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Old 2007-11-16, 16:51   #133
henryzz
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in what file does msieve do the primetest
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Old 2007-11-16, 18:30   #134
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Quote:
Originally Posted by henryzz View Post
in what file does msieve do the primetest
Believe it or not, the answer is complicated. The library maintains a collection of all the factors currently found, and whenever a new factor is added to the collection (by any of the built-in algorithms) it is tested for primality. The function is factor_list_add in common/driver.c, and the primality test is mp_is_prime (common/mp.c) a Rabin-Miller implementation straight out of the book by Crandall and Pomerance. Later, when the msieve_run library function is about to finish, any factors found that are smaller than the square of the trial factoring bound have their status upgraded from probably prime to definitely prime.
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Old 2007-11-16, 19:37   #135
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Quote:
Originally Posted by jasonp View Post
Believe it or not, the answer is complicated. The library maintains a collection of all the factors currently found, and whenever a new factor is added to the collection (by any of the built-in algorithms) it is tested for primality. The function is factor_list_add in common/driver.c, and the primality test is mp_is_prime (common/mp.c) a Rabin-Miller implementation straight out of the book by Crandall and Pomerance. Later, when the msieve_run library function is about to finish, any factors found that are smaller than the square of the trial factoring bound have their status upgraded from probably prime to definitely prime.
Hi,

I use gmp-ecm, ggnfs and msieve for aliquot sequences factorizations and I proove all the prp I find with apr-cl (I have never found a composite prp but I sleep better doing so ).
Would it be complicated to implement this deterministic primality test to msieve code ? This would avoid a manual check on the factors

However, thanks for msieve, a recent c132 filtering step with msieve was much more memory efficient that the ggnfs one (in cygwin).

regards.

Philippe.
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Old 2007-11-16, 19:55   #136
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Quote:
Originally Posted by Phil MjX View Post
I use gmp-ecm, ggnfs and msieve for aliquot sequences factorizations and I proove all the prp I find with apr-cl (I have never found a composite prp but I sleep better doing so ).
Would it be complicated to implement this deterministic primality test to msieve code ? This would avoid a manual check on the factors

However, thanks for msieve, a recent c132 filtering step with msieve was much more memory efficient that the ggnfs one (in cygwin).
My pleasure. The difference in efficiency between the two packages becomes larger and larger as the amount of oversieving increases.

Primality proving doesn't interest me all that much, and I already have my hands full with the factorization side of things. You're not the first that has requested a primality prover, but I just don't have the bandwidth to implement one.
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Old 2007-11-17, 09:22   #137
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so it is only a probable prime test
that explains why it is so fast
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Old 2007-11-17, 16:21   #138
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so it is only a probable prime test
that explains why it is so fast
When the inputs have less than 100 digits, I would think that even a primality proof would finish instantly. Is that not the case?

Many of the standalone primality proving applications are designed for much larger inputs. One exception is PPSIQS, which uses a math library that includes an implementation of APRCL and uses it on all factors found.
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Old 2007-11-17, 18:30   #139
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When the inputs have less than 100 digits, I would think that even a primality proof would finish instantly. Is that not the case?

Many of the standalone primality proving applications are designed for much larger inputs. One exception is PPSIQS, which uses a math library that includes an implementation of APRCL and uses it on all factors found.
I use the p-1 program from the same author (S Tomabechi : http://www.asahi-net.or.jp/~KC2H-MSM/cn/ ). It permits to check input numbers primality in batch, before doing any factorization (and also in my case to check smoothness of primes found +/-1 to detect a p-1 or p+1 miss). The primality test of 50-150 digits primes is a matter of seconds (but not instant).
Do you know if freely available c apr-cl routine exists to be put into msieve code ? For less than 150 digits numbers, even a non optimized demo code would be enough.

Thanks and regards.

Philippe.

Last fiddled with by Phil MjX on 2007-11-17 at 18:31
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Old 2007-11-21, 17:34   #140
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Nothing I can see; just modify common/lanczos/lanczos.c starting around line 1318.

