65,535
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 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).
It is the ninth number whose Euler totient has an aliquot sum that is : ,[2] and the twenty-eighth perfect totient number equal to the sum of its iterated totients.[3]
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 with 65535 sides (see, constructible polygon).
In computing
- 65535 occurs frequently in the field of computing because it is (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 Template:Code.[4]
- In older computers with processors having a 16-bit address bus such as the MOS Technology 6502 popular in the 1970s[5] and the Zilog Z80,[6] 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.[7]
- In some implementations of Tiny BASIC, entering a command that divides any number by zero will return 65535.Template:Efn
- In 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 color Aqua (#00FFFF) Template:Color strip.[8]
- in Dragon Quest 1, this is the number of experience points needed to reach the maximum character level of 30.
- In 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.