input: def sieve_eratosthenes(n: int) -> List[int]:
      """
      Find all prime numbers up to a given number `n` using the Sieve of Eratosthenes algorithm.
      
      >>> sieve_eratosthenes(10)
      [2, 3, 5, 7]
      >>> sieve_eratosthenes(20)
      [2, 3, 5, 7, 11, 13, 17, 19]
      """
      prime_list = [True] * (n + 1)
      prime_list[0] = prime_list[1] = False
      primes = []
  
      for i in range(2, n + 1):
          if prime_list[i]:
              primes.append(i)
              for j in range(i * i, n + 1, i):
                  prime_list[j] = False
      
      return primes
output:     prime_list = [True] * (n + 1)
      prime_list[0] = prime_list[1] = False
      primes = []
  
      for i in range(2, n + 1):
          if prime_list[i]:
              primes.append(i)
              for j in range(i * i, n + 1, i):
                  prime_list[j] = False
      
      return primes