Minimum absolute difference of a number and its closest prime

Given a positive integer N, the task is to find the absolute difference of N and the prime number closest to N . 
Note: The closest prime to N can be either less than, equal to or greater than N.
Examples:

Input: N = 25 
Output: 2 
For N = 25 
Closest prime greater than 25 is 29. So difference is 4. 
Closest prime less than 25 is 23. So difference is 2. 
The minimum of these two is 2.
Input: N = 2 
Output: 0 
As 2 itself is a prime number, closest prime number is 2. So difference is 0. 

Approach:

• If N is prime then print 0.
• Else, find the first prime number > N and note its difference with N.
• Then, find the first prime number < N and note its difference with N.
• And print the minimum of these two differences obtained.

Below is the implementation of the above approach: 

C++

// C++ program to find the minimum absolute
// difference between a number and its closest prime

#include <bits/stdc++.h>

using namespace std;

    // Function to check if a number is prime or not
    bool isPrime(int N)
    {
        for (int i = 2; i <= sqrt(N); i++) {
            if (N % i == 0)
                return false;
        }
        return true;
    }

    // Function to find the minimum absolute difference
    // between a number and its closest prime
    int getDifference(int N)
    {
        if (N == 0)
            return 2;
        else if (N == 1)
            return 1;
        else if (isPrime(N))
            return 0;

        // Variables to store first prime
        // above and below N
        int aboveN = -1, belowN = -1;
        int n1;

        // Finding first prime number greater than N
        n1 = N + 1;
        while (true) {
            if (isPrime(n1)) {
                aboveN = n1;
                break;
            }
            else
                n1++;
        }

        // Finding first prime number less than N
        n1 = N - 1;
        while (true) {
            if (isPrime(n1)) {
                belowN = n1;
                break;
            }
            else
                n1--;
        }

        // Variables to store the differences
        int diff1 = aboveN - N;
        int diff2 = N - belowN;

        return min(diff1, diff2);
    }

// Driver code
int main()
{
    int N = 25;
   cout << getDifference(N) << endl;
   return 0;
  // This code is contributed by Ryuga
}

Java

// Java program to find the minimum absolute
// difference between a number and its closest prime
class GFG {

    // Function to check if a number is prime or not
    static boolean isPrime(int N)
    {
        for (int i = 2; i <= Math.sqrt(N); i++) {
            if (N % i == 0)
                return false;
        }
        return true;
    }

    // Function to find the minimum absolute difference
    // between a number and its closest prime
    static int getDifference(int N)
    {
        if (N == 0)
            return 2;
        else if (N == 1)
            return 1;
        else if (isPrime(N))
            return 0;

        // Variables to store first prime
        // above and below N
        int aboveN = -1, belowN = -1;
        int n1;

        // Finding first prime number greater than N
        n1 = N + 1;
        while (true) {
            if (isPrime(n1)) {
                aboveN = n1;
                break;
            }
            else
                n1++;
        }

        // Finding first prime number less than N
        n1 = N - 1;
        while (true) {
            if (isPrime(n1)) {
                belowN = n1;
                break;
            }
            else
                n1--;
        }

        // Variables to store the differences
        int diff1 = aboveN - N;
        int diff2 = N - belowN;

        return Math.min(diff1, diff2);
    }

    // Driver code
    public static void main(String args[])
    {
        int N = 25;
        System.out.println(getDifference(N));
    }
}

Python3

# Python 3 program to find the minimum
# absolute difference between a number
# and its closest prime
from math import sqrt

# Function to check if a number is
# prime or not
def isPrime(N):
    k = int(sqrt(N)) + 1
    for i in range(2, k, 1):
        if (N % i == 0):
            return False

    return True

# Function to find the minimum absolute
# difference between a number and its
# closest prime
def getDifference(N):
    if (N == 0):
        return 2
    elif (N == 1):
        return 1
    elif (isPrime(N)):
        return 0

    # Variables to store first prime
    # above and below N
    aboveN = -1
    belowN = -1

    # Finding first prime number
    # greater than N
    n1 = N + 1
    while (True):
        if (isPrime(n1)):
            aboveN = n1
            break

        else:
            n1 += 1

    # Finding first prime number
    # less than N
    n1 = N - 1
    while (True):
        if (isPrime(n1)):
            belowN = n1
            break

        else:
            n1 -= 1

    # Variables to store the differences
    diff1 = aboveN - N
    diff2 = N - belowN

    return min(diff1, diff2)

