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.