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78 lines
2.6 KiB
Plaintext
78 lines
2.6 KiB
Plaintext
NAME
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factor - smallest prime factor not exceeding specified limit
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SYNOPSIS
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factor(n [, limit [, err]])
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TYPES
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n integer
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limit integer with abs(limit) < 2^32, defaults to 2^32 - 1
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err integer
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return positive integer or err
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DESCRIPTION
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This function ignores the signs of n and limit, so here we shall
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assume n and limit are both nonnegative.
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If n has a prime proper factor less than or equal to limit, then
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factor(n, limit) returns the smallest such factor.
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NOTE: A proper factor of n>1 is a factor < n. In other words,
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for n>1 is not a proper factor of itself. The value 1
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is a special case because 1 is a proper factor of 1.
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When every prime proper factor of n is greater than limit, 1 is
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returned. In particular, if limit < 2, factor(n, limit) always
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returns 1. Also, factor(n,2) returns 2 if and only if n is even
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and n > 2.
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If 1 < n < nextprime(limit)^2, then f(n, limit) == 1 <==> n is prime.
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For example, if 1 < n < 121, n is prime if and only if f(n,7) == 1.
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If limit >= 2^32, factor(n, limit) causes an error and
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factor(n, limit, err) returns the value of err.
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EXAMPLE
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; print factor(35,4), factor(35,5), factor(35), factor(-35)
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1 5 5 5
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; print factor(2^32 + 1), factor(2^47 - 1), factor(2^59 - 1)
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641 2351 179951
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LIMITS
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limit < 2^32
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LINK LIBRARY
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FLAG zfactor(ZVALUE n, ZVALUE limit, ZVALUE *res)
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SEE ALSO
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isprime, lfactor, nextcand, nextprime, prevcand, prevprime,
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pfact, pix, ptest
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## Copyright (C) 1999-2006 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## @(#) $Revision: 30.2 $
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## @(#) $Id: factor,v 30.2 2013/08/18 20:15:13 chongo Exp $
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## @(#) $Source: /usr/local/src/bin/calc/help/RCS/factor,v $
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##
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## Under source code control: 1995/12/18 12:34:57
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## File existed as early as: 1995
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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