new project ?

[R.D. Silverman]

Originally Posted by Wacky

The last of the relations for 11,206+ just arrived at the Warehouse for post-processing.

You may now safely delete the factor base for this project from your projects/ folder.

Thanks to all who helped in the sieving.

Richard

This will be a nice result (Cunningham first hole). We now have a backlog
of 4 numbers waiting for the lin. algebra to complete! Sieving capability
is outpacing the LA.

[Wacky]

Originally Posted by Bob Silverman

We now have a backlog of 4 numbers waiting for the lin. algebra to complete! Sieving capability is outpacing the LA.

Don't worry, Bob.

M811 gave us much more difficulty than we had anticipated. Hopefully, it will finish this weekend. And parallel to that effort, I have completed over 80% of the LA for 10,223+ on a single processor of my G5. I expect it to finish mid month.

11,206+ was an "easy" sieving requiring only a couple of weeks of hard effort. To make up for that, we have chosen 3,491+ because it is about 4 times as difficult and will give us an opportunity to "catch up" on the LA.

If our goal is "throughput" rather than "time-to-market", we should ALWAYS have something waiting to start the LA. By the end of July, that should not be the case.

Paul's cluster can sieve, and often has done so, but that is not the "best use" of the resource. (Most of the sievers could not do the LA) IMHO, we should use each resource for those tasks for which it is best suited.

[junky]

i've a question: where do ya guys take these numbers from ?

i saw they're not all Cunningham most wanted ( just the 206), but why not pick all the most wanted number to sieve ?

I'd like to know more about these numbers (which you're picking up), any link ?

Thanks.

[xilman]

Originally Posted by junky

i've a question: where do ya guys take these numbers from ?

i saw they're not all Cunningham most wanted ( just the 206), but why not pick all the most wanted number to sieve ?

I'd like to know more about these numbers (which you're picking up), any link ?

Thanks.

As hinted at by Wacky, the Cunningham Most Wanted and More Wanted numbers are usually too easy for us to do. The sieving phase would take two weeks or less but the other overheads would take longer than that. We would build up a rapidly growing queue of post-processing tasks if we did nothing but MWNs.

Also as hinted, some systems can perform particular tasks but should not, because it's not the best use of available resources. Other groups can factor MWNs in a reasonable time but would find factorizations that we are capable of doing far too challenging. It makes much more sense, IMO, to let those groups work on the MWNs while we do harder things.

As for how we choose numbers, the approach usually goes something like this. If there is a powerful research reason for doing a particular number and no-one else wants to do it, we take it on. This is the main reason why we factored 2^713-1 for Richard Brent, for example. Otherwise, we estimate how much sieving resources we have and how long we would like to use them for a particular project. Then we chose a number which is about that difficult to sieve. We bias it to numbers that have had a fair amount of ECM work done already and to numbers that have few or no known factors, as this gives us a chance at taking the record for the largest penultimate factor.

The complete Cunningham tables are available at Sam Wagstaff's site at http://www.cerias.purdue.edu/homes/ssw/cun/index.html. The same data, somewhat reformated to make the tables easier to parse by programs is available on my web site, http://research.microsoft.com/~pleyl...ngham/main.htm.

Finding other tables of factorizations is left as an exercise


Paul