text: import doctest
  import math
  
  
  def prime(n: int) -> set:
      """Computes all prime numbers below n.
  
      Computes the sieve of Eratosthenes
      >>> prime(20)
      {1, 2, 3, 5, 7, 11, 13, 17, 19}
      """
      p = set(range(1, n))
      for i in range(2, int(math.sqrt(n)) + 1):
          p = p - set(x * i for x in range(2, n // i + 1))
      return p
  
  
  if __name__ == "__main__":
      print(doctest.testmod())
  