608214957636859188617439640563208150384163881738373873556942454204082790415027851957410195271119880909701 m: 1000000000000000000000000000 c5: 11 c0: 7 skew: 0.91 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, 1150001) Primes: RFBsize:107126, AFBsize:107064, largePrimes:2237518 encountered Relations: rels:2366180, finalFF:298235 Max relations in full relation-set: 28 Initial matrix: 214255 x 298235 with sparse part having weight 20597668. Pruned matrix : 176349 x 177484 with weight 9366601. Total sieving time: 2.43 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.08 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 2.57 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹¹⁹+43)/9 = 1(2)₁₁₈7_<120> = 7 · 131 · C117
C117 = P31 · P39 · P48
P31 = 7726724306485600711748047366001_<31>
P39 = 125939710672765832787789653955253825423_<39>
P48 = 136969141012293087278356134180738215385520447897_<48>

Number: 12227_119 N=133284866109293590209620743971889010056948988246698170362292499697079849751605476796316490972979522597843208530231431 ( 117 digits) SNFS difficulty: 121 digits. Divisors found: r1=7726724306485600711748047366001 (pp31) r2=125939710672765832787789653955253825423 (pp39) r3=136969141012293087278356134180738215385520447897 (pp48) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.08 hours. Scaled time: 2.01 units (timescale=1.860). Factorization parameters were as follows: n: 133284866109293590209620743971889010056948988246698170362292499697079849751605476796316490972979522597843208530231431 m: 1000000000000000000000000 c5: 11 c0: 430 skew: 2.08 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:49742, largePrimes:1888339 encountered Relations: rels:1934625, finalFF:187269 Max relations in full relation-set: 28 Initial matrix: 98905 x 187269 with sparse part having weight 16529964. Pruned matrix : 80942 x 81500 with weight 4822120. Total sieving time: 1.03 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.02 hours. Time per square root: 0.01 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,600000,25,25,45,45,2.4,2.4,30000 total time: 1.08 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Feb 2, 2008: By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(11·10¹⁰²+43)/9 = 1(2)₁₀₁7_<103> = 3 · 5351 · 7417 · C95
C95 = P29 · P66
P29 = 15986555733012893316173285293_<29>
P66 = 642111998099621810502419011210481164093871271217524484541221231739_<66>
(11·10¹²²+43)/9 = 1(2)₁₂₁7_<123> = 1553 · 646855673 · 5495588970614054030497_<22> · C89
C89 = P30 · P60
P30 = 202819334939982598056638072887_<30>
P60 = 109156029776505315605230350032970862543603279732264658041597_<60>
(11·10¹⁰⁸+43)/9 = 1(2)₁₀₇7_<109> = 3 · 307 · 5179 · C102
C102 = P44 · P58
P44 = 52998473697593985191483510398970980470758279_<44>
P58 = 4834830709525647808402348659617169367180675927813342017607_<58>

Number: n N=256238648191114710565285519387936251830970731466532285801786220981002210384462564243979166307059018353 ( 102 digits) SNFS difficulty: 109 digits. Divisors found: r1=52998473697593985191483510398970980470758279 (pp44) r2=4834830709525647808402348659617169367180675927813342017607 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.70 hours. Scaled time: 1.29 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_2_107_7 n: 256238648191114710565285519387936251830970731466532285801786220981002210384462564243979166307059018353 skew: 0.33 deg: 5 c5: 11000 c0: 43 m: 1000000000000000000000 type: snfs rlim: 1000000 alim: 1000000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:78498, AFBsize:78512, largePrimes:3833985 encountered Relations: rels:3288688, finalFF:209248 Max relations in full relation-set: 48 Initial matrix: 157077 x 209248 with sparse part having weight 8669312. Pruned matrix : 107179 x 108028 with weight 3135973. Total sieving time: 0.60 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.03 hours. Total square root time: 0.03 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,109,5,0,0,0,0,0,0,0,0,1000000,1000000,28,28,48,48,2.5,2.5,50000 total time: 0.70 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(5·10¹⁶⁴+1)/3 = 1(6)₁₆₃7_<165> = 29 · 51109 · 145869523 · 45231717026801_<14> · C137
C137 = P43 · P94
P43 = 4540862105110602564100033680942535811201803_<43>
P94 = 3753249345081429166561888673069600257378807334363856510196087848823616338912185173489836353563_<94>

Number: n N=17042987722111448842955391614860266963453207743477456801387216880523122192828388238421867929811195976610704666895602314168554390251074089 ( 137 digits) SNFS difficulty: 165 digits. Divisors found: Sat Feb 02 12:46:52 2008 prp43 factor: 4540862105110602564100033680942535811201803 Sat Feb 02 12:46:52 2008 prp94 factor: 3753249345081429166561888673069600257378807334363856510196087848823616338912185173489836353563 Sat Feb 02 12:46:52 2008 elapsed time 01:14:11 (Msieve 1.33) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 49.04 hours. Scaled time: 64.34 units (timescale=1.312). Factorization parameters were as follows: name: KA_1_6_163_7 n: 17042987722111448842955391614860266963453207743477456801387216880523122192828388238421867929811195976610704666895602314168554390251074089 skew: 1.15 deg: 5 c5: 1 c0: 2 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 2000000) Primes: RFBsize:230209, AFBsize:230077, largePrimes:7364021 encountered Relations: rels:6905403, finalFF:556912 Max relations in full relation-set: 28 Initial matrix: 460350 x 556912 with sparse part having weight 41875479. Pruned matrix : 387141 x 389506 with weight 26752549. Total sieving time: 48.78 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,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 49.04 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(11·10¹¹⁰+43)/9 = 1(2)₁₀₉7_<111> = 51977 · C106
C106 = P47 · P59
P47 = 81184110247381809060406319688698040691781701091_<47>
P59 = 28964626395377574001973137610529281064629935087612238738761_<59>

