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Old 2020-08-26, 20:38   #5
VBCurtis's Avatar
Feb 2005
Riverside, CA

3·1,579 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 two flavors of NFS: Special, abbreviated SNFS, and general GNFS.

For numbers where SNFS is faster, a rule of thumb is to ECM up to 0.22 * the difficulty of the number; e.g. SNFS-300 would get ECM up to 66 digits (about 1.4 * T65).

For numbers where GNFS is faster or SNFS is not possible, a rule of thumb is ECM to 0.31 * the number of digits; a GNFS-200 would get 62 digits (2 * T60, or a T60 plus a T60 worth of T65-sized curves).

These rules of thumb are not super accurate; to be precise, one gives up on ECM when the marginal next set of ECM curves has less chance to factor the number than the fraction of expected NFS-solving time the set of curves takes. That calculation is tricky, to say the least, so the rules of thumb above exist; both my stated ratios are on the low side, many people do a bit more ECM than indicated here.
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