Program to find the next prime number

Last Updated : 27 Jul, 2021

Given an integer N. The task is to find the next prime number i.e. the smallest prime number greater than N.

Examples:

Input: N = 10
Output: 11
11 is the smallest prime number greater than 10.

Input: N = 0
Output: 2

Approach:

First of all, take a boolean variable found and initialize it to false.
Now, until that variable not equals to true, increment N by 1 in each iteration and check whether it is prime or not.
If it is prime then print it and change value of found variable to True. otherwise, iterate the loop until you will get the next prime number.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function that returns true if n 
// is prime else returns false 
bool isPrime(int n) 
{ 
    // Corner cases 
    if (n <= 1)  return false; 
    if (n <= 3)  return true; 
  
    // This is checked so that we can skip  
    // middle five numbers in below loop 
    if (n%2 == 0 || n%3 == 0) return false; 
  
    for (int i=5; i*i<=n; i=i+6) 
        if (n%i == 0 || n%(i+2) == 0) 
           return false; 
  
    return true; 
} 

// Function to return the smallest
// prime number greater than N
int nextPrime(int N)
{

    // Base case
    if (N <= 1)
        return 2;

    int prime = N;
    bool found = false;

    // Loop continuously until isPrime returns
    // true for a number greater than n
    while (!found) {
        prime++;

        if (isPrime(prime))
            found = true;
    }

    return prime;
}

// Driver code
int main()
{
    int N = 3;

    cout << nextPrime(N);

    return 0;
}

Java

// Java implementation of the approach 
class GFG 
{

    // Function that returns true if n 
    // is prime else returns false 
    static boolean isPrime(int n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
        
        // This is checked so that we can skip 
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
        
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
        
        return true; 
    } 
    
    // Function to return the smallest 
    // prime number greater than N 
    static int nextPrime(int N) 
    { 
    
        // Base case 
        if (N <= 1) 
            return 2; 
    
        int prime = N; 
        boolean found = false; 
    
        // Loop continuously until isPrime returns 
        // true for a number greater than n 
        while (!found) 
        { 
            prime++; 
    
            if (isPrime(prime)) 
                found = true; 
        } 
    
        return prime; 
    } 
    
    // Driver code 
    public static void main (String[] args)
    { 
        int N = 3; 
    
        System.out.println(nextPrime(N)); 
    } 
}

// This code is contributed by AnkitRai01

Python3

# Python3 implementation of the approach 
import math

# Function that returns True if n 
# is prime else returns False 
def isPrime(n):
    
    # Corner cases 
    if(n <= 1):
        return False
    if(n <= 3):
        return True
    
    # This is checked so that we can skip 
    # middle five numbers in below loop 
    if(n % 2 == 0 or n % 3 == 0):
        return False
    
    for i in range(5,int(math.sqrt(n) + 1), 6): 
        if(n % i == 0 or n % (i + 2) == 0):
            return False
    
    return True

# Function to return the smallest 
# prime number greater than N 
def nextPrime(N):

    # Base case 
    if (N <= 1):
        return 2

    prime = N
    found = False

    # Loop continuously until isPrime returns 
    # True for a number greater than n 
    while(not found):
        prime = prime + 1

        if(isPrime(prime) == True):
            found = True

    return prime

# Driver code 
N = 3
print(nextPrime(N))

# This code is contributed by Sanjit_Prasad

// C# implementation of the approach 
using System;
    
class GFG 
{

    // Function that returns true if n 
    // is prime else returns false 
    static bool isPrime(int n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
        
        // This is checked so that we can skip 
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 ||
                n % (i + 2) == 0) 
            return false; 
        
        return true; 
    } 
    
    // Function to return the smallest 
    // prime number greater than N 
    static int nextPrime(int N) 
    { 
    
        // Base case 
        if (N <= 1) 
            return 2; 
    
        int prime = N; 
        bool found = false; 
    
        // Loop continuously until isPrime 
        // returns true for a number 
        // greater than n 
        while (!found) 
        { 
            prime++; 
    
            if (isPrime(prime)) 
                found = true; 
        } 
        return prime; 
    } 
    
    // Driver code 
    public static void Main (String[] args)
    { 
        int N = 3; 
    
        Console.WriteLine(nextPrime(N)); 
    } 
}

// This code is contributed by 29AjayKumar

JavaScript

<script>

// Javascript implementation of the approach 

// Function that returns true if n 
// is prime else returns false 
function isPrime(n) 
{ 
    // Corner cases 
    if (n <= 1) return false; 
    if (n <= 3) return true; 
    
    // This is checked so that we can skip 
    // middle five numbers in below loop 
    if (n%2 == 0 || n%3 == 0) return false; 
    
    for (let i=5; i*i<=n; i=i+6) 
        if (n%i == 0 || n%(i+2) == 0) 
        return false; 
    
    return true; 
} 

// Function to return the smallest 
// prime number greater than N 

function nextPrime(N) 
{ 

    // Base case 
    if (N <= 1) 
        return 2; 

    let prime = N; 
    let found = false; 

    // Loop continuously until isPrime returns 
    // true for a number greater than n 
    while (!found) { 
        prime++; 

        if (isPrime(prime)) 
            found = true; 
    } 

    return prime; 
} 

// Driver code 

    let N = 3; 

    document.write(nextPrime(N)); 

// This code is contributed by Mayank Tyagi

</script>

Output:

Program to find the Nth Composite Number

Naman_Garg

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Program to find the next prime number

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