20130222, 19:40  #1 
Feb 2012
3^{4}·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 
20130222, 19:46  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
The time it takes to do one curve is proportional to the exponent in the same way that iteration time is proportional to the exponent.
So above 20M, it just takes way too long to do one curve. (Heck, I'm surprised anybody tries for something more than, say, 5M.) 
20130222, 20:02  #3 
Feb 2012
3^{4}·5 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 P1 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 P1 bounds already done? In particular, do ECM bounds correspond P1 bounds so if P1 has not found a factor within these bounds nether will ECM? Or ECM bounds are something else? Thank you 
20130222, 21:17  #4 
Einyen
Dec 2003
Denmark
2×11×137 Posts 
If an exponent have been trialfactored to 2^70 that is 70*log_{10}(2) ~ 20 digits, so you should at least start at 25 digit level or higher. From GMPECM 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 
20130222, 22:10  #5 
Feb 2012
3^{4}·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 P1 already performedâ€¦ 
20130222, 22:28  #6  
Einyen
Dec 2003
Denmark
2×11×137 Posts 
GMPECM readme again:
Quote:
P1 is something you run once unless you increase the bounds later. P1 will find the factor P with 100% certainty IF the factors of P1 is within the bounds B1 (and 1 factor in the B1B2 range). With ecm you run many curves with random "seeds" with a small probability of finding the factors. Last fiddled with by ATH on 20130222 at 22:32 

20130222, 22:34  #7 
Feb 2012
3^{4}×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 P1 bounds and ECM still has a chance of finding a factor. Right?
Last fiddled with by TObject on 20130222 at 22:57 
20130222, 22:54  #8 
Einyen
Dec 2003
Denmark
2×11×137 Posts 
These are the standard "optimal" bounds, yes it works in Prime95 as well.

20130223, 09:58  #9  
Jun 2003
12EE_{16} Posts 
Quote:
ATH's first post is the relevant one. But note that for large mersennes, GMPECM is not usable  you have to use P95. And P95 has a different stage 2 bound (default is 100x stage 1) compared to GMPECM and therefore recommended # of curves at each level is higher. 

20130223, 14:06  #10  
Nov 2003
2^{2}·5·373 Posts 
Quote:
is talking about. ECM bounds are related to P1 bounds. Read: Robert Silverman & Samuel Wagstaff Jr. A Practical Analysis of ECM. Mathematics of Computation This paper describes the relationship between P1 and ECM. To axn: do us all a favor: Study this subject before making further erroneous pronouncements. 

20130223, 15:30  #11 
Aug 2010
Kansas
1000100011_{2} Posts 

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