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.