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{{Infobox number
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| number = 121
| divisor = 1, 11, 121
}}
'''121''' ('''one hundred [and] twenty-one''') is the [[natural number]] following [[120 (number)|120]] and preceding [[122 (number)|122]].
 
==In mathematics==
 
'''One hundred [and] twenty-one''' is a [[Square (algebra)|square]] and is the sum of three consecutive [[prime number|prime]]s (37 + 41 + 43). There are no squares besides 121 known to be of the form <math>1 + p + p^2 + p^3 + p^4</math>, where ''p'' is prime (3, in this case). Other such squares must have at least 35 digits.
 
There are only two other squares known to be of the form n! + 1, supporting [[Brocard's conjecture]]. Another example of 121 being of the few examples supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form ''x''<sup>3</sup> - 4 (with ''x'' being 2 and 5, respectively).<ref>Wells, D., ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'', London: Penguin Group. (1987): 136</ref>
 
It is also a [[star number]] and a [[centered octagonal number]].
[[File:Chinese checkers start positions.svg|thumb|left|A [[Chinese checkers]] board has 121 holes]]
In base 10, it is a [[Smith number]] since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a [[Friedman number]] (11^2). But it can not be expressed as the sum of any other number plus that number's digits, making 121 a [[self number]].
 
==In other fields==
 
121 is also:
* The [[electricity]] [[emergency telephone number]] in [[Egypt]]
* The number for [[voicemail]] for [[mobile phone]]s on the [[Vodafone]] network<ref>Vodafone, [http://www.vodafone.co.uk/business/mobile-phones/calling-and-messaging/ Calling and messaging]</ref>
* The undiscovered [[chemical element]] [[Unbiunium]] has the atomic number 121
* The official end score for [[Cribbage]]<ref>[http://www.cribbage.org/rules/rule1.asp#section1 Rule 1.1], [[American Cribbage Congress]], retrieved 6 September 2011</ref>
 
==See also==
* [[List of highways numbered 121]]
* [[United States House of Representatives House Resolution 121]]
* [[United Nations Security Council Resolution 121]]
 
==References==
 
<references/>
 
{{Integers|1}}
 
{{DEFAULTSORT:121 (Number)}}
[[Category:Integers]]

Latest revision as of 19:28, 31 October 2014

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