65536 is the natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 65535 and preceding 65537.

65536 is a power of two

Power of two

In mathematics, a power of two means a number of the form 2n where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n....

: (2 to the 16th power).

65536 is the smallest number with exactly 17 divisor

Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...

s.

In mathematics

65536 is , so in tetration

Tetration

In mathematics, tetration is an iterated exponential and is the next hyper operator after exponentiation. The word tetration was coined by English mathematician Reuben Louis Goodstein from tetra- and iteration. Tetration is used for the notation of very large numbers...

 notation 65536 is .

When expressed using Knuth's up-arrow notation

Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated...

, 65536 is
,
which is equal to
,
which is equivalent to

or
.

65536 is a superperfect number

Superperfect number

In mathematics a superperfect number is a positive integer n that satisfies\sigma^2=\sigma=2n\, ,where σ is the divisor function...

 - a number such that σ

Divisor function

In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...

(σ(n))=2n.

A 16-bit

16-bit

-16-bit architecture:The HP BPC, introduced in 1975, was the world's first 16-bit microprocessor. Prominent 16-bit processors include the PDP-11, Intel 8086, Intel 80286 and the WDC 65C816. The Intel 8088 was program-compatible with the Intel 8086, and was 16-bit in that its registers were 16...

 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.

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

In computing

65536 (2¹⁶) is the number of different values representable in a number of 16 binary digits

Bit

A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

, also known as a short integer in many computer programming

Computer programming

Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...

 systems. Therefore,

• The Motorola 68000 family, x86 architecture
  X86 architecture
  The term x86 refers to a family of instruction set architectures based on the Intel 8086 CPU. The 8086 was launched in 1978 as a fully 16-bit extension of Intel's 8-bit based 8080 microprocessor and also introduced segmentation to overcome the 16-bit addressing barrier of such designs...
  
  , and other computing platforms have a word size of 16 bit
  Bit
  A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
  
  s, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern microprocessor
  Microprocessor
  A microprocessor incorporates the functions of a computer's central processing unit on a single integrated circuit, or at most a few integrated circuits. It is a multipurpose, programmable device that accepts digital data as input, processes it according to instructions stored in its memory, and...
  
  .)
• 65536 is the maximum number of spreadsheet rows supported by Excel
  Microsoft Excel
  Microsoft Excel is a proprietary commercial spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications...
  
   97, Excel 2000, Excel 2002 and Excel 2003 (Excel 2007 supports 1,048,576 rows (2²⁰)). Text files that are larger than 65536 rows cannot be imported to these versions of Excel.
• A 16-bit
  16-bit
  -16-bit architecture:The HP BPC, introduced in 1975, was the world's first 16-bit microprocessor. Prominent 16-bit processors include the PDP-11, Intel 8086, Intel 80286 and the WDC 65C816. The Intel 8088 was program-compatible with the Intel 8086, and was 16-bit in that its registers were 16...
  
   microprocessor chip can directly access 65536 memory addresses, and the 16-bit highcolor graphics standard supports a color palette of 65536 different colors.
• TCP
  Transmission Control Protocol
  The Transmission Control Protocol is one of the core protocols of the Internet Protocol Suite. TCP is one of the two original components of the suite, complementing the Internet Protocol , and therefore the entire suite is commonly referred to as TCP/IP...
  
   supports 65536 distinct ports (0-65535).
• Unreal Engine 2 only allows a view distance of 65536 UU, or Unreal Units.