Primality proof for n = 397:
Take b = 2.
b^(n-1) mod n = 1.
11 is prime.
b^((n-1)/11)-1 mod n = 289, which is a unit, inverse 136.
2 is prime.
b^((n-1)/2)-1 mod n = 395, which is a unit, inverse 198.
(2^2 * 11) divides n-1.
(2^2 * 11)^2 > n.
n is prime by Pocklington's theorem.