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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 <a>
=head1 DESCRIPTION
The B<isprime> program attempts to determine whether the arbitrary
precision integer I<a> is prime. It first tests I<a> for divisibility
by the first 170 or so small primes, and assuming I<a> 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<reason> is either:
divisible by small prime x
Or:
failed nth pseudoprime test
In the first case, I<x> indicates the first small prime factor that
was found. In the second case, I<n> 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<a> can be input in standard decimal notation, or, if it is
prefixed with I<Ox>, 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<RM_TESTS> environment variable
to an integer value before starting up B<isprime>. 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 <sting@linguist.dartmouth.edu>
Thayer School of Engineering, Hanover, New Hampshire, USA
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