Barrillion

Barrillion is equal to \(10^{3\times 10^{3\times 10^{3\times{10^{60}}}} + 3}\)Extended Tier 4 to 6 illions. The term was coined by Nirvana Supermind and is part of his unofficial extension of Bower's -illion system which ended at multillion. 
YouTube user BAT4423【Googology Bat】 calls this number housillion.-illion Numbers V2 Part.1 (Tier 1 ~ Tier 4) - YouTube (retrieved August 2 2022) 
== Etymology ==
This name is derived from the suffix -illion and the name The Barrel. It is the last number to have a verse-based name, due to the lack of other names, and it being the 20th number of Tier 4.
== Approximations ==
Notation 	Expression
Up-arrow notation 	\(10 \uparrow (3 \times (10 \uparrow (3 \times (10 \uparrow (3\times 10\uparrow 60))))+3)\) (exact)
Chained arrow notation 	\(10 \rightarrow (3 \times (10 \rightarrow (3 \times (10 \uparrow (3\times 10\rightarrow 60))))+3)\) (exact)
H* function 	H(H(H(H(19)-1)-1))
BEAF 	\(\{10,\{3\times \{10,3 \times \{10,3\times \{10,60\}\}\}+3\}\}\) (exact)
Munafo's ASCII-lexicographic ordering	p3_e060_3
Fast-growing hierarchy 	\(f_2^4(195)\)
== Sources ==
== See also ==
* Zillion Notation
* Extensible Illion System
Category:Numbers
Category:Class 5
Category:Illion
Category:Numbers and functions by CompactStar