Number: n N=2351467422556558135756627397160709972145799530989134082810131831814499148127483737465075364530892937688251 ( 106 digits) SNFS difficulty: 111 digits. Divisors found: Sat Feb 2 12:50:25 2008 prp47 factor: 81184110247381809060406319688698040691781701091 Sat Feb 2 12:50:25 2008 prp59 factor: 28964626395377574001973137610529281064629935087612238738761 Sat Feb 2 12:50:25 2008 elapsed time 00:04:27 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-k8 Total time: 0.67 hours. Scaled time: 0.56 units (timescale=0.836). Factorization parameters were as follows: name: KA_1_2_109_7 n: 2351467422556558135756627397160709972145799530989134082810131831814499148127483737465075364530892937688251 type: snfs deg: 5 c5: 11 c0: 43 skew: 1.31 m: 10000000000000000000000 rlim: 1000000 alim: 1000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1000000/1000000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [100000, 160001) Primes: RFBsize:78498, AFBsize:78392, largePrimes:1545266 encountered Relations: rels:1538936, finalFF:190994 Max relations in full relation-set: 28 Initial matrix: 156955 x 190994 with sparse part having weight 6912098. Pruned matrix : 119845 x 120693 with weight 3158427. Total sieving time: 0.60 hours. Total relation processing time: 0.03 hours. Total matrix solve time: 0.04 hours, sqrts: 32. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.5,2.5,50000 total time: 0.67 hours. --------- CPU info (if available) ---------- CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Total of 2 processors activated (12009.47 BogoMIPS).
(11·10¹²³+43)/9 = 1(2)₁₂₂7_<124> = 3² · 71 · 21179 · 38026953214673_<14> · C103
C103 = P36 · P67
P36 = 479001684843585031175534119002948761_<36>
P67 = 4958100159903010190304866660512588272578698548918562249510374124639_<67>
(11·10¹⁵¹+43)/9 = 1(2)₁₅₀7_<152> = 14454331 · 637792399301914965087547_<24> · 235218918106668005373009596143_<30> · C91
C91 = P42 · P49
P42 = 919097914080506766975348639423129323618987_<42>
P49 = 6132517724267022835952150979164863488281978181871_<49>

Number: n N=5636384248435557042913746716336205772629431650068022004880943778426067540786043932194784677 ( 91 digits) Divisors found: r1=919097914080506766975348639423129323618987 (pp42) r2=6132517724267022835952150979164863488281978181871 (pp49) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.32 hours. Scaled time: 4.80 units (timescale=1.445). Factorization parameters were as follows: name: KA_1_2_150_7 n: 5636384248435557042913746716336205772629431650068022004880943778426067540786043932194784677 m: 829092521266817765468 deg: 4 c4: 11928576 c3: 32904998720 c2: -68584145541624839 c1: -89054554649160018 c0: 84172890122121959585421 skew: 1635.250 type: gnfs # adj. I(F,S) = 51.742 # E(F1,F2) = 1.402664e-04 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1201912733. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 27 lpba: 27 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 20000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 44/44 Sieved algebraic special-q in [100000, 600001) Primes: RFBsize:56543, AFBsize:56816, largePrimes:2612032 encountered Relations: rels:2297204, finalFF:127409 Max relations in full relation-set: 28 Initial matrix: 113435 x 127409 with sparse part having weight 9286207. Pruned matrix : 107888 x 108519 with weight 6627776. Total sieving time: 3.02 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.15 hours. Total square root time: 0.07 hours, sqrts: 3. Prototype def-par.txt line would be: gnfs,90,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,27,27,44,44,2.4,2.4,40000 total time: 3.32 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(11·10¹⁴⁷+7)/9 = 1(2)₁₄₆3_<148> = 41 · 359 · 17987 · C139
C139 = P59 · P80
P59 = 60639450252175372852507882819631652825439122617058853904357_<59>
P80 = 76130359457876522538422881892238302321490455243664764661805980418638409324517663_<80>

Number: n N=4616503145026132276328029386285299255606452544697679073230547318885072673351337200374052419135004823660330017098096533201835850513359157691 ( 139 digits) SNFS difficulty: 148 digits. Divisors found: Sat Feb 02 15:21:37 2008 prp59 factor: 60639450252175372852507882819631652825439122617058853904357 Sat Feb 02 15:21:37 2008 prp80 factor: 76130359457876522538422881892238302321490455243664764661805980418638409324517663 Sat Feb 02 15:21:37 2008 elapsed time 01:02:11 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 12.68 hours. Scaled time: 22.27 units (timescale=1.756). Factorization parameters were as follows: name: KA_1_2_146_3 n: 4616503145026132276328029386285299255606452544697679073230547318885072673351337200374052419135004823660330017098096533201835850513359157691 type: snfs skew: 0.36 deg: 5 c5: 1100 c0: 7 m: 100000000000000000000000000000 rlim: 2500000 alim: 2500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 1799990) Primes: RFBsize:183072, AFBsize:182582, largePrimes:6521885 encountered Relations: rels:5914180, finalFF:433290 Max relations in full relation-set: 28 Initial matrix: 365721 x 433290 with sparse part having weight 25005284. Pruned matrix : Total sieving time: 12.49 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,148,5,0,0,0,0,0,0,0,0,2500000,2500000,28,28,48,48,2.3,2.3,100000 total time: 12.68 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+
(11·10¹²⁹+43)/9 = 1(2)₁₂₈7_<130> = 3 · 17 · 2269 · 8629 · 1012261 · C115
C115 = P33 · P82
P33 = 137168336280987058909192029624923_<33>
P82 = 8815331708024940951855441988686640906430791155889863737109891988891471546179563959_<82>
(11·10¹²⁰+43)/9 = 1(2)₁₁₉7_<121> = 3 · 2939 · C117
C117 = P53 · P65
P53 = 10360202665625776591605886682977757294938234539486161_<53>
P65 = 13380153130697716154258396236743209165877691612680584935690556371_<65>

