Prime pair sets

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.