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.