Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 9970, which is a unit, inverse 11380.

3 is prime.

b^((n-1)/3)-1 mod n = 4929, which is a unit, inverse 11077.

(3 * 53) divides n-1.

(3 * 53)^2 > n.

n is prime by Pocklington's theorem.