Primality proof for n = 3486877:
Take b = 2.
b^(n-1) mod n = 1.
1049 is prime.
b^((n-1)/1049)-1 mod n = 3102586, which is a unit, inverse 3095100.
277 is prime.
b^((n-1)/277)-1 mod n = 78115, which is a unit, inverse 846644.
(277 * 1049) divides n-1.
(277 * 1049)^2 > n.
n is prime by Pocklington's theorem.