One thing to watch out for is that the linear algebra has to do at least 4 iterations before checkpointing becomes possible (the code enforces this automatically). This means the input linear system has to have dimension > 256 or so.
Would it be possible to have msieve automatically save a check point file for matrices of any size, if one interrupts the process? This will be useful if you for some reason cannot finish your current job in one run.
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Old 2007-11-21, 17:55   #141
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Quote:
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Would it be possible to have msieve automatically save a check point file for matrices of any size, if one interrupts the process? This will be useful if you for some reason cannot finish your current job in one run.
For matrices that are large enough (dimension > 1 million currently) checkpointing is always turned on, and if this is the case then a checkpoint always happens when the library is interrupted. I didn't think checkpointing was necessary for matrices that would completely solve in less than 2 or 3 hours, and this includes all QS matrices and NFS matrices under about a million in size.

It's not optimal to solve a matrix in a week of lunch hours :)
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Old 2007-11-22, 00:25   #142
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Quote:
Originally Posted by jasonp View Post
It's not optimal to solve a matrix in a week of lunch hours :)
Nor is it optimal to "lunch" all of the hours that are required to solve a "real" matrix.

I appreciate your effort in creating something useful for the "cutting edge *NFS" processing rather than just finding trivial p70's.

:)
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Old 2007-11-22, 07:20   #143
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Originally Posted by Wacky View Post
I appreciate your effort in creating something useful for the "cutting edge *NFS" processing rather than just finding trivial p70's.

:)
Such as 2,779+. Here's the full log:

