Take b = 2.

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

2011 is prime.

b^((n-1)/2011)-1 mod n = 3706699, which is a unit, inverse 1506556.

97 is prime.

b^((n-1)/97)-1 mod n = 4185920, which is a unit, inverse 914856.

(97 * 2011) divides n-1.

(97 * 2011)^2 > n.

n is prime by Pocklington's theorem.