65,535
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | sixty-five thousand five hundred thirty-five | |||
| Ordinal | 65535th (sixty-five thousand five hundred thirty-fifth) | |||
| Factorization | 3 × 5 × 17 × 257 | |||
| Divisors | 16 total | |||
| Greek numeral | [math]\displaystyle{ \stackrel{\digamma}{\Mu} }[/math]͵εφλε´ | |||
| Roman numeral | LXVDXXXV | |||
| Binary | 11111111111111112 | |||
| Ternary | 100222200203 | |||
| Quaternary | 333333334 | |||
| Quinary | 40441205 | |||
| Senary | 12232236 | |||
| Octal | 1777778 | |||
| Duodecimal | 31B1312 | |||
| Hexadecimal | FFFF16 | |||
| Vigesimal | 83GF20 | |||
| Base 36 | 1EKF36 | |||
65535 is the integer after 65534 and before 65536.
It is the maximum value of an unsigned 16-bit integer.[1]
In mathematics
65535 is the product of the first four Fermat primes: 65535 = (2 + 1)(4 + 1)(16 + 1)(256 + 1). Because of this property, it is possible to construct with compass and straightedge a regular polygon with 65535 sides. See constructible polygon.
65535 is the sum of 20 through 215 (20 + 21 + 22 + ... + 215) and is therefore a repdigit in base 2 (1111111111111111), in base 4 (33333333), and in base 16 (FFFF).
65535 is the 15th 626-gonal number, the 5th 6555-gonal number, and the 3rd 21846-gonal number.
In computing
- 65535 occurs frequently in the field of computing because it is [math]\displaystyle{ 2^{16} - 1 }[/math] (one less than 2 to the 16th power), which is the highest number that can be represented by an unsigned 16-bit binary number.[1] Some computer programming environments may have predefined constant values representing 65535, with names like
MAX_UNSIGNED_SHORT. - In older computers with processors having a 16-bit address bus (such as the MOS Technology 6502 and the Zilog Z80), 65535 (FFFF16) is the highest addressable memory location, with 0 (000016) being the lowest. Such processors thus support at most 64 KiB of total byte-addressable memory.
- In Internet protocols, 65535 is also the number of TCP and UDP ports available for use, since port 0 is reserved.[2]
- In some implementations of Tiny BASIC, entering a command that divides any number by zero will return 65535.
- In an unpatched version of Microsoft Excel 2007, many mathematical computations evaluating to 65535 will display incorrectly. For example,
=850*77.1displays as 100000 rather than 65535. Microsoft reports[3] this to be a display-only bug for only 6 floating point numbers near 65535 and 65536. These display issues do not occur in editions of Excel that have been updated to Office 2007 service pack 2. - In Microsoft Word 2011 for Mac, 65535 is the highest line number that will be displayed.
See also
References
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