Primality proof for n = 379:
Take b = 2.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 124, which is a unit, inverse 162.
3 is prime.
b^((n-1)/3)-1 mod n = 326, which is a unit, inverse 143.
(3^3 * 7) divides n-1.
(3^3 * 7)^2 > n.
n is prime by Pocklington's theorem.