Using Prime95 for manual testing

[opyrt]

Has anyone used prime95 (or mprime) to run offline tests?
I'm curious about how the worktodo.txt should be set up for k*2^n+1.

I'm guessing the speed will be pretty much the same as the newest llr.exe?

:)

[TimSorbet]

11) Program can now do PRP tests of (k*b^n+c)/f.  Add a line worktodo.txt that
    looks like this:
        PRP=k,b,n,c[,how_far_factored,tests_saved][,known_factors]
    The optional how_far_factored (in bits) and tests_saved values are used
    to determine if P-1 factoring prior to the PRP test would be beneficial.
    The optional known_factors list is a quoted comma separated list of
    known factors of k*b^n+c.

e.g. this:

225931 6285056

becomes:

PRP=225931,2,6285056,1

(optionally with how_far_factored and tests_saved) With [Worker #x] tags as needed.
I think the speed will be about as fast as llr.exe, but in the last couple versions, a few minor speed improvements were made that might make it slightly better for these tests (I'm not sure if it is better or the same).

[mdettweiler]

Regarding the speed: usually, Proth tests (what LLR does) are faster than PRP tests (what Prime95 does) for k*2^n+1 numbers like PSP's. Also, the Proth test gives a conclusive primality proof, whereas a PRP test does not.

Recently, in Prime95 v25.9, some slight speed tweaks were added which, on some CPUs (most notably Core 2's), some small speed boosts were added. To quote the v25.9 release notes, the boosts are approximately:

32-bit Pentium 4: between 2% slower and 1% faster
32-bit Core 2: between 2% and 6% faster
64-bit Pentium 4: between 2% and 4% faster
64-bit Core 2: between 10% and 13% faster
64-bit Core i7: between 7% and 12% faster
64-bit Phenom: between 10% and 13% faster
AMD64: between 1% slower and 1% faster

Given that Proth tests are a bit faster than PRP tests anyway, I would guess that, on the whole, there would be no noticeable speed increase from using Prime95 instead of LLR for testing PSP numbers.

Also, keep in mind that the residuals from PRP tests are incompatible with those from Proth tests as well. Thus, even if the test results are accurate from a Prime95-produced test, when doublechecking handles that range in the future it will erroneously detect them as bad residuals, and a third check on that number will be performed. Essentially, every PRP residual in the DB would need three total checks performed on it, even if it's correct. At the size of n PSP is dealing with now, that's a whole lot of time.

Also, recently in Prime95 version 25.11, there have been further speed increases in the underlying math library. These ones are supposed to be very, very significant boosts. However, all of these modifications are for numbers that are not powers of 2. There are no boosts whatsoever to power-of-2 numbers (including PSP's) compared to version 25.9.

Interestingly enough, the SR5 project could benefit somewhat from utilizing Prime95 v25.11, and the residuals *would* be compatible.

[Prime95]

Originally Posted by mdettweiler

in Prime95 version 25.11, there have been further speed increases in the underlying math library. These ones are supposed to be very, very significant boosts. However, all of these modifications are for numbers that are not powers of 2. There are no boosts whatsoever to power-of-2 numbers (including PSP's) compared to version 25.9.

Not quite.

k*2^n+/-1 is probably 3-5% faster in 25.11 than 25.9 for SSE2 machines.

k*b^n+c where b>2 can be several times faster than 25.9, but expect about twice as fast for the most commonly tested values.

[mdettweiler]

Originally Posted by Prime95

Not quite.

k*2^n+/-1 is probably 3-5% faster in 25.11 than 25.9 for SSE2 machines.

k*b^n+c where b>2 can be several times faster than 25.9, but expect about twice as fast for the most commonly tested values.

Hmm, I see. I didn't know about that first tidbit of information (though the second was confirmed by my recent benchmark testing, as reported in the PFGW thread in the Software forum).

Most likely, though, it's still not enough to outweigh the speed advantage of LLR over PRP. I'd guess that at this point they'll probably about the same speed, in which case it's still best to use LLR because the residuals will be compatible with earlier testing, and because there isn't a need for a separate primality proof after a PRP is found.

The 3-5% speed boost in 25.11 for base 2 should, however, be quite useful for the Five or Bust project, which does base 2 numbers that can't be tested with LLR.

[axn]

Originally Posted by mdettweiler

outweigh the speed advantage of LLR over PRP.

LLR shouldn't have any speed advantage over PRP while testing k*2^n+1, since they are based on the same FFT.

On the flip side, LLR can be sped up by incorporating the new FFT.

[mdettweiler]

Originally Posted by axn

LLR shouldn't have any speed advantage over PRP while testing k*2^n+1, since they are based on the same FFT.

On the flip side, LLR can be sped up by incorporating the new FFT.

Really? I could have sworn I read a while back that LLR is faster than PRP for testing k*2^n+-1. Unless that was intended to say that they're the same in raw speed, but you save some time not having to do a separate primality proof?

Regarding incorporating the new improvements into LLR, from what I hear, an LLR with gwnum v25.11 will probably be coming out sometime soon. That should bring the speed increases to everything LLR does, including LLR, Proth, and PRP tests.

[axn]

Originally Posted by mdettweiler

Really? I could have sworn I read a while back that LLR is faster than PRP for testing k*2^n+-1.

The -1 form should be faster. Not so for the +1 form.

[opyrt]

Wow! Thanks for all the information! I was not aware that prime95 and llr runs different tests that create different residues. I'm currently running second pass tests for PSP; In other words, I can not use prime95.

The reason I wanted to know is because prime95 is able to run separate workers from the same worktodo. With llr.exe I need to split the candidates into one file per core and then hope they all finish at the same time. Which they don't! ;-)

Anyways, I'm very greatful for your explanations. :-)

[wolfemancs]

If LLR is faster than what Prime95 does, or takes the same amount of time, but doesn't require a primality test afterwards, does anybody know why Seventeen or Bust is using Prime95 rather than an LLR test?

[opyrt]

Originally Posted by wolfemancs

If LLR is faster than what Prime95 does, or takes the same amount of time, but doesn't require a primality test afterwards, does anybody know why Seventeen or Bust is using Prime95 rather than an LLR test?

Since noone has answered, I'll give a guess... And that's manageability. Prime95 is capable of doing prime testing, sieving and factoring, it's multicore capable, it's being maintained, it has a good networking component and it has a good server (from what I understand).

LLR (the application) does not have network support and is not multicore capable (needs one directory per core).
LLRNet is not being maintained, uses old LLR code (the newer is up to 25% faster) and does not work on Windows 2003.
PRPnet is not multicore capable.

Those are my guesses, but you would probably get a better answer if you ask Louie...

Here: http://www.free-dc.org/forum/forumdisplay.php?f=38