Listing Prime Numbers in C++ for Kids

Randomness of Prime Numbers | Maths Explanation for C++ Kids

Prime numbers are natural numbers greater than 1 with no positive divisors other than 1 and itself. Prime numbers, in ascending order, are:

2, 3, 5, 7, 11, 13, 17, 19, 23, ...

Because prime numbers are so random in their progression, they are very difficult to predict as they get larger.
For the reason of their unpredictability, prime number are applied in

Cryptography: RSA encryption relies on large prime numbers.
Hashing: Prime numbers help reduce collisions in hash functions.
Data structures: Primes are used in sizing hash tables and optimizing algorithms.

In this beginner-friendly Maths C++ tutorial for kids, we'll show how to list prime numbers in a fun and interactive way for STEM students.
Writing code in C++ to list prime numbers will involve checking every number in a range of interest and gathering those that are without factors.

Logic for Determining Prime Numbers | Detailed Explanation for C++ Kids

Say we want to implement a C++ algorithm to list all prime numbers between 2 and 100 inclusive, we would start from 2; check to see whether it has any factors; keep it as a prime number if it has no factors; otherwise discard it.
We would then go to 3, and repeat the same process.
Repeat same for 4, 5, 6, 7, ..., 98, 99, 100.

But we can always use a few tricks for the C++ algorithm...

We will take the following steps:

Step 1:

First, we'll start our range from 9 (keeping 2, 3, 5, and 7 as prime numbers).

Step 2:

Next, we'll only check through odd numbers.

Step 3:

Next, we'll check against the factors 2, 3, and 5.

Step 4:

Lastly, we'll check with a subset of smaller prime numbers that we'll gather as our check progresses.

Create a new C++ class file;
Call it PrimeNumbers.

Type out the adjoining C++ code for listing prime numbers.

Note: You can comment out the C++ code for the main class from the previous lesson if you have been following.

So! C++ Fun Practice Exercise - List Prime Numbers

As a fun practice exercise, feel free to try out your own boundary values, and see how the C++ code lists the prime numbers between those boundary values.

C++ Code for Prime Numbers - Header File.

#pragma once

#include <iostream>
#include <vector>
#include <string>
#include <sstream>
#include <math.h>

using namespace std;

class PrimeNumbers {
public:
    PrimeNumbers(unsigned, unsigned);
    virtual ~PrimeNumbers();
    string getPrimes();
private:
    vector<unsigned> list_of_primes; // We will house our gathered prime numbers here.
    unsigned int start; // Where to start.
    unsigned int stop; // Where to stop.
    unsigned int progress; // progress report
    unsigned int index; // index into array list_of_primes
    double square_root; // Our loop range for speed enhancement
    bool do_next_iteration;
    string result;
    stringstream aux;

};

C++ Code for Prime Numbers - Class File.

#include "stdafx.h"
#include "PrimeNumbers.h"

PrimeNumbers::PrimeNumbers(unsigned first, unsigned last) {
    start = first;
    stop = last;
    // STEP 1:
    progress = 9;

    list_of_primes = { 2, 3, 5, 7 };

    square_root = 0;
}

/**
* Garners the prime numbers between the requested range.
* @param - Nil
*/
string PrimeNumbers::getPrimes() {
    // STEP 2:
    for (; progress < stop; progress += 2) {

        do_next_iteration = false; // a flag

        // STEPS 3, 4:
        // Check through already accumulated prime numbers
        // to see if any is a factor of "progress".
        square_root = (int)ceil(sqrt(progress));

        index = 0;
        for (; list_of_primes[index] <= square_root; index++) {
            if ((progress % list_of_primes[index]) == 0) {
                do_next_iteration = true;
                break;
            }
        }
        if (do_next_iteration) {
            continue;
        }

        // if all checks are scaled,then "progress" is our guy.
        list_of_primes.push_back(progress);
    }

    list_of_primes.shrink_to_fit(); // not altogether necessary

    // Display result.
    aux << start;
    result = "The set of prime numbers between " + aux.str() + " and ";
    aux.str("");
    aux << stop;
    result += aux.str() + " are: \n";

    for (unsigned n : list_of_primes) {
        aux.str("");
        aux << n;
        result += aux.str() + "; ";
    }
    return result;
}

PrimeNumbers::~PrimeNumbers() {
}

C++ Code for Prime Numbers - Main class.

// Arithmetic.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include "PrimeNumbers.h"

#include <iostream>

using namespace std;

int main() {
    try {

        cout << "\n    Welcome to our demonstration sequels\n";
        cout << "Hope you enjoy (and follow) the lessons.\n\n";

        unsigned int start = 1, stop = 100;

        /*
        * List of Prime Numbers.
        */
        PrimeNumbers p_list(start, stop);
        cout << "\n\n" << p_list.getPrimes() << "\n";

    }    catch (exception& e) {
        cout << "\n" << e.what() << "\n";
    }
    return 0;
}

I have a better version / See other versions.