65,535

From HandWiki
Short description: Natural number
← 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[math]\displaystyle{ \stackrel{\digamma}{\Mu} }[/math]͵εφλε´
Roman numeralLXVDXXXV
Binary11111111111111112
Ternary100222200203
Quaternary333333334
Quinary40441205
Senary12232236
Octal1777778
Duodecimal31B1312
HexadecimalFFFF16
Vigesimal83GF20
Base 361EKF36

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 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

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

See also

References