Factoring M7777171
 

I'd like to factor [M]7777171[/M], 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?

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

[QUOTE=petrw1;527695]Yes. You've done a lot of TF AND PM1.[/QUOTE]

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.

[url]https://www.mersenne.org/report_ecm/?txt=0&ecmnof_lo=7777171&ecmnof_hi=2500&ecm_lo=1&ecm_hi=15000[/url]

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.

[QUOTE=petrw1;527697]I'd start with the lowest.: 50,000 (B2= 10x B1).
Run as many curves as you like.[/QUOTE]

Maybe B2 = 100 × B1 is more suitable?

[QUOTE=GP2;527698]Maybe B2 = 100 × B1 is more suitable?[/QUOTE]

Oops my mistake.

Yes 100X

Factoring M20825573
 

I'm doing something similiar at the moment: Trying to find a factor for [url=https://www.mersenne.org/report_exponent/?exp_lo=20825573&exp_hi=&full=1&ecmhist=1]M20825573[/url] 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 :*(

[QUOTE=gLauss;556586]I'm doing something similiar at the moment: Trying to find a factor for [url=https://www.mersenne.org/report_exponent/?exp_lo=20825573&exp_hi=&full=1&ecmhist=1]M20825573[/url] 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 :*([/QUOTE]

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.

[QUOTE=masser;556591]That's a lot of work to dedicate to one exponent. A quixotic quest, but one that I hope is fruitful for you.[/QUOTE]
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 [url=https://www.mersenne.org/report_ll/?exp_lo=2&exp_hi=999999999&exp_date=&end_date=&user_only=1&user_id=gLauss&dispdate=1&B1=]lifetime statistic[/url]. Previously there was also [url=https://www.mersenne.org/report_exponent/?exp_lo=21717953&full=1]M21717953[/url] 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.

[QUOTE=masser;556591]A quixotic quest, but one that I hope is fruitful for you.[/QUOTE]
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.

[QUOTE=gLauss;560320]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.[/QUOTE]

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).

[QUOTE=VBCurtis;560337]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).[/QUOTE]
I know. If you take a look, I did put more total effort into B1=250k curves than B1=50k. However, I ran only a few of them. According to the [URL="https://www.mersenne.org/report_ecm/?txt=0&ecmnof_lo=20825573&ecmnof_hi=20825573&ecm_lo=1&ecm_hi=15000"]report_ecm[/URL], what I did in total is equivalent to 170 curves of t25. I think it is kind of unlikely for this number to have a factor less than 30 digits because of the very large P-1 bounds, too. And t35 is way beyond what I'm willing to spend on this stupid task :wink:

TFed to 78bits
 

I TFed the M20825573 to 78 bits, 79 is on the way. So far, no factor.

[QUOTE=Viliam Furik;560392]I TFed the M20825573 to 78 bits, 79 is on the way. So far, no factor.[/QUOTE]
Hihi, thanks for that! My laptop GPU is too crappy for this bitlevels. However, I assume your chances for success are quite low because of the large P-1 and the ECM curves I already ran. I won't continue on this number for now, back to boring PRP testing...

Factoring M19491001
 

I'd like to factor [M]M19491001[/M], just because the way it looks.
I did TF to 2^75 and dozens of ECM curves because I noticed that a prior P-1 has been done. So far, no factor was found.
Should I do P+1 or try P-1 with larger bounds?

I wouldn't do another P-1 until I'd finished the B1 = 50k ECM level. I'd do a few curves at B1=250k also before repeating P-1.

If I did another P-1. I'd increase the bounds by 10x or so. You have to re-do all the work of the previous P-1, so increasing bounds just a little bit means you're mostly wasting work (and thus that there are better ways to use those cycles).

P+1 seems like a reasonable choice- again, pick big bounds- big enough that you won't be tempted to try even-bigger ones later. How big to pick depends quite a bit on how much effort you want to spend on this factoring effort- completing the B1=50k level is non-trivial, but completing the B1=250k level is a pretty serious effort. If you intend to go that far, choose bigger P+1 (and maybe P-1) bounds than would normally be reasonable.

[QUOTE=Zhangrc;591951]I'd like to factor [M]M19491001[/M], just because the way it looks.
I did TF to 2^75 and dozens of ECM curves because I noticed that a prior P-1 has been done. So far, no factor was found.
Should I do P+1 or try P-1 with larger bounds?[/QUOTE]

I wanted to go do TF on my new RTX 3080, but it seems I need a new version of mfaktc, compiled for CUDA runtime v11.40. So I'll do it on my RTX 2080Ti. 75 to 78 bits. See you tomorrow.

[QUOTE=VBCurtis;591970]If I did another P-1. I'd increase the bounds by 10x or so. You have to re-do all the work of the previous P-1, so increasing bounds just a little bit means you're mostly wasting work (and thus that there are better ways to use those cycles).

P+1 seems like a reasonable choice- again, pick big bounds- big enough that you won't be tempted to try even-bigger ones later.[/QUOTE]
As I am stuck with "my number" and don't want to waste full t30 level, I will now run a P-1 with B1=15M and then two P+1 with B1=7.5M for 19491001. Let's see if I get lucky...

[QUOTE=gLauss;593896]As I am stuck with "my number" and don't want to waste full t30 level, I will now run a P-1 with B1=15M and then two P+1 with B1=7.5M for 19491001. Let's see if I get lucky...[/QUOTE]

Stop! Investigate v30.8. Wait for a future version before trying P+1.

I gave it some more P-1, but still it resists...

[url]https://www.mersenne.ca/exponent/7777171[/url]

[QUOTE=gLauss;593896]As I am stuck with "my number" and don't want to waste full t30 level, I will now run a P-1 with B1=15M and then two P+1 with B1=7.5M for 19491001. Let's see if I get lucky...[/QUOTE]

Why so small? For the time you've put into trial factoring, why not put a core-week or more into P-1?

Using 30.8 with a bunch of memory (16GB or more), I imagine B1 = 50M with the big B2 from 30.8 will give you something like 7-8% chance to find a factor. Again, don't do a calculation that you'll be tempted to redo later. Do P-1 once, so big you won't ever consider repeating it.

[QUOTE=VBCurtis;604651] Again, don't do a calculation that you'll be tempted to redo later. Do P-1 once, so big you won't ever consider repeating it.[/QUOTE]
+1