



from __future__ import annotations

UpperCamelCase__ =						[True] * 1_00_00_01
UpperCamelCase__ =						2
while i * i <= 1_00_00_00:
			if seive[i]:
						for j in range(i * i, 1_00_00_01, i):
									UpperCamelCase__ =						False
			i += 1






def  UpperCAmelCase__    (    lowercase__   ) ->      bool:
						return seive[n]






def  UpperCAmelCase__    (    lowercase__   ) ->      bool:
						return any(digit in """02468""" for digit in str(lowercase__   )   )






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






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


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










def  UpperCAmelCase__    (    lowercase__ = 100   ) ->      int:
						__lowercase					=				n * (n + 1) * (2 * n + 1) / 6
						__lowercase					=				(n * (n + 1) / 2) ** 2
						return int(square_of_sum - sum_of_squares   )


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





