DONE - Polynomial selection for 2,2246M c221 and factoring

[charybdis]

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

24023387191766184217094927222587025087468868508838209688355658860897738047963529318736265313199625192712082581481439831563094403250831892547179972207284600405234081309183045488404642574713121441527058807512178264038863337

This will be a degree-6 search. The obvious target for a good score is Gimarel's score of 3.36e-16 for 3,697+, which to the best of my knowledge is the only GNFS-221 that has ever been run before. The c220 record is 4.178e-16, so it's reasonable to believe that 3.5e-16 or better is possible.

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 (pre-sizeopt) leading coefficient was in the 35M-40M range; unlike with degree-5, 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.

[swellman]

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

[charybdis]

Originally Posted by swellman

One question - is tasks.wutimeout = 24000 (default) sufficient?

Depends if you set ropteffort very high. With ropteffort=100 you'll be fine. 200 might potentially need more time on old/slow CPUs.
Your adrange is small enough that the length of the stage-1+sizeopt tasks won't be an issue.

[swellman]

FWIW, msieve is looking for an e-score of at least 2.71e-16 to > 3.12e-16. I’m running some msieve-GPU 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!

[VBCurtis]

Originally Posted by charybdis

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 (pre-sizeopt) leading coefficient was in the 35M-40M range; unlike with degree-5, 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.

If there is little dropoff in score for larger leading coeff's, doesn't that argue for incr-4620 rather than 420? That is, we should take advantage of the slightly better typical poly that an extra small-factor of c6 provides, since the downside of searching large c6 range doesn't seem to be a problem?

[charybdis]

Originally Posted by VBCurtis

If there is little dropoff in score for larger leading coeff's, doesn't that argue for incr-4620 rather than 420? That is, we should take advantage of the slightly better typical poly that an extra small-factor of c6 provides, since the downside of searching large c6 range doesn't seem to be a problem?

Perhaps. While I didn't see much dropoff up to 40M, that doesn't mean there won't be by 400M. I suppose the prudent thing to do would be to run smallish ranges (100k?) at 40M and 400M and compare the "exp_E" scores of the polynomials at the bottom of the priority queue from each run.

[Gimarel]

3.5e-16 is possible:

# norm 7.406551e-16 alpha -9.691472 e 3.501e-16 rroots 6
skew: 7000972.35
c0: 53635249950771487474963143079350712070525911980
c1: 34662949307835344131518242206719949955943
c2: -72498102600242091149685770153699749
c3: 3018341741417463336008367359
c4: 7813123654476017869721
c5: 45283110042666
c6: -25200
Y0: -1113552721024727138053628986496268142
Y1: 1434019800661087662503

[swellman]

Very nice!

A new record for C221, but can an even higher score be found? 3.7-3.8e-16 perhaps?

I’ll keep searching but you’ve set the high water mark!

[charybdis]

Originally Posted by Gimarel

3.5e-16 is possible:

Very nice!

This is good enough that I'll stay away for longer than I was planning; there are lots of new base-2 Cunninghams to do...

[VBCurtis]

Would Greg like some test-sieving 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 1-2% 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.

[swellman]

Originally Posted by swellman

Very nice!

A new record for C221, but can an even higher score be found? 3.7-3.8e-16 perhaps?

I’ll keep searching but you’ve set the high water mark!

Done searching. Can’t find a poly even close to Gimarel’s gem.