Take b = 2.

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

911 is prime.

b^((n-1)/911)-1 mod n = 5342602, which is a unit, inverse 24573073.

31 is prime.

b^((n-1)/31)-1 mod n = 19185763, which is a unit, inverse 14921555.

(31 * 911) divides n-1.

(31 * 911)^2 > n.

n is prime by Pocklington's theorem.