(Preying for) World Record P-1!

[lisanderke]

I'll post the save files of those exponents that experienced the 100% reporting in this zip archive. If anyone wishes to take a crack at these be my guest . I'm off to bed now.

[SethTro]

Something I've wanted for a long time and now more than ever I think we need is a repository of P-1 save files.

I have a bit of free time to work on this and I think it has several parts

1. Tool to extract current bounds from a save file [90% done MF post, Code]
2. Some extra code to compare two save files [50% done Code]
3. Webpage with status page & download links [20% done see one_line_status]
- I'm happy to write and maintain this for a year or so but ultimately it would be nice if James was willing to add it to their page.
4. Upload new results page
- Something simple like https://primegaps.cloudygo.com/ that can take a new save file and replace the existing file if better
- Automate George's trick to verify factors are found (increase B1 by 1000 and test that stage 1 factors are found)

If people were interested in helping out I'd like to start collecting all known save files for exponents less than say 1M.
If you have a large number of save files and want to help I'd love to hear from you.

[James Heinrich]

Originally Posted by SethTro

could you make the Factor Probability column on the exponent page a link to the prob calculator with the values of that row filled in?

SLIBRSLIB-Done.

[nordi]

Originally Posted by charybdis

M5231 is a good example of a potential huge P-1 factor having already been found by Ryan using ECM.

I would see the positive side here: The fact that this factor was found by ECM shows that no in-depth P-1 was run on this number, and likely other numbers in that range. At least not prior to October 2020, when that factor was discovered.

[Batalov]

Originally Posted by lisanderke

Oh, that did finish the P-1, but it didn't report a factor. Could it be that the save file already knows the 8 factors?

Just in case (because reading this thread is full of surprises, like "oh, he also doesn't know that", "oh, and that too", but surely the attitude is "what is that qualifying for regional/divisional college competition? ...No, I will go straight for the world record" "...Send me to Beijing, right now!")
-->
this is what you are competing against - https://members.loria.fr/PZimmermann...s/Pminus1.html
Stop thinking in bits, like you will find in many vanity threads: "Ah! Look at that factor, it is exceptionally large at 134.47 bits!"
No, 66 digits (or 218 bits) is what you want to beat. Good luck!

[SethTro]

Originally Posted by kruoli

Take the estimated T-Level that is already on your site, then calculate \((\text{T-level})/\log_{10}{2}\). This is your value.
Example: M1277 has an estimated T-Level of 62.878. The analog TF bit level would be 208 or 209 (yes, very high!).

For TF 100% of factors less than 2^67 have been found, and 0% of factors greater than 2^67.
For ECM T-level (say 200 bits) is the point where 50% of factors near that should have been found, at 195 bits maybe 80% should have been found and at 205 maybe 25% have been found.


Spitballing it looks like subtracting one from the log10 T-level converted to a log2 bit level is about the right correction to account for the asymmetry.

[kruoli]

Originally Posted by SethTro

If you have a large number of save files and want to help I'd love to hear from you.

petrw1 and masser gave me tons of files some time ago, but mostly from the <2K project. For these, I was planning something similar to your ideas. But I have not put much work into it yet.

[bur]

Instead, further increasing B1 with every round seems like the best option for now.

I'm not sure I got that right, but is the plan to run consecutive P-1 with increasing bounds on the same exponent? Isn't that a waste of the previous runs? Or does round apply to ranges of larger exponents?

[ATH]

Originally Posted by SethTro

If people were interested in helping out I'd like to start collecting all known save files for exponents less than say 1M.
If you have a large number of save files and want to help I'd love to hear from you.

I have quite a few P+1 save files, are those of interest as well?

[Prime95]

Originally Posted by Batalov

Just in case (because reading this thread is full of surprises, like "oh, he also doesn't know that", "oh, and that too", but surely the attitude is "what is that qualifying for regional/divisional college competition? ...No, I will go straight for the world record" ...

66 digits (or 218 bits) is what you want to beat. Good luck!

I think top 3 is quite likely (no I didn't do any calculations to back that up!). If we take all Mersennes below 100K to B1=10^9, B2=10^13 (or better) and consider that we get 5 free digits, that's a lot of chances to get lucky.

Even if a record is not found, any new factors are most welcome. One could even lead to a newly fully factored Mersenne.

IMO, that makes the effort worthwhile.

[bur]

Originally Posted by Batalov

this is what you are competing against - https://members.loria.fr/PZimmermann...s/Pminus1.html
Stop thinking in bits, like you will find in many vanity threads: "Ah! Look at that factor, it is exceptionally large at 134.47 bits!"
No, 66 digits (or 218 bits) is what you want to beat. Good luck!

What's the difference between thinking in log_10 vs log_2? And one might argue that the former website is but a vanity list as well. Just for the big boys with lots of university/company ressources.