/* primes.cpp
 * This program will generate primes up to and possibly including
 * a user specified number. The program will force the user to enter 
 * a number between 0 and 100,000.
 */
 
/* A number N is prime if the only divisors of N are 1 and N. EX.. 2, 3, 17, 41
 * 
*/

#include<iostream>
#include<iomanip>

using namespace std;

int main()
{
    int upperBound;
    // force the user to enter a positive integer less than 100000
    do {
        cout << "Enter a positive integer less than 100,000" << endl;
        cin >> upperBound;
    }while (upperBound <= 0 || upperBound >= 100000);
    cout << "The primes less than "  << upperBound <<" are: " << endl;
    
    // The first for loop generates the candidates.
    // The second for loop generates the integers used as divisors.
    int primeCandidate,possibleDivisor;
    for (primeCandidate = 2; primeCandidate <= upperBound; primeCandidate++ ) {
        for (possibleDivisor = 2; possibleDivisor < primeCandidate; possibleDivisor++ ) {
            // if possibleDivisor divides the primeCandidate, then the remainder
            // upon division of  ( primeCandidate / possibleDivisor ) is zero
            // Hence possibleCandidate is not prime, break out of the inner loop
            // then pick the next candidate.
            if (0 == (primeCandidate % possibleDivisor)){
                break;
            }
        }
        if (primeCandidate == possibleDivisor){
            cout << possibleDivisor << endl;
        }
    }
    system("pause");
    return 0;
}