Code:
Wed Nov  7 21:05:35 2007  Msieve v. 1.29
Wed Nov  7 21:05:35 2007  random seeds: a740f2b7 0cf1e780
Wed Nov  7 21:05:35 2007  factoring 21499173951598023655871526129741238864252274176505248438905816972331478841874026717266127459812853910615830233333737201439633130982196868280103768992238493630431515155684471825756247809234523310884830836516644313 (212 digits)
Wed Nov  7 21:05:35 2007  commencing number field sieve (212-digit input)
Wed Nov  7 21:05:36 2007  R0: -1361129467683753853853498429727072845824
Wed Nov  7 21:05:36 2007  R1:  1
Wed Nov  7 21:05:36 2007  A0:  2
Wed Nov  7 21:05:36 2007  A1:  0
Wed Nov  7 21:05:36 2007  A2:  0
Wed Nov  7 21:05:36 2007  A3:  0
Wed Nov  7 21:05:36 2007  A4:  0
Wed Nov  7 21:05:36 2007  A5:  0
Wed Nov  7 21:05:36 2007  A6:  1
Wed Nov  7 21:05:36 2007  size score = 2.834873e-11, Murphy alpha = 1.842138, combined = 1.674763e-11
Wed Nov  7 21:10:21 2007  restarting with 92301399 relations
Wed Nov  7 21:10:21 2007  
Wed Nov  7 21:10:21 2007  commencing relation filtering
Wed Nov  7 21:10:21 2007  commencing duplicate removal, pass 1
Wed Nov  7 21:11:25 2007  error -1 reading relation 7165101
Wed Nov  7 21:11:28 2007  error -4 reading relation 7430114
Wed Nov  7 21:22:34 2007  error -14 reading relation 84653095
Wed Nov  7 21:23:05 2007  error -14 reading relation 88388346
Wed Nov  7 21:23:39 2007  found 15480559 hash collisions in 92301354 relations
Wed Nov  7 21:23:39 2007  commencing duplicate removal, pass 2
Wed Nov  7 21:31:59 2007  found 1804416 duplicates and 90496938 unique relations
Wed Nov  7 21:31:59 2007  memory use: 504.8 MB
Wed Nov  7 21:32:31 2007  ignoring smallest 3236951 rational and 3236317 algebraic ideals
Wed Nov  7 21:32:31 2007  filtering ideals above 54192062
Wed Nov  7 21:32:31 2007  need 11004555 more relations than ideals
Wed Nov  7 21:32:31 2007  commencing singleton removal, pass 1
Wed Nov  7 21:46:32 2007  relations with 0 large ideals: 1440982
Wed Nov  7 21:46:32 2007  relations with 1 large ideals: 8084380
Wed Nov  7 21:46:32 2007  relations with 2 large ideals: 23156082
Wed Nov  7 21:46:32 2007  relations with 3 large ideals: 32649691
Wed Nov  7 21:46:32 2007  relations with 4 large ideals: 21306953
Wed Nov  7 21:46:32 2007  relations with 5 large ideals: 3858850
Wed Nov  7 21:46:32 2007  relations with 6 large ideals: 0
Wed Nov  7 21:46:32 2007  relations with 7+ large ideals: 0
Wed Nov  7 21:46:32 2007  90496938 relations and about 61560280 large ideals
Wed Nov  7 21:46:32 2007  commencing singleton removal, pass 2
Wed Nov  7 22:01:12 2007  found 15146451 singletons
Wed Nov  7 22:01:12 2007  current dataset: 75350487 relations and about 45339080 large ideals
Wed Nov  7 22:01:13 2007  commencing singleton removal, pass 3
Wed Nov  7 22:13:44 2007  relations with 0 large ideals: 1440982
Wed Nov  7 22:13:44 2007  relations with 1 large ideals: 7565914
Wed Nov  7 22:13:44 2007  relations with 2 large ideals: 20283422
Wed Nov  7 22:13:44 2007  relations with 3 large ideals: 26784097
Wed Nov  7 22:13:44 2007  relations with 4 large ideals: 16426523
Wed Nov  7 22:13:44 2007  relations with 5 large ideals: 2849549
Wed Nov  7 22:13:44 2007  relations with 6 large ideals: 0
Wed Nov  7 22:13:44 2007  relations with 7+ large ideals: 0
Wed Nov  7 22:13:44 2007  75350487 relations and about 57090163 large ideals
Wed Nov  7 22:13:44 2007  commencing singleton removal, pass 4
Wed Nov  7 22:26:52 2007  found 12496973 singletons
Wed Nov  7 22:26:52 2007  current dataset: 62853514 relations and about 43716489 large ideals
Wed Nov  7 22:26:52 2007  commencing singleton removal, pass 5
Wed Nov  7 22:39:03 2007  found 2820361 singletons
