9 days I think, and even then it only dies of thirst!
I can't recall the exact figures in question, and I'm no good at maths so I'll probably explain this quite badly

but there is a doomsday prediction based on the population of the planet. If 100-110 billion people have ever lived, and we assume that we exist at the halfway point of the human population, then no more than about 220 billion people will ever exist. Given current population growth, this would put the end of humanity at some point in the next few thousand years!