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Old 2015-06-12, 17:41   #111
philmoore's Avatar
Sep 2002
Tracktown, U.S.A.

3·373 Posts

Originally Posted by R.D. Silverman View Post
However, it is clear that rather than run a SINGLE ECM curve to high limits (which is what P-1 to high limits accomplishes)
it is much better to run MANY ECM curves with lower limits.
This is what I thought, too, but Ernst and I did some calculations a few years back that indicated it was generally worthwhile to spend on the order of 5-6% or so of your total ECM effort on Mersenne or Fermat numbers to run P-1 to high limits. I was surprised that the percentage was that high, but the fact that some factors of P-1 were already known boosted the success probability considerably. I would guess that for generic numbers this percentage would be lower.
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