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>
       
 
       
int main()
       
{
       
  // sieve based on trial division
       
  std::vector<unsigned int> primes = { 2 };
       
  for (unsigned int i = 3; ; i += 2)
       
  {
       
    bool isPrime = true;
       
 
       
    // test against all prime numbers we have so far (in ascending order)
       
    for (auto p : primes)
       
    {
       
      // next prime is too large to be a divisor ?
       
      if (p*p > i)
       
        break;
       
 
       
      // divisible ? => not prime
       
      if (i % p == 0)
       
      {
       
        isPrime = false;
       
        break;
       
      }
       
    }
       
 
       
    // no prime ?
       
    if (!isPrime)
       
      continue;
       
 
       
    primes.push_back(i);
       
 
       
    // only every "odd" prime
       
    if (primes.size() % 2 == 0)
       
      continue;
       
 
       
    // compute remainder
       
    auto remainder = 2 * i * primes.size();
       
    // exceeds 10^10 ?
       
    if (remainder >= 10000000000ULL)
       
      break;
       
  }
       
 
       
  // print result
       
  std::cout << primes.size() << std::endl;
       
  return 0;
       
}

This solution contains 8 empty lines, 9 comments and 2 preprocessor commands.