Step by Step solution about How to resolve the algorithm Loops/Increment loop index within loop body step by step in the C# programming language

The provided C# code defines a program that generates a series of prime numbers, counting up to 42 prime numbers, and displaying the count and the corresponding prime number in each iteration. A step-by-step explanation of the code:

1. First, it includes the necessary System and System.Globalization namespaces.

2. The isPrime method is defined to check if a given number is prime. It iterates through numbers from number - 1 down to 2 and checks if any of them evenly divides the input number. If it finds a divisor, it returns false, indicating that the number is not prime. Otherwise, it returns true.

3. In the Main method:

   • A NumberFormatInfo object called nfi is initialized with the number format for the "en-US" culture, with no decimal digits. This is used to format the output of prime numbers without decimal places.

   • Two variables, i (initialized to 42) and n (initialized to 0), are used to keep track of the current number being checked and the count of prime numbers found, respectively.

   • The program enters a while loop that continues until n reaches 42. Inside the loop:

     • It calls the isPrime method to check if the current number i is prime.
     • If i is prime, it increments n and prints the prime number i along with the count n.
     • It updates i to the next number to check, which is i - 1. This is done to avoid checking even numbers, as they cannot be prime except for 2.

   • The loop continues until 42 prime numbers are found.

This program efficiently generates and displays the first 42 prime numbers, using a simple is-prime check algorithm.

using System;
using System.Globalization;

namespace PrimeNumberLoopcs
{
    class Program
    {
        static bool isPrime(double number)
        {
            for(double i = number - 1; i > 1; i--)
            {
                if (number % i == 0)
                    return false;
            }
            return true;
        }
        static void Main(string[] args)
        {
            NumberFormatInfo nfi = new CultureInfo("en-US", false).NumberFormat;
            nfi.NumberDecimalDigits = 0;
            double i = 42;
            int n = 0;
            while (n < 42)
            {
                if (isPrime(i))
                {
                    n++;
                    Console.WriteLine("n = {0,-20} {1,20}", n, i.ToString("N", nfi));
                    i += i - 1;
                }
                i++;
            }
        }
    }
}