A Windows password cracker based on rainbow tables
Ophcrack is a Windows password cracker based on a time-memory trade-off using rainbow tables. This is a new variant of Hellman's original trade-off, with better performance. It recovers 99.9% of alphanumeric passwords in seconds.
...But furthermore this way of finding primes interestingly leaves a hard nut to crack for mathematicians: In very rare cases it finds numbers that are not primes. For all primes below one million this phenomenon arises in exactly two cases:
31213 which is 7 * 7 * 7 * 7 * 13
336141 which is 3 * 3 * 13 * 13 * 13 * 17
Who can explain, why?