Primality proof for n = 1361:
Take b = 2.
b^(n-1) mod n = 1.
17 is prime.
b^((n-1)/17)-1 mod n = 315, which is a unit, inverse 795.
5 is prime.
b^((n-1)/5)-1 mod n = 210, which is a unit, inverse 512.
(5 * 17) divides n-1.
(5 * 17)^2 > n.
n is prime by Pocklington's theorem.