Take b = 2.

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

227 is prime.

b^((n-1)/227)-1 mod n = 10183703, which is a unit, inverse 317399.

113 is prime.

b^((n-1)/113)-1 mod n = 1872389, which is a unit, inverse 4199685.

(113 * 227) divides n-1.

(113 * 227)^2 > n.

n is prime by Pocklington's theorem.