Right and tfeL truncatable primes
Jelly, 26 23 bytes

Forward

Ñ¶p9¶7ÆR2ĿV€$ÆPÐf$ÐĿFị@


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Words

Ñ ¶ p 9 ¶ 7ÆR2ĿV€$ÆPÐf$ÐĿFị@

Backward

7ÆR2ĿV€$ÆPÐf$ÐĿFị@¶9p¶Ñ


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Words

7ÆR2ĿV€$ÆPÐf$ÐĿFị@ ¶ 9 p ¶ Ñ

How it works

All Jelly programs consist of links (Jelly's take on functions), which are separated by linefeeds or pilcrows (¶). The last of them is the main link; it is called automatically when the program is run.

The forward program works as follows.

Ñ                   Helper link. Unused.


p9                  Helper link. Take the Cartesian product with [1, ..., 9].


7ÆR2ĿV€$ÆPÐf$ÐĿFị@  Main link. Argument: n

7ÆR                 Yield all primes up to 7.
             ÐĿ     
            $ÐĿ     Combine the two quicklinks to the left into a monadic chain,
                    and call it repeatedly until the results are no longer unique.
                    Return the array of all intermediate results.
       $              Combine the two links to the left into a monadic chain.
   2Ŀ               Call the helper link on line 2.
     Ṿ€                 Eval each array in the product. This casts to string
                        before evaluating, thus concatenating both numbers.
        ÆPÐf        Filter by primality; keep only primes.
               F    Flatten the resulting array.
                ị@  Retrieve the element at index n.


The backward program does almost exactly the same; there are only two differences.


The main link is now Ñ, which simply calls the link below it (wrapping around), i.e., the main link of the forward program.
9p instead of p9 return the reversed Cartesian product.