View source for 6

{{Short description|Integer number 6}}
{{About|the number|the years|6 BC|and|AD 6|other uses|6 (disambiguation)|and|Number Six (disambiguation)}}
{{Distinguish|Voiceless alveolo-palatal fricative}}
{{pp-pc|small=yes}}
{{Infobox number
|number=6
|numeral=[[senary]]
|divisor=1, 2, 3, 6
|roman =VI, vi, ↅ
|greek prefix=[[Wiktionary:hexa-|hexa-]]/[[Wiktionary:hex-|hex-]]
|latin prefix=[[Wiktionary:sexa-|sexa-]]/[[Wiktionary:sex-|sex-]]
|lang1=[[Greek numerals|Greek]]
|lang1 symbol=στ (or ΣΤ or ς)
|lang2=[[Arabic]], [[Central Kurdish|Kurdish]], [[Sindhi language|Sindhi]], [[Urdu numerals|Urdu]]|lang2 symbol={{resize|150%|٦}}
|lang3=[[Persian language|Persian]]
|lang3 symbol={{resize|150%|۶}}
|lang4=[[Amharic language|Amharic]]
|lang4 symbol=፮
|lang5=[[Bengali language|Bengali]]
|lang5 symbol={{resize|150%|৬}}
|lang6=[[Chinese numeral]]
|lang6 symbol=六，陸
|lang7=[[Devanāgarī]]
|lang7 symbol={{resize|150%|६}}
|lang8=[[Santali language|Santali]]
|lang8 symbol={{resize|150%|᱖}}
|lang9=[[Gujarati alphabet|Gujarati]]
|lang9 symbol={{resize|150%|૬}}
|lang10=[[Hebrew (language)|Hebrew]]
|lang10 symbol={{resize|150%|ו}}
|lang11=[[Khmer numerals|Khmer]]
|lang11 symbol=៦
|lang12=[[Thai numerals|Thai]]
|lang12 symbol=๖
|lang13=[[Telugu language|Telugu]]
|lang13 symbol=౬
|lang14=[[Tamil numerals|Tamil]]
|lang14 symbol=௬
|lang15=[[Saraiki language|Saraiki]]
|lang15 symbol={{resize|150%|٦}}
|lang16=[[Malayalam numerals|Malayalam]]
|lang16 symbol=൬
|lang17=[[Armenian numerals|Armenian]]|lang17 symbol=Զ|lang18=[[Babylonian cuneiform numerals|Babylonian numeral]]|lang18 symbol=𒐚|lang19=[[Egyptian numerals|Egyptian hieroglyph]]|lang19 symbol={{resize|200%|𓏿}}|lang20=[[Morse code]]|lang20 symbol={{resize|150%|_ ....}}}}
'''6''' ('''six''') is the [[natural number]] following [[5]] and preceding [[7]]. It is a [[composite number]] and the smallest [[perfect number]].<ref name=":0" />

==In mathematics==
A six-sided [[polygon]] is a [[hexagon]],<ref name=":0" /> one of the three [[regular polygon]]s capable of [[tessellation|tiling the plane]]. A hexagon also has 6 [[Edge (geometry)|edges]] as well as 6 [[internal and external angles]].

6 is the second smallest [[composite number]].<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=6|url=https://mathworld.wolfram.com/6.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> It is also the first number that is the sum of its proper divisors, making it the smallest [[perfect number]].<ref>{{cite book |title=Number Story: From Counting to Cryptography |url=https://archive.org/details/numberstoryfromc00higg_612 |url-access=registration |last=Higgins |first=Peter |year=2008 |publisher=Copernicus |location=New York |isbn=978-1-84800-000-1 |page=[https://archive.org/details/numberstoryfromc00higg_612/page/n20 11] }}</ref> It is also the only perfect number that doesn't have a [[digital root]] of 1.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Perfect Number |url=https://mathworld.wolfram.com/PerfectNumber.html |access-date=2025-03-20 |website=mathworld.wolfram.com |language=en}}</ref> 6 is the first [[unitary perfect number]], since it is the sum of its positive proper [[unitary divisor]]s, without including itself. Only five such numbers are known to exist.<ref>{{Cite OEIS|A002827|Unitary perfect numbers|access-date=2016-06-01}}</ref> 6 is the largest of the four [[Harshad number|all-Harshad number]]s.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Harshad Number|url=https://mathworld.wolfram.com/HarshadNumber.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> 

