Take b = 2.

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

419 is prime.

b^((n-1)/419)-1 mod n = 236159, which is a unit, inverse 533245.

97 is prime.

b^((n-1)/97)-1 mod n = 439587, which is a unit, inverse 345875.

(97 * 419) divides n-1.

(97 * 419)^2 > n.

n is prime by Pocklington's theorem.