# Prime Number of Set Bits in Binary Representation | Set 2

• Difficulty Level : Easy
• Last Updated : 24 May, 2021

Given two integers ‘L’ and ‘R’, we need to write a program that finds the count of numbers having the prime number of set bits in their binary representation in the range [L, R].

Examples:

```Input : 6 10
Output : 4
6 -> 110 (2 set bits, 2 is prime)
7 -> 111 (3 set bits, 3 is prime)
9 -> 1001 (2 set bits , 2 is prime)
10->1010 (2 set bits , 2 is prime)

Input : 10 15
Output : 5
10 -> 1010(2 number of set bits)
11 -> 1011(3 number of set bits)
12 -> 1100(2 number of set bits)
13 -> 1101(3 number of set bits)
14 -> 1110(3 number of set bits)
15 -> 1111(4 number of set bits)
Hence total count is 5 ```

For each number in the range [L, R], we calculate the number of set bits. Using Sieve of Eratosthenes we generate a prime array up to the last number in the range (i.e. R). If the number of set bits is prime, we increase the count of the numbers and print it.

## C++

 `// C++ code to find count of numbers``// having prime number of set bits``// in their binary representation in``// the range [L, R]``#include``using` `namespace` `std;``#include ` `// Function to create an array of prime``// numbers upto number 'n'``vector<``int``> SieveOfEratosthenes(``int` `n)``{``    ``// Create a boolean array "prime[0..n]"``    ``// and initialize all entries it as false.``    ``// A value in prime[i] will finally be``    ``// true if i is Not a prime, else false.``    ``bool` `prime[n + 1];``    ``memset``(prime, ``false``, ``sizeof``(prime));``    ``for``(``int` `p = 2; p * p <= n; p++)``    ``{``        ``// If prime[p] is not changed,``        ``// then it is a prime``        ``if` `(prime[p] == ``false``)``            ` `            ``// Update all multiples of p``            ``for` `(``int` `i = p * 2; i < n + 1; i += p)``                ``prime[i] = ``true``;``    ``}``    ``vector<``int``> lis;``    ` `    ``// Append all the prime numbers to the list``    ``for` `(``int` `p = 2; p <=n; p++)``        ``if` `(prime[p] == ``false``)``            ``lis.push_back(p);``    ``return` `lis;``}` `// Utility function to count``// the number of set bits``int` `setBits(``int` `n){``    ``return` `__builtin_popcount (n);``}` `// Driver code``int` `main ()``{``    ``int` `x = 4, y = 8;``    ``int` `count = 0;` `    ``// Here prime numbers are checked till the maximum``    ``// number of bits possible because that the maximum``    ``// bit sum possible is the number of bits itself.``    ``vector<``int``> primeArr = SieveOfEratosthenes(``ceil``(log2(y)));``    ``for``(``int` `i = x; i < y + 1; i++)``    ``{``        ``int` `temp = setBits(i);``        ``for``(``int` `j=0;j< primeArr.size();j++)``        ``{``if` `(temp == primeArr[j])``            ``{count += 1;``            ``break``;``            ``}``        ``}``    ``}``    ``cout << count << endl;``    ``return` `0;``}` `// This code is contributed by mits`

## Java

 `// Java code to find count of numbers having``// prime number of set bits in their binary ``// representation in the range[L, R]``import` `java.util.*;``import` `java.lang.Math;` `class` `GFG``{` `// function to create an array of prime``// numbers upto number 'n'``static` `ArrayList SieveOfEratosthenes(``int` `n)``{``    ``// Create a boolean array "prime[0..n]" and initialize``    ``// all entries it as false. A value in prime[i] will``    ``// finally be true if i is Not a prime, else false.``    ``boolean``[] prime = ``new` `boolean``[n + ``1``];``    ``for``(``int` `p = ``2``; p * p <= n;p++)``    ``{``        ``// If prime[p] is not changed, then it is a prime``        ``if` `(prime[p] == ``false``)``            ` `            ``// Update all multiples of p``            ``for` `(``int` `i = p * ``2``; i < n + ``1``; i += p)``                ``prime[i] = ``true``;``    ``}``    ``ArrayList lis = ``new` `ArrayList();``    ` `    ``// append all the prime numbers to the list``    ``for` `(``int` `p = ``2``; p <=n; p++)``        ``if` `(prime[p] == ``false``)``            ``lis.add(p);``    ``return` `lis;``}` `// utility function to count the number of set bits``static` `int` `setBits(``int` `n)``{``    ``return` `Integer.bitCount(n);``}``public` `static` `int` `log2(``int` `x)``{``    ``return` `(``int``) (Math.log(x) / Math.log(``2``) + 1e-``10``);``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `x = ``4``, y = ``8``;``    ``int` `count = ``0``;``    ``ArrayList primeArr = ``new` `ArrayList();` `    ``// Here prime numbers are checked till the maximum``    ``// number of bits possible because that the maximum``    ``// bit sum possible is the number of bits itself.