# Driver code
if __name__ == '__main__':
    N = 25
    print(getDifference(N))

# This code is contributed by
# Surendra_Gangwar

C#

// C# program to find the minimum absolute
// difference between a number and its closest prime
using System;
class GFG {

    // Function to check if a number is prime or not
    static bool isPrime(int N)
    {
        for (int i = 2; i <= Math.Sqrt(N); i++) {
            if (N % i == 0)
                return false;
        }
        return true;
    }

    // Function to find the minimum absolute difference
    // between a number and its closest prime
    static int getDifference(int N)
    {
        if (N == 0)
            return 2;
        else if (N == 1)
            return 1;
        else if (isPrime(N))
            return 0;

        // Variables to store first prime
        // above and below N
        int aboveN = -1, belowN = -1;
        int n1;

        // Finding first prime number greater than N
        n1 = N + 1;
        while (true) {
            if (isPrime(n1)) {
                aboveN = n1;
                break;
            }
            else
                n1++;
        }

        // Finding first prime number less than N
        n1 = N - 1;
        while (true) {
            if (isPrime(n1)) {
                belowN = n1;
                break;
            }
            else
                n1--;
        }

        // Variables to store the differences
        int diff1 = aboveN - N;
        int diff2 = N - belowN;

        return Math.Min(diff1, diff2);
    }

    // Driver code
    public static void Main()
    {
        int N = 25;
        Console.WriteLine(getDifference(N));
    }
}
// This code is contributed by  anuj_67..

PHP

<?php
// PHP program to find the minimum absolute
// difference between a number and its
// closest prime

// Function to check if a number
// is prime or not
function isPrime($N)
{
    for ($i = 2; $i <= sqrt($N); $i++)
    {
        if ($N % $i == 0)
            return false;
    }
    return true;
}

// Function to find the minimum absolute difference
// between a number and its closest prime
function getDifference($N)
{
    if ($N == 0)
        return 2;
    else if ($N == 1)
        return 1;
    else if (isPrime($N))
        return 0;

    // Variables to store first prime
    // above and below N
    $aboveN = -1; $belowN = -1;

    // Finding first prime number greater than N
    $n1 = $N + 1;
    while (true)
    {
        if (isPrime($n1))
        {
            $aboveN = $n1;
            break;
        }
        else
            $n1++;
    }

    // Finding first prime number less than N
    $n1 = $N - 1;
    while (true)
    {
        if (isPrime($n1))
        {
            $belowN = $n1;
            break;
        }
        else
            $n1--;
    }

    // Variables to store the differences
    $diff1 = $aboveN - $N;
    $diff2 = $N - $belowN;

    return min($diff1, $diff2);
}

// Driver code
$N = 25;
echo getDifference($N) . "\n";

// This code is contributed
// by Akanksha Rai

Javascript

// Javascript program to find the minimum absolute
// difference between a number and its
// closest prime

// Function to check if a number
// is prime or not
function isPrime(N)
{
    for (let i = 2; i <= Math.sqrt(N); i++)
    {
        if (N % i == 0)
            return false;
    }
    return true;
}

// Function to find the minimum absolute difference
// between a number and its closest prime
function getDifference(N)
{
    if (N == 0)
        return 2;
    else if (N == 1)
        return 1;
    else if (isPrime(N))
        return 0;

    // Variables to store first prime
    // above and below N
    let aboveN = -1;
    let belowN = -1;

    // Finding first prime number greater than N
    let n1 = N + 1;
    while (true)
    {
        if (isPrime(n1))
        {
            aboveN = n1;
            break;
        }
        else
            n1++;
    }

    // Finding first prime number less than N
    n1 = N - 1;
    while (true)
    {
        if (isPrime(n1))
        {
            belowN = n1;
            break;
        }
        else
            n1--;
    }

    // Variables to store the differences
    let diff1 = aboveN - N;
    let diff2 = N - belowN;

    return Math.min(diff1, diff2);
}

// Driver code
let N = 25;
document.write(getDifference(N) + "<br>");

// This code is contributed
// by gfgking

Output:

2

Time Complexity: O(N*sqrt(N)), where N represents the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.