NAME
    lfactor - smallest prime factor in first specified number of primes

SYNOPSIS
    lfactor(n, m)

TYPES
    n           integer
    m           nonnegative integer <= 203280221 (= number of primes < 2^32)

    return      positive integer

DESCRIPTION
    This function ignores the signs of n and m, so here we shall
    assume n and limit are both nonnegative.

    If n is nonzero and abs(n) has a prime proper factor in the first
    m primes (2, 3, 5, ...), then lfactor(n, m) returns the smallest
    such factor.  Otherwise 1 is returned.

    If n is nonzero and m = pix(limit), then lfactor(n, m) returns the
    same as factor(n, limit).

    Both lfactor(n, 0) and lfactor(1, m) return 1 for all n and m.
    Also lfactor(0, m) always returns 1, and factor(0, limit) always
    returns 2 if limit >= 2.

EXAMPLE
    ; print lfactor(35,2), lfactor(35,3), lfactor(-35, 3)
    1 5 5

    ; print lfactor(2^32+1,115), lfactor(2^32+1,116), lfactor(2^59-1,1e5)
    1 641 179951

LIMITS
    m <= 203280221 (= number of primes < 2^32)

LINK LIBRARY
    NUMBER *qlowfactor(NUMBER *n, NUMBER *count)
    FULL zlowfactor(ZVALUE z, long count)

SEE ALSO
    factor, isprime, nextcand, 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.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:   1995/12/18 12:34:57
## File existed as early as:    1995
##
## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
