20080320, 00:29  #12 
Oct 2006
vomit_frame_pointer
2^{3}×3^{2}×5 Posts 
Can't resist  an undeserved p47
Way back, working on 4^307+3^307. Only 1992 ECM curves at 3E6:
Code:
p47 = 14718260945227321993538833517239503165838463191 Seems as if everyone enjoys splitting a composite into two primes of similar magnitude. A p60.p90 is just as good as a p72.p78, but there is something prettier about the latter. 
20080420, 05:31  #13 
Oct 2006
vomit_frame_pointer
2^{3}×3^{2}×5 Posts 
Dare to dream
5^292 + 4^292 has p50 factor 93172475798334091708528467222762440891545544410081. Personal best as far as SNFS magnitude goes, at 205 digits. 200 digits ain't what it used to be.
Also, my first 3fold split on an SNFS: 11^187  3^187: c154 = p47.p51.p57 p47: 92534718300915679831411055777591569981607096953 p51: 180166869627938348894812913800373604941787732024067 p57: 440853492502687501432544008137866572998304338991768202689 Gratuitous? You bet. 
20080421, 12:32  #14  
"Ben"
Feb 2007
3,733 Posts 
Quote:
Code:
p50 = 65979282303804033736710199516519274949640336359553 

20080421, 12:50  #15  
Oct 2004
Austria
4662_{8} Posts 
Quote:
(from hp925, step 84) Code:
GMPECM 6.1.3 [powered by GMP 4.2.2] [ECM] Input number is 650576944675485979158248547237813070854356361040731543477683852267812333590882664750245192794302744609158946141500102167987396091343924283140710789700381 (153 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=468825063 Step 1 took 16454ms ********** Factor found in step 1: 546964903436902596245244724937998114463 Found probable prime factor of 39 digits: 546964903436902596245244724937998114463 Composite cofactor 1189430876803114625123780452913858718532798357398992380994476391429080412306589324674244054137888989886581304686787 has 115 digits 

20080501, 03:01  #16 
"Ben"
Feb 2007
3,733 Posts 
Just finished my largest SNFS to date: 12^163  11^163
C176, difficulty 176. Isn't it nice when there are no wasted factors in SNFS jobs :) Code:
Wed Apr 30 18:33:37 2008 Msieve v. 1.32 Wed Apr 30 18:33:37 2008 random seeds: 0f9bbe40 a72a3a5a Wed Apr 30 18:33:37 2008 factoring 80638567651605134105801341144295703524688610355698302434289991680094789293158377759055342137656314689398379368412370811546059861224314747399102796095874850337752864376275025997 (176 digits) Wed Apr 30 18:33:39 2008 searching for 15digit factors Wed Apr 30 18:33:41 2008 commencing number field sieve (176digit input) Wed Apr 30 18:33:41 2008 R0: 410186270246002225336426103593500672 Wed Apr 30 18:33:41 2008 R1: 23225154419887808141001767796309131 Wed Apr 30 18:33:41 2008 A0: 144 Wed Apr 30 18:33:41 2008 A1: 0 Wed Apr 30 18:33:41 2008 A2: 0 Wed Apr 30 18:33:41 2008 A3: 0 Wed Apr 30 18:33:41 2008 A4: 0 Wed Apr 30 18:33:41 2008 A5: 121 Wed Apr 30 18:33:41 2008 size score = 1.380090e012, Murphy alpha = 0.611155, combined = 1.125728e012 Wed Apr 30 18:34:01 2008 restarting with 9580213 relations Wed Apr 30 18:34:01 2008 Wed Apr 30 18:34:01 2008 commencing relation filtering Wed Apr 30 18:34:01 2008 commencing duplicate removal, pass 1 Wed Apr 30 18:35:26 2008 found 858406 hash collisions in 9580213 relations Wed Apr 30 18:35:26 2008 commencing duplicate removal, pass 2 Wed Apr 30 18:36:10 2008 found 713339 duplicates and 8866874 unique relations Wed Apr 30 18:36:10 2008 memory use: 50.6 MB Wed Apr 30 18:36:11 2008 ignoring smallest 395203 rational and 395015 algebraic ideals Wed Apr 30 18:36:11 2008 filtering ideals above 5724694 Wed Apr 30 18:36:11 2008 need 1343370 more relations than ideals Wed Apr 30 18:36:11 2008 commencing singleton removal, pass 1 Wed Apr 30 18:37:30 2008 relations with 0 large ideals: 19713 Wed Apr 30 18:37:30 2008 relations with 1 large ideals: 153993 Wed Apr 30 18:37:30 2008 relations with 2 large ideals: 1122054 Wed Apr 30 