Primality proof for n = 337:
Take b = 2.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 63, which is a unit, inverse 107.
3 is prime.
b^((n-1)/3)-1 mod n = 127, which is a unit, inverse 69.
(3 * 7) divides n-1.
(3 * 7)^2 > n.
n is prime by Pocklington's theorem.