Wed Nov  7 22:39:03 2007  current dataset: 60033153 relations and about 40845657 large ideals
Wed Nov  7 22:39:03 2007  commencing singleton removal, pass 6
Wed Nov  7 22:51:01 2007  found 588967 singletons
Wed Nov  7 22:51:01 2007  current dataset: 59444186 relations and about 40254338 large ideals
Wed Nov  7 22:51:02 2007  commencing singleton removal, pass 7
Wed Nov  7 23:03:07 2007  found 115899 singletons
Wed Nov  7 23:03:07 2007  current dataset: 59328287 relations and about 40138336 large ideals
Wed Nov  7 23:03:07 2007  commencing singleton removal, final pass
Wed Nov  7 23:15:29 2007  memory use: 2116.1 MB
Wed Nov  7 23:15:29 2007  commencing in-memory singleton removal
Wed Nov  7 23:15:37 2007  begin with 59328287 relations and 46506881 unique ideals
Wed Nov  7 23:17:13 2007  reduce to 52320955 relations and 39332648 ideals in 13 passes
Wed Nov  7 23:17:13 2007  max relations containing the same ideal: 34
Wed Nov  7 23:17:47 2007  removing 3309517 relations and 2909517 ideals in 400000 cliques
Wed Nov  7 23:17:50 2007  commencing in-memory singleton removal
Wed Nov  7 23:17:55 2007  begin with 49011438 relations and 39332648 unique ideals
Wed Nov  7 23:18:53 2007  reduce to 48890075 relations and 36300633 ideals in 9 passes
Wed Nov  7 23:18:53 2007  max relations containing the same ideal: 33
Wed Nov  7 23:19:25 2007  removing 2452808 relations and 2052808 ideals in 400000 cliques
Wed Nov  7 23:19:27 2007  commencing in-memory singleton removal
Wed Nov  7 23:19:32 2007  begin with 46437267 relations and 36300633 unique ideals
Wed Nov  7 23:20:20 2007  reduce to 46361623 relations and 34171573 ideals in 8 passes
Wed Nov  7 23:20:20 2007  max relations containing the same ideal: 33
Wed Nov  7 23:20:50 2007  removing 2178875 relations and 1778875 ideals in 400000 cliques
Wed Nov  7 23:20:51 2007  commencing in-memory singleton removal
Wed Nov  7 23:20:56 2007  begin with 44182748 relations and 34171573 unique ideals
Wed Nov  7 23:21:36 2007  reduce to 44118986 relations and 32328422 ideals in 7 passes
Wed Nov  7 23:21:36 2007  max relations containing the same ideal: 32
Wed Nov  7 23:22:03 2007  removing 2024077 relations and 1624077 ideals in 400000 cliques
Wed Nov  7 23:22:05 2007  commencing in-memory singleton removal
Wed Nov  7 23:22:10 2007  begin with 42094909 relations and 32328422 unique ideals
Wed Nov  7 23:22:41 2007  reduce to 42035244 relations and 30644206 ideals in 6 passes
Wed Nov  7 23:22:41 2007  max relations containing the same ideal: 32
Wed Nov  7 23:23:07 2007  removing 1862111 relations and 1475629 ideals in 386482 cliques
Wed Nov  7 23:23:09 2007  commencing in-memory singleton removal
Wed Nov  7 23:23:13 2007  begin with 40173133 relations and 30644206 unique ideals
Wed Nov  7 23:23:43 2007  reduce to 40119800 relations and 29114838 ideals in 6 passes
Wed Nov  7 23:23:43 2007  max relations containing the same ideal: 31
Wed Nov  7 23:24:07 2007  removing 4205 relations and 3799 ideals in 406 cliques
Wed Nov  7 23:24:08 2007  commencing in-memory singleton removal
Wed Nov  7 23:24:13 2007  begin with 40115595 relations and 29114838 unique ideals
Wed Nov  7 23:24:18 2007  reduce to 40115595 relations and 29111039 ideals in 1 passes
Wed Nov  7 23:24:18 2007  max relations containing the same ideal: 31
Wed Nov  7 23:24:24 2007  dataset has 70.0% excess relations
Wed Nov  7 23:24:52 2007  ignoring smallest 2931651 rational and 2931353 algebraic ideals
Wed Nov  7 23:24:52 2007  filtering ideals above 48772855
Wed Nov  7 23:24:52 2007  need 9904100 more relations than ideals
Wed Nov  7 23:24:52 2007  commencing singleton removal, final pass
