input: Write a function to print out the first n prime numbers using the Sieve of Eratosthenes algorithm. If n is less than or equal to 0, return an empty list.
  def sieve_of_eratosthenes(n):
      if n <= 0:
          return []
      primes = [True] * (n+1)
      primes[0] = primes[1] = False
      for i in range(2, int(n**0.5)+1):
          if primes[i]:
              for j in range(i*i, n+1, i):
                  primes[j] = False
  
      prime_numbers = []
      for i in range(len(primes)):
          if primes[i]:
              prime_numbers.append(i)
              if len(prime_numbers) == n:
                  break
      return prime_numbers
  
  assert sieve_of_eratosthenes(0) == []
  assert sieve_of_eratosthenes(1) == [2]
  assert sieve_of_eratosthenes(5) == [2, 3, 5, 7, 11]
  assert sieve_of_eratosthenes(10) == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
  assert sieve_of_eratosthenes(-5) == []
output: def sieve_of_eratosthenes(n):
      if n <= 0:
          return []
      limit = n * 10  # Assume a reasonable limit to find at least n primes
      primes = [True] * limit
      primes[0] = primes[1] = False
      for i in range(2, int(limit**0.5)+1):
          if primes[i]:
              for j in range(i*i, limit, i):
                  primes[j] = False
  
      prime_numbers = []
      for i in range(limit):
          if primes[i]:
              prime_numbers.append(i)
              if len(prime_numbers) == n:
                  break
      return prime_numbers