Primality proof for n = 1749899:
Take b = 2.
b^(n-1) mod n = 1.
6679 is prime. b^((n-1)/6679)-1 mod n = 310304, which is a unit, inverse 707558.
(6679) divides n-1.
(6679)^2 > n.
n is prime by Pocklington's theorem.