# 65536 (number)

 ← 65535 65536 65537 →
Cardinal sixty-five thousand five hundred thirty-six
Ordinal 65536th
(sixty-five thousand five hundred and thirty-sixth)
Factorization 216
Divisors 17 total
Roman numeral LXVDXXXVI
Binary 100000000000000002
Ternary 100222200213
Quaternary 1000000004
Quinary 40441215
Senary 12232246
Octal 2000008
Duodecimal 31B1412
Vigesimal 83GG20
Base 36 1EKG36

65536 is the natural number following 65535 and preceding 65537.

65536 is a power of two: $2^{16}$ (2 to the 16th power).

65536 is the smallest number with exactly 17 divisors.[1]

## In mathematics

65536 is $2^{2^{2^{2}}}$, so in tetration notation 65536 is $^42$.

When expressed using Knuth's up-arrow notation, 65536 is $2 \uparrow 16$, which is equal to $2 \uparrow 2 \uparrow 2 \uparrow 2$, which is equivalent to $2 \uparrow\uparrow 4$ or $2 \uparrow\uparrow\uparrow 3$.

65536 is a superperfect number - a number such that σ(σ(n))=2n.[2]

A 16-bit number can distinguish 65536 different possibilities, such as the numbers 0..65535. In unsigned binary notation, 65536 is thus the smallest number that can not be represented by 16 bits.

65536 is the only power of 2 less than 231000 that does not contain the digits 1, 2, 4 or 8 in its decimal representation.[3]

65536 is the largest known number such that the sum of its unitary divisors is prime (1 + 65536 = 65537, which is prime).[4]

## In computing

65536 (216) is the number of different values representable in a number of 16 binary digits, also known as a short integer in many computer programming systems. Therefore,

• The Motorola 68000 family, x86 architecture, and other computing platforms have a word size of 16 bits, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern microprocessors.)
• 65536 is the maximum number of spreadsheet rows supported by Excel 97, Excel 2000, Excel 2002 and Excel 2003 (Excel 2007, 2010 and 2013 support 1,048,576 rows (220)). Text files that are larger than 65536 rows cannot be imported to these versions of Excel.[5]
• A 16-bit microprocessor chip can directly access 65536 memory addresses, and the 16-bit highcolor graphics standard supports a color palette of 65536 different colors.
• TCP supports 65536 distinct ports (0-65535).
• As with TCP, UDP also supports 65536 ports (0-65535).
• Unreal Engine 2 only allows a view distance of 65536 UU, or Unreal Units.

## In popular culture

There are 65536 different charts in Western geomancy.

## References

1. ^ Sequence in OEIS
2. ^
3. ^ Wells, David (1997). The Penguin Dictionary of Curious and Interesting Numbers (revised ed.). Penguin. ISBN 0-14-026149-4.
4. ^
5. ^ Microsoft Help Q120596