# Find the smallest twins in given range

• Difficulty Level : Medium
• Last Updated : 11 Nov, 2021

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) ```
Recommended Practice

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++

 `// C++ program to find the smallest twin in given range``#include ``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 = prime = ``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"` `<

## Java

 `// 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`

## Python3

 `# 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`

## C#

 `    ` `// 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 = prime = ``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`

## PHP

 ``

## Javascript

 ``

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.

My Personal Notes arrow_drop_up