On 27 Oct 99, at 17:23, Eric Hahn wrote:
>
> I'm looking for program(s) capable of trial-factoring
> prime exponent Mersenne numbers (using 2kp+1) meeting
> the following requirements:
>
> 1) Capable of trial-factoring any exponent > 1
> (at least to some considerably large number,
> say 1 trillion?)
>
> As I recall, Brian [Beesley] mentioned something once
> about having a program that could test an exponent
> of an arbitrary size... Brian??
Umm - I did write a "quick hack" which could handle exponents up to
1/6 * 2^32, but I never got round to putting a usable front end on
it. Actually I thought that the release of the Prime95 v19 beta made
it pretty redundant, and I was having a hard time with kidney stones.
>
> 2) Capable of testing a factor of any size.
> (even over the 2^76 limit of Prime95).
>
> I just know somebody is going to have to mention the
> time involved in testing factors of such a large size.
> Let me just say, I realize *exactly* how much time
> would be required...
>
> 3) Capable of trial-factoring a range of k's.
> (example: from k=1000 to k=2500)
Well, I'm prepared to have a go. Could we tighten up the spec a bit?
(a) There's also been some interest in something else that Prime95
doesn't do - trial factoring 2^p+1.
(b) I assume we're only interested in 2kp+1 factors. This means that
we will miss any factors which are not of this form. (Applies to
Mersenne numbers with composite exponents, and all 2^p+1 numbers -
though I believe that the "missed" exponents are easy to derive
analytically.)
(c) I presume we're looking for a program optimized for IA32
architecture. The mersfac* programs are available but are unlikely to
be optimally efficient on any particular hardware platform.
Given that, I suggest limits on exponent < 2^62 and on factor < 2^95
(these are convenient for the architecture).
It's probably sensible to go for an application which runs in a "DOS
box" rather than a proper windowed application. This makes it a bit
easier (for me) to write & also makes deriving a linux variant almost
trivial. (Does anyone know for sure whether or not there's a DOS box
in "Millenium"? I heard a nasty rumour...)
If we can agree on that, then I have a basis to begin coding. Will
certainly take a month or two to produce even a pre-pre-release as I
am very pushed for time at the moment.
Regards
Brian Beesley
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