Number: n N=138621098131135558832054238655123309767746651040288331884112761962370672816402656484316913034163799730318954544881731 ( 117 digits) SNFS difficulty: 121 digits. Divisors found: r1=10360202665625776591605886682977757294938234539486161 (pp53) r2=13380153130697716154258396236743209165877691612680584935690556371 (pp65) Version: GGNFS-0.77.1-20051202-athlon Total time: 1.28 hours. Scaled time: 2.34 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_2_119_7 n: 138621098131135558832054238655123309767746651040288331884112761962370672816402656484316913034163799730318954544881731 skew: 1.31 deg: 5 c5: 11 c0: 43 m: 1000000000000000000000000 type: snfs rlim: 1500000 alim: 1500000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 20000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved algebraic special-q in [100000, 220001) Primes: RFBsize:114155, AFBsize:113573, largePrimes:4315307 encountered Relations: rels:3788011, finalFF:272120 Max relations in full relation-set: 48 Initial matrix: 227793 x 272120 with sparse part having weight 10596266. Pruned matrix : 179876 x 181078 with weight 5024465. Total sieving time: 1.10 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.09 hours. Total square root time: 0.03 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000 total time: 1.28 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
(11·10¹⁶⁷+7)/9 = 1(2)₁₆₆3_<168> = 3 · 41 · 79 · C164
C164 = P38 · P40 · P87
P38 = 14423979966512432432545987637860750601_<38>
P40 = 2524959991453561105199033616344355110857_<40>
P87 = 345365030444882216665762967853873494551988141411835789407073140545858646627934040752067_<87>
(11·10¹⁴⁸+7)/9 = 1(2)₁₄₇3_<149> = 17² · 1241573 · 1620767868131_<13> · C128
C128 = P61 · P67
P61 = 9977951392526419577166133150855561477582761570070861812038027_<61>
P67 = 2106288571161423902638665809382880013459521046170628246982291811907_<67>

Number: n N=21016444981682612225056203512237555804076311423045693833897029194807082815809370173856574425843518830726347224042488806215387489 ( 128 digits) SNFS difficulty: 149 digits. Divisors found: Sat Feb 2 23:03:45 2008 prp61 factor: 9977951392526419577166133150855561477582761570070861812038027 Sat Feb 2 23:03:45 2008 prp67 factor: 2106288571161423902638665809382880013459521046170628246982291811907 Sat Feb 2 23:03:45 2008 elapsed time 00:35:31 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 21.00 hours. Scaled time: 17.45 units (timescale=0.831). Factorization parameters were as follows: name: KA_1_2_147_3 n: 21016444981682612225056203512237555804076311423045693833897029194807082815809370173856574425843518830726347224042488806215387489 type: snfs deg: 5 c5: 11000 c0: 7 skew: 0.23 m: 100000000000000000000000000000 rlim: 2500000 alim: 2500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved special-q in [100000, 3200001) Primes: RFBsize:183072, AFBsize:182532, largePrimes:3031135 encountered Relations: rels:3055901, finalFF:404994 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 20.86 hours. Total relation processing time: 0.14 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,2500000,2500000,26,26,45,45,2.5,2.5,100000 total time: 21.00 hours. --------- CPU info (if available) ---------- CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Total of 2 processors activated (12009.47 BogoMIPS).
(11·10¹²⁶+43)/9 = 1(2)₁₂₅7_<127> = 3 · 149 · 163 · 142067 · 214141744783562320063_<21> · C96
C96 = P40 · P57
P40 = 1745478423811049629208332776515371425419_<40>
P57 = 315897374831811624279270914479096464615835238536442426593_<57>

Number: n N=551392051907478892905276839856959560249645709930693432714313355558298115017072124938461681767467 ( 96 digits) SNFS difficulty: 127 digits. Divisors found: r1=1745478423811049629208332776515371425419 (pp40) r2=315897374831811624279270914479096464615835238536442426593 (pp57) Version: GGNFS-0.77.1-20051202-athlon Total time: 2.72 hours. Scaled time: 3.93 units (timescale=1.446). Factorization parameters were as follows: name: KA_1_2_125_7 n: 551392051907478892905276839856959560249645709930693432714313355558298115017072124938461681767467 skew: 0.83 deg: 5 c5: 110 c0: 43 m: 10000000000000000000000000 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, 400001) Primes: RFBsize:114155, AFBsize:114453, largePrimes:4691482 encountered Relations: rels:4120461, finalFF:271046 Max relations in full relation-set: 28 Initial matrix: 228675 x 271046 with sparse part having weight 12982612. Pruned matrix : 188205 x 189412 with weight 6833727. Total sieving time: 2.23 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.35 hours. Total square root time: 0.05 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,127,5,0,0,0,0,0,0,0,0,1500000,1500000,28,28,48,48,2.5,2.5,50000 total time: 2.72 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(11·10¹³¹+43)/9 = 1(2)₁₃₀7_<132> = 7 · 19 · C129
C129 = P32 · P48 · P50
P32 = 32415240075876389291454435280241_<32>
P48 = 772883054289567450015728285748118755690584982373_<48>
P50 = 36680521954763531909701891063601113368415398966683_<50>

