Sure, but that's a technology that does not exist. If you can figure out how to create a blockchain-like concept, where the 'proof of work' actually contributes to humanity, you have invented the next big thing.
Edit: Reading the comments below me, it looks like this is a space that is being actively explored. Exciting!
> The innovative prime proof-of-work in Primecoin not only provides security and minting to the network, but also generates a special form of prime number chains of interest to mathematical research. Thus primecoin network is energy-multiuse, compared to bitcoin.
This is of course very basic, but still, it's interesting.
You have the contract host record all operations and output on a ledger, and then ship that ledger/log out to monitors. This improves the auditability of the system, and enforces the backend logic as a contract. Deviations from the code are detectable by replay, and then provable. Flag the host and readjust your trust.
You can also find ways to reduce the cost of switching between traditional hosting models, such as using data-sharing networks (Dat, IPFS) to quickly "hydrate" a new host, and good ole configurable endpoints to make the switch.
It's the opposite of a trustless network; it's a trust network built on accountability. You watch hosts for bad behavior (such as the violation of the backend contract) and reconfigure trust around violations. No decentralized operation, but much less wasteful than PoW.
That's pretty much something like Git.
Seems difficult to find an actually useful mathematical problems that fits all these prerequisites.
>Curecoin puts ASICs to work at what they are good at–securing a blockchain, while it puts GPUs and CPUs to work with work items that can only be done on them–protein folding.
Do you (or anyone) have more information in how this works? Does this reward you directly for doing the folding (as opposed to validating)? How does that work? That looks like a very interesting concept, and if it's technologically sound then I'd love to see it gain popularity.
The problem is that for most problems you don't want to explore the space of potential problems randomly, you want to select ones that people care about. If you allow an actor to dictate what problem to work on then you can have that actor pick a problem they have already solved and will be able to roll back tx arbitrarily once they have control.
Wouldn't a cheaper throttle be easier?