Primality proof for n = 2707:
Take b = 2.
b^(n-1) mod n = 1.
41 is prime.
b^((n-1)/41)-1 mod n = 631, which is a unit, inverse 2278.
11 is prime.
b^((n-1)/11)-1 mod n = 1084, which is a unit, inverse 452.
(11 * 41) divides n-1.
(11 * 41)^2 > n.
n is prime by Pocklington's theorem.