Prime Coincidence

\[\displaystyle \begin{align} \color{blue} 2 & \Longrightarrow {\color{blue} 2}{\color{red}2} = 2 \times 11 \\ \color{blue} 67 & \Longrightarrow {\color{blue}67}{\color{red}76} = 2 \times 3388 \\ \color{blue} 479 & \Longrightarrow {\color{blue}{479}}{\color{red}{974}} = 2 \times 239987 \\ \color{blue} 8123 & \Longrightarrow {\color{blue}{8123}}{\color{red}{3218}} = 2 \times 40616609 \\ \color{blue} 56209 & \Longrightarrow {\color{blue}{56209}}{\color{red}{90265}} = 5 \times 1124198053 \\ \color{blue} 999007 & \Longrightarrow {\color{blue}{999007}}{\color{red}{700999}} = 7 \times 142715385857 \end{align}\]

You have a machine that does some very interesting prime arithmetic. The machine takes in a prime number, reverses its digits, and attaches the resulting number to the prime input to form a new number.

It seems that for every prime number shown above (in the far left column), the machine produces a composite number (as implied by the right side of the equation).

Does there exist a prime for which the machine will produce another prime?

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