You're handed a single non-negative integer n. Your task: count how many primes live in the range below it — every prime p with p < n. Checking each candidate's primality independently repeats the same work over and over — the Sieve of Eratosthenes instead crosses off composites in bulk: once a number i is confirmed prime, every multiple of i starting at i² is guaranteed composite and can be marked in one pass, with no divisor checks needed for any of them individually.