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> one has to think there are useful hard problems to solve rather than just banging out SHA-256 hashes over and over.

I sincerely hope that a truly useful proof-of-work can be discovered. It would be a very big deal.

The problem is, the work has to be reliably verifiable, and easier to verify than just doing the work over again, which is why hashes are a good fit.

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Unless I am mistaken, you can verify arbitrary computations[0].

[0] http://arxiv.org/abs/1105.2003

The abstract says that "a practical general-purpose protocol for verifiable computation may be significantly closer to reality than previously realized". This should be interesting though, thanks for sharing!

You have a fair point, but I claim for a proof-of-work computation it might be good for it to be a bit unpractical. (Depending on the parameters, this paper is on my reading list but I haven't gone through it yet.) I think it's incredibly interesting also, in any case I hope you enjoy the paper :)

What about Primecoin?

See the discussion above. :) Prime number sequences are unlikely to be "useful" in the same sense as protein folding.

Another possibility.

Protein folding unfortunately isn't a good candidate, because verifying the work takes exactly as much effort as doing the work.

http://en.wikipedia.org/wiki/Proof-of-work_system

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