Can we have proof of work algorithm that compute something actually useful? Like finding large prime numbers or something like this that have distributed computation programs. This way all this power wasted is at least not completely lost.
Anubis author here. I looked into protein folding. The problem is that protein folding requires scientific data, which can easily get into the gigabyte range. That is more data than I want to serve to clients. Unless there's a way to solve the big data problem, a lot of "compute for good" schemes are frankly unworkable.
Zero knowledge proofs are basically arbitrary proof of work models. There is some interesting work being done with MPC and ZK proving, so only a small part needs to live on the client. I wonder if this would make it feasible again
Unfortunately useful things usually require much more computation to find a useful result, they require distributing the search, and so can't reliably verify that you performed the work (most searches will not find anything, and you can just pretend to not have found anything without doing any work).
If a service had enough concurrent clients to reliably hit useful results quickly, you could verify that most did the work by checking if a hit was found, and either let everyone in or block everyone according to that; but then you're relying on the large majority being honest for your service to work at all, and some dishonest clients would still slip through.
