This question already has an answer here:
Bitcoin miners work to solve a random puzzle as "proof of work". A huge amount of raw computing power is going into finding the solution to these puzzles, yet the actual solution to the puzzle serves no purpose other than to demonstrate that whoever found the solution has access to a great deal of computing power. Can the bitcoin protocol be modified to accept puzzles from the real world who's solution would actually have some social value? Perhaps some scientists, governments, or corporations would be willing to pay some amount to whoever solves some reasonably complex computational problem first, and they could contribute some BTC towards the reward a miner receives.
I understand that the particular puzzle chosen is very clever, particularly as its complexity may be easily adjusted as needed, the solution is well defined and easy to verify, and there's virtually no limit to the creation of new puzzles. I just wonder if something even more clever could be incorporated, if someone ever manages to come up with it.
To clarify, the analogy I have in mind is the way reCAPTCHAs have virtually replaced traditional CAPTCHAs, substituting socially valuable book digitization work for a socially useless text-guessing exercise.