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.