Polynomial Request Thread

[frmky]

I'm giving it about 6 GPU-months over 2 weeks total. Sieving will start in about a week or so.

[bdodson]

Originally Posted by firejuggler

hmm? get to factordb, type 3^766+1; find the C216...
and don't forget to add "polydegree=6" in your parameters

313068751706172934164029607615444196674154606234575242211641355472713959762783712390895701060952639425447396356557581585630115258626457263968597368593309998959766117756941753233822835800989497155176060903761800503381

Yes; a smaller composite, C216. Perhaps it is worth recalling that
the two previous gnfs from the 3+ extension, C202 (745+) and
C207 (706+) both had p62 factors, left after tests to p60; perhaps
2t60 if Sam finished an initial t60. Since there's already an extensive
polyn search in progress, perhaps it is too late for "more" ECM.

Ah; looks like I already finished my t60, so this number is no more
under-tested than the previous two. Seems that there's a sharp
difference between these and the numbers from pre-extension
Cunninghams that ryanp is sieving; no p6x's, hardly any p7x's.
Looks like his smallest snfs factor is a p68 from 7,334+ C205 ---
just slightly smaller than his spectacular ECMs p70, p69 and p68
from the oldest Cunninghams, 2^N-1, 1000 < N < 1200;
N = 1069, 1051 and 1067, from the Mersenne list. Maybe Bob's
right that lots of curves were run, by lots of people, to remove
most p<70s.

In any case, this gnfs216 is a large step up from the current
gnfs212; probably still twice as difficult for the extra 4-digits?
With some advance notice, we might have run a larger proportion
of a t65. Speaking of which, looks like Greg has reserved two more

7,394+	c197	NFS@Home gnfs
10,770M	c212	NFS@Home gnfs
3,766+	c216	NFS@Home gnfs
11,323+	c221	NFS@Home gnfs

-Bruce

PS - Ah; a nice p69 from 2, 2186L C227.

[frmky]

Yes, this one sneaked up on me. It's been a really crazy summer, and it just dawned on me last week how quickly the current c197 will finish. I quickly put all my gpus on it.

There is time to give 11,323+ some more ECM if it's needed.

Thanks!

[bdodson]

Originally Posted by frmky

Yes, this one sneaked up on me. It's been a really crazy summer, and it just dawned on me last week how quickly the current c197 will finish. I quickly put all my gpus on it.

There is time to give 11,323+ some more ECM if it's needed.

Thanks!

Yes, I see that we've switched to the c197, now that you
mention it. This one had a bunch of B1=900M curves,
23834-of-13061=t60, just on the dual-8core machine, during
burn-in.

For 11,323+ I have 3t55; I'll plan on adding 2-or-3 t60's,
depending how they go.

Looking forward to hear progress on postprocessing of 10, 770M. -Bruce

[VBCurtis]

Starting a week on the c216 today- glad you pointed out it's going to begin sieving quickly.

This will stretch the 16e siever quite a bit, yes? Can you compare the parameters for this vs the c212? Are you confident the c221 will be possible with 16e (perhaps that depends on how the 216 goes?).

[henryzz]

It should be possible to raise the large primes limit(a recompile after removing the check will be necessary). I have checked that the siever and msieve work with larger large primes(I think I checked 35 bits. It will have been at least 34. I think jasonp reckoned that >35 would be too many relations for msieve to handle). I haven't checked that it doesn't miss some of the relations with larger large primes but if that is an issue it will be discovered during parameter selection anyway.
I would imagine after raising the large prime limit there is a fair amount more room in 16e. You could also try sieving with >3 lp using the lasieve5 siever.

[frmky]

Here's a somewhat better one for 3,766+:

# norm 1.088509e-15 alpha -10.727690 e 4.501e-16 rroots 6
skew: 10476738.56
c0: -5369554424004030826402973140282841011572519398275
c1: -3414866216469788096538063790563208721226714
c2: 854150826092935212357938287070651342
c3: 341347932610455553798257621420
c4: -19812274695016079944507
c5: -1277018966659986
c6: 9218160
Y0: -56907029561383080746868850208970432
Y1: 20291767539399957581

[Gimarel]

Originally Posted by frmky

Here's a somewhat better one for 3,766+:

Although the skew is very high, this degree 5 poly seems to sieve 10%-20% better:

# norm 2.316186e-21 alpha -8.836349 e 3.282e-16 rroots 3
skew: 1161620713.03
c0: -150197586295000094627583800604174270758750606052640635
c1: -972901144347733530674190364546696103274696609
c2: -588214638592090440436049221701783597
c3: 2579751407152116188605093717
c4: -122719450234339820
c5: 102342240
Y0: -314135458405637114606970259658568784545142
Y1: 131759766057910809619

But that probably needs to be verified with the actual sieving parameters and for the Q-range to be sieved.

[lorgix]

Originally Posted by swellman

I can wait for as long as it takes. Not on any timetable.

Thanks again.

I'm done with C169_141_71. I didn't find anything better than the 3.7 I posted.

[swellman]

Originally Posted by lorgix

I'm done with C169_141_71. I didn't find anything better than the 3.7 I posted.

Thanks for all your efforts. I'll do some test sieving next week.

[wombatman]

It's not better than the polys posted, but here's my best so far on the C216:

#skew 4318719.56, size 6.192e-016, alpha -9.299, combined = 3.282e-016 rroots = 6
N 313068751706172934164029607615444196674154606234575242211641355472713959762783712390895701060952639425447396356557581585630115258626457263968597368593309998959766117756941753233822835800989497155176060903761800503381
SKEW 4318719.56
R0 -56118476053099371919661459200054844
R1 3376910376775132711
A0 422506237083294610548658191220217155380023123625
A1 838036371757770978178729323549824699235795
A2 202841735403297089138679493763867919
A3 -220430066293747906637149137727
A4 -15892839097395096736892
A5 7154030015548284
A6 10023156