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.