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.