3 (number)

3 was a prime number. (AUDIO: The Haunting)

According to Jo Grant, three sevens were equal to 21. Also according to her, 12 divided by 4 was 3. (TV: The Claws of Axos)

Some planets had three suns, including one visited by the First Doctor, (TV: Galaxy 4) one visited by the Second Doctor, (PROSE: The Sour Note) the Planet of Light, (COMIC: World Without Night) Knosson, (PROSE: The Castaway) Telios, (PROSE: K9 and the Zeta Rescue) Justicia, (PROSE: The Monsters Inside) Murigen, (PROSE: Predating the Predators) San Helios (TV: Planet of the Dead) and Desolation. (TV: The Ghost Monument)

The Time Lords assembled the first three incarnations of the Doctor to resolve the First Omega Crisis. Upon finding that there were three Doctors, the Brigadier remarked that he "didn't know when [he] was well off." (TV: The Three Doctors)

When Rose Tyler was fifteen years old, she was suspended from Jericho Street Comprehensive for three days after she convinced the choir to go on strike. (PROSE: Meet Rose)

During the 21st century Dalek invasion, Sarah Jane Smith and Rose Tyler observed that the Meta-Crisis Tenth Doctor and the DoctorDonna, in addition to the Tenth Doctor, made three Doctors, with Jack Harkness commenting "I can't tell you what I'm thinking right now." (TV: Journey's End)

At the fall of Gallifrey, the Eleventh General was contacted by the War Doctor along with the Tenth and Eleventh Doctors, remarking that the sight of three Doctors was "all [his] worst nightmares at once." (TV: The Day of the Doctor)

Hyph3n explained to the Thirteenth Doctor that her name was spelt with a 3 "after the second H and before the final N." (TV: Orphan 55)

Cathy Salt was three months pregnant when she met "Margaret Blaine". (TV: Boom Town)

To his recollection, Elton Pope saw the Tenth Doctor on the night of his mother's death when he was "three or four" years old. (TV: Love & Monsters)

Zheng Yi Sao's first son was 3 in 1807. (TV: Legend of the Sea Devils) The countdown towards the Ninth Doctor's eviction on Big Brother counted from 6 to 0, going through 5, 4, 3, 2, and 1. (TV: Bad Wolf)

In an emergency transmission sent by the TARDIS, the Thirteenth Doctor listed five things that she did in any worrying situation. The third was being kind, and being kinder than they were the day before, even if they were 'super kind'. She also said that the recipients should look out for each other, including friends, neighbours, people they hardly know, and family, and claimed that talking and sharing would help. (WC: Message from the Doctor)

Three dimensions
The Doctor's universe had three spatial dimensions, (TV: Flatline, AUDIO: Paradise 5) or "primary dimensions". (AUDIO: The Invasion of E-Space)

There were a total of eleven dimensions in all, (PROSE: Parasite) including 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 Boneless came from a universe with only two dimensions. (TV: Flatline)

Behind the scenes
Though unremarked in PROSE: Daisy Chain, 3 is also the fourth number in the Fibonacci sequence.

References in invalid sources
According to the Doctor's Five Hundred Year Diary, some would argue that Big Finish's success 'was in no small part thanks to three friendly words appended to all trailers announcing its existence', those words being 'We Love Stories'. (NOTVALID: Tom Baker stars in John Lloyd's lost Doctor Who adventure, The Doomsday Contract)