Nathan Russell wrote:
>
> Is it (at least) theoretically possible that some larger factors are
> unfindable with ECM due to the limited number of sigma producable by
> George's random number generator?
>
> Nathan
I dont think this is a problem. Limits in the RNG would only mean
problems if it causes many sigmas to be duplicated and the chance of
getting a fresh, yet untested sigma decreases substantially. The RNG in
Prime95 produces up to 16-digit numbers, and if the number of curves you
try stays well below the square root of the number of possible values
the RNG produces, then the chance of a duplicate sigma is negligible.
For Prime95, if you test less than 10^8 curves on one number, you're
safe. If you have to test more than a hundred million curves, then ECM
is not the proper algorithm for finding that particular factor, anyways.
Ciao,
Alex.
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