128 (number)

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title: "128 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["integers"] topic_path: "general/integers" source: "https://en.wikipedia.org/wiki/128_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::data[format=table title="Infobox number"]

FieldValue
number128
divisor1, 2, 4, 8, 16, 32, 64, 128
::

| number = 128 | divisor = 1, 2, 4, 8, 16, 32, 64, 128

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.{{citation | last = Sprague | first = R. | doi = 10.1007/BF01181594 | mr = 0027285 | journal = Math. Z. | pages = 289–290 | title = Über Zerlegungen in ungleiche Quadratzahlen | volume = 51 | year = 1948 | issue = 3| s2cid = 123515191

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 ::figure[src="https://upload.wikimedia.org/wikipedia/commons/d/d1/7-segment.svg" caption="All 128 possible states of the [[seven-segment display]]."] ::

  • 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

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]].

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integers