Primality proof for n = 820326650873:
Take b = 2.
b^(n-1) mod n = 1.
5396885861 is prime.
b^((n-1)/5396885861)-1 mod n = 152632546627, which is a unit, inverse 328259463411.
(5396885861) divides n-1.
(5396885861)^2 > n.
n is prime by Pocklington's theorem.