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.