Primality proof for n = 2400573761:
Take b = 3.
b^(n-1) mod n = 1.
1663 is prime.
b^((n-1)/1663)-1 mod n = 1701215345, which is a unit, inverse 1534051064.
347 is prime.
b^((n-1)/347)-1 mod n = 1380226035, which is a unit, inverse 1288538855.
(347 * 1663) divides n-1.
(347 * 1663)^2 > n.
n is prime by Pocklington's theorem.