Primality proof for n = 16446708426521:

Take b = 2.

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

709927 is prime.
b^((n-1)/709927)-1 mod n = 10217411517563, which is a unit, inverse 6434305701839.

5623 is prime.
b^((n-1)/5623)-1 mod n = 3854076456948, which is a unit, inverse 3421417553134.

(5623 * 709927) divides n-1.

(5623 * 709927)^2 > n.

n is prime by Pocklington's theorem.