So how hard would it be to design for example, a game where the general space contained 'prime numbers' for example, and that space was populated with primes to some extent, any that are already known, but the person could use whatever abilities they have, including creating bots, to find new primes and win prizes.
https://www.youtube.com/watch?v=EK32jo7i5LQWould that be a 'simple' Xaya project or would it need a lot of paid developers?
That's an interesting suggestion. I think the main difficulty would be to come up with the right sort of tasks, i.e. such that the task is hard but easy to verify. I'm no expert in number theory, so I don't know if there are efficient proofs for a number being prime (more efficient than finding one). I assume you don't want to go with one of the algorithms that just prove a number is prime "with high probability". The next difficulty probably would be coming up with a good economic model for the game, so it doesn't follow the typical hype-and-crash of play-to-earn games.
But all in all, if you can solve the design issues, it is probably not too hard to implement in Xaya.