On 12 Jun 00, at 23:20, Eric Hahn wrote:
> I was wondering if it was common practice (ie: the norm) for
> P-1 to take the product of two or more factors when giving out
> a found factor, if two of more factors are found?
I don't know about "common practice", but P-1 uses GCD to find the
factor. Consequently this factor may indeed be compound, unless extra
steps are taken to eliminate this possibility.
>
> To clarify, I was curious about how P-1 would indicate more
> than one factor being found. So, I took M113 and fed it into
> Prime95 with the bounds of B1=200, B2=20000. Prime95 notified
> me that P-1 had found a factor in Stage #1, and that the factor
> was 9734174361238150513. This factors out to 3391 * 23279 *
> 65993 * 1868569, all of which are known factors of M113.
True enough.
However, if P-1 finds a factor with P bits, and trial factoring to T
bits has already been done without finding any factor, then the
factor found by P-1 _must_ be prime unless P > 2T. (For the purposes
of Prime95, this situation is _most_ unlikely ever to occur,
therefore it seems reasonable to avoid the extra complications.)
If P-1 does find a factor which is compound, then running P-1 again
with smaller limits will eventually recover a smaller factor. These
extra runs will obviously take less time than the original
"discovery" run. Also, finding _any_ factor is sufficient to
eliminate an exponent as a Mersenne prime candidate, so decomposing
the factor found into its prime constituents is not neccessary if P-1
is being run purely for this reason.
Regards
Brian Beesley
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