Take b = 2.

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

167 is prime.

b^((n-1)/167)-1 mod n = 1986342, which is a unit, inverse 221100.

53 is prime.

b^((n-1)/53)-1 mod n = 2027033, which is a unit, inverse 1498234.

(53 * 167) divides n-1.

(53 * 167)^2 > n.

n is prime by Pocklington's theorem.