


from __future__ import annotations

UpperCAmelCase_				:			Dict   =	[True] * 100_0001
UpperCAmelCase_				:			Any   =	2
while i * i <= 100_0000:
   if seive[i]:
      for j in range(i * i, 100_0001, i):
         UpperCAmelCase_				:			Tuple   =	False
   i += 1







def 	SCREAMING_SNAKE_CASE_						(      __A			:      int    )     ->		bool:

       """simple docstring"""

       return seive[n]







def 	SCREAMING_SNAKE_CASE_						(      __A			:      int    )     ->		bool:

       """simple docstring"""

       return any(digit in '02468' for digit in str(__A    )    )







def 	SCREAMING_SNAKE_CASE_						(      __A			:      int = 1_00_00_00    )     ->		list[int]:

       """simple docstring"""

       a_ :		Dict							=  [2]  # result already includes the number 2.
       for num in range(3  ,   limit + 1  ,   2    ):
              if is_prime(__A    ) and not contains_an_even_digit(__A    ):
                     a_ :		Dict							=  str(__A    )
                     a_ :		Any							=  [int(str_num[j:] + str_num[:j]    ) for j in range(len(__A    )    )]
                     if all(is_prime(__A    ) for i in list_nums    ):
                            result.append(__A    )
       return result







def 	SCREAMING_SNAKE_CASE_						(      )     ->		int:

       """simple docstring"""

       return len(find_circular_primes()    )


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






def 	SCREAMING_SNAKE_CASE_						(      __A			:      list    )     ->		bool:

       """simple docstring"""

       if not isinstance(__A  ,   __A    ):
              raise ValueError('Input series is not valid, valid series - [2, 4, 6]'    )
       if len(__A    ) == 0:
              raise ValueError('Input list must be a non empty list'    )
       if len(__A    ) == 1:
              return True
       a_ :		Tuple							=  series[1] - series[0]
       for index in range(len(__A    ) - 1    ):
              if series[index + 1] - series[index] != common_diff:
                     return False
       return True







def 	SCREAMING_SNAKE_CASE_						(      __A			:      list    )     ->		float:

       """simple docstring"""

       if not isinstance(__A  ,   __A    ):
              raise ValueError('Input series is not valid, valid series - [2, 4, 6]'    )
       if len(__A    ) == 0:
              raise ValueError('Input list must be a non empty list'    )
       a_ :		str							=  0
       for val in series:
              answer += val
       return answer / len(__A    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()


