Primality proof for n = 4670377:
Take b = 2.
b^(n-1) mod n = 1.
11447 is prime. b^((n-1)/11447)-1 mod n = 4624071, which is a unit, inverse 224613.
(11447) divides n-1.
(11447)^2 > n.
n is prime by Pocklington's theorem.