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65535 is the sum of 2⁰ through 2¹⁵ (2⁰ + 2¹ + 2² + ... + 2¹⁵) and is therefore arepdigit in base 2 (1111111111111111), in base 4 (33333333), and in base 16 (FFFF).

It is the ninth number $n {\displaystyle n}$ whoseEuler totient has analiquot sum that is $n {\displaystyle n}$ : $\sigma (\varphi (65535))=65535$ ,^[2] and the twenty-eighthperfect 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 fourFermat primes: 65535 = (2 + 1)(4 + 1)(16 + 1)(256 + 1). Because of this property, it is possible to construct withcompass and straightedge aregular polygon with 65535 sides (see,constructible polygon).

In computing

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65535 occurs frequently in the field ofcomputing because it is $2^{16}-1$ (one less than 2 to the 16th power), which is the highest number that can be represented by an unsigned 16-bitbinary number.^[1] Some computer programming environments may have predefined constant values representing 65535, with names likeMAX_UNSIGNED_SHORT.^[4]
In older computers with processors having a 16-bit address bus such as theMOS Technology 6502 popular in the 1970s^[5] and theZilog Z80,^[6] 65535 (FFFF₁₆) is the highest addressable memory location, with 0 (0000₁₆) being the lowest. Such processors thus support at most 64KiB of total byte-addressable memory.
InInternet protocols, 65535 is also the number ofTCP and UDP ports available for use, since port 0 is reserved.^[7]
In some implementations ofTiny BASIC, entering a command thatdivides any number by zero will return 65535.^[a]
InMicrosoft Word 2011 for Mac, 65535 is the highest line number that will be displayed.
InHTML, 65535 is the decimal value of theweb color Aqua (#00FFFF) .^[11]
inDragon Quest 1, this is the number ofexperience points needed to reach the maximum character level of 30.
InFallout 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 tocrash.