Primality proof for n = 196911713:

Take b = 2.

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

6153491 is prime.
b^((n-1)/6153491)-1 mod n = 159821322, which is a unit, inverse 114640451.

(6153491) divides n-1.

(6153491)^2 > n.

n is prime by Pocklington's theorem.