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.