nextcand

Calc Software Package for Number Calc

NAME
    nextcand - next candidate for primeness

SYNOPSIS
    nextcand(n [,count [, skip [, residue [,modulus]]]])

TYPES
    n		integer
    count	integer with absolute value less than 2^24, defaults to 1
    skip	integer. defaults to 1
    residue	integer, defaults to 0
    modulus	integer, defaults to 1

    return	integer

DESCRIPTION
    If modulus is nonzero, nextcand(n, count, skip, residue, modulus)
    returns the least integer i greater than abs(n) expressible as
    residue + k * modulus, where k is an integer, for which
    ptest(i,count,skip) == 1, or if there is no such integer, zero.

    If abs(n) < 2^32, count >= 0, and the returned value i is not zero, then
    i is definitely prime.  If count is not zero and the returned
    value i is greater than 2^32, then i is probably prime, particularly
    if abs(count) > 1.

    If skip == 0, and abs(n) >= 2^32 or count < 0, the probabilistic test with
    random bases is used so that if n is composite the
    probability that it passes ptest() is less than 4^-abs(count).

    If skip == 1 (the default value), the bases used in the probabilistic
    test are the first abs(count) primes 2, 3, 5, ...

    For other values of skip, the bases used in the probabilistic tests
    are the abs(count) consecutive integers, skip, skip + 1, skip + 2, ...

    In any case, if the integer returned by nextcand() is not zero,
    all integers between abs(n) and that integer are composite.

    If modulus is zero, the value returned is that of residue if this is
    greater than abs(n) and ptest(residue,count,skip) = 1. Otherwise
    zero is returned.

RUNTIME
    The runtime for v = nextcand(n, ...) will depend strongly on the
    number and nature of the integers between n and v.	If this number
    is reasonably large the size of count is largely irrelevant as the
    compositeness of the numbers between n and v will usually be
    determined by the test for small prime factors or one pseudoprime
    test with some base b.  If N > 1, count should be positive so that
    candidates divisible by small primes will be passed over quickly.

    On the average for random n with large word-count N, the runtime seems
    to be roughly K/N^3 some constant K.

EXAMPLE
    ; print nextcand(50), nextcand(112140,-2), nextcand(112140,-3)
    53 112141 112153

    ; print nextcand(100,1,1,1,6), nextcand(100,1,1,-1,6)
    103 101

    ; print nextcand(100,1,1,2,6), nextcand(100,1,1,303,202)
    1 101

    ; print nextcand(2e60, 1, 1, 31, 1e30)
    2000000000000000000000000000053000000000000000000000000000031

LIMITS
    none

LINK LIBRARY
    int znextcand(ZVALUE n, long count, long skip, ZVALUE res, ZVALUE mod,
	ZVALUE *cand)

SEE ALSO
    factor, isprime, lfactor, nextprime, prevcand, prevprime,
    pfact, pix, ptest

## Copyright (C) 1999-2006  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
##
## @(#) $Revision: 29.4 $
## @(#) $Id: nextcand,v 29.4 2006/06/25 22:16:55 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/nextcand,v $
##
## Under source code control:	1996/02/25 00:27:43
## File existed as early as:	1996
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/