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2008-10-22, 00:36
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#1 |
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Oct 2008
24 Posts |
who can factor 10^100+27?
I take great interest in factorization.
It is difficult for me to fact 10^100+27,I have spent about 15 hours to fact it by using pari/gp which is an especial famous software in number theory ,but I failed. Maybe someone could help me , Is there any volunteer to help me to fact it Or give me some advice ? |
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2008-10-22, 01:56
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#2 |
Aug 2002
847710 Posts |
Here is a start:
Code:
37 x 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 |
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2008-10-22, 02:14
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#3 |
May 2008
100010001112 Posts |
37 is the only factor to 2^63.
The cofactor is composite. |
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2008-10-22, 03:08
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#4 | |
"Ben"
Feb 2007
E2316 Posts |
Quote:
I estimate it would take about 30 minutes, total, to factor using SNFS and msieve. Msieve's siqs could also tackle it in a few hours on a fast machine, and that's fire and forget. Look msieve up on google and you'll be on your way. - ben. |
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2008-10-22, 03:33
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#5 |
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"Ben"
Feb 2007
7·11·47 Posts |
I'm procrastinating before starting my homework... and I was slightly wrong, it only took about 20 minutes.
prp47 factor: 78175003767451466482080068931559338109988065279 prp52 factor: 3457246654880221174947428776620112459038765878240449 |
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2008-10-22, 06:57
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#6 | |
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Oct 2008
208 Posts |
extremely incredible!
Quote:
How did you get the other two factors of 10^100+27? I think pari/gp maybe the most powerful software in number theory.Pari/gp have run about 15 hours on my computer , but I can't get any factor of it.So I put this problem on this forum!I can't believe that there is someone who can fact it just in 20 minutes! Which software do you use ?thank you . Note:my operating system is windows. |
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2008-10-22, 11:16
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#7 | |
Apr 2004
Copenhagen, Denmark
22·29 Posts |
Quote:
 PARI is great for general number theory. Factorization is not 'general' number theory though, and specialized tools, such as GMP-ECM, Msieve and GGNFS, are faster at this particular task. They cannot help you with anything else in number theory though. If you want to work with polymonial ideals or whatever, PARI is still your application of choice. -- Cheers, Jes Last fiddled with by JHansen on 2008-10-22 at 11:16 Reason: typo |
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2008-10-22, 12:08
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#8 |
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Tribal Bullet
Oct 2004
5·709 Posts |
Pari is a powerful tool, but many of its primitive parts are not well optimized. The factoring code is many years old by now and modern tools are enormously faster. Your input number factors especially quickly using the number field sieve, which Pari does not have.
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2008-10-22, 13:33
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#9 | |
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"Ben"
Feb 2007
1110001000112 Posts |
Quote:
(10^25)^4 + 27. Which is a polynomial in x=10^25 with small coefficients, namely: x^4 + 27. Numbers which can be written as polynomials of degree 4, 5, or 6, with small coefficients, are good candidates for factoring using the special number field sieve algorithm. Google is your friend here as well, if you're interested. I believe several generally accessable websites like wikipedia will tell you the basics of the SNFS. As far as software goes, msieve will take a polynomial you define and produce your factors with no other effort required. Jason has windows binaries available for download (just google msieve). However to get to 20 minutes, I used the lattice siever available with the ggnfs software suite followed by post-processing using msieve. If you don't know what any of that means, start seaching for those terms. If you have other questions, feel free to post them here. Good luck and have fun! |
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2008-10-22, 18:29
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#10 |
Oct 2006
vomit_frame_pointer
23·32·5 Posts |
gnfs-lasieve4I12e
Whoa: .00093 sec./relation.
Doing this on a dual-core laptop now. I saw your 20-minute job, and I jumped in. This is only the 4th or 5th time I have used the 4I12e lattice siever. We're spoiled -- jobs like this are tiny now. Last fiddled with by FactorEyes on 2008-10-22 at 18:42 |
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2008-10-22, 18:53
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#11 | |
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"Ben"
Feb 2007
7·11·47 Posts |
Quote:
That's why I couldn't resist just factoring it. It's worth it just for the novelty of seeing 16000 new relations every time the screen updates. 0.00034 sec/rel with 4I12eOn a more serious note, I ended up vastly oversieving using the heuristic that I needed 0.8 * (pi(2^25) + pi(2^25)) ~ 3M rels. msieve refused to build the matrix until I had manually pruned this back to 1.2M rels. Is the heuristic broken for jobs this tiny, or is msieve not handleing it right somehow? Here's the complete log Code:
Tue Oct 21 22:22:00 2008 Tue Oct 21 22:22:00 2008 Tue Oct 21 22:22:00 2008 Msieve v. 1.38 Tue Oct 21 22:22:00 2008 random seeds: a83334ec 7ad1c7de Tue Oct 21 22:22:00 2008 factoring 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 (99 digits) Tue Oct 21 22:22:00 2008 no P-1/P+1/ECM available, skipping Tue Oct 21 22:22:00 2008 commencing number field sieve (99-digit input) Tue Oct 21 22:22:00 2008 R0: 10000000000000000000000000 Tue Oct 21 22:22:00 2008 R1: -1 Tue Oct 21 22:22:00 2008 A0: 27 Tue Oct 21 22:22:00 2008 A1: 0 Tue Oct 21 22:22:00 2008 A2: 0 Tue Oct 21 22:22:00 2008 A3: 0 Tue Oct 21 22:22:00 2008 A4: 1 Tue Oct 21 22:22:00 2008 size score = 3.100724e-10, Murphy alpha = 0.835783, combined = 2.219590e-10 Tue Oct 21 22:22:00 2008 Tue Oct 21 22:22:00 2008 commencing relation filtering Tue Oct 21 22:22:00 2008 commencing duplicate removal, pass 1 Tue Oct 21 22:22:15 2008 found 126924 hash collisions in 3218006 relations Tue Oct 21 22:22:16 2008 added 228674 free relations Tue Oct 21 22:22:16 2008 commencing duplicate removal, pass 2 Tue Oct 21 22:22:17 2008 found 111355 duplicates and 3335325 unique relations Tue Oct 21 22:22:17 2008 memory use: 37.8 MB Tue Oct 21 22:22:17 2008 reading rational ideals above 720896 Tue Oct 21 22:22:17 2008 reading algebraic ideals above 720896 Tue Oct 21 22:22:17 2008 commencing singleton removal, pass 1 Tue Oct 21 22:22:35 2008 relations with 0 large ideals: 124368 Tue Oct 21 22:22:35 2008 relations with 1 large ideals: 788726 Tue Oct 21 22:22:35 2008 relations with 2 large ideals: 1511105 Tue Oct 21 22:22:35 2008 relations with 3 large ideals: 622099 Tue Oct 21 22:22:35 2008 relations with 4 large ideals: 67554 Tue Oct 21 22:22:35 2008 relations with 5 large ideals: 221473 Tue Oct 21 22:22:35 2008 relations with 6 large ideals: 0 Tue Oct 21 22:22:35 2008 relations with 7+ large ideals: 0 Tue Oct 21 22:22:35 2008 3335325 relations and about 2514354 large ideals Tue Oct 21 22:22:35 2008 commencing singleton removal, pass 2 Tue Oct 21 22:22:52 2008 found 860682 singletons Tue Oct 21 22:22:52 2008 current dataset: 2474643 relations and about 1308998 large ideals Tue Oct 21 22:22:52 2008 commencing singleton removal, pass 3 Tue Oct 21 22:23:04 2008 found 317117 singletons Tue Oct 21 22:23:04 2008 current dataset: 2157526 relations and about 983599 large ideals Tue Oct 21 22:23:04 2008 commencing singleton removal, final pass Tue Oct 21 22:23:15 2008 memory use: 32.2 MB Tue Oct 21 22:23:15 2008 commencing in-memory singleton removal Tue Oct 21 22:23:16 2008 begin with 2157526 relations and 997171 unique ideals Tue Oct 21 22:23:16 2008 reduce to 2107659 relations and 947042 ideals in 6 passes Tue Oct 21 22:23:16 2008 max relations containing the same ideal: 31 Tue Oct 21 22:23:16 2008 reading rational ideals above 360448 Tue Oct 21 22:23:16 2008 reading algebraic ideals above 360448 Tue Oct 21 22:23:16 2008 commencing singleton removal, final pass Tue Oct 21 22:23:29 2008 keeping 982065 ideals with weight <= 20, new excess is 90063 Tue Oct 21 22:23:29 2008 memory use: 44.9 MB Tue Oct 21 22:23:29 2008 commencing in-memory singleton removal Tue Oct 21 22:23:29 2008 begin with 2109525 relations and 982065 unique ideals Tue Oct 21 22:23:30 2008 reduce to 2107659 relations and 972977 ideals in 2 passes Tue Oct 21 22:23:30 2008 max relations containing the same ideal: 20 Tue Oct 21 22:23:30 2008 removing 677103 relations and 380075 ideals in 297028 cliques Tue Oct 21 22:23:31 2008 commencing in-memory singleton