Primality proof for n = 333814693:
Take b = 2.
b^(n-1) mod n = 1.
6247 is prime.
b^((n-1)/6247)-1 mod n = 84522612, which is a unit, inverse 260870676.
73 is prime.
b^((n-1)/73)-1 mod n = 125608130, which is a unit, inverse 187263298.
(73 * 6247) divides n-1.
(73 * 6247)^2 > n.
n is prime by Pocklington's theorem.