input: Write a function that generates a list of the prime numbers between two given numbers using the Sieve of Eratosthenes algorithm. The function should take two parameters: the start and end of the range. If either the start or end is less than 2, the function should return an empty list. If the start is greater than or equal to the end, the function should also return an empty list.
  
  assert sieve_of_eratosthenes(1, 20)==[2, 3, 5, 7, 11, 13, 17, 19]
  assert sieve_of_eratosthenes(5, 5)==[]
  assert sieve_of_eratosthenes(-1, 10)==[]
  assert sieve_of_eratosthenes(10, 1)==[]
  assert sieve_of_eratosthenes(100, 110)==[101, 103, 107, 109]
  assert sieve_of_eratosthenes(2, 2)==[]
  assert sieve_of_eratosthenes(2, 3)==[2, 3]
  assert sieve_of_eratosthenes(10, 10)==[]
output: def sieve_of_eratosthenes(start, end):
      if start < 2 or end < 2 or start >= end:
          return []
      sieve = [True] * (end + 1)
      sieve[0] = sieve[1] = False
      for i in range(2, int(end**0.5) + 1):
          if sieve[i]:
              for j in range(i*i, end + 1, i):
                  sieve[j] = False
      return [i for i in range(start, end + 1) if sieve[i]]