removal Tue Oct 21 22:23:31 2008 begin with 1430556 relations and 972977 unique ideals Tue Oct 21 22:23:31 2008 reduce to 1406368 relations and 566828 ideals in 4 passes Tue Oct 21 22:23:31 2008 max relations containing the same ideal: 20 Tue Oct 21 22:23:32 2008 removing 186369 relations and 97220 ideals in 89149 cliques Tue Oct 21 22:23:32 2008 commencing in-memory singleton removal Tue Oct 21 22:23:32 2008 begin with 1219999 relations and 566828 unique ideals Tue Oct 21 22:23:32 2008 reduce to 1216703 relations and 466220 ideals in 4 passes Tue Oct 21 22:23:32 2008 max relations containing the same ideal: 20 Tue Oct 21 22:23:32 2008 removing 72284 relations and 36861 ideals in 35423 cliques Tue Oct 21 22:23:32 2008 commencing in-memory singleton removal Tue Oct 21 22:23:32 2008 begin with 1144419 relations and 466220 unique ideals Tue Oct 21 22:23:32 2008 reduce to 1143731 relations and 428661 ideals in 3 passes Tue Oct 21 22:23:32 2008 max relations containing the same ideal: 19 Tue Oct 21 22:23:33 2008 removing 32699 relations and 16513 ideals in 16186 cliques Tue Oct 21 22:23:33 2008 commencing in-memory singleton removal Tue Oct 21 22:23:33 2008 begin with 1111032 relations and 428661 unique ideals Tue Oct 21 22:23:33 2008 reduce to 1110866 relations and 411982 ideals in 3 passes Tue Oct 21 22:23:33 2008 max relations containing the same ideal: 19 Tue Oct 21 22:23:33 2008 too much excess; switching to 3-cliques Tue Oct 21 22:23:33 2008 removing 380587 relations and 146570 ideals in 95332 cliques Tue Oct 21 22:23:33 2008 commencing in-memory singleton removal Tue Oct 21 22:23:33 2008 begin with 730279 relations and 411982 unique ideals Tue Oct 21 22:23:33 2008 reduce to 725336 relations and 260078 ideals in 4 passes Tue Oct 21 22:23:33 2008 max relations containing the same ideal: 17 Tue Oct 21 22:23:34 2008 removing 190901 relations and 78764 ideals in 56797 cliques Tue Oct 21 22:23:34 2008 commencing in-memory singleton removal Tue Oct 21 22:23:34 2008 begin with 534435 relations and 260078 unique ideals Tue Oct 21 22:23:34 2008 reduce to 532235 relations and 178962 ideals in 3 passes Tue Oct 21 22:23:34 2008 max relations containing the same ideal: 16 Tue Oct 21 22:23:34 2008 removing 129569 relations and 52387 ideals in 38341 cliques Tue Oct 21 22:23:34 2008 commencing in-memory singleton removal Tue Oct 21 22:23:34 2008 begin with 402666 relations and 178962 unique ideals Tue Oct 21 22:23:34 2008 reduce to 401156 relations and 124980 ideals in 3 passes Tue Oct 21 22:23:34 2008 max relations containing the same ideal: 13 Tue Oct 21 22:23:34 2008 removing 98166 relations and 39541 ideals in 28860 cliques Tue Oct 21 22:23:34 2008 commencing in-memory singleton removal Tue Oct 21 22:23:34 2008 begin with 302990 relations and 124980 unique ideals Tue Oct 21 22:23:34 2008 reduce to 301830 relations and 84224 ideals in 3 passes Tue Oct 21 22:23:34 2008 max relations containing the same ideal: 12 Tue Oct 21 22:23:34 2008 removing 74592 relations and 30170 ideals in 21754 cliques Tue Oct 21 22:23:34 2008 commencing in-memory singleton removal Tue Oct 21 22:23:34 2008 begin with 227238 relations and 84224 unique ideals Tue Oct 21 22:23:34 2008 reduce to 226362 relations and 53135 ideals in 4 passes Tue Oct 21 22:23:34 2008 max relations containing the same ideal: 11 Tue Oct 21 22:23:34 2008 removing 52806 relations and 21294 ideals in 15693 cliques Tue Oct 21 22:23:34 2008 commencing in-memory singleton removal Tue Oct 21 22:23:34 2008 begin with 173556 relations and 53135 unique ideals Tue Oct 21 22:23:34 2008 reduce to 173070 relations and 31328 ideals in 3 passes Tue Oct 21 22:23:34 2008 max relations containing the same ideal: 9 Tue Oct 21 22:23:34 2008 removing 33180 relations and 13103 ideals in 10195 cliques Tue Oct 21 22:23:34 2008 commencing in-memory singleton removal Tue Oct 21 22:23:34 2008 begin with 139890 relations and 31328 unique ideals Tue Oct 21 22:23:34 2008 reduce to 139734 relations and 18062 ideals in 2 passes Tue Oct 21 22:23:34 2008 max relations containing the same ideal: 9 Tue Oct 21 22:23:34 2008 dataset too sparse, retrying Tue Oct 21 22:23:34 2008 reading rational ideals above 360448 Tue Oct 21 22:23:34 2008 reading algebraic ideals above 360448 Tue Oct 21 22:23:34 2008 commencing singleton removal, final pass Tue Oct 21 22:23:47 2008 keeping 998563 ideals with weight <= 25, new excess is 73565 Tue Oct 21 22:23:47 2008 memory use: 44.9 MB Tue Oct 21 22:23:47 2008 commencing in-memory singleton removal Tue Oct 21 22:23:48 2008 begin with 2109525 relations and 998563 unique ideals Tue Oct 21 22:23:48 2008 reduce to 2107659 relations and 989475 ideals in 2 passes Tue Oct 21 22:23:48 2008 max relations containing the same ideal: 25 Tue Oct 21 22:23:49 2008 removing 677103 relations and 380075 ideals in 297028 cliques Tue Oct 21 22:23:49 2008 commencing in-memory singleton removal Tue Oct 21 22:23:49 2008 begin with 1430556 relations and 989475 unique ideals Tue Oct 21 22:23:50 2008 reduce to 1406368 relations and 583326 ideals in 4 passes Tue Oct 21 22:23:50 2008 max relations containing the same ideal: 25 Tue Oct 21 22:23:50 2008 removing 186369 relations and 97220 ideals in 89149 cliques Tue Oct 21 22:23:50 2008 commencing in-memory singleton removal Tue Oct 21 22:23:50 2008 begin with 1219999 relations and 583326 unique ideals Tue Oct 21 22:23:50 2008 reduce to 1216703 relations and 482718 ideals in 4 passes Tue Oct 21 22:23:50 2008 max relations containing the same ideal: 23 Tue Oct 21 22:23:50 2008 removing 72284 relations and 36861 ideals in 35423 cliques Tue Oct 21 22:23:50 2008 commencing in-memory singleton removal Tue Oct 21 22:23:50 2008 begin with 1144419 relations and 482718 unique ideals Tue Oct 21 22:23:51 2008 reduce to 1143731 relations and 445159 ideals in 3 passes Tue Oct 21 22:23:51 2008 max relations containing the same ideal: 23 Tue Oct 21 22:23:51 2008 removing 32699 relations and 16513 ideals in 16186 cliques Tue Oct 21 22:23:51 2008 commencing in-memory singleton removal Tue Oct 21 22:23:51 2008 begin with 1111032 relations and 445159 unique ideals Tue Oct 21 22:23:51 2008 reduce to 1110866 relations and 428480 ideals in 3 passes Tue Oct 21 22:23:51 2008 max relations containing the same ideal: 23 Tue Oct 21 22:23:51 2008 too much excess; switching to 3-cliques Tue Oct 21 22:23:51 2008 removing 380587 relations and 146570 ideals in 95332 cliques Tue Oct 21 22:23:52 2008 commencing in-memory singleton removal Tue Oct 21 22:23:52 2008 begin with 730279 relations and 428480 unique ideals Tue Oct 21 22:23:52 2008 reduce to 725336 relations and 276576 ideals in 4 passes Tue Oct 21 22:23:52 2008 max relations containing the same ideal: 20 Tue Oct 21 22:23:52 2008 removing 190977 relations and 78800 ideals in 56807 cliques Tue Oct 21 22:23:52 2008 commencing in-memory singleton removal Tue Oct 21 22:23:52 2008 begin with 534359 relations and 276576 unique ideals Tue Oct 21 22:23:52 2008 reduce to 532151 relations and 195415 ideals in 3 passes Tue Oct 21 22:23:52 2008 max relations containing the same ideal: 17 Tue Oct 21 22:23:52 2008 removing 130408 relations and 52763 ideals in 38515 cliques Tue Oct 21 22:23:52 2008 commencing in-memory singleton removal Tue Oct 21 22:23:52 2008 begin with 401743 relations and 195415 unique ideals Tue Oct 21 22:23:52 2008 reduce to 400159 relations and 140972 ideals in 3 passes Tue Oct 21 22:23:52 2008 max relations containing the same ideal: 15 Tue Oct 21 22:23:52 2008 removing 101083 relations and 40878 ideals in 29454 cliques Tue Oct 21 22:23:52 2008 commencing in-memory singleton removal Tue Oct 21 22:23:52 2008 begin with 299076 relations and 140972 unique ideals Tue Oct 21 22:23:52 2008 reduce to 297700 relations and 98656 ideals in 3 passes Tue Oct 21 22:23:52 2008 max relations containing the same ideal: 13 Tue Oct 21 22:23:52 2008 removing 80720 relations and 33093 ideals in 22970 cliques Tue Oct 21 22:23:52 2008 commencing in-memory singleton removal Tue Oct 21 22:23:52 2008 begin with 216980 relations and 98656 unique ideals Tue Oct 21 22:23:52 2008 reduce to 215671 relations and 64177 ideals in 4 passes Tue Oct 21 22:23:52 2008 max relations containing the same ideal: 13 Tue Oct 21 22:23:52 2008 removing 62257 relations and 26037 ideals in 17395 cliques Tue Oct 21 22:23:53 2008 commencing in-memory singleton removal Tue Oct 21 22:23:53 2008 begin with 153414 relations and 64177 unique ideals Tue Oct 21 22:23:53 2008 reduce to 152389 relations and 37039 ideals in 3 passes Tue Oct 21 22:23:53 2008 max relations containing the same ideal: 11 Tue Oct 21 22:23:53 2008 removing 42210 relations and 17688 ideals in 12127 cliques Tue Oct 21 22:23:53 2008 commencing in-memory singleton removal Tue Oct 21 22:23:53 2008 begin with 110179 relations and 37039 unique ideals Tue Oct 21 22:23:53 2008 reduce to 109690 relations and 18814 ideals in 3 passes Tue Oct 21 22:23:53 2008 max relations containing the same ideal: 10 Tue Oct 21 22:23:53 2008 dataset too sparse, retrying Tue Oct 21 22:23:53 2008 reading rational ideals above 360448 Tue Oct 21 22:23:53 2008 reading algebraic ideals above 360448 Tue Oct 21 22:23:53 2008 commencing singleton removal, final pass Tue Oct 21 22:24:05 2008 keeping 1007045 ideals with weight <= 30, new excess is 65083 Tue Oct 21 22:24:06 2008 memory use: 44.9 MB Tue Oct 21 22:24:06 2008 commencing in-memory singleton removal Tue Oct 21 22:24:06 