Primality proof for n = 2707339:
Take b = 2.
b^(n-1) mod n = 1.
691 is prime.
b^((n-1)/691)-1 mod n = 551432, which is a unit, inverse 1779950.
653 is prime.
b^((n-1)/653)-1 mod n = 1340424, which is a unit, inverse 683401.
(653 * 691) divides n-1.
(653 * 691)^2 > n.
n is prime by Pocklington's theorem.