20080926, 13:07  #639  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10100000010000_{2} Posts 
Quote:
Paul 

20081002, 17:29  #640 
"Ben"
Feb 2007
2·5·7·47 Posts 
Here is my petition to join the "100 digit cofactor club".
3^439 + 2^439 factors as: Code:
Wed Oct 1 15:35:11 2008 Msieve v. 1.38 Wed Oct 1 15:35:11 2008 random seeds: 00d945fe aa2fb785 Wed Oct 1 15:35:11 2008 factoring 57182194393475387954810827224380735288919928867272127169467340082047563029566248187678442999408615699468589299198401102871170390688509792127442043240038186973436639332471330173723125996590602752739978375455631 (209 digits) Wed Oct 1 15:35:13 2008 no P1/P+1/ECM available, skipping Wed Oct 1 15:35:13 2008 commencing number field sieve (209digit input) Wed Oct 1 15:35:13 2008 R0: 67585198634817523235520443624317923 Wed Oct 1 15:35:13 2008 R1: 9444732965739290427392 Wed Oct 1 15:35:13 2008 A0: 2 Wed Oct 1 15:35:13 2008 A1: 0 Wed Oct 1 15:35:13 2008 A2: 0 Wed Oct 1 15:35:13 2008 A3: 0 Wed Oct 1 15:35:13 2008 A4: 0 Wed Oct 1 15:35:13 2008 A5: 0 Wed Oct 1 15:35:13 2008 A6: 3 Wed Oct 1 15:35:13 2008 size score = 4.006280e10, Murphy alpha = 1.523098, combined = 2.592680e10 Wed Oct 1 15:35:13 2008 Wed Oct 1 15:35:13 2008 commencing relation filtering Wed Oct 1 15:35:13 2008 commencing duplicate removal, pass 1 Wed Oct 1 15:38:12 2008 error 6 reading relation 24855462 Wed Oct 1 15:39:15 2008 error 11 reading relation 34831650 Wed Oct 1 15:40:21 2008 error 11 reading relation 45177723 Wed Oct 1 15:41:09 2008 found 8449033 hash collisions in 52896721 relations Wed Oct 1 15:41:24 2008 added 249 free relations Wed Oct 1 15:41:24 2008 commencing duplicate removal, pass 2 Wed Oct 1 15:42:06 2008 found 5773904 duplicates and 47123066 unique relations Wed Oct 1 15:42:06 2008 memory use: 270.4 MB Wed Oct 1 15:42:06 2008 reading rational ideals above 30998528 Wed Oct 1 15:42:06 2008 reading algebraic ideals above 30998528 Wed Oct 1 15:42:06 2008 commencing singleton removal, pass 1 Wed Oct 1 15:47:23 2008 relations with 0 large ideals: 1189094 Wed Oct 1 15:47:24 2008 relations with 1 large ideals: 6071978 Wed Oct 1 15:47:24 2008 relations with 2 large ideals: 14593991 Wed Oct 1 15:47:24 2008 relations with 3 large ideals: 16576324 Wed Oct 1 15:47:24 2008 relations with 4 large ideals: 7631350 Wed Oct 1 15:47:24 2008 relations with 5 large ideals: 552 Wed Oct 1 15:47:24 2008 relations with 6 large ideals: 0 Wed Oct 1 15:47:24 2008 relations with 7+ large ideals: 1059777 Wed Oct 1 15:47:24 2008 47123066 relations and about 36241839 large ideals Wed Oct 1 15:47:24 2008 commencing singleton removal, pass 2 Wed Oct 1 15:52:41 2008 found 10527467 singletons Wed Oct 1 15:52:41 2008 current dataset: 36595599 relations and about 24577891 large ideals Wed Oct 1 15:52:41 2008 commencing singleton removal, pass 3 Wed Oct 1 15:56:50 2008 found 2110200 singletons Wed Oct 1 15:56:50 2008 current dataset: 34485399 relations and about 22408736 large ideals Wed Oct 1 15:56:50 2008 commencing singleton removal, pass 4 Wed Oct 1 16:00:44 2008 found 424769 singletons Wed Oct 1 16:00:44 2008 current dataset: 34060630 relations and about 21981295 large