Find the smallest twins in given range

Given a range [low..high], print the smallest twin numbers in given range (low and high inclusive). Two numbers are twins if they are primes and there difference is 2.

Example:

Input:  low = 10,  high = 100
Output: Smallest twins in given range: (11, 13)
Both 11 and 13 are prime numbers and difference 
between them is two, therefore twins.  And these
are the smallest twins in [10..100]

Input:  low = 50,  high = 100
Output: Smallest twins in given range: (59, 61) 

A Simple Solution is to start to start from low and for every number x check if x and x + 2 are primes are not. Here x varies from low to high-2.



An Efficient Solution is to use Sieve of Eratosthenes

1) Create a boolean array "prime[0..high]" and initialize all 
   entries in it as true. A value in prime[i] will finally 
   be false if i is not a prime number, else true.

2) Run a loop from p = 2 to high. 
    a) If prime[p] is true, then p is prime. [See this]
    b) Mark all multiples of p as not prime in prime[]. 

3) Run a loop from low to high and print the first twins
   using prime[] built in step 2.   

Below is the implementation of above idea.

C++

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// C++ program to find the smallest twin in given range 
#include <bits/stdc++.h> 
using namespace std; 
  
void printTwins(int low, int high) 
    // Create a boolean array "prime[0..high]" and initialize 
    // all entries it as true. A value in prime[i] will finally 
    // be false if i is Not a prime, else true. 
    bool prime[high+1], twin = false
    memset(prime, true, sizeof(prime)); 
  
    prime[0] = prime[1] = false
  
    // Look for the smallest twin 
    for (int p=2; p<=floor(sqrt(high))+1; p++) 
    
        // If p is not marked, then it is a prime 
        if (prime[p]) 
        
            // Update all multiples of p 
            for (int i=p*2; i<=high; i += p) 
                prime[i] = false
        
    
  
    // Now print the smallest twin in range 
    for (int i=low; i<=high; i++) 
    
        if (prime[i] && prime[i+2]) 
        
            cout << "Smallest twins in given range: ("
                << i << ", " << i+2 << ")"
            twin = true;
            break
        
    
      
    if (twin == false)
      cout << "No such pair exists" <<endl;
  
// Driver program 
int main() 
    printTwins(10, 100); 
    return 0; 

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Java

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// Java program to find the smallest twin in given range 
  
class GFG {
  
    static void printTwins(int low, int high) {
        // Create a boolean array "prime[0..high]" and initialize 
        // all entries it as true. A value in prime[i] will finally 
        // be false if i is Not a prime, else true. 
        boolean prime[] = new boolean[high + 1], twin = false;
        for (int i = 0; i < prime.length; i++) {
            prime[i] = true;
        }
  
        prime[0] = prime[1] = false;
  
        // Look for the smallest twin 
        for (int p = 2; p <= Math.floor(Math.sqrt(high)) + 1; p++) {
            // If p is not marked, then it is a prime 
            if (prime[p]) {
                // Update all multiples of p 
                for (int i = p * 2; i <= high; i += p) {
                    prime[i] = false;
                }
            }
        }
  
        // Now print the smallest twin in range 
        for (int i = low; i <= high; i++) {
            if (prime[i] && prime[i + 2]) {
                int a = i + 2 ;
                System.out.print("Smallest twins in given range: ("
                        + i + ", " + a + ")");
                twin = true;
                break;
            }
        }
  
        if (twin == false) {
            System.out.println("No such pair exists");
        }
    }
  
// Driver program 
    public static void main(String[] args) {
  
        printTwins(10, 100);
    }
}
// This code contributed by Rajput-Ji

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Python3

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# Python3 program to find the smallest 
# twin in given range 
import math
  
def printTwins(low, high): 
  
    # Create a boolean array "prime[0..high]" 
    # and initialize all entries it as true. 
    # A value in prime[i] will finally be 
    # false if i is Not a prime, else true. 
    prime = [True] * (high + 1);
    twin = False
  
    prime[0] = prime[1] = False
  
    # Look for the smallest twin 
    for p in range(2, int(math.floor(
                          math.sqrt(high)) + 2)):
          
        # If p is not marked, then it
        # is a prime 
        if (prime[p]): 
              
            # Update all multiples of p 
            for i in range(p * 2, high + 1, p): 
                prime[i] = False
  
    # Now print the smallest twin in range 
    for i in range(low, high + 1): 
        if (prime[i] and prime[i + 2]): 
            print("Smallest twins in given range: ("
                               i, ",", (i + 2), ")"); 
            twin = True;
            break
      
    if (twin == False):
        print("No such pair exists");
  
# Driver Code
printTwins(10, 100); 
      
# This code is contributed 
# by chandan_jnu

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C#

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// C# program to find the smallest twin in given range 
  
using System; 
public class GFG {
   
    static void printTwins(int low, int high) {
        // Create a boolean array "prime[0..high]" and initialize 
        // all entries it as true. A value in prime[i] will finally 
        // be false if i is Not a prime, else true. 
        bool []prime = new bool[high + 1]; bool twin = false;
        for (int i = 0; i < prime.Length; i++) {
            prime[i] = true;
        }
   
        prime[0] = prime[1] = false;
   
        // Look for the smallest twin 
        for (int p = 2; p <= Math.Floor(Math.Sqrt(high)) + 1; p++) {
            // If p is not marked, then it is a prime 
            if (prime[p]) {
                // Update all multiples of p 
                for (int i = p * 2; i <= high; i += p) {
                    prime[i] = false;
                }
            }
        }
   
        // Now print the smallest twin in range 
        for (int i = low; i <= high; i++) {
            if (prime[i] && prime[i + 2]) {
                int a = i + 2 ;
                Console.Write("Smallest twins in given range: ("
                        + i + ", " + a + ")");
                twin = true;
                break;
            }
        }
   
        if (twin == false) {
            Console.WriteLine("No such pair exists");
        }
    }
   
// Driver program 
    public static void Main() {
   
        printTwins(10, 100);
    }
}
//this code contributed by Rajput-Ji

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PHP

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<?php
// PHP program to find the smallest 
// twin in given range 
  
function printTwins($low, $high
    // Create a boolean array "prime[0..high]" 
    // and initialize all entries it as true. 
    // A value in prime[i] will finally be 
    // false if i is Not a prime, else true. 
    $prime = array_fill(0, $high + 1, true);
    $twin = false; 
  
    $prime[0] = $prime[1] = false; 
  
    // Look for the smallest twin 
    for ($p = 2; $p <= floor(sqrt($high)) + 1; $p++) 
    
        // If p is not marked, then it is a prime 
        if ($prime[$p]) 
        
            // Update all multiples of p 
            for ($i = $p * 2; $i <= $high; $i += $p
                $prime[$i] = false; 
        
    
  
    // Now print the smallest twin in range 
    for ($i = $low; $i <= $high; $i++) 
    
        if ($prime[$i] && $prime[$i + 2]) 
        
            print("Smallest twins in given range: ($i, "
                                          ($i + 2). ")"); 
            $twin = true;
            break
        
    
      
    if ($twin == false)
    print("No such pair exists\n");
  
// Driver Code
printTwins(10, 100); 
      
// This code is contributed by mits
?>

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Output:

Smallest twins in given range: (11, 13)

Thanks to Utkarsh Trivedi for suggesting this solution.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



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