Take b = 2.

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

1439 is prime.

b^((n-1)/1439)-1 mod n = 401513288, which is a unit, inverse 116350268.

503 is prime.

b^((n-1)/503)-1 mod n = 407725782, which is a unit, inverse 199125093.

(503 * 1439) divides n-1.

(503 * 1439)^2 > n.

n is prime by Pocklington's theorem.