Wed Nov  7 23:35:28 2007  memory use: 1307.2 MB
Wed Nov  7 23:35:28 2007  commencing in-memory singleton removal
Wed Nov  7 23:35:33 2007  begin with 40115595 relations and 29721058 unique ideals
Wed Nov  7 23:36:02 2007  reduce to 40111934 relations and 29717397 ideals in 6 passes
Wed Nov  7 23:36:02 2007  max relations containing the same ideal: 33
Wed Nov  7 23:36:26 2007  removing 1207640 relations and 962422 ideals in 245218 cliques
Wed Nov  7 23:36:27 2007  commencing in-memory singleton removal
Wed Nov  7 23:36:31 2007  begin with 38904294 relations and 29717397 unique ideals
Wed Nov  7 23:37:00 2007  reduce to 38880627 relations and 28731195 ideals in 6 passes
Wed Nov  7 23:37:00 2007  max relations containing the same ideal: 33
Wed Nov  7 23:37:23 2007  removing 1133753 relations and 888535 ideals in 245218 cliques
Wed Nov  7 23:37:24 2007  commencing in-memory singleton removal
Wed Nov  7 23:37:28 2007  begin with 37746874 relations and 28731195 unique ideals
Wed Nov  7 23:37:55 2007  reduce to 37723983 relations and 27819630 ideals in 6 passes
Wed Nov  7 23:37:55 2007  max relations containing the same ideal: 32
Wed Nov  7 23:38:18 2007  removing 2442 relations and 2190 ideals in 252 cliques
Wed Nov  7 23:38:18 2007  commencing in-memory singleton removal
Wed Nov  7 23:38:23 2007  begin with 37721541 relations and 27819630 unique ideals
Wed Nov  7 23:38:27 2007  reduce to 37721541 relations and 27817440 ideals in 1 passes
Wed Nov  7 23:38:27 2007  max relations containing the same ideal: 32
Wed Nov  7 23:38:33 2007  dataset has 53.0% excess relations
Wed Nov  7 23:38:58 2007  ignoring smallest 2624651 rational and 2623879 algebraic ideals
Wed Nov  7 23:38:58 2007  filtering ideals above 43353649
Wed Nov  7 23:38:58 2007  need 7923280 more relations than ideals
Wed Nov  7 23:38:58 2007  commencing singleton removal, final pass
Wed Nov  7 23:49:32 2007  memory use: 1307.2 MB
Wed Nov  7 23:49:33 2007  commencing in-memory singleton removal
Wed Nov  7 23:49:37 2007  begin with 37721541 relations and 28431904 unique ideals
Wed Nov  7 23:49:56 2007  reduce to 37721267 relations and 28431630 ideals in 4 passes
Wed Nov  7 23:49:56 2007  max relations containing the same ideal: 32
Wed Nov  7 23:50:20 2007  removing 1717234 relations and 1317234 ideals in 400000 cliques
Wed Nov  7 23:50:21 2007  commencing in-memory singleton removal
Wed Nov  7 23:50:25 2007  begin with 36004033 relations and 28431630 unique ideals
Wed Nov  7 23:50:57 2007  reduce to 35951920 relations and 27061826 ideals in 7 passes
Wed Nov  7 23:50:57 2007  max relations containing the same ideal: 31
Wed Nov  7 23:51:20 2007  removing 1735027 relations and 1335027 ideals in 400000 cliques
Wed Nov  7 23:51:21 2007  commencing in-memory singleton removal
Wed Nov  7 23:51:25 2007  begin with 34216893 relations and 27061826 unique ideals
Wed Nov  7 23:51:55 2007  reduce to 34162060 relations and 25671488 ideals in 7 passes
Wed Nov  7 23:51:55 2007  max relations containing the same ideal: 30
Wed Nov  7 23:52:16 2007  removing 1698236 relations and 1298236 ideals in 400000 cliques
Wed Nov  7 23:52:18 2007  commencing in-memory singleton removal
Wed Nov  7 23:52:21 2007  begin with 32463824 relations and 25671488 unique ideals
Wed Nov  7 23:52:49 2007  reduce to 32405137 relations and 24313985 ideals in 7 passes
Wed Nov  7 23:52:49 2007  max relations containing the same ideal: 29
Wed Nov  7 23:53:09 2007  removing 816534 relations and 648663 ideals in 167871 cliques
Wed Nov  7 23:53:10 2007  commencing in-memory singleton removal
Wed Nov  7 23:53:14 2007  begin with 31588603 relations and 24313985 unique ideals
