k = const Continuing the theme

What would prove
  k = const

It suffices to prove

Prove that the integral part of the middle space has a limit

I'll try one more time, we assume there is a whole middle part of the gap (m) that would prove that this limit is sufficient to prove that a certain prime P_n for which the average gap is equal to (m) increase in size among the space is infinite, but does not exceed unity. You know, growth is not from the beginning, but with a certain number of P_n. On any of your proof enough for me to take a new (initial) prime number greater than P_n. For which the average gap (m +1) and all first