11 was a prime number. (AUDIO: The Haunting)
The Doctor's universe had 11 dimensions in all, (PROSE: Parasite) including three "primary dimensions" of space, (TV: Flatline, AUDIO: The Invasion of E-Space, Paradise 5) and either two dimensions of time, (PROSE: The Quantum Archangel) or time and space as the fourth and fifth dimensions. (TV: "An Unearthly Child") The remaining planes formed the Six-Fold-Realm. (PROSE: The Quantum Archangel)
The newly-regenerated Eleventh Doctor decided that 11 was his new favourite number. He also told himself this was his eleventh face. (PROSE: The Day of the Doctor) He considered himself to be in his eleventh incarnation, (TV: The Lodger, The Name of the Doctor) despite technically having used up all twelve regenerations afforded to him. At the end of this incarnation, the Eleventh Doctor affirmed that he was "Number Eleven", despite the existence of "Captain Grumpy", his actual ninth incarnation and his previous self who he called "Number Ten" having used up two further regenerations in his cycle. (TV: The Time of the Doctor)
The Eleventh Doctor's room in the prison ship hotel, which contained his greater fear, was number 11. (TV: The God Complex) Aboard the Parliament of the Daleks, he told Rory Williams that, out of ten, the amount of trouble they were in was eleven. (TV: Asylum of the Daleks)
The Twelfth Doctor once told Bill that "eleven plus two" was an anagram of "twelve plus one", to which Bill responded that both of these were equal to 13. (COMIC: Harvest of the Daleks)
Epsilon Eridani was "about 11 light-years or so" from Earth. (COMIC: Is Anyone There?)
Behind the scenes[]
A cut scene from AUDIO: Return of the Cybermen would have referred to the Tenth Doctor as the Doctor's "eleventh bod[y]".