Primality proof for n = 449:
Take b = 3.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 323, which is a unit, inverse 253.
2 is prime.
b^((n-1)/2)-1 mod n = 447, which is a unit, inverse 224.
(2^6 * 7) divides n-1.
(2^6 * 7)^2 > n.
n is prime by Pocklington's theorem.