While I like the large gaps in the eleventh Doctor's life -- I like to believe that the Doctor, in every life, has lots of adventures we never see -- I won't say that the gaps in that life aren't problematic. Because they are. There's two hundred years between periods of adventures with Amy and Rory, and then there's the "Time of the Doctor" problem. That episode spans nine hundred years, the Doctor sees Clara for about an hour over that span of time, and she should realistically, by the end, be a complete stranger to the Doctor, yet he never behaves like, from his perspective, his time with Clara spanned anything more than a compressed few weeks. (One of my issues with Moffat era, in general, is that his stories raise questions about the characters and the universe that it never bothers to answer.) The only conclusion I can draw is that the eleventh Doctor essentially imprinted on Amy and Clara in ways not unlike a duckling imprints on its mother (which the eleventh Doctor basically says in "The Power of Three"), which explains, as thin as it is, why the Doctor returns to them after hundreds of years.
Given that "The Day of the Doctor" treats the ages the three Doctors state in a consistent and meaningful way, then seeing as the War Doctor regenerates when he's eight hundred and the tenth Doctor is 904, then the ninth Doctor has a century, give or take, before the events of "Rose." The ironic thing about that is that the ninth Doctor, who has the second-shortest on-screen tenure (leaving aside Jo Martin and the other cameo Doctors), has one of the longer lifespans.
True. Of the Doctors to have had been leads in the show (I include performed media on this, so the War Doctor and Eighth Doctor naturally count), he has the shortest run, and jury's still out for Jo Martin.
As the actual longest-lived Doctor, I think its a bit silly since at the end of the day the 13th has all the years of the previous incarnations, so she is, right? THAT SAID, I do enjoy thinking how long has each incarnation lived through.
For my money, the Second and Tenth Doctors have the shortest span. The Tenth for reasons mentioned, but the Second I don't think has been around for a really long time. Jamie mentions that the events of
The Invasion for him and the Doctor are just a few weeks after they last saw the Brigadier in
The Web of Fear. So unless they had a myriad we never saw/heard of between then and
The War Games, I doubt he has been around for a long while.
Interestingly, the Seventh has been implied to be one of the longest-lived ones, also, mainly due to his appearence being startkly different in the TV Movie. It is implied in the audios, but never explicit, that he's really old and weary by this time, and is indeed slowly preparing for the possibility of regenerating. An interesting viewpoint. Also, the Eighth seems to be a long-lived one, too, given how his interpretation of the incarnation has slowly but steadily become a little more dissilusioned and rougher around the edges. The Sixth Doctor also spent
centuries while trying to find a cure for Charley in one of the audios, which is certainly interesting.
Bottom line, the Twelfth Doctor is the longest lived.
