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.