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.