Take b = 2.

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

163 is prime.

b^((n-1)/163)-1 mod n = 95770, which is a unit, inverse 64012.

11 is prime.

b^((n-1)/11)-1 mod n = 69552, which is a unit, inverse 23118.

(11 * 163) divides n-1.

(11 * 163)^2 > n.

n is prime by Pocklington's theorem.