Primey Palindromes

Let \(a\) be an \(n\) digit palindrome.
Let \(f(x) =\) the sum of the digits of \(x\).
Given that there are 13 values such that \(a\) is prime and \( a + f(a) \) is also prime, what is the value of \(n\)?

- \(383\) is a prime palindrome
- \(f(383) = 3+8+3=14 \)
- \(383+f(383)=397\) which is also prime

I also made a slightly harder version of this problem - Primey Palindromes V2


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