input: Write a function to generate a list of prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. The function should take two parameters, `start` and `end`, and return a list of prime numbers between `start` and `end` (inclusive).
  
  def sieve_of_eratosthenes(start, end):
      primes = [True] * (end + 1)
      p = 2
      while p * p <= end:
          if primes[p]:
              for i in range(p * p, end + 1, p):
                  primes[i] = False
          p += 1
      prime_numbers = [p for p in range(start, end + 1) if primes[p] and p >= 2]
      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(2, 2) == [2]
  assert sieve_of_eratosthenes(0, 1) == []
  assert sieve_of_eratosthenes(0, 0) == []
output: def sieve_of_eratosthenes(start, end):
      primes = [True] * (end + 1)
      p = 2
      while p * p <= end:
          if primes[p]:
              for i in range(p * p, end + 1, p):
                  primes[i] = False
          p += 1
      prime_numbers = [p for p in range(start, end + 1) if primes[p] and p >= 2]
      return prime_numbers