2008 begin with 2109525 relations and 1007045 unique ideals Tue Oct 21 22:24:06 2008 reduce to 2107659 relations and 997957 ideals in 2 passes Tue Oct 21 22:24:06 2008 max relations containing the same ideal: 30 Tue Oct 21 22:24:07 2008 removing 677103 relations and 380075 ideals in 297028 cliques Tue Oct 21 22:24:07 2008 commencing in-memory singleton removal Tue Oct 21 22:24:07 2008 begin with 1430556 relations and 997957 unique ideals Tue Oct 21 22:24:08 2008 reduce to 1406368 relations and 591808 ideals in 4 passes Tue Oct 21 22:24:08 2008 max relations containing the same ideal: 29 Tue Oct 21 22:24:08 2008 removing 186369 relations and 97220 ideals in 89149 cliques Tue Oct 21 22:24:08 2008 commencing in-memory singleton removal Tue Oct 21 22:24:08 2008 begin with 1219999 relations and 591808 unique ideals Tue Oct 21 22:24:08 2008 reduce to 1216703 relations and 491200 ideals in 4 passes Tue Oct 21 22:24:08 2008 max relations containing the same ideal: 28 Tue Oct 21 22:24:09 2008 removing 72284 relations and 36861 ideals in 35423 cliques Tue Oct 21 22:24:09 2008 commencing in-memory singleton removal Tue Oct 21 22:24:09 2008 begin with 1144419 relations and 491200 unique ideals Tue Oct 21 22:24:09 2008 reduce to 1143731 relations and 453641 ideals in 3 passes Tue Oct 21 22:24:09 2008 max relations containing the same ideal: 27 Tue Oct 21 22:24:09 2008 removing 32699 relations and 16513 ideals in 16186 cliques Tue Oct 21 22:24:09 2008 commencing in-memory singleton removal Tue Oct 21 22:24:09 2008 begin with 1111032 relations and 453641 unique ideals Tue Oct 21 22:24:09 2008 reduce to 1110866 relations and 436962 ideals in 3 passes Tue Oct 21 22:24:09 2008 max relations containing the same ideal: 27 Tue Oct 21 22:24:09 2008 too much excess; switching to 3-cliques Tue Oct 21 22:24:10 2008 removing 380587 relations and 146570 ideals in 95332 cliques Tue Oct 21 22:24:10 2008 commencing in-memory singleton removal Tue Oct 21 22:24:10 2008 begin with 730279 relations and 436962 unique ideals Tue Oct 21 22:24:10 2008 reduce to 725336 relations and 285058 ideals in 4 passes Tue Oct 21 22:24:10 2008 max relations containing the same ideal: 22 Tue Oct 21 22:24:10 2008 removing 190982 relations and 78802 ideals in 56808 cliques Tue Oct 21 22:24:10 2008 commencing in-memory singleton removal Tue Oct 21 22:24:10 2008 begin with 534354 relations and 285058 unique ideals Tue Oct 21 22:24:10 2008 reduce to 532145 relations and 203894 ideals in 3 passes Tue Oct 21 22:24:10 2008 max relations containing the same ideal: 19 Tue Oct 21 22:24:10 2008 removing 130505 relations and 52811 ideals in 38525 cliques Tue Oct 21 22:24:10 2008 commencing in-memory singleton removal Tue Oct 21 22:24:10 2008 begin with 401640 relations and 203894 unique ideals Tue Oct 21 22:24:11 2008 reduce to 400052 relations and 149398 ideals in 3 passes Tue Oct 21 22:24:11 2008 max relations containing the same ideal: 18 Tue Oct 21 22:24:11 2008 removing 101689 relations and 41139 ideals in 29583 cliques Tue Oct 21 22:24:11 2008 commencing in-memory singleton removal Tue Oct 21 22:24:11 2008 begin with 298363 relations and 149398 unique ideals Tue Oct 21 22:24:11 2008 reduce to 296923 relations and 106755 ideals in 3 passes Tue Oct 21 22:24:11 2008 max relations containing the same ideal: 15 Tue Oct 21 22:24:11 2008 removing 82535 relations and 33954 ideals in 23310 cliques Tue Oct 21 22:24:11 2008 commencing in-memory singleton removal Tue Oct 21 22:24:11 2008 begin with 214388 relations and 106755 unique ideals Tue Oct 21 22:24:11 2008 reduce to 212935 relations and 71256 ideals in 4 passes Tue Oct 21 22:24:11 2008 max relations containing the same ideal: 13 Tue Oct 21 22:24:11 2008 removing 66223 relations and 28063 ideals in 17991 cliques Tue Oct 21 22:24:11 2008 commencing in-memory singleton removal Tue Oct 21 22:24:11 2008 begin with 146712 relations and 71256 unique ideals Tue Oct 21 22:24:11 2008 reduce to 145272 relations and 41644 ideals in 3 passes Tue Oct 21 22:24:11 2008 max relations containing the same ideal: 11 Tue Oct 21 22:24:11 2008 removing 47186 relations and 20457 ideals in 12775 cliques Tue Oct 21 22:24:11 2008 commencing in-memory singleton removal Tue Oct 21 22:24:11 2008 begin with 98086 relations and 41644 unique ideals Tue Oct 21 22:24:11 2008 reduce to 97137 relations and 20157 ideals in 4 passes Tue Oct 21 22:24:11 2008 max relations containing the same ideal: 10 Tue Oct 21 22:24:11 2008 dataset too sparse, retrying Tue Oct 21 22:24:11 2008 reading rational ideals above 360448 Tue Oct 21 22:24:11 2008 reading algebraic ideals above 360448 Tue Oct 21 22:24:11 2008 commencing singleton removal, final pass Tue Oct 21 22:24:23 2008 keeping 1009959 ideals with weight <= 35, new excess is 62169 Tue Oct 21 22:24:24 2008 memory use: 44.9 MB Tue Oct 21 22:24:24 2008 commencing in-memory singleton removal Tue Oct 21 22:24:24 2008 begin with 2109525 relations and 1009959 unique ideals Tue Oct 21 22:24:24 2008 reduce to 2107659 relations and 1000871 ideals in 2 passes Tue Oct 21 22:24:24 2008 max relations containing the same ideal: 35 Tue Oct 21 22:24:25 2008 removing 677103 relations and 380075 ideals in 297028 cliques Tue Oct 21 22:24:26 2008 commencing in-memory singleton removal Tue Oct 21 22:24:26 2008 begin with 1430556 relations and 1000871 unique ideals Tue Oct 21 22:24:26 2008 reduce to 1406368 relations and 594722 ideals in 4 passes Tue Oct 21 22:24:26 2008 max relations containing the same ideal: 32 Tue Oct 21 22:24:26 2008 removing 186369 relations and 97220 ideals in 89149 cliques Tue Oct 21 22:24:27 2008 commencing in-memory singleton removal Tue Oct 21 22:24:27 2008 begin with 1219999 relations and 594722 unique ideals Tue Oct 21 22:24:27 2008 reduce to 1216703 relations and 494114 ideals in 4 passes Tue Oct 21 22:24:27 2008 max relations containing the same ideal: 30 Tue Oct 21 22:24:27 2008 removing 72284 relations and 36861 ideals in 35423 cliques Tue Oct 21 22:24:27 2008 commencing in-memory singleton removal Tue Oct 21 22:24:27 2008 begin with 1144419 relations and 494114 unique ideals Tue Oct 21 22:24:27 2008 reduce to 1143731 relations and 456555 ideals in 3 passes Tue Oct 21 22:24:27 2008 max relations containing the same ideal: 30 Tue Oct 21 22:24:27 2008 removing 32699 relations and 16513 ideals in 16186 cliques Tue Oct 21 22:24:27 2008 commencing in-memory singleton removal Tue Oct 21 22:24:27 2008 begin with 1111032 relations and 456555 unique ideals Tue Oct 21 22:24:28 2008 reduce to 1110866 relations and 439876 ideals in 3 passes Tue Oct 21 22:24:28 2008 max relations containing the same ideal: 30 Tue Oct 21 22:24:28 2008 too much excess; switching to 3-cliques Tue Oct 21 22:24:28 2008 removing 380587 relations and 146570 ideals in 95332 cliques Tue Oct 21 22:24:28 2008 commencing in-memory singleton removal Tue Oct 21 22:24:28 2008 begin with 730279 relations and 439876 unique ideals Tue Oct 21 22:24:28 2008 reduce to 725336 relations and 287972 ideals in 4 passes Tue Oct 21 22:24:28 2008 max relations containing the same ideal: 24 Tue Oct 21 22:24:28 2008 removing 190982 relations and 78802 ideals in 56808 cliques Tue Oct 21 22:24:29 2008 commencing in-memory singleton removal Tue Oct 21 22:24:29 2008 begin with 534354 relations and 287972 unique ideals Tue Oct 21 22:24:29 2008 reduce to 532144 relations and 206807 ideals in 3 passes Tue Oct 21 22:24:29 2008 max relations containing the same ideal: 21 Tue Oct 21 22:24:29 2008 removing 130513 relations and 52815 ideals in 38526 cliques Tue Oct 21 22:24:29 2008 commencing in-memory singleton removal Tue Oct 21 22:24:29 2008 begin with 401631 relations and 206807 unique ideals Tue Oct 21 22:24:29 2008 reduce to 400043 relations and 152306 ideals in 3 passes Tue Oct 21 22:24:29 2008 max relations containing the same ideal: 18 Tue Oct 21 22:24:29 2008 removing 101749 relations and 41166 ideals in 29594 cliques Tue Oct 21 22:24:29 2008 commencing in-memory singleton removal Tue Oct 21 22:24:29 2008 begin with 298294 relations and 152306 unique ideals Tue Oct 21 22:24:29 2008 reduce to 296849 relations and 109629 ideals in 3 passes Tue Oct 21 22:24:29 2008 max relations containing the same ideal: 15 Tue Oct 21 22:24:29 2008 removing 82874 relations and 34118 ideals in 23351 cliques Tue Oct 21 22:24:29 2008 commencing in-memory singleton removal Tue Oct 21 22:24:29 2008 begin with 213975 relations and 109629 unique ideals Tue Oct 21 22:24:29 2008 reduce to 212491 relations and 73930 ideals in 4 passes Tue Oct 21 22:24:29 2008 max relations containing the same ideal: 13 Tue Oct 21 22:24:29 2008 removing 67114 relations and 28526 ideals in 18104 cliques Tue Oct 21 22:24:29 2008 commencing in-memory singleton removal Tue Oct 21 22:24:29 2008 begin with 145377 relations and 73930 unique ideals Tue Oct 21 22:24:29 2008 reduce to 143828 relations and 43726 ideals in 3 passes Tue Oct 21 22:24:29 2008 max relations containing the same ideal: 12 Tue Oct 21 22:24:29 2008 removing 48691 relations and 21308 ideals in 12920 cliques Tue Oct 21 22:24:29 2008 commencing in-memory singleton removal Tue Oct 21 22:24:29 2008 begin with 95137 relations and 43726 unique ideals Tue Oct 21 22:24:29 2008 reduce to 94014 relations and 21188 ideals in 4 passes Tue Oct 21 22:24:29 2008 max relations containing the same ideal: 10 Tue Oct 21 22:24:29 2008 dataset too sparse, retrying Tue Oct 21 22:24:29 2008 reading