Quote:
Originally Posted by R.D. Silverman
However, it is clear that rather than run a SINGLE ECM curve to high limits (which is what P1 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 56% or so of your total ECM effort on Mersenne or Fermat numbers to run P1 to high limits. I was surprised that the percentage was that high, but the fact that some factors of P1 were already known boosted the success probability considerably. I would guess that for generic numbers this percentage would be lower.