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-   -   P-1 factoring anyone? (https://www.mersenneforum.org/showthread.php?t=11101)

bcp19 2011-11-14 22:32

[QUOTE=James Heinrich;278340]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: [URL]http://mersenne-aries.sili.net/7000163[/URL]

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 [URL="http://mersenne-aries.sili.net/6877433"]this relatively large factor[/URL] I found yesterday which was easily found with P-1 but would take a current GPU a few billion years to TF.[/QUOTE]

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 2011-11-14 22:44

[QUOTE=bcp19;278357]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?[/QUOTE]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 [i]and[/i] 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 2011-11-14 23:09

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

aketilander 2011-11-15 12:46

Save files
 
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 2011-11-15 12:58

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

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

markr 2011-11-15 13:26

[QUOTE=aketilander;278469]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?[/QUOTE]
There are two kinds of p-1 worktodo lines:
[CODE]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[/CODE]
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 2011-11-15 14:05

[QUOTE=James Heinrich;278471] if you don't want to keep them you should add [COLOR=blue]KeepPminus1SaveFiles=1[/COLOR] to [I]prime.txt[/I][/QUOTE]

Copy/Paste typo?

James Heinrich 2011-11-15 14:32

[QUOTE=LaurV;278478]Copy/Paste typo?[/QUOTE]Oh... oops :redface:

That should of course be [quote]if you don't want to keep them you should add [color=blue]KeepPminus1SaveFiles=[/color][color=red]0[/color] to prime.txt[/quote]

James Heinrich 2011-11-20 03:11

[QUOTE=James Heinrich;276848]Just found another one where the previous P-1 apparently didn't find the factor for some reason: [url=http://mersenne-aries.sili.net/exponent.php?exponentdetails=6853937]M6,853,937[/url].[/QUOTE]Just keeping track for myself, I found two more P-1 factors that should have already been found based on previous P-1 bounds:
[url]http://mersenne-aries.sili.net/6853967[/url]
[url]http://mersenne-aries.sili.net/6854297[/url]

Dubslow 2011-11-20 04:40

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 2011-11-20 11:56

[QUOTE=Dubslow;279257]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?)[/QUOTE]

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.


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