Primality proof for n = 9361973132609:
Take b = 3.
b^(n-1) mod n = 1.
105465631 is prime.
b^((n-1)/105465631)-1 mod n = 8513967533808, which is a unit, inverse 7570366960336.
(105465631) divides n-1.
(105465631)^2 > n.
n is prime by Pocklington's theorem.