65536 is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

following 65535 and preceding 65537. 65536 is a

power of two A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent. In a context where only integers are considered, is restricted to non-negat ...

2^

(2 to the 16th power). 65536 is the smallest number with ''exactly'' 17

divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...

In mathematics

65536 is

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

2 \uparrow\uparrow\uparrow 3

. 65536 is a

superperfect number In mathematics, a superperfect number is a positive integer ''n'' that satisfies :\sigma^2(n)=\sigma(\sigma(n))=2n\, , where σ is the divisor summatory function. Superperfect numbers are a generalization of perfect numbers. The term was coine ...

– a number such that σ(σ(''n'')) = 2''n''. A

16-bit 16-bit microcomputers are microcomputers that use 16-bit microprocessors. A 16-bit register can store 216 different values. The range of integer values that can be stored in 16 bits depends on the integer representation used. With the two ...

number can distinguish 65536 different possibilities. For example, unsigned binary notation exhausts all possible 16-bit codes in uniquely identifying the numbers 0 to 65535. In this scheme, 65536 is the least

that can ''not'' be represented with 16 bits. Conversely, it is the "first" or smallest positive integer that requires 17 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. The sum of the unitary divisors of 65536 is prime (1 + 65536 = 65537, which is prime). 65536 is an untouchable number.

In computing

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

binary digits The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

(or ''bits''), also known as an unsigned short integer in many

computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...

systems. * A 65,536-bit integer can represent up to 2⁶⁵⁵³⁶ (2.00352993...) values. *65,536 is the number of characters in the original

Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...

, and currently in a Unicode plane. This number is a limit in many common hardware and software implementations, some examples of which are: * The Motorola 68000 family,

x86 architecture x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant. The 8086 was int ...

, and other

computing platform A computing platform or digital platform is an environment in which a piece of software is executed. It may be the hardware or the operating system (OS), even a web browser and associated application programming interfaces, or other underlying so ...

s have a

word A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...

size of 16 bits, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern

microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circ ...

s.) * Many modern CPUs allow a memory page size of 64

KiB The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...

(65536 bytes) to be configured in their memory-management hardware. * The default buffer size of a pipeline (Unix) is 64KiB (65536 bytes). * 65536 is the maximum number of spreadsheet rows supported by Excel 97, Excel 2000, Excel 2002 and Excel 2003. Text files that are larger than 65536 rows cannot be imported to these versions of Excel. (Excel 2007, 2010 and 2013 support 1,048,576 rows (2²⁰)). * A

microprocessor chip can directly access 65536 memory addresses, and the 16-bit highcolor graphics standard supports a color palette of 65536 different colors. * The maximum number of methods allowed in a single dex file Android application is 65536. * The limit for the amount of code in bytes for a non-native, non-abstract method in Java. * The number of available ports to combine with a

network address A network address is an identifier for a node or host on a telecommunications network. Network addresses are designed to be unique identifiers across the network, although some networks allow for local, private addresses, or locally admini ...

to create a

network socket A network socket is a software structure within a network node of a computer network that serves as an endpoint for sending and receiving data across the network. The structure and properties of a socket are defined by an application programmin ...

. *The maximum character limit for one message in

WhatsApp WhatsApp (also called WhatsApp Messenger) is an internationally available freeware, cross-platform, centralized instant messaging (IM) and voice-over-IP (VoIP) service owned by American company Meta Platforms (formerly Facebook). It allows use ...

is 65536.

In popular culture

*There are 65536 different charts in Western geomancy.

References

{{DEFAULTSORT:65536 (Number) Integers