Find all natural numbers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which every natural number whose decimal representation has
![n - 1](/media/m/b/9/f/b9f2e24ffd917df5f63d30599dd3220c.png)
digits
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
and one digit
![7](/media/m/5/1/9/519154d5119d15088eebb25b656d58dd.png)
is prime.
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Find all natural numbers $n$ for which every natural number whose decimal representation has $n - 1$ digits $1$ and one digit $7$ is prime.