Primality proof for n = 2995763:

Take b = 2.

b^(n-1) mod n = 1.

397 is prime.
b^((n-1)/397)-1 mod n = 1477917, which is a unit, inverse 1007766.

11 is prime.
b^((n-1)/11)-1 mod n = 936915, which is a unit, inverse 2974989.

(11 * 397) divides n-1.

(11 * 397)^2 > n.

n is prime by Pocklington's theorem.