Listing Prime Numbers in C# for Kids

Randomness of Prime Numbers

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 in C# - A Detailed Explanation

Say we want 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...

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 class file; Project, Add Class.
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.

C# code for Prime Numbers class.

using System;
using System.Collections.Generic;

namespace Arithmetic
{
    class PrimeNumbers
    {
        private List<int> list_of_primes; // We will house our gathered prime numbers here.
        private int start; // Where to start.
        private int stop; // Where to stop.
        private int progress; // progress report
        private int index; // index into array list_of_primes
        private double square_root; // Our loop range for speed enhancement
        private bool do_next_iteration;

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

            list_of_primes = new List<int>();
            list_of_primes.Add(2);
            list_of_primes.Add(3);
            list_of_primes.Add(5);
            list_of_primes.Add(7);

            square_root = 0;
        }

        /**
         * Garners the prime numbers between the requested range.
         *
         * @return String value
         */
        public List<int> 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)Math.Ceiling(Math.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.Add(progress);
            }

            // Display result.
            return list_of_primes;
        }
    }
}

C# code for Prime Numbers - Main Class.

using System;
using System.Collections.Generic;

namespace Arithmetic
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Welcome to our demonstration sequels");
            Console.WriteLine("Hope you enjoy (and follow) the lessons.");
            Console.WriteLine("\r\n");

            /*
            * List Prime Numbers.
             */
            int start = 1;
            int end = 100;
            List<int> answer;

            PrimeNumbers my_list = new PrimeNumbers(5, 500);
            answer = my_list.getPrimes();

            Console.WriteLine("Prime numbers between " + start + " and " + end + " are:");
            Console.WriteLine(String.Join(", ", answer));

        }
    }
}

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