This is a basic question about bitcoin security that I don't see answered adequately.

I'm not an expert in anything, so it is possible I am missing the obvious, but would still like an answer.

The bitcoin private key is a 256 bit number that contains a numerical address and a key to decrypt numerical messages sent to that address.

The number of key is quite high. The security of the bitcoin system seems to be based on the difficulty of using a public address to work backwords and find the private key. But there seems to be an obvious proof that shows that to be flawed.

In order to show that the current bitcoin key system is flawed, all that a person would need to do is show that there was a correlation between the relative position of a private key and the relative position of its corresponding public address.

In other words, if you took the lowest possible private key, a 256 bit number starting with 00000... etc, and the highest possible private key, a 256 bit number starting with 11111... etc, and you were able to show that the two public addresses for those keys formed hard boundaries, i.e., that all bitcoin public addresses fell between those two numbers in some mathematical formula or progression, then you would be showing that an accessible formula existed to work backwords from the public adrress to the private key.

The obvious question then, does some formula or progression exist that could put bitcoin addresses in sequence? Any set of numbers that are derived from another set of numbers ultimately can be ordered in the same sequence as the original set. Therefore it seems that the "security" of the cryptography used in bitcoin would come not from the size of the number set but rather from the computational difficulty of converting private key to public address or vice versa. Since in bitcoin the conversion in one direction, i.e., private key to public address, requires little effort, there is really no security once a formula or progression rule for addresses is discovered. And such a fomula or progression is easily findable by anyone with a little skill in that kind of thing.

... Is that accurate?