Take b = 2.

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

163 is prime.

b^((n-1)/163)-1 mod n = 39742528, which is a unit, inverse 102025030.

157 is prime.

b^((n-1)/157)-1 mod n = 23857135, which is a unit, inverse 20957351.

(157 * 163) divides n-1.

(157 * 163)^2 > n.

n is prime by Pocklington's theorem.