Primality proof for n = 50711861:

Take b = 2.

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

3919 is prime.
b^((n-1)/3919)-1 mod n = 49876571, which is a unit, inverse 28475661.

647 is prime.
b^((n-1)/647)-1 mod n = 41583436, which is a unit, inverse 34551630.

(647 * 3919) divides n-1.

(647 * 3919)^2 > n.

n is prime by Pocklington's theorem.