The way blockchain works is that you generate a problem based on the contents of the block. If the proof you find is in no way related to a block it cannot be a

The way blockchain works is that you generate a problem based on the contents of the block. If the proof you find is in no way related to a block it cannot be a cryptocurrency. You could make a system to reward people for finding proofs, but it would be more of a Bounty system or a Leaderboard than a cryptocurrency. Indeed people do put up prizes for those kind of things today.