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Would the solving of the problem have a "difficulty" that could be adjusted to ensure that blocks appeared approximately every ten minutes? Is checking that the solution is valid a very fast operation? Are we sure that there is no "final" answer which would make the calculation unusable at some point? (Those are the three main factors for choosing what kind of work to do, as far as I can see)

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> Would the solving of the problem have a "difficulty" that could be adjusted to ensure that blocks appeared approximately every ten minutes

I am fairly certain you can design your problem to behave in a similar manner or in some manner that increases the complexity based on some criteria

> Is checking that the solution is valid a very fast operation?

That's the NP part in my question. Plenty of scientific problems out there that are fast to verify hard to compute. Ex. Prime Factorization

> Are we sure that there is no "final" answer which would make the calculation unusable at some point?

I would argue, and I might be wrong due to my ignorance on the subject here, that we can never "know" that. That's why P=NP is still an open question

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