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.