255 (two hundred
ndfifty-five) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
254
Year 254 ( CCLIV) was a common year starting on Sunday of the Julian calendar. At the time, it was known as the Year of the Consulship of Valerianus and Gallienus (or, less frequently, year 1007 ''Ab urbe condita''). The denomination 254 for th ...
and preceding
256
Year 256 ( CCLVI) was a leap year starting on Tuesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Glabrio (or, less frequently, year 1009 ''Ab urbe condita''). The denomination 256 for this y ...
.
In mathematics
Its factorization makes it a
sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
. Since 255 = 2
8 – 1, it is a
Mersenne number
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17t ...
(though not a
pernicious one), and the fourth such number not to be a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
. It is a
perfect totient number
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, one applies the totient function to a number ''n'', apply it again to the resulting totient, and so on, until the number 1 is rea ...
, the smallest such number to be neither a power of three nor thrice a prime.
Since 255 is the product of the first three
Fermat prime
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have 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, ...
s, the regular 255-gon is
constructible.
In base 10, it is a
self number
In number theory, a self number or Devlali number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combin ...
.
255 is 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".
Ex ...
in base 2 (11111111), in base 4 (3333), and in base 16 (FF).
In computing
255 is a special number in some tasks having to do with computing. This is the maximum value representable by an eight-digit
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two values (0 and 1) for each digit
* Binary function, a function that takes two arguments
* Binary operation, a mathematical op ...
number, and therefore the maximum representable by an unsigned
8-bit
byte
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 un ...
(the most common size of byte, also called an
octet
Octet may refer to:
Music
* Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble
** String octet, a piece of music written for eight string instruments
*** Octet (Mendelssohn), 1825 compo ...
), the smallest common
variable size used in high level
programming language
A programming language is a system of notation for writing computer programs.
Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...
s (
bit
The bit is the most basic unit of information in computing and digital communication. 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 as ...
being smaller, but rarely used for value storage). The range is
0 to 255, which is
256
Year 256 ( CCLVI) was a leap year starting on Tuesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Glabrio (or, less frequently, year 1009 ''Ab urbe condita''). The denomination 256 for this y ...
total values.
:
For example, 255 is the maximum value of
* components in the
24-bit RGB color
Color (or colour in English in the Commonwealth of Nations, Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is the visual perception based on the electromagnetic spectrum. Though co ...
model, since each color channel is allotted eight bits;
* any dotted quad in an
IPv4 address
Internet Protocol version 4 (IPv4) is the first version of the Internet Protocol (IP) as a standalone specification. It is one of the core protocols of standards-based internetworking methods in the Internet and other packet-switched networks ...
; and
* the
alpha blending
In computer graphics, alpha compositing or alpha blending is the process of combining one image with a background to create the appearance of partial or full transparency. It is often useful to render picture elements (pixels) in separate pass ...
scale in
Delphi
Delphi (; ), in legend previously called Pytho (Πυθώ), was an ancient sacred precinct and the seat of Pythia, the major oracle who was consulted about important decisions throughout the ancient Classical antiquity, classical world. The A ...
(255 being 100% visible and 0 being fully transparent) and
* a
DMX512
DMX512 is a technical standard, standard for digital communication networks that are commonly used to control lighting and effects. It was originally intended as a standardized method for controlling stage lighting dimmers, which, prior to D ...
channel
The use of eight bits for storage in older video games has had the consequence of it appearing as a hard limit in many video games. For example, in the original ''
The Legend of Zelda
is a media franchise, video game series created by the Japanese game designers Shigeru Miyamoto and Takashi Tezuka. It is primarily developed and published by Nintendo; some portable installments and re-releases have been outsourced to Flags ...
'' game,
Link can carry a maximum of 255 rupees. It was often used for numbers where casual gameplay would not cause anyone to exceed the number. However, in most situations it is reachable given enough time. This can cause many other peculiarities to appear when the number
wraps back to 0, such as the infamous "
kill screen
Since the origin of video games in the early 1970s, the video game industry, the players, and surrounding culture have spawned a wide range of technical and slang terms.
0–9
A
...
" seen after clearing level 255 of
Pac-Man
''Pac-Man,'' originally called in Japan, is a 1980 maze video game developed and published by Namco for arcades. In North America, the game was released by Midway Manufacturing as part of its licensing agreement with Namco America. The pla ...
.
[Clewett, James.]
255 and Pac-Man
. ''Numberphile''. 2007-17-11.
This number could be interpreted by a computer as
−1
In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.
...
if a programmer is not careful about which 8-bit values are
signed and unsigned, and the
two's complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''s ...
representation of −1 in a signed byte is equal to that of 255 in an unsigned byte.
References
{{Integers, 2
Integers