


from __future__ import annotations




def    a__    (		snake_case__					:							Union[str, Any]     ):
  _UpperCAmelCase		:							Tuple							=     [True] * limit
  _UpperCAmelCase		:							Optional[Any]							=     False
  _UpperCAmelCase		:							Optional[Any]							=     False
  _UpperCAmelCase		:							Tuple							=     True

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

  _UpperCAmelCase		:							str							=     [2]

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

  return primes




def    a__    (		snake_case__					:							Optional[int] = 100_0000     ):
  _UpperCAmelCase		:							Optional[Any]							=     prime_sieve(snake_case__     )
  _UpperCAmelCase		:							int							=     0
  _UpperCAmelCase		:							Optional[int]							=     0

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

      if sol in primes:
        _UpperCAmelCase		:							int							=     j - i
        _UpperCAmelCase		:							int							=     sol

  return largest


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






def _lowerCamelCase  (		snake_case = 10  ):
							if not isinstance(snake_case     , snake_case  ) or n < 0:
														raise ValueError('Invalid input'  )
							_lowerCAmelCase							=							10**n
							_lowerCAmelCase							=							28_433 * (pow(2     , 7_830_457     , snake_case  )) + 1
							return str(number % modulus  )


if __name__ == "__main__":
				from doctest import testmod

				testmod()
				print(f"""{solution(1_0) = }""")






