Primality proof for n = 5676017:
Take b = 2.
b^(n-1) mod n = 1.
354751 is prime. b^((n-1)/354751)-1 mod n = 65535, which is a unit, inverse 2348183.
(354751) divides n-1.
(354751)^2 > n.
n is prime by Pocklington's theorem.