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.