Number: n N=28349753841333173597883662813592007973807145936190394697664372879321221423868495390013541969278759 ( 98 digits) SNFS difficulty: 132 digits. Divisors found: Sun Feb 3 00:04:25 2008 prp48 factor: 772883054289567450015728285748118755690584982373 Sun Feb 3 00:04:25 2008 prp50 factor: 36680521954763531909701891063601113368415398966683 Sun Feb 3 00:04:25 2008 elapsed time 00:05:46 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 3.06 hours. Scaled time: 2.56 units (timescale=0.837). Factorization parameters were as follows: name: KA_1_2_130_7 n: 28349753841333173597883662813592007973807145936190394697664372879321221423868495390013541969278759 type: snfs deg: 5 c5: 110 c0: 43 skew: 0.83 m: 100000000000000000000000000 rlim: 1500000 alim: 1500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved special-q in [100000, 550337) Primes: RFBsize:114155, AFBsize:114453, largePrimes:1541470 encountered Relations: rels:1615701, finalFF:252787 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 3.00 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1500000,1500000,25,25,44,44,2.5,2.5,50000 total time: 3.06 hours. --------- CPU info (if available) ---------- CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Total of 2 processors activated (12009.47 BogoMIPS).
(11·10¹⁵⁸+43)/9 = 1(2)₁₅₇7_<159> = 71 · C157
C157 = P29 · P30 · P98
P29 = 73609322750518380920243244497_<29>
P30 = 699257274423233790983654844817_<30>
P98 = 33444292414172749749400378136524476926764366571801070725522241132909588873350783579759308359249013_<98>
(11·10¹³⁶+43)/9 = 1(2)₁₃₅7_<137> = 17327 · 677426430691_<12> · C121
C121 = P50 · P71
P50 = 15069402715240311151513397026733944991125470105653_<50>
P71 = 69098500671942225559710465911019554432414961727090137082577263863265187_<71>

Number: n N=1041273133644800638436966964039937301980376146456499962236974820226681909664960757201914741690067877385787858958446802111 ( 121 digits) SNFS difficulty: 137 digits. Divisors found: r1=15069402715240311151513397026733944991125470105653 (pp50) r2=69098500671942225559710465911019554432414961727090137082577263863265187 (pp71) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.83 hours. Scaled time: 7.01 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_2_135_7 n: 1041273133644800638436966964039937301980376146456499962236974820226681909664960757201914741690067877385787858958446802111 skew: 0.83 deg: 5 c5: 110 c0: 43 m: 1000000000000000000000000000 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, 650001) Primes: RFBsize:148933, AFBsize:149531, largePrimes:5785695 encountered Relations: rels:5177843, finalFF:352761 Max relations in full relation-set: 48 Initial matrix: 298531 x 352761 with sparse part having weight 20544999. Pruned matrix : 252227 x 253783 with weight 11036455. Total sieving time: 3.39 hours. Total relation processing time: 0.10 hours. Matrix solve time: 0.29 hours. Total square root time: 0.06 hours, sqrts: 2. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,2000000,2000000,28,28,48,48,2.5,2.5,75000 total time: 3.83 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Feb 1, 2008 (6th): The factor table of 122...227 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.
Feb 1, 2008 (5th): By Sinkiti Sibata / GGNFS, Msieve
(11·10¹²⁸+7)/9 = 1(2)₁₂₇3_<129> = 3 · 61 · 79 · 38841953 · 3001001404133_<13> · C104
C104 = P47 · P58
P47 = 17820426575258291271812216801778273828263811949_<47>
P58 = 4069927209397961264478571968552512687964124279931746688039_<58>

Number: 12223_128 N=72527839001722245343433093247741785957812868472563178292041549315582239211939650085232450024037863578011 ( 104 digits) SNFS difficulty: 129 digits. Divisors found: r1=17820426575258291271812216801778273828263811949 (pp47) r2=4069927209397961264478571968552512687964124279931746688039 (pp58) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 6.18 hours. Scaled time: 4.18 units (timescale=0.676). Factorization parameters were as follows: name: 12223_128 n: 72527839001722245343433093247741785957812868472563178292041549315582239211939650085232450024037863578011 m: 10000000000000000000000000 c5: 11000 c0: 7 skew: 0.23 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, 1050001) Primes: RFBsize:63951, AFBsize:63749, largePrimes:1505085 encountered Relations: rels:1503095, finalFF:170416 Max relations in full relation-set: 28 Initial matrix: 127767 x 170416 with sparse part having weight 12944744. Pruned matrix : 115378 x 116080 with weight 7079599. Total sieving time: 5.82 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.22 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: 6.18 hours. --------- CPU info (if available) ----------
(11·10¹²⁹+7)/9 = 1(2)₁₂₈3_<130> = 1459219821067_<13> · 82785343995961669807_<20> · C98
C98 = P47 · P51
P47 = 36382216950136191665275319616069319317105322207_<47>
P51 = 278090938993464323621253478672588687018603974937181_<51>

