Primality proof for n = 1051:
Take b = 2.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 800, which is a unit, inverse 984.
5 is prime.
b^((n-1)/5)-1 mod n = 306, which is a unit, inverse 79.
(5^2 * 7) divides n-1.
(5^2 * 7)^2 > n.
n is prime by Pocklington's theorem.