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 n ...

following 65535 and preceding

65537 65537 is the integer after 65536 and before 65538. In mathematics 65537 is the largest known prime number of the form 2^ +1 (n = 4). Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge. Johann ...

. 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-negative ...

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 In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though \uparrow \uparrow and the left-exponent ''xb'' are common. Under the definition as rep ...

notation 65536 is ⁴2. When expressed using

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. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperati ...

, 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 coined b ...

– 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 mos ...

number can distinguish 65536 different possibilities. For example,

unsigned Unsigned can refer to: * An unsigned artist is a musical artist or group not attached or signed to a record label ** Unsigned Music Awards, ceremony noting achievements of unsigned artists ** Unsigned band web, online community * Similarly, the c ...

binary notation A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notatio ...

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 A decimal representation of a non-negative real number is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator: r = b_k b_\ldots b_0.a_1a_2\ldots Here is the decimal separator, is ...

. The sum of the

unitary divisor In mathematics, a natural number ''a'' is a unitary divisor (or Hall divisor) of a number ''b'' if ''a'' is a divisor of ''b'' and if ''a'' and \frac are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 an ...

s of 65536 is prime (1 + 65536 =

, which is prime). 65536 is an

untouchable number An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...

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 represented a ...

(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 ana ...

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 Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ...

, 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 The Motorola 68000 series (also known as 680x0, m68000, m68k, or 68k) is a family of 32-bit complex instruction set computer (CISC) microprocessors. During the 1980s and early 1990s, they were popular in personal computers and workstations and w ...

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 introd ...

, 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 s ...

s have a

word A word is a basic element of language that carries an semantics, objective or pragmatics, practical semantics, meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of w ...

size of 16

bit 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 ...

s, 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 circu ...

s.) * Many modern CPUs allow a

memory page A page, memory page, or virtual page is a fixed-length contiguous block of virtual memory, described by a single entry in the page table. It is the smallest unit of data for memory management in a virtual memory operating system. Similarly, a p ...

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) In Unix-like computer operating systems, a pipeline is a mechanism for inter-process communication using message passing. A pipeline is a set of processes chained together by their standard streams, so that the output text of each process (''stdou ...

is 64KiB (65536 bytes). * 65536 is the maximum number of spreadsheet rows supported by

Excel ExCeL London (an abbreviation for Exhibition Centre London) is an exhibition centre, international convention centre and former hospital in the Custom House area of Newham, East London. It is situated on a site on the northern quay of the ...

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 administere ...

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 programming ...

. *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 us ...

is 65536.

In popular culture

*There are 65536 different charts in Western

geomancy Geomancy (Greek: γεωμαντεία, "earth divination") is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls of soil, rocks, or sand. The most prevalent form of divinatory geomancy invo ...

References

{{DEFAULTSORT:65536 (Number) Integers