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65,535 - Wikipedia
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Natural number
65535 is the integer after 65534 and before 65536.
It is the maximum value of an unsigned 16-bit integer.[1]
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 n {\displaystyle n} whose Euler totient has an aliquot sum that is n {\displaystyle n} : σ ( φ ( 65535 ) ) = 65535 {\displaystyle \sigma (\varphi (65535))=65535} ,[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).
- 65535 occurs frequently in the field of computing because it is 2 16 − 1 {\displaystyle 2^{16}-1} (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.[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.[a]
- 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) .[11]
- 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.
- ^ In Altar 4k BASIC (1975),[8] Tiny BASIC Extended (1976),[9] 6800 Tiny BASIC (1976),[9] and MICRO BASIC 1.3 (1976).[10]
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