C# program to find nth prime number

Here is the C# program that can find the nth (100000 in this program) prime number:

using System;

class Program
{
    static void Main(string[] args)
    {
        int primeCount = 0; // to count the number of prime numbers found
        int currentNumber = 2; // start checking from the first prime number
        int targetPrimeIndex = 100000; // the index of the target prime number

        while (primeCount < targetPrimeIndex)
        {
            if (IsPrime(currentNumber))
            {
                primeCount++;
                if (primeCount == targetPrimeIndex)
                {
                    Console.WriteLine("The {0}th prime number is: {1}", targetPrimeIndex, currentNumber);
                    break;
                }
            }
            currentNumber++;
        }
    }

    static bool IsPrime(int number)
    {
        if (number <= 1)
        {
            return false;
        }

        for (int i = 2; i <= Math.Sqrt(number); i++)
        {
            if (number % i == 0)
            {
                return false;
            }
        }

        return true;
    }
}

The program starts by initializing primeCount to 0, which counts the number of prime numbers found so far, and currentNumber to 2, which is the first prime number. The program then enters a while loop that continues until the primeCount equals the index of the target prime number.

For each iteration of the while loop, the program checks whether the current number is prime by calling the IsPrime function. If the current number is prime, the primeCount is incremented by 1. If the primeCount is equal to the target prime index, the program displays the target prime number and exits the loop.

The IsPrime function checks whether a given number is prime by dividing it by all the numbers from 2 up to its square root. If any of these divisions results in a remainder of 0, the number is not prime, and the function returns false. If none of the divisions results in a remainder of 0, the number is prime, and the function returns true.