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.

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
       [http://core.tcl.tk/tcllib/reportlist].  Please also report any ideas for enhancements you
       may have for either package and/or documentation.

KEYWORDS

       number theory, prime

CATEGORY

       Mathematics

COPYRIGHT

       Copyright (c) 2010 Lars Hellström <Lars dot Hellstrom at residenset dot net>