|
|
| Line 1: |
Line 1: |
| {{infobox number
| | Hi there. Let me begin by introducing the writer, her name is Sophia. For years she's been living in Kentucky but her husband desires them to move. My day job is an invoicing officer but I've currently utilized for an additional 1. What I adore doing is soccer but I don't have the time lately.<br><br>my blog: psychics online ([http://fashionlinked.com/index.php?do=/profile-13453/info/ fashionlinked.com]) |
| | number = 65536
| |
| | divisor = 17 total
| |
| }}
| |
| '''65536''' is the [[natural number]] following [[65535 (number)|65535]] and preceding [[65537 (number)|65537]].
| |
| | |
| 65536 is a [[power of two]]: <math>2^{16}</math> (2 to the 16th power).
| |
| | |
| 65536 is the smallest number with ''exactly'' 17 [[divisor]]s.<ref>Sequence {{OEIS2C|A005179}} in [[On-Line Encyclopedia of Integer Sequences|OEIS]]</ref>
| |
| | |
| == In mathematics ==
| |
| 65536 is <math>2^{2^{2^{2}}}</math>, so in [[tetration]] notation 65536 is <math>^42</math>.
| |
| | |
| When expressed using [[Knuth's up-arrow notation]], 65536 is
| |
| <math>
| |
| 2 \uparrow 16
| |
| </math>,
| |
| which is equal to
| |
| <math>
| |
| 2 \uparrow 2 \uparrow 2 \uparrow 2
| |
| </math>,
| |
| which is equivalent to
| |
| <math>
| |
| 2 \uparrow\uparrow 4
| |
| </math>
| |
| or
| |
| <math>
| |
| 2 \uparrow\uparrow\uparrow 3
| |
| </math>.
| |
| | |
| 65536 is a [[superperfect number]] - a number such that [[divisor function|σ]](σ(''n''))=2''n''.<ref>{{MathWorld|urlname=SuperperfectNumber |title=Superperfect Number}}</ref>
| |
| | |
| A [[16-bit]] number can distinguish 65536 different possibilities, such as the numbers 0..65535. In unsigned binary notation, 65536 is thus the smallest number that can ''not'' be represented by 16 bits.
| |
| | |
| 65536 is the only power of 2 less than 2<sup>31000</sup> that does not contain the digits 1, 2, 4 or 8 in its [[decimal representation]].<ref>{{cite book|last=Wells|first=David|title=[[The Penguin Dictionary of Curious and Interesting Numbers]]|publisher=Penguin|year=1997|edition=revised|isbn=0-14-026149-4}}</ref>
| |
| | |
| 65536 is the largest known number such that the sum of its [[unitary divisor]]s is prime (1 + 65536 = [[65537]], which is prime).<ref>[http://primes.utm.edu/curios/page.php/65536.html 65536] at [[Prime Pages]]</ref>
| |
| | |
| == In computing ==
| |
| 65536 (2<sup>16</sup>) is the number of different values representable in a number of 16 [[bit|binary digits]], also known as a [[short integer]] in many [[computer programming]] systems. Therefore,
| |
| * The [[Motorola 68000 family]], [[x86 architecture]], and other [[computing platform]]s have a [[Word (data type)|word]] size of 16 [[bit]]s, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern [[microprocessor]]s.)
| |
| * 65536 is the maximum number of spreadsheet rows supported by [[Microsoft Excel|Excel]] 97, Excel 2000, Excel 2002 and Excel 2003 (Excel 2007, 2010 and 2013 support [[1048576 (number)|1,048,576]] rows (2<sup>20</sup>)). Text files that are larger than 65536 rows cannot be imported to these versions of Excel.<ref>[http://support.microsoft.com/kb/120596 Microsoft Help Q120596]</ref>
| |
| * A [[16-bit]] microprocessor chip can directly access 65536 memory addresses, and the [[Highcolor|16-bit highcolor]] graphics standard supports a color palette of 65536 different colors.
| |
| * [[Transmission Control Protocol|TCP]] supports 65536 distinct ports (0-65535).
| |
| * [[Unreal Engine 2#Unreal Engine 2|Unreal Engine 2]] only allows a view distance of 65536 UU, or Unreal Units.
| |
| | |
| == In popular culture ==
| |
| There are 65536 different charts in Western [[geomancy]].
| |
| | |
| 65536 is a zip code in [[Lebanon, MO]].
| |
| | |
| == References ==
| |
| {{reflist}}
| |
| | |
| [[Category:Integers|69e04 65536]]
| |
Hi there. Let me begin by introducing the writer, her name is Sophia. For years she's been living in Kentucky but her husband desires them to move. My day job is an invoicing officer but I've currently utilized for an additional 1. What I adore doing is soccer but I don't have the time lately.
my blog: psychics online (fashionlinked.com)