Primality proof for n = 1584017372081:

Take b = 2.

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

138463057 is prime.
b^((n-1)/138463057)-1 mod n = 1174215046025, which is a unit, inverse 1338218265832.

(138463057) divides n-1.

(138463057)^2 > n.

n is prime by Pocklington's theorem.