Primality proof for n = 50993:
Take b = 2.
b^(n-1) mod n = 1.
3187 is prime. b^((n-1)/3187)-1 mod n = 14542, which is a unit, inverse 31605.
(3187) divides n-1.
(3187)^2 > n.
n is prime by Pocklington's theorem.