Idea for secure password hash-likes, is this feasible/usable/workable?
I don't see anything horribly wrong with your proposal.  On the other hand, the obvious question would be "what advantage would this approach have over, say, PBKDF2 with a good salt"?


In your proposal, it is infeasible to recover the password from the hash (short of brute-force); that's also true of PBKDF2.
In your proposal, the hash is randomized (and so the same password doesn't always result in the same hash); that's also true of PBKDF2.


In addition, in your proposal, generating a hash is moderately expensive (it isn't cheap to find large random primes); with PBKDF2, it's no more expensive than validating a password.  I can't see any reason why you'd want to make generating a hash an expensive operation.  

Given that this proposal doesn't appear to have an advantage over well-accepted techniques, I can't recommend it.