|
|
| Line 1: |
Line 1: |
| {{Infobox number
| | Individual who wrote the guide is called Eusebio. South Carolina is your boyfriend's birth place. The favourite hobby for him as well as the his kids is to fish and he's resulted in being doing it for quite some time. Filing has been his profession for some time. Go to his website to discover a out more: http://circuspartypanama.com<br><br>Have a look at my web site [http://circuspartypanama.com clash of clans generator] |
| | number = 68
| |
| | divisor = 1, 2, 4, 17, 34, 68
| |
| }}
| |
| '''68''' ('''sixty-eight''') is the [[natural number]] following [[67 (number)|67]] and preceding [[69 (number)|69]].
| |
| | |
| ==In mathematics==
| |
| 68 is a [[Perrin number]].<ref>{{SloanesRef|sequencenumber=A001608|name=Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3)}}</ref>
| |
| | |
| It is the largest known number to be the sum of two primes in exactly two different ways: 68 = 7 + 61 = 31 + 37.<ref>http://math.fau.edu/richman/Interesting/WebSite/Number68.pdf retrieved 13 March 2013</ref> All higher even numbers that have been checked are the sum of three or more pairs of primes; the conjecture that 68 is the largest number with this property is closely related to the [[Goldbach conjecture]] and like it remains unproven.<ref>{{SloanesRef|sequencenumber=A000954|name=Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways}}</ref>
| |
| | |
| Because of the factorization of 68 as <math>2^2\cdot (2^{2^2}+1)</math>, a 68-sided [[regular polygon]] may be constructed with [[compass and straightedge]].<ref>{{SloanesRef|sequencenumber=A003401|name=Numbers of edges of polygons constructible with ruler and compass}}</ref>
| |
| | |
| [[File:Tamari lattice.svg|thumb|A Tamari lattice, with 68 upward paths of length zero or more from one element of the lattice to another.]]
| |
| There are exactly 68 10-bit [[binary number]]s in which each bit has an adjacent bit with the same value,<ref>{{SloanesRef|sequencenumber=A006355|name=Number of binary vectors of length n containing no singletons}}</ref> exactly 68 combinatorially distinct [[Point set triangulation|triangulations]] of a given triangle with four points interior to it,<ref name="A000260">{{SloanesRef|sequencenumber=A000260|name=Number of rooted simplicial 3-polytopes with n+3 nodes}}</ref>and exactly 68 [[Partially ordered set#Interval|intervals]] in the [[Tamari lattice]] describing the ways of parenthesizing five items.<ref name="A000260"/> The largest [[graceful graph]] on 13 nodes has exactly 68 edges.<ref>{{SloanesRef|sequencenumber=A004137|name=Maximal number of edges in a graceful graph on n nodes}}</ref> There are 68 different [[undirected graph]]s with six edges and no isolated nodes,<ref>{{SloanesRef|sequencenumber=A000664|name=Number of graphs with n edges}}</ref> 68 different minimally [[k-vertex-connected graph|2-connected graphs]] on seven unlabeled nodes,<ref>{{SloanesRef|sequencenumber=A003317|name=Number of unlabeled minimally 2-connected graphs with n nodes (also called "blocks")}}</ref> 68 different [[degree sequence]]s of four-node connected graphs,<ref>{{SloanesRef|sequencenumber=A007721|name=Number of distinct degree sequences among all connected graphs with n nodes}}</ref> and 68 [[matroid]]s on four labeled elements.<ref>{{SloanesRef|sequencenumber=A058673|name=Number of matroids on n labeled points}}</ref>
| |
| | |
| [[Størmer's theorem]] proves that, for every number ''p'', there are a finite number of pairs of consecutive numbers that are both [[smooth number|''p''-smooth]] (having no prime factor larger than ''p''). For ''p'' = 13 this finite number is exactly 68.<ref>{{SloanesRef|sequencenumber=A002071|name=Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime}}</ref> On an infinite chessboard, there are 68 squares three knight's moves away from any cell.<ref>{{SloanesRef|sequencenumber=A018842|name=Number of squares on infinite chess-board at n knight's moves from center}}</ref>
| |
| | |
| As a [[decimal number]], 68 is the last two-digit number to appear in the digits of [[pi]].<ref>{{SloanesRef|sequencenumber=A032510|name=Scan decimal expansion of Pi until all n-digit strings have been seen; a(n) is last string seen}}</ref> It is a [[happy number]], meaning that repeatedly summing the squares of its digits eventually leads to 1:<ref>{{SloanesRef|sequencenumber=A007770|name=Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map includes 1}}</ref>
| |
| :<math>68\to 6^2+8^2=100\to 1^2+0^2+0^2=1.</math>
| |
| | |
| ==Other uses==
| |
| *68 is the [[atomic number]] of [[erbium]], a lanthanide
| |
| *In the restaurant industry, 68 may be used as a code meaning "put back on the menu", being the opposite of [[86 (number)|86]] which means "remove from the menu".<ref>{{citation|title=Words at Work: An Insider’s Guide to the Language of Professions|first=Mim|last=Harrison|publisher=Bloomsbury Publishing USA|year=2009|isbn=9780802718686|page=7|url=http://books.google.com/books?id=dAf_HxF1HTwC&pg=PA7}}.</ref>
| |
| *68 may also be used as [[slang]] for [[oral sex]], based on a play on words involving the number [[69 (number)|69]].<ref>{{citation|title=The Concise New Partridge Dictionary of Slang and Unconventional English|first1=Terry|last1=Victor|first2=Tom|last2=Dalzell|edition=8th|publisher=Psychology Press|year=2007|isbn=9780203962114|page=585|url=http://books.google.com/books?id=7UIjVGcSe8MC&pg=PA585}}.</ref>
| |
| | |
| ==See also==
| |
| *[[68 (disambiguation)]]
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| {{Integers|zero}}
| |
| | |
| [[Category:Integers]]
| |
Individual who wrote the guide is called Eusebio. South Carolina is your boyfriend's birth place. The favourite hobby for him as well as the his kids is to fish and he's resulted in being doing it for quite some time. Filing has been his profession for some time. Go to his website to discover a out more: http://circuspartypanama.com
Have a look at my web site clash of clans generator