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.