[QUOTE=jasonp;373317]The alpha score is a lottery ticket, for SNFS you are stuck with it but for GNFS you can tweak the polynomial to greatly improve alpha. Yes, the better alpha score means that sieve values for the third problem are smaller than sieve values for the first problem by a factor of about e^4.4[/QUOTE]

If there are multiple possible snfs polynomials possible then I suppose this could be the deciding factor. That could save some trial sieving if the difference is as obvious as this.

@jasonp
Thanks, that explains it. Now I just have to update my script to sanity check polys to also call msieve to rate the poly, then terminate without doing anything significant.

@henryzz
If there are multiple SNFS polys they are usually different degree. And E-scores don't compare for polys of different degree. So it may not help much unless the candidates are the same degree.

Chris

[QUOTE=chris2be8;373361]@jasonp
@henryzz
If there are multiple SNFS polys they are usually different degree. And E-scores don't compare for polys of different degree. So it may not help much unless the candidates are the same degree.

Chris[/QUOTE]

I think Henry's point was to look at the alphas of the SNFS options, as opposed to the E-scores. I think trial sieving is still the better choice if there is any doubt which is better!

I'm working to factor 7211^59-1 with SNFS. Just in case anyone else is about to start work on it.

Is there a better place to keep track of who is working on OPNs? Or somewhere else I should look?

Chris

I think here is the best place to check. I am not aware of much current activity. There is some low level ECM on low impact targets and some high level ECM on very high impact targets. 7211^59-1 shows up on Pascal's Most Wanted list, so it's factorization will be useful. Pascal's method of bypassing roadblocks requires looking at chains from "all small bases," so this number with no known factors will often trigger an additional level of bypass operations.

What I'm doing is working through Pascal's Most Wanted list in order of weight/(estimated time to factor). I'll stop when I get to 6115909044841454629^17-1 since that would take me 20-30 years. Just doing the ones before that will take about 3 months so if anyone wants to help by doing something around SNFS 230 just ask.

Chris

[QUOTE=chris2be8;375357]I'll stop when I get to 6115909044841454629^17-1 since that would take me 20-30 years.[/QUOTE]

That's the infamous Phi_17(Phi_19(11)). Everybody that looks at OPN factor chains has wanted that factorization for over a decade. It's had a lot of ECM, so it will probably hold out until Moore's Law brings it into SNFS range, unless an algorithmic improvement shows up sooner. It's tempting to think the nested Phi should help, but the only case I know where that helps is when the inner phi mod the outer phi is "-1" (such as Phi_3(Phi_5(x)) and Phi_5(Phi_19(x))).

I've been giving yoyo@home the smallest numbers on that list, alternating with some of the earliest composites in factor chains. Most Wanted numbers through C214 are presently queued (at least at the time I queued them - factoring numbers on this list sometimes causes the list to change).

[QUOTE=wblipp;375359]That's the infamous Phi_17(Phi_19(11)). Everybody that looks at OPN factor chains has wanted that factorization for over a decade. It's had a lot of ECM, so it will probably hold out until Moore's Law brings it into SNFS range, unless an algorithmic improvement shows up sooner. It's tempting to think the nested Phi should help, but the only case I know where that helps is when the inner phi mod the outer phi is "-1" (such as Phi_3(Phi_5(x)) and Phi_5(Phi_19(x))).

I've been giving yoyo@home the smallest numbers on that list, alternating with some of the earliest composites in factor chains. Most Wanted numbers through C214 are presently queued (at least at the time I queued them - factoring numbers on this list sometimes causes the list to change).[/QUOTE]

Judging purely by size it is about the same difficulty as 2^1061-1 which was done by snfs. Unfortunately it is either a quartic with a large leading coefficient or a sextic with 18/17 of the difficulty. That is assuming that the nested phi doesn't give a better polynomial.
If the number is that critical then I would suggest making a case to nfs@home. At least the ecm level should be brought to a good level for snfs if it isn't already.

[QUOTE=henryzz;375368]Judging purely by size it is about the same difficulty as 2^1061-1 which was done by snfs. Unfortunately it is either a quartic with a large leading coefficient or a sextic with 18/17 of the difficulty. That is assuming that the nested phi doesn't give a better polynomial.
If the number is that critical then I would suggest making a case to nfs@home. At least the ecm level should be brought to a good level for snfs if it isn't already.[/QUOTE]

Another alternative for that size number might be an octic from the halving degree trick. That would be 16/17 of the size.

[QUOTE=henryzz;375379]Another alternative for that size number might be an octic from the halving degree trick. That would be 16/17 of the size.[/QUOTE]

Yes, I was looking into this a couple months ago before I moved. I can't find my notes now.

You end up with a monic and a skew of 1.0 which are both desirable. I seem to recall it sieved better on the algebraic side though. The base has to be "large enough" before this option reaps any benefits. (I think SNFS 220-230 or larger??)

[QUOTE=RichD;375416]Yes, I was looking into this a couple months ago before I moved. I can't find my notes now.

You end up with a monic and a skew of 1.0 which are both desirable. I seem to recall it sieved better on the algebraic side though. The base has to be "large enough" before this option reaps any benefits. (I think SNFS 220-230 or larger??)[/QUOTE]

I have done some trial sieving(with poor parameters). The octic is by far the fastest of the polynomials for 6115909044841454629^17-1. It sieves slightly slower than the obvious sextic for 2^1061-1. This factorization is very possible for [EMAIL="nfs@home. The"]nfs@home. The[/EMAIL] algebraic slide is better.