That could really be a great thing! The problem is that Mersenne primes are "sparse", i.e. there aren't many of them. Finding one could be like minting a new block, but it would be so rare that it won't be practical. For crypto, you would need something with many solutions, but then it's probably not so useful to find yet another solution...
you also generally speaking need something that is much easier to verify than it is to generate. I'm not saying it's impossible, but I don't think that "verifying" a protein folding in the "cryptocurrency" sense is a meaningful operation in the "useful" way you're hoping it to be.
