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>