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.