Primality proof for n = 3774773:
Take b = 2.
b^(n-1) mod n = 1.
943693 is prime. b^((n-1)/943693)-1 mod n = 15, which is a unit, inverse 3271470.
(943693) divides n-1.
(943693)^2 > n.
n is prime by Pocklington's theorem.