Primality proof for n = 2969:
Take b = 2.
b^(n-1) mod n = 1.
53 is prime.
b^((n-1)/53)-1 mod n = 2784, which is a unit, inverse 2311.
7 is prime.
b^((n-1)/7)-1 mod n = 2945, which is a unit, inverse 2103.
(7 * 53) divides n-1.
(7 * 53)^2 > n.
n is prime by Pocklington's theorem.