rational ideals above 360448 Tue Oct 21 22:24:29 2008 reading algebraic ideals above 360448 Tue Oct 21 22:24:29 2008 commencing singleton removal, final pass Tue Oct 21 22:24:42 2008 keeping 1010622 ideals with weight <= 40, new excess is 61506 Tue Oct 21 22:24:42 2008 memory use: 44.9 MB Tue Oct 21 22:24:42 2008 commencing in-memory singleton removal Tue Oct 21 22:24:42 2008 begin with 2109525 relations and 1010622 unique ideals Tue Oct 21 22:24:43 2008 reduce to 2107659 relations and 1001534 ideals in 2 passes Tue Oct 21 22:24:43 2008 max relations containing the same ideal: 40 Tue Oct 21 22:24:44 2008 removing 677103 relations and 380075 ideals in 297028 cliques Tue Oct 21 22:24:44 2008 commencing in-memory singleton removal Tue Oct 21 22:24:44 2008 begin with 1430556 relations and 1001534 unique ideals Tue Oct 21 22:24:45 2008 reduce to 1406368 relations and 595385 ideals in 4 passes Tue Oct 21 22:24:45 2008 max relations containing the same ideal: 34 Tue Oct 21 22:24:45 2008 removing 186369 relations and 97220 ideals in 89149 cliques Tue Oct 21 22:24:45 2008 commencing in-memory singleton removal Tue Oct 21 22:24:45 2008 begin with 1219999 relations and 595385 unique ideals Tue Oct 21 22:24:45 2008 reduce to 1216703 relations and 494777 ideals in 4 passes Tue Oct 21 22:24:45 2008 max relations containing the same ideal: 32 Tue Oct 21 22:24:45 2008 removing 72284 relations and 36861 ideals in 35423 cliques Tue Oct 21 22:24:45 2008 commencing in-memory singleton removal Tue Oct 21 22:24:45 2008 begin with 1144419 relations and 494777 unique ideals Tue Oct 21 22:24:46 2008 reduce to 1143731 relations and 457218 ideals in 3 passes Tue Oct 21 22:24:46 2008 max relations containing the same ideal: 32 Tue Oct 21 22:24:46 2008 removing 32699 relations and 16513 ideals in 16186 cliques Tue Oct 21 22:24:46 2008 commencing in-memory singleton removal Tue Oct 21 22:24:46 2008 begin with 1111032 relations and 457218 unique ideals Tue Oct 21 22:24:46 2008 reduce to 1110866 relations and 440539 ideals in 3 passes Tue Oct 21 22:24:46 2008 max relations containing the same ideal: 30 Tue Oct 21 22:24:46 2008 too much excess; switching to 3-cliques Tue Oct 21 22:24:46 2008 removing 380587 relations and 146570 ideals in 95332 cliques Tue Oct 21 22:24:47 2008 commencing in-memory singleton removal Tue Oct 21 22:24:47 2008 begin with 730279 relations and 440539 unique ideals Tue Oct 21 22:24:47 2008 reduce to 725336 relations and 288635 ideals in 4 passes Tue Oct 21 22:24:47 2008 max relations containing the same ideal: 25 Tue Oct 21 22:24:47 2008 removing 190982 relations and 78802 ideals in 56808 cliques Tue Oct 21 22:24:47 2008 commencing in-memory singleton removal Tue Oct 21 22:24:47 2008 begin with 534354 relations and 288635 unique ideals Tue Oct 21 22:24:47 2008 reduce to 532144 relations and 207470 ideals in 3 passes Tue Oct 21 22:24:47 2008 max relations containing the same ideal: 24 Tue Oct 21 22:24:47 2008 removing 130513 relations and 52815 ideals in 38526 cliques Tue Oct 21 22:24:47 2008 commencing in-memory singleton removal Tue Oct 21 22:24:47 2008 begin with 401631 relations and 207470 unique ideals Tue Oct 21 22:24:47 2008 reduce to 400043 relations and 152969 ideals in 3 passes Tue Oct 21 22:24:47 2008 max relations containing the same ideal: 22 Tue Oct 21 22:24:47 2008 removing 101758 relations and 41170 ideals in 29595 cliques Tue Oct 21 22:24:47 2008 commencing in-memory singleton removal Tue Oct 21 22:24:47 2008 begin with 298285 relations and 152969 unique ideals Tue Oct 21 22:24:47 2008 reduce to 296837 relations and 110285 ideals in 3 passes Tue Oct 21 22:24:47 2008 max relations containing the same ideal: 15 Tue Oct 21 22:24:47 2008 removing 82932 relations and 34144 ideals in 23362 cliques Tue Oct 21 22:24:48 2008 commencing in-memory singleton removal Tue Oct 21 22:24:48 2008 begin with 213905 relations and 110285 unique ideals Tue Oct 21 22:24:48 2008 reduce to 212417 relations and 74556 ideals in 4 passes Tue Oct 21 22:24:48 2008 max relations containing the same ideal: 13 Tue Oct 21 22:24:48 2008 removing 67250 relations and 28598 ideals in 18122 cliques Tue Oct 21 22:24:48 2008 commencing in-memory singleton removal Tue Oct 21 22:24:48 2008 begin with 145167 relations and 74556 unique ideals Tue Oct 21 22:24:48 2008 reduce to 143587 relations and 44249 ideals in 3 passes Tue Oct 21 22:24:48 2008 max relations containing the same ideal: 12 Tue Oct 21 22:24:48 2008 removing 49027 relations and 21489 ideals in 12958 cliques Tue Oct 21 22:24:48 2008 commencing in-memory singleton removal Tue Oct 21 22:24:48 2008 begin with 94560 relations and 44249 unique ideals Tue Oct 21 22:24:48 2008 reduce to 93389 relations and 21478 ideals in 4 passes Tue Oct 21 22:24:48 2008 max relations containing the same ideal: 10 Tue Oct 21 22:24:48 2008 dataset too sparse, retrying Tue Oct 21 22:25:27 2008 Tue Oct 21 22:25:27 2008 Tue Oct 21 22:25:27 2008 Msieve v. 1.38 Tue Oct 21 22:25:27 2008 random seeds: 2a87b66a 229fd541 Tue Oct 21 22:25:27 2008 factoring 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 (99 digits) Tue Oct 21 22:25:28 2008 no P-1/P+1/ECM available, skipping Tue Oct 21 22:25:28 2008 commencing number field sieve (99-digit input) Tue Oct 21 22:25:28 2008 R0: 10000000000000000000000000 Tue Oct 21 22:25:28 2008 R1: -1 Tue Oct 21 22:25:28 2008 A0: 27 Tue Oct 21 22:25:28 2008 A1: 0 Tue Oct 21 22:25:28 2008 A2: 0 Tue Oct 21 22:25:28 2008 A3: 0 Tue Oct 21 22:25:28 2008 A4: 1 Tue Oct 21 22:25:28 2008 size score = 3.100724e-10, Murphy alpha = 0.835783, combined = 2.219590e-10 Tue Oct 21 22:25:28 2008 Tue Oct 21 22:25:28 2008 commencing relation filtering Tue Oct 21 22:25:28 2008 commencing duplicate removal, pass 1 Tue Oct 21 22:25:37 2008 found 53417 hash collisions in 1999999 relations Tue Oct 21 22:25:38 2008 added 203954 free relations Tue Oct 21 22:25:38 2008 commencing duplicate removal, pass 2 Tue Oct 21 22:25:39 2008 found 47009 duplicates and 2156944 unique relations Tue Oct 21 22:25:39 2008 memory use: 36.9 MB Tue Oct 21 22:25:39 2008 reading rational ideals above 458752 Tue Oct 21 22:25:39 2008 reading algebraic ideals above 458752 Tue Oct 21 22:25:39 2008 commencing singleton removal, pass 1 Tue Oct 21 22:25:50 2008 relations with 0 large ideals: 41474 Tue Oct 21 22:25:50 2008 relations with 1 large ideals: 329210 Tue Oct 21 22:25:50 2008 relations with 2 large ideals: 870977 Tue Oct 21 22:25:50 2008 relations with 3 large ideals: 601131 Tue Oct 21 22:25:50 2008 relations with 4 large ideals: 114960 Tue Oct 21 22:25:50 2008 relations with 5 large ideals: 199192 Tue Oct 21 22:25:50 2008 relations with 6 large ideals: 0 Tue Oct 21 22:25:50 2008 relations with 7+ large ideals: 0 Tue Oct 21 22:25:50 2008 2156944 relations and about 2124068 large ideals Tue Oct 21 22:25:50 2008 commencing singleton removal, pass 2 Tue Oct 21 22:26:02 2008 found 773428 singletons Tue Oct 21 22:26:02 2008 current dataset: 1383516 relations and about 948724 large ideals Tue Oct 21 22:26:02 2008 commencing singleton removal, pass 3 Tue Oct 21 22:26:09 2008 found 291472 singletons Tue Oct 21 22:26:09 2008 current dataset: 1092044 relations and about 643849 large ideals Tue Oct 21 22:26:09 2008 commencing singleton removal, final pass Tue Oct 21 22:26:15 2008 memory use: 22.6 MB Tue Oct 21 22:26:15 2008 commencing in-memory singleton removal Tue Oct 21 22:26:15 2008 begin with 1092044 relations and 651264 unique ideals Tue Oct 21 22:26:15 2008 reduce to 1034935 relations and 593520 ideals in 7 passes Tue Oct 21 22:26:15 2008 max relations containing the same ideal: 29 Tue Oct 21 22:26:15 2008 reading rational ideals above 229376 Tue Oct 21 22:26:15 2008 reading algebraic ideals above 229376 Tue Oct 21 22:26:15 2008 commencing singleton removal, final pass Tue Oct 21 22:26:22 2008 keeping 668163 ideals with weight <= 20, new excess is 49837 Tue Oct 21 22:26:22 2008 memory use: 23.5 MB Tue Oct 21 22:26:22 2008 commencing in-memory singleton removal Tue Oct 21 22:26:22 2008 begin with 1044628 relations and 668163 unique ideals Tue Oct 21 22:26:22 2008 reduce to 1034935 relations and 620311 ideals in 2 passes Tue Oct 21 22:26:22 2008 max relations containing the same ideal: 20 Tue Oct 21 22:26:23 2008 removing 433418 relations and 255011 ideals in 178407 cliques Tue Oct 21 22:26:23 2008 commencing in-memory singleton removal Tue Oct 21 22:26:23 2008 begin with 601517 relations and 620311 unique ideals Tue Oct 21 22:26:23 2008 reduce to 564972 relations and 324287 ideals in 6 passes Tue Oct 21 22:26:23 2008 max relations containing the same ideal: 19 Tue Oct 21 22:26:23 2008 removing 156747 relations and 87054 ideals in 69693 cliques Tue Oct 21 22:26:23 2008 commencing in-memory singleton removal Tue Oct 21 22:26:23 2008 begin with 408225 relations and 324287 unique ideals Tue Oct 21 22:26:23 2008 reduce to 395379 relations and 223413 ideals in 5 passes Tue Oct 21 22:26:23 2008 max relations containing the same ideal: 17 Tue Oct 21 22:26:24 2008 removing 86178 relations and 47165 ideals in 39013 cliques Tue Oct 21 22:26:24 2008 commencing in-memory singleton removal Tue Oct 21 22:26:24 2008 begin with 309201 relations and 223413 unique ideals Tue Oct 21 22:26:24 2008 reduce to 302110 relations and 168718 ideals in 5 passes Tue Oct 21 22:26:24 2008 max relations containing the same ideal: 14 Tue Oct 21 22:26:24 2008 removing 61939 relations and 33684 ideals in 