20211126, 00:56  #1 
Apr 2020
39B_{16} Posts 
DONE  Polynomial selection for 2,2246M c221 and factoring
This is one of only two remaining unambiguous GNFS numbers from the 1987 edition of the Cunningham book (base 2 <1200 bits), the other being 2,1109+ c225.
Bob Silverman suggested that the forum run polynomial selection for this number, and Greg has agreed to sieve it with NFS@Home once a suitable poly is found. The composite is Code:
24023387191766184217094927222587025087468868508838209688355658860897738047963529318736265313199625192712082581481439831563094403250831892547179972207284600405234081309183045488404642574713121441527058807512178264038863337 For those who prefer to use CADO, the parameters used to find the aforementioned c220 record polynomial might be a useful starting point: these are P=12M, incr=420, nq=46656, sopteffort=10, ropteffort=100. I am not claiming that these are optimal. The (presizeopt) leading coefficient was in the 35M40M range; unlike with degree5, there did not appear to be a significant decrease in average polynomial quality with larger leading coefficients, so there was no need to move to higher values of incr. NFS@Home have a number of SNFS jobs queued up, so don't worry if you've been sieving 3,748+ for the last month and would like a break: there's no rush. It'll probably be about a week before I start any searching myself. 
20211126, 22:46  #2 
Jun 2012
2×19×101 Posts 
Sounds fun. Love your recipe for CADO, though I may increase ropteffort and sopteffort a bit.
One question  is tasks.wutimeout = 24000 (default) sufficient? Reserving 1e3 < c6 < 2e6. ETA: adrange = 1680 Last fiddled with by swellman on 20211127 at 00:55 Reason: Add adrange 
20211127, 02:01  #3  
Apr 2020
13×71 Posts 
Quote:
Your adrange is small enough that the length of the stage1+sizeopt tasks won't be an issue. 

20211127, 02:26  #4 
Jun 2012
2·19·101 Posts 
FWIW, msieve is looking for an escore of at least 2.71e16 to > 3.12e16. I’m running some msieveGPU for c6 < 1M. Not expecting much from msieve on a C221 but blind squirrels etc.
CADO is running on one of my old quad core laptops. It is SLOW but fingers crossed a flare pops up. Thank you for the advice @charybdis! 
20211127, 06:38  #5  
"Curtis"
Feb 2005
Riverside, CA
1010111110110_{2} Posts 
Quote:


20211127, 14:38  #6  
Apr 2020
13·71 Posts 
Quote:


20211129, 08:14  #7 
Apr 2010
2^{3}·31 Posts 
3.5e16 is possible:
Code:
# norm 7.406551e16 alpha 9.691472 e 3.501e16 rroots 6 skew: 7000972.35 c0: 53635249950771487474963143079350712070525911980 c1: 34662949307835344131518242206719949955943 c2: 72498102600242091149685770153699749 c3: 3018341741417463336008367359 c4: 7813123654476017869721 c5: 45283110042666 c6: 25200 Y0: 1113552721024727138053628986496268142 Y1: 1434019800661087662503 
20211129, 21:06  #8 
Jun 2012
2·19·101 Posts 
Very nice! A new record for C221, but can an even higher score be found? 3.73.8e16 perhaps? I’ll keep searching but you’ve set the high water mark! 
20211129, 23:13  #9 
Apr 2020
39B_{16} Posts 

20211129, 23:43  #10 
"Curtis"
Feb 2005
Riverside, CA
1010111110110_{2} Posts 
Would Greg like some testsieving done?
I can try to quantify the tradeoff between 34LP and 34/35 for this job, for instance. This poly is "good enough", but this is a very big job and saving even 12% of sieve time is quite a few workunits from the elves; a 2% savings is roughly a C190 sieve job in time saved! So, we should continue to look for a 3.6. There's some chance of "spin" still, too. Edit: I'm busy with ECM pretesting a couple jobs for 15e queue to meet the upcoming "challenge" demand, I'll work on CADO select on this job in a couple weeks once I get two jobs posted to 15e. Last fiddled with by VBCurtis on 20211129 at 23:45 
20211206, 15:48  #11 
Jun 2012
2·19·101 Posts 

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