factor(1) [opensolaris man page]

factor(1)							   User Commands							 factor(1)

NAME

       factor - obtain the prime factors of a number

SYNOPSIS

       factor [integer]

DESCRIPTION

       factor  writes  to standard input all prime factors for any positive integer less than or equal to 10^14. The prime factors are written the
       proper number of times.

       If factor is used without an argument, it waits for an integer to be entered. After entry of the integer, it factors it, writes	its  prime
       factors the proper number of times, and then waits for another integer. factor exits if a 0 or any non-numeric character is entered.

       If factor is invoked with an argument (integer), it writes the integer, factors it and writes all the prime factors as described above, and
       then exits. If the argument is 0 or non-numeric, factor writes a 0 and then exits.

       The maximum time to factor an integer is proportional to sqrt(n), where n is the integer which is entered. factor will take this time  when
       n is prime or the square of a prime.

OPERANDS

       integer	  Any positive integer less than or equal to 10^14.

EXIT STATUS

       0    Successful completion.

       1    An error occurred.

DIAGNOSTICS

       factor prints the error message Ouch! for input out of range or for garbage input.

ATTRIBUTES

       See attributes(5) for descriptions of the following attributes:

       +-----------------------------+-----------------------------+
       |      ATTRIBUTE TYPE	     |	    ATTRIBUTE VALUE	   |
       +-----------------------------+-----------------------------+
       |Availability		     |SUNWesu			   |
       +-----------------------------+-----------------------------+

SEE ALSO

       attributes(5)

SunOS 5.11							    31 Jan 1996 							 factor(1)

math::numtheory(3tcl)						 Tcl Math Library					     math::numtheory(3tcl)

__________________________________________________________________________________________________________________________________________________

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 number-theoretic operations, though at the moment it only provides that of testing whether an inte-
       ger 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 proba-
	      bly  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 Hellstrom <Lars dot Hellstrom at residenset dot net>

math									1.0						     math::numtheory(3tcl)