input: Write a function to generate a list of prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. The function should return a list of prime numbers found between the start and end values.
  
  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 = [p for p in range(start, end) if prime[p]]
      return prime_numbers
  
  assert sieve_of_eratosthenes(1, 20) == [2, 3, 5, 7, 11, 13, 17, 19]
  assert sieve_of_eratosthenes(5, 30) == [5, 7, 11, 13, 17, 19, 23, 29]
  assert sieve_of_eratosthenes(10, 15) == [11, 13]
  assert sieve_of_eratosthenes(1, 2) == [2]
  assert sieve_of_eratosthenes(1, 1) == []
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 = [p for p in range(max(2, start), end + 1) if prime[p]]
      return prime_numbers