Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 2784, which is a unit, inverse 2311.

7 is prime.

b^((n-1)/7)-1 mod n = 2945, which is a unit, inverse 2103.

(7 * 53) divides n-1.

(7 * 53)^2 > n.

n is prime by Pocklington's theorem.