def eratosthenes_sieve_for(n):
    if n < 2:
        return []
    is_composite = [False] * (n + 1)
    primes = []
    for i in range(2, n + 1):
        if is_composite[i]:
            continue
        primes.append(i)
        # 内层循环j从i*i开始，步长为i
        for j in range(i * i, n + 1, i):
            is_composite[j] = True
    return primes