Kevin Acres wrote:

I'm currently testing out a new algorithm for finding factors of

composite Mersenne numbers.

New algorithms are welcome, of course, but any that are used for

finding factors of Mersenne numbers that don't take advantage of the

restricted form of Mersenne numbers in every way known is likely to be

considerably slower than existing methods.

Two numbers that I am testing the algorithm on are 2^83 -1 and

2^47777783 -1.

Others have already mentioned the factors in my data and one that

isn't (the largest of the latter Mersenne), but you (and others on the

list) might like to know that I maintain a large database of

information about all Mersenne numbers (including those with a

composite exponent). Part of the data is on my web site, but I don't

have enough web-accessible disk space for all of it, so feel free to

send me direct queries about specific numbers that aren't on the web

site.

Currently I'm only able to test about one factor a second on my

2.8GHz Pentium, so next I need to be able to sieve numbers before I

put them through the software.

Sieving is also used by the fastest known programs, notably George

Woltman's Prime95.

Also, if anyone has any idea about how long it should take to test

a potential divisor for numbers at the 2^47777783 -1 range then I

would be interested to hear.

For programs that take advantage of the form of Mersenne numbers and

the restrictions on their factors, the time for a single potential

divisor is in the microseconds on a fairly modern CPU until the

Mersenne exponent itself gets larger than 31 bits (2^31) or so and

probably a ways past that.

Ignacio Larrosa Canestro <

ilarrosa@...> writes:

Also for k = 4*909957, 2*4*909957*47777783 + 1 is a factor of

2^47777783 -1. No others factos with k <= 4*10^6.

Thanks for the new factor. Was this last search restricted to trial

factors that are 1 modulo 8 ? I try to record how far trial factoring

has been done as well as any factors found.

Will

http://www.garlic.com/~wedgingt/mersenne.html