





def        __lowercase       (				_SCREAMING_SNAKE_CASE     )			->       list[int]:


      '''simple docstring'''


      if num <= 0:
            raise ValueError("""Input must be a positive integer"""     )

      SCREAMING_SNAKE_CASE		=						[True] * (num + 1)

      SCREAMING_SNAKE_CASE		=						2
      while p * p <= num:
            if primes[p]:
                  for i in range(p * p			,						num + 1			,						_SCREAMING_SNAKE_CASE     ):
                        SCREAMING_SNAKE_CASE		=						False
            p += 1

      return [prime for prime in range(2			,						num + 1     ) if primes[prime]]


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      SCREAMING_SNAKE_CASE_						       =	int(input("""Enter a positive integer: """).strip())
      print(prime_sieve_eratosthenes(user_num))









def        __lowercase       (				_SCREAMING_SNAKE_CASE = 1			,						_SCREAMING_SNAKE_CASE = 10_00     )			->       int:


      '''simple docstring'''


      SCREAMING_SNAKE_CASE		=						1
      SCREAMING_SNAKE_CASE		=						0

      for divide_by_number in range(_SCREAMING_SNAKE_CASE			,						digit + 1     ):
            SCREAMING_SNAKE_CASE		=						[]
            SCREAMING_SNAKE_CASE		=						numerator
            for _ in range(1			,						digit + 1     ):
                  if now_divide in has_been_divided:
                        if longest_list_length < len(_SCREAMING_SNAKE_CASE     ):
                              SCREAMING_SNAKE_CASE		=						len(_SCREAMING_SNAKE_CASE     )
                              SCREAMING_SNAKE_CASE		=						divide_by_number
                  else:
                        has_been_divided.append(_SCREAMING_SNAKE_CASE     )
                        SCREAMING_SNAKE_CASE		=						now_divide * 10 % divide_by_number

      return the_digit


# Tests
if __name__ == "__main__":
      import doctest

      doctest.testmod()


