65535 (number)

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← 65534 65536 → 65535
List of numbers — Integers ← 10k 20k 30k 40k 50k 60k 70k 80k 90k →
Cardinal	sixty-five thousand five hundred thirty-five
Ordinal	65535th (sixty-five thousand five hundred thirty-fifth)
Factorization	3 x 5 x 17 x 257
Divisor(s)	16
Binary	1111111111111111
Hexadecimal	FFFF

65535 is the integer after 65534 and before 65536.

1 In mathematics
2 In computing
- 2.1 Examples
3 References

[edit] In mathematics

65535 is a Mersenne number, being $216 - 1$ . But since its index, 16, is not prime, 65535 cannot be a Mersenne prime. It 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 15th 626-gonal number, the 5th 6555-gonal number, the 3rd 21846-gonal number.

[edit] In computing

65535 is a frequently occurring number in the field of computing because it is the highest number which can be represented by an unsigned 16 bit binary number.

65535 is sometimes expressed as 2¹⁶-1 (two to the power of sixteen, minus one)

[edit] Examples

65535 is the limit for many player variables in video games, such as experience points in Dragon Warrior, maximum enchant of items in Lineage 2, money carried in Phantasy Star, score in Star Wars: TIE Fighter and stats in The 4th Coming.
In Internet protocols, 65535 is also the number of TCP and UDP ports available at an IP address, since port 0 is reserved.
Indices in chat groups may well max out at 65535.
In older computers with processors operating with a 16-bit address bus (such as the MOS Technology 6502 and the Zilog Z80), 65535 was the highest addressable memory location. Such processors thus supported at most 64 kibibytes (64 KiB) of total memory.
A Java class or interface can have max. 65535 number of methods.
Also of note: In Microsoft Excel 2007, many (not all) mathematical computations evaluating to 65535 will display incorrectly. For example =850*77.1 displays as 100000 rather than 65535. Microsoft reports^[1] this to be a display-only bug for only 6 floating point numbers near 65535 and 6 near 65536.