Primality proof for n = 1381:
Take b = 2.
b^(n-1) mod n = 1.
23 is prime.
b^((n-1)/23)-1 mod n = 424, which is a unit, inverse 114.
5 is prime.
b^((n-1)/5)-1 mod n = 100, which is a unit, inverse 1091.
(5 * 23) divides n-1.
(5 * 23)^2 > n.
n is prime by Pocklington's theorem.