


'''simple docstring'''






from maths.prime_check import is_prime





def      UpperCAmelCase      (		lowerCamelCase_  :int ):







		'''simple docstring'''
		if not isinstance(lowerCamelCase_				,      lowerCamelCase_ ):
				snake_case_		:							Union[str, 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()



'''simple docstring'''






from __future__ import annotations





def      UpperCAmelCase      (		lowerCamelCase_  :int ):







		'''simple docstring'''
		snake_case_		:							List[str]			       =						[True] * limit
		snake_case_		:							Union[str, Any]			       =						False
		snake_case_		:							List[str]			       =						False
		snake_case_		:							Any			       =						True

		for i in range(3				,      int(limit**0.5 + 1 )				,      2 ):
				snake_case_		:							Tuple			       =						i * 2
				while index < limit:
						snake_case_		:							Any			       =						False
						snake_case_		:							Optional[Any]			       =						index + i

		snake_case_		:							List[str]			       =						[2]

		for i in range(3				,      lowerCamelCase_				,      2 ):
				if is_prime[i]:
						primes.append(lowerCamelCase_ )

		return primes





def      UpperCAmelCase      (		lowerCamelCase_  :int = 1_00_00_00 ):







		'''simple docstring'''
		snake_case_		:							Optional[int]			       =						prime_sieve(lowerCamelCase_ )
		snake_case_		:							Optional[Any]			       =						0
		snake_case_		:							Optional[int]			       =						0

		for i in range(len(lowerCamelCase_ ) ):
				for j in range(i + length				,      len(lowerCamelCase_ ) ):
						snake_case_		:							Optional[int]			       =						sum(primes[i:j] )
						if sol >= ceiling:
								break

						if sol in primes:
								snake_case_		:							Optional[Any]			       =						j - i
								snake_case_		:							Tuple			       =						sol

		return largest


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