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# math::numtheory(n) 1.0 "Tcl Math Library"

## Name

math::numtheory - Number Theory

## Synopsis

- package require
**Tcl ?8.5?** - package require
**math::numtheory ?1.0?**

## 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:

Unknown options are silently ignored.

## Bugs, Ideas, Feedback

This document, and the package it describes, will undoubtedly
contain bugs and other problems. Please report such in the category
*math :: numtheory* of the Tcllib Trackers. Please
also report any ideas for enhancements you may have for either
package and/or documentation.

## Category

Mathematics

## Copyright

Copyright © 2010 Lars Hellström <Lars dot Hellstrom at residenset dot net>