Base-6 speed for prime testing vs. base-2

[jasong]

It has been suggested to me that, when compared with the same size numbers(like 2 one million digit numbers, one base-6, one base-2) that base-6 tests faster than base-2. I think my computer is just wonky enough to not be trustworthy for Prime95, but still 100% stable for everything else.

Could someone run a test or 2 and compare base-6 total time to a base-2 of a similar size?

[mdettweiler]

Originally Posted by jasong

It has been suggested to me that, when compared with the same size numbers(like 2 one million digit numbers, one base-6, one base-2) that base-6 tests faster than base-2. I think my computer is just wonky enough to not be trustworthy for Prime95, but still 100% stable for everything else.

Could someone run a test or 2 and compare base-6 total time to a base-2 of a similar size?

A while back we ran some tests of that nature (see from here to the end of that thread) on 100,000 digit numbers (big enough to get reasonably good experimental data, but not so big that they'd take hours to run, as with your suggested 1M digit numbers). The conclusion was that base 2 is a little faster than other bases for the same # of digits, similarly sized k, and the same FFT length. How much faster can vary somewhat depending on the specific numbers in question.

I'm not sure where the idea that base 6 is faster than base 2 came from. The only way that would happen is if the programs you were doing the tests with used different versions of the underlying gwnum FFT library (say, using LLR 3.7.1 for base 2 and the latest PFGW for base 6). Do you know which programs your source used for each base?

[jasong]

Originally Posted by mdettweiler

A while back we ran some tests of that nature (see from here to the end of that thread) on 100,000 digit numbers (big enough to get reasonably good experimental data, but not so big that they'd take hours to run, as with your suggested 1M digit numbers). The conclusion was that base 2 is a little faster than other bases for the same # of digits, similarly sized k, and the same FFT length. How much faster can vary somewhat depending on the specific numbers in question.

I'm not sure where the idea that base 6 is faster than base 2 came from. The only way that would happen is if the programs you were doing the tests with used different versions of the underlying gwnum FFT library (say, using LLR 3.7.1 for base 2 and the latest PFGW for base 6). Do you know which programs your source used for each base?

I'm going to do something that may be grasping at straws, but I just want to be thorough. I know that when it comes to the conjecture testing, the sieving programs are specialized for that particular base. Is that also possible for the LLR stuff? Not really sure how hard that would be. My friend said there's another library(or whatever the word is) for LLR that George doesn't use, but that works better for AMD, which is what he prefers. His claim was that, in addition to base-6 being faster, that using the integer registers on the various new graphics cards are about 100 times faster than with a cpu. He actually developed a prime number finder that used the original ipods as processors(the ones that did video, but only had half the ipod covered with the screen).

The only stuff he did that I know of that was actually publicly known was one of the sieving programs that was used by Riesel Sieve., JJSieve. Lately, though, he's been working on long prime series, those equations where you change one or more values according to a pattern and you get a steady stream of primes for a short time. I think PrimeGrid set a record recently having to do with that. He's been trying to come up with a super equation(or maybe I should say method) for generating these sequences. Last I talked to him, he was needing to make a siever type that isn't available, I forget the details. I say siever, but it was a bit different, kind of like looking at a file full of people and trying to get all the males with blue eyes, except the subjects are numbers and the criteria was mathematical qualities.

[mdettweiler]

Originally Posted by jasong

I'm going to do something that may be grasping at straws, but I just want to be thorough. I know that when it comes to the conjecture testing, the sieving programs are specialized for that particular base. Is that also possible for the LLR stuff? Not really sure how hard that would be. My friend said there's another library(or whatever the word is) for LLR that George doesn't use, but that works better for AMD, which is what he prefers. His claim was that, in addition to base-6 being faster, that using the integer registers on the various new graphics cards are about 100 times faster than with a cpu. He actually developed a prime number finder that used the original ipods as processors(the ones that did video, but only had half the ipod covered with the screen).

The only stuff he did that I know of that was actually publicly known was one of the sieving programs that was used by Riesel Sieve., JJSieve. Lately, though, he's been working on long prime series, those equations where you change one or more values according to a pattern and you get a steady stream of primes for a short time. I think PrimeGrid set a record recently having to do with that. He's been trying to come up with a super equation(or maybe I should say method) for generating these sequences. Last I talked to him, he was needing to make a siever type that isn't available, I forget the details. I say siever, but it was a bit different, kind of like looking at a file full of people and trying to get all the males with blue eyes, except the subjects are numbers and the criteria was mathematical qualities.

Hmm...interesting. Do you know by chance if this better-for-AMDs FFT library is available publicly, or is it something that your friend developed himself and hasn't yet released? If it's public, can you provide a link?

I do know that gwnum, George Woltman's FFT library which is used by Prime95, LLR, and PFGW (the major prime-testing applications used today), has a gazillion different code branches for different CPU types. That includes optimizations specific to certain Intel and AMD architectures, and due to this gwnum is considered the premier FFT library out there now for this kind of work. That said, I would be interested in seeing some comparison data showing how it stacks up against the library your friend mentioned.

Note that while sieving programs may have at one time been specialized by base, they are not any more. Currently the only "base specialized" sieve programs I know of are sr5sieve and ppsieve. sr5sieve is not any faster than running sr2sieve on the same base 5 numbers; it may have been at one time, but I don't believe that is the case any more. ppsieve is a sieve developed by PrimeGrid for use with their Proth Prime Search subproject; it currently works for Riesel and Sierpinski base 2 only. While at this time it is not designed for any other bases, I would expect that there would be no speed difference in making a specialized version of it for those rather than just using the general program. Base-generalized sieve programs like sr2sieve dynamically calculate the optimal way to sieve a given sequence at startup; as I understand, there is no speed increase to be gained by hardcoding those methods into separate programs rather than calculating which to use dynamically.

