Smallest prime number in given Range

Given two integers L and R, denoting a range [L, R], the task is to find the smallest prime number present in the range.

Examples:

Input: L = 6, R = 11
Output: 7
Explanation: In the range of 6 to 11
6 is divisible by 1, 2, 3 and 6.
7  is divisible by 1 and 7, hence this is a prime and the first in the range.
So 7 is smallest prime in the given range.

Input: L = 14, R = 19
Output: 17
Explanation: 14 is divisible by 1, 2, 7 and 14.
15  is divisible by 1, 3, 5 and 15.
16 is divisible by 1, 2, 4, 8 and 16.
17 is divisible by 1 and 17.
So, in the range of 14 to 19, 17 is the smallest prime.

Approach: The problem can be solved based on the following idea:

Traverse from L to R and check if the number is prime or not. The first prime number is the smallest, as we are traversing from smaller end to higher end.

Follow the steps mentioned below to implement the idea:

• Start iteration from i = L to R:
  • Check if i is prime or not:
    • For this run a loop from j = 2 to the square root of i:
      • If i is divisible by any value of j, it is not a prime.
    • Otherwise, if i is not divisible by any value of j, i is a prime.
  • If i is a prime, break the loop and i the smallest prime.
• Return the value of the smallest prime as the required answer.

Below is the implementation of the above approach:

C++

// C++ code to implement the idea:

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

// Function to check if the number
// is a prime or not
int isPrime(int n)
{
    if (n < 2) {
        return 0;
    }
    else {
        for (int i = 2; i < sqrt(n); i++) {
            if (n % i == 0)
                return 0;
        }
    }
    return 1;
}

// Function to find the smallest
// prime in range
int minPrimeRange(int x, int y)
{
    for (int i = x; i <= y; i++) {
        if (isPrime(i))
            return i;
    }
    return -1;
}

// Driver code
int main()
{
    int L = 14, R = 19;

    // Function call
    int ans = minPrimeRange(L, R);
    cout << ans;

    return 0;
}

Java

import java.util.*;

public class Main {

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

    // Function to find the smallest prime in range
    public static int minPrimeRange(int x, int y) {
        for (int i = x; i <= y; i++) {
            if (isPrime(i))
                return i;
        }
        return -1;
    }

    // Driver code
    public static void main(String[] args) {
        int L = 14, R = 19;

        // Function call
        int ans = minPrimeRange(L, R);
        System.out.println(ans);
    }
}

Python

import math

# Function to check if the number is a prime or not
def isPrime(n):
    if n < 2:
        return False
    else:
        for i in range(2, int(math.sqrt(n))+1):
            if n % i == 0:
                return False
    return True

# Function to find the smallest prime in range
def minPrimeRange(x, y):
    for i in range(x, y+1):
        if isPrime(i):
            return i
    return -1

# Driver code
if __name__ == "__main__":
    L = 14
    R = 19

    # Function call
    ans = minPrimeRange(L, R)
    print(ans)

C#

using System;

namespace PrimeRange
{
    class Program
    {
        // Function to check if the number
        // is a prime or not
        static bool IsPrime(int n)
        {
            if (n < 2)
            {
                return false;
            }
            else
            {
                for (int i = 2; i * i <= n; i++)
                {
                    if (n % i == 0)
                        return false;
                }
            }
            return true;
        }

        // Function to find the smallest
        // prime in range
        static int MinPrimeRange(int x, int y)
        {
            for (int i = x; i <= y; i++)
            {
                if (IsPrime(i))
                    return i;
            }
            return -1;
        }

        static void Main(string[] args)
        {
            int L = 14, R = 19;

            // Function call
            int ans = MinPrimeRange(L, R);
            Console.WriteLine(ans);
        }
    }
}

// This code is contributed by Dwaipayan Bandyopadhyay

Javascript

// JS code to implement the approach:
function isPrime(n) {
    if (n < 2) {
        return 0;
    } else {
        for (let i = 2; i <= Math.sqrt(n); i++) {
            if (n % i === 0) {
                return 0;
            }
        }
    }
    return 1;
}

function minPrimeRange(x, y) {
    for (let i = x; i <= y; i++) {
        if (isPrime(i)) {
            return i;
        }
    }
    return -1;
}

// Driver code
const L = 14;
const R = 19;

// Function call
const ans = minPrimeRange(L, R);
console.log(ans);

Output

17

Time Complexity: O(N√N)
Auxiliary Space: O(1)