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/*
* mersenne - perform a primality test of 2^p-1, for prime p>1
*
* Copyright (C) 1999 David I. Bell and Landon Curt Noll
*
* Primary author: David I. Bell
*
* 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.
*
* Under source code control: 1991/05/22 21:56:36
* File existed as early as: 1991
*
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* NOTE: See lucas.cal for a more general routine.
*/
define mersenne(p)
{
local u, i, p_mask;
/* firewall */
if (! isint(p))
quit "p is not an integer";
/* two is a special case */
if (p == 2)
return 1;
/* if p is not prime, then 2^p-1 is not prime */
if (! ptest(p,1))
return 0;
/* lltest: u(i+1) = u(i)^2 - 2 mod 2^p-1 */
u = 4;
for (i = 2; i < p; ++i) {
u = hnrmod(u^2 - 2, 1, p, -1);
}
/* 2^p-1 is prime iff u(p) = 0 mod 2^p-1 */
return (u == 0);
}