On 8 Mar 00, at 20:30, Steinar H. Gunderson wrote:
> On Wed, Mar 08, 2000 at 03:17:31PM -0500, Lucas Wiman wrote:
> >With regards to factoring, if prime finds a factor then it can start on
> >another one more quickly increasing the factors found per time.
>
> I thought it continued factoring (at least to a certain level), to
> get more statistical data?
Up to v18 the factoring ran in 16 streams; if it found a factor, it
did the remaining streams up to the factor found so as to be sure the
factor found was the smallest. (The size of the _smallest_ factor
being of interest to at least some mathematicians).
v19 works slightly differently in that it works in single-bit layers
instead of from bottom to top of the whole range. This saves a
considerable amount of time when, as commonly happens, a factor is
found at the low end of a later stream.
Note that, if trial factoring fails but a factor is found using P-1,
ECM or some other advanced method, we _don't_ know that the factor we
found is the smallest (though this is probable) - we do however know
that there are no factors up to the trial factoring limit. Using
advanced factoring techniques, the only sure way we can find the
smallest factor is to completely factorize the number. Unfortunately
this is not always feasible, even for some Mersenne numbers with
fairly small exponents.
Regards
Brian Beesley
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