Files for pseudo primes up to 2^32

Tester7 — Thu, 28 Jan 2021 21:09:45 -0000

I could now download 32.dat, and this is what I searched (sadly division filtered up to 7, but usable)
I got a "download forbidden" message first.
thanks

Welcome!

Arthur Norman — Mon, 17 Jul 2017 20:02:50 -0000

This project has some code to check if 64-bit integers are primes. It uses One, two or three rounds of Miller Rabin with the last one picking a base via a hashing scheme so that the resulys should be fully reliable. I have emphasised SMALL hash tables here, and that means I do not get all the way to 64-bits using Miller Rabin: beyond that I used BPSW (ie one round of Miller Rabin combined with a Lucas test).

The code is intended to behave properly on a range of platforms, and specifically this should include both 32 and
64-bit systems. The difference that is that on (many) 64-bit systems if you use g++ as your compiler you can
make use of a non-standard 128-bit integer type, while elsewhere it is neceesarty to code up the operation
(a*b)%c on 64-bit inputs using just 64-bit internal working.

I have used generously licensed code from the Hacker's Delight and for a Mersenne Twister pseudo-random generator here: thanks are due to the authors of those ocmponents and I hope that my incorporating their code as part of my project gives them extra recognition.

I use the "isprime" function from here in the CSL system that supports the Reduce algebra system. Before I put this material together I had looked for other freely licensed and tidy prime checkers and I hope that what is here will be of interest to those who do similar searches in the future. I believe that what I have here differs from most of the other code bodies that I found in the following ways:

(1) Respectably portable C++ code that includes support for the case where you need to do (a*b)%c without an extra precision type to use for the intermediate result.
(2) A deterministic hashing scheme for Miller-Rabin style testing that uses rather compact tables.
(3) An implementation of BPSW which incoludes an option (which only makes sense for small inputs!) to give a trace that shows its internal workings. The main C++ version here is only usable as is up to 64-bits, but the Reduce-coded version (using the Reduce big-number system) will work for much larger cases, and given any particular bignum package this version would provide a straightforward starting point for adaptation.
(4) Code and tables involved with the search for and creation of the hash tables.
(5) A CUDA variant of code that lists false witnesses for 32-bit composites. The output from this was not in fact used, because by the time I wrote it I had run a much more laborious ordinary multi-threaded search - but it may be of interest as a small sample of CUDAode to people very early in their exposure to that.

So good luck and enjoy - and I would appreciate any comments.

        Arthur Norman

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Files for pseudo primes up to 2^32

Welcome!