Take b = 2.

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

41 is prime.

b^((n-1)/41)-1 mod n = 423, which is a unit, inverse 23150.

19 is prime.

b^((n-1)/19)-1 mod n = 7813, which is a unit, inverse 13404.

(19 * 41) divides n-1.

(19 * 41)^2 > n.

n is prime by Pocklington's theorem.