Which number will be next after 2^713-1???

[andi314]

Which number will be next after 2^713-1 ???

Will it also be a mersenne number???
Thanks for your answer

ps: it woud be nice if the participants could select which number should be factored next!!

[jocelynl]

ps: it woud be nice if the participants could select which number should be factored next!!

It would be nice so we could coordinate the effort with ECM work prior to NFS work. We might eliminate candidate before the big crunch.


Joss

[smh]

It would be nice so we could coordinate the effort with ECM work prior to NFS work. We might eliminate candidate before the big crunch.

Especially when a number like M811 is going to be tried anytime soon.

According to http://www.mersenne.org/ecmm.htm this number could use a lot more ECM to bring it to the P50 level, and with a year or more sieving, it might be worth to spend some more time and run a few curves with B1=110M

[Wacky]

Rest assured that we will not start sieving on any number that has not already received "enough" searching by ECM and other methods to be reasonably sure that there are not any small (eg 50 digit) unknown factors. There are plenty of candidates that have been adequately screened.

If you would like for us to consider factoring a number such as M811 that has not already received adequate preliminary searching, you might wish to address that problem.

[xilman]

Originally Posted by andi314

Which number will be next after 2^713-1 ???

Will it also be a mersenne number???
Thanks for your answer

ps: it woud be nice if the participants could select which number should be factored next!!

No-one in this thread has yet answered the principal question.

A few days ago I created the project files for 2,757-.c213, aka the 213-digit cofactor of M757. So it is a Mersenne number

It has had a good amount of ECM work done on it, according to George Woltman and Paul Zimmermann's tables. It seems quite likely that there are no factors under 50 digits and very unlikely that there are any under 45 though neither can be ruled out. Trial sieving has shown that it will be slightly harder to sieve than 10,227-. The post-processing should be intrinsically about as hard as for 10,227- but it should be easier in practice as we have learned some valuable lessons in post-processing from that number.

To answer the supplemental (followers of Prime Minister's question time in the House of Commons will know what that means) participants are always welcome to suggest factorizations for NFSNET. We can't guarantee that a project will follow, perhaps because it would be too hard or too easy, but they will certainly be considered. An email to nfsnet-l@nfsnet.org is the best way to suggest a target.


Paul

[xilman]

Originally Posted by Wackerbarth

If you would like for us to consider factoring a number such as M811 that has not already received adequate preliminary searching, you might wish to address that problem.

Addressing that problem can be done quite easily in two ways. In this forum, the politically correct way is to use prime95 to run ECM factoring on M811. There are a number of other good ECM programs available, including my favourite, gmp-ecm, available from Paul Zimmermann at http://www.loria.fr/~zimmerma/records/ecmnet.html.


Paul

[xilman]

Originally Posted by xilman

Addressing that problem can be done quite easily in two ways. In this forum, the politically correct way is to use prime95 to run ECM factoring on M811.

I started running ECM at B1=11M on M811. Each curve is taking under 6 minutes, so it won't be long until this B1 is completed and we can think about doing b1=44M.

Paul

[hyh1048576]

Originally Posted by xilman

I started running ECM at B1=11M on M811. Each curve is taking under 6 minutes, so it won't be long until this B1 is completed and we can think about doing b1=44M.

Paul

Emmm......So fast !!!!!!What's your CPU?

[xilman]

Originally Posted by "hyh1048576

Emmm......So fast !!!!!!What's your CPU?

A 2.53GHz P4.


Paul

[wblipp]

2^713-1 reached the target of 43 million relations. The server is now handing out assignments for 2^757-1.

[Wacky]

2^713-1 reached the target of 43 million relations. The server is now handing out assignments for 2^757-1.

That is generally true. However, the revised target is 43.7 million and only the MSRC pool has switched. The Longhorn pool still has a few assignments to give out before it switches. That should happen this evening.