Primality proof for n = 821796863:
Take b = 2.
b^(n-1) mod n = 1.
11105363 is prime. b^((n-1)/11105363)-1 mod n = 334418062, which is a unit, inverse 419309132.
(11105363) divides n-1.
(11105363)^2 > n.
n is prime by Pocklington's theorem.