Take b = 2.

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

50380057830419 is prime. b^((n-1)/50380057830419)-1 mod n = 16383, which is a unit, inverse 278632501977575.

(50380057830419) divides n-1.

(50380057830419)^2 > n.

n is prime by Pocklington's theorem.