2000 was a number.
In one state of reality, the Doctor was one of only two members of the High Council of Time Lords, the other being the Magistrate, who were less than 2000 years old. (PROSE: The Infinity Doctors [+]Lance Parkin, BBC Books (1998).)
As recalled by the Shadow Architect, the planet Pyrovillia disappeared over two thousand years prior to 2009. (TV: The Stolen Earth [+]Russell T Davies, Doctor Who series 4 (BBC One, 2008).)
According to the Ninth Doctor, there would be more than two thousand Daleks aboard a single Dalek flying saucer of the Last Great Time War. (TV: Bad Wolf [+]Russell T Davies, Doctor Who series 1 (BBC One, 2005).)
Shortly after his regeneration, the Twelfth Doctor claimed to have lived for over 2000 years. (TV: Deep Breath [+]Steven Moffat, Doctor Who series 8 (BBC One, 2014).) He possessed a Two Thousand Year Diary which he used to identify the Mire. (TV: The Girl Who Died [+]Jamie Mathieson and Steven Moffat, Doctor Who series 9 (BBC One, 2015).) Before his first adventure together with Bill Potts, the Doctor told Nardole that he was over 2000 years old. (TV: Smile [+]Frank Cottrell-Boyce, Doctor Who series 10 (BBC One, 2017).) A few hours after this, he echoed the same thing to Bill herself. (TV: Thin Ice [+]Sarah Dollard, Doctor Who series 10 (BBC One, 2017).) On meeting the Monks in a simulation, the Doctor gave his age as "two thousand years at the last count". (TV: Extremis [+]Steven Moffat, Doctor Who series 10 (BBC One, 2017).)