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Old 2020-07-30, 10:49   #6
keisentraut
 
Jul 2020

1010 Posts
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Thanks for your feedback. My assumption was that a single ECM curve is equally likely to find a factor like a P-1 run, but for P-1 computations are easier and you additionally gain extra "B1" because you can multiply the p of 2*k*p+1 Mersenne factors. Therefore, if we already did a P-1 test with B1=2000000, the chance that a new ECM curve with B1=50000 will find something is probably very unlikely. And that's what I have experienced, never found a factor with this work type so far (with P-1, quite a few). But at least it seems possible, given kruoli's examples!
Quote:
Originally Posted by axn View Post
Even if we jump directly to 250K, you're saving 50/600 or about 8%. Hardly worth the complications in adding more rules to the server.
8% seems a lot and it shouldn't be hard to implement "start with higher B1" :) But yes, it is not saving much, an two stage ECM curve with B1=50000 for the 2M range takes a few minutes on my laptop.
Quote:
Originally Posted by axn View Post
Also, it is not like 50k ECM will magically stop at 25 digits. There is a small chance that it can find bigger factors (maybe as big as mid 30 digits).
I know, but this is unlikely and we would find the factor with a larger curve, too. It's quite hard to optimize the ECM bounds given P-1/trial factorization bounds, even if you have a M.Sc. in math :)

Last fiddled with by keisentraut on 2020-07-30 at 10:56
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