Inspired by this post by striderl, here are the explanations for my characters' serials.
Inspired by a Cheapshow (podcast) episode in which a character mangled some bingo calls, calling 22 as 'two little swans' instead of the traditional 'two little ducks'. Instantly I knew I had to use that for a character somehow: give them a serial ending in 22 and call them Cygnus (the genus of swans).
The 'Fifty' came later just because I liked the sound of 'Fifty-Twenty-Two'.
This one actually gets explained in-universe. As Phaeton is a human, they weren't automatically assigned a serial, so they had the opportunity to choose their own one. Phaeton chose 1842 because the atomic numbers of hydrogen, oxygen and molybdenum are 1, 8 and 42. The chemical abbreviations of those elements are H, O and Mo, which can be put together to spell Homo (the genus of humans).
In this way, Phaeton and Cygnus have 'matching' serials; Cygnus's name is an organic genus derived from their serial, whereas Phaeton's serial is digits derived from their organic genus.
Engineer 1668 (lead engineer on the TV Titan's maintenance crew)
It's the melting point (in degrees Celsius) of titanium. (Geddit, titan-ium?)
I wanted to use the Kelvin temperature because Kelvin seems more Science than Celsius, but 1668Β°C is 1941Β°K, and 1668 was just a more pleasing number.
Agent 1791 (TV Titan's identity pre-upgrade)
(Yes, the Titan's not actually my character, but [fart])
It's the year of discovery of the element titanium. (Although it was initially named maccanite, and didn't receive the name titanium until 1795.)
Primus (1153) and Icarus (1566) (TV Matriarch's bodyguards)
(Also not actually my characters. But also it appears to be fanon that these two are the Matriarch's bodyguards at all! We've never seen them since their first appearance.)
I devised their nicknames and serials concurrently; I wanted to give them serials that Phaeton could turn into nicknames.
I decided I wanted one of them to be called Primus, so I looked up 4-digit primes looking for one that was both 'pleasing' and was splittable into a pair of 2-digit primes.
For Icarus I looked up asteroid names and numbers until I found one that was both a reasonable character name and had a pleasing number.
The number was just one I found pleasing. The hard part was later coming up with a nickname, after I decided I'd got attached to this character enough to name them.
I initially wanted to carry over Cygnus's theme of 'bird name that's also a constellation'. Unfortunately the birb constellations don't have terribly pleasing names. Besides Cygnus, there's Apus (bird of paradise), Aquila (eagle), Columba (pigeon), Corvus (crow), Grus (crane), Pavo (peafowl), Phoenix (not a real birb), and Tucana (toucan).
Corvus is admittedly kinda cool-sounding, but was a bit too close to Cygnus for my liking. I initially wanted to go with Grus, because I noticed that so far all my named TVs had names ending in -us (Cygnus, Primus, Icarus) and I wanted to continue that theme, but I just couldn't make myself like it as a name, plus it just didn't feel like something Phaeton would pick for them.
In the end I threw out the bird link and kept just the constellation link. Phaeton chooses Fornax as a name just because of that and because 'four' and 'for' sound similar.
(Fornax means 'furnace', and Phaeton means 'one who shines'. So the trio are basically called Shiny, Swan and Oven.)
I literally used random.org to generate numbers, and picked the first 15 that fulfilled my criterion of 'last digit can't be 0' (see link below for why not).
I wanted to give myself a little challenge of coming up with nicknames for existing numbers that I didn't pick, instead of picking numbers that would fit a specific name.
I ended up with two characters with serials ending in 07, so they'll get nicknames to tell them apart. 5007 and 9807 both work on the Titan's propulsion systems and are collectively referred to as 'the Sevens'; 5007 is nicknamed 'Stannum' (Latin for tin, which has atomic number 50) and 9807 is nicknamed 'Ianthe' (for the asteroid 98-Ianthe).
Engineer 9779 is nicknamed Palindrome for obvious reasons.
Unfortunately, one of the numbers random.org gave me was 6918. I considered not using that one, because people will likely assume I added the 69 to be funny, then I thought 'nah, just add it, things like this would be inevitable with procgenned serials'.
There are two engineers with nearly identical serials (because that happens with true randomness): 7672 and 7678. They'll probably get nicknames at some point.
That's the Doylist explanation. The Watsonian explanation of how TV serials are generated is in this post I made earlier this year.
