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.