Primality proof for n = 359767:
Take b = 2.
b^(n-1) mod n = 1.
79 is prime.
b^((n-1)/79)-1 mod n = 296958, which is a unit, inverse 92621.
23 is prime.
b^((n-1)/23)-1 mod n = 10691, which is a unit, inverse 335538.
(23 * 79) divides n-1.
(23 * 79)^2 > n.
n is prime by Pocklington's theorem.