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.