The other day, I encountered a theorem that suggested if a number of the form $\underbrace{1...111}_\text{p}$ is prime, then $p$ is prime as well. The proof was rather simple but it got me thinking about the following: How many prime numbers of the form $\underbrace{1...111}_\text{p}$ are there?I tried using the fact that $\underbrace{1...111}_\text{p} = \underbrace{1...111}_\text{p-1} * 10 + 1$ but I don't know what to do from here.
Any help would be appreciated!