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Old 2008-01-11, 16:16   #1
fivemack
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Default Bernoulli and Euler numbers (Sam Wagstaff project)

http://homes.cerias.purdue.edu/~ssw/...lli/index.html is the main page for this project; http://homes.cerias.purdue.edu/~ssw/bernoulli/bnum and http://homes.cerias.purdue.edu/~ssw/bernoulli/enum list the factors known.

http://en.wikipedia.org/wiki/Euler_numbers and http://en.wikipedia.org/wiki/Bernoulli_number define the Euler and Bernoulli numbers; the N### being factorised here are the numerators of the Bernoulli numbers, obtained in gp as
Code:
numerator(bernfrac(###))
and the E### by
Code:
N=###
default(seriesprecision, N+10)
T=taylor(1/cosh(x),x)
polcoeff(T,N) * prod(i=1,N,i)
The numbers are not as far as I know SNFS-amenable, and they grow quite large quite quickly, so this is mostly an ECM project; Sam has done a fair amount of ECM over these and found at least one 50-digit factor. Though sievers (OK, sievers with incredible resources in the cases of the last four numbers) might be interested in

Code:
*N176  C138  561602126238949966093208044713565096735647776816214118967637030543319164290535687405179873997375297259308787285343674519616007041894252147
*N218  C141 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907
N190  C152 15715496152776982489778142635341275866050684476125452035397458516486943107317760601061082109700169864160537677622973197179487906036510768485502942125239
N222  C160 1944507419702020239105947860297224309650538619435034558524428604333013765995502187641029511486447333003210637642920189364415139564903097189370535817294173277263
E122  C169 3818723881495031819672087511891226633108668231418417614458853563199270304677387223426769127666923474708712472353170702968802174836014233752821322232673203335351690972993
E120  C170 30614112198603477540294953453509600250642722488962340055423980380793433321880177726367467667922713955685560746809449855119053214908867791649739871010411068882989664254337
N202  C173 17207166720977090018555554232695219240449673152984728941390151653840542465501186304298189852428343402432734665195226293993239530334336681612897891942559122093290584231690241
N236  C174 138118725770091309803503176746772215425355788906411993609345186278517863537509783400599679746045473713900370128406411687517775462051181593984806553696358200115520161404684413
ECM work

Code:
E120 4590@11e6, 7000@43e6 (sean)
GNFS results
Code:
N176 finished by fivemack, 14/2/2008
N218 finished by fivemack, 23/2/2008

Last fiddled with by fivemack on 2008-02-23 at 17:21
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Old 2008-01-13, 00:54   #2
bdodson
 
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Default

Quote:
Originally Posted by fivemack View Post
Sam reports that he is updating the bernouli, euler and bell lists as soon
as he gets factors. He's also added a link with the remaining composites
(all three lists combined),

http://homes.cerias.purdue.edu/~ssw/bernoulli/composite

we had 82 when we started our current run (I had three factors from an
earlier run, 2004). Sam reports the current count as 76 (which includes
remaining composite cofactors, so we found more than six). I'm about
to finish a t45, then switch that cluster back to Cunninghams. -bruce

[the Bell numbers are perhaps snfs candidates?]
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Old 2008-02-14, 18:31   #3
fivemack
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Default

N176 splits as

Code:
P60 161682280601750017807051565594123306297091203059258385807467
P79 3473492111496547587945366626225248021650210851846887340916568090835384897238041
Half a day to get the polynomials, four and a half days on about four CPUs to get 23725909 relations of which 21708585 unique, twelve hours on two CPUs to solve a 2063037 x 2063285 matrix with weight 145645111 (70.59/col), 70 minutes for the square root, factors from the first dependency.
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Old 2008-02-23, 17:20   #4
fivemack
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Default

N218 splits as

Code:
P66 529041127136621894810092661001283800527316908098655885710614302743
P75 575062201126629614470645738970165209255701496570272209233469241277154408549
This took about 48 CPU-hours polynomial search, almost exactly 600 CPU-hours to sieve, 48 CPU-hours on two cores to do the linear algebra, and a slightly frustrating 18 hours on one core to find the factors on the ninth dependency.