ideals Wed Oct 1 16:00:44 2008 commencing singleton removal, final pass Wed Oct 1 16:06:14 2008 memory use: 578.5 MB Wed Oct 1 16:06:14 2008 commencing inmemory singleton removal Wed Oct 1 16:06:18 2008 begin with 34060630 relations and 26897667 unique ideals Wed Oct 1 16:07:04 2008 reduce to 27102783 relations and 19623163 ideals in 15 passes Wed Oct 1 16:07:04 2008 max relations containing the same ideal: 36 Wed Oct 1 16:07:10 2008 reading rational ideals above 720000 Wed Oct 1 16:07:10 2008 reading algebraic ideals above 720000 Wed Oct 1 16:07:10 2008 commencing singleton removal, final pass Wed Oct 1 16:14:10 2008 keeping 20805648 ideals with weight <= 20, new excess is 2650524 Wed Oct 1 16:14:43 2008 memory use: 694.3 MB Wed Oct 1 16:14:43 2008 commencing inmemory singleton removal Wed Oct 1 16:14:46 2008 begin with 27103034 relations and 20805648 unique ideals Wed Oct 1 16:15:23 2008 reduce to 27099477 relations and 20800743 ideals in 11 passes Wed Oct 1 16:15:23 2008 max relations containing the same ideal: 20 Wed Oct 1 16:15:41 2008 removing 2842628 relations and 2442628 ideals in 400000 cliques Wed Oct 1 16:15:44 2008 commencing inmemory singleton removal Wed Oct 1 16:15:47 2008 begin with 24256849 relations and 20800743 unique ideals Wed Oct 1 16:16:10 2008 reduce to 24039695 relations and 18136568 ideals in 8 passes Wed Oct 1 16:16:10 2008 max relations containing the same ideal: 20 Wed Oct 1 16:16:26 2008 removing 2095174 relations and 1695174 ideals in 400000 cliques Wed Oct 1 16:16:28 2008 commencing inmemory singleton removal Wed Oct 1 16:16:30 2008 begin with 21944521 relations and 18136568 unique ideals Wed Oct 1 16:16:49 2008 reduce to 21818533 relations and 16313389 ideals in 7 passes Wed Oct 1 16:16:49 2008 max relations containing the same ideal: 20 Wed Oct 1 16:17:03 2008 removing 1854764 relations and 1454764 ideals in 400000 cliques Wed Oct 1 16:17:05 2008 commencing inmemory singleton removal Wed Oct 1 16:17:07 2008 begin with 19963769 relations and 16313389 unique ideals Wed Oct 1 16:17:24 2008 reduce to 19854502 relations and 14747546 ideals in 7 passes Wed Oct 1 16:17:24 2008 max relations containing the same ideal: 20 Wed Oct 1 16:17:37 2008 removing 1730226 relations and 1330226 ideals in 400000 cliques Wed Oct 1 16:17:38 2008 commencing inmemory singleton removal Wed Oct 1 16:17:40 2008 begin with 18124276 relations and 14747546 unique ideals Wed Oct 1 16:17:56 2008 reduce to 18019580 relations and 13310731 ideals in 7 passes Wed Oct 1 16:17:56 2008 max relations containing the same ideal: 20 Wed Oct 1 16:18:07 2008 removing 1648586 relations and 1248586 ideals in 400000 cliques Wed Oct 1 16:18:09 2008 commencing inmemory singleton removal Wed Oct 1 16:18:11 2008 begin with 16370994 relations and 13310731 unique ideals Wed Oct 1 16:18:22 2008 reduce to 16268164 relations and 11957379 ideals in 6 passes Wed Oct 1 16:18:22 2008 max relations containing the same ideal: 20 Wed Oct 1 16:18:33 2008 removing 1590640 relations and 1190640 ideals in 400000 cliques Wed Oct 1 16:18:34 2008 commencing inmemory singleton removal Wed Oct 1 16:18:36 2008 begin with 14677524 relations