Primality proof for n = 198280883:

Take b = 2.

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

99140441 is prime.
b^((n-1)/99140441)-1 mod n = 3, which is a unit, inverse 66093628.

(99140441) divides n-1.

(99140441)^2 > n.

n is prime by Pocklington's theorem.