Code:
Thu Feb 21 18:15:08 2008  Msieve v. 1.33
Thu Feb 21 18:15:08 2008  random seeds: 1a29a284 f5aafdbe
Thu Feb 21 18:15:08 2008  factoring 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 (141 digits)
Thu Feb 21 18:15:09 2008  no P-1/P+1/ECM available, skipping
Thu Feb 21 18:15:09 2008  commencing number field sieve (141-digit input)
Thu Feb 21 18:15:09 2008  R0: -811108827276972422199078148
Thu Feb 21 18:15:09 2008  R1:  455195620287979
Thu Feb 21 18:15:09 2008  A0:  57184039631828920586603735624145
Thu Feb 21 18:15:09 2008  A1: -7783023214726791392303474410
Thu Feb 21 18:15:09 2008  A2:  28580437883961308732287
Thu Feb 21 18:15:09 2008  A3:  287657668694377976
Thu Feb 21 18:15:09 2008  A4: -154800049518
Thu Feb 21 18:15:09 2008  A5:  866580
Thu Feb 21 18:15:09 2008  size score = 1.504655e-14, Murphy alpha = -5.292384, combined = 8.781893e-14
Thu Feb 21 18:17:04 2008  restarting with 40737161 relations
Thu Feb 21 18:17:08 2008  added 3741 free relations
Thu Feb 21 18:17:08 2008  
Thu Feb 21 18:17:08 2008  commencing relation filtering
Thu Feb 21 18:17:08 2008  commencing duplicate removal, pass 1
Thu Feb 21 18:23:35 2008  found 5048404 hash collisions in 40740902 relations
Thu Feb 21 18:23:35 2008  commencing duplicate removal, pass 2
Thu Feb 21 18:24:23 2008  found 3077851 duplicates and 37663051 unique relations
Thu Feb 21 18:24:23 2008  memory use: 153.2 MB
Thu Feb 21 18:24:24 2008  ignoring smallest 78498 rational and 78521 algebraic ideals
Thu Feb 21 18:24:24 2008  filtering rational ideals above 1000000
Thu Feb 21 18:24:24 2008  filtering algebraic ideals above 1000000
Thu Feb 21 18:24:24 2008  need 266932 more relations than ideals
Thu Feb 21 18:24:24 2008  commencing singleton removal, pass 1
Thu Feb 21 18:31:08 2008  relations with 0 large ideals: 645
Thu Feb 21 18:31:08 2008  relations with 1 large ideals: 927
Thu Feb 21 18:31:08 2008  relations with 2 large ideals: 26089
Thu Feb 21 18:31:08 2008  relations with 3 large ideals: 300411
Thu Feb 21 18:31:08 2008  relations with 4 large ideals: 1796078
Thu Feb 21 18:31:08 2008  relations with 5 large ideals: 5867662
Thu Feb 21 18:31:08 2008  relations with 6 large ideals: 10537022
Thu Feb 21 18:31:08 2008  relations with 7+ large ideals: 19134217
Thu Feb 21 18:31:08 2008  37663051 relations and about 35123001 large ideals
Thu Feb 21 18:31:09 2008  commencing singleton removal, pass 2
Thu Feb 21 18:37:57 2008  found 11945747 singletons
Thu Feb 21 18:37:57 2008  current dataset: 25717304 relations and about 21390814 large ideals
Thu Feb 21 18:37:58 2008  commencing singleton removal, pass 3
Thu Feb 21 18:42:56 2008  found 2710394 singletons
Thu Feb 21 18:42:56 2008  current dataset: 23006910 relations and about 18560255 large ideals
Thu Feb 21 18:42:57 2008  commencing singleton removal, pass 4
Thu Feb 21 18:47:14 2008  found 669266 singletons
Thu Feb 21 18:47:14 2008  current dataset: 22337644 relations and about 17882645 large ideals
Thu Feb 21 18:47:15 2008  commencing singleton removal, pass 5
Thu Feb 21 18:51:26 2008  found 165033 singletons
Thu Feb 21 18:51:26 2008  current dataset: 22172611 relations and about 17717079 large ideals
Thu Feb 21 18:51:27 2008  commencing singleton removal, final pass
Thu Feb 21 18:58:34 2008  memory use: 715.7 MB
Thu Feb 21 18:59:10 2008  commencing in-memory singleton removal
