I know there is a solution for
$x=3051$. Because when:
$$n_1=29,n_2=41,n_3=23,n_4=1,n_5=37,n_6=41,n_7=47,n_8=1,n_9=29$$
My system of equations is satisfied.
So, maybe there is something missing in the code that you've written. I am not that well in writing Mathematica code so I will try to understand what you've written.
