Prime numbers / pseudo-random

What I find worth thinking about is that there are many statements about prime numbers which I think are not possible at all without considering the prime numbers as pseudo-random, but this has never been proved.

So it is true: If prime numbers are pseudo-random, then certain properties apply, from which in turn it follows that they are pseudo-random. A circular argument.

I think this is worth discussing. The "last digit" of my closed thread is an example, which shows randomness or not.