#!/usr/bin/perl
# bigfact - calculate prime factors
use strict;
use integer;

use vars qw{ $opt_b $opt_d };
use Getopt::Std;

@ARGV && getopts('bd')		or die "usage: $0 [-b] number ...";

my $BIG;

load_biglib() if $opt_b;

ARG: foreach my $orig ( @ARGV ) {
    my ($n, $root, %factors, $factor);
    $n = $opt_b ? Math::BigInt->new($orig) : $orig;
    if ($n + 0 ne $n) { # don't use -w for this
	printf STDERR "bignum: %s would become %s\n", $n, $n+0 if $opt_d;
	load_biglib();
	$n = Math::BigInt->new($orig);
    }
    printf "%-10s ", $n;

    # Here $sqi will be the square of $i. We will take advantage
    # of the fact that ($i + 1) ** 2 == $i ** 2 + 2 * $i + 1.
    for (my ($i, $sqi) = (2, 4); $sqi <= $n; $sqi += 2 * $i ++ + 1) {
	while ($n % $i == 0) {
	    $n /= $i;
	    print STDERR "<$i>" if $opt_d;
	    $factors {$i} ++;
	}
    }

    if ($n != 1 && $n != $orig) { $factors{$n}++ }
    if (! %factors) {
	print "PRIME\n";
	next ARG;
    }
    for $factor ( sort { $a <=> $b } keys %factors ) {
	print "$factor";
	if ($factors{$factor} > 1) {
	    print "**$factors{$factor}";
	}
	print " ";
    }
    print "\n";
}

# this simulates a use, but at run time
sub load_biglib {
    require Math::BigInt;
    Math::BigInt->import();
    $BIG++;
}