Primality proof for n = 119611:

Take b = 2.

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

443 is prime.
b^((n-1)/443)-1 mod n = 106494, which is a unit, inverse 54585.

(443) divides n-1.

(443)^2 > n.

n is prime by Pocklington's theorem.