mersenneforum.org > Data ECM for exponents above 20,000,000
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 2013-02-22, 19:40 #1 TObject     Feb 2012 34·5 Posts ECM for exponents above 20,000,000 Judging by the Exponent Status Distribution report, PrimeNet participants are not expected to return ECM results for exponents above 20,000,000. What is the reason for that? Is diminishing efficiency? Thanks
 2013-02-22, 19:46 #2 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2013-02-22, 20:02 #3 TObject     Feb 2012 40510 Posts If someone is really persistent at finding a factor of a given exponent, and TF has been done to a fairly high level, so has the P-1 with good bounds. Would the next logical step be to run ECM? What is a good strategy then for choosing ECM bounds in regards to the levels of TF and P-1 bounds already done? In particular, do ECM bounds correspond P-1 bounds so if P-1 has not found a factor within these bounds nether will ECM? Or ECM bounds are something else? Thank you
 2013-02-22, 21:17 #4 ATH Einyen     Dec 2003 Denmark 1100000001012 Posts If an exponent have been trialfactored to 2^70 that is 70*log10(2) ~ 20 digits, so you should at least start at 25 digit level or higher. From GMP-ECM readme file here is the standard optimal bounds and curve count for the different digit levels: Code:  digits D optimal B1 default B2 expected curves 20 11e3 1.9e6 74 25 5e4 1.3e7 214 30 25e4 1.3e8 430 35 1e6 1.0e9 904 40 3e6 5.7e9 2350 But it will take a very long time just for the 214 curves for the 25 digit level.
 2013-02-22, 22:10 #5 TObject     Feb 2012 34×5 Posts Thank you, that is very helpful. What about P1 bounds? Are P1 and ECM bounds numerically compatible? I imagine, for a chance to find a factor, ECM bounds should be above of P-1 already performed…
2013-02-22, 22:28   #6
ATH
Einyen

Dec 2003
Denmark

17×181 Posts

Quote:
 2 - run once P-1 with 10*B1, and the default B2 chosen by GMP-ECM
So for 25digit instead of B1=50,000 from ecm you use B1=500,000 for P-1.

P-1 is something you run once unless you increase the bounds later. P-1 will find the factor P with 100% certainty IF the factors of P-1 is within the bounds B1 (and 1 factor in the B1-B2 range). With ecm you run many curves with random "seeds" with a small probability of finding the factors.

Last fiddled with by ATH on 2013-02-22 at 22:32

 2013-02-22, 22:34 #7 TObject     Feb 2012 34×5 Posts Thank you. So, I gather that, unless limited by other factors, ECM bounds can be as low as 1/10th of already run P-1 bounds and ECM still has a chance of finding a factor. Right? Last fiddled with by TObject on 2013-02-22 at 22:57
 2013-02-22, 22:54 #8 ATH Einyen     Dec 2003 Denmark 60058 Posts These are the standard "optimal" bounds, yes it works in Prime95 as well.
2013-02-23, 09:58   #9
axn

Jun 2003

133516 Posts

Quote:
 Originally Posted by TObject ECM bounds can be as low as 1/10th of already run P-1 bounds and ECM still has a chance of finding a factor. Right?
ECM bounds are in no way relatable to P-1 bounds. ECM search space is different from P-1 search space. The 1/10th stuff is what you'd call a "rule of thumb". Don't bother.

ATH's first post is the relevant one. But note that for large mersennes, GMP-ECM is not usable -- you have to use P95. And P95 has a different stage 2 bound (default is 100x stage 1) compared to GMP-ECM and therefore recommended # of curves at each level is higher.

2013-02-23, 14:06   #10
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by axn ECM bounds are in no way relatable to P-1 bounds. ECM search space is different from P-1 search space. The 1/10th stuff is what you'd call a "rule of thumb". Don't bother.
My suggestion: Do not bother listening to axn. He does not know what he
is talking about. ECM bounds are related to P-1 bounds.

Robert Silverman & Samuel Wagstaff Jr.
A Practical Analysis of ECM.
Mathematics of Computation

This paper describes the relationship between P-1 and ECM.

To axn: do us all a favor: Study this subject before making further
erroneous pronouncements.

2013-02-23, 15:30   #11
c10ck3r

Aug 2010
Kansas

547 Posts

Quote:
 Originally Posted by R.D. Silverman Robert Silverman & Samuel Wagstaff Jr. A Practical Analysis of ECM. Mathematics of Computation

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