Primality proof for n = 2916841:
Take b = 3.
b^(n-1) mod n = 1.
223 is prime.
b^((n-1)/223)-1 mod n = 1906604, which is a unit, inverse 1517285.
109 is prime.
b^((n-1)/109)-1 mod n = 1472766, which is a unit, inverse 2690537.
(109 * 223) divides n-1.
(109 * 223)^2 > n.
n is prime by Pocklington's theorem.