




from __future__ import annotations

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





def __UpperCamelCase			(       _A  ):
						return seive[n]





def __UpperCamelCase			(       _A  ):
						return any(digit in '''02468''' for digit in str(_A  )  )





def __UpperCamelCase			(       _A = 1000000  ):
						lowerCAmelCase_      			=  [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  ):
																		lowerCAmelCase_      			=  str(_A  )
																		lowerCAmelCase_      			=  [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 __UpperCamelCase			(       ):
						return len(find_circular_primes()  )


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










from functools import lru_cache





@lru_cache
def __UpperCamelCase			(       _A  ):
						if num < 0:
												raise ValueError('''Number should not be negative.'''  )

						return 1 if num in (0, 1) else num * factorial(num - 1  )


if __name__ == "__main__":
						import doctest

						doctest.testmod()