18:37:30 2008 relations with 3 large ideals: 2848021 Wed Apr 30 18:37:30 2008 relations with 4 large ideals: 2997837 Wed Apr 30 18:37:30 2008 relations with 5 large ideals: 1401728 Wed Apr 30 18:37:30 2008 relations with 6 large ideals: 292605 Wed Apr 30 18:37:30 2008 relations with 7+ large ideals: 30923 Wed Apr 30 18:37:30 2008 8866874 relations and about 8123394 large ideals Wed Apr 30 18:37:31 2008 commencing singleton removal, pass 2 Wed Apr 30 18:38:52 2008 found 3558693 singletons Wed Apr 30 18:38:52 2008 current dataset: 5308181 relations and about 4081278 large ideals Wed Apr 30 18:38:52 2008 commencing singleton removal, pass 3 Wed Apr 30 18:39:47 2008 found 565853 singletons Wed Apr 30 18:39:47 2008 current dataset: 4742328 relations and about 3493865 large ideals Wed Apr 30 18:39:47 2008 commencing singleton removal, pass 4 Wed Apr 30 18:40:38 2008 found 118348 singletons Wed Apr 30 18:40:38 2008 current dataset: 4623980 relations and about 3374392 large ideals Wed Apr 30 18:40:38 2008 commencing singleton removal, final pass Wed Apr 30 18:42:07 2008 memory use: 176.9 MB Wed Apr 30 18:42:07 2008 commencing inmemory singleton removal Wed Apr 30 18:42:07 2008 begin with 4623980 relations and 3554647 unique ideals Wed Apr 30 18:42:11 2008 reduce to 4281327 relations and 3207505 ideals in 10 passes Wed Apr 30 18:42:11 2008 max relations containing the same ideal: 44 Wed Apr 30 18:42:12 2008 dataset has 35.9% excess relations Wed Apr 30 18:42:13 2008 ignoring smallest 358343 rational and 358057 algebraic ideals Wed Apr 30 18:42:13 2008 filtering ideals above 5152224 Wed Apr 30 18:42:13 2008 need 966439 more relations than ideals Wed Apr 30 18:42:13 2008 commencing singleton removal, final pass Wed Apr 30 18:43:05 2008 memory use: 176.9 MB Wed Apr 30 18:43:05 2008 commencing inmemory singleton removal Wed Apr 30 18:43:05 2008 begin with 4623980 relations and 3628453 unique ideals Wed Apr 30 18:43:10 2008 reduce to 4281008 relations and 3280982 ideals in 10 passes Wed Apr 30 18:43:10 2008 max relations containing the same ideal: 44 Wed Apr 30 18:43:12 2008 removing 139153 relations and 122360 ideals in 16793 cliques Wed Apr 30 18:43:12 2008 commencing inmemory singleton removal Wed Apr 30 18:43:12 2008 begin with 4141855 relations and 3280982 unique ideals Wed Apr 30 18:43:15 2008 reduce to 4139759 relations and 3156511 ideals in 6 passes Wed Apr 30 18:43:15 2008 max relations containing the same ideal: 43 Wed Apr 30 18:43:17 2008 removing 105818 relations and 89025 ideals in 16793 cliques Wed Apr 30 18:43:17 2008 commencing inmemory singleton removal Wed Apr 30 18:43:18 2008 begin with 4033941 relations and 3156511 unique ideals Wed Apr 30 18:43:20 2008 reduce to 4032602 relations and 3066137 ideals in 5 passes Wed Apr 30 18:43:20 2008 max relations containing the same ideal: 42 Wed Apr 30 18:43:22 2008 dataset has 22.3% excess relations Wed Apr 30 18:43:23 2008 ignoring smallest 321126 rational and 320784 algebraic ideals Wed Apr 30 18:43:23 2008 filtering ideals above 4579755 Wed Apr 30 18:43:23 2008 need 853435 more relations than ideals Wed Apr 30 18:43:23 2008 commencing singleton removal, final pass Wed Apr 30 18:44:10 2008 memory use: 176.9 MB Wed Apr 30 18:44:10 2008 commencing inmemory singleton removal Wed Apr 30 18:44:10 2008 begin with 4032602 relations and 3140616 unique ideals Wed Apr 30 18:44:12 2008 reduce to 4032391 relations and 3140405 ideals in 4 passes Wed Apr 30 18:44:12 2008 max relations containing the same ideal: 42 Wed Apr 30 18:44:14 2008 removing 107862 relations and 88587 ideals in 19275 cliques Wed Apr 30 18:44:14 2008 commencing inmemory singleton removal Wed Apr 30 18:44:14 2008 begin with 3924529 relations and 3140405 unique ideals Wed Apr 30 18:44:16 