20080311, 12:58  #45 
Nov 2003
2^{2}·5·373 Posts 

20080311, 15:40  #46 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
The difficulty is only 226 with a sextic while 163*3/2 = 244.5, so I figured SNFS would be the way to go. I didn't look for GNFS polynomials, though, so I cannot directly compare yield. The SNFS polynomial is the 6th cyclotomic so no real roots and the root properties are lousy, but I think the difference of size should more than make up for it.
Alex 
20080311, 15:46  #47  
Nov 2003
1110100100100_{2} Posts 
Quote:
the ratio should be (64/9)^1/3 : (32/9)^1/3 

20080314, 09:56  #48 
Sep 2002
Vienna, Austria
3·73 Posts 

20080314, 10:08  #49 
"Nancy"
Aug 2002
Alexandria
4643_{8} Posts 
I'll do a polynomial search and compare sieving yield to get some data on how the equivalent size estimates between SNFS and GNFS work out.
Alex 
20080319, 20:43  #50 
(loop (#_fork))
Feb 2006
Cambridge, England
18D1_{16} Posts 
According to my records, on similar hardware with reasonable management for the polynomial search, 1300 hours will split a C149 by GNFS, and comparable or slightly less effort splits an S218 by SNFS.
For slightly smaller numbers, fibonacci(1057)  an S190  took 350 hours, and a G138 was 240; a G141 took about 600, though with the benefit of hindsight I should probably have used 28bit rather than 29bit large primes for it. Fitting to my entire collection of factorisations done to date, GNFS takes about exp(0.114 * log_10(N)  9.4) sieving hours, and SNFS takes about exp(0.075 * log_10(difficulty)  8.2) hours, on 2.4GHz Core2 or similar (there's a lot of fuzz in the constant terms) 
20080610, 08:17  #51 
"Nancy"
Aug 2002
Alexandria
4643_{8} Posts 
I finally did a comparison between GNFS and SNFS for 3,553. A relatively short search (a few hours) found a poly with Murphy_E 6.57e13, sieving with afb 30M, rfb 20M, lpb 2^30, sq in [30M,30M+1000] produced 943 relations over 69 specialq, for SNFS with the same parameters 2208 relations over 66 specialq, so the yield per specialq is almost 2.5 times as high for SNFS. Sieving SNFS was also a bit faster, about 4:30 vs. 3:45. A longer poly search may be able to reduce this gap, but most likely not close it. The difference is much less than I had expected from comparing SNFS difficulty to cofactor size, however.
Alex 
20080610, 09:08  #52  
"Robert Gerbicz"
Oct 2005
Hungary
2541_{8} Posts 
Quote:


20080610, 11:16  #53  
Bamboozled!
May 2003
Down not across
2^{2}×3×7×11^{2} Posts 
Quote:
Paul 

20080719, 13:17  #54  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
prp78 factor:22932169041497578656101635893906350495601781188\ 2813174487175975135341417478309 and prp165 factor: 122914703941908311355702961196522843507 18584674423029707827350973961621122882489095148212477085420\ 53379331195812489501111064875263191361424956117603449488246\ 79539983 using msieve 1.34 for the matrix. This is 3of4 successes, with 7,311+ and a 2nd pass at 10,257+ using 1.36. New wanted lists are out, with largest composite 3, 523 C233 More Wanted at difficulty 249.5; as well as 3, 529 C237 being just a bit further out at difficulty 252.4. (The above was difficulty 261, our largest so far.) NFSNET already has two first holes reserved, M823 = 2,823 C197 and P823 = 2,823+ C229, at difficulty 247.75. Seems like this base3 list is due to get even shorter yet in the nottodistant future! Bruce 

20080807, 09:48  #55 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
3,553 c163:
1496011698256808140870327017215159254210989805180702509984299821 1311856567988975419611247459617464197060581406673461639594334403781089672393080946888216894062632439 Sieving with the Franke/Kleinjung siever, rest with Jason's Msieve. Alex Edit: I'll do 3,527 c160 next. Last fiddled with by akruppa on 20080807 at 09:54 
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