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.