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

Below is the implementation of the above approach: 

C++

// C++ 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;
}

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<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

Python3

# Python3 program to the nth prime number
primes = []

# Function to generate N prime numbers using
# Sieve of Eratosthenes
def SieveOfEratosthenes():

    n = 1000005

    # Create a boolean array "prime[0..n]" and
    # initialize all entries it as true. A value
    # in prime[i] will finally be false if i is
    # Not a prime, else true.
    prime = [True for i in range(n + 1)]

    p = 2
    while (p * p <= n):

        # If prime[p] is not changed,
        # then it is a prime
        if (prime[p] == True):

            # Update all multiples of p
            for i in range(p * p, n + 1, p):
                prime[i] = False

        p += 1

    # Print all prime numbers
    for p in range(2, n + 1):
        if prime[p]:
            primes.append(p)

# Driver code
if __name__=='__main__':

    # Function call
    SieveOfEratosthenes()

    print("5th prime number is", primes[4]);
    print("16th prime number is", primes[15]);
    print("1049th prime number is", primes[1048]);

# This code is contributed by grand_master

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

Javascript

<script>

// Javascript program to the nth prime number

// initializing the max value
var MAX_SIZE = 1000005;

// Function to generate N prime numbers using
// Sieve of Eratosthenes
function SieveOfEratosthenes(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.
    var IsPrime = Array(MAX_SIZE).fill(true);

    var p,i;
    for (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(i = p * p; i < MAX_SIZE; i += p)
                IsPrime[i] = false;
        }
    }

    // Store all prime numbers
    for (p = 2; p < MAX_SIZE; p++)
        if (IsPrime[p])
            primes.push(p);
}

// Driver Code
    // To store all prime numbers
    var primes = [];

    // Function call
    SieveOfEratosthenes(primes);

    document.write(
    "5th prime number is "+primes[4]+"<br>"
    );
    document.write(
    "16th prime number is "+primes[15]+"<br>"
    );
    document.write(
    "1049th prime number is "+primes[1048]+"<br>"
    );

</script>

Output

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

Another approach : 

• for finding prime number at given position write a isPrime function to check number is prime or not
• write a function to get prime number at given position 
  

Below is the implementation of the above approach : 

C++

// c++ program to find the n-th prime number

#include <bits/stdc++.h>
using namespace std;


// function to check given number is prime or not
// basic idea is numbers not divided by any primes are primes
int isPrime(int k)
{
    // Corner cases
    if (k <= 1)
        return 0;
    if (k==2 || k==3)
        return 1;

    // below 5 there is only two prime numbers 2 and 3
    if (k % 2 == 0 || k % 3 == 0)
        return 0;

  // Using concept of prime number can be represented in form of (6*k + 1) or(6*k - 1)
    for (int i = 5; i * i <= k; i = i + 6)
        if (k % i == 0 || k % (i + 2) == 0)
            return 0;

    return 1;
}


// function which gives prime at position n
int nThPrime(int n)
{
    int i=2;

    while(n>0)
    {
        // each time if a prime number found decrease n
        if(isPrime(i))
          n--;

        i++;  //increase the integer to go ahead
    }
    i-=1; // since decrement of k is being done before
          //Increment of i , so i should be decreased by 1
    return i;
}

int main()
{
    cout<<"5th prime number is : "<<nThPrime(5)<<"\n";
    cout<<"7th prime number is : "<<nThPrime(7)<<"\n";
    cout<<"10th prime number is : "<<nThPrime(10)<<"\n";
    return 0;
}
// This code is contributed by Ujjwal Kumar Bhardwaj

Java

// Java program to find the n-th prime number
import java.util.*;
class GFG {

  // function to check given number is prime or not
  // basic idea is numbers not divided by any primes are
  // primes
  static int isPrime(int k)
  {

    // Corner cases
    if (k <= 1)
      return 0;
    if (k == 2 || k == 3)
      return 1;

    // below 5 there is only two prime numbers 2 and 3
    if (k % 2 == 0 || k % 3 == 0)
      return 0;