28255 cliques Tue Oct 21 22:26:24 2008 commencing in-memory singleton removal Tue Oct 21 22:26:24 2008 begin with 240171 relations and 168718 unique ideals Tue Oct 21 22:26:24 2008 reduce to 234759 relations and 129301 ideals in 5 passes Tue Oct 21 22:26:24 2008 max relations containing the same ideal: 13 Tue Oct 21 22:26:24 2008 removing 48610 relations and 26553 ideals in 22057 cliques Tue Oct 21 22:26:24 2008 commencing in-memory singleton removal Tue Oct 21 22:26:24 2008 begin with 186149 relations and 129301 unique ideals Tue Oct 21 22:26:24 2008 reduce to 181429 relations and 97746 ideals in 5 passes Tue Oct 21 22:26:24 2008 max relations containing the same ideal: 12 Tue Oct 21 22:26:24 2008 removing 40597 relations and 22282 ideals in 18315 cliques Tue Oct 21 22:26:24 2008 commencing in-memory singleton removal Tue Oct 21 22:26:24 2008 begin with 140832 relations and 97746 unique ideals Tue Oct 21 22:26:24 2008 reduce to 136290 relations and 70628 ideals in 5 passes Tue Oct 21 22:26:24 2008 max relations containing the same ideal: 11 Tue Oct 21 22:26:24 2008 dataset too sparse, retrying Tue Oct 21 22:26:24 2008 reading rational ideals above 229376 Tue Oct 21 22:26:24 2008 reading algebraic ideals above 229376 Tue Oct 21 22:26:24 2008 commencing singleton removal, final pass Tue Oct 21 22:26:30 2008 keeping 673606 ideals with weight <= 25, new excess is 44394 Tue Oct 21 22:26:31 2008 memory use: 23.5 MB Tue Oct 21 22:26:31 2008 commencing in-memory singleton removal Tue Oct 21 22:26:31 2008 begin with 1044628 relations and 673606 unique ideals Tue Oct 21 22:26:31 2008 reduce to 1034935 relations and 625754 ideals in 2 passes Tue Oct 21 22:26:31 2008 max relations containing the same ideal: 25 Tue Oct 21 22:26:31 2008 removing 434288 relations and 255446 ideals in 178842 cliques Tue Oct 21 22:26:32 2008 commencing in-memory singleton removal Tue Oct 21 22:26:32 2008 begin with 600647 relations and 625754 unique ideals Tue Oct 21 22:26:32 2008 reduce to 564102 relations and 329295 ideals in 6 passes Tue Oct 21 22:26:32 2008 max relations containing the same ideal: 23 Tue Oct 21 22:26:32 2008 removing 155877 relations and 86619 ideals in 69258 cliques Tue Oct 21 22:26:32 2008 commencing in-memory singleton removal Tue Oct 21 22:26:32 2008 begin with 408225 relations and 329295 unique ideals Tue Oct 21 22:26:32 2008 reduce to 395379 relations and 228856 ideals in 5 passes Tue Oct 21 22:26:32 2008 max relations containing the same ideal: 19 Tue Oct 21 22:26:32 2008 removing 86180 relations and 47166 ideals in 39014 cliques Tue Oct 21 22:26:32 2008 commencing in-memory singleton removal Tue Oct 21 22:26:32 2008 begin with 309199 relations and 228856 unique ideals Tue Oct 21 22:26:32 2008 reduce to 302106 relations and 174158 ideals in 5 passes Tue Oct 21 22:26:32 2008 max relations containing the same ideal: 17 Tue Oct 21 22:26:32 2008 removing 61991 relations and 33716 ideals in 28275 cliques Tue Oct 21 22:26:32 2008 commencing in-memory singleton removal Tue Oct 21 22:26:32 2008 begin with 240115 relations and 174158 unique ideals Tue Oct 21 22:26:32 2008 reduce to 234693 relations and 134698 ideals in 5 passes Tue Oct 21 22:26:32 2008 max relations containing the same ideal: 16 Tue Oct 21 22:26:32 2008 removing 48757 relations and 26640 ideals in 22117 cliques Tue Oct 21 22:26:32 2008 commencing in-memory singleton removal Tue Oct 21 22:26:32 2008 begin with 185936 relations and 134698 unique ideals Tue Oct 21 22:26:32 2008 reduce to 181132 relations and 102968 ideals in 5 passes Tue Oct 21 22:26:32 2008 max relations containing the same ideal: 14 Tue Oct 21 22:26:33 2008 removing 41036 relations and 22552 ideals in 18484 cliques Tue Oct 21 22:26:33 2008 commencing in-memory singleton removal Tue Oct 21 22:26:33 2008 begin with 140096 relations and 102968 unique ideals Tue Oct 21 22:26:33 2008 reduce to 135320 relations and 75321 ideals in 5 passes Tue Oct 21 22:26:33 2008 max relations containing the same ideal: 13 Tue Oct 21 22:26:33 2008 removing 21288 relations and 12787 ideals in 8501 cliques Tue Oct 21 22:26:33 2008 commencing in-memory singleton removal Tue Oct 21 22:26:33 2008 begin with 114032 relations and 75321 unique ideals Tue Oct 21 22:26:33 2008 reduce to 110782 relations and 59073 ideals in 5 passes Tue Oct 21 22:26:33 2008 max relations containing the same ideal: 12 Tue Oct 21 22:26:33 2008 dataset too sparse, retrying Tue Oct 21 22:26:33 2008 reading rational ideals above 229376 Tue Oct 21 22:26:33 2008 reading algebraic ideals above 229376 Tue Oct 21 22:26:33 2008 commencing singleton removal, final pass Tue Oct 21 22:26:39 2008 keeping 675860 ideals with weight <= 30, new excess is 42140 Tue Oct 21 22:26:39 2008 memory use: 23.5 MB Tue Oct 21 22:26:39 2008 commencing in-memory singleton removal Tue Oct 21 22:26:39 2008 begin with 1044628 relations and 675860 unique ideals Tue Oct 21 22:26:39 2008 reduce to 1034935 relations and 628008 ideals in 2 passes Tue Oct 21 22:26:39 2008 max relations containing the same ideal: 30 Tue Oct 21 22:26:40 2008 removing 434648 relations and 255626 ideals in 179022 cliques Tue Oct 21 22:26:40 2008 commencing in-memory singleton removal Tue Oct 21 22:26:40 2008 begin with 600287 relations and 628008 unique ideals Tue Oct 21 22:26:40 2008 reduce to 563742 relations and 331369 ideals in 6 passes Tue Oct 21 22:26:40 2008 max relations containing the same ideal: 27 Tue Oct 21 22:26:41 2008 removing 155517 relations and 86439 ideals in 69078 cliques Tue Oct 21 22:26:41 2008 commencing in-memory singleton removal Tue Oct 21 22:26:41 2008 begin with 408225 relations and 331369 unique ideals Tue Oct 21 22:26:41 2008 reduce to 395379 relations and 231110 ideals in 5 passes Tue Oct 21 22:26:41 2008 max relations containing the same ideal: 21 Tue Oct 21 22:26:41 2008 removing 86180 relations and 47166 ideals in 39014 cliques Tue Oct 21 22:26:41 2008 commencing in-memory singleton removal Tue Oct 21 22:26:41 2008 begin with 309199 relations and 231110 unique ideals Tue Oct 21 22:26:41 2008 reduce to 302106 relations and 176412 ideals in 5 passes Tue Oct 21 22:26:41 2008 max relations containing the same ideal: 19 Tue Oct 21 22:26:41 2008 removing 61993 relations and 33717 ideals in 28276 cliques Tue Oct 21 22:26:41 2008 commencing in-memory singleton removal Tue Oct 21 22:26:41 2008 begin with 240113 relations and 176412 unique ideals Tue Oct 21 22:26:41 2008 reduce to 234691 relations and 136950 ideals in 5 passes Tue Oct 21 22:26:41 2008 max relations containing the same ideal: 17 Tue Oct 21 22:26:41 2008 removing 48766 relations and 26646 ideals in 22120 cliques Tue Oct 21 22:26:41 2008 commencing in-memory singleton removal Tue Oct 21 22:26:41 2008 begin with 185925 relations and 136950 unique ideals Tue Oct 21 22:26:41 2008 reduce to 181115 relations and 105208 ideals in 5 passes Tue Oct 21 22:26:41 2008 max relations containing the same ideal: 15 Tue Oct 21 22:26:41 2008 removing 41105 relations and 22599 ideals in 18506 cliques Tue Oct 21 22:26:41 2008 commencing in-memory singleton removal Tue Oct 21 22:26:41 2008 begin with 140010 relations and 105208 unique ideals Tue Oct 21 22:26:41 2008 reduce to 135196 relations and 77471 ideals in 5 passes Tue Oct 21 22:26:41 2008 max relations containing the same ideal: 13 Tue Oct 21 22:26:41 2008 removing 22049 relations and 13207 ideals in 8842 cliques Tue Oct 21 22:26:41 2008 commencing in-memory singleton removal Tue Oct 21 22:26:41 2008 begin with 113147 relations and 77471 unique ideals Tue Oct 21 22:26:41 2008 reduce to 109681 relations and 60569 ideals in 5 passes Tue Oct 21 22:26:41 2008 max relations containing the same ideal: 12 Tue Oct 21 22:26:41 2008 dataset too sparse, retrying Tue Oct 21 22:26:41 2008 reading rational ideals above 229376 Tue Oct 21 22:26:41 2008 reading algebraic ideals above 229376 Tue Oct 21 22:26:41 2008 commencing singleton removal, final pass Tue Oct 21 22:26:48 2008 keeping 676535 ideals with weight <= 35, new excess is 41465 Tue Oct 21 22:26:48 2008 memory use: 23.5 MB Tue Oct 21 22:26:48 2008 commencing in-memory singleton removal Tue Oct 21 22:26:48 2008 begin with 1044628 relations and 676535 unique ideals Tue Oct 21 22:26:48 2008 reduce to 1034935 relations and 628683 ideals in 2 passes Tue Oct 21 22:26:48 2008 max relations containing the same ideal: 35 Tue Oct 21 22:26:49 2008 removing 434756 relations and 255680 ideals in 179076 cliques Tue Oct 21 22:26:49 2008 commencing in-memory singleton removal Tue Oct 21 22:26:49 2008 begin with 600179 relations and 628683 unique ideals Tue Oct 21 22:26:49 2008 reduce to 563634 relations and 331990 ideals in 6 passes Tue Oct 21 22:26:49 2008 max relations containing the same ideal: 29 Tue Oct 21 22:26:49 2008 removing 155409 relations and 86385 ideals in 69024 cliques Tue Oct 21 22:26:49 2008 commencing in-memory singleton removal Tue Oct 21 22:26:49 2008 begin with 408225 relations and 331990 unique ideals Tue Oct 21 22:26:49 2008 reduce to 395379 relations and 231785 ideals in 5 passes Tue Oct 21 22:26:49 2008 max relations containing the same ideal: 23 Tue Oct 21 22:26:50 2008 removing 86180 relations and 47166 ideals in 39014 cliques Tue Oct 21 22:26:50 2008 commencing in-memory singleton removal Tue Oct 21 22:26:50 2008 begin with 309199 relations and 231785 unique ideals Tue Oct 21 22:26:50 2008 reduce to 302106 relations and 177087 ideals in 5 passes Tue Oct 21 