Number: 12223_129 N=10117564874327307322152950912916434067947268348447696910741179744918424161798658125524733589278467 ( 98 digits) SNFS difficulty: 131 digits. Divisors found: r1=36382216950136191665275319616069319317105322207 (pp47) r2=278090938993464323621253478672588687018603974937181 (pp51) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 5.73 hours. Scaled time: 3.88 units (timescale=0.676). Factorization parameters were as follows: name: 12223_129 n: 10117564874327307322152950912916434067947268348447696910741179744918424161798658125524733589278467 m: 100000000000000000000000000 c5: 11 c0: 70 skew: 1.45 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, 1000001) Primes: RFBsize:63951, AFBsize:63989, largePrimes:1484925 encountered Relations: rels:1479962, finalFF:166211 Max relations in full relation-set: 28 Initial matrix: 128005 x 166211 with sparse part having weight 12291328. Pruned matrix : 116824 x 117528 with weight 6896601. Total sieving time: 5.39 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.22 hours. Time per square root: 0.05 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.73 hours. --------- CPU info (if available) ----------
(11·10¹⁴⁵+7)/9 = 1(2)₁₄₄3_<146> = 13 · 31 · 823 · 151593136619_<12> · 28621596899570201856329127192281_<32> · C97
C97 = P34 · P64
P34 = 1738141979248770825019597995643561_<34>
P64 = 4886373338108512536231001803679542238062728247725780926025401273_<64>

Thu Jan 31 09:05:46 2008 Msieve v. 1.30 Thu Jan 31 09:05:46 2008 random seeds: ed732f90 2131a286 Thu Jan 31 09:05:46 2008 factoring 8493210625248353223145884402754220986747232289349364818181442507813118382434252707555080903653153 (97 digits) Thu Jan 31 09:05:47 2008 commencing quadratic sieve (97-digit input) Thu Jan 31 09:05:48 2008 using multiplier of 1 Thu Jan 31 09:05:48 2008 using 64kb Pentium 2 sieve core Thu Jan 31 09:05:48 2008 sieve interval: 18 blocks of size 65536 Thu Jan 31 09:05:48 2008 processing polynomials in batches of 6 Thu Jan 31 09:05:48 2008 using a sieve bound of 2404033 (88167 primes) Thu Jan 31 09:05:48 2008 using large prime bound of 360604950 (28 bits) Thu Jan 31 09:05:48 2008 using double large prime bound of 2527301234494800 (43-52 bits) Thu Jan 31 09:05:48 2008 using trial factoring cutoff of 52 bits Thu Jan 31 09:05:48 2008 polynomial 'A' values have 13 factors Fri Feb 01 21:32:16 2008 88420 relations (21239 full + 67181 combined from 1335767 partial), need 88263 Fri Feb 01 21:32:44 2008 begin with 1357006 relations Fri Feb 01 21:34:37 2008 reduce to 233037 relations in 12 passes Fri Feb 01 21:34:38 2008 attempting to read 233037 relations Fri Feb 01 21:35:21 2008 recovered 233037 relations Fri Feb 01 21:35:21 2008 recovered 220181 polynomials Fri Feb 01 21:35:54 2008 attempting to build 88420 cycles Fri Feb 01 21:35:56 2008 found 88420 cycles in 6 passes Fri Feb 01 21:36:02 2008 distribution of cycle lengths: Fri Feb 01 21:36:02 2008 length 1 : 21239 Fri Feb 01 21:36:02 2008 length 2 : 15084 Fri Feb 01 21:36:02 2008 length 3 : 14823 Fri Feb 01 21:36:02 2008 length 4 : 12183 Fri Feb 01 21:36:02 2008 length 5 : 9263 Fri Feb 01 21:36:02 2008 length 6 : 6192 Fri Feb 01 21:36:02 2008 length 7 : 4006 Fri Feb 01 21:36:02 2008 length 9+: 5630 Fri Feb 01 21:36:02 2008 largest cycle: 18 relations Fri Feb 01 21:36:10 2008 matrix is 88167 x 88420 with weight 5866985 (avg 66.35/col) Fri Feb 01 21:36:58 2008 filtering completed in 3 passes Fri Feb 01 21:36:58 2008 matrix is 84507 x 84571 with weight 5639170 (avg 66.68/col) Fri Feb 01 21:37:03 2008 saving the first 48 matrix rows for later Fri Feb 01 21:37:03 2008 matrix is 84459 x 84571 with weight 4459365 (avg 52.73/col) Fri Feb 01 21:37:03 2008 matrix includes 64 packed rows Fri Feb 01 21:37:04 2008 using block size 10922 for processor cache size 256 kB Fri Feb 01 21:37:07 2008 commencing Lanczos iteration Fri Feb 01 21:43:24 2008 lanczos halted after 1337 iterations (dim = 84459) Fri Feb 01 21:43:25 2008 recovered 17 nontrivial dependencies Fri Feb 01 21:57:06 2008 prp34 factor: 1738141979248770825019597995643561 Fri Feb 01 21:57:06 2008 prp64 factor: 4886373338108512536231001803679542238062728247725780926025401273 Fri Feb 01 21:57:06 2008 elapsed time 36:51:20
Feb 1, 2008 (4th): By Jo Yeong Uk / GGNFS
(11·10¹²⁷+7)/9 = 1(2)₁₂₆3_<128> = 13 · 41 · 39930894669768828456551609_<26> · C99
C99 = P39 · P61
P39 = 131553635963448102867023745823633166713_<39>
P61 = 4365269589315262899723003685730075290012150262832120397531843_<61>

Number: 12223_127 N=574267086435090699768103539203445300361508173374549994005694693376903137493747861523667279345142059 ( 99 digits) SNFS difficulty: 128 digits. Divisors found: r1=131553635963448102867023745823633166713 (pp39) r2=4365269589315262899723003685730075290012150262832120397531843 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 2.18 hours. Scaled time: 4.05 units (timescale=1.859). Factorization parameters were as follows: n: 574267086435090699768103539203445300361508173374549994005694693376903137493747861523667279345142059 m: 10000000000000000000000000 c5: 1100 c0: 7 skew: 0.36 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, 950001) Primes: RFBsize:78498, AFBsize:78502, largePrimes:1568919 encountered Relations: rels:1614187, finalFF:218469 Max relations in full relation-set: 28 Initial matrix: 157067 x 218469 with sparse part having weight 11091121. Pruned matrix : 130554 x 131403 with weight 5278948. Total sieving time: 2.10 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,128,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 2.18 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹³⁰+7)/9 = 1(2)₁₂₉3_<131> = 31 · 857 · 109891 · C121
C121 = P52 · P69
P52 = 6368333907666863327198144994659776908553310493558001_<52>
P69 = 657384875534192380051162907704171430655174054549731898566209496449859_<69>

