Take b = 2.

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

41 is prime.

b^((n-1)/41)-1 mod n = 816, which is a unit, inverse 1499.

31 is prime.

b^((n-1)/31)-1 mod n = 751, which is a unit, inverse 2201.

(31 * 41) divides n-1.

(31 * 41)^2 > n.

n is prime by Pocklington's theorem.