Thu Feb 21 18:59:17 2008  begin with 22172611 relations and 21691047 unique ideals
Thu Feb 21 19:01:02 2008  reduce to 14595796 relations and 13630413 ideals in 23 passes
Thu Feb 21 19:01:02 2008  max relations containing the same ideal: 176
Thu Feb 21 19:01:28 2008  removing 2771538 relations and 2422313 ideals in 349225 cliques
Thu Feb 21 19:01:30 2008  commencing in-memory singleton removal
Thu Feb 21 19:01:34 2008  begin with 11824258 relations and 13630413 unique ideals
Thu Feb 21 19:02:15 2008  reduce to 11460968 relations and 10833677 ideals in 12 passes
Thu Feb 21 19:02:15 2008  max relations containing the same ideal: 137
Thu Feb 21 19:02:33 2008  removing 2035086 relations and 1685861 ideals in 349225 cliques
Thu Feb 21 19:02:35 2008  commencing in-memory singleton removal
Thu Feb 21 19:02:37 2008  begin with 9425882 relations and 10833677 unique ideals
Thu Feb 21 19:03:05 2008  reduce to 9162490 relations and 8876526 ideals in 10 passes
Thu Feb 21 19:03:05 2008  max relations containing the same ideal: 114
Thu Feb 21 19:03:19 2008  removing 187553 relations and 168522 ideals in 19031 cliques
Thu Feb 21 19:03:20 2008  commencing in-memory singleton removal
Thu Feb 21 19:03:23 2008  begin with 8974937 relations and 8876526 unique ideals
Thu Feb 21 19:03:38 2008  reduce to 8972392 relations and 8705456 ideals in 6 passes
Thu Feb 21 19:03:38 2008  max relations containing the same ideal: 112
Thu Feb 21 19:03:42 2008  dataset has 70.0% excess relations
Thu Feb 21 19:03:42 2008  ignoring smallest 71274 rational and 71232 algebraic ideals
Thu Feb 21 19:03:42 2008  filtering rational ideals above 900000
Thu Feb 21 19:03:42 2008  filtering algebraic ideals above 900000
Thu Feb 21 19:03:42 2008  need 240242 more relations than ideals
Thu Feb 21 19:03:42 2008  commencing singleton removal, final pass
Thu Feb 21 19:06:13 2008  memory use: 288.0 MB
Thu Feb 21 19:06:18 2008  commencing in-memory singleton removal
Thu Feb 21 19:06:21 2008  begin with 8972392 relations and 8719969 unique ideals
Thu Feb 21 19:06:23 2008  reduce to 8972392 relations and 8719969 ideals in 1 passes
Thu Feb 21 19:06:24 2008  max relations containing the same ideal: 126
Thu Feb 21 19:06:39 2008  dataset has 60.8% excess relations
Thu Feb 21 19:06:40 2008  ignoring smallest 63951 rational and 63944 algebraic ideals
Thu Feb 21 19:06:40 2008  filtering rational ideals above 800000
Thu Feb 21 19:06:40 2008  filtering algebraic ideals above 800000
Thu Feb 21 19:06:40 2008  need 201938 more relations than ideals
Thu Feb 21 19:06:40 2008  commencing singleton removal, final pass
Thu Feb 21 19:09:15 2008  memory use: 292.4 MB
Thu Feb 21 19:09:23 2008  commencing in-memory singleton removal
Thu Feb 21 19:09:25 2008  begin with 8972392 relations and 8734580 unique ideals
Thu Feb 21 19:09:28 2008  reduce to 8972392 relations and 8734580 ideals in 1 passes
Thu Feb 21 19:09:28 2008  max relations containing the same ideal: 134
Thu Feb 21 19:09:43 2008  removing 144301 relations and 126364 ideals in 17937 cliques
Thu Feb 21 19:09:43 2008  commencing in-memory singleton removal
Thu Feb 21 19:09:46 2008  begin with 8828091 relations and 8734580 unique ideals
Thu Feb 21 19:09:58 2008  reduce to 8826558 relations and 8606679 ideals in 5 passes
Thu Feb 21 19:09:58 2008  max relations containing the same ideal: 132
