draft of the formula

Formula for calculating the number of primes in the interval

P_n - a prime number
  (n) - a prime number

 

We denote

  a (x)

- A power series

 

Geometric progression

 

converges for

 

and diverges for

 

The domain of convergence is the interval (-1, 1), which excludes both ends, x = +1 and x = -1. The sum of the series in the region of convergence is

 

- Formula for calculating the number of primes in the interval

 

Sergey Sitnikov