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.