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Sure, but that only works if you both know the answer. Zero knowledge proofs are neat because you can prove you know the answer to somebody who doesn't know it.

That can reveal the secret.

If I know one value out of a known set of values then by sharing a hash anybody can hash the known values until they arrive at my hash, revealing my "secret."

One can also iterate over all primes and brute-force them to break RSA.

Yes, it works, but it doesn't because we'll all be dead when your computer has the answer.

> known set of values

This is false. When doing a hash commitment you include some randomness along with the value.

How is this verified?

Hashing parts of the problem works for interactive proofs.

I know a graph colouring, so I hash the {color, random salt} pair for every node. The other party chooses two connected nodes at random at asks me to reveal the {color, salt} pairs and checks if colors are different.