# 65,535

 ← 65534 65535 65536 →
Cardinalsixty-five thousand five hundred thirty-five
Ordinal65535th
(sixty-five thousand five hundred thirty-fifth)
Factorization3 × 5 × 17 × 257
Divisors16 total
Greek numeral${\displaystyle {\stackrel {\digamma }{\mathrm {M} }}}$͵εφλε´
Roman numeralLXVDXXXV
Binary11111111111111112
Ternary100222200203
Senary12232236
Octal1777778
Duodecimal31B1312

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 ${\displaystyle n}$ whose Euler totient has an aliquot sum that is ${\displaystyle n}$: ${\displaystyle \sigma (\varphi (65535))=65535}$,[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).

## In computing

• 65535 occurs frequently in the field of computing because it is ${\displaystyle 2^{16}-1}$ (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.

## References

1. ^ In Altar 4k BASIC (1975),[8] Tiny BASIC Extended (1976),[9] 6800 Tiny BASIC (1976),[9] and MICRO BASIC 1.3 (1976).[10]
1. ^ a b "Chapter 3: Numbers, Characters and Strings -- Valvano". users.ece.utexas.edu. Retrieved 2022-09-25.
2. ^ Sloane, N. J. A. (ed.). "Sequence A018784 (Numbers n such that sigma phi n is n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-06-27.
3. ^ Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-13.
4. ^ "Windows Data Types". Microsoft (Learn). 2 February 2023. Retrieved 2023-09-13.
5. ^ Blance, Andrew (August 5, 2020). "How do Processors Actually Work?". Medium. Retrieved 2023-09-13.
6. ^ "Z80 Microprocessors Z80 CPU User Manual (UM008011-0816)" (PDF). Zilog. Retrieved 2023-09-13.
7. ^ "TCP and UDP Ports Explained". BleepingComputer. Retrieved 2022-09-25.
8. ^ "MITS ALTAIR BASIC REFERENCE MANUAL" (PDF). Archived (PDF) from the original on 2022-10-09.
9. ^ a b "Dr. Dobb's Journal of Computer Calisthenics and Orthodontia: Running Light Without Overbyte" (PDF). Archived (PDF) from the original on 2022-10-09.
10. ^
11. ^ "Basic HTML data types". www.w3.org. Retrieved 2022-12-28.