Primes
Calculate primes by using extremely fast sorting
...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.