Primality proof for n = 1557805355357:

Take b = 2.

b^(n-1) mod n = 1.

67153 is prime.
b^((n-1)/67153)-1 mod n = 1533053947245, which is a unit, inverse 128777833945.

10301 is prime.
b^((n-1)/10301)-1 mod n = 225752064249, which is a unit, inverse 573103266259.

(10301 * 67153) divides n-1.

(10301 * 67153)^2 > n.

n is prime by Pocklington's theorem.