22:26:50 2008 max relations containing the same ideal: 20 Tue Oct 21 22:26:50 2008 removing 61993 relations and 33717 ideals in 28276 cliques Tue Oct 21 22:26:50 2008 commencing in-memory singleton removal Tue Oct 21 22:26:50 2008 begin with 240113 relations and 177087 unique ideals Tue Oct 21 22:26:50 2008 reduce to 234691 relations and 137625 ideals in 5 passes Tue Oct 21 22:26:50 2008 max relations containing the same ideal: 18 Tue Oct 21 22:26:50 2008 removing 48766 relations and 26646 ideals in 22120 cliques Tue Oct 21 22:26:50 2008 commencing in-memory singleton removal Tue Oct 21 22:26:50 2008 begin with 185925 relations and 137625 unique ideals Tue Oct 21 22:26:50 2008 reduce to 181111 relations and 105879 ideals in 5 passes Tue Oct 21 22:26:50 2008 max relations containing the same ideal: 15 Tue Oct 21 22:26:50 2008 removing 41109 relations and 22602 ideals in 18507 cliques Tue Oct 21 22:26:50 2008 commencing in-memory singleton removal Tue Oct 21 22:26:50 2008 begin with 140002 relations and 105879 unique ideals Tue Oct 21 22:26:50 2008 reduce to 135181 relations and 78132 ideals in 5 passes Tue Oct 21 22:26:50 2008 max relations containing the same ideal: 13 Tue Oct 21 22:26:50 2008 removing 22273 relations and 13324 ideals in 8949 cliques Tue Oct 21 22:26:50 2008 commencing in-memory singleton removal Tue Oct 21 22:26:50 2008 begin with 112908 relations and 78132 unique ideals Tue Oct 21 22:26:50 2008 reduce to 109392 relations and 61057 ideals in 5 passes Tue Oct 21 22:26:50 2008 max relations containing the same ideal: 12 Tue Oct 21 22:26:50 2008 dataset too sparse, retrying Tue Oct 21 22:26:50 2008 reading rational ideals above 229376 Tue Oct 21 22:26:50 2008 reading algebraic ideals above 229376 Tue Oct 21 22:26:50 2008 commencing singleton removal, final pass Tue Oct 21 22:26:56 2008 keeping 676666 ideals with weight <= 40, new excess is 41334 Tue Oct 21 22:26:57 2008 memory use: 23.5 MB Tue Oct 21 22:26:57 2008 commencing in-memory singleton removal Tue Oct 21 22:26:57 2008 begin with 1044628 relations and 676666 unique ideals Tue Oct 21 22:26:57 2008 reduce to 1034935 relations and 628814 ideals in 2 passes Tue Oct 21 22:26:57 2008 max relations containing the same ideal: 40 Tue Oct 21 22:26:57 2008 removing 434778 relations and 255691 ideals in 179087 cliques Tue Oct 21 22:26:58 2008 commencing in-memory singleton removal Tue Oct 21 22:26:58 2008 begin with 600157 relations and 628814 unique ideals Tue Oct 21 22:26:58 2008 reduce to 563612 relations and 332110 ideals in 6 passes Tue Oct 21 22:26:58 2008 max relations containing the same ideal: 29 Tue Oct 21 22:26:58 2008 removing 155387 relations and 86374 ideals in 69013 cliques Tue Oct 21 22:26:58 2008 commencing in-memory singleton removal Tue Oct 21 22:26:58 2008 begin with 408225 relations and 332110 unique ideals Tue Oct 21 22:26:58 2008 reduce to 395379 relations and 231916 ideals in 5 passes Tue Oct 21 22:26:58 2008 max relations containing the same ideal: 24 Tue Oct 21 22:26:58 2008 removing 86180 relations and 47166 ideals in 39014 cliques Tue Oct 21 22:26:58 2008 commencing in-memory singleton removal Tue Oct 21 22:26:58 2008 begin with 309199 relations and 231916 unique ideals Tue Oct 21 22:26:58 2008 reduce to 302106 relations and 177218 ideals in 5 passes Tue Oct 21 22:26:58 2008 max relations containing the same ideal: 20 Tue Oct 21 22:26:58 2008 removing 61993 relations and 33717 ideals in 28276 cliques Tue Oct 21 22:26:58 2008 commencing in-memory singleton removal Tue Oct 21 22:26:58 2008 begin with 240113 relations and 177218 unique ideals Tue Oct 21 22:26:58 2008 reduce to 234691 relations and 137756 ideals in 5 passes Tue Oct 21 22:26:58 2008 max relations containing the same ideal: 19 Tue Oct 21 22:26:58 2008 removing 48766 relations and 26646 ideals in 22120 cliques Tue Oct 21 22:26:58 2008 commencing in-memory singleton removal Tue Oct 21 22:26:58 2008 begin with 185925 relations and 137756 unique ideals Tue Oct 21 22:26:59 2008 reduce to 181111 relations and 106010 ideals in 5 passes Tue Oct 21 22:26:59 2008 max relations containing the same ideal: 15 Tue Oct 21 22:26:59 2008 removing 41111 relations and 22603 ideals in 18508 cliques Tue Oct 21 22:26:59 2008 commencing in-memory singleton removal Tue Oct 21 22:26:59 2008 begin with 140000 relations and 106010 unique ideals Tue Oct 21 22:26:59 2008 reduce to 135180 relations and 78262 ideals in 5 passes Tue Oct 21 22:26:59 2008 max relations containing the same ideal: 13 Tue Oct 21 22:26:59 2008 removing 22318 relations and 13348 ideals in 8970 cliques Tue Oct 21 22:26:59 2008 commencing in-memory singleton removal Tue Oct 21 22:26:59 2008 begin with 112862 relations and 78262 unique ideals Tue Oct 21 22:26:59 2008 reduce to 109335 relations and 61149 ideals in 5 passes Tue Oct 21 22:26:59 2008 max relations containing the same ideal: 12 Tue Oct 21 22:26:59 2008 dataset too sparse, retrying Tue Oct 21 22:27:27 2008 Tue Oct 21 22:27:27 2008 Tue Oct 21 22:27:27 2008 Msieve v. 1.38 Tue Oct 21 22:27:27 2008 random seeds: 21d71147 0c9a7b9b Tue Oct 21 22:27:27 2008 factoring 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 (99 digits) Tue Oct 21 22:27:28 2008 no P-1/P+1/ECM available, skipping Tue Oct 21 22:27:28 2008 commencing number field sieve (99-digit input) Tue Oct 21 22:27:28 2008 R0: 10000000000000000000000000 Tue Oct 21 22:27:28 2008 R1: -1 Tue Oct 21 22:27:28 2008 A0: 27 Tue Oct 21 22:27:28 2008 A1: 0 Tue Oct 21 22:27:28 2008 A2: 0 Tue Oct 21 22:27:28 2008 A3: 0 Tue Oct 21 22:27:28 2008 A4: 1 Tue Oct 21 22:27:28 2008 size score = 3.100724e-10, Murphy alpha = 0.835783, combined = 2.219590e-10 Tue Oct 21 22:27:28 2008 Tue Oct 21 22:27:28 2008 commencing relation filtering Tue Oct 21 22:27:28 2008 commencing duplicate removal, pass 1 Tue Oct 21 22:27:35 2008 found 30804 hash collisions in 1499999 relations Tue Oct 21 22:27:36 2008 added 186144 free relations Tue Oct 21 22:27:36 2008 commencing duplicate removal, pass 2 Tue Oct 21 22:27:36 2008 found 27045 duplicates and 1659098 unique relations Tue Oct 21 22:27:36 2008 memory use: 36.5 MB Tue Oct 21 22:27:36 2008 reading rational ideals above 327680 Tue Oct 21 22:27:36 2008 reading algebraic ideals above 327680 Tue Oct 21 22:27:36 2008 commencing singleton removal, pass 1 Tue Oct 21 22:27:45 2008 relations with 0 large ideals: 18954 Tue Oct 21 22:27:45 2008 relations with 1 large ideals: 168919 Tue Oct 21 22:27:45 2008 relations with 2 large ideals: 566344 Tue Oct 21 22:27:45 2008 relations with 3 large ideals: 561417 Tue Oct 21 22:27:45 2008 relations with 4 large ideals: 160811 Tue Oct 21 22:27:45 2008 relations with 5 large ideals: 182653 Tue Oct 21 22:27:45 2008 relations with 6 large ideals: 0 Tue Oct 21 22:27:45 2008 relations with 7+ large ideals: 0 Tue Oct 21 22:27:45 2008 1659098 relations and about 1892995 large ideals Tue Oct 21 22:27:45 2008 commencing singleton removal, pass 2 Tue Oct 21 22:27:54 2008 found 705292 singletons Tue Oct 21 22:27:54 2008 current dataset: 953806 relations and about 770527 large ideals Tue Oct 21 22:27:54 2008 commencing singleton removal, pass 3 Tue Oct 21 22:27:59 2008 found 268155 singletons Tue Oct 21 22:27:59 2008 current dataset: 685651 relations and about 483890 large ideals Tue Oct 21 22:27:59 2008 commencing singleton removal, final pass Tue Oct 21 22:28:03 2008 memory use: 15.3 MB Tue Oct 21 22:28:03 2008 commencing in-memory singleton removal Tue Oct 21 22:28:03 2008 begin with 685651 relations and 488707 unique ideals Tue Oct 21 22:28:04 2008 reduce to 616663 relations and 418299 ideals in 9 passes Tue Oct 21 22:28:04 2008 max relations containing the same ideal: 24 Tue Oct 21 22:28:04 2008 reading rational ideals above 163840 Tue Oct 21 22:28:04 2008 reading algebraic ideals above 163840 Tue Oct 21 22:28:04 2008 commencing singleton removal, final pass Tue Oct 21 22:28:08 2008 keeping 476403 ideals with weight <= 20, new excess is 37325 Tue Oct 21 22:28:08 2008 memory use: 16.8 MB Tue Oct 21 22:28:08 2008 commencing in-memory singleton removal Tue Oct 21 22:28:08 2008 begin with 624541 relations and 476403 unique ideals Tue Oct 21 22:28:08 2008 reduce to 616659 relations and 437311 ideals in 3 passes Tue Oct 21 22:28:08 2008 max relations containing the same ideal: 20 Tue Oct 21 22:28:08 2008 removing 210971 relations and 142946 ideals in 68025 cliques Tue Oct 21 22:28:08 2008 commencing in-memory singleton removal Tue Oct 21 22:28:08 2008 begin with 405688 relations and 437311 unique ideals Tue Oct 21 22:28:08 2008 reduce to 372616 relations and 256979 ideals in 6 passes Tue Oct 21 22:28:08 2008 max relations containing the same ideal: 19 Tue Oct 21 22:28:09 2008 removing 162464 relations and 94439 ideals in 68025 cliques Tue Oct 21 22:28:09 2008 commencing in-memory singleton removal Tue Oct 21 22:28:09 2008 begin with 210152 relations and 256979 unique ideals Tue Oct 21 22:28:09 2008 reduce to 179228 relations and 126755 ideals in 8 passes Tue Oct 21 22:28:09 2008 max relations containing the same ideal: 15 Tue Oct 21 22:28:09 2008 removing 35008 relations and 25833 ideals in 9175 cliques Tue Oct 21 22:28:09 2008 commencing in-memory singleton removal Tue Oct 21 22:28:09 2008 begin with 144220 relations and 126755 unique ideals Tue Oct 21 22:28:09 2008 reduce to 138977 relations and 95393 ideals in 7 passes Tue Oct 21 22:28:09 2008 max relations containing the same ideal: 13 Tue Oct 21 