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.