    // Using concept of prime number can be represented
    // in form of (6*k + 1) or(6*k - 1)
    for (int i = 5; i * i <= k; i = i + 6)
      if (k % i == 0 || k % (i + 2) == 0)
        return 0;

    return 1;
  }

  // function which gives prime at position n
  static int nThPrime(int n)
  {
    int i = 2;

    while (n > 0)
    {

      // each time if a prime number found decrease n
      if (isPrime(i) == 1)
        n--;

      i++; // increase the integer to go ahead
    }
    i -= 1; // since decrement of k is being done before
    // Increment of i , so i should be decreased
    // by 1
    return i;
  }

  public static void main(String[] args)
  {
    System.out.println("5th prime number is : "
                       + nThPrime(5));
    System.out.println("7th prime number is : "
                       + nThPrime(7));
    System.out.println("10th prime number is : "
                       + nThPrime(10));
  }
}

// This code is contributed by phasing17

Python3

# Python3 program to find the n-th prime number

# function to check given number is prime or not
# basic idea is numbers not divided by any primes are primes
def isPrime(k):

    # Corner cases
    if (k <= 1):
        return 0
    if (k == 2 or k == 3):
        return 1

    # below 5 there is only two prime numbers 2 and 3
    if (k % 2 == 0 or k % 3 == 0):
        return 0

  # Using concept of prime number can be represented in form of (6*k + 1) or(6*k - 1)
    for i in range(5, 1 + int(k ** 0.5), 6):
        if (k % i == 0 or k % (i + 2) == 0):
            return 0

    return 1

# function which gives prime at position n
def nThPrime(n):
    i = 2
    while(n > 0):

        # each time if a prime number found decrease n
        if(isPrime(i)):
            n -= 1

        i += 1  # increase the integer to go ahead

    i -= 1  # since decrement of k is being done before
    # Increment of i , so i should be decreased by 1
    return i

# Driver code
print("5th prime number is :", nThPrime(5))
print("7th prime number is :", nThPrime(7))
print("10th prime number is :", nThPrime(10))

# This code is contributed by phasing17

C#

// C# program to find the n-th prime number
using System;
using System.Collections.Generic;

class GFG
{

  // function to check given number is prime or not
  // basic idea is numbers not divided by any primes are
  // primes
  static int isPrime(int k)
  {
    // Corner cases
    if (k <= 1)
      return 0;
    if (k == 2 || k == 3)
      return 1;

    // below 5 there is only two prime numbers 2 and 3
    if (k % 2 == 0 || k % 3 == 0)
      return 0;

    // Using concept of prime number can be represented
    // in form of (6*k + 1) or(6*k - 1)
    for (int i = 5; i * i <= k; i = i + 6)
      if (k % i == 0 || k % (i + 2) == 0)
        return 0;

    return 1;
  }

  // function which gives prime at position n
  static int nThPrime(int n)
  {
    int i = 2;

    while (n > 0) {
      // each time if a prime number found decrease n
      if (isPrime(i) == 1)
        n--;

      i++; // increase the integer to go ahead
    }
    i -= 1; // since decrement of k is being done before
    // Increment of i , so i should be decreased
    // by 1
    return i;
  }

  public static void Main(string[] args)
  {
    Console.WriteLine("5th prime number is : "
                      + nThPrime(5));
    Console.WriteLine("7th prime number is : "
                      + nThPrime(7));
    Console.WriteLine("10th prime number is : "
                      + nThPrime(10));
  }
}

// This code is contributed by phasing17

Javascript

// JS program to find the n-th prime number


// function to check given number is prime or not
// basic idea is numbers not divided by any primes are primes
function isPrime(k)
{
    // Corner cases
    if (k <= 1)
        return 0;
    if (k==2 || k==3)
        return 1;

    // below 5 there is only two prime numbers 2 and 3
    if (k % 2 == 0 || k % 3 == 0)
        return 0;

  // Using concept of prime number can be represented in form of (6*k + 1) or(6*k - 1)
    for (let i = 5; i * i <= k; i = i + 6)
        if (k % i == 0 || k % (i + 2) == 0)
            return 0;

    return 1;
}


// function which gives prime at position n
function nThPrime(n)
{
    let i=2;

    while(n>0)
    {
        // each time if a prime number found decrease n
        if(isPrime(i))
          n--;

        i++;  //increase the integer to go ahead
    }
    i-=1; // since decrement of k is being done before
          //Increment of i , so i should be decreased by 1
    return i;
}


// Driver code
console.log("5th prime number is : "+nThPrime(5));
console.log("7th prime number is : "+nThPrime(7));
console.log("10th prime number is : "+nThPrime(10));


// This code is contributed by phasing17

Output

5th prime number is : 11
7th prime number is : 17
10th prime number is : 29