Program to find the next prime number (original) (raw)

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:

1. First of all, take a boolean variable found and initialize 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 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#

// 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

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