Factoring M7777171

[mrh]

I'd like to factor 7777171, for no particular reason, other than I like the way it looks.
I threw some time at it, but it resists. What do you think would be best to try next? Just a bunch of ECM curves?

[petrw1]

Yes. You've done a lot of TF AND PM1.

[mrh]

Originally Posted by petrw1

Yes. You've done a lot of TF AND PM1.

Thanks! How best to choose B1,B2? I'm not sure I understand the math for how to pick those based on PM1 work already done.

[petrw1]

https://www.mersenne.org/report_ecm/...1&ecm_hi=15000

Tells you how much is done/ remaining at each digit level.
I'd start with the lowest.: 50,000 (B2= 10x B1).
Run as many curves as you like.

[GP2]

Originally Posted by petrw1

I'd start with the lowest.: 50,000 (B2= 10x B1).
Run as many curves as you like.

Maybe B2 = 100 × B1 is more suitable?

[petrw1]

Originally Posted by GP2

Maybe B2 = 100 × B1 is more suitable?

Oops my mistake.

Yes 100X

[gLauss]

I'm doing something similiar at the moment: Trying to find a factor for M20825573 in order to make up for my bad DC 11 years ago (which was one of my very first tests!).
I assume ECM is the way to go from now? Or should I increase P-1 again? Currently I'm running another ECM curve with B1=250000, B2=100*B1 and TF up to 75bits with mfaktc. However they take around 6 hours one, this is so long ... I might never find a factor :*(

[masser]

Originally Posted by gLauss

I'm doing something similiar at the moment: Trying to find a factor for M20825573 in order to make up for my bad DC 11 years ago (which was one of my very first tests!).
I assume ECM is the way to go from now? Or should I increase P-1 again? Currently I'm running another ECM curve with B1=250000, B2=100*B1 and TF up to 75bits with mfaktc. However they take around 6 hours one, this is so long ... I might never find a factor :*(

Here is my suggestion:

1) Finish the TF to 75 bits - you'll have then put about 300 GPU GhzDays into TF.
2) One more P-1 attempt: B1 = 7,000,000, B2 = 200,000,000.
3) Complete the recommended set of 280 ECM curves at B1=50,000, B2 = 5,000,000.

Steps 2 and 3 are about 300 CPU GhzDays.

Note that each ECM curve gives you an independent chance of finding a factor. There's no point in increasing B1,B2 for ECM until you complete the recommended set of curves at the 25 digit level.

I estimate that steps 2 and 3 represent about 2 weeks of work for my Haswell i5 cpu. That's a lot of work to dedicate to one exponent. A quixotic quest, but one that I hope is fruitful for you.

[gLauss]

Originally Posted by masser

That's a lot of work to dedicate to one exponent. A quixotic quest, but one that I hope is fruitful for you.

Thanks, I know it's not useful and might sound strange, but I like the thrill of throwing a few ECM curves in-between a long boring PRP assignment. One can get a result after a short amount of time and you always have a - albeit little - chance of "success".

Also, it is the only exponent showing up as "bad" in my lifetime statistic. Previously there was also M21717953 in it, which I was able to move to the category "Factor found later" with P-1.

I probably won't do complete t25, but maybe 100 curves or so.

[gLauss]

Originally Posted by masser

A quixotic quest, but one that I hope is fruitful for you.

This stupid number doesn't want to reveal its factors, so my quest will stop after a lot of TF and P-1 and half of t25.

[VBCurtis]

Originally Posted by gLauss

This stupid number doesn't want to reveal its factors, so my quest will stop after a lot of TF and P-1 and half of t25.

Consider how many bits is equivalent to 25 digits. If you TF to, say, 75 or 76, you've already done 80% or so of a t25. Any ECM should be done with B1 larger than 50k after TF to 75+.

Curves at B1=50k could still find a factor, but B1=250k will have more than 5x the chance per curve (while taking about 5x as long, so odds-per-day improve).