input: Write a function to generate a list of all prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. The function 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 + 1):
          if prime[p] and p > 1:
              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, 5)==[2, 3, 5]
  assert sieve_of_eratosthenes(1, 1)==[]
  assert sieve_of_eratosthenes(8, 10)==[]
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(start, end + 1):
          if prime[p] and p > 1:
              prime_numbers.append(p)
      return prime_numbers