6 is the 2nd [[superior highly composite number]],<ref>{{Cite web |title=A002201 - OEIS |url=https://oeis.org/A002201 |access-date=2024-11-28 |website=oeis.org}}</ref> the 2nd [[colossally abundant number]],<ref>{{Cite web |title=A004490 - OEIS |url=https://oeis.org/A004490 |access-date=2024-11-28 |website=oeis.org}}</ref> the 3rd [[triangular number]],<ref>{{Cite web |title=A000217 - OEIS |url=https://oeis.org/A000217 |access-date=2024-11-28 |website=oeis.org}}</ref> the 4th [[highly composite number]],<ref>{{Cite web |title=A002182 - OEIS |url=https://oeis.org/A002182 |access-date=2024-11-28 |website=oeis.org}}</ref> a [[pronic number]],<ref>{{Cite web|url=https://oeis.org/A002378|title=Sloane's A002378: Pronic numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2020-11-30}}</ref> a [[congruent number]],<ref>{{Cite OEIS|A003273|Congruent numbers|access-date=2016-06-01}}</ref> a [[harmonic divisor number]],<ref>{{Cite web |title=A001599 - OEIS |url=https://oeis.org/A001599 |access-date=2024-11-28 |website=oeis.org}}</ref> and a [[semiprime]].<ref>{{Cite OEIS|A001358 |Semiprimes (or biprimes): products of two primes. |access-date=2023-08-03 }}</ref> 6 is also the first [[Granville number]], or <math>\mathcal{S}</math>-perfect number. A [[Golomb ruler]] of length 6 is a "perfect ruler".<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 72</ref>

The [[six exponentials theorem]] guarantees that under certain conditions one of a set of six exponentials is [[Transcendental number|transcendental]].<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Six Exponentials Theorem|url=https://mathworld.wolfram.com/SixExponentialsTheorem.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref> The smallest non-[[abelian group]] is the [[symmetric group]] <math>\mathrm {S_{3}}</math> which has [[factorial|3!]] = 6 elements.<ref name=":0" /> 6 the answer to the two-dimensional [[kissing number problem]].<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Kissing Number |url=https://mathworld.wolfram.com/KissingNumber.html |access-date=2020-08-03 |website=mathworld.wolfram.com |language=en}}</ref>

[[File:120px-Hexahedron-slowturn.gif|left|thumb|A regular [[cube]], with six [[Face (geometry)|faces]]]]

A [[cube]] has 6 [[Face (geometry)|face]]s. A [[tetrahedron]] has 6 [[Edge (geometry)|edges]]. In [[Four-dimensional space|four dimensions]], there are a total of six [[Convex regular 4-polytope|convex regular polytopes]].

In the [[classification of finite simple groups]], twenty of twenty-six [[sporadic group]]s in the [[Sporadic group#Organization|happy family]] are part of three families of groups which divide the order of the [[Monster group|friendly giant]], the largest sporadic group: five ''first generation'' [[Mathieu group]]s, seven ''second generation'' [[subquotient]]s of the [[Leech lattice]], and eight ''third generation'' [[subgroup]]s of the friendly giant. The remaining '''six''' sporadic groups do not divide the order of the friendly giant, which are termed the ''[[Pariah group|'''pariahs''']]'' ([[Lyons group|''Ly'']], [[O'Nan group|''O'N'']], [[Rudvalis group|''Ru'']], [[Janko group J4|''J''<sub>4</sub>]], [[Janko group J3|''J''<sub>3</sub>]], and [[Janko group J1|''J''<sub>1</sub>]]).<ref>{{Cite journal |last=Griess, Jr. |first=Robert L. |url=https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46608/222_2005_Article_BF01389186.pdf?sequence=1 |title=The Friendly Giant |journal=[[Inventiones Mathematicae]] |volume=69 |date=1982 |pages=91–96 |doi=10.1007/BF01389186 |bibcode=1982InMat..69....1G  |hdl=2027.42/46608 |mr=671653 |zbl=0498.20013 |s2cid=123597150 }}</ref>

