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{{Infobox number
| number= 65535
| divisor = 16 total
}}

'''65535''' is the integer after 65534 and before 65536.

It is the maximum value of an unsigned 16-bit integer.<ref name=":0">{{Cite web |title=Chapter 3: Numbers, Characters and Strings -- Valvano |url=http://users.ece.utexas.edu/~valvano/embed/chap3/chap3.htm |access-date=2022-09-25 |website=users.ece.utexas.edu}}</ref>

== In mathematics ==
65535 is the sum of 2<sup>0</sup> through 2<sup>15</sup> (2<sup>0</sup> + 2<sup>1</sup> + 2<sup>2</sup> + ... + 2<sup>15</sup>) and is therefore a [[Repdigit|repdigit]] in base 2 (1111111111111111), in base 4 (33333333), and in base 16 (FFFF).

It is the ninth number <math>n</math> whose Euler totient has an [[Aliquot sum|aliquot sum]] that is <math>n</math>: <math>\sigma(\varphi(65535)) = 65535</math>,<ref>{{Cite OEIS |A018784 |Numbers n such that sigma phi n is n. |access-date=2023-06-27 }}</ref> and the twenty-eighth [[Perfect totient number|perfect totient number]] equal to the sum of its iterated totients.<ref>{{Cite OEIS |A082897 |Perfect totient numbers. |access-date=2023-09-13 }}</ref>

65535 is the fifteenth 626-gonal number, the fifth 6555-gonal number, and the third 21846-gonal number. 

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|regular polygon]] with 65535 sides (see, [[Constructible polygon|constructible polygon]]).

== In computing ==
*65535 occurs frequently in the field of [[Computing|computing]] because it is <math>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.<ref name=":0" /> Some computer programming environments may have predefined constant values representing 65535, with names like {{code|MAX_UNSIGNED_SHORT}}.<ref>{{Cite web|title=Windows Data Types |url=https://learn.microsoft.com/en-us/windows/win32/winprog/windows-data-types |website=[[Company:Microsoft|Microsoft]] (Learn) |access-date=2023-09-13 }}</ref>
*In older computers with processors having a 16-bit address bus such as the MOS Technology 6502 popular in the 1970s<ref>{{Cite web |last=Blance |first=Andrew |title=How do Processors Actually Work? |url=https://codeburst.io/how-do-processors-actually-work-91dce24fbb44 |website=[[Software:Medium (website)|Medium]] |date=August 5, 2020 |access-date=2023-09-13 }}</ref> and the Zilog Z80,<ref>{{Cite web |title= Z80 Microprocessors Z80 CPU User Manual (UM008011-0816) |website=Zilog |url=https://www.zilog.com/docs/z80/um0080.pdf |access-date=2023-09-13 }}</ref> 65535 (FFFF<sub>[[Hexadecimal|16]]</sub>) is the highest addressable memory location, with 0 (0000<sub>[[Hexadecimal|16]]</sub>) being the lowest. Such processors thus support at most 64 [[Kibibyte|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.<ref>{{Cite web |title=TCP and UDP Ports Explained |url=https://www.bleepingcomputer.com/tutorials/tcp-and-udp-ports-explained/ |access-date=2022-09-25 |website=BleepingComputer |language=en-us}}</ref>
*In some implementations of [[Tiny BASIC]], entering a command that [[Division by zero|divides any number by zero]] will return 65535.{{efn|1=In Altar 4k BASIC (1975),<ref>{{cite web|url=https://deramp.com/downloads/mfe_archive/010-S100%20Computers%20and%20Boards/00-MITS/40-Software/BASIC/Altair%20BASIC%203.0/Documentation/Altair_8800_BASIC_Reference_Manual_1975.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://deramp.com/downloads/mfe_archive/010-S100%20Computers%20and%20Boards/00-MITS/40-Software/BASIC/Altair%20BASIC%203.0/Documentation/Altair_8800_BASIC_Reference_Manual_1975.pdf |archive-date=2022-10-09 |url-status=live|title=MITS ALTAIR BASIC REFERENCE MANUAL}}</ref> Tiny BASIC Extended (1976),<ref name="Dr.D">{{cite web|url=http://www.classiccmp.org/cini/pdf/DrDobbs/DrDobbs-1976-02-v1n2.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.classiccmp.org/cini/pdf/DrDobbs/DrDobbs-1976-02-v1n2.pdf |archive-date=2022-10-09 |url-status=live|title=Dr. Dobb's Journal of Computer Calisthenics and Orthodontia: Running Light Without Overbyte}}</ref> 6800 Tiny BASIC (1976),<ref name="Dr.D" /> and MICRO BASIC 1.3 (1976).<ref>{{cite web|url=http://www.swtpc.com/mholley/NewsLetter1/MicroBasic.htm|title=Robert Uiterwyk's MICRO BASIC}}</ref> }}
*In [[Software:Microsoft Word|Microsoft Word]] 2011 for Mac, 65535 is the highest line number that will be displayed.
*In [[HTML]], 65535 is the decimal value of the [[Web colors|web color]] [[Aqua (color)|Aqua (#00FFFF)]] {{Color strip|aqua}}.<ref>{{Cite web |title=Basic HTML data types |url=https://www.w3.org/TR/REC-html40/types.html#h-6.5 |access-date=2022-12-28 |website=www.w3.org}}</ref>
*in ''Dragon Quest 1'', this is the number of experience points needed to reach the maximum character level of 30.
*In ''[[Software:Fallout 4|Fallout 4]]'', level 65535 is the last possible level that the player can reach as there is no level cap. Gaining one more after this causes the game to [[Crash (computing)|crash]].

==See also==
* [[4,294,967,295|4,294,967,295]]
* [[255 (number)|255 (number)]]
* [[16-bit computing|16-bit computing]]

==References==
{{Notelist}}
{{Reflist}}

{{DEFAULTSORT:65535 (Number)}}
[[Category:Integers]]

{{Sourceattribution|65,535}}