primecert() vs Primo

bur · 2022-01-04, 09:40

My main issue with Primo is that is requires a GUI. I recently found out that PARI offers an ECPP test via primecert(). How fast is it compared to Primo? In another thread it was mentioned that a 30k digits number was proven prime with PARI, so I assume it can be very fast - was it done without any modifications to primcert()?

And(1) since they used MPI it seems to be possible to run it multithreaded. I know there are options for parallel programming in PARI, but I don't know how to use them for this specific problem.

And(2), I wanted to test it with a random 300 digits PRP from factordb but the certificate isn't accepted: "No input number found in file." I attached the cert, it seems to contain the input number.

kruoli · 2022-01-04, 09:49

It occurred to me that my Primo certificates have lines of the format [capital letter]=[-]$[hex digits], while your certificate has [capital letter]=[-]0x[hex digits]. I changed the format and tried your file - "number already proven", which seems to be a different error than you have got. Maybe you can try this with another number and report back?

bur · 2022-01-04, 10:29

Ah, thanks. Number already proven just means that in the meantime the number was proven prime. I tested your suggestion with another number and it works.

bur · 2022-01-05, 08:48

I found this presentation by Jared Asuncion. According to them, the speed they achieved is even higher than that of Primo. At least of the ecpp() they present and I am not sure if that is the same algorithm PARI is using for primecert(), but I assume it is.

The question remains how to make this run multithreaded and also preferrably with checkpoints.

kruoli · 2022-01-05, 09:43

Have you tried contacting them?

Regarding MPI, there is a limited amount of functions that can make use of MPI, according to the manual. The Cert functions do not belong to them, unfortunately. So there is surely some kind of manual intervention involved.

bur · 2022-01-05, 12:42

Yes, I am in contact with them, it should be possible to have it run multithreaded.

He also wrote that the certificate can be generated in steps. I am not sure if these steps are independent, which would allow distributed computing, but let's see. For now I'd be happy to finally be able to use ECPP via terminal.

2022-01-04, 09:49	#2
kruoli "Oliver" Sep 2017 Porta Westfalica, DE 2100₈ Posts	It occurred to me that my Primo certificates have lines of the format [capital letter]=[-]$[hex digits], while your certificate has [capital letter]=[-]0x[hex digits]. I changed the format and tried your file - "number already proven", which seems to be a different error than you have got. Maybe you can try this with another number and report back? Last fiddled with by kruoli on 2022-01-04 at 10:31 Reason: Additions. Grammar.

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2022-01-04, 10:29	#3
bur Aug 2020 796581e-4;32539e-3 2³·73 Posts	Ah, thanks. Number already proven just means that in the meantime the number was proven prime. I tested your suggestion with another number and it works.

2022-01-05, 08:48	#4
bur Aug 2020 796581e-4;32539e-3 248₁₆ Posts	I found this presentation by Jared Asuncion. According to them, the speed they achieved is even higher than that of Primo. At least of the ecpp() they present and I am not sure if that is the same algorithm PARI is using for primecert(), but I assume it is. The question remains how to make this run multithreaded and also preferrably with checkpoints.

2022-01-05, 09:43	#5
kruoli "Oliver" Sep 2017 Porta Westfalica, DE 10001000000₂ Posts	Have you tried contacting them? Regarding MPI, there is a limited amount of functions that can make use of MPI, according to the manual. The Cert functions do not belong to them, unfortunately. So there is surely some kind of manual intervention involved.

2022-01-05, 12:42	#6
bur Aug 2020 796581e-4;32539e-3 248₁₆ Posts	Yes, I am in contact with them, it should be possible to have it run multithreaded. He also wrote that the certificate can be generated in steps. I am not sure if these steps are independent, which would allow distributed computing, but let's see. For now I'd be happy to finally be able to use ECPP via terminal.