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I cleaned up the code for cf_exam.pl just now. Making the script better also made it a little shorter, but I doubt that it is any faster. Anyway, have at it!
#!/usr/bin/perl
use strict;
use warnings;
use POSIX qw/ceil/;
my $m = $ARGV[0];
my ( $r_cand, $s_cand, $rc_ceil, $n_iters, $factor );
$n_iters = 1;
$s_cand = ceil( sqrt( $m ) );
$r_cand = $s_cand * $s_cand - $m;
# print "$s_cand,$r_cand\n";
$rc_ceil = ceil( sqrt( $r_cand ) );
while ( ( $rc_ceil * $rc_ceil ) > $r_cand ) {
$s_cand++;
$r_cand = $s_cand * $s_cand - $m;
$rc_ceil = ceil( sqrt( $r_cand ) );
$n_iters++;
}
$factor = $s_cand - $rc_ceil;
print "\n$m = $factor * ", $m/$factor, ".\n";;
print "Factorization found in $n_iters iterations.\n";
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