Primality proof for n = 1019771:
Take b = 2.
b^(n-1) mod n = 1.
101977 is prime. b^((n-1)/101977)-1 mod n = 1023, which is a unit, inverse 210334.
(101977) divides n-1.
(101977)^2 > n.
n is prime by Pocklington's theorem.