Is there any information on P+1/P-1 for the numbers. I assume that they have been run up 2-3 levels higher than ECM, but does anyone know for certain?

For those composites not done at the 40 digit level (and not reserved), I will do the curves for B1=3e6. I will do P+1/P-1 up to 11e7.

There is some P-1 information on Paul Zimmerman's page of composites

[url]http://webloria.loria.fr/~zimmerma/records/c120-355[/url]

But I suspect it is incomplete as well.

I still don't have a response from Bob about whether his comment applies to the 12- tables as well.

[QUOTE=rogue]For those composites not done at the 40 digit level (and not reserved), I will do the curves for B1=3e6. I will do P+1/P-1 up to 11e7.[/QUOTE]
I suggest that you delay the P \pm 1 runs until you have checked with Alex Kruppa (akruppa on the forum) and/or Paul Zimmermann. I believe that either or both of them have spent a lot of effort running P \pm 1 on the Cunningham tables.


Paul

Paul Z, mostly. I did a bit of P-1 on Fibonacci/Lucas numbers (that was before I learned about the 23/11 trick for P+1).

I sent an email to Paul asking him about his P+-1 effort, I'll post his reply here as soon as I get it. I seem to remember he did a P-1 pass at B1=1G, it's probably better to stick with ECM for a while. I'd start with B1=11M, it does a good job finding ~40 digit factors if any should remain and is more efficient at finding ~p45 of which there should be several left in the tables.

Alex

Here is his reply:

[QUOTE]I did a complete P-1 pass at B1=1e9, B2=518473376255, x^120,
and I'm currently doing B1=4e9, B2=3737307598223, x^120.

For P+1, I did 3 partials runs at B1=1e9, B2=1392010951306, up to c140.

When the new gmp-ecm is released, it would make sense to start new runs
at B1=1e10.

Paul[/QUOTE]


Alex

Two things:

1) What is the 23/11 trick?
2) When is the new GMP-ECM due?


--
Cheers,
Jes

When factoring the Lucas number L_n or the Fibonacci number F_n, choosing -x0 23/11 for the P+1 method always gives group order divisible by n. I.e. you get order p-1 for p == +-1 (mod 10) and p+1 for p == +-3 (mod 10).

We're currently busy finishing the code. There was a major last-minute change, a split into library and app so that Pari, Magma and others can use the ECM code. This requires rather a lot of changes in the sources. I guess the answer is "real soon now".

Alex

I had started this only to take a break from a different ECM project which I've had little success with. I'll do the curves at B1=3e6 since it should only take a few weeks. If I continue after that I will take one of the remaining composites and focus ECM efforts on it.

I also look forward to the next release of GMP-ECM. Alex, are there any features of the next release of GMP-ECM that ECMNet should support?

(This is getting seriously off-topic)

Jim Fougeron has written an expression parser for gmp-ecm, i.e. you can now say

echo "(2^761-1)/4567/6089/738686421813192728921171408273447" | ./ecm 44e6

The new version also computes the expected number of curves and expected time for finding a factor of different sizes. And the code will be split into a library with the actual factoring routines, and an application, however the gmp-ecm app still looks and feels the same.

Other than that, I think it was mostly speedups in stage 2.

It's probably primarily the expression parser that could be of interest for the ECMNet client.

Alex

[quote]I think it was mostly speedups in stage 2.[/quote]

Will B2 change (when not specified and considering constant B1)?
I think Bob said/proved(?) it is optimal for both stages to take about equal time...

Oops, another reply I forgot! :( Sorry.

Actually, it looks as if we'll just leave the default B2 the same. We did some experimenting and the default usually gave close to optimal expected time to find factors. The optimal B2/B1 ratio depends on all sorts of things, such as type of cpu, size of input number (far more O(n) operations in stage 2) and type of number (base-2 much faster in stage 1). Anyone who wants to squeeze the last drop of performance out of ecm can do so relatively comfortably by trying different parameters now that gmp-ecm prints expected times to find factors. And the old default B2 still looks good for typical jobs.

Alex

I've done the required 2440 curves with ECM 6 for those not done to the 40 digit level. I'll do P+1 and P-1 at B1=1e10 and then start ECM at B1=11e6 for all except 12,239- and 12,297-.

P-1 crashed due to a memory issue. I have 2 GB RAM, which I thought should be enough. I am using bash on OS X, so I will try to increase the limits and see if that helps.

BTW, I have not reported my curves to anybody.

I finished P-1 at 1e10 (using -k 20). I will start P+1 at 1e10 after I return from vacation.