input: def sieve_of_eratosthenes(start: int, end: int) -> List[int]:
      """Generate a list of prime numbers between the given start and end numbers using the Sieve of Eratosthenes algorithm.
      >>> sieve_of_eratosthenes(1, 20)
      [2, 3, 5, 7, 11, 13, 17, 19]
      """
      prime = [True] * (end + 1)
      p = 2
      while p * p <= end:
          if prime[p]:
              for i in range(p * p, end + 1, p):
                  prime[i] = False
          p += 1
      prime_numbers = []
  
      for p in range(start, end):
          if prime[p]:
              prime_numbers.append(p)
  
      return prime_numbers
output:     if start <= 1:
          start = 2
      return [p for p in range(start, end + 1) if prime[p]]