Primality proof for n = 959170211:

Take b = 2.

b^(n-1) mod n = 1.

732191 is prime.
b^((n-1)/732191)-1 mod n = 241595738, which is a unit, inverse 728121441.

(732191) divides n-1.

(732191)^2 > n.

n is prime by Pocklington's theorem.