Primality proof for n = 2281:
Take b = 2.
b^(n-1) mod n = 1.
19 is prime.
b^((n-1)/19)-1 mod n = 1358, which is a unit, inverse 1248.
5 is prime.
b^((n-1)/5)-1 mod n = 1513, which is a unit, inverse 1785.
(5 * 19) divides n-1.
(5 * 19)^2 > n.
n is prime by Pocklington's theorem.