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As long as the work is hard to compute but quick to verify, sure. But you're probably going to run into the problem of having one central entity providing work units.

Well for the example: calculating primes does not require a central authority

If the problem was purely mathematical in nature, that's where you don't really need authority.

That's not right. It must be hard to produce, easy to verify, and be deterministically linked to the previous POW. That last feature is critical.

Hash the folded protein with the previous POW. Problem solved, no?

(I think the important thing is that you have to prove you didn't start the current pow until the previous work unit is done, right? Fortunately, there are lots of proteins to be folded. You can use the previous pow to select the parameters for the next pow. The hashes are uniformly distributed, so that will eventually range over the set of proteins.)

Not at all. What's stopping me from hashing the result with something else? The base of the work must be in changeable. That's the whole point of POW in this case. If you want to rewrite history you need to do the POW again, in your system that doesn't need to happen.

Check out Primecoin: https://en.wikipedia.org/wiki/Primecoin

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