Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 7150, which is a unit, inverse 2122.

19 is prime.

b^((n-1)/19)-1 mod n = 15757, which is a unit, inverse 4918.

(19 * 53) divides n-1.

(19 * 53)^2 > n.

n is prime by Pocklington's theorem.