128 (number)
Appearance
| ||||
---|---|---|---|---|
Cardinal | one hundred twenty-eight | |||
Ordinal | 128th (one hundred twenty-eighth) | |||
Factorization | 27 | |||
Divisors | 1, 2, 4, 8, 16, 32, 64, 128 | |||
Greek numeral | ΡΚΗ´ | |||
Roman numeral | CXXVIII, cxxviii | |||
Binary | 100000002 | |||
Ternary | 112023 | |||
Senary | 3326 | |||
Octal | 2008 | |||
Duodecimal | A812 | |||
Hexadecimal | 8016 |
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]
128 is the only 3-digit number that is a 7th power (27).
In computing
[edit]- 128-bit key size encryption for secure communications over the Internet
- 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]- The number of US fluid ounces in a US gallon
Notes
[edit]- ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, doi:10.1007/BF01181594, MR 0027285, S2CID 123515191
- ^ 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).
- ^ OEIS:A033950.
- ^ OEIS:A002088.
- ^ OEIS:A036057.
References
[edit]- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
External links
[edit]Wikimedia Commons has media related to 128 (number).