


from ..utils import DummyObject, requires_backends







class       lowerCamelCase__   (       metaclass=a__):
     SCREAMING_SNAKE_CASE__      			=			['''torch''', '''torchsde''']





     def __init__(self		,     *UpperCAmelCase		,     **UpperCAmelCase       )     ->   Any:
      requires_backends(self		,     ['''torch''', '''torchsde''']       )





     @classmethod
     def      __A					(cls		,     *UpperCAmelCase		,     **UpperCAmelCase       )     ->   Union[str, Any]:
      requires_backends(cls		,     ['''torch''', '''torchsde''']       )





     @classmethod
     def      __A					(cls		,     *UpperCAmelCase		,     **UpperCAmelCase       )     ->   str:
      requires_backends(cls		,     ['''torch''', '''torchsde''']       )



"""simple docstring"""




import math
import unittest

def lowercase_  (   _snake_case						):
							assert isinstance(_snake_case   ,_snake_case						) 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(_snake_case						) + 1						)   ,6						):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True



class 	lowerCAmelCase_						(unittest.TestCase  ):


				"""simple docstring"""



				def 	__magic_name__    (self    )					->		Dict:



											"""simple docstring"""




											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 	__magic_name__    (self    )					->		List[Any]:



											"""simple docstring"""




											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()




