Choosing the best polynomial

[VBCurtis]

Originally Posted by Batalov

The c212 is the cofactor of 10^770+1 - here. It could be fun to improve on Greg's polynomial, whose parameters are listed above: e 5.467e-16 but don't try to compare it to the 6th degree directly by value. Let's just try to get the best possible 6th degree poly: between them, they can be roughly compared by e value, but let's try to get several top contenders.

The c210 that OP is working on is one of the RSAs, I think?

This is the first search I've done with the individual np1-nps-npr controls; I've never factored anything bigger than 145 digits before. Please comment on any parameters I've messed up- I did a series of 5-10 min trial runs to get the hit-rates I wanted. I started coeff at 1e6.
I set the stage 1 norm to 4e25, resulting in 30-50 hits per minute.
I set the stage 2 norm to 7e26, resulting in 5-10 hits per hour.
I plan to let root optimization run on the entire list of 100-200 daily nps hits, with min e-value set to 3e-16.
After one hour with these parameters, my best find is 3.35 e-16 with a half-dozen polys above 3e-16. I'll update as better finds turn up.
-Curtis

[VBCurtis]

Originally Posted by wombatman

You are correct--I just went with one of the ones that hadn't (at least, not that I can find) been factored yet. And I think you're right about the low coefficients not being very useful. I'm thinking I'll move up to higher coefficients starting tonight.

I would also be interested in doing some polynomial searching for 6th degree. I have a GTX 570 that can run pretty much uninterrupted.

Edit: Also, I'm noticing in trying to run the polynomial selection step with '-nps' that I'm getting "expand failed" for every result. That seems a bit unusual, given that I've got ~700MB worth of potential starting factors. Any ideas what might be wrong?

I got that too- nps assumes degree 5, so you have to leave "polydegree=6" in the nps command.

[wombatman]

Should have known I was missing something that obvious. Thanks!

[VBCurtis]

Originally Posted by wombatman

Should have known I was missing something that obvious. Thanks!

This is all new to me, too- I was just lucky to think of one idea before asking the very same question here.

I can say that when I made the stage 1 norm VERY restrictive, the search got much faster (measured by time per coeff). I think the screen/disk write take up lots of cycles that can be better spent searching. Try a few settings for stage1_norm; for me, reducing the norm far enough to cut hits to sometimes none for a coeff but usually 2-8 per coeff has resulted in a huge speed improvement.

[wombatman]

That makes a lot of sense. I'm fortunate to have an SSD right now, so read/write might be as much of an issue, but it's probably a good idea to restrict the Stage 1 norm a bit anyway to be more selective and get higher quality polynomials.

[VBCurtis]

4 hours of searching, multiple polys from a single coeff above 5e-16.
Best so far is 5.07e-16. stage 2 norm was 1.41e26.
I've had 6 hits so far with stage 2 below 5e26 on a 460M card.

[wombatman]

I'm trying a stage 1 norm of 9e25. I'll probably let it run overnight, then do the nps during the day. From there I'll grab the top hundred or so and do npr and see how it turns out!

[Batalov]

As far as I remember from the B200 simulated sieving, for equal E values, 6th degree poly could be already better.

So, this is nice progress! And these are only first hits - if the whole week is spent on these exercises you could find some impressive polynomials.

[VBCurtis]

Dear experts:
Am I missing anything by setting the stage2 norm so strict that I don't need to bother sorting for the top 100? If we discard all but the top 1% anyway, why not just set the norm to collect ~100 a day and save a step?

wombatman-
Thanks for joining me on the degree 6 search for this c212. We have a decent chance between us to find a competitive poly in the 4-5 days we have to get it done, while also adding some data to locate the degree 5-6 transition. My attention span wouldn't last more than 5 days for this, anyway...
-Curtis

[wombatman]

Curtis,

Happy to do it! I'm already up to 35000+ for the coefficient, so it's likely that I'll get through a nice chunk overnight. Hopefully it'll produce some good results!

Ben

[jasonp]

Originally Posted by wombatman

Edit: Also, I'm noticing in trying to run the polynomial selection step with '-nps' that I'm getting "expand failed" for every result. That seems a bit unusual, given that I've got ~700MB worth of potential starting factors. Any ideas what might be wrong?

The 'expand failed' errors occur when the stage 1 hit does not correspond to the N. Either the hit is wrong or N is incorrect (either at stage 1 time or at stage 2 time). EDIT: never mind, issue dealt with above.

Also, even for a really nice graphics card you can probably get higher throughput with just a few threads, not 10. I'd try 2 to start with.

The reason we make the size bound loose is that we don't know how much size we will be sacrificing to get a good root score. The best poly might have a great root score but comparatively mediocre size score. To prevent pruning it by accident, the bounds have to be loose. Once all the size scores are computed, it's very unlikely that you'll find a root score to the 1000th best polynomial that is so good as to unseat the other 999 polynomials in front of it.