Take b = 2.

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

11351 is prime.

b^((n-1)/11351)-1 mod n = 586497401, which is a unit, inverse 39408624.

3637 is prime.

b^((n-1)/3637)-1 mod n = 200893089, which is a unit, inverse 444174805.

(3637 * 11351) divides n-1.

(3637 * 11351)^2 > n.

n is prime by Pocklington's theorem.