mersenne.cal

Calc Software Package for Number Calc

/*
 * 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.
 * 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
 *
 * @(#) $Revision: 29.2 $
 * @(#) $Id: mersenne.cal,v 29.2 2000/06/07 14:02:25 chongo Exp $
 * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/mersenne.cal,v $
 *
 * 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);
}