Primality proof for n = 4349:
Take b = 2.
b^(n-1) mod n = 1.
1087 is prime. b^((n-1)/1087)-1 mod n = 15, which is a unit, inverse 290.
(1087) divides n-1.
(1087)^2 > n.
n is prime by Pocklington's theorem.