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Old 2015-06-12, 17:41   #111
philmoore
 
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Quote:
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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Old 2015-06-13, 03:18   #112
Madpoo
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Quote:
Originally Posted by R.D. Silverman View Post
A better question:

Why would you want to? If people would ever bother to READ my ECM paper they might actually learn something.

Running P-1 is equivalent to running a single ECM curve. If it is known a priori that P-1 is divisible by (say) q, then one
simply reduces the size of the factor you are looking for by log(q) and then chooses the ECM parameters appropriately
for running just one curve.

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 @&*!&*#%^ fascination with running P-1 to high limits is simply WRONG-HEADED. [unless of course, ECM is not
available]
A colorful reply as always.

I only asked because I was lurking on the forum where they were talking about the 332M-333M range (or whatever...I'm sure that's not exactly right). The concept of factoring some grandfathered LL assignments in that range came up, and I'd noted that quite a few of those assignments hadn't had any P-1 done at all. They were going to do some extra TF work on them up to 79 bits or something and I just wondered about the feasibility of doing the P-1 work on some of my systems with lots of RAM.

I have zero built-in idea of how long it takes to run P-1 work at all in that range, for any B1/B2 values, so I thought I'd first see if GMP-ECM would be advantageous.
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