The Forum (dxdy) proved that it is possible k = const

The Forum (dxdy) showed that k can be k - constant. And the inequality 

with (k = const), will be performed for any (P_n).

This problem did not arise out of nowhere 

And so to formulate it, assume there is an interval in which at least one prime number

(n>16)

Question. Is there such a coefficient k (constant), which,  

(Evidence that is) it follows in the interval

There is no prime number.

 What can it give? For example. Determine the interval (2, k) such that the coefficient of the end of the interval will be a prime number.

formula

the inequality

does not give any prime number, because the result, the value, the net error of the calculations As a result of calculations

it is a pure calculation error.

 

Hence the question of how legitimate the proof on the forum (dxdy) compared a formula which gives a net value of the error calculations and an asymptotic formula giving the number of primes?