Primality proof for n = 12320708804681:

Take b = 2.

b^(n-1) mod n = 1.

28287053 is prime.
b^((n-1)/28287053)-1 mod n = 5861960871100, which is a unit, inverse 3774419832656.

(28287053) divides n-1.

(28287053)^2 > n.

n is prime by Pocklington's theorem.