Primality proof for n = 102244957:
Take b = 2.
b^(n-1) mod n = 1.
774583 is prime. b^((n-1)/774583)-1 mod n = 14263047, which is a unit, inverse 99398968.
(774583) divides n-1.
(774583)^2 > n.
n is prime by Pocklington's theorem.