Formula for calculating the number of primes in the interval

P_n - a prime number

(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

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