
def 						UpperCAmelCase			(	a_ = 1_0_0_0_0_0_0						)		->	int:







				"""simple docstring"""



				__A   			= [i - 1 for i in range(limit + 1						)]

				for i in range(2		,   limit + 1						):
								if phi[i] == i - 1:
												for j in range(2 * i		,   limit + 1		,   a_						):
																phi[j] -= phi[j] // i

				return sum(phi[2 : limit + 1]						)


if __name__ == "__main__":
					print(solution())








from maths.prime_check import is_prime
def 					snake_case_						(   lowerCAmelCase_				:  int					):
							if not isinstance(lowerCAmelCase_				,				lowerCAmelCase_					):
														__lowercase					:							Dict			=   F"Input value of [number={number}] must be an integer"
														raise TypeError(lowerCAmelCase_					)
							if is_prime(lowerCAmelCase_					) and is_prime(number + 2					):
														return number + 2
							else:
														return -1


if __name__ == "__main__":
	import doctest

	doctest.testmod()