Wed Nov  7 23:53:37 2007  reduce to 31576572 relations and 23653241 ideals in 6 passes
Wed Nov  7 23:53:37 2007  max relations containing the same ideal: 29
Wed Nov  7 23:53:42 2007  dataset has 22.4% excess relations
Wed Nov  7 23:54:04 2007  ignoring smallest 2315237 rational and 2314817 algebraic ideals
Wed Nov  7 23:54:04 2007  filtering ideals above 37934443
Wed Nov  7 23:54:04 2007  need 6991129 more relations than ideals
Wed Nov  7 23:54:04 2007  commencing singleton removal, final pass
Thu Nov  8 00:03:21 2007  memory use: 1069.9 MB
Thu Nov  8 00:03:21 2007  commencing in-memory singleton removal
Thu Nov  8 00:03:24 2007  begin with 31576572 relations and 24271691 unique ideals
Thu Nov  8 00:03:44 2007  reduce to 31576012 relations and 24271131 ideals in 5 passes
Thu Nov  8 00:03:44 2007  max relations containing the same ideal: 29
Thu Nov  8 00:04:04 2007  removing 691553 relations and 534677 ideals in 156876 cliques
Thu Nov  8 00:04:05 2007  commencing in-memory singleton removal
Thu Nov  8 00:04:08 2007  begin with 30884459 relations and 24271131 unique ideals
Thu Nov  8 00:04:28 2007  reduce to 30873985 relations and 23725935 ideals in 5 passes
Thu Nov  8 00:04:28 2007  max relations containing the same ideal: 29
Thu Nov  8 00:04:47 2007  removing 671735 relations and 514859 ideals in 156876 cliques
Thu Nov  8 00:04:48 2007  commencing in-memory singleton removal
Thu Nov  8 00:04:51 2007  begin with 30202250 relations and 23725935 unique ideals
Thu Nov  8 00:05:14 2007  reduce to 30191796 relations and 23200587 ideals in 6 passes
Thu Nov  8 00:05:14 2007  max relations containing the same ideal: 29
Thu Nov  8 00:05:19 2007  dataset has 8.0% excess relations
Thu Nov  8 00:05:23 2007  relations with 0 large ideals: 725653
Thu Nov  8 00:05:23 2007  relations with 1 large ideals: 3184961
Thu Nov  8 00:05:23 2007  relations with 2 large ideals: 7785145
Thu Nov  8 00:05:23 2007  relations with 3 large ideals: 9619145
Thu Nov  8 00:05:23 2007  relations with 4 large ideals: 6321596
Thu Nov  8 00:05:23 2007  relations with 5 large ideals: 2130989
Thu Nov  8 00:05:23 2007  relations with 6 large ideals: 338678
Thu Nov  8 00:05:23 2007  relations with 7+ large ideals: 85629
Thu Nov  8 00:05:23 2007  commencing 2-way merge
Thu Nov  8 00:05:51 2007  reduce to 20454949 relation sets and 13463740 unique ideals
Thu Nov  8 00:05:51 2007  commencing full merge
Thu Nov  8 00:10:21 2007  found 9985606 cycles, need 7633940
Thu Nov  8 00:10:26 2007  weight of 7633940 cycles is about 496411432 (65.03/cycle)
Thu Nov  8 00:10:27 2007  distribution of cycle lengths:
Thu Nov  8 00:10:27 2007  1 relations: 1127903
Thu Nov  8 00:10:27 2007  2 relations: 851202
Thu Nov  8 00:10:27 2007  3 relations: 892981
Thu Nov  8 00:10:27 2007  4 relations: 881405
Thu Nov  8 00:10:27 2007  5 relations: 853667
Thu Nov  8 00:10:27 2007  6 relations: 797427
Thu Nov  8 00:10:27 2007  7 relations: 731527
Thu Nov  8 00:10:27 2007  8 relations: 646893
Thu Nov  8 00:10:27 2007  9 relations: 537108
Thu Nov  8 00:10:27 2007  10+ relations: 313827
Thu Nov  8 00:10:27 2007  heaviest cycle: 13 relations
Thu Nov  8 00:10:27 2007  commencing cycle optimization
Thu Nov  8 00:11:24 2007  start with 36366518 relations
Thu Nov  8 00:14:37 2007  pruned 681229 relations
Thu Nov  8 00:14:38 2007  distribution of cycle lengths:
Thu Nov  8 00:14:38 2007  1 relations: 1127903
Thu Nov  8 00:14:38 2007  2 relations: 867972
Thu Nov  8 00:14:38 2007  3 relations: 922881
Thu Nov  8 00:14:38 2007  4 relations: 904546
Thu Nov  8 00:14:38 2007  5 relations: 883486
Thu Nov  8 00:14:38 2007  6 relations: 819090
