Take b = 2.

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

119194609 is prime.
b^((n-1)/119194609)-1 mod n = 2860124223111, which is a unit, inverse 3071778908036.

(119194609) divides n-1.

(119194609)^2 > n.

n is prime by Pocklington's theorem.