Take b = 2.

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

263 is prime.

b^((n-1)/263)-1 mod n = 209813, which is a unit, inverse 255618.

113 is prime.

b^((n-1)/113)-1 mod n = 141423, which is a unit, inverse 1906.

(113 * 263) divides n-1.

(113 * 263)^2 > n.

n is prime by Pocklington's theorem.