New formula for obtaining prime numbers with examples (related to the queens placement problem and the millennium problem)  has been formulated:

Are there infinitely many primes

of form

(Kublanovsky Primes Problem )?

This is a generalization of Mersenne Primes Problem, because it is easy to see that for

it is the Mersenne Primes Problem.

example 1.

is prime.

example2.

is prime.

example3.

is prime.