Primality proof for n = 77867:
Take b = 2.
b^(n-1) mod n = 1.
38933 is prime. b^((n-1)/38933)-1 mod n = 3, which is a unit, inverse 25956.
(38933) divides n-1.
(38933)^2 > n.
n is prime by Pocklington's theorem.