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Program to find the next prime number
  • Difficulty Level : Easy
  • Last Updated : 10 Mar, 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:
 

 

Approach: 
 

  1. First of all, take a boolean variable found and initialise it to false.
  2. Now, until that variable not equals to true, increment N by 1 in each iteration and check whether it is prime or not.
  3. If it is prime then print it and change value of found variable to True. otherwise, iterate the loop untill 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#




// 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: 
5

 

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