Jump to content

128 (number)

From Wikipedia, the free encyclopedia
← 127 128 129 →
Cardinalone hundred twenty-eight
Ordinal128th
(one hundred twenty-eighth)
Factorization27
Divisors1, 2, 4, 8, 16, 32, 64, 128
Greek numeralΡΚΗ´
Roman numeralCXXVIII, cxxviii
Binary100000002
Ternary112023
Senary3326
Octal2008
DuodecimalA812
Hexadecimal8016

128 (one hundred [and] twenty-eight) is the natural number following 127 and preceding 129.

In mathematics

[edit]

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.[1][2] However, it is divisible by the total number of its divisors, making it a refactorable number.[3]

The sum of Euler's totient function φ(x) over the first twenty integers is 128.[4]

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.[5]

A hepteract has 128 vertices.

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

In computing

[edit]
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

[edit]

Notes

[edit]
  1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, doi:10.1007/BF01181594, MR 0027285, S2CID 123515191
  2. ^ OEIS:A001422. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 (sequence A001661 in the OEIS).
  3. ^ OEIS:A033950.
  4. ^ OEIS:A002088.
  5. ^ OEIS:A036057.

References

[edit]
[edit]