Primality proof for n = 7899817:
Take b = 2.
b^(n-1) mod n = 1.
3259 is prime. b^((n-1)/3259)-1 mod n = 5840065, which is a unit, inverse 7593854.
(3259) divides n-1.
(3259)^2 > n.
n is prime by Pocklington's theorem.