6 is the smallest integer which is not an exponent of a [[prime number]], making it the smallest integer greater than 1 for which there does not exist a [[finite field]] of that size.<ref>{{Cite book |last=Dummit |first=David S. |title=Abstract algebra |last2=Foote |first2=Richard M. |date=2009 |publisher=Wiley |isbn=978-0-471-43334-7 |edition=3. ed., [Nachdr.] |location=New York}}</ref>

===List of basic calculations===
{|class="wikitable" style="text-align: center; background: white"
|-
! style="width:105px;"|[[Multiplication]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
!25
!50
!100
!1000
|-
|'''6 × ''x'''''
|'''6'''
|[[12 (number)|12]]
|[[18 (number)|18]]
|[[24 (number)|24]]
|[[30 (number)|30]]
|[[36 (number)|36]]
|[[42 (number)|42]]
|[[48 (number)|48]]
|[[54 (number)|54]]
|[[60 (number)|60]]
|[[66 (number)|66]]
|[[72 (number)|72]]
|[[78 (number)|78]]
|[[84 (number)|84]]
|[[90 (number)|90]]
|[[96 (number)|96]]
|[[102 (number)|102]]
|[[108 (number)|108]]
|[[114 (number)|114]]
|[[120 (number)|120]]
|[[150 (number)|150]]
|[[300 (number)|300]]
|[[600 (number)|600]]
|[[6000 (number)|6000]]
|}

{|class="wikitable" style="text-align: center; background: white"
|-
! style="width:105px;"|[[Division (mathematics)|Division]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
! style="width:5px;"|
!11
!12
!13
!14
!15
|-
|'''6 ÷ ''x'''''
|'''6'''
|3
|2
|1.5
|1.2
|1
|0.{{overline|857142}}
|0.75
|0.{{overline|6}}
|0.6
!
|0.{{overline|54}}
|0.5
|0.{{overline|461538}}
|0.{{overline|428571}}
|0.4
|-
|'''''x'' ÷ 6'''
|0.1{{overline|6}}
|0.{{overline|3}}
|0.5
|0.{{overline|6}}
|0.8{{overline|3}}
|1
|1.1{{overline|6}}
|1.{{overline|3}}
|1.5
|1.{{overline|6}}
!
|1.8{{overline|3}}
|2
|2.1{{overline|6}}
|2.{{overline|3}}
|2.5
|}

{|class="wikitable" style="text-align: center; background: white"
|-
! style="width:105px;"|[[Exponentiation]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
! style="width:5px;"|
!11
!12
!13
|-
|'''6{{sup|''x''}}'''
|'''6'''
|36
|[[216 (number)|216]]
|1296
|7776
|46656
|279936
|1679616
|10077696
|60466176
!
|362797056
|2176782336
|13060694016
|-
|'''''x''{{sup|6}}'''
|1
|[[64 (number)|64]]
|729
|4096
|15625
|46656
|117649
|262144
|531441
|[[1000000 (number)|1000000]]
!
|1771561
|2985984
|4826809
|}

==Greek and Latin word parts==

===''{{lang|grc-Latn|Hexa}}''===
'''''{{lang|grc-Latn|Hexa}}''''' is classical [[Greek language#Periods|Greek]] for "six".<ref name=":0" /> Thus:
*"[[Hexadecimal]]" combines ''{{lang|grc-Latn|hexa-}}'' with the Latinate ''{{lang|la|decimal}}'' to name a [[number base]] of 16<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Hexadecimal|url=https://mathworld.wolfram.com/Hexadecimal.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
*A [[hexagon]] is a [[regular polygon]] with six sides<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Hexagon|url=https://mathworld.wolfram.com/Hexagon.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
**''{{lang|fr|L'Hexagone}}'' is a French nickname for the continental part of [[Metropolitan France]] for its resemblance to a [[hexagon#Regular hexagon|regular hexagon]]
*A [[hexahedron]] is a [[polyhedron]] with six faces, with a [[cube (geometry)|cube]] being a special case<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Hexahedron|url=https://mathworld.wolfram.com/Hexahedron.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
*[[Hexameter]] is a poetic form consisting of six feet per line
*A "hex nut" is a [[nut (hardware)|nut]] with six sides, and a hex [[Screw|bolt]] has a six-sided head
*The prefix "{{lang|grc-Latn|hexa-}}" also occurs in the [[systematic name]] of many [[chemical compound]]s, such as [[hexane]] which has 6 carbon atoms ({{chem2|C6H14}}).