2008 reduce to 3923183 relations and 3050467 ideals in 5 passes Wed Apr 30 18:44:17 2008 max relations containing the same ideal: 41 Wed Apr 30 18:44:19 2008 removing 100018 relations and 80743 ideals in 19275 cliques Wed Apr 30 18:44:19 2008 commencing inmemory singleton removal Wed Apr 30 18:44:19 2008 begin with 3823165 relations and 3050467 unique ideals Wed Apr 30 18:44:21 2008 reduce to 3821719 relations and 2968276 ideals in 4 passes Wed Apr 30 18:44:21 2008 max relations containing the same ideal: 40 Wed Apr 30 18:44:23 2008 dataset has 8.0% excess relations Wed Apr 30 18:44:23 2008 relations with 0 large ideals: 15975 Wed Apr 30 18:44:23 2008 relations with 1 large ideals: 97711 Wed Apr 30 18:44:23 2008 relations with 2 large ideals: 531047 Wed Apr 30 18:44:23 2008 relations with 3 large ideals: 1124161 Wed Apr 30 18:44:23 2008 relations with 4 large ideals: 1177621 Wed Apr 30 18:44:23 2008 relations with 5 large ideals: 645289 Wed Apr 30 18:44:23 2008 relations with 6 large ideals: 197638 Wed Apr 30 18:44:23 2008 relations with 7+ large ideals: 32277 Wed Apr 30 18:44:23 2008 commencing 2way merge Wed Apr 30 18:44:27 2008 reduce to 2580540 relation sets and 1727097 unique ideals Wed Apr 30 18:44:27 2008 commencing full merge Wed Apr 30 18:45:09 2008 found 1318214 cycles, need 1109297 Wed Apr 30 18:45:09 2008 weight of 1109297 cycles is about 72265196 (65.15/cycle) Wed Apr 30 18:45:09 2008 distribution of cycle lengths: Wed Apr 30 18:45:09 2008 1 relations: 147858 Wed Apr 30 18:45:09 2008 2 relations: 126177 Wed Apr 30 18:45:09 2008 3 relations: 128724 Wed Apr 30 18:45:09 2008 4 relations: 122790 Wed Apr 30 18:45:09 2008 5 relations: 116458 Wed Apr 30 18:45:09 2008 6 relations: 104451 Wed Apr 30 18:45:09 2008 7 relations: 93102 Wed Apr 30 18:45:09 2008 8 relations: 80795 Wed Apr 30 18:45:09 2008 9 relations: 69549 Wed Apr 30 18:45:09 2008 10+ relations: 119393 Wed Apr 30 18:45:09 2008 heaviest cycle: 14 relations Wed Apr 30 18:45:10 2008 commencing cycle optimization Wed Apr 30 18:45:11 2008 start with 5684484 relations Wed Apr 30 18:45:23 2008 pruned 106871 relations Wed Apr 30 18:45:23 2008 distribution of cycle lengths: Wed Apr 30 18:45:23 2008 1 relations: 147858 Wed Apr 30 18:45:23 2008 2 relations: 127848 Wed Apr 30 18:45:23 2008 3 relations: 132107 Wed Apr 30 18:45:23 2008 4 relations: 125542 Wed Apr 30 18:45:23 2008 5 relations: 120051 Wed Apr 30 18:45:23 2008 6 relations: 107210 Wed Apr 30 18:45:23 2008 7 relations: 95119 Wed Apr 30 18:45:23 2008 8 relations: 81592 Wed Apr 30 18:45:23 2008 9 relations: 68643 Wed Apr 30 18:45:23 2008 10+ relations: 103327 Wed Apr 30 18:45:23 2008 heaviest cycle: 14 relations Wed Apr 30 18:45:28 2008 Wed Apr 30 18:45:28 2008 commencing linear algebra Wed Apr 30 18:45:30 2008 read 1109297 cycles Wed Apr 30 18:45:33 2008 cycles contain 3031409 unique relations Wed Apr 30 18:47:45 2008 read 3031409 relations Wed Apr 30 18:47:50 2008 using 32 quadratic characters above 134216912 Wed Apr 30 18:49:11 2008 read 1109297 cycles Wed Apr 30 18:50:06 2008 matrix is 1108626 x 1109297 with weight 97696276 (avg 88.07/col) Wed Apr 30 18:50:27 2008 filtering completed in 3 passes Wed Apr 30 18:50:27 2008 matrix is 1102784 x 1102984 with weight 97251784 (avg 88.17/col) Wed Apr 30 18:51:04 2008 read 1102984 cycles Wed Apr 30 18:53:54 2008 matrix is 1102784 x 1102984 with weight 97251784 (avg 88.17/col) Wed Apr 30 18:53:54 2008 saving the first 48 matrix rows for later Wed Apr 30 18:53:55 2008 matrix is 1102736 x 1102984 with weight 74094589 (avg 67.18/col) Wed Apr 30 18:53:55 2008 matrix includes 64 packed rows Wed Apr 30 18:53:55 2008 using block size 65536 for processor cache size 4096 kB Wed Apr 30 18:54:01 2008 commencing Lanczos iteration (2 threads) Wed