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.