Take b = 2.

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

457 is prime.

b^((n-1)/457)-1 mod n = 1574612, which is a unit, inverse 1978403.

11 is prime.

b^((n-1)/11)-1 mod n = 970484, which is a unit, inverse 1436321.

(11 * 457) divides n-1.

(11 * 457)^2 > n.

n is prime by Pocklington's theorem.