Primality proof for n = 119802223514406673:
Take b = 2.
b^(n-1) mod n = 1.
2305472951 is prime.
b^((n-1)/2305472951)-1 mod n = 1639099712776573, which is a unit, inverse 112787762709745973.
(2305472951) divides n-1.
(2305472951)^2 > n.
n is prime by Pocklington's theorem.