Take b = 2.

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

31 is prime.

b^((n-1)/31)-1 mod n = 1546, which is a unit, inverse 449.

5 is prime.

b^((n-1)/5)-1 mod n = 757, which is a unit, inverse 1802.

(5 * 31) divides n-1.

(5 * 31)^2 > n.

n is prime by Pocklington's theorem.