Primality proof for n = 1559777:
Take b = 2.
b^(n-1) mod n = 1.
617 is prime.
b^((n-1)/617)-1 mod n = 1316979, which is a unit, inverse 1067062.
79 is prime.
b^((n-1)/79)-1 mod n = 949707, which is a unit, inverse 71110.
(79 * 617) divides n-1.
(79 * 617)^2 > n.
n is prime by Pocklington's theorem.