PROJECT EULER #60

Link to Project Euler problem 60

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.

A more brute-force approach is probably not possible to achieve...but it runs in less than 8 seconds so I'm not complaining! I also took for granted that the first result would be the lowest sum.

using System;
using System.Collections.Generic;

namespace project_euler
{
class Program
{
  static void Main()
  {
      //Problem 60
      DateTime start = DateTime.Now;
      List<int> primes = GeneratePrimes(10000);
      int sum;
      bool finished = false;
      for (int i = 0; i < primes.Count-4; i++)
      {
          string s = primes[i].ToString();
          for (int j = i+1; j < primes.Count-3; j++)
          {
              string t = primes[j].ToString();
              if (IsPrime(int.Parse(s + t)) &&
                  IsPrime(int.Parse(t + s)))
              {
                  for (int k = j+1; k < primes.Count-2; k++)
                  {
                      string u = primes[k].ToString();
                      if (IsPrime(int.Parse(s + u)) &&
                          IsPrime(int.Parse(u + s)) &&
                          IsPrime(int.Parse(t + u)) &&
                          IsPrime(int.Parse(u + t)))
                      {
                          for (int l = k+1; l < primes.Count-1; l++)
                          {
                              string v = primes[l].ToString();
                              if (IsPrime(int.Parse(s + v))&&
                                  IsPrime(int.Parse(t + v))&&
                                  IsPrime(int.Parse(u + v))&&
                                  IsPrime(int.Parse(v + s))&&
                                  IsPrime(int.Parse(v + t))&&
                                  IsPrime(int.Parse(v + u)))
                              {
                                  for (int m = l+1; m < primes.Count; m++)
                                  {
                                      string w = primes[m].ToString();
                                      if (IsPrime(int.Parse(s + w))&&
                                          IsPrime(int.Parse(t + w))&&
                                          IsPrime(int.Parse(u + w))&&
                                          IsPrime(int.Parse(v + w))&&
                                          IsPrime(int.Parse(w + s))&&
                                          IsPrime(int.Parse(w + t))&&
                                          IsPrime(int.Parse(w + u))&&
                                          IsPrime(int.Parse(w + v)))
                                      {
                                          sum = primes[i] +
                                                primes[j] +
                                                primes[k] +
                                                primes[l] +
                                                primes[m];
                                          //min = sum < min ? sum : min;
                                          Console.WriteLine(sum);
                                          Console.WriteLine(primes[i] + " " +
                                                            primes[j] + " " +
                                                            primes[k] + " " +
                                                            primes[l] + " " +
                                                            primes[m]);
                                          finished = true;
                                          break;
                                      }
                                  }
                                  if (finished) break;
                              }
                          }
                          if (finished) break;
                      }
                  }
                  if (finished) break;
              }
           }
          if (finished) break;
      }
      TimeSpan time = DateTime.Now - start;
      Console.WriteLine("This took {0}", time);
      Console.ReadKey();
  }
  public static bool IsPrime(int n)
  {
      if (n < 2) return false;
      if (n == 2) return true;
      for (long i = 2; i <= Math.Sqrt(n); i++)
          if (n % i == 0) return false;
      return true;
  }
  public static List<int> GeneratePrimes(int n)
  {
      var primes = new List<int> { 2, 3 };
      for (int i = 5; i <= n; i += 2)
          if (IsPrime(i))
              primes.Add(i);
      return primes;
  }
}
}

Triple-click for answer: 26033