Primality proof for n = 1553407:
Take b = 2.
b^(n-1) mod n = 1.
2909 is prime. b^((n-1)/2909)-1 mod n = 1312388, which is a unit, inverse 1538480.
(2909) divides n-1.
(2909)^2 > n.
n is prime by Pocklington's theorem.