input: def sieve_eratosthenes(n: int) -> List[int]:
      """
      Finds all prime numbers up to a given limit n using the Sieve of Eratosthenes algorithm.
  
      >>> sieve_eratosthenes(100)
      [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
      """
      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