and 11957379 unique ideals Wed Oct 1 16:18:48 2008 reduce to 14567680 relations and 10654579 ideals in 7 passes Wed Oct 1 16:18:48 2008 max relations containing the same ideal: 20 Wed Oct 1 16:18:57 2008 removing 1547894 relations and 1147894 ideals in 400000 cliques Wed Oct 1 16:18:59 2008 commencing inmemory singleton removal Wed Oct 1 16:19:00 2008 begin with 13019786 relations and 10654579 unique ideals Wed Oct 1 16:19:11 2008 reduce to 12901584 relations and 9385751 ideals in 7 passes Wed Oct 1 16:19:11 2008 max relations containing the same ideal: 19 Wed Oct 1 16:19:19 2008 removing 1523077 relations and 1123077 ideals in 400000 cliques Wed Oct 1 16:19:20 2008 commencing inmemory singleton removal Wed Oct 1 16:19:22 2008 begin with 11378507 relations and 9385751 unique ideals Wed Oct 1 16:19:31 2008 reduce to 11249010 relations and 8129728 ideals in 7 passes Wed Oct 1 16:19:31 2008 max relations containing the same ideal: 18 Wed Oct 1 16:19:38 2008 removing 257797 relations and 213123 ideals in 44674 cliques Wed Oct 1 16:19:38 2008 commencing inmemory singleton removal Wed Oct 1 16:19:39 2008 begin with 10991213 relations and 8129728 unique ideals Wed Oct 1 16:19:46 2008 reduce to 10987798 relations and 7913179 ideals in 5 passes Wed Oct 1 16:19:46 2008 max relations containing the same ideal: 18 Wed Oct 1 16:19:49 2008 relations with 0 large ideals: 473520 Wed Oct 1 16:19:49 2008 relations with 1 large ideals: 2038558 Wed Oct 1 16:19:49 2008 relations with 2 large ideals: 3672027 Wed Oct 1 16:19:49 2008 relations with 3 large ideals: 3139724 Wed Oct 1 16:19:49 2008 relations with 4 large ideals: 1329754 Wed Oct 1 16:19:49 2008 relations with 5 large ideals: 272841 Wed Oct 1 16:19:49 2008 relations with 6 large ideals: 28266 Wed Oct 1 16:19:49 2008 relations with 7+ large ideals: 33108 Wed Oct 1 16:19:49 2008 commencing 2way merge Wed Oct 1 16:19:58 2008 reduce to 7317493 relation sets and 4242874 unique ideals Wed Oct 1 16:19:58 2008 commencing full merge Wed Oct 1 16:20:55 2008 memory use: 377.5 MB Wed Oct 1 16:20:56 2008 found 3682766 cycles, need 3267074 Wed Oct 1 16:20:59 2008 weight of 3267074 cycles is about 229114508 (70.13/cycle) Wed Oct 1 16:20:59 2008 distribution of cycle lengths: Wed Oct 1 16:20:59 2008 1 relations: 528665 Wed Oct 1 16:20:59 2008 2 relations: 346234 Wed Oct 1 16:20:59 2008 3 relations: 326745 Wed Oct 1 16:20:59 2008 4 relations: 307981 Wed Oct 1 16:20:59 2008 5 relations: 294961 Wed Oct 1 16:20:59 2008 6 relations: 271364 Wed Oct 1 16:20:59 2008 7 relations: 247800 Wed Oct 1 16:20:59 2008 8 relations: 220954 Wed Oct 1 16:20:59 2008 9 relations: 196157 Wed Oct 1 16:20:59 2008 10+ relations: 526213 Wed Oct 1 16:20:59 2008 heaviest cycle: 16 relations Wed Oct 1 16:20:59 2008 commencing cycle optimization Wed Oct 1 16:21:07 2008 start with 17768235 relations Wed Oct 1 16:21:40 2008 pruned 706496 relations Wed Oct 1 16:21:41 2008 memory use: 568.4 MB Wed Oct 1 16:21:41 2008 distribution of cycle lengths: Wed Oct 1 16:21:41 2008 1 relations: 528665 Wed Oct 1 16:21:41 2008 2 relations: 358311 Wed Oct 1 16:21:41 2008 3 relations: 344913 Wed Oct 1 16:21:41 2008 4 