Primality proof for n = 1545857:

Take b = 2.

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

929 is prime.
b^((n-1)/929)-1 mod n = 1293945, which is a unit, inverse 82137.

13 is prime.
b^((n-1)/13)-1 mod n = 681680, which is a unit, inverse 288.

(13 * 929) divides n-1.

(13 * 929)^2 > n.

n is prime by Pocklington's theorem.