20221013, 21:15  #34 
"Curtis"
Feb 2005
Riverside, CA
3×1,999 Posts 
Nice work!
Was the job run 34/35, or 35 on both sides? Looks like there's room for one more bit of LP on one side while staying comfortably within msieve's relationscount bound. 
20221013, 21:57  #35 
Jul 2003
So Cal
5172_{8} Posts 

20221014, 00:28  #36 
Jun 2012
7·11·53 Posts 
Congratulations on factoring that beast!
Looking ahead to the Gang of 31, 2,2222L is a GNFS 228 or a SNFS 334, very similar to 2,1109+, i.e. a GNFS 225 or SNFS 334. No idea how efficiently 2,2222L sieves as a SNFS but if it’s similar to 2,1109+ do we need to bother running ECM on it and instead just jump right to SNFS via NFS@Home or perhaps a team CADO effort? Keep in mind that I currently have 2,2222L first in the Gang of 31 ECM list, and I plan to keep it there unless this matter is decided otherwise. But I ask the question. Alternatively, should we add 2,1109+ to the Gang of 31 before attempting to sieve it by whatever method? 
20221014, 00:45  #37 
Jun 2012
7·11·53 Posts 
2,2222L
I got the following SNFS polynomial for 2,2222L, with a competitive escore.
Code:
n: 498182294243708816934953758200571293828380952324990796450108172678901306777660557394701463533080260632512879410875999929172206863194431411006233976375867957164259819114952920343808614673946286820544900427755366971820147029014473 skew: 1.22639 type: snfs c6: 2 c5: 0 c4: 0 c3: 2 c2: 0 c1: 0 c0: 1 Y1: 1 Y0: 49039857307708443467467104868809893875799651909875269632 # cownoise score = 1.652e16 (same skew recommended, no surprise) 
20221014, 00:49  #38  
"Bob Silverman"
Nov 2003
North of Boston
7633_{10} Posts 
Quote:
Too big for NFS@Home. He has said SNFS 330/GNFS 225 is the limit. This places even 2,1097+ and 2, 2194L or M out of reach. Quote:
GNFS (even though it is at the stated size limit) and is clearly too big via SNFS. NFS@Home had to hit a ceiling sooner or later. C'est la vie. 

20221014, 01:02  #39  
"Bob Silverman"
Nov 2003
North of Boston
1DD1_{16} Posts 
Quote:


20221014, 01:06  #40  
Apr 2020
2165_{8} Posts 
Quote:
The work on 2,1109+ seems to suggest that SNFS334 is easier than GNFS225, so I don't see how "SNFS330/GNFS225" makes sense as a limit. If GNFS225 is possible  which it probably is, given that there was room to spare with 2,2246M  then SNFS335 should be too. Yes, sieving will take a while, and the memory limitations of the clients make it a harder lift than it should be, but I don't see why sieving up to Q=5G or so would be infeasible. 35bit large primes will help. 

20221014, 01:33  #41  
"Bob Silverman"
Nov 2003
North of Boston
17×449 Posts 
Quote:
However, a suitable polynomial for 2,1109+ could not be found. Perhaps it is just an outlier for GNFS. Prior work suggests that a typical C225 would be easier than 2,1109+. Thus, I am not sure that your conclusion that SNFS 334 is easier than GNFS 225 is justified. A single data point is bad statistics. It is also possible that the polynomial search was unlucky. OTOH, I am not sure that your conclusion is false either. Greg is the one who suggested SNFS 330 as a limit. Note that I would be quite happy to learn that SNFS 334 is doable. Clearly, if SNFS 334 is possible, then the "gang of 32" will need adjustment. Last fiddled with by R.D. Silverman on 20221014 at 01:36 

20221014, 01:41  #42  
Jun 2012
7·11·53 Posts 
Quote:
Quote:
Last fiddled with by swellman on 20221014 at 01:44 

20221014, 02:27  #43  
Apr 2020
7×163 Posts 
Quote:
(Caveat: I haven't actually testsieved the best GNFS poly to see how feasible it is. A task for another day.) 

20221014, 02:42  #44  
"Bob Silverman"
Nov 2003
North of Boston
17·449 Posts 
Quote:
Of course small variations in escore can make a significant difference. I am just trying to adjust my expectations about relative difficulty, since my initial guess was that GNFS 225 was doable. 

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