Take b = 2.

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

91309423 is prime. b^((n-1)/91309423)-1 mod n = 63631457236067, which is a unit, inverse 58727005515932.

(91309423) divides n-1.

(91309423)^2 > n.

n is prime by Pocklington's theorem.