22:28:09 2008 dataset too sparse, retrying Tue Oct 21 22:28:09 2008 reading rational ideals above 163840 Tue Oct 21 22:28:09 2008 reading algebraic ideals above 163840 Tue Oct 21 22:28:09 2008 commencing singleton removal, final pass Tue Oct 21 22:28:13 2008 keeping 479728 ideals with weight <= 25, new excess is 34000 Tue Oct 21 22:28:13 2008 memory use: 16.8 MB Tue Oct 21 22:28:13 2008 commencing in-memory singleton removal Tue Oct 21 22:28:13 2008 begin with 624541 relations and 479728 unique ideals Tue Oct 21 22:28:13 2008 reduce to 616659 relations and 440636 ideals in 3 passes Tue Oct 21 22:28:13 2008 max relations containing the same ideal: 25 Tue Oct 21 22:28:13 2008 removing 211503 relations and 143212 ideals in 68291 cliques Tue Oct 21 22:28:14 2008 commencing in-memory singleton removal Tue Oct 21 22:28:14 2008 begin with 405156 relations and 440636 unique ideals Tue Oct 21 22:28:14 2008 reduce to 371947 relations and 259869 ideals in 6 passes Tue Oct 21 22:28:14 2008 max relations containing the same ideal: 23 Tue Oct 21 22:28:14 2008 removing 162991 relations and 94700 ideals in 68291 cliques Tue Oct 21 22:28:14 2008 commencing in-memory singleton removal Tue Oct 21 22:28:14 2008 begin with 208956 relations and 259869 unique ideals Tue Oct 21 22:28:14 2008 reduce to 177883 relations and 129216 ideals in 8 passes Tue Oct 21 22:28:14 2008 max relations containing the same ideal: 16 Tue Oct 21 22:28:14 2008 removing 35234 relations and 26008 ideals in 9226 cliques Tue Oct 21 22:28:14 2008 commencing in-memory singleton removal Tue Oct 21 22:28:14 2008 begin with 142649 relations and 129216 unique ideals Tue Oct 21 22:28:14 2008 reduce to 137205 relations and 97474 ideals in 7 passes Tue Oct 21 22:28:14 2008 max relations containing the same ideal: 14 Tue Oct 21 22:28:14 2008 dataset too sparse, retrying Tue Oct 21 22:28:14 2008 reading rational ideals above 163840 Tue Oct 21 22:28:14 2008 reading algebraic ideals above 163840 Tue Oct 21 22:28:14 2008 commencing singleton removal, final pass Tue Oct 21 22:28:18 2008 keeping 481112 ideals with weight <= 30, new excess is 32616 Tue Oct 21 22:28:18 2008 memory use: 16.8 MB Tue Oct 21 22:28:18 2008 commencing in-memory singleton removal Tue Oct 21 22:28:18 2008 begin with 624541 relations and 481112 unique ideals Tue Oct 21 22:28:18 2008 reduce to 616659 relations and 442020 ideals in 3 passes Tue Oct 21 22:28:18 2008 max relations containing the same ideal: 30 Tue Oct 21 22:28:19 2008 removing 211725 relations and 143323 ideals in 68402 cliques Tue Oct 21 22:28:19 2008 commencing in-memory singleton removal Tue Oct 21 22:28:19 2008 begin with 404934 relations and 442020 unique ideals Tue Oct 21 22:28:19 2008 reduce to 371689 relations and 261085 ideals in 6 passes Tue Oct 21 22:28:19 2008 max relations containing the same ideal: 26 Tue Oct 21 22:28:19 2008 removing 163223 relations and 94821 ideals in 68402 cliques Tue Oct 21 22:28:19 2008 commencing in-memory singleton removal Tue Oct 21 22:28:19 2008 begin with 208466 relations and 261085 unique ideals Tue Oct 21 22:28:19 2008 reduce to 177341 relations and 130260 ideals in 8 passes Tue Oct 21 22:28:19 2008 max relations containing the same ideal: 18 Tue Oct 21 22:28:19 2008 removing 35315 relations and 26069 ideals in 9246 cliques Tue Oct 21 22:28:19 2008 commencing in-memory singleton removal Tue Oct 21 22:28:19 2008 begin with 142026 relations and 130260 unique ideals Tue Oct 21 22:28:19 2008 reduce to 136470 relations and 98341 ideals in 7 passes Tue Oct 21 22:28:19 2008 max relations containing the same ideal: 17 Tue Oct 21 22:28:19 2008 dataset too sparse, retrying Tue Oct 21 22:28:19 2008 reading rational ideals above 163840 Tue Oct 21 22:28:19 2008 reading algebraic ideals above 163840 Tue Oct 21 22:28:19 2008 commencing singleton removal, final pass Tue Oct 21 22:28:23 2008 keeping 481484 ideals with weight <= 35, new excess is 32244 Tue Oct 21 22:28:24 2008 memory use: 16.8 MB Tue Oct 21 22:28:24 2008 commencing in-memory singleton removal Tue Oct 21 22:28:24 2008 begin with 624541 relations and 481484 unique ideals Tue Oct 21 22:28:24 2008 reduce to 616659 relations and 442392 ideals in 3 passes Tue Oct 21 22:28:24 2008 max relations containing the same ideal: 35 Tue Oct 21 22:28:24 2008 removing 211785 relations and 143353 ideals in 68432 cliques Tue Oct 21 22:28:24 2008 commencing in-memory singleton removal Tue Oct 21 22:28:24 2008 begin with 404874 relations and 442392 unique ideals Tue Oct 21 22:28:24 2008 reduce to 371601 relations and 261398 ideals in 6 passes Tue Oct 21 22:28:24 2008 max relations containing the same ideal: 29 Tue Oct 21 22:28:24 2008 removing 163280 relations and 94848 ideals in 68432 cliques Tue Oct 21 22:28:24 2008 commencing in-memory singleton removal Tue Oct 21 22:28:24 2008 begin with 208321 relations and 261398 unique ideals Tue Oct 21 22:28:24 2008 reduce to 177186 relations and 130533 ideals in 8 passes Tue Oct 21 22:28:24 2008 max relations containing the same ideal: 19 Tue Oct 21 22:28:24 2008 removing 35337 relations and 26088 ideals in 9249 cliques Tue Oct 21 22:28:25 2008 commencing in-memory singleton removal Tue Oct 21 22:28:25 2008 begin with 141849 relations and 130533 unique ideals Tue Oct 21 22:28:25 2008 reduce to 136290 relations and 98589 ideals in 7 passes Tue Oct 21 22:28:25 2008 max relations containing the same ideal: 17 Tue Oct 21 22:28:25 2008 dataset too sparse, retrying Tue Oct 21 22:28:25 2008 reading rational ideals above 163840 Tue Oct 21 22:28:25 2008 reading algebraic ideals above 163840 Tue Oct 21 22:28:25 2008 commencing singleton removal, final pass Tue Oct 21 22:28:29 2008 keeping 481531 ideals with weight <= 40, new excess is 32197 Tue Oct 21 22:28:29 2008 memory use: 16.8 MB Tue Oct 21 22:28:29 2008 commencing in-memory singleton removal Tue Oct 21 22:28:29 2008 begin with 624541 relations and 481531 unique ideals Tue Oct 21 22:28:29 2008 reduce to 616659 relations and 442439 ideals in 3 passes Tue Oct 21 22:28:29 2008 max relations containing the same ideal: 40 Tue Oct 21 22:28:29 2008 removing 211793 relations and 143357 ideals in 68436 cliques Tue Oct 21 22:28:29 2008 commencing in-memory singleton removal Tue Oct 21 22:28:29 2008 begin with 404866 relations and 442439 unique ideals Tue Oct 21 22:28:29 2008 reduce to 371595 relations and 261440 ideals in 6 passes Tue Oct 21 22:28:29 2008 max relations containing the same ideal: 29 Tue Oct 21 22:28:30 2008 removing 163282 relations and 94846 ideals in 68436 cliques Tue Oct 21 22:28:30 2008 commencing in-memory singleton removal Tue Oct 21 22:28:30 2008 begin with 208313 relations and 261440 unique ideals Tue Oct 21 22:28:30 2008 reduce to 177171 relations and 130570 ideals in 8 passes Tue Oct 21 22:28:30 2008 max relations containing the same ideal: 19 Tue Oct 21 22:28:30 2008 removing 35339 relations and 26087 ideals in 9252 cliques Tue Oct 21 22:28:30 2008 commencing in-memory singleton removal Tue Oct 21 22:28:30 2008 begin with 141832 relations and 130570 unique ideals Tue Oct 21 22:28:30 2008 reduce to 136270 relations and 98624 ideals in 7 passes Tue Oct 21 22:28:30 2008 max relations containing the same ideal: 17 Tue Oct 21 22:28:30 2008 dataset too sparse, retrying Tue Oct 21 22:28:37 2008 Tue Oct 21 22:28:37 2008 Tue Oct 21 22:28:37 2008 Msieve v. 1.38 Tue Oct 21 22:28:37 2008 random seeds: a5d0e9b0 4ce80b6d Tue Oct 21 22:28:37 2008 factoring 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 (99 digits) Tue Oct 21 22:28:38 2008 no P-1/P+1/ECM available, skipping Tue Oct 21 22:28:38 2008 commencing number field sieve (99-digit input) Tue Oct 21 22:28:38 2008 R0: 10000000000000000000000000 Tue Oct 21 22:28:38 2008 R1: -1 Tue Oct 21 22:28:38 2008 A0: 27 Tue Oct 21 22:28:38 2008 A1: 0 Tue Oct 21 22:28:38 2008 A2: 0 Tue Oct 21 22:28:38 2008 A3: 0 Tue Oct 21 22:28:38 2008 A4: 1 Tue Oct 21 22:28:38 2008 size score = 3.100724e-10, Murphy alpha = 0.835783, combined = 2.219590e-10 Tue Oct 21 22:28:38 2008 Tue Oct 21 22:28:38 2008 commencing relation filtering Tue Oct 21 22:28:38 2008 commencing duplicate removal, pass 1 Tue Oct 21 22:28:43 2008 found 19978 hash collisions in 1199999 relations Tue Oct 21 22:28:44 2008 added 171605 free relations Tue Oct 21 22:28:44 2008 commencing duplicate removal, pass 2 Tue Oct 21 22:28:45 2008 found 17441 duplicates and 1354163 unique relations Tue Oct 21 22:28:45 2008 memory use: 36.5 MB Tue Oct 21 22:28:45 2008 reading rational ideals above 327680 Tue Oct 21 22:28:45 2008 reading algebraic ideals above 327680 Tue Oct 21 22:28:45 2008 commencing singleton removal, pass 1 Tue Oct 21 22:28:53 2008 relations with 0 large ideals: 16012 Tue Oct 21 22:28:53 2008 relations with 1 large ideals: 136082 Tue Oct 21 22:28:53 2008 relations with 2 large ideals: 455054 Tue Oct 21 22:28:53 2008 relations with 3 large ideals: 450226 Tue Oct 21 22:28:53 2008 relations with 4 large ideals: 128675 Tue Oct 21 22:28:53 2008 relations with 5 large ideals: 168114 Tue Oct 21 22:28:53 2008 relations with 6 large ideals: 0 Tue Oct 21 22:28:53 2008 relations with 7+ large ideals: 0 Tue Oct 21 22:28:53 2008 1354163 relations and about 1704796 large ideals Tue Oct 21 22:28:53 2008 commencing singleton removal, pass 2 Tue Oct 21 22:29:00 2008 found 647410 singletons Tue Oct 21 22:29:00 2008 current dataset: 706753 relations and about 635908 large ideals Tue Oct 21 22:29:00 2008 commencing singleton