Primality proof for n = 1627771:

Take b = 2.

b^(n-1) mod n = 1.

1871 is prime.
b^((n-1)/1871)-1 mod n = 910795, which is a unit, inverse 589711.

(1871) divides n-1.

(1871)^2 > n.

n is prime by Pocklington's theorem.