Primality proof for n = 3935887:

Take b = 2.

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

12377 is prime.
b^((n-1)/12377)-1 mod n = 3742781, which is a unit, inverse 2804747.

(12377) divides n-1.

(12377)^2 > n.

n is prime by Pocklington's theorem.