input: Write a function to print out the first n prime numbers using the sieve of Eratosthenes algorithm. If the input n is 0, the function should return an empty list. Otherwise, it should return a list of prime numbers up to the nth prime number.
  
  
  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(15)==[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
  
output: def sieve_of_eratosthenes(n):
      if n == 0:
          return []
      limit = 50  # Initial guess for the limit
      primes = []
      while len(primes) < n:
          limit *= 2
          sieve = [True] * limit
          sieve[0] = sieve[1] = False
          for start in range(2, limit):
              if sieve[start]:
                  primes.append(start)
                  for multiple in range(start*start, limit, start):
                      sieve[multiple] = False
                  if len(primes) == n:
                      break
      return primes[:n]