Primality proof for n = 2249645791783395932842367:
Take b = 2.
b^(n-1) mod n = 1.
6015095699955604098509 is prime.
b^((n-1)/6015095699955604098509)-1 mod n = 1251268795712853646826547, which is a unit, inverse 567319654237115625048395.
(6015095699955604098509) divides n-1.
(6015095699955604098509)^2 > n.
n is prime by Pocklington's theorem.