Thu Feb 21 19:10:11 2008  removing 133397 relations and 115460 ideals in 17937 cliques
Thu Feb 21 19:10:12 2008  commencing in-memory singleton removal
Thu Feb 21 19:10:15 2008  begin with 8693161 relations and 8606679 unique ideals
Thu Feb 21 19:10:29 2008  reduce to 8691658 relations and 8489713 ideals in 6 passes
Thu Feb 21 19:10:29 2008  max relations containing the same ideal: 130
Thu Feb 21 19:10:33 2008  dataset has 28.6% excess relations
Thu Feb 21 19:10:33 2008  ignoring smallest 56543 rational and 56481 algebraic ideals
Thu Feb 21 19:10:33 2008  filtering rational ideals above 700000
Thu Feb 21 19:10:33 2008  filtering algebraic ideals above 700000
Thu Feb 21 19:10:33 2008  need 169580 more relations than ideals
Thu Feb 21 19:10:33 2008  commencing singleton removal, final pass
Thu Feb 21 19:12:56 2008  memory use: 287.8 MB
Thu Feb 21 19:13:04 2008  commencing in-memory singleton removal
Thu Feb 21 19:13:07 2008  begin with 8691658 relations and 8504584 unique ideals
Thu Feb 21 19:13:10 2008  reduce to 8691658 relations and 8504584 ideals in 1 passes
Thu Feb 21 19:13:10 2008  max relations containing the same ideal: 143
Thu Feb 21 19:13:25 2008  removing 66828 relations and 58081 ideals in 8747 cliques
Thu Feb 21 19:13:25 2008  commencing in-memory singleton removal
Thu Feb 21 19:13:28 2008  begin with 8624830 relations and 8504584 unique ideals
Thu Feb 21 19:13:40 2008  reduce to 8624469 relations and 8446138 ideals in 5 passes
Thu Feb 21 19:13:40 2008  max relations containing the same ideal: 143
Thu Feb 21 19:13:53 2008  removing 62131 relations and 53384 ideals in 8747 cliques
Thu Feb 21 19:13:53 2008  commencing in-memory singleton removal
Thu Feb 21 19:13:56 2008  begin with 8562338 relations and 8446138 unique ideals
Thu Feb 21 19:14:08 2008  reduce to 8562020 relations and 8392436 ideals in 5 passes
Thu Feb 21 19:14:08 2008  max relations containing the same ideal: 142
Thu Feb 21 19:14:12 2008  dataset has 8.0% excess relations
Thu Feb 21 19:14:15 2008  relations with 0 large ideals: 476
Thu Feb 21 19:14:15 2008  relations with 1 large ideals: 332
Thu Feb 21 19:14:15 2008  relations with 2 large ideals: 7818
Thu Feb 21 19:14:15 2008  relations with 3 large ideals: 76541
Thu Feb 21 19:14:15 2008  relations with 4 large ideals: 393865
Thu Feb 21 19:14:15 2008  relations with 5 large ideals: 1185580
Thu Feb 21 19:14:15 2008  relations with 6 large ideals: 2151598
Thu Feb 21 19:14:15 2008  relations with 7+ large ideals: 4745810
Thu Feb 21 19:14:15 2008  commencing 2-way merge
Thu Feb 21 19:14:34 2008  reduce to 5042656 relation sets and 4873072 unique ideals
Thu Feb 21 19:14:34 2008  commencing full merge
Thu Feb 21 19:17:07 2008  memory use: 591.0 MB
Thu Feb 21 19:17:07 2008  found 2721571 cycles, need 2665272
Thu Feb 21 19:17:09 2008  weight of 2665272 cycles is about 173381650 (65.05/cycle)
Thu Feb 21 19:17:09 2008  distribution of cycle lengths:
Thu Feb 21 19:17:09 2008  1 relations: 407063
Thu Feb 21 19:17:09 2008  2 relations: 357605
Thu Feb 21 19:17:09 2008  3 relations: 341292
Thu Feb 21 19:17:09 2008  4 relations: 303387
Thu Feb 21 19:17:09 2008  5 relations: 258936
Thu Feb 21 19:17:09 2008  6 relations: 224016
Thu Feb 21 19:17:09 2008  7 relations: 187295
Thu Feb 21 19:17:09 2008  8 relations: 152413
Thu Feb 21 19:17:09 2008  9 relations: 122717
Thu Feb 21 19:17:09 2008  10+ relations: 310548
