numtheory (n)  Linux Manuals
numtheory: Number Theory
NAME
math::numtheory  Number Theory
SYNOPSIS
package require Tcl ?8.5?package require math::numtheory ?1.0?
math::numtheory::isprime N ?option value ...?
DESCRIPTION
This package is for collecting various numbertheoretic 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 nonprime 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 MillerRabin 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 MillerRabin 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, primeCATEGORY
MathematicsCOPYRIGHT
Copyright (c) 2010 Lars Hellström <Lars dot Hellstrom at residenset dot net>