# Primey Palindromes V2

This problem is a slightly harder version of Primey Palindromes.

Let $$f(x)$$ be the sum of the digits of $$x$$.
Let $$g(n)$$ be the number of $$n$$ digit palindromes $$a$$ such that
- $$a$$ is prime,
- $$a + f(a)$$ is also prime.

What is the smallest value of $$n > 2$$ such that $$g(n)$$ is not 0 and not prime?

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

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