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͵εφλε´
Roman numeralLXVDXXXV
Binary11111111111111112
Ternary100222200203
Senary12232236
Octal1777778
Duodecimal31B1312
HexadecimalFFFF16

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 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.

See also

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. ^ "Robert Uiterwyk's MICRO BASIC".
  11. ^ "Basic HTML data types". www.w3.org. Retrieved 2022-12-28.