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isprime.pod


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# This Source Code Form is subject to the terms of the Mozilla Public # License, v. 2.0. If a copy of the MPL was not distributed with this # file, You can obtain one at http://mozilla.org/MPL/2.0/. =head1 NAME isprime - probabilistic primality testing =head1 SYNOPSIS isprime =head1 DESCRIPTION The B program attempts to determine whether the arbitrary precision integer I is prime. It first tests I for divisibility by the first 170 or so small primes, and assuming I is not divisible by any of these, applies 15 iterations of the Rabin-Miller probabilistic primality test. If the program discovers that the number is composite, it will print: Not prime (reason) Where I is either: divisible by small prime x Or: failed nth pseudoprime test In the first case, I indicates the first small prime factor that was found. In the second case, I indicates which of the pseudoprime tests failed (numbered from 1) If this happens, the number is definitely not prime. However, if the number succeeds, this message results: Probably prime, 1 in 4^15 chance of false positive If this happens, the number is prime with very high probability, but its primality has not been absolutely proven, only demonstrated to a very convincing degree. The value I can be input in standard decimal notation, or, if it is prefixed with I, it will be read as hexadecimal. =head1 ENVIRONMENT You can control how many iterations of Rabin-Miller are performed on the candidate number by setting the I environment variable to an integer value before starting up B. This will change the output slightly if the number passes all the tests. =head1 SEE ALSO gcd(1), invmod(1), lap(1) =head1 AUTHOR Michael J. Fromberger Thayer School of Engineering, Hanover, New Hampshire, USA