Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 537587, which is a unit, inverse 282134.

11 is prime.

b^((n-1)/11)-1 mod n = 199177, which is a unit, inverse 229735.

7 is prime.

b^((n-1)/7)-1 mod n = 116903, which is a unit, inverse 687840.

(7 * 11 * 53) divides n-1.

(7 * 11 * 53)^2 > n.

n is prime by Pocklington's theorem.