Apr 30 20:37:56 2008 lanczos halted after 17441 iterations (dim = 1102735) Wed Apr 30 20:37:59 2008 recovered 50 nontrivial dependencies Wed Apr 30 20:37:59 2008 Wed Apr 30 20:37:59 2008 commencing square root phase Wed Apr 30 20:37:59 2008 reading relations for dependency 1 Wed Apr 30 20:38:01 2008 read 551332 cycles Wed Apr 30 20:38:02 2008 cycles contain 1849397 unique relations Wed Apr 30 20:40:27 2008 read 1849397 relations Wed Apr 30 20:40:39 2008 multiplying 2777790 relations Wed Apr 30 20:45:52 2008 multiply complete, coefficients have about 84.06 million bits Wed Apr 30 20:45:53 2008 initial square root is modulo 1080791 Wed Apr 30 20:52:43 2008 reading relations for dependency 2 Wed Apr 30 20:52:45 2008 read 550793 cycles Wed Apr 30 20:52:46 2008 cycles contain 1847871 unique relations Wed Apr 30 20:54:28 2008 read 1847871 relations Wed Apr 30 20:54:39 2008 multiplying 2774172 relations Wed Apr 30 20:59:53 2008 multiply complete, coefficients have about 83.95 million bits Wed Apr 30 20:59:54 2008 initial square root is modulo 1062121 Wed Apr 30 21:06:44 2008 reading relations for dependency 3 Wed Apr 30 21:06:46 2008 read 551584 cycles Wed Apr 30 21:06:47 2008 cycles contain 1850780 unique relations Wed Apr 30 21:09:07 2008 read 1850780 relations Wed Apr 30 21:09:19 2008 multiplying 2782286 relations Wed Apr 30 21:14:33 2008 multiply complete, coefficients have about 84.20 million bits Wed Apr 30 21:14:34 2008 initial square root is modulo 1105861 Wed Apr 30 21:21:26 2008 prp80 factor: 34957698771189765331782973598371343662802452976654329112913699889505994900648923 Wed Apr 30 21:21:27 2008 prp97 factor: 2306747025295127756657870419577411038780260831935613811132503821954020694612281320931385429666039 Wed Apr 30 21:21:27 2008 elapsed time 02:47:50 
20080501, 03:10  #17 
Feb 2005
100000100_{2} Posts 
Would anybody be willing to complete factorizations of some numbers of the form 2^x  3 that are specified in http://www.immortaltheory.com/NumberTheory/2nm3_db.txt
They may lead to new solutions to the congruence 2^n == 3 (mod n). See http://www.immortaltheory.com/NumberTheory/ for details. 
20080502, 10:17  #18  
Oct 2004
Austria
2×17×73 Posts 
Quote:
Last fiddled with by Andi47 on 20080502 at 10:17 

20080502, 11:34  #19  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
There are enough projects already. 

20080531, 08:09  #20 
(loop (#_fork))
Feb 2006
Cambridge, England
2·7·461 Posts 
Fibonacci(1079) has 13 dividing the index, which leads to the rather hairy SNFS polynomial
Code:
X6 233 X5 924 X4 330 X3 2630 X2 3230 X1 361 X0 547 Y0 29518856641470372602077458635151025 Y1 9839618880490124200692486211717008 SNFS difficulty around 208, so used 29bit large primes, 24bit small primes, sieved 16*2^20 to 28.5*2^20 on both rational and algebraic sides at about 53 CPUhours per 2^20 per side. 3898433 x 3898681 matrix of sparse weight 237324495 took about 33 hours on a quadcore, four dependencies at about 100 minutes each to get Code:
prp77 factor: 18727110802459085713612355138358090816535653522436895514996063854215718011073 prp77 factor: 44880947869994501075054379581241898325627426706522382877689328360578549344673 Last fiddled with by fivemack on 20080531 at 08:17 
20080630, 17:27  #21 
(loop (#_fork))
Feb 2006
Cambridge, England
6454_{10} Posts 
1061 is prime; Fibonacci(1061) is
Code:
93514417 * 43560958890354764963930018391355194517824960526673705978607400537437661703590480182627863527694377 * 59762024502667954496467866668111126040902657986182974323716858091462517843782397838677155890803832980467807587783629 
20080630, 20:08  #22  
Aug 2002
Buenos Aires, Argentina
3·499 Posts 
Quote:
Last fiddled with by alpertron on 20080630 at 20:09 

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