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.