Primality proof for n = 438281:

Take b = 2.

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

10957 is prime.
b^((n-1)/10957)-1 mod n = 27604, which is a unit, inverse 232938.

(10957) divides n-1.

(10957)^2 > n.

n is prime by Pocklington's theorem.