There are many people mining for Bitcoin right this second.[Citation needed]
Bitcoin's proof-of-work mining system is based on a hash function (SHA-256, I believe), and there are ASICs built specifically for mining this.
Would it be possible to engineer a cryptocurrency such that the calculations of the mining process could be used to break hashed passwords? Without the miners knowing?
And, assuming a worldwide mining community approximately equivalent to Bitcoin's and with dedicated hardware for the purpose, would this be a feasible way of breaking hashed passwords?