Primality proof for n = 2551:
Take b = 2.
b^(n-1) mod n = 1.
17 is prime.
b^((n-1)/17)-1 mod n = 2088, which is a unit, inverse 1135.
5 is prime.
b^((n-1)/5)-1 mod n = 1500, which is a unit, inverse 1784.
(5^2 * 17) divides n-1.
(5^2 * 17)^2 > n.
n is prime by Pocklington's theorem.