P-1 savefiles

[lycorn]

Hi all,

I have recently started running some P-1 tests on small exponents, trying to dig out some more new factors (one found already!... ). I noticed that the savefiles, including the .bu ones, are left in the working directory when the test finishes. Disk space is not an issue, but still I found it funny that the files are not erased, like in the other work types. It´s a long time now since I ran P-1 on a regular basis, and I vaguely remember there was a reason for this to be done in this particular work type. Would someone care to enlighten me on this subject?
Thx in advance.

[GP2]

If you run a new P−1 test with a higher B1, it will use the old savefile to resume the calculation, instead of starting from scratch.

[lycorn]

Fine. That´s interesting. I´ll give it a try, for sure.
Thank you very much for your prompt answer.

[petrw1]

I tried this lately and observed the following:
From the PC with the save files I ran another P1 with both B1 and B2 larger.
Stage 1 continued from the last B1 value running proportionately faster.
Stage 2 seemed to rerun entirely based on its elapsed run time.

Is this as designed?

PS once a P1 completes you only need to keep the main backup file; the one without a .bu extension.

[axn]

Originally Posted by petrw1

Is this as designed?

Yes.

I suppose, if you keep the same B1, but larger B2, it might run it incrementally (not sure, gotta check it). But if you change B1, then it must run stage 2 from scratch, since it must use the result from stage 1 as input to stage 2.

[ATH]

With GMPECM I have run huge P-1 curves doing both B1 and B2 in stages. You only need to run stage1 incrementally, then when you reach some desired B1 for example 1e9, you can run any stage2 intervals you like on that stage1 file in any order, like 1e11-1e12 then 1e10-1e11 or whatever.

In Prime95 though I only think it allows you to run stage2 incrementally from the current B1 and up.

[lycorn]

Originally Posted by ATH

With GMPECM I have run huge P-1 curves doing both B1 and B2 in stages. You only need to run stage1 incrementally, then when you reach some desired B1 for example 1e9, you can run any stage2 intervals you like on that stage1 file in any order, like 1e11-1e12 then 1e10-1e11 or whatever.
and up.

That means the first runs (till you reach the desired B1 value) are Stage 1 only, and then you perform runs of Stage 2 only?

Also, what range of exponents have you tried with GMPECM? I have done a lot of work with GMPECM, not P-1 testing, though, and it only pays for really small (< 30,000) exponents. I don´t know how it goes for P-1.

[ATH]

Originally Posted by lycorn

That means the first runs (till you reach the desired B1 value) are Stage 1 only, and then you perform runs of Stage 2 only?

Also, what range of exponents have you tried with GMPECM? I have done a lot of work with GMPECM, not P-1 testing, though, and it only pays for really small (< 30,000) exponents. I don´t know how it goes for P-1.

Yes, since stage1 has to be done incrementally it can only be done on one computer while stage2 can be split to as many cores/computers as you like.

Here is a random example:

4437613266767947934612882360369779858184509124945083658308877174193087878506071380993 = 
5416454354354334983409847 * 819283792763897632487263487263897276392763982763928379283719

and 5416454354354334983409846 = 2*3*71*3769*13180897*255937771847

So B1 has to be 1.32*10^7 and B2=256*10^9 to find the factor.

If I run stage1 with only B1=10^7 and save to a file, then resume from that file doing B2=250e9 to 260e9 it does not find the factor.
But when I do stage1 to B1=2*10^7 and save to a new file and resume that file doing stage2 B2=250e9 to 260e9 it finds the factor. (see output in attached file)

So it finds the factor even if I skipped doing stage2 from B2=2*10^7 to 250e9, as long as you are lucky your stage2 interval contains the largest P-1 factor, it does not matter. This also applies to P+1 and ECM
(though for ECM it is not a factor but the curve group order depending on the sigma for the curve).

But each B1 value has it own separate B2-"space", so you have to take B1 as high as you want to go before starting to do stage2, or you have to do stage2 over again when you increase B1.




I did not do P-1 on a lot of Mersenne numbers, I just did some big P-1 on special numbers like F12, M1277, different stages of HP49 and Euclid-Mullin EM52 and such.

By big/huge P-1 I did not mean big/huge Mersenne numbers, but I meant B1~ 10^12 and B2 ~ 10^17 - 10^18.

[lycorn]

Thanks for the very useful explanation.
I´ll try to find the time to test several combinations of B1 / B2 and different exponent ranges.

[petrw1]

So it seems a n efficient method to maximize factors and minimize work (ummm PC work...actually more manual labor) is to start with a relatively low B1 only...and increment it in steps to a desired maximum or until it finds a factor and only run B2 as a last step if necessary

[VBCurtis]

Doesn't stage 1 spit out a factor when it's found, rather than at the end of the stage? I mean, you can just run a single large B1 rather than a bunch of iterations working up to the large B1 (if you're not going to do stage 2 at any intermediate B1, that is).
Doing a single run should spit out factors just as quickly as iterating B1 upward- at least, that's how GMP-ECM behaves. Perhaps P95 isn't the same?