The primes `3`, `7`, `109`, and `673`, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking `7` and `109`, both `7109` and `1097` are prime. The sum of these four primes, `792`, represents the lowest sum for a set of four primes with this property.

Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime.