





from __future__ import annotations





def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ )  ->				list[int]:







			'''simple docstring'''

			UpperCAmelCase   		=				[True] * limit
			UpperCAmelCase   		=				False
			UpperCAmelCase   		=				False
			UpperCAmelCase   		=				True

			for i in range(3			,			int(limit**0.5 + 1 )			,			2 ):
						UpperCAmelCase   		=				i * 2
						while index < limit:
									UpperCAmelCase   		=				False
									UpperCAmelCase   		=				index + i

			UpperCAmelCase   		=				[2]

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

			return primes





def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ = 100_0000 )  ->				int:







			'''simple docstring'''

			UpperCAmelCase   		=				prime_sieve(UpperCamelCase__ )
			UpperCAmelCase   		=				0
			UpperCAmelCase   		=				0

			for i in range(len(UpperCamelCase__ ) ):
						for j in range(i + length			,			len(UpperCamelCase__ ) ):
									UpperCAmelCase   		=				sum(primes[i:j] )
									if sol >= ceiling:
												break

									if sol in primes:
												UpperCAmelCase   		=				j - i
												UpperCAmelCase   		=				sol

			return largest


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










def 						__SCREAMING_SNAKE_CASE  (				UpperCamelCase__ )  ->				list[int]:







			'''simple docstring'''

			if length <= 0 or not isinstance(UpperCamelCase__			,			UpperCamelCase__ ):
						raise ValueError('''Length must be a positive integer.''' )
			return [n * (2 * n - 1) for n in range(UpperCamelCase__ )]


if __name__ == "__main__":
				print(hexagonal_numbers(length=5))
				print(hexagonal_numbers(length=10))



