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>

tcllib                                                 1.0                                 math::numtheory(3tcl)