



from maths.prime_check import is_prime




def 	UpperCAmelCase   (						_lowerCamelCase    ):
			if not isinstance(_lowerCamelCase ,    _lowerCamelCase    ):
						A							:					Optional[Any]              =						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()




from math import sqrt




def 	UpperCAmelCase   (						_lowerCamelCase = 100_0000    ):
			A							:					int              =						0
			A							:					int              =						0
			A							:					int

			while num_cuboids <= limit:
						max_cuboid_size += 1
						for sum_shortest_sides in range(2 ,    2 * max_cuboid_size + 1    ):
									if sqrt(sum_shortest_sides**2 + max_cuboid_size**2    ).is_integer():
												num_cuboids += (
												    min(_lowerCamelCase ,    sum_shortest_sides // 2    )
												    - max(1 ,    sum_shortest_sides - max_cuboid_size    )
												    + 1
												)

			return max_cuboid_size


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