Primality proof for n = 9374403413:

Take b = 2.

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

693989 is prime.
b^((n-1)/693989)-1 mod n = 8211844134, which is a unit, inverse 6020600718.

(693989) divides n-1.

(693989)^2 > n.

n is prime by Pocklington's theorem.