Take b = 2.

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

7240555601 is prime.
b^((n-1)/7240555601)-1 mod n = 82534153614, which is a unit, inverse 5074107516104.

(7240555601) divides n-1.

(7240555601)^2 > n.

n is prime by Pocklington's theorem.