/usr/share/calc/help/prevcand is in apcalc-common 2.12.4.4-2.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | NAME
prevcand - previous candidate for primeness
SYNOPSIS
prevcand(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
The sign of n is ignored; in the following it is assumed that n >= 0.
prevcand(n, count, skip, residue, modulus) returns the greatest
positive integer i less 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 i, zero.
If n < 2^32, count >= 0, and the returned value i is not zero, i is
definitely prime. If n > 2^32, count != 0, and i is not zero,
i is probably prime, particularly if abs(count) is greater than 1.
With the default argument values, if n > 2, prevcand(n) returns the a
probably prime integer i less than n such that every integer
between i and n is composite.
If skip == 0, the bases used in the probabilistic test are random
and then the probability that the returned value is composite is
less than 1/4^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 are the abs(count) consecutive
integer skip, skip + 1, ...
If modulus = 0, the only values that may be returned are zero and the
value of residue. The latter is returned if it is positive, less
than n, and is such that ptest(residue, count, skip) = 1.
RUNTIME
The runtime for v = prevcand(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 between roughly K/N^3 some constant K.
EXAMPLE
; print prevcand(50), prevcand(2), prevcand(125,-1), prevcand(125,-2)
47 1 113 113
; print prevcand(100,1,1,1,6), prevcand(100,1,1,-1,6)
97 89
; print prevcand(100,1,1,2,6), prevcand(100,1,1,4,6),
2 0
; print prevcand(100,1,1,53,0), prevcand(100,1,1,53,106)
53 53
; print prevcand(125,1,3), prevcand(125,-1,3), prevcand(125,-2,3)
113 121 113
; print prevcand(2e60, 1, 1, 31, 1e30)
1999999999999999999999999999914000000000000000000000000000031
LIMITS
none
LINK LIBRARY
int zprevcand(ZVALUE n, long count, long skip, ZVALUE res, ZVALUE mod,
ZVALUE *cand)
SEE ALSO
factor, isprime, lfactor, nextcand, nextprime, 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.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: prevcand,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/prevcand,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/
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