Factoring EM47 - Page 2

Andi47 · 2010-03-11, 06:05

Quote:

Originally Posted by R. Gerbicz

Code:

48 c256

p-1: B1=1e9, B2=1e14, no factor.

grandpascorpion · 2010-03-11, 16:28

Very exciting stuff

fivemack · 2010-03-11, 17:06

Will try to run a large number of curves at 43e6 while I'm on vacation (set off 16 jobs at 1e8 but this made the machine swap beyond the point of usability).

R.D. Silverman · 2010-03-11, 17:07

Quote:

Originally Posted by fivemack

Will try to run a large number of curves at 43e6 while I'm on vacation (set off 16 jobs at 1e8 but this made the machine swap beyond the point of usability).

Ask Bruce to take a whack at it.

axn · 2010-03-11, 17:34

2000 curves completed @ 3e6.

currently running 43e6

bdodson · 2010-03-12, 16:45

Quote:

Originally Posted by R.D. Silverman

Ask Bruce to take a whack at it.

I've spent the past 10-days-or-so "whack"ing on the current NFS@Home
reservation, with another 10-days-or-so left to go. I recently completed
p55-tests on the Cunninghams from c190-c209.99 (either 7t50 or 6t50,
depending on the difficulty); and am currently working toward t55's on
c210-c233, in between NFS@Home and Batalov+Dodson numbers. I'm also
making a lower priority run through c234-c289.487 plus the 2- and 2+
numbers (not including 2LMs) the rest of the way up, through C355; working
toward 3t50. Likely enough to keep our cpus busy the rest of 2010.

Almost all curves are with p60-optimal limits (B1=26e7=260e6, gmp-ecm
default B2); except for a few xp's with just 500Mb available for condor jobs,
running p55-limits.

Uhm. This is a c256 gnfs number, currently in testing for p50's? I'm having
some trouble seeing this as the first gnfs number above 768-bits
(232-digits). -Bruce

Batalov · 2010-03-12, 18:53

By definition, the single smallest factor is enough to continue the sequence.

But from the current status, it is going to take a leap of faith, if (e.g.) a p54 factor is found. This iteration may need a lot of subsequent ECM to minimize the probability that that would be the smallest factor (and still not remove the doubt entirely). Tough!

(The same was or still is the case on the -1 analog of EM sequence, right? I don't see the p51 there, it was mentioned earlier in this thread. Sloane's A005265)

10metreh · 2010-03-12, 18:59

Remember that if we do find a factor with ECM and the cofactor is composite, we will still have to factor the cofactor to check that the ECM factor is indeed the smallest prime factor.

bdodson · 2010-03-12, 19:03

Quote:

Originally Posted by Batalov

By definition, the single smallest factor is enough to continue the sequence.

But from the current status, it is going to take a leap of faith, if (e.g.) a p54 factor is found. This iteration may need a lot of subsequent ECM to minimize the probability that that would be the smallest factor (and still not remove the doubt entirely). Tough! ...

A p54 would go a long way towards making a composite cofactor nearer
to our current gnfs range; or perhaps better yet, leave a large prime
cofactor. I'd consider running a second t55, once the first one fails.
So somewhere past the effort of 4 t50's (with t55 = c. 5.7*t50?). Finding
a p53/p54 isn't among my objectives, unless it's from a Cunningham.
Once p53/p54 is unlikely, EM48 is as good as any other candidate for
finding a nice p60+ factor (which would get recorded, for a while at least
.... uhm, maybe p62+, Brent's list of p60+ is already past 10). -Bruce

CRGreathouse · 2010-03-12, 20:03

10,000 curves done at 11M, so the smallest factor should be at least 45 digits. Just for fun, I'm running some curves at 260M... but even if there was a factor in the appropriate range, there's only about a $1-(1-1/52000)^{1000}\approx$ 2% chance I'd find it with as few curves as I'm running.

Andi47 · 2010-03-12, 20:08

Has any p+/-1 been done besides my p-1 with B1=1e9, B2=1e14?

For p-1 I have extended B1 to 1e10 (no factor with B2=1e13) and I'm currently extending it to B1=2e10 or even further (maybe 5e10).

As soon as my laptop will get free (currently running a GNFS-job, will be finished around Wednesday) I will do B2=1e15 for whatever B1 I will have reached by then. (B2=1e18 will be left to someone with a machine with 8 cores and 32+ GB RAM)

2010-03-12, 20:03	#21
CRGreathouse Aug 2006 2²·1,493 Posts	10,000 curves done at 11M, so the smallest factor should be at least 45 digits. Just for fun, I'm running some curves at 260M... but even if there was a factor in the appropriate range, there's only about a $1-(1-1/52000)^{1000}\approx$ 2% chance I'd find it with as few curves as I'm running. Last fiddled with by CRGreathouse on 2010-03-12 at 20:25

2010-03-12, 20:08	#22
Andi47 Oct 2004 Austria 2·17·73 Posts	p+/-1 Has any p+/-1 been done besides my p-1 with B1=1e9, B2=1e14? For p-1 I have extended B1 to 1e10 (no factor with B2=1e13) and I'm currently extending it to B1=2e10 or even further (maybe 5e10). As soon as my laptop will get free (currently running a GNFS-job, will be finished around Wednesday) I will do B2=1e15 for whatever B1 I will have reached by then. (B2=1e18 will be left to someone with a machine with 8 cores and 32+ GB RAM) Last fiddled with by Andi47 on 2010-03-12 at 20:08

2010-03-11, 16:28	#13
grandpascorpion Jan 2005 Transdniestr 503 Posts	Very exciting stuff

2010-03-11, 17:06	#14
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2·3,191 Posts	Will try to run a large number of curves at 43e6 while I'm on vacation (set off 16 jobs at 1e8 but this made the machine swap beyond the point of usability).

2010-03-11, 17:34	#16
axn Jun 2003 4856₁₀ Posts	2000 curves completed @ 3e6. currently running 43e6

2010-03-12, 18:53	#18
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×3,109 Posts	By definition, the single smallest factor is enough to continue the sequence. But from the current status, it is going to take a leap of faith, if (e.g.) a p54 factor is found. This iteration may need a lot of subsequent ECM to minimize the probability that that would be the smallest factor (and still not remove the doubt entirely). Tough! (The same was or still is the case on the -1 analog of EM sequence, right? I don't see the p51 there, it was mentioned earlier in this thread. Sloane's A005265)

2010-03-12, 18:59	#19
10metreh Nov 2008 2×3³×43 Posts	Remember that if we do find a factor with ECM and the cofactor is composite, we will still have to factor the cofactor to check that the ECM factor is indeed the smallest prime factor.