Primality proof for n = 2665442657:
Take b = 2.
b^(n-1) mod n = 1.
83295083 is prime. b^((n-1)/83295083)-1 mod n = 1629524638, which is a unit, inverse 1920438269.
(83295083) divides n-1.
(83295083)^2 > n.
n is prime by Pocklington's theorem.