Take b = 2.

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

503 is prime.

b^((n-1)/503)-1 mod n = 199417, which is a unit, inverse 95122.

29 is prime.

b^((n-1)/29)-1 mod n = 667, which is a unit, inverse 473652.

(29 * 503) divides n-1.

(29 * 503)^2 > n.

n is prime by Pocklington's theorem.