The algorithm to keep the private key a secret is very complicated.
just because something is complicated for you to understand it doesn't mean it is not safe and should collapse! for example you don't understand how the universe works and how earth just doesn't disintegrate but that doesn't mean it should!!!
If such a pattern exists, we would have broken a lot of encryption algorithms by now, but only a few have been broken thus far (SHA-1, among others).
SHA-1 isn't exactly broken. they just found an easier way to find a hash collision which is still pretty hard to find which means you can find 2 messages if you look hard enough that return same hash. other than that you still can't reverse it (find the message by having the hash result) and you can't find a second preimage for it (meaning find another message that hashes to same result by having the hash).