# Binary Primes

Let $$f$$ be a function in the natural numbers, such that $$f(n)$$ gives the binary representation of $$n$$ in base 10. For example, $$f(5) = 101$$, because 5 is represented as 101 in binary.

A number $$n$$ is called good if $$n$$ and $$f(n)$$ are both prime numbers. For example, 5 is good, because 5 and 101 are prime numbers. 7 is not good, since $$f(7) = 111 = 3 \times 37$$ is not prime.

The smallest good number is 3. The second smallest good number is 5. Find the $$19^\text{th}$$ smallest good number.

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