Primality proof for n = 365300797:
Take b = 2.
b^(n-1) mod n = 1.
4348819 is prime. b^((n-1)/4348819)-1 mod n = 301206970, which is a unit, inverse 271940863.
(4348819) divides n-1.
(4348819)^2 > n.
n is prime by Pocklington's theorem.