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.