input: Write a function to generate a list of prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. The function should accept two parameters: start and end. It should return a list of prime numbers within the specified range.
  def sieve_of_eratosthenes(start, end):
      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
  
  assert sieve_of_eratosthenes(1, 20) == [2, 3, 5, 7, 11, 13, 17, 19]
  assert sieve_of_eratosthenes(10, 30) == [11, 13, 17, 19, 23, 29]
  assert sieve_of_eratosthenes(1, 10) == [2, 3, 5, 7]
  assert sieve_of_eratosthenes(1, 1) == []
  assert sieve_of_eratosthenes(2, 3) == [2]
output: def sieve_of_eratosthenes(start, end):
      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(max(2, start), end + 1):
          if prime[p]:
              prime_numbers.append(p)
  
      return prime_numbers