Mr Plutonium would not know what you are talking about, as he does not know what the adjective "infinite" means.
Anyway, your (1) is plain false. It is not an "=", but a crude approximation that you are talking about there. How close your approximation gets to reality depends sensitively on the exact distribution of the primes. Which is what everybody discusses anyway, and why the Riemann hypothesis is considered so important.
If you are willing to study any publications on the topic, I can give you pointers to literature. I assume that you are not simply a crank. Cranks as a rule have absolutely no desire to learn anything about the subject they are cranking about.