Primality proof for n = 360863:
Take b = 2.
b^(n-1) mod n = 1.
2693 is prime. b^((n-1)/2693)-1 mod n = 85222, which is a unit, inverse 190738.
(2693) divides n-1.
(2693)^2 > n.
n is prime by Pocklington's theorem.