Thu Feb 21 19:17:09 2008  heaviest cycle: 16 relations
Thu Feb 21 19:17:10 2008  commencing cycle optimization
Thu Feb 21 19:17:15 2008  start with 13209822 relations
Thu Feb 21 19:17:42 2008  pruned 67989 relations
Thu Feb 21 19:17:43 2008  memory use: 477.3 MB
Thu Feb 21 19:17:43 2008  distribution of cycle lengths:
Thu Feb 21 19:17:43 2008  1 relations: 407063
Thu Feb 21 19:17:43 2008  2 relations: 358360
Thu Feb 21 19:17:43 2008  3 relations: 343421
Thu Feb 21 19:17:43 2008  4 relations: 304652
Thu Feb 21 19:17:43 2008  5 relations: 261024
Thu Feb 21 19:17:43 2008  6 relations: 224900
Thu Feb 21 19:17:43 2008  7 relations: 188093
Thu Feb 21 19:17:43 2008  8 relations: 152385
Thu Feb 21 19:17:43 2008  9 relations: 122611
Thu Feb 21 19:17:43 2008  10+ relations: 302763
Thu Feb 21 19:17:43 2008  heaviest cycle: 16 relations
Thu Feb 21 19:17:53 2008  
Thu Feb 21 19:17:53 2008  commencing linear algebra
Thu Feb 21 19:17:56 2008  read 2665272 cycles
Thu Feb 21 19:18:08 2008  cycles contain 8270613 unique relations
Thu Feb 21 19:19:44 2008  read 8270613 relations
Thu Feb 21 19:20:01 2008  using 32 quadratic characters above 536868594
Thu Feb 21 19:21:24 2008  building initial matrix
Thu Feb 21 19:23:30 2008  memory use: 1101.8 MB
Thu Feb 21 19:23:37 2008  read 2665272 cycles
Thu Feb 21 19:23:44 2008  matrix is 2665100 x 2665272 (769.7 MB) with weight 255503864 (95.86/col)
Thu Feb 21 19:23:44 2008  sparse part has weight 169800303 (63.71/col)
Thu Feb 21 19:24:34 2008  filtering completed in 2 passes
Thu Feb 21 19:24:35 2008  matrix is 2659205 x 2659377 (769.2 MB) with weight 255252074 (95.98/col)
Thu Feb 21 19:24:35 2008  sparse part has weight 169740539 (63.83/col)
Thu Feb 21 19:25:26 2008  read 2659377 cycles
Thu Feb 21 19:25:35 2008  matrix is 2659205 x 2659377 (769.2 MB) with weight 255252074 (95.98/col)
Thu Feb 21 19:25:35 2008  sparse part has weight 169740539 (63.83/col)
Thu Feb 21 19:25:35 2008  saving the first 48 matrix rows for later
Thu Feb 21 19:25:36 2008  matrix is 2659157 x 2659377 (743.7 MB) with weight 196294453 (73.81/col)
Thu Feb 21 19:25:36 2008  sparse part has weight 168360661 (63.31/col)
Thu Feb 21 19:25:36 2008  matrix includes 64 packed rows
Thu Feb 21 19:25:36 2008  using block size 65536 for processor cache size 4096 kB
Thu Feb 21 19:25:57 2008  commencing Lanczos iteration (2 threads)
Thu Feb 21 19:25:57 2008  memory use: 728.0 MB
Fri Feb 22 18:32:38 2008  lanczos halted after 42058 iterations (dim = 2659157)
Fri Feb 22 18:32:44 2008  recovered 44 nontrivial dependencies
Fri Feb 22 18:32:46 2008  
Fri Feb 22 18:32:46 2008  commencing square root phase
Fri Feb 22 18:32:46 2008  reading relations for dependency 64
Fri Feb 22 18:32:46 2008  read 0 cycles
Fri Feb 22 18:32:46 2008  elapsed time 24:17:38
 (I was out that evening)
Sat Feb 23 00:01:25 2008  
Sat Feb 23 00:01:25 2008  
Sat Feb 23 00:01:25 2008  Msieve v. 1.33
Sat Feb 23 00:01:25 2008  random seeds: 47e8057e 95e77763
Sat Feb 23 00:01:25 2008  factoring 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 (141 digits)
Sat Feb 23 00:01:26 2008  no P-1/P+1/ECM available, skipping
Sat Feb 23 00:01:26 2008  commencing number field sieve (141-digit input)
Sat Feb 23 00:01:26 2008  R0: -811108827276972422199078148
Sat Feb 23 00:01:26 2008  R1:  455195620287979
Sat Feb 23 00:01:26 2008  A0:  57184039631828920586603735624145
