Primality proof for n = 9211861:
Take b = 2.
b^(n-1) mod n = 1.
2437 is prime.
b^((n-1)/2437)-1 mod n = 7725236, which is a unit, inverse 5788243.
7 is prime.
b^((n-1)/7)-1 mod n = 7075515, which is a unit, inverse 3946268.
(7 * 2437) divides n-1.
(7 * 2437)^2 > n.
n is prime by Pocklington's theorem.