65535 (number)
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65535 is the integer after 65534 and before
65536 65536 is the natural number following 65535 and preceding 65537. 65536 is a power of two: 2^ (2 to the 16th power). 65536 is the smallest number with ''exactly'' 17 divisors. In mathematics 65536 is 2^, so in tetration notation 65536 is  ...
. It is the maximum value of an unsigned 16-bit integer.


In mathematics

65535 is the product of the first four
Fermat primes In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 4294967 ...
: 65535 = (2 + 1)(4 + 1)(16 + 1)(256 + 1). Because of this property, it is possible to construct with
compass and straightedge In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...
a
regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either convex p ...
with 65535 sides. See
constructible polygon In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. There are infinite ...
. 65535 is the sum of 20 through 215 (20 + 21 + 22 + ... + 215) and is therefore a
repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit. Example ...
in base 2 (1111111111111111), in base 4 (33333333), and in base 16 (FFFF). 65535 is the 15th 626- gonal number, the 5th 6555-gonal number, and the 3rd 21846-gonal number.


In computing

*65535 occurs frequently in the field of
computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, e ...
because it is 2^ - 1 (one less than 2 to the 16th power), which is the highest number that can be represented by an unsigned 16-bit
binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that t ...
number. Some computer programming environments may have predefined constant values representing 65535, with names like . *In older computers with processors having a 16-bit address bus (such as the
MOS Technology 6502 The MOS Technology 6502 (typically pronounced "sixty-five-oh-two" or "six-five-oh-two") William Mensch and the moderator both pronounce the 6502 microprocessor as ''"sixty-five-oh-two"''. is an 8-bit microprocessor that was designed by a small t ...
and the
Zilog Z80 The Z80 is an 8-bit microprocessor introduced by Zilog as the startup company's first product. The Z80 was conceived by Federico Faggin in late 1974 and developed by him and his 11 employees starting in early 1975. The first working samples wer ...
), 65535 (FFFF 16) is the highest addressable memory location, with 0 (0000 16) being the lowest. Such processors thus support at most 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 ...
of total byte-addressable memory. *In
Internet protocols The Internet protocol suite, commonly known as TCP/IP, is a framework for organizing the set of communication protocols used in the Internet and similar computer networks according to functional criteria. The foundational protocols in the suit ...
, 65535 is also the number of
TCP and UDP port In computer networking, a port is a number assigned to uniquely identify a connection endpoint and to direct data to a specific service. At the software level, within an operating system, a port is a logical construct that identifies a specific ...
s available for use, since port 0 is reserved. *In some implementations of
Tiny BASIC Tiny BASIC is a family of dialects of the BASIC programming language that can fit into 4 or fewer KBs of memory. Tiny BASIC was designed in response to the open letter published by Bill Gates complaining about users pirating Altair BASIC, which ...
, entering a command that divides any number by zero will return 65535. *In an unpatched version of
Microsoft Excel Microsoft Excel is a spreadsheet developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (comp ...
2007, many mathematical computations evaluating to 65535 will display incorrectly. For example, displays as 100000 rather than 65535. Microsoft reports this to be a display-only bug for only 6
floating point numbers In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be r ...
near 65535 and 65536. These display issues do not occur in editions of Excel that have been updated to Office 2007
service pack In computing, a service pack comprises a collection of updates, fixes, or enhancements to a software program delivered in the form of a single installable package. Companies often release a service pack when the number of individual patches to a ...
2. *In
Microsoft Word Microsoft Word is a word processing software developed by Microsoft. It was first released on October 25, 1983, under the name ''Multi-Tool Word'' for Xenix systems. Subsequent versions were later written for several other platforms includin ...
2011 for Mac, 65535 is the highest line number that will be displayed. *In
HTML The HyperText Markup Language or HTML is the standard markup language for documents designed to be displayed in a web browser. It can be assisted by technologies such as Cascading Style Sheets (CSS) and scripting languages such as JavaScri ...
, 65535 is the decimal value of the
web color Web colors are colors used in Web design, displaying web pages on the World Wide Web, and the methods for describing and specifying those colors. Colors may be specified as an RGB color model, RGB triplet or in hexadecimal format (a ''hex triple ...
Aqua (#00FFFF) .


See also

*
4,294,967,295 The number 4,294,967,295 is an integer equal to 2 − 1. It is a perfect totient number. It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of 3 \cdot 5 \cdot 17 \cdot 257 \cdot 65537. It is the highest unsigned ...
*
255 (number) 255 (two hundred ndfifty-five) is the natural number following 254 and preceding 256. In mathematics Its factorization makes it a sphenic number. Since 255 = 28 – 1, it is a Mersenne number (though not a pernicious one), and the fourth such nu ...
*
16-bit computing 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 ...


References

{{DEFAULTSORT:65535 (Number) Integers