Generating plausible private keys isn't that trivial. They are derived in a specific process from a part of the public key, and this process involves double hashing.

This I did not know. It cleared up the issue!

Yes, I've read about Generative Adversarial Networks. There are two parts: a generative network that generates possible solutions and an adversarial network that judges them.

But let's get back to plausible private key.

How far from having a plausible keys are you to finding the actual key that corresponds to a public key in general terms?