Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 1274, which is a unit, inverse 2784.

5 is prime.

b^((n-1)/5)-1 mod n = 1732, which is a unit, inverse 2900.

(5 * 53) divides n-1.

(5 * 53)^2 > n.

n is prime by Pocklington's theorem.