


from __future__ import annotations




def     UpperCamelCase    (      _a		)					->							list[int]:
     '''simple docstring'''





     lowercase_       :Tuple     =       [True] * limit
     lowercase_       :Dict     =       False
     lowercase_       :Dict     =       False
     lowercase_       :Optional[Any]     =       True

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

     lowercase_       :List[str]     =       [2]

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

     return primes




def     UpperCamelCase    (      _a = 1_0_0_0_0_0_0		)					->							int:
     '''simple docstring'''





     lowercase_       :Union[str, Any]     =       prime_sieve(_a		)
     lowercase_       :Optional[int]     =       0
     lowercase_       :Optional[int]     =       0

     for i in range(len(_a		)		):
          for j in range(i + length       ,		len(_a		)		):
               lowercase_       :List[Any]     =       sum(primes[i:j]		)
               if sol >= ceiling:
                    break

               if sol in primes:
                    lowercase_       :List[str]     =       j - i
                    lowercase_       :Optional[int]     =       sol

     return largest


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





def     UpperCamelCase    (      _a		)					->							int:
     '''simple docstring'''





     assert isinstance(_a       ,		_a		), f"The input value of [n={number}] is not an integer"

     if number == 1:
          return 2
     elif number < 1:
          lowercase_       :str     =       f"The input value of [n={number}] has to be > 0"
          raise ValueError(_a		)
     else:
          lowercase_       :List[str]     =       sylvester(number - 1		)
          lowercase_       :Union[str, Any]     =       num - 1
          lowercase_       :List[str]     =       num
          return lower * upper + 1


if __name__ == "__main__":
   print(f"The 8th number in Sylvester's sequence: {sylvester(8)}")

