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.