Long time ago there was Primecoin which used some algorithm to find prime numbers. Why are they so important is simply explaind here:
https://stackoverflow.com/questions/439870/why-are-primes-important-in-cryptography

It looks like that the idea to both secure currency and do something more usefull while mining has not developed. I mined some of them at the very begininng of the project, but it did not make me millionaire - Primecoin is now nearly dead