Find the minimum number to be added to N to make it a prime number

Given an integer N, the task is to find the minimum number K to be added to N such that N + K becomes a prime number.
Examples:

Input: N = 10 
Output: 1 
Explanation:
1 is the minimum number to be added to N such that 10 + 1 = 11 is a prime number
Input: N = 20 
Output: 3 

Approach: The idea is to check whether the number is a prime or not by incrementing the value to be added K by 1 in each iteration. Therefore, the following steps can be followed to compute the answer: 

1. Initially, check whether the given number is prime or not. If it is, then the value to be added(K) is 0.
2. Now, in every iteration, increment the value of N by 1 and check if the number is prime or not. Let the first value at which N becomes a prime is M. Then, the minimum value that needs to be added to make N prime is M – N.

Below is the implementation of the above approach:

C++

// C++ program to find the minimum
// number to be added to N to
// make it a prime number

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

// Function to check if a given number
// is a prime or not
bool isPrime(int n)
{
    // Base 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 all the remaining numbers, check if
    // any number is a factor if the number
    // or not
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;

    // If none of the above numbers are the
    // factors for the number, then the
    // given number is prime
    return true;
}

// Function to return the smallest
// number to be added to make a
// number prime
int findSmallest(int N)
{

    // Base case
    if (N == 0)
        return 2;
    if (N == 1)
        return 1;

    int prime = N, counter = 0;
    bool found = false;

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

            // If the number is not a prime, then
            // increment the number by 1 and the
            // counter which stores the number
            // to be added
            prime++;
            counter++;
        }
    }

    return counter;
}

// Driver code
int main()
{
    int N = 10;

    cout << findSmallest(N);

    return 0;
}

Java

// Java program to find the minimum
// number to be added to N to
// make it a prime number
import java.util.*;

class GFG{

// Function to check if a given number
// is a prime or not
static boolean isPrime(int n)
{
    // Base 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 all the remaining numbers, check if
    // any number is a factor if the number
    // or not
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;

    // If none of the above numbers are the
    // factors for the number, then the
    // given number is prime
    return true;
}

// Function to return the smallest
// number to be added to make a
// number prime
static int findSmallest(int N)
{

    // Base case
    if (N == 0)
        return 2;
    if (N == 1)
        return 1;

    int prime = N, counter = 0;
    boolean found = false;

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

            // If the number is not a prime, then
            // increment the number by 1 and the
            // counter which stores the number
            // to be added
            prime++;
            counter++;
        }
    }

    return counter;
}

// Driver code
public static void main(String[] args)
{
    int N = 10;

    System.out.print(findSmallest(N));
}
}

// This code is contributed by sapnasingh4991

Python3

# Python 3 program to find the minimum
# number to be added to N to
# make it a prime number

# Function to check if a given number
# is a prime or not
def isPrime(n):

    # Base 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 all the remaining numbers, check if
    # any number is a factor if the number
    # or not
    i = 5
    while (i * i <= n ):
        if (n % i == 0 or n % (i + 2) == 0):
            return False
        i += 6

    # If none of the above numbers are the
    # factors for the number, then the
    # given number is prime
    return True

# Function to return the smallest
# number to be added to make a
# number prime
def findSmallest(N):

    # Base case
    if (N == 0):
        return 2
    if (N == 1):
        return 1

    prime , counter = N, 0
    found = False

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

            # If the number is not a prime, then
            # increment the number by 1 and the
            # counter which stores the number
            # to be added
            prime += 1
            counter += 1
    return counter

# Driver code
if __name__ == "__main__":

    N = 10

    print(findSmallest(N))

# This code is contributed by chitranayal

C#

// C# program to find the minimum
// number to be added to N to
// make it a prime number
using System;

class GFG{

// Function to check if a given number
// is a prime or not
static bool isPrime(int n)
{
    // Base 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 all the remaining numbers, check if
    // any number is a factor if the number
    // or not
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;

    // If none of the above numbers are the
    // factors for the number, then the
    // given number is prime
    return true;
}

// Function to return the smallest
// number to be added to make a
// number prime
static int findSmallest(int N)
{

    // Base case
    if (N == 0)
        return 2;
    if (N == 1)
        return 1;

    int prime = N, counter = 0;
    bool found = false;

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

            // If the number is not a prime, then
            // increment the number by 1 and the
            // counter which stores the number
            // to be added
            prime++;
            counter++;
        }
    }

    return counter;
}

// Driver code
public static void Main()
{
    int N = 10;

    Console.Write(findSmallest(N));
}
}

// This code is contributed by AbhiThakur

Javascript

<script>

// Javascript program to find the minimum
// number to be added to N to
// make it a prime number

// Function to check if a given number
// is a prime or not
function isPrime(n)
{

    // Base 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 all the remaining numbers, check if
    // any number is a factor if the number
    // or not
    for (var i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;

    // If none of the above numbers are the
    // factors for the number, then the
    // given number is prime
    return true;
}

// Function to return the smallest
// number to be added to make a
// number prime
function findSmallest(N)
{

    // Base case
    if (N == 0)
        return 2;
    if (N == 1)
        return 1;

    var prime = N, counter = 0;
    var found = false;

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

            // If the number is not a prime, then
            // increment the number by 1 and the
            // counter which stores the number
            // to be added
            prime++;
            counter++;
        }
    }

    return counter;
}

// Driver code
var N = 10;
document.write( findSmallest(N));

// This code is contributed by noob2000.
</script>

Output:

1

Time Complexity: O(k*sqrt(k)) (where k = M-N, N = input, M = first prime no.)

Space Complexity: O(1)