## FANDOM

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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 — $$^52$$ has 19,729 decimal digits, and $$^62$$ has well over a googol decimal digits.

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.[1]

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.[2]

## In googological notations Edit

There are many notations where 65,536 can be expressed:

Notation Expression
Scientific notation $$6.5536 \times 10^{4}$$
Up-arrow notation $$2 \uparrow 16$$, $$2 \uparrow\uparrow 4$$, $$2 \uparrow\uparrow\uparrow 3$$
BEAF $$\lbrace 2,16 \rbrace$$, $$\lbrace 2,4,2 \rbrace$$, $$\lbrace 2,3,3 \rbrace$$
Chained arrow notation $$2 \rightarrow 16$$, $$2 \rightarrow 4 \rightarrow 2$$, $$2 \rightarrow 3 \rightarrow 3$$
Hyper-E notation $$E(2)1\#4$$
Hyperfactorial array notation $$8!$$
Strong array notation $$s(2,16), s(2,4,2), s(2,3,3)$$
Fast-growing hierarchy $$f_2(12)$$
Hardy hierarchy $$H_{\omega^2} (12)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^{\omega}}}} (2)$$ (exact)

## Sources Edit

1. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2016-07-17.
2. Part 1 - My Large Numbers

Large numbers in computers

-minutia group
n-ary numbers with multipliers
Eyelash mite group: eyelash mite-speck · eyelash mite-crumb · eyelash mite-chunk · (binary/ternary/octal)eyelash mite · eyelash mite-bunch · eyelash mite-crowd · eyelash mite-swarm
Dust mite group: dust mite-speck · dust mite-crumb · dust mite-chunk · (binary/ternary/octal)dust mite · dust mite-bunch · dust mite-crowd · dust mite-swarm
Cheese mite group: cheese mite-speck · cheese mite-crumb · cheese mite-chunk · (binary/ternary/octal)cheese mite · cheese mite-bunch · cheese mite-crowd · cheese mite-swarm
Clover mite group: clover mite-speck · clover mite-crumb · clover mite-chunk · (binary/ternary/octal)clover mite · clover mite-bunch · clover mite-crowd · clover mite-swarm
Pipsqueak group: (binary/ternary/octal)pipsqueak
Little squeaker group: (binary/ternary/octal)little squeaker
Small fry group: (binary/ternary/octal)small fry
Guppy group: (binary/ternary/octal)guppyspeck · (binary/ternary/octal)guppycrumb · (binary/ternary/octal)guppychunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)guppy(bit/byte)
Minnow group: (binary/ternary/octal)minnowspeck · (binary/ternary/octal)minnowcrumb · (binary/ternary/octal)minnowchunk · (ternary)minnow(bit/byte)
Goby group: (binary/ternary/octal)gobyspeck · (binary/ternary/octal)gobycrumb · (binary/ternary/octal)gobychunk · (ternary)goby(bit/byte)
Jumbo shrimp group: (binary/ternary/octal)jumbo shrimp
Lightweight group: (binary/ternary/octal)lightweight
Ogol group: (binary/ternary/octal)ogolspeck · (binary/ternary/octal)ogolcrumb · (binary/ternary/octal)ogolchunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)ogol(bit/byte)
Tiny twerpuloid group: (binary/ternary/octal)tiny twerpuloid
Googol group: (binary/ternary/octal)googolspeck · (binary/ternary/octal)googolcrumb · (binary/ternary/octal)googolchunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)googol(bit/byte) · googolbunch · googolcrowd · googolswarm
Eceton group: ecetonspeck · ecetoncrumb · ecetonchunk · ecetonbunch · ecetoncrowd · ecetonswarm
Numbers with base-multipliers
Numbers with -plex