Primality proof for n = 1468672999:

Take b = 2.

b^(n-1) mod n = 1.

1399 is prime.
b^((n-1)/1399)-1 mod n = 1030835878, which is a unit, inverse 1148455144.

313 is prime.
b^((n-1)/313)-1 mod n = 975356196, which is a unit, inverse 1464338507.

(313 * 1399) divides n-1.

(313 * 1399)^2 > n.

n is prime by Pocklington's theorem.