 # Prime Number of Set Bits in Binary Representation

Given two integers L and R, find the count of numbers in the range [L, R] (inclusive) having a prime number of set bits in their binary representation.

(Recall that the number of set bits an integer has is the number of 1s present when written in binary. For example, 21 written in binary is 10101 which has 3 set bits. Also, 1 is not a prime.)

Example 1:

``````Input: L = 6, R = 10
Output: 4
Explanation:
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)
``````

Example 2:

``````Input: L = 10, R = 15
Output: 5
Explanation:
10 -> 1010 (2 set bits, 2 is prime)
11 -> 1011 (3 set bits, 3 is prime)
12 -> 1100 (2 set bits, 2 is prime)
13 -> 1101 (3 set bits, 3 is prime)
14 -> 1110 (3 set bits, 3 is prime)
15 -> 1111 (4 set bits, 4 is not prime)
``````

### Solution

``````/**
* Determine whether or not a given number is a prime number
* @param {number} n
* @return {boolean}
* @time complexity: O(√n)
* @space complexity: O(1)
*/
var isPrime = function(n) {
if (n < 2) {
return false;
}

const sqrt = Math.sqrt(n);

for (let i = 2; i <= sqrt; i++) {
if (n % i === 0) {
return false;
}
}

return true;
}

/**
* Get number of 1's in binary representation
* @param {number} n
* @return {number}
* @time complexity: O(log n)
* @space complexity: O(1)
*/
var getBit = function(n) {
let count = 0;

while (n > 0) {
count += n % 2;
n = Math.floor(n / 2);
}

return count;

/*
// Alternative
let count = 0;

while (n > 0) {
n = n & (n - 1);
count++;
}

return count;
*/
}
/**
* @param {number} L
* @param {number} R
* @return {number}
* @time complexity: O(d log d), where d = R - L
* @space complexity: O(1)
*/
var countPrimeSetBits = function(L, R) {
let res = 0;

for (let i = L; i <= R; i++) {
if (isPrime(getBit(i))) {
res++;
}
}

return res;
};
``````

### Test Case

``````const assert = require('chai').assert;

describe('Prime Number of Set Bits in Binary Representation', () => {

it('should return 4 when given L = 6 and R = 10', () => {
assert.strictEqual(countPrimeSetBits(6, 10), 4);
});

it('should return 5 when given L = 10 and R = 15', () => {
assert.strictEqual(countPrimeSetBits(10, 15), 5);
});

});
``````
``````  Prime Number of Set Bits in Binary Representation
✓ should return 4 when given L = 6 and R = 10
✓ should return 5 when given L = 10 and R = 15

2 passing (11ms)
`````` Mike Mai   Brooklyn, New York
I am full-stack web developer, passionate about building world class web applications. Knowledge in designing, coding, testing, and debugging. I love to solve problems.