Number: 12223_130 N=4186446393251757937089321095384294030882377489367556216227186001816279187420481326563415495130071266809768698299004771859 ( 121 digits) SNFS difficulty: 131 digits. Divisors found: r1=6368333907666863327198144994659776908553310493558001 (pp52) r2=657384875534192380051162907704171430655174054549731898566209496449859 (pp69) Version: GGNFS-0.77.1-20050930-nocona Total time: 1.93 hours. Scaled time: 3.60 units (timescale=1.860). Factorization parameters were as follows: n: 4186446393251757937089321095384294030882377489367556216227186001816279187420481326563415495130071266809768698299004771859 m: 100000000000000000000000000 c5: 11 c0: 7 skew: 0.91 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:78392, largePrimes:1557066 encountered Relations: rels:1615830, finalFF:230414 Max relations in full relation-set: 28 Initial matrix: 156955 x 230414 with sparse part having weight 11524693. Pruned matrix : 122946 x 123794 with weight 5035615. Total sieving time: 1.87 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,131,5,0,0,0,0,0,0,0,0,1000000,1000000,25,25,46,46,2.2,2.2,50000 total time: 1.93 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹³²+7)/9 = 1(2)₁₃₁3_<133> = 17 · 41 · 241 · 249729043237740918459457607_<27> · C101
C101 = P35 · P67
P35 = 15627040354064215471639879571774527_<35>
P67 = 1864466429448898434587464768488764084002767058127712202281064401391_<67>

Number: 12223_132 N=29136092131795957409269524543599123164049664084769673527820555195490040265768211379642590850877167057 ( 101 digits) SNFS difficulty: 133 digits. Divisors found: r1=15627040354064215471639879571774527 (pp35) r2=1864466429448898434587464768488764084002767058127712202281064401391 (pp67) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.19 hours. Scaled time: 5.93 units (timescale=1.858). Factorization parameters were as follows: n: 29136092131795957409269524543599123164049664084769673527820555195490040265768211379642590850877167057 m: 100000000000000000000000000 c5: 1100 c0: 7 skew: 0.36 type: snfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [600000, 1250001) Primes: RFBsize:92938, AFBsize:92875, largePrimes:1687326 encountered Relations: rels:1749659, finalFF:237564 Max relations in full relation-set: 28 Initial matrix: 185880 x 237564 with sparse part having weight 13207043. Pruned matrix : 163716 x 164709 with weight 7305591. Total sieving time: 3.08 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,133,5,0,0,0,0,0,0,0,0,1200000,1200000,25,25,46,46,2.2,2.2,50000 total time: 3.19 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
(11·10¹³³+7)/9 = 1(2)₁₃₂3_<134> = 13² · 216967 · 274877791810536202415819_<24> · C103
C103 = P49 · P54
P49 = 7288838851121349921757605985046744807118531852797_<49>
P54 = 166368762117567129996632571508461763704342293538361807_<54>

Number: 12223_133 N=1212635096935489162985899520225286878375226922845226590025671623905132630667309062931776714979850924179 ( 103 digits) SNFS difficulty: 136 digits. Divisors found: r1=7288838851121349921757605985046744807118531852797 (pp49) r2=166368762117567129996632571508461763704342293538361807 (pp54) Version: GGNFS-0.77.1-20050930-nocona Total time: 3.81 hours. Scaled time: 7.07 units (timescale=1.858). Factorization parameters were as follows: n: 1212635096935489162985899520225286878375226922845226590025671623905132630667309062931776714979850924179 m: 1000000000000000000000000000 c5: 11 c0: 700 skew: 2.29 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, 1400001) Primes: RFBsize:107126, AFBsize:106864, largePrimes:2327353 encountered Relations: rels:2474302, finalFF:297230 Max relations in full relation-set: 28 Initial matrix: 214057 x 297230 with sparse part having weight 23663112. Pruned matrix : 186367 x 187501 with weight 11941864. Total sieving time: 3.64 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.11 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,136,5,0,0,0,0,0,0,0,0,1400000,1400000,25,25,47,47,2.3,2.3,50000 total time: 3.81 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 Memory for crash kernel (0x0 to 0x0) notwithin permissible range Memory: 8178280k/8912896k available (2434k kernel code, 208060k reserved, 1235k data, 192k init) Calibrating delay using timer specific routine.. 4812.90 BogoMIPS (lpj=2406453) Calibrating delay using timer specific routine.. 4810.23 BogoMIPS (lpj=2405118) Calibrating delay using timer specific routine.. 4810.24 BogoMIPS (lpj=2405123) Calibrating delay using timer specific routine.. 4810.22 BogoMIPS (lpj=2405114)
Feb 1, 2008 (3rd): By Robert Backstrom / GGNFS, GMP-ECM, Msieve
(11·10¹⁴⁰+7)/9 = 1(2)₁₃₉3_<141> = 3 · 3461 · 1095607588589_<13> · 834558173034127_<15> · 4419964196853031_<16> · C94
C94 = P47 · P48
P47 = 23791675036360545008892228841804329617387361131_<47>
P48 = 122425505136829100536474798340818755144635369207_<48>