removal, pass 3 Tue Oct 21 22:29:04 2008 found 246584 singletons Tue Oct 21 22:29:04 2008 current dataset: 460169 relations and about 365519 large ideals Tue Oct 21 22:29:04 2008 commencing singleton removal, final pass Tue Oct 21 22:29:06 2008 memory use: 15.3 MB Tue Oct 21 22:29:06 2008 commencing in-memory singleton removal Tue Oct 21 22:29:07 2008 begin with 460169 relations and 368708 unique ideals Tue Oct 21 22:29:07 2008 reduce to 371730 relations and 277103 ideals in 13 passes Tue Oct 21 22:29:07 2008 max relations containing the same ideal: 17 Tue Oct 21 22:29:07 2008 reading rational ideals above 163840 Tue Oct 21 22:29:07 2008 reading algebraic ideals above 163840 Tue Oct 21 22:29:07 2008 commencing singleton removal, final pass Tue Oct 21 22:29:09 2008 keeping 407054 ideals with weight <= 20, new excess is 32104 Tue Oct 21 22:29:09 2008 memory use: 15.3 MB Tue Oct 21 22:29:09 2008 commencing in-memory singleton removal Tue Oct 21 22:29:09 2008 begin with 392984 relations and 407054 unique ideals Tue Oct 21 22:29:10 2008 reduce to 371618 relations and 301222 ideals in 4 passes Tue Oct 21 22:29:10 2008 max relations containing the same ideal: 20 Tue Oct 21 22:29:10 2008 removing 87849 relations and 71271 ideals in 16578 cliques Tue Oct 21 22:29:10 2008 commencing in-memory singleton removal Tue Oct 21 22:29:10 2008 begin with 283769 relations and 301222 unique ideals Tue Oct 21 22:29:10 2008 reduce to 270721 relations and 216216 ideals in 7 passes Tue Oct 21 22:29:10 2008 max relations containing the same ideal: 20 Tue Oct 21 22:29:10 2008 removing 66184 relations and 49606 ideals in 16578 cliques Tue Oct 21 22:29:10 2008 commencing in-memory singleton removal Tue Oct 21 22:29:10 2008 begin with 204537 relations and 216216 unique ideals Tue Oct 21 22:29:10 2008 reduce to 193022 relations and 154380 ideals in 7 passes Tue Oct 21 22:29:10 2008 max relations containing the same ideal: 17 Tue Oct 21 22:29:10 2008 dataset too sparse, retrying Tue Oct 21 22:29:10 2008 reading rational ideals above 163840 Tue Oct 21 22:29:10 2008 reading algebraic ideals above 163840 Tue Oct 21 22:29:10 2008 commencing singleton removal, final pass Tue Oct 21 22:29:13 2008 keeping 407398 ideals with weight <= 25, new excess is 31760 Tue Oct 21 22:29:13 2008 memory use: 15.3 MB Tue Oct 21 22:29:13 2008 commencing in-memory singleton removal Tue Oct 21 22:29:13 2008 begin with 392984 relations and 407398 unique ideals Tue Oct 21 22:29:13 2008 reduce to 371618 relations and 301566 ideals in 4 passes Tue Oct 21 22:29:13 2008 max relations containing the same ideal: 25 Tue Oct 21 22:29:13 2008 removing 87936 relations and 71331 ideals in 16605 cliques Tue Oct 21 22:29:13 2008 commencing in-memory singleton removal Tue Oct 21 22:29:13 2008 begin with 283682 relations and 301566 unique ideals Tue Oct 21 22:29:13 2008 reduce to 270615 relations and 216476 ideals in 7 passes Tue Oct 21 22:29:13 2008 max relations containing the same ideal: 23 Tue Oct 21 22:29:13 2008 removing 66259 relations and 49654 ideals in 16605 cliques Tue Oct 21 22:29:13 2008 commencing in-memory singleton removal Tue Oct 21 22:29:13 2008 begin with 204356 relations and 216476 unique ideals Tue Oct 21 22:29:13 2008 reduce to 192814 relations and 154564 ideals in 7 passes Tue Oct 21 22:29:13 2008 max relations containing the same ideal: 18 Tue Oct 21 22:29:13 2008 relations with 0 large ideals: 5410 Tue Oct 21 22:29:13 2008 relations with 1 large ideals: 23322 Tue Oct 21 22:29:13 2008 relations with 2 large ideals: 57237 Tue Oct 21 22:29:13 2008 relations with 3 large ideals: 63778 Tue Oct 21 22:29:13 2008 relations with 4 large ideals: 32647 Tue Oct 21 22:29:13 2008 relations with 5 large ideals: 9921 Tue Oct 21 22:29:13 2008 relations with 6 large ideals: 482 Tue Oct 21 22:29:13 2008 relations with 7+ large ideals: 17 Tue Oct 21 22:29:13 2008 commencing 2-way merge Tue Oct 21 22:29:13 2008 reduce to 118818 relation sets and 80568 unique ideals Tue Oct 21 22:29:13 2008 commencing full merge Tue Oct 21 22:29:14 2008 memory use: 6.5 MB Tue Oct 21 22:29:14 2008 found 48417 cycles, need 44768 Tue Oct 21 22:29:14 2008 weight of 44768 cycles is about 3448626 (77.03/cycle) Tue Oct 21 22:29:14 2008 distribution of cycle lengths: Tue Oct 21 22:29:14 2008 1 relations: 5973 Tue Oct 21 22:29:14 2008 2 relations: 2931 Tue Oct 21 22:29:14 2008 3 relations: 2962 Tue Oct 21 22:29:14 2008 4 relations: 2854 Tue Oct 21 22:29:14 2008 5 relations: 2837 Tue Oct 21 22:29:14 2008 6 relations: 2807 Tue Oct 21 22:29:14 2008 7 relations: 2693 Tue Oct 21 22:29:14 2008 8 relations: 2504 Tue Oct 21 22:29:14 2008 9 relations: 2365 Tue Oct 21 22:29:14 2008 10+ relations: 16842 Tue Oct 21 22:29:14 2008 heaviest cycle: 24 relations Tue Oct 21 22:29:14 2008 commencing cycle optimization Tue Oct 21 22:29:14 2008 start with 364901 relations Tue Oct 21 22:29:15 2008 pruned 18693 relations Tue Oct 21 22:29:15 2008 memory use: 10.3 MB Tue Oct 21 22:29:15 2008 distribution of cycle lengths: Tue Oct 21 22:29:15 2008 1 relations: 5973 Tue Oct 21 22:29:15 2008 2 relations: 3018 Tue Oct 21 22:29:15 2008 3 relations: 3090 Tue Oct 21 22:29:15 2008 4 relations: 3016 Tue Oct 21 22:29:15 2008 5 relations: 3005 Tue Oct 21 22:29:15 2008 6 relations: 2997 Tue Oct 21 22:29:15 2008 7 relations: 2876 Tue Oct 21 22:29:15 2008 8 relations: 2626 Tue Oct 21 22:29:15 2008 9 relations: 2547 Tue Oct 21 22:29:15 2008 10+ relations: 15620 Tue Oct 21 22:29:15 2008 heaviest cycle: 24 relations Tue Oct 21 22:29:15 2008 elapsed time 00:00:38 Tue Oct 21 22:30:26 2008 Tue Oct 21 22:30:26 2008 Tue Oct 21 22:30:26 2008 Msieve v. 1.38 Tue Oct 21 22:30:26 2008 random seeds: 40d76bda 2a186be0 Tue Oct 21 22:30:26 2008 factoring 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 (99 digits) Tue Oct 21 22:30:26 2008 no P-1/P+1/ECM available, skipping Tue Oct 21 22:30:26 2008 commencing number field sieve (99-digit input) Tue Oct 21 22:30:26 2008 R0: 10000000000000000000000000 Tue Oct 21 22:30:26 2008 R1: -1 Tue Oct 21 22:30:26 2008 A0: 27 Tue Oct 21 22:30:26 2008 A1: 0 Tue Oct 21 22:30:26 2008 A2: 0 Tue Oct 21 22:30:26 2008 A3: 0 Tue Oct 21 22:30:26 2008 A4: 1 Tue Oct 21 22:30:26 2008 size score = 3.100724e-10, Murphy alpha = 0.835783, combined = 2.219590e-10 Tue Oct 21 22:30:26 2008 Tue Oct 21 22:30:26 2008 commencing linear algebra Tue Oct 21 22:30:27 2008 read 44768 cycles Tue Oct 21 22:30:27 2008 cycles contain 161577 unique relations Tue Oct 21 22:30:28 2008 read 161577 relations Tue Oct 21 22:30:28 2008 using 32 quadratic characters above 33518624 Tue Oct 21 22:30:29 2008 building initial matrix Tue Oct 21 22:30:30 2008 memory use: 25.1 MB Tue Oct 21 22:30:30 2008 read 44768 cycles Tue Oct 21 22:30:30 2008 matrix is 44597 x 44768 (13.8 MB) with weight 4385294 (97.96/col) Tue Oct 21 22:30:30 2008 sparse part has weight 3123800 (69.78/col) Tue Oct 21 22:30:30 2008 filtering completed in 2 passes Tue Oct 21 22:30:30 2008 matrix is 44462 x 44633 (13.8 MB) with weight 4375849 (98.04/col) Tue Oct 21 22:30:30 2008 sparse part has weight 3118261 (69.86/col) Tue Oct 21 22:30:31 2008 read 44633 cycles Tue Oct 21 22:30:31 2008 matrix is 44462 x 44633 (13.8 MB) with weight 4375849 (98.04/col) Tue Oct 21 22:30:31 2008 sparse part has weight 3118261 (69.86/col) Tue Oct 21 22:30:31 2008 saving the first 48 matrix rows for later Tue Oct 21 22:30:31 2008 matrix is 44414 x 44633 (13.0 MB) with weight 3423042 (76.69/col) Tue Oct 21 22:30:31 2008 sparse part has weight 2967577 (66.49/col) Tue Oct 21 22:30:31 2008 matrix includes 64 packed rows Tue Oct 21 22:30:31 2008 using block size 17853 for processor cache size 4096 kB Tue Oct 21 22:30:32 2008 commencing Lanczos iteration Tue Oct 21 22:30:32 2008 memory use: 11.4 MB Tue Oct 21 22:30:44 2008 lanczos halted after 704 iterations (dim = 44412) Tue Oct 21 22:30:44 2008 recovered 47 nontrivial dependencies Tue Oct 21 22:30:44 2008 elapsed time 00:00:18 Tue Oct 21 22:30:49 2008 Tue Oct 21 22:30:49 2008 Tue Oct 21 22:30:49 2008 Msieve v. 1.38 Tue Oct 21 22:30:49 2008 random seeds: d128e8af ff339179 Tue Oct 21 22:30:49 2008 factoring 270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270270271 (99 digits) Tue Oct 21 22:30:50 2008 no P-1/P+1/ECM available, skipping Tue Oct 21 22:30:50 2008 commencing number field sieve (99-digit input) Tue Oct 21 22:30:50 2008 R0: 10000000000000000000000000 Tue Oct 21 22:30:50 2008 R1: -1 Tue Oct 21 22:30:50 2008 A0: 27 Tue Oct 21 22:30:50 2008 A1: 0 Tue Oct 21 22:30:50 2008 A2: 0 Tue Oct 21 22:30:50 2008 A3: 0 Tue Oct 21 22:30:50 2008 A4: 1 Tue Oct 21 22:30:50 2008 size score = 3.100724e-10, Murphy alpha = 0.835783, combined = 2.219590e-10 Tue Oct 21 22:30:50 2008 Tue Oct 21 22:30:50 2008 commencing square root phase Tue Oct 21 22:30:50 2008 reading relations for dependency 1 Tue Oct 21 22:30:50 2008 read 22308 cycles Tue Oct 21 22:30:50 2008 cycles contain 103201 unique relations Tue Oct 21 22:30:51 2008 read 103201 relations Tue Oct 21 22:30:51 2008 multiplying 80370 relations Tue Oct 21 22:30:53 2008 multiply complete, coefficients have about 1.54 million bits Tue Oct 21 22:30:53 2008 initial square root is modulo 13426121 Tue Oct 21 22:30:56 2008 prp47 factor: 78175003767451466482080068931559338109988065279 Tue Oct 21 22:30:56 2008 prp52 factor: 3457246654880221174947428776620112459038765878240449 Tue Oct 21 22:30:56 2008 elapsed time 00:00:07 |
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