Primality proof for n = 1373:
Take b = 2.
b^(n-1) mod n = 1.
7 is prime. b^((n-1)/7)-1 mod n = 332, which is a unit, inverse 244.
(7^3) divides n-1.
(7^3)^2 > n.
n is prime by Pocklington's theorem.