Sat Feb 23 00:01:26 2008  A1: -7783023214726791392303474410
Sat Feb 23 00:01:26 2008  A2:  28580437883961308732287
Sat Feb 23 00:01:26 2008  A3:  287657668694377976
Sat Feb 23 00:01:26 2008  A4: -154800049518
Sat Feb 23 00:01:26 2008  A5:  866580
Sat Feb 23 00:01:26 2008  size score = 1.504655e-14, Murphy alpha = -5.292384, combined = 8.781893e-14
Sat Feb 23 00:01:26 2008  
Sat Feb 23 00:01:26 2008  commencing square root phase
Sat Feb 23 00:01:26 2008  reading relations for dependency 1
Sat Feb 23 00:01:26 2008  read 1331041 cycles
Sat Feb 23 00:01:31 2008  cycles contain 4945480 unique relations
Sat Feb 23 00:03:50 2008  read 4945480 relations
Sat Feb 23 00:04:35 2008  multiplying 6575590 relations
Sat Feb 23 00:46:32 2008  multiply complete, coefficients have about 350.42 million bits
Sat Feb 23 00:46:48 2008  initial square root is modulo 1939279
Sat Feb 23 01:45:23 2008  reading relations for dependency 2
Sat Feb 23 01:45:23 2008  read 1328665 cycles
Sat Feb 23 01:45:28 2008  cycles contain 4938185 unique relations
Sat Feb 23 01:46:28 2008  read 4938185 relations
Sat Feb 23 01:47:13 2008  multiplying 6562068 relations
Sat Feb 23 02:28:38 2008  multiply complete, coefficients have about 349.69 million bits
Sat Feb 23 02:28:54 2008  initial square root is modulo 1881949
Sat Feb 23 03:26:18 2008  reading relations for dependency 3
Sat Feb 23 03:26:19 2008  read 1329478 cycles
Sat Feb 23 03:26:24 2008  cycles contain 4941515 unique relations
Sat Feb 23 03:27:51 2008  read 4941515 relations
Sat Feb 23 03:28:35 2008  multiplying 6566668 relations
Sat Feb 23 04:10:00 2008  multiply complete, coefficients have about 349.93 million bits
Sat Feb 23 04:10:16 2008  initial square root is modulo 1901027
Sat Feb 23 05:07:37 2008  reading relations for dependency 4
Sat Feb 23 05:07:38 2008  read 1330019 cycles
Sat Feb 23 05:07:43 2008  cycles contain 4944160 unique relations
Sat Feb 23 05:08:43 2008  read 4944160 relations
Sat Feb 23 05:09:28 2008  multiplying 6574662 relations
Sat Feb 23 05:51:20 2008  multiply complete, coefficients have about 350.37 million bits
Sat Feb 23 05:51:36 2008  initial square root is modulo 1935589
Sat Feb 23 06:49:58 2008  reading relations for dependency 5
Sat Feb 23 06:49:59 2008  read 1330461 cycles
Sat Feb 23 06:50:04 2008  cycles contain 4946758 unique relations
Sat Feb 23 06:51:08 2008  read 4946758 relations
Sat Feb 23 06:51:53 2008  multiplying 6576428 relations
Sat Feb 23 07:33:20 2008  multiply complete, coefficients have about 350.46 million bits
Sat Feb 23 07:33:36 2008  initial square root is modulo 1942657
Sat Feb 23 08:31:02 2008  reading relations for dependency 6
Sat Feb 23 08:31:03 2008  read 1329134 cycles
Sat Feb 23 08:31:08 2008  cycles contain 4942230 unique relations
Sat Feb 23 08:32:08 2008  read 4942230 relations
Sat Feb 23 08:32:53 2008  multiplying 6568714 relations
Sat Feb 23 09:14:20 2008  multiply complete, coefficients have about 350.04 million bits
Sat Feb 23 09:14:36 2008  initial square root is modulo 1909637
Sat Feb 23 10:12:20 2008  reading relations for dependency 7
Sat Feb 23 10:12:21 2008  read 1328681 cycles
Sat Feb 23 10:12:26 2008  cycles contain 4939463 unique relations
Sat Feb 23 10:14:17 2008  read 4939463 relations
Sat Feb 23 10:15:02 2008  multiplying 6566370 relations
 (stopped job to replace CPU heatsink on NFS server)
