input: Write a function to generate a list of prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. If the start number is less than 2, the function should return an empty list. The function should return a list of prime numbers within the specified range.
  
  def sieve_of_eratosthenes(start, end):
      if start < 2:
          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(max(2, start), end + 1):
          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, 50) == [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
  assert sieve_of_eratosthenes(1, 1) == []
  assert sieve_of_eratosthenes(-5, 10) == [2, 3, 5, 7]
  assert sieve_of_eratosthenes(2, 2) == [2]
output: def sieve_of_eratosthenes(start, end):
      if start < 2:
          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(max(2, start), end + 1):
          if prime[p]:
              prime_numbers.append(p)
  
      return prime_numbers