``    ``primeArr = SieveOfEratosthenes((``int``)Math.ceil(log2(y)));``    ``for``(``int` `i = x; i < y + ``1``; i++)``    ``{``        ``int` `temp = setBits(i);``        ``if``(primeArr.contains(temp))``            ``count += ``1``;``    ``}``    ``System.out.println(count);``}``}` `// This code is contributed by mits.`

## Python

 `# Python code to find  count of numbers having prime number``# of set bits in their binary representation in the range``# [L, R]` `# Function to create an array of prime``# numbers upto number 'n'``import` `math as m` `def` `SieveOfEratosthenes(n):` `    ``# Create a boolean array "prime[0..n]" 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``(n``+``1``)]``    ``p ``=` `2``    ``while``(p ``*` `p <``=` `n):` `        ``# If prime[p] is not changed, then it is a prime``        ``if` `(prime[p] ``=``=` `True``):``            ` `            ``# Update all multiples of p``            ``for` `i ``in` `range``(p ``*` `2``, n``+``1``, p):``                ``prime[i] ``=` `False``        ``p ``+``=` `1``    ``lis ``=` `[]``    ` `    ``# Append all the prime numbers to the list``    ``for` `p ``in` `range``(``2``, n``+``1``):``        ``if` `prime[p]:``            ``lis.append(p)``    ``return` `lis` `# Utility function to count the number of set bits``def` `setBits(n):``    ``return` `bin``(n)[``2``:].count(``'1'``)` `# Driver program``if` `__name__ ``=``=` `"__main__"``:``    ``x, y ``=` `[``4``, ``8``]``    ``count ``=` `0` `    ``# Here prime numbers are checked till the maximum``    ``# number of bits possible because that the maximum``    ``# bit sum possible is the number of bits itself.``    ``primeArr ``=` `SieveOfEratosthenes(``int``(m.ceil(m.log(y,``2``))))``    ``for` `i ``in` `range``(x, y``+``1``):``        ``temp ``=` `setBits(i)``        ``if` `temp ``in` `primeArr:``            ``count ``+``=` `1``    ``print``(count)`

## C#

 `// C# code to find count of numbers having prime number``// of set bits in their binary representation in the range``// [L, R]``using` `System;``using` `System.Linq;``using` `System.Collections;``class` `GFG{` `// Function to create an array of prime``// numbers upto number 'n'``static`     `ArrayList SieveOfEratosthenes(``int` `n)``{``    ``// Create a boolean array "prime[0..n]" and initialize``    ``// all entries it as false. A value in prime[i] will``    ``// finally be true if i is Not a prime, else false.``    ``bool``[] prime = ``new` `bool``[n+1];``    ``for``(``int` `p=2;p * p <= n;p++)``    ``{``        ``// If prime[p] is not changed, then it is a prime``        ``if` `(prime[p] == ``false``)``            ` `            ``// Update all multiples of p``            ``for` `(``int` `i=p * 2;i c == ``'1'``);``}` `// Driver program``public` `static` `void` `Main () {` `    ``int` `x=4, y=8;``    ``int` `count = 0;``    ``ArrayList primeArr=``new` `ArrayList();` `    ``// Here prime numbers are checked till the maximum``    ``// number of bits possible because that the maximum``    ``// bit sum possible is the number of bits itself.``    ``primeArr = SieveOfEratosthenes(Convert.ToInt32(Math.Ceiling(Math.Log(y,2.0))));``    ``for``(``int` `i=x;i

## PHP

 `>=1;};``    ``return` `\$cnt``;``}` `    ``// Driver program``    ``\$x` `= 4;``    ``\$y` `= 8;``    ``\$count` `= 0;` `    ``// Here prime numbers are checked till the maximum``    ``// number of bits possible because that the maximum``    ``// bit sum possible is the number of bits itself.``    ``\$primeArr` `= SieveOfEratosthenes(``ceil``(log(``\$y``,2)));``    ``for` `(``\$i``=``\$x``;``\$i``<``\$y``+1;``\$i``++)``    ``{``        ``\$temp` `= setBits(``\$i``);``        ``if``(in_array(``\$temp``, ``\$primeArr``))``            ``\$count` `+= 1;``    ``}``    ``print``(``\$count``);` `// This code is contributed by mits``?>`

## Javascript

 ``

Output:

`3`

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