Take b = 3.

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

41 is prime.

b^((n-1)/41)-1 mod n = 1217, which is a unit, inverse 10196.

13 is prime.

b^((n-1)/13)-1 mod n = 6210, which is a unit, inverse 19906.

(13 * 41) divides n-1.

(13 * 41)^2 > n.

n is prime by Pocklington's theorem.