Regarding base-specialization for primality tests (LLR, Proth, PRP, etc.), until recently the gwnum library (as I understand it--I may be wrong with some of the specifics) could do special modular arithmetic on base 2 numbers, but had to do general modular arithmetic on other bases. In gwnum v25.11, the ability to do special modular arithmetic on all bases was added, so now all gwnum-based programs are almost as fast on non-base-2 tests as they are for base 2. I would expect that there is a little room for improvement, to bring base >2 calculations up to par with base 2, but I don't really know enough about this stuff to be entirely sure.

BTW, based on your comments regarding GPUs and prime searching, I'm wondering, has your friend by chance developed a program for doing primality tests on k*b^n+-c numbers on GPUs? Currently a program has been developed in this forum for doing LL tests (i.e. Mersenne numbers/GIMPS for the uninitiated) on CUDA graphics cards, but so far nobody's come up with something similar to do LLR (a small modification of LL), Proth, or PRP tests to cover the rest of the k*b^n+-c spectrum.

[axn]

Originally Posted by jasong

My friend said there's another library(or whatever the word is) for LLR that George doesn't use, but that works better for AMD, which is what he prefers. His claim was that, in addition to base-6 being faster, that using the integer registers on the various new graphics cards are about 100 times faster than with a cpu. He actually developed a prime number finder that used the original ipods as processors(the ones that did video, but only had half the ipod covered with the screen).

Would you ask your "friend" to kindly cut all this secrecy crap and actually post some hard data and software? At this point, the whole thing sounds like BS -- I have no idea whether you're just misremembering or your "friend" is full of **it.

[jasong]

Originally Posted by axn

Would you ask your "friend" to kindly cut all this secrecy crap and actually post some hard data and software? At this point, the whole thing sounds like BS -- I have no idea whether you're just misremembering or your "friend" is full of **it.

People have figured out who he is in the past and harassed him. His friendship is more important to me than impressing Mersenne Forum.

When I originally met him, I thought he was someone who needed medication, a person like me who wasn't doing quite as well. But the thing about delusional people is that their delusions inevitably have cracks, and if you point out the cracks, they can't deal with it. He is nothing like that. And if he was a compulsive liar(I considered this, since I don't have the mathematical education to comprehend a lot of his stuff) my own personal knowledge should've been able to catch him at some point in the last couple years. The thing is, other than some mental lapses where he gets confused he is very intelligent and very genuine. He had major kidney failure a while back and he's still recovering from a mental faculty standpoint, or it was liver failure, I forget; sent him into a temporary coma if I remember correctly.

He doesn't do what he does because he wants notoriety. I can't tell you the reason he does his research(or part of the reason) because he would be very angry with me. It's not just about prime numbers, though that's his major focus when he talks to me. When he developed JJSieve, the result we have is an incomplete program, the Riesel Sieve guys were getting impatient. His original program(maybe it still does it, not sure) printed out "bucket numbers" which were basically used in a shortcut to improve sieving speed(I forget how buckets work). The siever we mostly use now(not newpgen, but the other one, can't remember the name) uses the factors of 2^666-1, which he said was a hack, because it only partially used the potential of "buckets." He tried to explain it to me, but I didn't understand much past his explanation of what modulo means.

[kar_bon]

Originally Posted by jasong

People have figured out who he is in the past and harassed him. His friendship is more important to me than impressing Mersenne Forum.

So then why do you mention him and his 'new' method here?

Originally Posted by jasong

When he developed JJSieve, [...]

JJSieve was done by JoeO, that's no secret!

If I remeber correct, this is not the first time you're talking about something really new and a big advance in prime search!

Stop talking about it! Give details and results!

Until then stop rumouring!

[henryzz]

jasong has done this type of thing before. He has posted lots more than usual and in this way over the last few days elsewhere on the forum. I suspect that unfortunately he is in one of his "ill" phases.
Please do look at ppsieve GPU though for NPLB(and compare ppsieve CPU to s2sieve). ppsieve might be useful.

[KEP]

Originally Posted by axn

Would you ask your "friend" to kindly cut all this secrecy crap and actually post some hard data and software? At this point, the whole thing sounds like BS -- I have no idea whether you're just misremembering or your "friend" is full of **it.

Why is it that you write this insulting? There is no reason to answer people this way. Even though what Jason is writing sounds like something out of the air, and apparently a lot of misremembering, but could you at least stop insulting people who thinks differently and in a matter that you don't approve of. Sometimes the best is just to say nothing at all, if what you have to say is of no good for either yourself or the part that you intentionally or unintentionally is going to insult one way or another. No offense, but I have seen it before and you appears to be one of the people who base his responses on emotions rather than sense, and to be honest it doesn't become you.

And at Jason, why is it that you keep referring to a "friend", who is always kept in the anonymous. I remember a while back, long before an actual 10M digit prime was found, that you claimed that one of your friends found a 10M digit prime and was elagibel (not sure that is spelled correct) for claiming the EFF price. We never saw such a prime, from your friend and GIMPs, as expected claimed the price less than a year later. So why is Jason that you keeps pushing peoples patience rather than starting to work with people? I know life isn't easy on you, heck it isn't easy on most people, but you could do yourself and everyone else a favour, by following the politely written advices that Karsten has come up with. It would really solve a lot of stupid problems.

Thank you.

Now everyone, take care and be good to one another

KEP!

[10metreh]

Originally Posted by KEP

elagibel (not sure that is spelled correct)

Eligible

[KEP]

Originally Posted by 10metreh

Eligible

Thanks, I'll try to remember that in the future