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)
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.