Primality proof for n = 720869:
Take b = 2.
b^(n-1) mod n = 1.
10601 is prime. b^((n-1)/10601)-1 mod n = 357937, which is a unit, inverse 411018.
(10601) divides n-1.
(10601)^2 > n.
n is prime by Pocklington's theorem.