Primality proof for n = 336113:
Take b = 2.
b^(n-1) mod n = 1.
3001 is prime. b^((n-1)/3001)-1 mod n = 327311, which is a unit, inverse 120935.
(3001) divides n-1.
(3001)^2 > n.
n is prime by Pocklington's theorem.