I think the question of
@kolleamm is well worth asking.
In the Bitcoin protocol, the mining process involves the computation of hashes with a certain number of leading zeros. The result of this computation has worth for the integrity of the blockchain but it is meaningless outside the blockchain. Can we devise a different protocol where the results of the computations in the mining process
both ensure the integrity of the blockchain and are meaningful outside the blockchain?
In an ideal world, we could use computations which would be done in any case. This would offset the environmental impact of proof-of-work entirely, solving a big problem with blockchains. (By the way, I think that there even bigger problems which aren't related to the topic at hand.)
Unfortunately, the computations need to be of a very special kind. As far as I can see, the following conditions need to apply
1) Solutions must be easily verifiable.
2) Solutions must not be pre-computable but linked to the previously computed solution.
3) The difficulty of the problems must be easily adjustable.
1)+2) are necessary to ensure the integrity of the blockchain, 3) is necessary to control the rate of transactions.
Obviously, the vast majority of interesting computations doesn't fulfill these conditions. So we don't live in an ideal world. But maybe there are computations of the required type which provide some value outside the blockchain?
Primecoin (https://www.coinbase.com/price/primecoin) thinks finding prime numbers is it and claims to have implemented a protocol which yields primes as a byproduct of the mining process. This plausibly fulfills condition 1) and there's some talk from the author about condition 3), but I don't see how condition 2) would be fulfilled. Also their white paper kind of reads like a high school project.
(I learned about it from
this question on Stackexchange which
@LucasB has linked to above. People there also make the point that having a byproduct with economic value might screw up the incentives.)