trjhtr

I have just started learning C# and decided to do some problems from Project Euler. I wrote a code to find 10 001st prime and I thought it would be cool optimize it to make it as fast as possible. How could I improve this to make it even faster?

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Diagnostics;

namespace primes

 class Program
 
 static void Main(string args)
 
 long prime = 2;
 long largestprime = 2;
 long potentialprime = 3;
 Console.WriteLine("Enter the prime you want to find: ");
 long primenum = Convert.ToInt64(Console.ReadLine());
 long primearray = new long[primenum + 1];
 primearray[1] = 2;
 Stopwatch sw = new Stopwatch();
 sw.Start();
 while (prime <= primenum)
 
 bool isprime = true;
 for (long x = 1; x < prime; x += 3)
 
 if (isprime)
 
 primearray[prime] = potentialprime;
 prime += 1;
 largestprime = potentialprime;
 
 potentialprime += 2;
 
 sw.Stop();
 Console.WriteLine(sw.ElapsedMilliseconds + "ms to find ");
 Console.WriteLine(largestprime);
 Console.ReadKey();
 
 

As mentioned in the comments, you should go for more readable code:

1) Split by responsibility:

One method for user input:

ulong GetPrimeIndex() // TODO: Get User input from Console 

The algorithm itself:

ulong FindNthPrime(ulong n) // TODO: the algorithm 

print the result...

public static void Main(string args)
 
 ulong primeIndex = GetPrimeIndex();

 Stopwatch watch = Stopwatch.StartNew();
 ulong nthPrime = FindNthPrime(primeIndex);
 watch.Stop();

 Console.WriteLine($"primeIndex prime is: nthPrime");
 Console.WriteLine($"Elapsed time: watch.ElapsedMilliseconds");

2) Naming:

In C# local variable names use camelCase: largestprime should be largestPrime

Because primes are always positive, you should use ulong instead of long. It will give you a broader range to operate in.

I think you're missing a couple of breaks in these tests:

 if (primearray[x] * primearray[x] > potentialprime)
 break;
 if (prime > 3 && (potentialprime % primearray[x] == 0 || potentialprime % primearray[x+1] == 0 || potentialprime % primearray[x+2] == 0))
 isprime = false;
 if (prime <= 3 && potentialprime % primearray[x] == 0)
 isprime = false;

It should be:

 if (primearray[x] * primearray[x] > potentialprime)
 break;
 if (prime > 3 && (potentialprime % primearray[x] == 0 || potentialprime % primearray[x + 1] == 0 || potentialprime % primearray[x + 2] == 0))
 
 isprime = false;
 break;
 
 if (prime <= 3 && potentialprime % primearray[x] == 0)
 
 isprime = false;
 break;
 

Be aware that

primearray[x] * primearray[x]

may overflow the domain range. You should maybe make the check by sqrt instead?