Primality proof for n = 379979:
Take b = 2.
b^(n-1) mod n = 1.
189989 is prime. b^((n-1)/189989)-1 mod n = 3, which is a unit, inverse 126660.
(189989) divides n-1.
(189989)^2 > n.
n is prime by Pocklington's theorem.