Primality proof for n = 2851:
Take b = 2.
b^(n-1) mod n = 1.
19 is prime.
b^((n-1)/19)-1 mod n = 2823, which is a unit, inverse 1120.
5 is prime.
b^((n-1)/5)-1 mod n = 2743, which is a unit, inverse 2719.
(5^2 * 19) divides n-1.
(5^2 * 19)^2 > n.
n is prime by Pocklington's theorem.