Take b = 2.

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

31 is prime. b^((n-1)/31)-1 mod n = 1027, which is a unit, inverse 203.

7 is prime. b^((n-1)/7)-1 mod n = 97, which is a unit, inverse 403.

(7 * 31) divides n-1.

(7 * 31)^2 > n.

n is prime by Pocklington's theorem.