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.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

       
#include <iostream>
       
#include <vector>
       
 
       
int main()
       
{
       
  const unsigned int MaxNumber = 1000;
       
  // store number of ways to represent a number as a sum of primes
       
  std::vector<unsigned long long> combinations(MaxNumber + 1, 0);
       
  // degenerated case
       
  combinations[0] = 1;
       
 
       
  // store all primes
       
  std::vector<unsigned int> primes;
       
  for (unsigned int i = 2; i <= MaxNumber; i++)
       
  {
       
    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;
       
      }
       
    }
       
 
       
    // only primes after this point ...
       
    if (!isPrime)
       
      continue;
       
 
       
    primes.push_back(i);
       
 
       
    // now add all solutions
       
    for (unsigned int pos = 0; pos <= MaxNumber - i; pos++)
       
      combinations[pos + i] += combinations[pos];
       
  }
       
 
       
//#define ORIGINAL

       
#ifdef ORIGINAL
       
  // find first number with more than 5000 combinations
       
  for (size_t i = 0; i < combinations.size(); i++)
       
    if (combinations[i] > 5000)
       
    {
       
      std::cout << i << std::endl;
       
      break;
       
    }
       
#else
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    // look up combinations
       
    unsigned int n;
       
    std::cin >> n;
       
    std::cout << combinations[n] << std::endl;
       
  }
       
#endif
       
 
       
  return 0;
       
}

This solution contains 9 empty lines, 11 comments and 5 preprocessor commands.