===The prefix ''sex-''===
'''''Sex-''''' is a [[Latin]] [[Prefix (linguistics)|prefix]] meaning "six".<ref name=":0" /> Thus:
*''Senary'' is the ordinal adjective meaning "sixth"<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Base|url=https://mathworld.wolfram.com/Base.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>
*People with [[sexdactyly]] have six fingers on each hand
*The measuring instrument called a [[sextant]] got its name because its shape forms one-sixth of a whole [[circle]]
*A group of six musicians is called a [[sextet]]
*Six babies delivered in one birth are [[sextuplet]]s
*[[Sexy prime]] pairs – Prime pairs differing by six are ''sexy'', because sex is the Latin word for six.<ref>{{cite book |last1=Chris K. Caldwell |last2=G. L. Honaker Jr. |date=2009 |title=Prime Curios!: The Dictionary of Prime Number Trivia |url=https://primes.utm.edu/curios/ |publisher=CreateSpace Independent Publishing Platform |page=11 |isbn=978-1-4486-5170-2 }}</ref><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Sexy Primes|url=https://mathworld.wolfram.com/SexyPrimes.html|access-date=2020-08-03|website=mathworld.wolfram.com|language=en}}</ref>

The [[SI prefix]] for 1000<sup>6</sup> is [[exa-]] (E), and for its reciprocal [[atto-]] (a).

==Evolution of the Hindu-Arabic digit==
[[File:Edicts of Ashoka numerals.jpg|thumb|upright=1.5|The first appearance of 6 is in the [[Edicts of Ashoka]] {{Circa|250 BCE}}. These are [[Brahmi numerals]], ancestors of Hindu-Arabic numerals.]]
[[File:Ashoka Brahmi numerals 256.jpg|thumb|right|upright=0.6|The first known digit "6" in the number "256" in Ashoka's [[Minor Rock Edict]] No.1 in [[Sasaram]], {{Circa|250 BCE}}]]
The evolution of the modern digit 6 appears to be more simple when compared with the other digits. The modern 6 can be traced back to the [[Brahmi numerals]] of [[India]], which are first known from the [[Edicts of Ashoka]] {{Circa|250 BCE}}.<ref>{{cite book |last1=Hollingdale |first1=Stuart |title=Makers of Mathematics |date=2014 |publisher=Courier Corporation |isbn=978-0-486-17450-1 |pages=95–96 |url=https://books.google.com/books?id=ZET_AwAAQBAJ&pg=PA95 |language=en}}</ref><ref>{{cite book |last1=Publishing |first1=Britannica Educational |title=The Britannica Guide to Theories and Ideas That Changed the Modern World |date=2009 |publisher=Britannica Educational Publishing |isbn=978-1-61530-063-1 |page=64 |url=https://books.google.com/books?id=QcOcAAAAQBAJ&pg=PA65 |language=en}}</ref><ref>{{cite book |last1=Katz |first1=Victor J. |last2=Parshall |first2=Karen Hunger |title=Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century |date=2014 |publisher=Princeton University Press |isbn=978-1-4008-5052-5 |page=105 |url=https://books.google.com/books?id=nQLHAgAAQBAJ&pg=PA105 |language=en}}</ref><ref>{{cite book |last1=Pillis |first1=John de |title=777 Mathematical Conversation Starters |date=2002 |publisher=MAA |isbn=978-0-88385-540-9 |page=286 |url=https://books.google.com/books?id=YB4wS-N9qb0C&pg=PA286 |language=en}}</ref> It was written in one stroke like a cursive lowercase e rotated 90 degrees clockwise. Gradually, the upper part of the stroke (above the central squiggle) became more curved, while the lower part of the stroke (below the central squiggle) became straighter. The Arabs dropped the part of the stroke below the squiggle. From there, the European evolution to our modern 6 was very straightforward, aside from a flirtation with a glyph that looked more like an uppercase G.<ref>Georges Ifrah, ''The Universal History of Numbers: From Prehistory to the Invention of the Computer'' transl. David Bellos et al. London: The Harvill Press (1998): 395, Fig. 24.66</ref>

On the [[seven-segment display]]s of calculators and watches, 6 is usually written with six segments. Some historical calculator models use just five segments for the 6, by omitting the top horizontal bar. This glyph variant has not caught on; for calculators that can display results in hexadecimal, a 6 that looks like a "b" is not practical.

