Primality proof for n = 329053:
Take b = 2.
b^(n-1) mod n = 1.
1613 is prime. b^((n-1)/1613)-1 mod n = 211610, which is a unit, inverse 8977.
(1613) divides n-1.
(1613)^2 > n.
n is prime by Pocklington's theorem.