Primality proof for n = 243259963:

Take b = 2.

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

41413 is prime.
b^((n-1)/41413)-1 mod n = 186016206, which is a unit, inverse 231035809.

(41413) divides n-1.

(41413)^2 > n.

n is prime by Pocklington's theorem.