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Old 2020-08-26, 20:37   #4
Batalov's Avatar
Mar 2008

9,391 Posts

Originally Posted by Ensigm View Post
I see, thank you. For a given number, at what level shall we stop using ECM and switch to NFS?
There are different heuristics, they depend on a lot of factors/considerations.
Usually. people pre-factor with TF, ECM etc until X% of the SNFS-complexity, or of GNFS-size. (where X varies between different opinions; search the forum, as well as SSW webpage and mathworld and similar).

The problem in a nutshell is: 1) when factor is already known - you can easily look retrospectively and make a conclusion: "We would have needed N times _more_ time to keep ECMming and we would have found it ..or not" (and we could even arrive at paradoxical conslusion: "we would have saved so much time by not ECMming, skipping it altogether"); 2) we don't know the factor. We ecm up to the point when time to factor by NFS becomes less than the estimated time to get lucky with ECM (and factoring in probability that maybe it is out of reach of ECM).
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