Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 1794, which is a unit, inverse 747.

11 is prime.

b^((n-1)/11)-1 mod n = 222, which is a unit, inverse 2443.

(11 * 53) divides n-1.

(11 * 53)^2 > n.

n is prime by Pocklington's theorem.