P7.cs

//What is the 10 001st prime number?
using System;

namespace P1 {
    class Program {

        // Here, I am referring to an algorithm to determine if a number is prime from a book called "Algorithms" by Sedgewick and Wayne, pp. 23 (saw this from project three)
        public static bool IsPrime(long n) {
            if (n < 2) return false;
            for (long i = 2; i * i <= n; i++)
                if (n % i == 0)
                    return false;
            return true;
        }
        
        public static void Main(string[] args) {
            // Considerations/steps
            // Primes! 
            // Step 1: I believe we will have to first determine if a given number is a prime
            // Step 2: once a number is determined to be a prime, we can then say it is the Xth prime
            // How will we do this? Yet TBD. One idea is a multi-dimensional array/List with one element being the prime number itself and the other being the # of the prime in relation to all primes
            // Step 3: Step 2 will be embedded in a loop that stops once we reach 10,001
            // The crucial piece is: do I need to add these into some kind of data structure? Or can I simply hold the "place" in a variable. I think the latter

            int primeSequence = 1;
            int limit = 10_001;
            long number = 2;            

            while (primeSequence < limit) {
                //Console.WriteLine("Prime Sequence is: {0}, Number is {1}, Limit is {2}", primeSequence, number, limit);
                //Console.ReadKey();
                if (IsPrime(number))
                    primeSequence++;
                number++;
            }
            Console.WriteLine("The {0:n0} prime is {1:n0}", primeSequence, number - 1);
        }
    }
}