I've found this online currency someone has built as a project and it's "miner" / Proof of Work algorithm is as follows:
- Generate 32 bytes of random data and hash it, store the original value and the hash
- Test if the hash begins with a "server key" which is the 3 bytes the hash has to begin with to be valid
- Submit the value to the server and it will award you with some of the currency and change the server key if the value that you sent's hash begins with these first 3 bytes.
Since a SHA-256 hash is 32 bytes, and I would only need to guarantee the first 3 bytes to mine the currency, would it be possible to get values that produce a hash with these first 3 bytes, but faster than just random hashing?