128 (number)

128 (one hundred [and] twenty-eight) is the natural number 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.<ref>Template:Citation</ref><ref>OEIS:A001422. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 Template:OEIS.</ref> However, it is divisible by the total number of its divisors, making it a refactorable number.<ref>OEIS:A033950.</ref>

The sum of Euler's totient function φ(Template:Mvar) over the first twenty integers is 128.<ref>OEIS:A002088.</ref>

128 can be expressed by a combination of its digits with mathematical operators, thus 128 Template:Math 2^{8 − 1}, making it a Friedman number in base 10.<ref>OEIS:A036057.</ref>

A hepteract has 128 vertices.

128 is the only 3-digit number that is a 7th power (2⁷).

In computing

128-bit key size encryption for secure communications over the Internet
- IPv6 uses 128-bit (16-byte) addresses
- Any bit with a binary prefix is 128 bytes of a lesser binary prefix value, such as 1 gibibit is 128 mebibytes
- 128-bit integers, memory addresses, or other data units are those that are at most 128 bits 16 octets wide

File:7-segment.svg

All 128 possible states of the seven-segment display.

A 128-bit integer can represent up to 3.40282366...e+38 values (2¹²⁸ Template:Math 340,282,366,920,938,463,463,374,607,431,768,211,456).
CAST-128 is a block cipher used in a number of products, notably as the default cipher in some versions of GPG and PGP.