Find the largest twins in given range

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

Examples:

Input: low = 10, high = 100
Output: Largest twins in given range: (71, 73)

Input: low = 1, high = 20
Output: Largest twins in given range: (17, 19)

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

    • If prime[p] is true, then p is prime.
    • Mark all multiples of p as not prime in prime[].
  3. Run a loop from high to low and print the first twins using prime[] built in step 2.

C++

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// C++ program to find the largest twin in given range
#include <bits/stdc++.h>
using namespace std;
  
// Function to find twins
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 largest twin in range
    for (int i = high; i >= low; i--) {
        if (prime[i] && (i - 2 >= low && prime[i - 2] == true)) {
            cout << "Largest twins in given range: ("
                 << i - 2 << ", " << i << ")";
            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  


// largest twin in given range 


import java.io.*; 


  


class GFG  


{ 


      


// Function to find twins 


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]; 


    boolean twin = false; 


    for(int i = 0; i < high + 1; 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 largest twin in range 


    for (int i = high; i >= low; i--)  


    { 


        if (prime[i] && (i - 2 >= low &&  


            prime[i - 2] == true)) 


        { 


            System.out.println("Largest twins in given range: (" +  


                                      (i - 2) + ", " + (i) + ")"); 


            twin = true; 


            break; 


        } 


    } 


  


    if (twin == false) 


        System.out.println("No such pair exists"); 


} 


  


// Driver Code 


public static void main (String[] args)  


{ 


    printTwins(10, 100); 


} 


} 


  


// This code is contributed  


// by inder_verma. 



















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Python3














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# Python 3 program to find the largest twin  


# in given range 


  


# Function to find twins 


from math import sqrt,floor 


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 for i in range(high + 1)] 


    twin = False


  


    prime[0] = False


    prime[1] = False


  


    # Look for the smallest twin 


    k = floor(sqrt(high)) + 2


    for p in range(2, k, 1): 


          


        # 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 largest twin in range 


    i = high 


    while(i >= low): 


        if (prime[i] and (i - 2 >= low and 


                          prime[i - 2] == True)): 


            print("Largest twins in given range:(", (i - 2),     


                                             ",", (i), ")") 


            twin = True


            break


              


        i -= 1


      


    if (twin == False): 


        print("No such pair exists") 


  


# Driver Code 


if __name__ == '__main__': 


    printTwins(10, 100) 


  


# This code is contributed by 


# Sanjit_Prasad 



















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C#














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// C# program to find the  


// largest twin in given range 


class GFG  


{ 


      


// Function to find twins 


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 < high + 1; i++) 


    prime[i] = true; 


  


    prime[0] = prime[1] = false; 


  


    // Look for the smallest twin 


    for (int p = 2;  


             p <= System.Math.Floor( 


                         System.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 largest twin in range 


    for (int i = high; i >= low; i--)  


    { 


        if (prime[i] && (i - 2 >= low &&  


            prime[i - 2] == true)) 


        { 


            System.Console.WriteLine("Largest twins in given range: (" +  


                                    (i - 2) + ", " + (i) + ")"); 


            twin = true; 


            break; 


        } 


    } 


  


    if (twin == false) 


        System.Console.WriteLine("No such pair exists"); 


} 


  


// Driver Code 


public static void Main()  


{ 


    printTwins(10, 100); 


} 


} 


  


// This code is contributed  


// by mits 



















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PHP














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<?php 


//PHP  program to find the largest twin in given range  


// Function to find twins  


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.  


    $prime[$high + 1]=array(); 


    $twin = false;  


    $prime = array_fill(0, ($high + 1), true);  


      


    $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 largest twin in range  


    for ($i = $high; $i >= $low; $i--) {  


        if ($prime[$i] && ($i - 2 >= $low && $prime[$i - 2] == true)) {  


            echo "Largest twins in given range: (", 


                $i - 2 , ", " , $i , ")";  


            $twin = true;  


            break;  


        }  


    }  


  


    if ($twin == false)  


         echo  "No such pair exists" ;  


}  


  


// Driver program  


  


    printTwins(10, 100);  


  


#This code is contributed by ajit. 


?> 



















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Output:


Largest twins in given range: (71, 73)







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