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.