Take b = 3.

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

53 is prime.

b^((n-1)/53)-1 mod n = 3290, which is a unit, inverse 3778.

3 is prime.

b^((n-1)/3)-1 mod n = 941, which is a unit, inverse 4138.

(3^2 * 53) divides n-1.

(3^2 * 53)^2 > n.

n is prime by Pocklington's theorem.