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

// 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 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.
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 [tabby title="C#"] // 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 [tabbyending]

Output:

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


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Improved By : ihritik