Following my recent post
'Casting out nines' instead of leading zeros on Proof of Work,
I came up with another idea that might be interesting:
The sha-256 hash found in block mining, A, would need to be such that:
A^2+(sha256(A))^2=C^2, and C was an integer.So for instance, miners would try a nonce and find the sha-256 hash when mining a block.
The hash of that hash would have to be so that the two numbers, in base10, were "a" and "b" of a Pythagorean triple (a^2+b^2=c^2).
Of course you would be discarding a lot of potential candidates in the way B gets tied to A as an hash of it, but still, you would always be finding a Pythagorean triple in each block created.
And finding out how difficult the problem is, statistically/experimentally, would also be interesting.
We would get to know how hard is finding 'Pythagorean triples' with numbers of this magnitude, and eventually this could reveal interesting for mathematical study and research.