Because of this comic, I actually did some calculations.

Assuming people have the same death rate as 25-34 year olds did in 2010, which is to say, a death rate of 104.9 per 100,000, we would expect .1% of the population to die per year (.1049% to be precise). At this death rate, the 50th percentile of people (that is to say, half the population) who made it to age 25 would die in 634 years, meaning that 50% of the population would die before the age of 659.

The overall average life expectancy at 25 years would be +914 years, for an average life expectancy at 25 of 939 years. Note that only about a third of the population (36.8%) makes it that long.

Assuming a global population of 10^10 people, out of any given cohort of 10^10 people, we would expect one, on average, to make it to the age of +21,036 from 25, so assuming we had 10 billion people make it to that age, there would be a reasonable chance of one of them making it to a total age of 21,061.

One oddity of all this, I'll note, is that your expected life expectancy would never change; that is to say, regardless of your age, you can expect a 50% chance of living another 634 years, and on average will survive another 939 years. There is nothing preventing anyone from living indefinitely, but it is increasingly unlikely.

The odds of outliving human history thus far, however (5,100 years) is non-negligible; out of a population of only a thousand people, you'd expect 3 or 4 to make it that long.