Tell whether $\dfrac{10^{91}-1}{9}$ is prime or not? I really have no idea how to start. The only theorem considering prime numbers I know of is Fermat's little theorem and maybe its related with binomial theorem.
Any help will be appreciated.

Hint: Note that $91=7\cdot 13$, so the numerator is divisible by $10^7-1$. 
If this is not obvious, it may be clearer if we let $x=10^7$. Then $10^{91}=x^{13}$, and it is a familiar fact that $x-1$ divides $x^n-1$ for any positive integer $n$. 
