Brian Beesley wrote:
>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:
>>
>> [...requirements...]
>
>Well, I'm prepared to have a go. Could we tighten up the spec a bit?
Wow!! I was going to post a message with regard to the fact
that it looked like I was going to have write some code to
produce my own program. While the programs that were suggested
are well written, perform their designed functions, etc., they
were either not capable of the tasks required or too slow to
be useful.
Now, look. I even have a volunteer to write some code!! :)
>(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.)
I'm not opposed or take exception to any possible additional
capabilities... It just might require a little extra effort
for the coding.
>(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.
Optimized for IA32 would be beneficial (which processor
architechure runs >80% of PCs?). If possible, the ability
to modify so as to optimize for other architectures would
be a plus, however. One big concern is speed though!
>Given that, I suggest limits on exponent < 2^62 and on factor < 2^95
>(these are convenient for the architecture).
After waking up several nights ago with some pretty *scary*
thoughts, I realized a couple of things.
As such, exponents through 2^62 should do fine. Anything
that might be necessary above 4.6 x 10^18 could probably
be extrapolated (not that I can think of any reason, currently,
that would cause it to be necessary).
Factors, however, would be slightly different. I suppose 2^95
would be acceptable for a base level (or default), especially
if testing an entire bit depth (or a large range of factors).
However, if testing a small and specific range of K, say
K=2^143 to K=2^143+500, it might need to go considerable
higher. I'm willing to make a few sacrifices for this to
be possible...
Admittedly, I'm not "in the loop" regarding the division
of the massive numbers for which I'm talking. I'm sure
somebody is, however (and maybe could explain it).
>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...)
I heard the same nasty rumor... Actually, I've heard several,
including ones about the floppy and Win16 support, among others.
Eric
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