Primality proof for n = 9105937:

Take b = 2.

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

661 is prime.
b^((n-1)/661)-1 mod n = 8058054, which is a unit, inverse 8867705.

41 is prime.
b^((n-1)/41)-1 mod n = 5328277, which is a unit, inverse 8050327.

(41 * 661) divides n-1.

(41 * 661)^2 > n.

n is prime by Pocklington's theorem.