If the human race comes to an end relatively shortly, then we have been born at a fairly typical time in history of humanity. On the other hand, if humanity lasts for much longer and trillions of people eventually exist, then we have been born in the first surprisingly tiny fraction of all people. According to the Doomsday Argument, this means that the chance of a disaster which would obliterate humanity is much larger than usually thought. I will defend the position that the chance of existing at all is larger in a race which is long-lived, and this cancels the Doomsday Argument, so that the chance of a disaster is only what one would ordinarily estimate.