Fugagargoogolplex

A fugagargoogolplex is the result of repeatedly exponentiating gargoogolplex a gargoogolplex times. This is the largest number mentioned by Alistair Cockburn on his A fuga really big numbers blog, and is thus the largest official number of the fuga- series. Alistair also noted that his son, Kieran, might say out this number after being introduced to the fuga- prefix.
The name is formed by applying the fuga- suffix to gargoogolplex, where fuga- means "n to the power of n to the power of n and so on, n times" and gar- turns out to simply be the square of the number. He predicted that Kieran will top fugagoogolplex with fugagargoogolplex instead.
After disambiguating from megafuga-, the fugagargoogolplex is equal to gargoogolplexgargoogolplexgargoogolplex-1
It is therefore \(\text{gargoogolplex} \downarrow\downarrow \text{gargoogolplex}\) in down-arrow notation. 
In exponential notation, it is exactly \(10^{10^{10^{10^{x}+x}+x-10^{x}}}\) where \(x = 100 + \log 2\); it is closely approximated by the quadruply exponential expression \(10^{10^{10^{10^{100.301}}}}\).
== See also ==
*megafugagargoogolplex, the other possible intended value.
== Sources ==
Category:Numbers
Category:Numbers_discussed_by_Alistair_Cockburn
Category:Class 4
Category:Fuga-