Primality proof for n = 397429:
Take b = 2.
b^(n-1) mod n = 1.
33119 is prime. b^((n-1)/33119)-1 mod n = 4095, which is a unit, inverse 287857.
(33119) divides n-1.
(33119)^2 > n.
n is prime by Pocklington's theorem.