Primality proof for n = 5077:
Take b = 2.
b^(n-1) mod n = 1.
47 is prime.
b^((n-1)/47)-1 mod n = 4342, which is a unit, inverse 3509.
3 is prime.
b^((n-1)/3)-1 mod n = 3446, which is a unit, inverse 2235.
(3^3 * 47) divides n-1.
(3^3 * 47)^2 > n.
n is prime by Pocklington's theorem.