Take b = 2.

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

419 is prime.

b^((n-1)/419)-1 mod n = 462977, which is a unit, inverse 360540.

113 is prime.

b^((n-1)/113)-1 mod n = 331310, which is a unit, inverse 391197.

(113 * 419) divides n-1.

(113 * 419)^2 > n.

n is prime by Pocklington's theorem.