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.