Thu Nov  8 00:14:38 2007  7 relations: 743998
Thu Nov  8 00:14:38 2007  8 relations: 634524
Thu Nov  8 00:14:38 2007  9 relations: 484816
Thu Nov  8 00:14:38 2007  10+ relations: 244724
Thu Nov  8 00:14:38 2007  heaviest cycle: 13 relations
Thu Nov  8 00:14:53 2007  
Thu Nov  8 00:14:57 2007  commencing linear algebra
Thu Nov  8 00:14:59 2007  read 7633940 cycles
Thu Nov  8 00:15:49 2007  cycles contain 21694261 unique relations
Thu Nov  8 00:23:48 2007  read 21694261 relations
Thu Nov  8 00:27:25 2007  using 32 quadratic characters above 1073740698
Thu Nov  8 00:54:21 2007  read 7633940 cycles
Thu Nov  8 01:00:54 2007  filtering completed in 3 passes
Thu Nov  8 01:00:56 2007  matrix is 7490253 x 7490451 with weight 666958089 (avg 89.04/col)
Thu Nov  8 01:05:43 2007  read 7490451 cycles
Thu Nov  8 01:06:57 2007  matrix is 7490253 x 7490451 with weight 666958089 (avg 89.04/col)
Thu Nov  8 01:06:57 2007  saving the first 48 matrix rows for later
Thu Nov  8 01:07:02 2007  matrix is 7490205 x 7490451 with weight 503129773 (avg 67.17/col)
Thu Nov  8 01:07:02 2007  matrix includes 64 packed rows
Thu Nov  8 01:07:02 2007  using block size 43690 for processor cache size 1024 kB
Thu Nov  8 01:07:48 2007  commencing Lanczos iteration
Wed Nov 21 12:03:07 2007  lanczos halted after 118456 iterations (dim = 7490189)
Wed Nov 21 12:03:42 2007  recovered 41 nontrivial dependencies
Wed Nov 21 12:03:43 2007  
Wed Nov 21 12:03:43 2007  commencing square root phase
Wed Nov 21 12:03:43 2007  reading relations for dependency 1
Wed Nov 21 12:04:03 2007  read 3747844 cycles
Wed Nov 21 12:04:20 2007  cycles contain 12888418 unique relations
Wed Nov 21 12:10:30 2007  read 12888418 relations
Wed Nov 21 12:12:48 2007  multiplying 17639522 relations
Wed Nov 21 13:06:14 2007  multiply complete, coefficients have about 429.68 million bits
Wed Nov 21 13:06:27 2007  initial square root is modulo 51259543
Wed Nov 21 14:45:09 2007  reading relations for dependency 2
Wed Nov 21 14:45:32 2007  read 3745287 cycles
Wed Nov 21 14:45:50 2007  cycles contain 12884684 unique relations
Wed Nov 21 14:51:57 2007  read 12884684 relations
Wed Nov 21 14:54:15 2007  multiplying 17635716 relations
Wed Nov 21 15:47:40 2007  multiply complete, coefficients have about 429.58 million bits
Wed Nov 21 15:47:53 2007  initial square root is modulo 51053479
Wed Nov 21 17:26:44 2007  reading relations for dependency 3
Wed Nov 21 17:27:07 2007  read 3745608 cycles
Wed Nov 21 17:27:25 2007  cycles contain 12885791 unique relations
Wed Nov 21 17:33:31 2007  read 12885791 relations
Wed Nov 21 17:35:49 2007  multiplying 17636998 relations
Wed Nov 21 18:28:49 2007  multiply complete, coefficients have about 429.61 million bits
Wed Nov 21 18:29:02 2007  initial square root is modulo 51114421
Wed Nov 21 20:06:52 2007  reading relations for dependency 4
Wed Nov 21 20:07:16 2007  read 3746693 cycles
Wed Nov 21 20:07:33 2007  cycles contain 12885473 unique relations
Wed Nov 21 20:13:40 2007  read 12885473 relations
Wed Nov 21 20:15:58 2007  multiplying 17638674 relations
Wed Nov 21 21:09:12 2007  multiply complete, coefficients have about 429.65 million bits
Wed Nov 21 21:09:25 2007  initial square root is modulo 51212101
Wed Nov 21 22:47:26 2007  prp86 factor: 17315878129048863927974905480696448369723747093035498799994851681384411684778961025249
Wed Nov 21 22:47:26 2007  prp127 factor: 124158727564219361367740120938200983008
4399769371108904801198294935706207364264832500354031378698910359793960404372927442514937
Wed Nov 21 22:47:27 2007  elapsed time 337:41:52
Greg
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