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.