Primality proof for n = 365357:

Take b = 2.

b^(n-1) mod n = 1.

379 is prime.
b^((n-1)/379)-1 mod n = 207697, which is a unit, inverse 310280.

241 is prime.
b^((n-1)/241)-1 mod n = 212435, which is a unit, inverse 112886.

(241 * 379) divides n-1.

(241 * 379)^2 > n.

n is prime by Pocklington's theorem.