relations: 324136 Wed Oct 1 16:21:41 2008 5 relations: 311856 Wed Oct 1 16:21:41 2008 6 relations: 284811 Wed Oct 1 16:21:41 2008 7 relations: 259136 Wed Oct 1 16:21:41 2008 8 relations: 226083 Wed Oct 1 16:21:41 2008 9 relations: 195556 Wed Oct 1 16:21:41 2008 10+ relations: 433607 Wed Oct 1 16:21:41 2008 heaviest cycle: 16 relations Wed Oct 1 16:21:47 2008 Wed Oct 1 16:21:48 2008 commencing linear algebra Wed Oct 1 16:21:49 2008 read 3267074 cycles Wed Oct 1 16:22:08 2008 cycles contain 9454323 unique relations Wed Oct 1 16:23:15 2008 read 9454323 relations Wed Oct 1 16:23:33 2008 using 32 quadratic characters above 536869590 Wed Oct 1 16:24:47 2008 building initial matrix Wed Oct 1 16:26:58 2008 memory use: 1164.2 MB Wed Oct 1 16:27:00 2008 read 3267074 cycles Wed Oct 1 16:27:22 2008 matrix is 3266474 x 3267074 (967.6 MB) with weight 301471637 (92.28/col) Wed Oct 1 16:27:22 2008 sparse part has weight 217719647 (66.64/col) Wed Oct 1 16:28:27 2008 filtering completed in 3 passes Wed Oct 1 16:28:28 2008 matrix is 3256011 x 3256211 (965.6 MB) with weight 300764154 (92.37/col) Wed Oct 1 16:28:28 2008 sparse part has weight 217300097 (66.73/col) Wed Oct 1 16:29:42 2008 read 3256211 cycles Wed Oct 1 16:30:02 2008 matrix is 3256011 x 3256211 (965.6 MB) with weight 300764154 (92.37/col) Wed Oct 1 16:30:02 2008 sparse part has weight 217300097 (66.73/col) Wed Oct 1 16:30:03 2008 saving the first 48 matrix rows for later Wed Oct 1 16:30:04 2008 matrix is 3255963 x 3256211 (923.4 MB) with weight 230852110 (70.90/col) Wed Oct 1 16:30:04 2008 sparse part has weight 209492109 (64.34/col) Wed Oct 1 16:30:04 2008 matrix includes 64 packed rows Wed Oct 1 16:30:04 2008 using block size 65536 for processor cache size 4096 kB Wed Oct 1 16:30:49 2008 commencing Lanczos iteration (4 threads) Wed Oct 1 16:30:49 2008 memory use: 969.7 MB Thu Oct 2 10:59:58 2008 lanczos halted after 51489 iterations (dim = 3255963) Thu Oct 2 11:00:04 2008 recovered 49 nontrivial dependencies Thu Oct 2 11:00:05 2008 Thu Oct 2 11:00:05 2008 commencing square root phase Thu Oct 2 11:00:05 2008 reading relations for dependency 1 Thu Oct 2 11:00:06 2008 read 1628118 cycles Thu Oct 2 11:00:14 2008 cycles contain 5793745 unique relations Thu Oct 2 11:01:02 2008 read 5793745 relations Thu Oct 2 11:01:38 2008 multiplying 4723334 relations Thu Oct 2 11:11:20 2008 multiply complete, coefficients have about 120.09 million bits Thu Oct 2 11:11:22 2008 initial square root is modulo 416483917 Thu Oct 2 11:28:02 2008 prp101 factor: 11002793910811144161014435718793615004311480896638730218231971013529964454715868109708331887058226403 Thu Oct 2 11:28:02 2008 prp109 factor: 5197061297066485000559393207060920940844164610691496239505184142209538391789630949485266788650611017865714277 Thu Oct 2 11:28:02 2008 elapsed time 19:52:51 
20081005, 09:41  #641 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24020_{8} Posts 
Update
The tables have just been uploaded. There were 7 new complete factorizations in the last week, leaving 188 composites still to be done. Of the "old" tables, only 3+2, 32 and 5+4 need completing. The last of these has only one entry.
