Primality proof for n = 2377:

Take b = 2.

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

11 is prime.
b^((n-1)/11)-1 mod n = 1719, which is a unit, inverse 1044.

3 is prime.
b^((n-1)/3)-1 mod n = 1654, which is a unit, inverse 240.

(3^3 * 11) divides n-1.

(3^3 * 11)^2 > n.

n is prime by Pocklington's theorem.