There are three that try to find primes - Primecoin, Riecoin, and Nexus. This isn't "useful" but it's a bit more intellectually interesting than finding partial

There are three that try to find primes - Primecoin, Riecoin, and Nexus. This isn't "useful" but it's a bit more intellectually interesting than finding partial collisions in sha-2. (I wrote the miner that's now used for Riecoin.) There have been attempts to do others but none that really work, because in part of the problem you cite. It's also very hard to have a tune-able difficulty for the mining process.