



"""simple docstring"""






from __future__ import annotations

__snake_case							:     Optional[int]   =					[True] * 1_000_001
__snake_case							:     int   =					2
while i * i <= 1_000_000:
 if seive[i]:
  for j in range(i * i, 1_000_001, i):
   __snake_case							:     List[str]   =					False
 i += 1


def     _lowercase       (						__snake_case			)		->     bool:
   return seive[n]


def     _lowercase       (						__snake_case			)		->     bool:
   return any(digit in "02468" for digit in str(__snake_case			)			)


def     _lowercase       (						__snake_case = 1_000_000			)		->     list[int]:
   __lowerCAmelCase   :						Tuple				= [2]  # result already includes the number 2.
   for num in range(3      ,limit + 1      ,2			):
      if is_prime(__snake_case			) and not contains_an_even_digit(__snake_case			):
         __lowerCAmelCase   :						Union[str, Any]				= str(__snake_case			)
         __lowerCAmelCase   :						Any				= [int(str_num[j:] + str_num[:j]			) for j in range(len(__snake_case			)			)]
         if all(is_prime(__snake_case			) for i in list_nums			):
            result.append(__snake_case			)
   return result


def     _lowercase       (						)		->     int:
   return len(find_circular_primes()			)


if __name__ == "__main__":
 print(F"""{len(find_circular_primes()) = }""")




"""simple docstring"""






from ..utils import DummyObject, requires_backends



class     A__     (						metaclass=__SCREAMING_SNAKE_CASE							):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE					   =			['torch', 'scipy']

	def __init__(  self:	Tuple ,    *_SCREAMING_SNAKE_CASE:	Dict ,    **_SCREAMING_SNAKE_CASE:	str)       -> Union[str, Any]:

				"""simple docstring"""

				requires_backends(self ,    ["torch", "scipy"])

	@classmethod
	def 							_SCREAMING_SNAKE_CASE     (  cls:	Optional[Any] ,    *_SCREAMING_SNAKE_CASE:	Tuple ,    **_SCREAMING_SNAKE_CASE:	Optional[Any])       -> Optional[Any]:

				"""simple docstring"""

				requires_backends(cls ,    ["torch", "scipy"])







	@classmethod
	def 							_SCREAMING_SNAKE_CASE     (  cls:	int ,    *_SCREAMING_SNAKE_CASE:	List[Any] ,    **_SCREAMING_SNAKE_CASE:	Dict)       -> Union[str, Any]:

				"""simple docstring"""

				requires_backends(cls ,    ["torch", "scipy"])