For which types of primes is GPU primality test software available?

[bur]

Which types of primes can be (sort of efficiently) tested for primality using GPU software? Or rather, for which types is software available?


I know of generalized Fermat and Mersenne. Also arithmetic progressions. Is there software for other primes, e.g. Proth primes? Or their -1 counterpart (is there a name for those?)?



The reason I'm asking is that I'd like to do some manual prime hunting (currently doing Primegrid) but I don't want to move CPUs away from PG. So I thought of buying a card like a 1650 and use it to play around. But for primes that are already covered by either PG or GIMPS it doesn't really make sense to work individually.


Proth primes are also searched by PG, but it's easy to choose a k not within their range.

[VBCurtis]

Originally Posted by bur

Or their -1 counterpart (is there a name for those?)?

The -1 side is called Riesel.

llrCUDA can test Riesel form, but the software is best described as "alpha".
Have a peek at https://mersenneforum.org/showthread.php?t=14608 for some details on that. If you're feeling adventurous, you could perhaps get it working; I've done so, but with less than impressive speed.

Now that GPUowl is doing prp tests, I wonder if it could easily be adapted to run prp tests on riesel inputs, or proth for that matter. Getting a "probable prime" result from the GPU could then be proven with the usual CPU software packages available.

[henryzz]

Originally Posted by VBCurtis

The -1 side is called Riesel.

llrCUDA can test Riesel form, but the software is best described as "alpha".
Have a peek at https://mersenneforum.org/showthread.php?t=14608 for some details on that. If you're feeling adventurous, you could perhaps get it working; I've done so, but with less than impressive speed.

Now that GPUowl is doing prp tests, I wonder if it could easily be adapted to run prp tests on riesel inputs, or proth for that matter. Getting a "probable prime" result from the GPU could then be proven with the usual CPU software packages available.

I think llr testing is on the long todo list for GPUowl but is one of those things that never seems to reach the top. How hard is it to add this?

[bur]

Originally Posted by VBCurtis

The -1 side is called Riesel.

I thought Riesel numbers are those k in k*2^n-1 that never produce primes. Or is the whole construct also called Riesel number?

Now that GPUowl is doing prp tests, I wonder if it could easily be adapted to run prp tests on riesel inputs, or proth for that matter. Getting a "probable prime" result from the GPU could then be proven with the usual CPU software packages available.

That sounds like a very interesting idea, Proth sieving can be done on GPU with high efficiency, so if GPUowl could indeed PRP the candidates, then only a few remaining numbers would have to be LLR checked with CPU.

Originally Posted by henryzz

I think llr testing is on the long todo list for GPUowl but is one of those things that never seems to reach the top.

According to rieselprime.de, GPUowl supports LL?


What are the chances PRP checking Proth/Riesel will be implemented? Is there active development on GPUowl? How can the coder(s) be approached?



If all else fails, I might just do the sieving using GPU and then LLR the candidates with CPU.

[Viliam Furik]

Originally Posted by bur

I thought Riesel numbers are those k in k*2^n-1 that never produce primes. Or is the whole construct also called Riesel number?

Yes, Riesel number is k in k*2^n-1, but when the number in this form is prime, it is called Riesel prime. Also, I think that the numbers themselves are called Riesel numbers (depends on the context)

Originally Posted by bur

According to rieselprime.de, GPUowl supports LL?

Yes, it does support LL - Lucas-Lehmer test. But what you need for the Proth and Riesel primes is LLR - Lucas-Lehmer-Riesel test, which is almost the same except you need to determine the starting value, which is 4 in LL, but other numbers in LLR.

Originally Posted by bur

What are the chances PRP checking Proth/Riesel will be implemented? Is there active development on GPUowl? How can the coder(s) be approached?

Coder is Mihai Preda (forum username: preda)

[kriesel]

Welcome to the gpu side.
There's a considerable wish list in the queue for gpuowl. See https://www.mersenneforum.org/showpo...35&postcount=6
Plus more, that did not make that poll.
Lots of info on gpuowl at its reference thread https://www.mersenneforum.org/showthread.php?t=23391
A GTX1650 is excellent at trial factoring (which does not currently involve gpuowl). See mfaktc for that.
A 5700XT is decent for gpuowl. Or RadeonVII is excellent, if you can find one at an acceptable price.

[bur]

Ok, so PRP for Proth didn't make the list... I read in a post from 2016 or so that generally GPUs aren't that great for LLR. And there are many tasks such as TF of Mersenne or PRP of GFN where they excel so apparently it doesn't make sense to waste them on LLR.


But will GPUs generally be able to efficiently do a PRP test on Proth or Riesel numbers? It would be the same approach PG takes for GFN. GPUs are used for doing the PRP test and if positive a CPU checks with LLR. According to PG stats testing a GFN-18 takes less than one hour on GPU and more than 30 hours on CPU. If similar results could be obtained for Proth/Riesel it would speed things up considerably.


I have no idea though if it's just a specific property of GFNs that makes GPUs that efficient.