Primality proof for n = 4957:
Take b = 2.
b^(n-1) mod n = 1.
59 is prime.
b^((n-1)/59)-1 mod n = 2576, which is a unit, inverse 483.
7 is prime.
b^((n-1)/7)-1 mod n = 2694, which is a unit, inverse 4911.
(7 * 59) divides n-1.
(7 * 59)^2 > n.
n is prime by Pocklington's theorem.