Take b = 2.

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

31 is prime.

b^((n-1)/31)-1 mod n = 1966, which is a unit, inverse 62657.

11 is prime.

b^((n-1)/11)-1 mod n = 77599, which is a unit, inverse 22752.

(11^2 * 31) divides n-1.

(11^2 * 31)^2 > n.

n is prime by Pocklington's theorem.