Isn't it possible to create a crypto currency where mining it computes something useful? Like larger and larger prime numbers or digits of pi or protein folding or something like that.
Yes, but a useful proof-of-work leads to a less secure block chain. Bitcoin is secure because you know that an attacker that wants to change the second to last block has to spend X million on computational peer to do that. But if those computations are useful outside mining itself, then the attack might become much chapter or almost free
