Primality proof for n = 2861:
Take b = 2.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 1384, which is a unit, inverse 2338.
11 is prime.
b^((n-1)/11)-1 mod n = 2367, which is a unit, inverse 1361.
(11 * 13) divides n-1.
(11 * 13)^2 > n.
n is prime by Pocklington's theorem.