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448. Numbers with prime set bits in a given range using Sieve of Eratosthenes Algorithm
Objective: Given a range, find all the numbers in the range which has prime set bits using Sieve of Eratosthenes Algorithm.
Earlier we had seen a similar problem Numbers with prime set bits in a given range solved in the naive approach. in this algorithm, we will improve the time complexity using the Sieve of Eratosthenes.
Example:
L = 4, R = 10 Output: 5 Explanation: 4 = 1 0 0 ( not prime) 5 = 1 0 1 (prime) 6 = 1 1 0 (prime) 7 = 1 1 1 (prime) 8 = 1 0 0 0 ( not prime) 9 = 1 0 0 1 (prime) 10 = 1 1 0 0 (prime) Total 5 numbers which has prime set bits.
Approach:
Please read the Sieve of Eratosthenes Algorithm before continue reading.
 Let's say the given range is L and R.
 Find all the prime numbers from 1 to R (higher limit) using Sieve of Eratosthenes Algorithm and store it in the list.
 Now iterate through L to R and for each integer, count the number of set bits and check if that count is present in the list created in step 2. print it.
Output:
Numbers found for which set bits count is prime: 5 6 7 9 10
Reference: https://www.geeksforgeeks.org/primenumberofsetbitsinbinaryrepresentationset2/