Number: n N=2912707834377726580270175322931490941526698320396340756910726140921366521664757928917626093117 ( 94 digits) Divisors found: r1=23791675036360545008892228841804329617387361131 (pp47) r2=122425505136829100536474798340818755144635369207 (pp48) Version: GGNFS-0.77.1-20051202-athlon Total time: 4.46 hours. Scaled time: 8.16 units (timescale=1.829). Factorization parameters were as follows: name: KA_1_2_139_3 n: 2912707834377726580270175322931490941526698320396340756910726140921366521664757928917626093117 m: 4536326114264324860543 deg: 4 c4: 6878280 c3: 33377034 c2: -62303463404508495 c1: -64779800640570195830 c0: -1496909709532791612456 skew: 1635.250 type: gnfs # adj. I(F,S) = 54.762 # E(F1,F2) = 4.865863e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1201707937. # 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, 940001) Primes: RFBsize:92938, AFBsize:92957, largePrimes:1797298 encountered Relations: rels:1838774, finalFF:224475 Max relations in full relation-set: 48 Initial matrix: 185979 x 224475 with sparse part having weight 15141846. Pruned matrix : 161730 x 162723 with weight 8462261. Polynomial selection time: 0.17 hours. Total sieving time: 4.09 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: gnfs,93,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000 total time: 4.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
6·10¹⁶⁶-1 = 5(9)₁₆₆_<167> = 1415744095201_<13> · 12712979409464320156621733_<26> · C130
C130 = P35 · P38 · P58
P35 = 37154591566665333519909747568949477_<35>
P38 = 64960406415076577673529410226373905391_<38>
P58 = 1381204303898828183886023860415270650257402155513930927929_<58>

Number: n N=89723592923520817279753844783907710962661690251065459520368194642257369051521960751508285565239 ( 95 digits) Divisors found: r1=64960406415076577673529410226373905391 (pp38) r2=1381204303898828183886023860415270650257402155513930927929 (pp58) Version: GGNFS-0.77.1-20051202-athlon Total time: 6.46 hours. Scaled time: 9.34 units (timescale=1.446). Factorization parameters were as follows: name: KA_5_9_166 n: 89723592923520817279753844783907710962661690251065459520368194642257369051521960751508285565239 m: 5984868794652303062657 deg: 4 c4: 69933960 c3: 104353378371 c2: 1096699571646412484 c1: -848692618763956120 c0: -668297857122058317044800 skew: 1635.250 type: gnfs # adj. I(F,S) = 55.465 # E(F1,F2) = 3.088979e-05 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=60.00000000, seed=1201785727. # maxskew=2000.0 # These parameters should be manually set: rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 45 mfba: 45 rlambda: 2.4 alambda: 2.4 qintsize: 50000 type: gnfs Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [100000, 1000001) Primes: RFBsize:92938, AFBsize:93074, largePrimes:2445364 encountered Relations: rels:2348038, finalFF:215671 Max relations in full relation-set: 28 Initial matrix: 186089 x 215671 with sparse part having weight 14207860. Pruned matrix : 168592 x 169586 with weight 9112248. Total sieving time: 5.83 hours. Total relation processing time: 0.11 hours. Matrix solve time: 0.42 hours. Total square root time: 0.10 hours, sqrts: 3. Prototype def-par.txt line would be: gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,26,26,45,45,2.4,2.4,60000 total time: 6.46 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
(5·10¹⁶⁶-17)/3 = 1(6)₁₆₅1_<167> = 313 · 713279355969704807587_<21> · C143
C143 = P43 · P101
P43 = 6906530378904595777299619718427335413392823_<43>
P101 = 10808982929600989913554744120661733333612409183010564466357031082357367707270870872976077015961379497_<101>

Number: n N=74652568968350432571858162428041298959592617781581769536102339784684274263627848893862771900886916705702120332595381912452867047041224239150031 ( 143 digits) SNFS difficulty: 166 digits. Divisors found: Fri Feb 1 15:09:29 2008 prp43 factor: 6906530378904595777299619718427335413392823 Fri Feb 1 15:09:29 2008 prp101 factor: 10808982929600989913554744120661733333612409183010564466357031082357367707270870872976077015961379497 Fri Feb 1 15:09:29 2008 elapsed time 00:49:24 (Msieve 1.33) Version: GGNFS-0.77.1-20050930-k8 Total time: 46.58 hours. Scaled time: 39.13 units (timescale=0.840). Factorization parameters were as follows: name: KA_1_6_165_1 n: 74652568968350432571858162428041298959592617781581769536102339784684274263627848893862771900886916705702120332595381912452867047041224239150031 type: snfs deg: 5 c5: 50 c0: -17 skew: 0.81 m: 1000000000000000000000000000000000 rlim: 3000000 alim: 3000000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000469) Primes: RFBsize:216816, AFBsize:217226, largePrimes:5601777 encountered Relations: rels:5457799, finalFF:447969 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 46.40 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,166,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.5,2.5,100000 total time: 46.58 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).
(11·10¹²⁶+7)/9 = 1(2)₁₂₅3_<127> = 47 · C125
C125 = P34 · P39 · P54
P34 = 2028013358477151338981105966488181_<34>
P39 = 100997020886744923001474572087204796497_<39>
P54 = 126961762538913698290780642666257974194325729545261037_<54>

