






from math import isqrt

def   snake_case (UpperCAmelCase__  )	->    bool:
  return all(number % divisor != 0 for divisor in range(2     ,   isqrt(UpperCAmelCase__  ) + 1  )  )

def   snake_case (UpperCAmelCase__ = 1_0**6  )	->    int:
  UpperCamelCase_: str   				=    0
  UpperCamelCase_: Union[str, Any]   				=    1
  UpperCamelCase_: Dict   				=    7
  while prime_candidate < max_prime:
    primes_count += is_prime(UpperCAmelCase__  )

    cube_index += 1
    prime_candidate += 6 * cube_index

  return primes_count


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







def   snake_case (UpperCAmelCase__  )	->    int:
  assert isinstance(UpperCAmelCase__     ,   UpperCAmelCase__  ), F'''The input value of [n={number}] is not an integer'''

  if number == 1:
    return 2
  elif number < 1:
    UpperCamelCase_: List[Any]   				=    F'''The input value of [n={number}] has to be > 0'''
    raise ValueError(UpperCAmelCase__  )
  else:
    UpperCamelCase_: str   				=    sylvester(number - 1  )
    UpperCamelCase_: str   				=    num - 1
    UpperCamelCase_: Any   				=    num
    return lower * upper + 1


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