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.