**Problem Statement:**
Given the required input arguments, write an efficient algorithm to solve the **Count Primes** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge.
**Hint / Expected Approach:**
Sieve of Eratosthenes
**Edge Cases to Consider:**
- (1) n ≤ 2 (zero primes)
- (2) n = 3
- (3) Large n memory concern