Primality proof for n = 3499799:

Take b = 2.

b^(n-1) mod n = 1.

1749899 is prime.
b^((n-1)/1749899)-1 mod n = 3, which is a unit, inverse 1166600.

(1749899) divides n-1.

(1749899)^2 > n.

n is prime by Pocklington's theorem.