Take b = 2.

b^(n-1) mod n = 1.

97911833 is prime. b^((n-1)/97911833)-1 mod n = 1027272621776529, which is a unit, inverse 1930049869346804.

(97911833) divides n-1.

(97911833)^2 > n.

n is prime by Pocklington's theorem.