Prime Computer

A Prime Computer, often known simply as a "Prime" and sometimes referred to as the "supreme computer", was a type of computer originating from the planet Earth in the constellation Sol, (TV: "Dr. Who and the Aliens") although they were also known to exist on the planet Gallifrey in the constellation of Kasterborous. (TV: Step Into the 80's!)

Abilities
Prime Computers were capable of obtaining advanced orbital coordinates at high rates, obtaining the coordinates of 900 planets in the constellation of Kasterborous in only a matter of seconds. The Fourth Doctor was able to use a Prime to keep "up to date".

The machine was also capable of measuring the length of items in metres down to the third decimal place while accounting for variables, measuring the Doctor's scarf at 7.013 metres, exclusive of loose threads. They could also understand seven computer languages - (TV: Step Into the 80's!) apparently "all industry standard languages" - (TV: "Dr. Who and the Aliens") and five protocols, the latter of which allowed it to " [ talk ] to other computers". (TV: Step Into the 80's!) According to the Doctor, a Prime's power could be increased by five times in 111 seconds. (TV: "Dr. Who meets his match") Indeed, the Liprogopolisians claimed that its power could be increased easily. (TV: "Dr. Who and the Aliens") It offered "automation", and allowed instant around-the-planet communication. The Doctor once reflected that, using it, he could "design ships, run power stations", as well as mentioning oil and gas before wondering where the energy industry would be without Prime. Seemingly, Prime Computers were also capable of giving advice on people's personal lives, giving such suggestions as "MARRY THE GIRL, DOCTOR." (TV: "Dr. Who meets his match")

According to the Liprogopolisians, it had a "fantastic range of software solutions". The computer was also capable of figuring out the location of other individuals such as the aforementioned Liprogopolosians, a feature apparently exclusive to Primes. (TV: "Dr. Who and the Aliens")

Installation in the Doctor's TARDIS
Romana II, who had seemingly developed romantic feelings for the Fourth Doctor, installed a Prime Computer in the TARDIS, something which the Doctor apparently loved, recalling seeing them on Gallifrey. He immediately switched it on, claiming to at last be "up to date". He then asked the machine the length of his scarf, to which it responded that it was 7.013 metres, exclusive of loose threads. The Doctor continued to reveal its various abilities, such as how it could communicate with other computers. The Doctor told the Prime "you're gonna be alright, kid", leading to the machine asking the Doctor not to patronise it, as it was a Prime Computer. (TV: Step Into the 80's!)

Saving the universe
While in the TARDIS, Romana reported to the Doctor that the universe was about to end, with them needing the orbital coordinates of 900 planets in the constellation of Kasterborous within 17 seconds in order to save it, with the remaining time ticking down to 1 second before the Doctor was able to resolve the situation with his Prime. (TV: Step Into the 80's!)

Impacting the Doctor and Romana II's personal life
The Doctor later discovered that he could increase his Prime's power by five times in 111 seconds, reflecting on the things which could be done with a Prime, and wondering where the energy industry would be without it. When Romana suggested that the Doctor "ask it how to handle a woman", it gave the suggestion "MARRY THE GIRL, DOCTOR.". The Doctor proceeded to propose to Romana, to which she accepted, complimenting the Prime's intelligence. (TV: "Dr. Who meets his match")

Searched for by the Liprogopilisians
The Doctor was later contacted by the Liprogopolisians, who knew that he knew the "supreme computer", demanding that he tell them its name. Although the Doctor initially refused, they revealed that they had seemingly kidnapped Romana, a live feed of her tied by rope to a chair being shown to the Doctor on a monitor. The aliens continued to reveal their knowledge of the computer's abilities, as the Doctor used his Prime to reveal that the aliens hailed from Liprogopolis, which he declared, only for them to reveal that no other computer could have achieved that, proving that he owned one. As Romana's safety was further threatened on the monitor, he revealed the machine's name, with the Liprogoplolisians revealing that they simply wanted to buy one. Romana was returned, with the Doctor telling her that the aliens were "just some overexcited Prime buyers". (TV: "Dr. Who and the Aliens")

Further history
To be added

Behind the scenes
The Prime Computers main appearances - Step Into the 80's! and On Through the 80's! - were created as advertisements for the real world Prime Computers, with the advertisements only being broadcast in Australia. They were apparently written by Tom Baker, the main actor who portrayed the Fourth Doctor. The later appearance by a Prime Computer in the Virgin New Adventures novel Christmas on a Rational Planet was presumably a reference to these advertisements.