Hi Bob, I'm guessing many others on this list will be able to provide a more comprehensive answer, but here's what I've got from looking around a bit! It looks like PARI/GP now has code for ECPP primality proving and certificate generation, in addition to existing APRCL and Selfridge backends. It can also write out ECPP certificates in human-readable, Primo, and MAGMA formats as of time of writing. I'm no major PARI/GP user by any means, but this seems to work! gp > N = (2^3539+1)/3; /* Example prime number */ gp > ispseudoprime(N) /* Make sure N is a PRP before doing full testing */ %2 = 1 gp > allocatemem(128*10^6) /* Allocate enough memory; otherwise the PARI stack overflows */ gp > primecert(N, 0) /* If N is prime, should produce an ECPP primality certificate given enough time. Otherwise, returns 0. */ After a few minutes, this produces a primality certificate that can be written out to a file. See the function documentation for isprime, ispseudoprime, primecert, and primecertexport at https://pari.math.u-bordeaux.fr/dochtml/html/Arithmetic_functions.html#prime... for more information. I don't know enough about ECPP or PARI's implementation to know what the limits of this approach are, or if this works in theory (given enough time and memory!) for arbitrarily large numbers without additional work. Additionally, the Prime Pages has a list of top programs for finding primes at https://primes.utm.edu/bios/top20.php?type=program; many of these are sieves, programs for proving primality for specific types of primes (such as primes of the form k*2^n+-1), or don't implement ECPP. However, OpenPFGW is maintained and fun to work with. There's also this forum thread from the Mersenne Forum from 2015 about ECPP primality proving, which might help as well? https://www.mersenneforum.org/showthread.php?t=20478 --Neil Bickford On Sun, Mar 3, 2019 at 10:26 AM Robert Baillie <rjbaillie@frii.com> wrote:
Hi Everyone,
I am looking for a primality-proving program (presumably, based on ECPP) that runs on Windows, and which will work with numbers up to several thousand digits.
For numbers that are not too large, Mathematica has the ability to produce primality certificates. I think it uses (recursively) partial factorizations of n + 1 and n - 1.
However, on Linux, the primo program http://www.ellipsa.eu/public/primo/primo.html can prove primality of much larger numbers.
Thanks for any info you might have! Bob Baillie
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