128 (one hundred ndtwenty-eight) 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 127 and preceding 129.

In mathematics

128 is the seventh power of 2. It is the largest number which cannot be expressed as the sum of any number of distinct

squares In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

. However, it is divisible by the total number of its divisors, making it a refactorable number. The sum of

Euler's totient function In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...

φ() over the first twenty integers is 128. 128 can be expressed by a combination of its digits with mathematical operators, thus 128 2^{8 − 1}, making it a

Friedman number A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, ...

in base 10. OEIS:A036057. A hepteract has 128 vertices. 128 is the only 3-digit number that is a 7th power (2⁷).

In computing

128-bit General home computing and gaming utility emerged at 8-bit word sizes, as 28=256 Word (computer architecture), words, a natural unit of data, became possible. Early 8-bit CPUs (such as the Zilog Z80 and MOS Technology 6502, used in the 1977 Co ...

key size In cryptography, key size or key length refers to the number of bits in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest known a ...

encryption In Cryptography law, cryptography, encryption (more specifically, Code, encoding) is the process of transforming information in a way that, ideally, only authorized parties can decode. This process converts the original representation of the inf ...

for secure communications over the Internet **

IPv6 Internet Protocol version 6 (IPv6) is the most recent version of the Internet Protocol (IP), the communication protocol, communications protocol that provides an identification and location system for computers on networks and routes traffic ...

uses 128-bit (16-byte) addresses ** Any

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 ...

with a

binary prefix A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes are kibi (symbol Ki, meaning ), mebi (), and gibi (). They are most often used in inform ...

is 128

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 ...

s of a lesser binary prefix value, such as 1

gibibit 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 ...

is 128

mebibyte The byte is a units of information, 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 (computing), character of text in a computer and for this ...

s ** 128-bit integers, memory addresses, or other data units are those that are at most 128 bits 16 octets wide 7-segment

* A 128-bit integer can represent up to 3.40282366...e+38 values (2¹²⁸ 340,282,366,920,938,463,463,374,607,431,768,211,456). * CAST-128 is a

block cipher In cryptography, a block cipher is a deterministic algorithm that operates on fixed-length groups of bits, called ''blocks''. Block ciphers are the elementary building blocks of many cryptographic protocols. They are ubiquitous in the storage a ...

used in a number of products, notably as the default

cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...

in some versions of GPG and PGP.

In other fields

* The number of US fluid ounces in a

US gallon The gallon is a unit of volume in British imperial units and United States customary units. The imperial gallon (imp gal) is defined as , and is or was used in the United Kingdom and its former colonies, including Ireland, Canada, Australia, ...

Notes

References

* Wells, D. ''

The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, a ...

'' London: Penguin Group. (1987): 138

External links

Code 128 specification at OpenBarcode.org
{{DEFAULTSORT:128 (Number) Integers