Primality proof for n = 67763:

Take b = 2.

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

1993 is prime.
b^((n-1)/1993)-1 mod n = 51319, which is a unit, inverse 17188.

(1993) divides n-1.

(1993)^2 > n.

n is prime by Pocklington's theorem.