Project Euler Problem 6, C#

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//Rextester.Program.Main is the entry point for your code. Don't change it
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;

namespace Rextester
{
    public class Program
    {
        static int primes_found = 0, target = 10001;
        static List<int> primes = new List<int>();
        
        public static void Main(string[] args)
        {
            int n = 2, last_prime_found = 0; 
            
            do
            {
                if (IsPrime (n))
                {
                    primes.Add(n);
                    last_prime_found = n;
                    primes_found++;
                } 
                n++;

} while (primes_found < target);
            
            Console.WriteLine("The solution is: " + last_prime_found);
        }
        
        public static bool IsPrime(int n)
        {
            
            // Console.WriteLine("Testing: " + n);
            
            foreach (int prime in primes)
            {
                if (prime * prime > n)
                {
                   break;
                } else if (n % prime == 0)
                {
                   return false;
                }
            }
            return true;
        }
    }
}

Show compiler warnings [ + ] Show input
Compilation time: 0,12 sec, absolute running time: 0,08 sec, cpu time: 0,08 sec, average memory usage: 13 Mb, average nr of threads: 3