Number: n N=12822759782960615911248464548662628250867681715191527970142640677251818434976713082328187389 ( 92 digits) Divisors found: r1=100997020886744923001474572087204796497 (pp39) r2=126961762538913698290780642666257974194325729545261037 (pp54) Version: GGNFS-0.77.1-20051202-athlon Total time: 3.79 hours. Scaled time: 5.48 units (timescale=1.448). Factorization parameters were as follows: name: KA_1_2_125_3 n: 12822759782960615911248464548662628250867681715191527970142640677251818434976713082328187389 m: 828222499879303485153 deg: 4 c4: 27251688 c3: 116985641150 c2: -35161021028079089 c1: -401192335890363161 c0: 14492918840677471284545 skew: 1635.250 type: gnfs # adj. I(F,S) = 52.000 # E(F1,F2) = 1.265408e-04 # GGNFS version 0.77.1-20051202-athlon polyselect. # Options were: # lcd=1, enumLCD=24, maxS1=58.00000000, seed=1201825203. # maxskew=2000.0 # These parameters should be manually set: rlim: 700000 alim: 700000 lpbr: 26 lpba: 26 mfbr: 44 mfba: 44 rlambda: 2.4 alambda: 2.4 qintsize: 50000 type: gnfs Factor base limits: 700000/700000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 44/44 Sieved algebraic special-q in [100000, 650001) Primes: RFBsize:56543, AFBsize:56107, largePrimes:2044474 encountered Relations: rels:1905213, finalFF:138257 Max relations in full relation-set: 28 Initial matrix: 112725 x 138257 with sparse part having weight 10597229. Pruned matrix : 104195 x 104822 with weight 6271740. Total sieving time: 3.55 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.13 hours. Total square root time: 0.02 hours, sqrts: 1. Prototype def-par.txt line would be: gnfs,91,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,26,26,44,44,2.4,2.4,40000 total time: 3.79 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3400+
7·10¹⁹²+3 = 7(0)₁₉₁3_<193> = 31 · 1105109 · 1243211 · 4470822866051487481_<19> · 5290673163123042490177645270463_<31> · C130
C130 = P39 · P92
P39 = 360922089125386739265100361213804922199_<39>
P92 = 19251941213231301805507821363673906075280686340797762406923312617295075302212157369103874171_<92>
9·10¹⁶⁵+7 = 9(0)₁₆₄7_<166> = 43 · 23131 · 1418088383_<10> · 35942958881_<11> · C141
C141 = P45 · P47 · P49
P45 = 316632999964816314980011979278660259022505001_<45>
P47 = 74603769316589492099122294657235536113237612649_<47>
P49 = 7515287056062349794626336991939024137322161656577_<49>

Number: n N=177526225727465427375076325956215494327313122747943829679376540302091740288043953526266170975409861004259333830654434655259996183735344107473 ( 141 digits) SNFS difficulty: 165 digits. Divisors found: Fri Feb 01 18:19:06 2008 prp45 factor: 316632999964816314980011979278660259022505001 Fri Feb 01 18:19:06 2008 prp47 factor: 74603769316589492099122294657235536113237612649 Fri Feb 01 18:19:06 2008 prp49 factor: 7515287056062349794626336991939024137322161656577 Fri Feb 01 18:19:06 2008 elapsed time 01:04:51 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 40.01 hours. Scaled time: 73.18 units (timescale=1.829). Factorization parameters were as follows: name: KA_9_0_164_7 n: 177526225727465427375076325956215494327313122747943829679376540302091740288043953526266170975409861004259333830654434655259996183735344107473 skew: 0.95 deg: 5 c5: 9 c0: 7 m: 1000000000000000000000000000000000 type: snfs rlim: 3200000 alim: 3200000 lpbr: 28 lpba: 28 mfbr: 48 mfba: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 48/48 Sieved special-q in [100000, 3000791) Primes: RFBsize:230209, AFBsize:230717, largePrimes:7426505 encountered Relations: rels:6885081, finalFF:513570 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 39.83 hours. Total relation processing time: 0.18 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 40.01 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 X2 6000+
Feb 1, 2008 (2nd): By Yousuke Koide
(10¹⁴¹⁷-1)/9 is divisible by 57691258324093633641909137807790199_<35>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)
Feb 1, 2008: By Robert Backstrom / GGNFS, Msieve
(4·10¹⁶⁵+41)/9 = (4)₁₆₄9_<165> = 5849891987_<10> · 12569892767983_<14> · C142
C142 = P70 · P73
P70 = 1281570790751209261870606118509601319231489235378717382008982025914249_<70>
P73 = 4716235264308885999918029689628367436288591731976079138987327132460971981_<73>

Number: n N=6044189357049077446644490449750213711247494210862836335124304401771018375433568259682738692991215544680682817617072084546641347382952697657269 ( 142 digits) SNFS difficulty: 165 digits. Divisors found: Fri Feb 01 03:34:11 2008 prp70 factor: 1281570790751209261870606118509601319231489235378717382008982025914249 Fri Feb 01 03:34:11 2008 prp73 factor: 4716235264308885999918029689628367436288591731976079138987327132460971981 Fri Feb 01 03:34:11 2008 elapsed time 01:59:28 (Msieve 1.33) Version: GGNFS-0.77.1-20051202-athlon Total time: 60.53 hours. Scaled time: 106.11 units (timescale=1.753). Factorization parameters were as follows: name: KA_4_164_9 n: 6044189357049077446644490449750213711247494210862836335124304401771018375433568259682738692991215544680682817617072084546641347382952697657269 type: snfs skew: 1.59 deg: 5 c5: 4 c0: 41 m: 1000000000000000000000000000000000 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, 2900119) Primes: RFBsize:230209, AFBsize:230843, largePrimes:7459245 encountered Relations: rels:6912771, finalFF:514265 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 60.28 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,165,5,0,0,0,0,0,0,0,0,3200000,3200000,28,28,48,48,2.5,2.5,100000 total time: 60.53 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

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