Primality proof for n = 297159362677:
Take b = 2.
b^(n-1) mod n = 1.
1627771 is prime. b^((n-1)/1627771)-1 mod n = 114170894340, which is a unit, inverse 44169280672.
(1627771) divides n-1.
(1627771)^2 > n.
n is prime by Pocklington's theorem.