128 (number)

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.{{citation

The sum of Euler's totient function φ(x) over the first twenty integers is 128.

128 can be expressed by a combination of its digits with mathematical operators, thus 128 28 − 1, making it a Friedman number in base 10.

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

• 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 used in a number of products, notably as the default cipher in some versions of GPG and PGP.

In other fields

• The number of US fluid ounces in a US gallon.

Notes

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138

References

1. [[OEIS:A001422]]. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 {{OEIS
2. [[OEIS:A033950]].
3. [[OEIS:A002088]].
4. [[OEIS:A036057]].