


'''simple docstring'''




import math
import unittest





def   _a		(lowercase__			:   int						)			->			bool:






     """simple docstring"""
     assert isinstance(lowercase__							,   lowercase__						) and (
         number >= 0
     ), "'number' must been an int and positive"

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5							,   int(math.sqrt(lowercase__						) + 1						)							,   6						):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True




class 			_lowercase (	unittest.TestCase							):
   def a  (						self       :      Optional[Any]      ) ->							Any:
        self.assertTrue(is_prime(2      )      )
        self.assertTrue(is_prime(3      )      )
        self.assertTrue(is_prime(5      )      )
        self.assertTrue(is_prime(7      )      )
        self.assertTrue(is_prime(11      )      )
        self.assertTrue(is_prime(13      )      )
        self.assertTrue(is_prime(17      )      )
        self.assertTrue(is_prime(19      )      )
        self.assertTrue(is_prime(23      )      )
        self.assertTrue(is_prime(29      )      )





   def a  (						self       :      Tuple      ) ->							Dict:
        with self.assertRaises(SCREAMING_SNAKE_CASE_      ):
             is_prime(-19      )
        self.assertFalse(
            is_prime(0      )       ,   'Zero doesn\'t have any positive factors, primes must have exactly two.'       ,   )
        self.assertFalse(
            is_prime(1      )       ,   'One only has 1 positive factor, primes must have exactly two.'       ,   )
        self.assertFalse(is_prime(2 * 2      )      )
        self.assertFalse(is_prime(2 * 3      )      )
        self.assertFalse(is_prime(3 * 3      )      )
        self.assertFalse(is_prime(3 * 5      )      )
        self.assertFalse(is_prime(3 * 5 * 7      )      )


if __name__ == "__main__":
       unittest.main()









import itertools
import math

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     bool:

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5	,   int(math.sqrt(_snake_case				) + 1				)	,   6				):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True

def 	SCREAMING_SNAKE_CASE_							(	)  ->     Dict:
   _A      =       2
   while True:
      if is_prime(_snake_case				):
         yield num
      num += 1

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int = 10_001				)  ->     int:
   return next(itertools.islice(prime_generator()	,   nth - 1	,   _snake_case				)				)


if __name__ == "__main__":
   print(f'{solution() = }')



