Primality proof for n = 7959649:
Take b = 2.
b^(n-1) mod n = 1.
82913 is prime. b^((n-1)/82913)-1 mod n = 7818849, which is a unit, inverse 2512773.
(82913) divides n-1.
(82913)^2 > n.
n is prime by Pocklington's theorem.