Primes

This project considers the problem of calculating primes as a sorting problem. It includes the most efficient tree-based sorting algorithm that is possible and shows that finding a new prime can be done by sorting the differences between the previous primes in the right way.

Unfortunately it has turned out that going this way is even more slowly than trying to find primes by brute force. So it can only be used as a test with heavy load for the sorting algorithm, which can be used for sorting any kind of data. And as already mentioned, it's just the most efficient tree-based sorting algorithm that you can get.

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?