he longest sum of consecutive primes that adds to a prime

/*******************************************************************************
 * Written by I.F. Luis Mex Dzib 4/sep/2013
 * [email protected]
 *
 * This program Solve the following:
 *
 * The prime 41, can be written as the sum of six consecutive primes:
        41 = 2 + 3 + 5 + 7 + 11 + 13
        This is the longest sum of consecutive primes that adds to a prime below one-hundred.
        The longest sum of consecutive primes below one-thousand that adds to a prime,
        contains 21 terms, and is equal to 953.Which prime, below one hundred-thousand,
        can be written as the sum of the most consecutive primes?
********************************************************************************
* /*****************************************************************************/


#include <iostream>
#include <vector>
#include <list>
#include <iomanip>
#include <cstdlib>
#include <cmath>
#include <algorithm>


using namespace std;
struct Pair_vect {
        long int sum;
        vector<long int> consecutive;
        void print() const {
                cout << "(" << sum << ", " ;
                cout <<"[" << consecutive.front() ;
                for (int i = 1 ; i < consecutive.size() ; i++){
                        cout <<", "<< consecutive[i] ;
                }
                cout << "]"<< ")";
        }
};

bool is_prime(long int x){
        for(int i = 2 ; i <= sqrt(x)  ; i++){
                if ( x % i == 0) {
                        return false;
                }
        }
        return true;
}

vector <long int> lista_de_primos( int x = 2){
        vector<long int> lista_ini;
        for (int i = 2 ; i<= x ; i++){
                if(is_prime(i)) lista_ini.push_back(i);
        }
        return lista_ini;
}

template <class T>
void prind_list(const vector<T>&v){
        cout << "[";
        if (!v.empty()){
                cout << v.front();
                typename vector<T> :: const_iterator it = v.begin();
                it++;
                for (; it != v.end() ; it++){
                        cout <<", "<<*it ;
                }
                cout << "]" << endl;
        }
}

long int suma_elemn(const vector<long int> &v, int ini = 0, int fin = 0){
        long int suma = 0;
        if (v.empty()) return suma;
        if ( fin == 0 ){
                for (long int i = ini ; i < v.size() ; i++){
                        suma = suma + v[i];
                }
        }
        else{
                for (long int i = ini-1 ; i < fin ; i++){

                        suma = suma + v[i];
                }
        }
        return suma;
}

vector <long int > cut_vect( const vector<long int> &v , int ini = 0 , int fin = 0){
        vector <long int > cortado;

        if ( fin == 0) {
                for (int i = 0 ; i < v.size(); i++){
                        cortado.push_back(v[i]);
                }
        }else {
                for (int i = ini ; i < fin; i++){
                        cortado.push_back(v[i]);
                }
        }
        return cortado;
}

bool compare_max(const Pair_vect &uno, const Pair_vect &dos){
        return  uno.consecutive.size() > dos.consecutive.size();
}

int main(){
        // Input value  : below
        int below = 1000;

        vector<long int> primos(lista_de_primos(below));
        list< Pair_vect> long_list;

        for ( int I = 0 ; I < primos.size(); I++){
                Pair_vect piv;

                for (int J = I + 1 ; J < primos.size() ; J++ ){
                        piv.sum = suma_elemn(primos,I+1,J+1);

                        if ( is_prime(piv.sum) && piv.sum < below){
                                piv.consecutive = cut_vect(primos,I,J+1);
                                long_list.push_back(piv);
                        }
                }
        }

        cout << "El vector corresponde : " << endl;
        long_list.sort(compare_max);
        list<Pair_vect> :: iterator it = long_list.begin();
        it->print(); cout << endl << endl;;
        cout << "con " << it-> consecutive.size() << " elementos " << endl;

        return 0;
}