Primality proof for n = 377554267:
Take b = 2.
b^(n-1) mod n = 1.
20975237 is prime. b^((n-1)/20975237)-1 mod n = 262143, which is a unit, inverse 288008937.
(20975237) divides n-1.
(20975237)^2 > n.
n is prime by Pocklington's theorem.