65,535

From Wikipedia, the free encyclopedia
← 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[edit]

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 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).

65535 is the 15th 626-gonal number, the 5th 6555-gonal number, and the 3rd 21846-gonal number.

In computing[edit]

  • 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.
  • In older computers with processors having a 16-bit address bus (such as the MOS Technology 6502 and the Zilog Z80), 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.[2]
  • In some implementations of Tiny BASIC, entering a command that divides any number by zero will return 65535.
  • In an unpatched version of Microsoft Excel 2007, many mathematical computations evaluating to 65535 will display incorrectly. For example, =850*77.1 displays as 100000 rather than 65535. Microsoft reports[3] this to be a display-only bug for only 6 floating point numbers near 65535 and 65536. These display issues do not occur in editions of Excel that have been updated to Office 2007 service pack 2.
  • 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)  .[4]

See also[edit]

References[edit]

  1. ^ a b "Chapter 3: Numbers, Characters and Strings -- Valvano". users.ece.utexas.edu. Retrieved 2022-09-25.
  2. ^ "TCP and UDP Ports Explained". BleepingComputer. Retrieved 2022-09-25.
  3. ^ Microsoft Excel: Calculation Issue Update Archived 2007-10-06 at the Wayback Machine
  4. ^ "Basic HTML data types". www.w3.org. Retrieved 2022-12-28.