My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <vector>
       
 
       
// return (base^exponent) % modulo

       
unsigned int powmod(unsigned int base, unsigned int exponent, unsigned int modulo)
       
{
       
  unsigned int result = 1;
       
  while (exponent > 0)
       
  {
       
    // fast exponentation:
       
    // odd exponent ? a^b = a*a^(b-1)
       
    if (exponent & 1)
       
      result = (result * (unsigned long long)base) % modulo; // enforce 64-multiplication
       
 
       
    // even exponent ? a^b = (a*a)^(b/2)
       
    base = (base * (unsigned long long)base) % modulo;       // enforce 64-multiplication
       
    exponent >>= 1;
       
  }
       
  return result;
       
}
       
 
       
int main()
       
{
       
  unsigned int numFactors = 40;
       
  unsigned long long digits = 1000000000;
       
  std::cin >> digits >> numFactors;
       
 
       
  unsigned int sum = 0;
       
  std::vector<unsigned int> primes = { 2 }; // two is never a prime factor of a repunit
       
  for (unsigned int i = 3; numFactors > 0; i++)
       
  {
       
    bool isPrime = true;
       
 
       
    // test against all prime numbers we have so far (in ascending order)
       
    for (auto x : primes)
       
    {
       
      // prime is too large to be a divisor
       
      if (x*x > i)
       
        break;
       
 
       
      // divisible => not prime
       
      if (i % x == 0)
       
      {
       
        isPrime = false;
       
        break;
       
      }
       
    }
       
 
       
    // no prime
       
    if (!isPrime)
       
      continue;
       
 
       
    primes.push_back(i);
       
 
       
    // check for divisibility by 9*prime
       
    auto modulo = 9 * i;
       
    // remainder must be 1
       
    auto remainder = powmod(10, digits, modulo);
       
    if (remainder == 1)
       
    {
       
      sum += i;
       
      numFactors--;
       
    }
       
 
       
    // don't analyze huge primes
       
    // => not needed for the original problem, but avoids malicious input in live test
       
    // => e.g. user asks for more primes than the repunit has
       
    if (i > 1111111)
       
      break;
       
  }
       
 
       
  std::cout << sum << std::endl;
       
 
       
  return 0;
       
}

This solution contains 12 empty lines, 13 comments and 2 preprocessor commands.