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.