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The program to use to prove a number prime depends entirely on the prime and your goal. If you just want any large prime n, then choose a form for which the classical tests apply (a for for which either n+1 or n-1 factors, see The Classical Tests. Proth.exe, PrimeForm, pfgw and prp are popular examples of programs to use for these numbers and are often preceeded by the use of a screening program such as NewPGen. Using the classical tests numbers with tens of thousands of digits may be easily proven prime.

If instead you already have your number and know very few factors of n2-1 (e.g., primes from certain sequences, cryptographic primes...) then you must use a general test (see The general purpose tests. These tests are far slower than the classical test (because of the lack of special form) but are improving rapidly. The current record holder here is Titanix, followed by ECPP. APRT-CLE in UBASIC is nice for smaller numbers. There is also CYCLOPROVE and ...

It is not possible to give a general answer to what is the best program because it depends on too many factors! You might consider asking around (e.g. on the Primes Numbers mailing list).

Top : programs : seeking large primes Next 10 of 11 links
Resources in programs : seeking large primes
  • Yves Gallot's Proth.exe - Classical n+1 testing for primes of special forms. Easy interface forfinding twins, Sophie Germain's... Most of the 5000 largest known primes were found with this program. pop
    (Added: 2-Aug-2000 Hits: 13329 Rating: 7.68 Votes: 41) Rate It
  • François Morain's ECPP - ECPP is a fast routine for proving the primality of general numbers. François Morain's C-code includes the BigNum package and binaries for several operating systems. It can be difficult to set up.
    (Added: 3-Aug-2000 Hits: 6979 Rating: 5.50 Votes: 12) Rate It
  • George Woltman's PRP - Takes an input file from NewPGen, applies a prp test, then writes a file of the numbers that pass for Proth.exe to prove. (Get prp.zip for Windows, prp.tgz for Intel/Linux.)
    (Added: 14-Nov-2000 Hits: 4235 Rating: 8.88 Votes: 9) Rate It
  • Jim Fougeron's Cert_Val - Titanix CERTifcate_VALidation program. Double verify primality certificates produced by Titanix. With source and explanation of what things in the certificate are being checked. (version 1.01) Requires Miracl MP library to build (located at http://indigo.ie/~mscott )
    (Added: 25-Oct-2000 Hits: 3509 Rating: 9.67 Votes: 3) Rate It
  • Jim Fougeron's Pr_Prob.exe - Prime number probability calculator. Helps to quickly determine benefits of additional trial factoring. Includes full source.
    (Added: 22-Oct-2000 Hits: 5227 Rating: 6.17 Votes: 6) Rate It
  • Marcel Martin's PRIMO - A general primality proving program based on ECPP methods. Primo (formally Titanix) has repeatedly set records for the largest numbers proven prime with ECPP. It is easy to set up and run on Windows systems.
    (Added: 2-Aug-2000 Hits: 6279 Rating: 9.16 Votes: 34) Rate It
  • Mersenne Prime Number Benchmarks - Times of CPUs doing P95 iterations. Planning on adding historical information of times for Cray, Numerix, Elxsi, SGI and Mercury.
    (Added: 25-Nov-2004 Hits: 2610 Rating: 9.00 Votes: 3) Rate It
  • MultiSieve - Sieve program for factorials, Cullens, Woodalls, etc. to be used with PFGW
    (Added: 13-Nov-2002 Hits: 4082 Rating: 10.00 Votes: 4) Rate It
  • Paul Jobling'sNewPGen - A trial division program for sieving special forms before using programs like Proth.exe or PrimeForm for the actual proof
    (Added: 2-Aug-2000 Hits: 4230 Rating: 9.56 Votes: 18) Rate It
  • PrimeForm by Chris Nash's et. al. - Built with the same arithmetic library as Proth.exe, PrimeForm allows much move variety in the form of the prime numbers sought--at the cost of some simplicity and speed.
    (Added: 2-Aug-2000 Hits: 3809 Rating: 8.59 Votes: 12) Rate It

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