2000 was a number.
Shortly after his regeneration, the Twelfth Doctor claimed to have lived for over 2000 years. (TV: Deep Breath) He possessed a Two Thousand Year Diary which he used to identify the Mire. (TV: The Girl Who Died) Before his first adventure together with Bill Potts, the Doctor told Nardole that he was over 2000 years old. (TV: Smile) A few hours after this, he echoed the same thing to Bill herself. (TV: Thin Ice) On meeting the Monks in a simulation, the Doctor gave his age as "two thousand years at the last count". (TV: Extremis)