Sat Feb 23 11:14:16 2008  
Sat Feb 23 11:14:16 2008  
Sat Feb 23 11:14:16 2008  Msieve v. 1.33
Sat Feb 23 11:14:16 2008  random seeds: a0e0453c 17a5295d
Sat Feb 23 11:14:16 2008  factoring 304231555057698888502708670679920297446936633334755377559718454327465917469538949036477054533335898617528911439255596338155475711196193349907 (141 digits)
Sat Feb 23 11:14:17 2008  no P-1/P+1/ECM available, skipping
Sat Feb 23 11:14:17 2008  commencing number field sieve (141-digit input)
Sat Feb 23 11:14:17 2008  R0: -811108827276972422199078148
Sat Feb 23 11:14:17 2008  R1:  455195620287979
Sat Feb 23 11:14:17 2008  A0:  57184039631828920586603735624145
Sat Feb 23 11:14:17 2008  A1: -7783023214726791392303474410
Sat Feb 23 11:14:17 2008  A2:  28580437883961308732287
Sat Feb 23 11:14:17 2008  A3:  287657668694377976
Sat Feb 23 11:14:17 2008  A4: -154800049518
Sat Feb 23 11:14:17 2008  A5:  866580
Sat Feb 23 11:14:17 2008  size score = 1.504655e-14, Murphy alpha = -5.292384, combined = 8.781893e-14
Sat Feb 23 11:14:17 2008  
Sat Feb 23 11:14:17 2008  commencing square root phase
Sat Feb 23 11:14:17 2008  reading relations for dependency 7
Sat Feb 23 11:14:21 2008  read 1328681 cycles
Sat Feb 23 11:14:26 2008  cycles contain 4939463 unique relations
Sat Feb 23 11:18:15 2008  read 4939463 relations
Sat Feb 23 11:19:00 2008  multiplying 6566370 relations
Sat Feb 23 12:03:24 2008  multiply complete, coefficients have about 349.92 million bits
Sat Feb 23 12:03:41 2008  initial square root is modulo 1899917
Sat Feb 23 13:11:52 2008  reading relations for dependency 8
Sat Feb 23 13:11:53 2008  read 1327644 cycles
Sat Feb 23 13:11:58 2008  cycles contain 4938431 unique relations
Sat Feb 23 13:13:25 2008  read 4938431 relations
Sat Feb 23 13:14:15 2008  multiplying 6561678 relations
Sat Feb 23 14:02:05 2008  multiply complete, coefficients have about 349.67 million bits
Sat Feb 23 14:02:22 2008  initial square root is modulo 1880581
Sat Feb 23 15:12:01 2008  reading relations for dependency 9
Sat Feb 23 15:12:02 2008  read 1330553 cycles
Sat Feb 23 15:12:09 2008  cycles contain 4944016 unique relations
Sat Feb 23 15:13:25 2008  read 4944016 relations
Sat Feb 23 15:14:16 2008  multiplying 6572596 relations
Sat Feb 23 16:03:02 2008  multiply complete, coefficients have about 350.26 million bits
Sat Feb 23 16:03:21 2008  initial square root is modulo 1926481
Sat Feb 23 17:14:02 2008  prp66 factor: 529041127136621894810092661001283800527316908098655885710614302743
Sat Feb 23 17:14:02 2008  prp75 factor: 575062201126629614470645738970165209255701496570272209233469241277154408549
Sat Feb 23 17:14:02 2008  elapsed time 05:59:46
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Old 2008-02-24, 00:39   #5
jasonp
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Quote:
Originally Posted by fivemack View Post
Thu Feb 21 18:24:24 2008 filtering rational ideals above 1000000
Thu Feb 21 18:24:24 2008 filtering algebraic ideals above 1000000
Ouch, 9 dependencies is pretty crazy. For the record, I'm working on changes to the filtering that will always choose a low bound and keep only the ideals that occur a few times. This will make the filtering work a bit more like the CWI suite, allowing it to hopefully produce better matrices without an explosion in memory use.
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