Primality proof for n = 37967:

Take b = 2.

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

463 is prime.
b^((n-1)/463)-1 mod n = 17755, which is a unit, inverse 30797.

(463) divides n-1.

(463)^2 > n.

n is prime by Pocklington's theorem.