# [Brachylog], 16 bytes

    ⟦₂{ṗṗᵐ}ˢ⟨⌋≡⌉⟩|∧0

[Try it online!][TIO-jb6b3ucu]

[Brachylog]: https://github.com/JCumin/Brachylog
[TIO-jb6b3ucu]: https://tio.run/##SypKTM6ozMlPN/r//9H8ZY@amqof7pwOQlsn1J5e9Gj@ikc93Y86Fz7q6Xw0f2XNo47lBv//RxtaGugYGRjE/o8CAA "Brachylog – Try It Online"

The completely non-sensical "return 0 if there's no prime" makes us lose 3 bytes (`|∧0`) for no reason (it would return `false.` if we didnt add them)

###Explanation

    ⟦₂                Range from the smallest element of the input to the biggest
      {   }ˢ          Select on that range:
       ṗ                Numbers that are primes
        ṗᵐ              And whose digits are primes
            ⟨   ⟩     Fork on this new list:
             ⌋          Minimum
               ⌉        maximum
              ≡         Do nothing and return [Minimum, Maximum]
                 |∧0  If all of this fails (i.e. the list after selection is empty), return 0