Primality proof for n = 2963:
Take b = 2.
b^(n-1) mod n = 1.
1481 is prime. b^((n-1)/1481)-1 mod n = 3, which is a unit, inverse 988.
(1481) divides n-1.
(1481)^2 > n.
n is prime by Pocklington's theorem.