I said I would change the content I upload on this, but it’s been a while since I uploaded a bit of googology.
(It’s been a while since I uploaded anything, come to think of it.)
The number that the entire branch of googology originated from: googol. The number defined as 10^100, the number that can be written as “1 followed by 100 zeroes”, the beginning of googology.
Other insanely large numbers arise out of this number. For example, then commonly known googolplex is 10^googol, or 1 followed by googol zeroes. Another is googolplexian, 10^googolplex. But what if… what if we dug deeper?
Gooprol, the first prime after googol, is 10^100+267. This highlights the insane prime gap in the high (and I mean HIGH) levels, and shows how advanced technology has become (I think this is done with technology).
In fact, googol comes from a prefix (googo-), and some examples of numbers using this prefix are googoc (200^100, which is 20^100 times larger than googol), gogocci (402^201) and googol (10^100). See the pattern? Numbers with the googo- prefix take the form of (2n)^n. In googoc, n = 100, and in googol, n = 50. Why? Because 10^100 = (10^2)^50 = 100^50.
People have come up with many… interesting names for this one number. Guppyding was coined by Sbiis Saibian, unoohol/100-noogol/booioplex by Aarex Tiaokhiao, and many others (how do you come up with “unoohol”? That’s such a unique name, but it sounds so weird).
Ever wondered what a greater version of googol would be? Me neither, but “Great googol”, defined by Andrew Joyce, is 10^1000. And the opposite, “Little googol”, 2^100, is the smaller of the two prime power factors of googol. Funnily enough, the other prime power factor, 5^100, is “Little bigger little googol”, which is… descriptive. Little bigger little googol, unlike its name, is not a little bigger than little googol. Rather, it is more than 6*10^9 times the square of Little googol. Not very little.
An incredibly small number relating to googol is googolminex, which is the reciprocal of googol. There is, most likely, nothing on Earth that requires googolminex to represent it, whether it be velocity, time, or distance. Even smaller, googolplexminex is the reciprocal of googolplexian (1 followed by googolplex zeroes). At this point, why even bother creating these?
The last number I will cover is fzgoogolplex (how do you pronounce this?). Fzgoogolplex is googolplex to the power of googolplex, which is… big. This might look like it is similar in size to googolplexian, but in fact, fzgoogolplex is equal to googolplexian to the power of googol (googolplexian is 10^googolplex, while fzgoogolplex is googolplex^googolplex). Very big.
In short, googol is very big.