Prime number

A prime number was a number with special properties. The first six prime numbers were 1, 3, 5, 7, 11 and 13, (AUDIO: The Haunting) while four other prime numbers (which were also happy numbers) were 313, 331, 367, and 379. (TV: 42)

The Tenth Doctor could quickly compute happy primes to get access to computer systems. He claimed that happy primes were studied in recreational mathematics. (TV: 42)

Mrs Multravers tested intelligence of humans, to select victims with suitable brains, by first asking them a question about prime numbers. Strax had no problem deducing that 13 would be the fifth number in her sequence, but he failed on the second question. Those who passed all three had their brains extracted. (AUDIO: The Haunting)

April MacLean mistook prames of the Renyalin, known from the planet Rhodia, for primes. (PROSE: The Stone House)

Behind the scenes
A prime number is a positive integer that has exactly two divisors: 1 and the number itself.

Though AUDIO: The Haunting establishes that 1 is itself a prime number in the DWU, this is a point of contention among mathematicians.

Generally, 1 is considered neither prime nor composite. It would certainly have been considered a prime, however, in the story's time period of the 1890s. In particular, the entry for Number published in 1890 in the 9th edition of Encyclopædia Britannica stated that every positive number was either prime or composite, and explicitly listed 1 as prime.