


'''simple docstring'''



def 			_a			(		_lowercase      :			int = 50000000						):





     '''simple docstring'''






     __UpperCAmelCase			:				List[str]													=    set()
     __UpperCAmelCase			:				Tuple													=    int((limit - 24) ** (1 / 2)						)

     __UpperCAmelCase			:				Tuple													=    set(range(3    ,      prime_square_limit + 1    ,      2						)						)
     primes.add(2						)
     for p in range(3    ,      prime_square_limit + 1    ,      2						):
          if p not in primes:
               continue
          primes.difference_update(set(range(p * p    ,      prime_square_limit + 1    ,      _lowercase						)						)						)

     for primea in primes:
          __UpperCAmelCase			:				Any													=    primea * primea
          for primea in primes:
               __UpperCAmelCase			:				Any													=    primea * primea * primea
               if square + cube >= limit - 16:
                    break
               for primea in primes:
                    __UpperCAmelCase			:				Optional[Any]													=    primea * primea * primea * primea
                    __UpperCAmelCase			:				Union[str, Any]													=    square + cube + tetr
                    if total >= limit:
                         break
                    ret.add(_lowercase						)

     return len(_lowercase						)


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



'''simple docstring'''



from __future__ import annotations




def 			_a			(		_lowercase      :			int						):





     '''simple docstring'''






     __UpperCAmelCase			:				str													=    [True] * limit
     __UpperCAmelCase			:				Tuple													=    False
     __UpperCAmelCase			:				List[str]													=    False
     __UpperCAmelCase			:				List[Any]													=    True

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

     __UpperCAmelCase			:				Optional[Any]													=    [2]

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

     return primes




def 			_a			(		_lowercase      :			int = 1000000						):





     '''simple docstring'''






     __UpperCAmelCase			:				List[str]													=    prime_sieve(_lowercase						)
     __UpperCAmelCase			:				Optional[Any]													=    0
     __UpperCAmelCase			:				int													=    0

     for i in range(len(_lowercase						)						):
          for j in range(i + length    ,      len(_lowercase						)						):
               __UpperCAmelCase			:				Optional[Any]													=    sum(primes[i:j]						)
               if sol >= ceiling:
                    break

               if sol in primes:
                    __UpperCAmelCase			:				Any													=    j - i
                    __UpperCAmelCase			:				List[Any]													=    sol

     return largest


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