Program to find the Nth Prime Number

Given an integer N. The task is to find the Nth prime number.

Examples:

Input : 5
Output : 11



Input : 16
Output : 53

Input : 1049
Output : 8377

Approach:

  • Find the prime numbers upto MAX_SIZE using Sieve of Eratosthenes.
  • Store all primes in a vector.
  • For a given number N, return element at (N-1)th index in a vector.

Below is the implementation of the above approach:

C++

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// CPP program to the nth prime number 
  
#include <bits/stdc++.h>
using namespace std;
  
// initializing the max value 
#define MAX_SIZE 1000005
  
// Function to generate N prime numbers using 
// Sieve of Eratosthenes
void SieveOfEratosthenes(vector<int> &primes) 
    // Create a boolean array "IsPrime[0..MAX_SIZE]" and 
    // initialize all entries it as true. A value in 
    // IsPrime[i] will finally be false if i is 
    // Not a IsPrime, else true. 
    bool IsPrime[MAX_SIZE]; 
    memset(IsPrime, true, sizeof(IsPrime)); 
    
    for (int p = 2; p * p < MAX_SIZE; p++) 
    
        // If IsPrime[p] is not changed, then it is a prime 
        if (IsPrime[p] == true
        
            // Update all multiples of p greater than or  
            // equal to the square of it 
            // numbers which are multiple of p and are 
            // less than p^2 are already been marked.  
            for (int i = p * p; i <  MAX_SIZE; i += p) 
                IsPrime[i] = false
        
    
    
    // Store all prime numbers 
    for (int p = 2; p < MAX_SIZE; p++) 
       if (IsPrime[p]) 
            primes.push_back(p);
             
  
// Driver Code
int main()
{
    // To store all prime numbers
    vector<int> primes;
      
    // Function call
    SieveOfEratosthenes(primes);
  
    cout << "5th prime number is " << primes[4] << endl;
    cout << "16th prime number is " << primes[15] << endl;
    cout << "1049th prime number is " << primes[1048];
  
    return 0;
}

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Java

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// Java program to the nth prime number  
import java.util.ArrayList;
class GFG
{
      
    // initializing the max value 
    static int MAX_SIZE = 1000005;
      
    // To store all prime numbers
    static ArrayList<Integer> primes =
       new ArrayList<Integer>();
      
    // Function to generate N prime numbers 
    // using Sieve of Eratosthenes
    static void SieveOfEratosthenes() 
    
        // Create a boolean array "IsPrime[0..MAX_SIZE]" 
        // and initialize all entries it as true. 
        // A value in IsPrime[i] will finally be false 
        // if i is Not a IsPrime, else true. 
        boolean [] IsPrime = new boolean[MAX_SIZE]; 
          
        for(int i = 0; i < MAX_SIZE; i++)
            IsPrime[i] = true;
          
        for (int p = 2; p * p < MAX_SIZE; p++) 
        
            // If IsPrime[p] is not changed, 
            // then it is a prime 
            if (IsPrime[p] == true
            
                // Update all multiples of p greater than or 
                // equal to the square of it 
                // numbers which are multiple of p and are 
                // less than p^2 are already been marked. 
                for (int i = p * p; i < MAX_SIZE; i += p) 
                    IsPrime[i] = false
            
        
      
        // Store all prime numbers 
        for (int p = 2; p < MAX_SIZE; p++) 
        if (IsPrime[p] == true
                primes.add(p);
    
      
    // Driver Code
    public static void main (String[] args) 
    {
          
        // Function call
        SieveOfEratosthenes();
      
        System.out.println("5th prime number is "
                                    primes.get(4));
        System.out.println("16th prime number is "
                                    primes.get(15));
        System.out.println("1049th prime number is "
                                    primes.get(1048));
    }
}
  
// This code is contributed by ihritik

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C#

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// C# program to the nth prime number 
using System;
using System.Collections;
  
class GFG
{
      
// initializing the max value 
static int MAX_SIZE = 1000005;
  
// To store all prime numbers
static ArrayList primes = new ArrayList();
  
// Function to generate N prime numbers using 
// Sieve of Eratosthenes
static void SieveOfEratosthenes() 
    // Create a boolean array "IsPrime[0..MAX_SIZE]" 
    // and initialize all entries it as true. 
    // A value in IsPrime[i] will finally be false
    // if i is Not a IsPrime, else true. 
    bool [] IsPrime = new bool[MAX_SIZE]; 
      
    for(int i = 0; i < MAX_SIZE; i++)
        IsPrime[i] = true;
      
    for (int p = 2; p * p < MAX_SIZE; p++) 
    
        // If IsPrime[p] is not changed,
        // then it is a prime 
        if (IsPrime[p] == true
        
            // Update all multiples of p greater than or 
            // equal to the square of it 
            // numbers which are multiple of p and are 
            // less than p^2 are already been marked. 
            for (int i = p * p; i < MAX_SIZE; i += p) 
                IsPrime[i] = false
        
    
  
    // Store all prime numbers 
    for (int p = 2; p < MAX_SIZE; p++) 
    if (IsPrime[p] == true
            primes.Add(p);
  
// Driver Code
public static void Main () 
{
      
    // Function call
    SieveOfEratosthenes();
  
    Console.WriteLine("5th prime number is "
                                   primes[4]);
    Console.WriteLine("16th prime number is " +
                                   primes[15]);
    Console.WriteLine("1049th prime number is " +
                                   primes[1048]);
}
}
  
// This code is contributed by ihritik

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Output:

5th prime number is 11
16th prime number is 53
1049th prime number is 8377


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Improved By : ihritik