The following numbers are prime:
$ 31 $
$ 331 $
$ 3331 $
$ 33331 $
$ 333331 $
$ 3333331 $
$ 33333331 $
Which made me think, is there something we can use to prove/disprove the statement that there are infinitely many primes of this form?
More precisely, can we prove/disprove that there are infinitely many primes of form:
This is prime for $n=1,2,3,4,5,6,7,17,39,49,59\dots$ since I tested all $n\le60$
The only proofs for "infinitely many primes of form X" I know of are using the Dirichlet's theorem, but I don't see that it would be helpful in cases like this one.