65536

65,536 is a positive integer equal to \(2^{16} = 2^{2^{2^{2}}} = 2 \uparrow\uparrow 4 = 2 \uparrow\uparrow\uparrow 3\). It is the largest power tower of 2's that can be expressed in a compact digital form (as \(2 \uparrow\uparrow 5\) is an integer of 19,729 decimal digits). It is also the only nontrivial result of pentation expressible in compact digital form, and 1 of the 2 nontrivial results of pentation expressible in decimal (the other is \(3\uparrow^32\)) — \(^52\) has 19,729 decimal digits, and \(^62\) has well over a googol decimal digits.
It is one less than the largest known Fermat prime, 65537.
It is the largest known power of two which does not contain the digits 1, 2, 4, or 8.
It is found commonly in computer science, being the number of different values expressible in 16 bits (a short integer).
Its full name in English is "sixty-five thousand five hundred thirty-six."
Sbiis Saibian calls this number octal-clover mite.
Username5243 calls this number Binary-Dooquol or Binary-Tootol, and it's equal to 2[2]4 = 2[3]3 in Username5243's Array Notation.Part 1 - My Large Numbers
Licorneuhh also calls this number Tails-Bi-3-primol, and it's equal to Я***(2) using Primarial Functions.Primarial functions numbers | Licorneuhh's numbers site (retrieved at UTC 16:20 12/02/2021) 
Binary198 calls this number alphagol, and it's equal to {2,3,1} in BIP-array notation.
==In googological notations==
There are many notations where 65,536 can be expressed:
Notation 	Lower bound 	Upper bound
Scientific notation 	\(6.5536\times10^4\) 	\(6.5536\times10^4\)
Arrow notation 	\(2\uparrow\uparrow4\) 	\(2\uparrow\uparrow4\)
Steinhaus-Moser Notation 	6[3] 	7[3]
Copy notation 	5[5] 	6[5]
Taro's multivariable Ackermann function	A(3,13) 	A(3,14)
Pound-Star Notation 	#*(27)*3 	#*(28)*3
BEAF 	{2,4,2} 	{2,4,2}
Hyper-E notation 	E[2]1#4 	E[2]1#4
Bashicu matrix system 	(0)[256] 	(0)[256]
Hyperfactorial array notation 	8! 	4!1
Fast-growing hierarchy 	\(f_2(12)\) 	\(f_2(13)\)
Hardy hierarchy 	\(H_{\omega^2}(12)\) 	\(H_{\omega^2}(13)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega2}}(4)\)	\(g_{\omega^{\omega2}}(4)\)
Wiki User Plain'N'Simple showed that 65536 can be expressed in the language of FOST in at most 1219 symbols. After building on the work of several other users, including 12AbBa and P bot, this bound was reduced to 340 symbols. Therefore, Rayo(340) is at least 65537.
==Sources==
==See also==
*2,147,483,647
*7,625,597,484,987
Category:Numbers
Category:Class 1
Category:Computers
Category:Numbers with 4 to 6 digits
Category:Powers of 2
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Category:Toogol Regiment