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.
Note: the source code for both solutions are available on github here.
This solution runs in just over 29 seconds on my machine, not great, but within the 1 minute rule for Euler solutions.
Using Set intersections
Here’s an alternative solution, using set intersections.
This solution is slightly more efficient, running in just over 17 seconds on my machine.