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63 lines
1.7 KiB
Plaintext
63 lines
1.7 KiB
Plaintext
=head1 NAME
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isprime - probabilistic primality testing
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=head1 SYNOPSIS
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isprime <a>
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=head1 DESCRIPTION
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The B<isprime> program attempts to determine whether the arbitrary
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precision integer I<a> is prime. It first tests I<a> for divisibility
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by the first 170 or so small primes, and assuming I<a> is not
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divisible by any of these, applies 15 iterations of the Rabin-Miller
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probabilistic primality test.
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If the program discovers that the number is composite, it will print:
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Not prime (reason)
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Where I<reason> is either:
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divisible by small prime x
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Or:
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failed nth pseudoprime test
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In the first case, I<x> indicates the first small prime factor that
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was found. In the second case, I<n> indicates which of the
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pseudoprime tests failed (numbered from 1)
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If this happens, the number is definitely not prime. However, if the
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number succeeds, this message results:
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Probably prime, 1 in 4^15 chance of false positive
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If this happens, the number is prime with very high probability, but
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its primality has not been absolutely proven, only demonstrated to a
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very convincing degree.
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The value I<a> can be input in standard decimal notation, or, if it is
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prefixed with I<Ox>, it will be read as hexadecimal.
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=head1 ENVIRONMENT
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You can control how many iterations of Rabin-Miller are performed on
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the candidate number by setting the I<RM_TESTS> environment variable
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to an integer value before starting up B<isprime>. This will change
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the output slightly if the number passes all the tests.
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=head1 SEE ALSO
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gcd(1), invmod(1), lap(1)
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=head1 AUTHOR
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Michael J. Fromberger <sting@linguist.dartmouth.edu>
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Thayer School of Engineering, Hanover, New Hampshire, USA
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$Date: 2000/07/14 00:44:33 $
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