I'm already thinking about extending the tables but extensions won't be posted until the number of composites falls much lower. Paul 
20081128, 12:18  #642 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24020_{8} Posts 
Update
The tables have just been updated. There are 174 remaining composites now.
Thanks are due in this instance to Bob Silverman, Alex Greenbank, Ben Buhrow, Greg Childers, Tom Womack and Andreas Schindel for finding and then sending their factors to me. My sincere apologies for taking very nearly 2 months to post an update. I can only plead illhealth, an excessive amount of work in Real Life(tm) and a machine which required a complete OS reinstall before I could do anything useful. Please keep the factors coming and I'll try to post updates a bit more frequently in future. Paul 
20081128, 14:01  #643  
May 2003
11100111_{2} Posts 
Quote:


20081201, 17:25  #644  
May 2003
3×7×11 Posts 
Quote:
By luck I selected this row from 11+4: 187 6733.234499.7394729.7078756689004636971786089. C126 And I noticed the complete lack of 121260888412901704504061185001770658050780795481 as a factor. I bet the cofactor splits very easily once that's taken out. I suppose I ought to check 4+3, 54, 7+4,8+3,8+5, 8+7, 9+2, 95, 9+7, 9+8, 10+9, 11+4, etc. for other omissions. 

20081201, 17:55  #645  
"Ben"
Feb 2007
3290_{10} Posts 
Quote:
Code:
5709159772448037211922834074597972300554167586081064642060063215601487922318323 

20081201, 18:05  #646  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Code:
6H 6H 2H 2H 3 + 2 = (3 + 2 )L.M L = A  B M = A + B H = 2K  1 2H H 2H K H H A = 3 + 3.6 + 2 B = 6 (3 + 2 ) 

20081201, 18:19  #647  
Nov 2003
2^{2}×5×373 Posts 
Quote:
5^k + 2^k for k an odd multiple of 10 5^k + 3^k for k an odd multiple of 15 6^k + 5^k for k an odd multiple of 30, 7^k + 2^k for k an odd multiple of 14, 7,3 for odd multiples of 21 (minus side because 21 = 1 mod 4) 7,5+ for odd multiples of 35 7,6+ for odd multiples of 42 10,3+ for odd multiples of 30 10,7+ for odd multiples of 70 11,9+ for odd multiples of 11 (not 99 because 9 is already a square) 12,5+ for odd multiples of 15 (square free part of 60) 12,7 for odd multiples of 21 (square free part of 84) 12,11 for odd multiples of 33 (square free part of 132, 33=1 mod 4) etc. etc. etc. Last fiddled with by R.D. Silverman on 20081201 at 18:37 Reason: Omission 

20081201, 18:40  #648  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Note that 11,9,187+ listed as C130 has an Aurefeullian. 

20081201, 18:41  #649  
May 2003
347_{8} Posts 
Quote:
187 1871.210784524898267.75233596333117435159. C130 C130 = 260777275385646300545894010485844710967932854733 * 8599161748379175860762190516255619473244408528122663325731373718516088821182884919 

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