P-1 factoring anyone?

[bcp19]

Originally Posted by James Heinrich

TF and P-1 typically find different types of factors; the ones that are "easy" to find by one method are not necessarily "easy" for the other method.

TF is easy to understand: try each prime number between 2^63 and 2^64 and see if it divides into 2^exponent-1. If it does, it's a factor.

P-1 factors are only found when they meet certain criteria. The so-called "k-value" of any P-1 factor is the prime factorization of the discovered factor minus one, with 2 and the Mersenne exponent removed. Trying to clarify that with an example:For P-1 to find the factor, B2 and B2 need to be greater or equal to the largest and second-largest prime powers respectively, which means that the minimum bounds for P-1 to find the factor is B1=81 (that is, 3^4) and B2=12,096,811

You can see these numbers, plus some pretty graphs to try and help visualize that, on my site: http://mersenne-aries.sili.net/7000163

The factor you found isn't very "smooth", which makes it more difficult (as in larger bounds are needed) to find with P-1 and therefore more likely to show up with TF. Compare with this relatively large factor I found yesterday which was easily found with P-1 but would take a current GPU a few billion years to TF.

Thank you for that explanation, I am beginning to understand P-1 a bit better. I think the other one I was trying to learn from was actually TOO simplified (read too small a number to P-1), which ended up confusing me more that it helped.

Looks like it is a good idea to both expand the P-1 bounds AND extend the TF a few extra bits in finding factors in the lower ranges.

So, if an exponent was P-1'd to say 30000/600000 and you want to extend it to 85000/1500000, is there a 'shortcut' to extending it or does it still have to do all the work again?

[James Heinrich]

Originally Posted by bcp19

TSo, if an exponent was P-1'd to say 30000/600000 and you want to extend it to 85000/1500000, is there a 'shortcut' to extending it or does it still have to do all the work again?

If you have the P-1 save file(s) then not all the work needs to be repeated. If you have the stage2 savefile (from when the first P-1 was complete) you could extend it to 30000/1500000 by simply continuing. But if you increase the B1, you need a stage1 savefile to continue from and most/all of the Stage2 work will need to be re-done after extending the B1, you can't just extend B1 from 30k -> 85k and continue B2 starting at 600k (where stage 2 ended on the first try), because you could potentially miss a factor that requires B2 <= 600k but also B1 > 30k (which would not have been found in the first attempt).

Short answer: If you're planning to methodically work P-1 to progressively higher bounds it can be done somewhat efficiently to minimize wasted work, but it's not particularly easy. If you want to redo P-1 that someone else did but to higher bounds, then you're out of luck, just start fresh.

[bcp19]

I kind of had that feeling from what I had read, thank you for clarifying lt for me.

[aketilander]

undoc.txt

"By default P-1 work does not delete the save files when the work unit completes.
This lets you run P-1 to a higher bound at a later date. You can force
the program to delete save files by adding this line to prime.txt:
KeepPminus1SaveFiles=0"

I am a little confused by this information in undoc.txt. I think that by default the P-1 save files are deleted? At least I cannot find any save files from my completed P-1s.

If I want to keep all save files should I add:

"KeepPminus1SaveFiles=1"

Can this variable (KeepPminus1SaveFiles) have other values then 0, 1 and if so what is the significance of the other values?

[James Heinrich]

Before v26(?) it was normal that the savefiles are deleted after the assignment is complete. Since v26.? the KeepPminus1SaveFiles option has been added, with the default value of keeping the savefiles; if you don't want to keep them you should add KeepPminus1SaveFiles=1 to prime.txt

It's an on/off switch (1 means they're kept, 0 means they're deleted), no other values make sense.

[markr]

Originally Posted by aketilander

undoc.txt

"By default P-1 work does not delete the save files when the work unit completes.
This lets you run P-1 to a higher bound at a later date. You can force
the program to delete save files by adding this line to prime.txt:
KeepPminus1SaveFiles=0"

I am a little confused by this information in undoc.txt. I think that by default the P-1 save files are deleted? At least I cannot find any save files from my completed P-1s.

If I want to keep all save files should I add:

"KeepPminus1SaveFiles=1"

Can this variable (KeepPminus1SaveFiles) have other values then 0, 1 and if so what is the significance of the other values?

There are two kinds of p-1 worktodo lines:

Pfactor=k,b,n,c,how_far_factored,num_primality_tests_saved
Pminus1=k,b,n,c,B1,B2

for example
Pfactor=1,2,2700067,-1,61,10
Pminus1=1,2,2700067,-1,150000,3000000

Pfactor lines tell the client to work out bounds itself, Pminus1 lines specify the bounds. Primenet hands out Pfactor lines.

I think the KeepPminus1SaveFiles option must apply to p-1 work done with Pminus1 lines, not Pfactor lines. My prime.txt files do not have "KeepPminus1SaveFiles" in them, I have Pfactor lines, and the save files go away when the work is done. A long time ago I tried using Pminus1 lines and I had to delete the save files manually.

[LaurV]

Originally Posted by James Heinrich

if you don't want to keep them you should add KeepPminus1SaveFiles=1 to prime.txt

Copy/Paste typo?

[James Heinrich]

Originally Posted by LaurV

Copy/Paste typo?

Oh... oops

That should of course be

if you don't want to keep them you should add KeepPminus1SaveFiles=0 to prime.txt

[James Heinrich]

Originally Posted by James Heinrich

Just found another one where the previous P-1 apparently didn't find the factor for some reason: M6,853,937.

Just keeping track for myself, I found two more P-1 factors that should have already been found based on previous P-1 bounds:
http://mersenne-aries.sili.net/6853967
http://mersenne-aries.sili.net/6854297

[Dubslow]

Those exponents are too close to be a coincidence. Probably somebody was running P95 with hardware errors. (Now that I think about it, how much does P95 in terms of error catching for non LL work?)

[bcp19]

Originally Posted by Dubslow

Those exponents are too close to be a coincidence. Probably somebody was running P95 with hardware errors. (Now that I think about it, how much does P95 in terms of error catching for non LL work?)

Might not be hardware error, if you look at the P-1 work done in the lower ranges, you'll see some completed to 85K/1.5M while others are 30K/30K. If someone new started doing P-1 work with not much memory available, they'd probably have gotten several exponents in a row and not have done good P-1 work.