input: Write a function to print out the first n prime numbers using the Sieve of Eratosthenes algorithm. The function should accept an integer n as input and return a list of the first n prime numbers.
  
  def print_first_n_primes(n):
      if n <= 0:
          return []
      limit = n * 20  # A reasonable upper limit to find n primes
      primes = [True] * (limit+1)
      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+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 print_first_n_primes(0) == []
  assert print_first_n_primes(1) == [2]
  assert print_first_n_primes(5) == [2, 3, 5, 7, 11]
  assert print_first_n_primes(10) == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
output: def print_first_n_primes(n):
      if n <= 0:
          return []
      limit = n * 20  # A reasonable upper limit to find n primes
      primes = [True] * (limit+1)
      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+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