Take b = 2.

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

41 is prime.

b^((n-1)/41)-1 mod n = 631, which is a unit, inverse 2278.

11 is prime.

b^((n-1)/11)-1 mod n = 1084, which is a unit, inverse 452.

(11 * 41) divides n-1.

(11 * 41)^2 > n.

n is prime by Pocklington's theorem.