Primality proof for n = 2998279:
Take b = 2.
b^(n-1) mod n = 1.
166571 is prime. b^((n-1)/166571)-1 mod n = 262143, which is a unit, inverse 426873.
(166571) divides n-1.
(166571)^2 > n.
n is prime by Pocklington's theorem.