Take b = 3.

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

41 is prime.

b^((n-1)/41)-1 mod n = 36, which is a unit, inverse 2871.

3 is prime.

b^((n-1)/3)-1 mod n = 799, which is a unit, inverse 717.

(3^2 * 41) divides n-1.

(3^2 * 41)^2 > n.

n is prime by Pocklington's theorem.