Just as in most modern [[typeface]]s, in typefaces with [[text figures]] the character for the digit 6 usually has an [[Ascender (typography)|ascender]], as, for example, in [[File:Text figures 036.svg|52px]].<ref>{{Cite book|last=Negru|first=John|url=https://books.google.com/books?id=4A9UAAAAMAAJ&q=text+figures+the+6+character+usually+has+an+ascender,|title=Computer Typesetting|date=1988|publisher=Van Nostrand Reinhold|isbn=978-0-442-26696-7|page=59|language=en|quote=slight ascenders that rise above the cap height ( in 4 and 6 )}}</ref>

This digit resembles an inverted ''9''. To disambiguate the two on objects and documents that can be inverted, the 6 has often been underlined, both in handwriting and on printed labels.

[[File:Bienenwabe mit Eiern und Brut 5.jpg|thumb|150px|The cells of a [[beehive]] are six-sided.]]

==Chemistry==
[[File:Benzene structure.png|200px|right|A [[molecule]] of [[benzene]] has a [[Aromaticity|ring]] of six [[carbon]] and six [[hydrogen]] [[atom]]s.]]
*The sixfold [[symmetry]] of [[snowflake]]s arises from the [[hexagon]]al [[crystal structure]] of [[Ice|ordinary ice]].<ref>{{Cite book|last1=Webb|first1=Stephen|url=https://books.google.com/books?id=3AJdTYu3m5sC&q=sixfold+symmetry+of+snowflakes+arises+from+the+hexagonal+crystal&pg=PA16|title=Out of this World: Colliding Universes, Branes, Strings, and Other Wild Ideas of Modern Physics|last2=Webb|first2=Professor of Australian Studies Stephen|date=2004-05-25|publisher=Springer Science & Business Media|isbn=978-0-387-02930-6|page=16|language=en|quote=snowflake, with its familiar sixfold rotational symmetry}}</ref>

==Anthropology==
*A [[coffin]] is traditionally buried six feet under the ground; thus, the phrase "six feet under" means that a person (or thing, or concept) is dead.<ref>{{Cite web|last=Rimes|first=Wendy|date=2016-04-01|title=The Reason Why The Dead Are Buried Six Feet Below The Ground|url=https://www.elitereaders.com/six-feet-under-ground-explanation/|access-date=2020-08-06|website=Elite Readers|language=en-US}}</ref>
*Six is a lucky [[numbers in Chinese culture|number in Chinese culture]].<ref>"Chinese Numbers 1 to 10 | maayot". ''maayot • Bite-size daily Chinese stories''. 2021-11-22. Retrieved 2025-01-17.</ref>
*"Six" is used as an informal slang term for the British [[Secret Intelligence Service]], MI6.<ref>{{Cite book|last=Smith|first=Michael|url=https://books.google.com/books?id=qvCtAwAAQBAJ&q=SIX:+A+History+of+Britain's+Secret+Intelligence+Service|title=Six: The Real James Bonds 1909-1939|date=2011-10-31|publisher=Biteback Publishing|isbn=978-1-84954-264-7|language=en}}</ref>

== See also ==
*[[Six degrees (disambiguation)]].

==References==
{{Reflist}}
*{{cite journal
| title=The 'odd' number six
| last1=Todd | first1=J. A. | authorlink1=J. A. Todd
| journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]]
| volume=41
| issue=1
| date=1945
| pages=66–68
| doi=10.1017/S0305004100022374}}
*''A Property of the Number Six'', Chapter 6, P Cameron, JH v. Lint, ''Designs, Graphs, Codes and their Links'' {{ISBN|0-521-42385-6}}
*Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 67 - 69

==External links==
{{Wiktionary|six}}
*[https://web.archive.org/web/20161023134003/http://numdic.com/6 The Number 6]
*[http://www.positiveintegers.org/6 The Positive Integer 6]
*[http://primes.utm.edu/curios/page.php/6.html Prime curiosities: 6]

{{Integers|zero}}
{{Authority control}}

{{DEFAULTSORT:6 (Number)}}
[[Category:Integers]]
[[Category:6 (number)]]