Primality proof for n = 899183:

Take b = 2.

b^(n-1) mod n = 1.

449591 is prime.
b^((n-1)/449591)-1 mod n = 3, which is a unit, inverse 299728.

(449591) divides n-1.

(449591)^2 > n.

n is prime by Pocklington's theorem.