# 65,535

From HandWiki

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

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 | 1111111111111111_{2} | |||

Ternary | 10022220020_{3} | |||

Quaternary | 33333333_{4} | |||

Quinary | 4044120_{5} | |||

Senary | 1223223_{6} | |||

Octal | 177777_{8} | |||

Duodecimal | 31B13_{12} | |||

Hexadecimal | FFFF_{16} | |||

Vigesimal | 83GF_{20} | |||

Base 36 | 1EKF_{36} |

**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 2^{0} through 2^{15} (2^{0} + 2^{1} + 2^{2} + ... + 2^{15}) 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 (FFFF
_{16}) is the highest addressable memory location, with 0 (0000_{16}) 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*77.1`

displays 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

Original source: https://en.wikipedia.org/wiki/65,535.
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