Primality proof for n = 1560953:
Take b = 2.
b^(n-1) mod n = 1.
4759 is prime. b^((n-1)/4759)-1 mod n = 548174, which is a unit, inverse 386199.
(4759) divides n-1.
(4759)^2 > n.
n is prime by Pocklington's theorem.