




'''simple docstring'''



from __future__ import annotations

UpperCAmelCase_							:	Union[str, Any]	     =		[True] * 1_0_0_0_0_0_1
UpperCAmelCase_							:	Optional[Any]	     =		2
while i * i <= 1_0_0_0_0_0_0:
     if seive[i]:
          for j in range(i * i, 1_0_0_0_0_0_1, i):
               UpperCAmelCase_							:	Any	     =		False
     i += 1







def       _UpperCamelCase			(_lowerCamelCase				:  int						)-> bool:




     '''simple docstring'''





     return seive[n]







def       _UpperCamelCase			(_lowerCamelCase				:  int						)-> bool:




     '''simple docstring'''





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







def       _UpperCamelCase			(_lowerCamelCase				:  int = 1_00_00_00						)-> list[int]:




     '''simple docstring'''





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







def       _UpperCamelCase			()-> int:




     '''simple docstring'''





     return len(find_circular_primes()						)


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












'''simple docstring'''



def       _UpperCamelCase			(_lowerCamelCase				:  int						)-> int:




     '''simple docstring'''





     if divisor % 5 == 0 or divisor % 2 == 0:
          return 0
     __snake_case            =	1
     __snake_case            =	1
     while repunit:
          __snake_case            =	(10 * repunit + 1) % divisor
          repunit_index += 1
     return repunit_index







def       _UpperCamelCase			(_lowerCamelCase				:  int = 1_00_00_00						)-> int:




     '''simple docstring'''





     __snake_case            =	limit - 1
     if divisor % 2 == 0:
          divisor += 1
     while least_divisible_repunit(_lowerCamelCase						) <= limit:
          divisor += 2
     return divisor


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






