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.