using System;

​

public class Program

{

    public static void Main()

    {

        var desiredCliqueSize = 5;

        var suspect = 3;

        var minSum = int.MaxValue;

        var foundPrimes = new System.Collections.Generic.HashSet<int>();

        var graph = new System.Collections.Generic.Dictionary<int, System.Collections.Generic.HashSet<int>>();

        Console.WriteLine("checking for cliques of size " + desiredCliqueSize); 

        while (suspect < minSum) {

            if (IsPrime(suspect)) {

                var friends = FindFriendsOf(suspect, foundPrimes) ;

                minSum = FindSmallerCliqueOfSize(desiredCliqueSize, minSum, suspect, friends, graph);

                foundPrimes.Add(suspect);

                if (FriendsHaveCliquePotential(friends, desiredCliqueSize)) 

                {

                    graph.Add(suspect, friends);

                }

            }

            ++suspect;

        }

        Console.WriteLine("Min sum is " + minSum);

    }

    public static bool FriendsHaveCliquePotential(System.Collections.Generic.HashSet<int> friends, int desiredCliqueSize) 

    {

        return friends.Count >= desiredCliqueSize - 2;

    }

    public static int FindSmallerCliqueOfSize(int desiredCliqueSize, int currMinSum, int suspect, System.Collections.Generic.HashSet<int> friends, System.Collections.Generic.Dictionary<int, System.Collections.Generic.HashSet<int>> graph) 

    {

        var minSum = currMinSum;

        var targetIntersectSize = desiredCliqueSize - 2;

        if (friends.Count >= targetIntersectSize) {

            foreach (var friend in friends) {

                if (graph.ContainsKey(friend)) {

                    var potentialClique = new System.Collections.Generic.HashSet<int>(friends);

                    potentialClique.IntersectWith(graph[friend]);

                    if (potentialClique.Count >= targetIntersectSize) 

                    {

                        var sum = friend + suspect;

                        var cliqueString = "";

                        foreach (var element in potentialClique) { cliqueString += (element.ToString() + ", "); sum += element; }

                        cliqueString += friend.ToString() + ", " + suspect; 

                        Console.WriteLine("Found Clique " + cliqueString + " sum is " + sum);

                        minSum = Math.Min(sum, minSum);

                    }

                }

            }

        }

        return minSum;  

    }

    public static System.Collections.Generic.HashSet<int> FindFriendsOf(int suspect, System.Collections.Generic.HashSet<int> foundPrimes) 

    {

        var friends = new System.Collections.Generic.HashSet<int>();

        foreach (var prime in foundPrimes) {

            if (AreFriends(suspect, prime)) {

                friends.Add(prime);

            }

        }

        return friends;

    }

    public static bool AreFriends(int a, int b) 

    {

        return IsPrime(Concat(a, b)) && IsPrime(Concat(b, a));

    }

    public static int Concat(int a, int b) 

    {    

        if (b < 10) return 10 * a + b;

        if (b < 100) return 100 * a + b;

        if (b < 1000) return 1000 * a + b;

        if (b < 10000) return 10000 * a + b;

        if (b < 100000) return 100000 * a + b;

        if (b < 1000000) return 1000000 * a + b;

        if (b < 10000000) return 10000000 * a + b;

        if (b < 100000000) return 100000000 * a + b;

        return 1000000000 * a + b;

    }

    public static bool IsPrime(int suspect) 

    {

        var limit = Math.Sqrt(suspect);

        for (var i = 2; i <= limit; ++i) {

            if (suspect % i == 0) {return false;}

        }

        return true;

    }

}