Who will be the next??
 

How long will the search for a factor of 10^227-1 take?? :question:
What will be the next number that will be factorized with NFSNET??
:arrow: Andi314

Re: Who will be the next??
 

[quote="andi314"]How long will the search for a factor of 10^227-1 take? [/quote]

Until it is done! Our initial estimate is that we will need about 82 million relations. At the present rate, the sieving will take another 6 weeks. (But with more participants, the time will be shorter. Hint, hint). After that, there is quite a bit of processing left to be done. But the sievers already will be working on the next project.

Unfortunately, we don't know for sure whether the 82M relations is really the right number. And we won't know until we get there. So we may need a few more or less.

[quote="andi314"]What will be the next number that will be factorized with NFSNET?[/quote]

I expect it to be a number that came up at a recent conference. It happens to be a Mersenne Number that was already "Wanted" by the Cunningham Project.

Re: Who will be the next??
 

[quote="andi314"]How long will the search for a factor of 10^227-1 take?? :question:
What will be the next number that will be factorized with NFSNET??
:arrow: Andi314[/quote]

Um, this number is divisible by 9, right?

Re: Who will be the next??
 

[quote="trif"]Um, this number is divisible by 9, right?[/quote]

We are actually looking for the largest prime factor of the number, not just any factor.

Jeff.

Re: Who will be the next??
 

[quote="Jeff Gilchrist"]
We are actually looking for the largest prime factor of the number, not just any factor. [/quote]

Not [b] just [/b] the largest prime factor. We actually want [b] all [/b] of the prime factors. But, given one large prime factor, it is usually easy to finish the factoring.

[i]What will be the next number that will be factorized with NFSNET?? [/i]

It's by no means certain yet but the front-runner at present is 2^713-1. This is the smallest Mersenne number not yet completely factored. As Richard Wackerbarth said it is a Cunningham Most Wanted Number. At a number theory conference in Banff (Canada, not Scotland) Richard Brent announced that it was the sticking point for his work in searching for primitive trinomials --- which also seems like a good reason to factor this number.


Paul

P.S. I like this guy, so here's an entirely gratuitous banana for you: :banana:

[quote="xilman"][i]What will be the next number that will be factorized with NFSNET?? [/i]

It's by no means certain yet but the front-runner at present is 2^713-1. This is the smallest Mersenne number not yet completely factored.[/quote]

Will Edgington's lowM.txt file shows very little ECM work has been done on this so far. But it seems likely the smallest unfactored Mersenne number has actually had more attention that didn't get reported to Will. Is there someplace else that reports on this?

There are two other sources of ECM work done in addition to the information in Will's file. One is the GIMPS page on:
http://www.mersenne.org/ecm.htm
which has links to two status pages on Cunningham numbers of the forms 2^n+/-1. The first shows that M713 has had 10,600 curves run looking for 45-digit factors and 1006 curves so far looking for 50-digit factors. I think this is mainly curves run with prime95/mprime and may not include curves run with GMP-ECM. The other page is Paul Zimmerman's page at:
http://www.loria.fr/~zimmerma/records/c120-355
which lists the status of a number of Cunningham composites. Under 171 digits, we find listed "2, 713-" and a claim that ecmnet has run enough curves to test it up to 40 digits.

[quote="wblipp"]
Is there someplace else that reports on this?
[/quote]
I report my work to George Woltman who updates http://www.mersenne.org/ecmm.htm . I have recently been doing some work on M713 and a few other small exponents. See also my post at http://www.mersenneforum.org/viewtopic.php?t=678

I also do curves for Woltman, and I am currently running curves at the 44000000 bound. I expect to complete 1000 such curves at the end of the week, and approx 3000 to 4000 curves at the time when the current NFSNET number has been completely sieved. This still leaves a lot of curves which should be done before factoring M713 with NFSNET. Anybody out there who want to help ?

I think that's great, that you and Patrik are doing ECM on possible future NFSNET targets. I've got an old Pentium working on M713 also, but it is only doing 100 or so curves a week. Patrik, can you run second stage using GMP-ECM under windows, or is that something that you have to run under a different operating system?