Provided by: tcllib_1.15-dfsg-2_all 
NAME
math::numtheory - Number Theory
SYNOPSIS
package require Tcl ?8.5?
package require math::numtheory ?1.0?
math::numtheory::isprime N ?option value ...?
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DESCRIPTION
This package is for collecting various number-theoretic operations, though at the moment it only provides
that of testing whether an integer is a prime.
math::numtheory::isprime N ?option value ...?
The isprime command tests whether the integer N is a prime, returning a boolean true value for
prime N and a boolean false value for non-prime N. The formal definition of ´prime' used is the
conventional, that the number being tested is greater than 1 and only has trivial divisors.
To be precise, the return value is one of 0 (if N is definitely not a prime), 1 (if N is
definitely a prime), and on (if N is probably prime); the latter two are both boolean true values.
The case that an integer may be classified as "probably prime" arises because the Miller-Rabin
algorithm used in the test implementation is basically probabilistic, and may if we are unlucky
fail to detect that a number is in fact composite. Options may be used to select the risk of such
"false positives" in the test. 1 is returned for "small" N (which currently means N <
118670087467), where it is known that no false positives are possible.
The only option currently defined is:
-randommr repetitions
which controls how many times the Miller-Rabin test should be repeated with randomly chosen
bases. Each repetition reduces the probability of a false positive by a factor at least 4.
The default for repetitions is 4.
Unknown options are silently ignored.
KEYWORDS
number theory, prime
CATEGORY
Mathematics
COPYRIGHT
Copyright (c) 2010 Lars Hellström <Lars dot Hellstrom at residenset dot net>