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.