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.