Primality proof for n = 138463057:
Take b = 2.
b^(n-1) mod n = 1.
961549 is prime. b^((n-1)/961549)-1 mod n = 75069463, which is a unit, inverse 96854655.
(961549) divides n-1.
(961549)^2 > n.
n is prime by Pocklington's theorem.