Primality proof for n = 50619101710669:

Take b = 2.

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

78797 is prime.
b^((n-1)/78797)-1 mod n = 8578086428227, which is a unit, inverse 11041571632918.

21101 is prime.
b^((n-1)/21101)-1 mod n = 12274997290450, which is a unit, inverse 47867361158379.

(21101 * 78797) divides n-1.

(21101 * 78797)^2 > n.

n is prime by Pocklington's theorem.