Primality proof for n = 6153491:
Take b = 2.
b^(n-1) mod n = 1.
5171 is prime. b^((n-1)/5171)-1 mod n = 3624545, which is a unit, inverse 4104544.
(5171) divides n-1.
(5171)^2 > n.
n is prime by Pocklington's theorem.