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{{infobox number
| 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]]

Revision as of 21:55, 26 November 2013

Template:Infobox number 65536 is the natural number following 65535 and preceding 65537.

65536 is a power of two: 216 (2 to the 16th power).

65536 is the smallest number with exactly 17 divisors.[1]

In mathematics

65536 is 2222, so in tetration notation 65536 is 42.

When expressed using Knuth's up-arrow notation, 65536 is 2↑16, which is equal to 2↑2↑2↑2, which is equivalent to 2↑↑4 or 2↑↑↑3.

65536 is a superperfect number - a number such that σ(σ(n))=2n.[2]

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 231000 that does not contain the digits 1, 2, 4 or 8 in its decimal representation.[3]

65536 is the largest known number such that the sum of its unitary divisors is prime (1 + 65536 = 65537, which is prime).[4]

In computing

65536 (216) is the number of different values representable in a number of 16 binary digits, also known as a short integer in many computer programming systems. Therefore,

  • The Motorola 68000 family, x86 architecture, and other computing platforms have a word size of 16 bits, representing 65536 possible values. (32- or 64-bit operations are supported equally or better in modern microprocessors.)
  • 65536 is the maximum number of spreadsheet rows supported by Excel 97, Excel 2000, Excel 2002 and Excel 2003 (Excel 2007, 2010 and 2013 support 1,048,576 rows (220)). Text files that are larger than 65536 rows cannot be imported to these versions of Excel.[5]
  • A 16-bit microprocessor chip can directly access 65536 memory addresses, and the 16-bit highcolor graphics standard supports a color palette of 65536 different colors.
  • TCP supports 65536 distinct ports (0-65535).
  • 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

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  1. ↑ Sequence Physiotherapist Rave from Cobden, has hobbies and interests which includes skateboarding, commercial property for sale developers in singapore and coin collecting. May be a travel freak and in recent years made a journey to Wet Tropics of Queensland. in OEIS
  2. ↑

    I had like 17 domains hosted on single account, and never had any special troubles. If you are not happy with the service you will get your money back with in 45 days, that's guaranteed. But the Search Engine utility inside the Hostgator account furnished an instant score for my launched website. Fantastico is unable to install WordPress in a directory which already have any file i.e to install WordPress using Fantastico the destination directory must be empty and it should not have any previous installation files. When you share great information, others will take note. Once your hosting is purchased, you will need to setup your domain name to point to your hosting. Money Back: All accounts of Hostgator come with a 45 day money back guarantee. If you have any queries relating to where by and how to use Hostgator Discount Coupon, you can make contact with us at our site. If you are starting up a website or don't have too much website traffic coming your way, a shared plan is more than enough. Condition you want to take advantage of the worldwide web you prerequisite a HostGator web page, -1 of the most trusted and unfailing web suppliers on the world wide web today. Since, single server is shared by 700 to 800 websites, you cannot expect much speed.



    Hostgator tutorials on how to install Wordpress need not be complicated, especially when you will be dealing with a web hosting service that is friendly for novice webmasters and a blogging platform that is as intuitive as riding a bike. After that you can get Hostgator to host your domain and use the wordpress to do the blogging. Once you start site flipping, trust me you will not be able to stop. I cut my webmaster teeth on Control Panel many years ago, but since had left for other hosting companies with more commercial (cough, cough) interfaces. If you don't like it, you can chalk it up to experience and go on. First, find a good starter template design. When I signed up, I did a search for current "HostGator codes" on the web, which enabled me to receive a one-word entry for a discount. Your posts, comments, and pictures will all be imported into your new WordPress blog.
  3. ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  4. ↑ 65536 at Prime Pages
  5. ↑ Microsoft Help Q120596
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