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.