Primality proof for n = 298882421:
Take b = 2.
b^(n-1) mod n = 1.
14944121 is prime. b^((n-1)/14944121)-1 mod n = 1048575, which is a unit, inverse 168996585.
(14944121) divides n-1.
(14944121)^2 > n.
n is prime by Pocklington's theorem.