input: Write a function to generate a list of prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. Implement the function with the given inputs. If both start and end input are the same, return an empty list.
  def sieve_of_eratosthenes(start, end):
      if start == end:
          return []
      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(2, 2) == []
  assert sieve_of_eratosthenes(50, 55) == []
  assert sieve_of_eratosthenes(1, 5) == [2, 3, 5]
output: def sieve_of_eratosthenes(start, end):
      if start == end:
          return []
      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