Primality proof for n = 91309423:
Take b = 2.
b^(n-1) mod n = 1.
208469 is prime. b^((n-1)/208469)-1 mod n = 42114267, which is a unit, inverse 3379069.
(208469) divides n-1.
(208469)^2 > n.
n is prime by Pocklington's theorem.