What can I change when doing p-1 one and it won't reset?

[Joshua2]

I have been doing p-1 on a fermat number, my workline is Pminus1=262144,64000000,0,1,0
I was wondering if as long as I get the same number, I could lower and raise the 64M? And the stage 2 number as well? (Which seems to be set at the limit of 4.29B)
Thx

[geoff]

Originally Posted by Joshua2

I could lower and raise the 64M? And the stage 2 number as well? (Which seems to be set at the limit of 4.29B)

If you mean changing the limits before the curve has finished, then I don't know. It should work, but make a backup of the save file just in case.

However once the curve has finished, the save file with the stage one residue will remain, and you can then add a new Pminus1 line to your worktodo.ini with a higher B1 limit, and Prime95 will then resume stage 1 from the old save file.

You can lower the B2 limit by specifying it in the third field of the Pminus1 line, but 4.29 billion is as high as it can go for the current version of Prime95.

It is possible to use gmp-ecm to do the stage 2 step (from the Prime95 stage 1 residue) to a much higher B2 limit, but for numbers of this size it would have to be done by breaking the stage 2 step into separate ranges unless you have a huge amount of memory.

If you want to continue the stage 2 step with gmp-ecm then I can help you convert the save file into a suitable format, but if you are using a P4 then Prime95 is so fast on the stage 1 step that it would probably be worthwhile continuing well beyond B1=64 million before starting stage 2.

I was considering doing some P-1 on a large fermat number myself, and so I would be interested to hear what machine you are using and what iteration times you get for stage one. Whatever you do, keep your save file, there will be someone interested in continuing from it eventually.

[Joshua2]

I am interested in continueing stage 2 with gmp-ecm, can it do p-1 as well? I have an Athlonxp 2600+ w/ 512 MB of DDR, of which 384 is available for P95. I was planning on extending it to 128 Million after the GCD finished. I was unable to download the lowm.txt, is that ok? How do i find the iteration timings? It is 52.05% done right now with stage 1. Ah, I think i might know. 500000 iterations are set to be done every time it updates the screen. The times are 416 to 502 seconds.

[geoff]

I am interested in continueing stage 2 with gmp-ecm, can it do p-1 as well?

Yes gmp-ecm can do P-1, P+1 and ECM, however Prime95 only has the facility for producing ECM stage 1 residues suitable for gmp-ecm automatically, the P-1 residue needs to be extracted from the save file manually.

I was unable to download the lowm.txt, is that ok?

Since you are working on the number 2^262144+1 directly, you don't need the lowm.txt file, but the lowp.txt file instead. But all that will happen if it is missing is that Prime95 will find a few small known factors during the stage one GCD step and stop. This is actually a usefull check that the computation went OK. (If there was an error then these known factors would not be found).

Unless you intend to continue the stage 2 step beyond 4.29 billion it is probably better to use Prime95 than gmp-ecm. I think gmp-ecm would need a few GB to test a number of this size efficiently. My only experience is with a P4 though, and gmp-ecm probably runs quite a bit faster on an Athlon.

Thanks for the timings, I will time the number on my machine for comparison and post later.

[akruppa]

The upcoming release of gmp-ecm is much faster for Fermat numbers in stage 2 than the previous version. However, it still wants lots of memory to work efficiently. For a number as large as F_18, even poly degree dF=1024 uses 512MB memory. With dF=1024, gmp-ecm will probably be slower than Prime95, surely on the P4, likely on the Athlon. If you have >1GB, you can use dF=2048 and gmp-ecm could be a little faster than Prime95. If we manage to fit Prime95's DWT into gmp-ecm yet, gmp-ecm+DWT should be quite a bit faster. In any case, RAM is your friend: doubling available memory approximately doubles speed.

To extract P-1 residues from Prime95 save files, geoff posted the pm1dump program in this thread.

Alex

[geoff]

500000 iterations are set to be done every time it updates the screen. The times are 416 to 502 seconds.

For comparison a 2.8GHz P4 does 500000 iterations of M(524288) in about 400 seconds (testing F18 directly is much slower). I estimate that it would take about a month to bring stage one right up to the Prime95 limit of B1=4.29 billion.

From Alex's comment about the new gmp-ecm, perhaps your best strategy would be to do stage 1 to B1=128 million then stage 2 to 4.29 billion with Prime95. At that point you can decide whether to continue stage 2 from 4.29 billion to a higher limit with gpm-ecm, or perhaps go back and extend stage one.

[Joshua2]

If I extend stage 1 past 128 million, wouldnt i lose all my stage 2 work i have done? If it only takes a month to do stage 1 to the limit, i think i will do that.

No one has every gone past 32 million for stage 1 right? (and reported it, which they prob would)

It appears that when I am not using the comp the times is between 416 and 420 seconds, which is slightly quicker than I had thought. (cuase i was using it)

Also it only seems to be using 2 megs of ram. Is this normal with stage 1? I think it is stage two that takes loads of ram.

p.s. it is almost %85 to 64 million.

[Joshua2]

Another question, is bigger always better? If a factor would be found with 96 million, would it be found with 128?
Is there multiples ways to do a number like ecm? Or is there only one for each number? I mean if two people go to 96 million the results will be the same right?
Is there a need to keep the stage 1 at some round number? Could it be 74 million or whatever? Or does it have to like 64,96, or 128?

[akruppa]

1. Yes. Any factor that is found with B1,B2 is also found with any bounds that are both at least as large.
2. No, yes, yes. There is a theoretical possibility to find a factor with one starting value that is not found by another, but for larger factors it is exceedingly small and thus Prime95 doesn't let you pick a starting value, it always uses 3.
3. No. The bound values can be any integers, but for stage 1 it is internally rounded down to a prime or prime power, for stage 2 rounded up to a multiple of some internal parameter (usually 30, 210 or 2310). But this is a technicality of little meaning to the user, just pick the B1,B2 values you like.

Alex

[geoff]

Originally Posted by Joshua2

If it only takes a month to do stage 1 to the limit, i think i will do that.

Sorry to put you wrong, the time to test F18 to the stage 1 limit was two months, one month for F17, but you should check this yourself to be sure. If you have the patience then good on you.

[R.D. Silverman]

Originally Posted by geoff

Sorry to put you wrong, the time to test F18 to the stage 1 limit was two months, one month for F17, but you should check this yourself to be sure. If you have the patience then good on you.

Please note that much P-1 work on F_n has already been done.

See:

http://www.mersenne.org/ecmf.htm

Unlike ECM, running P-1 a second time (to the same limits) gains you nothing.

BTW, I will express an *opinion* here....

I will be (happily) astonished if all this P-1 work on the "medium" sized Fermat
numbers ever turns up a factor. [just on rough probabilistic grounds].
The same comment applies to ECM.