View source for 666 (number)

{{Infobox number
| number = 666
| lang2 = Chinese numeral
| lang2 symbol = 六百六十六
| lang3 = Devanagari numeral
| lang3 symbol = ६६६
| Greek prefix=ἑξακόσιοι ἑξήκοντα ἕξ<br>hexakósioi hexēkonta héx
| Latin prefix=sescenti sexaginta sex
|divisor=1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666|roman=DCLXVI}}
'''666''' ('''six hundred [and] sixty-six''') is the [[Natural number|natural number]] following [[600 (number)#660s|665]] and preceding [[600 (number)#660s|667]].

In [[Religion:Christianity|Christianity]], 666 is referred to in (most manuscripts of) chapter 13 of the [[Religion:Book of Revelation|Book of Revelation]] of the [[Religion:New Testament|New Testament]] as the "[[Unsolved:Number of the beast|number of the beast]]."<ref>{{bibleverse|Revelation|13|niv}}</ref><ref name = "Beale, 718">Beale, Gregory K. (1999). The Book of Revelation: A Commentary on the Greek Text. Grand Rapids, Michigan: Wm. B. Eerdmans Publishing. p. 718. {{ISBN|080282174X}}. Retrieved 9 July 2012.</ref><ref>{{Cite web|title=The Numerology of the Beast|url=http://people.math.harvard.edu/~elkies/mp666.html|access-date=2021-03-30|website=people.math.harvard.edu}}</ref>

== In mathematics==
'''666''' is the [[Addition|sum]] of the first thirty-six natural numbers, which makes it a [[Triangular number|triangular number]]:<ref name="triang">{{Cite OEIS |A000217 |Triangular numbers |access-date=2023-07-11 }}</ref>

:<math>\sum_{i=1}^{36} i = 1 + 2 + 3 + \cdots + 34 + 35 + 36 = 666</math>. 

Since [[36 (number)|36]] is also triangular, 666 is a [[Doubly triangular number|doubly triangular number]].<ref>{{Cite OEIS |A002817 |Doubly triangular numbers |access-date=2023-07-11 }}</ref> Also, {{nowrap|1=36 = 15 + 21}} where [[15 (number)|15]] and [[21 (number)|21]] are triangular as well, whose [[Square number|squares]] ({{nowrap|1=15<sup>2</sup> = 225}} and {{nowrap|1=21<sup>2</sup> = 441}}) add to 666 and have a difference of {{nowrap|1=216 = 6 × 6 × 6}}. 

The number of integers which are relatively prime to 666 is also [[216 (number)|216]], <math>\phi (666) = 216</math>;<ref>{{Cite OEIS |A000010 |Euler totient function phi(n): count numbers less than or equal to n and prime to n. |access-date=2023-07-11 }}</ref>  and for an [[Angle|angle]] measured in degrees, <math>\sin {(666^{\circ})} = \cos{(216^{\circ})} = -\tfrac {\varphi}{2}</math> (where here <math>\varphi</math> is the [[Golden ratio|golden ratio]]).<ref name="Wells">{{Cite book |last=Wells |first= D. |title=The Penguin Dictionary of Curious and Interesting Numbers |url=https://archive.org/details/penguindictionar0000well_f3y1/mode/2up |url-access=registration |publisher=Penguin Books |location=London |year=1987 |pages=145–146 |isbn=0-14-008029-5 |oclc=39262447 |s2cid=118329153 }}</ref><ref>{{Cite journal |last=Wang |first= Steve C. |title=The Sign of the Devil...and the Sine of the Devil |url=https://paleo.domains.swarthmore.edu/Publications/jrecmath1994.pdf |archive-url=https://web.archive.org/web/20230712105905/https://paleo.domains.swarthmore.edu/Publications/jrecmath1994.pdf |url-status=live |archive-date=2023-07-12 |journal=[[Journal of Recreational Mathematics]] |publisher=Baywood Publishing |volume=26 |issue=3 |pages=201–205 |year=1994 |issn=0022-412X |oclc=938842643 }}</ref>{{efn|1=Other relevant [[Trigonometry|trigonometric]] equalities include:<ref>{{Cite web |last=Bogomolny |first=Alexander |title=Beauty and the Beast - in Trigonometry |url=https://www.cut-the-knot.org/arithmetic/algebra/BeautyBeast.shtml |archive-url=https://web.archive.org/web/20230712105608/https://www.cut-the-knot.org/arithmetic/algebra/BeautyBeast.shtml |url-status=live |archive-date=2023-07-12 |website=Cut The Knot (Interactive Mathematics Miscellany and Puzzles)|access-date=2023-07-11 }}</ref>
*{{math|1=sin(6°) − sin(66°) = sin(666°)}}, 
*{{math|1=cos(6°) − cos(66°) = cos(666°)}}, and
*{{math|1=tan(666°) × tan(216) = −1}}. 

Where, {{math|1=sin(666°) = cos(216)° =}} −{{sfrac|''φ''|''2''}}, also equivalently {{math|1=−cos(36°)}}.}}

666 is also the sum of the squares of the first seven primes {{nowrap|1=(2<sup>2</sup> + 3<sup>2</sup> + 5<sup>2</sup> + 7<sup>2</sup> + 11<sup>2</sup> + 13<sup>2</sup> + 17<sup>2</sup>)}},<ref name="Wells" /><ref>{{Cite OEIS |A024450 |Sum of squares of the first n primes. |access-date=2023-07-12 }}</ref> while the number of twin primes less than {{nowrap|6<sup>6</sup> + 666}} is 666.<ref>{{Cite web |last1=Caldwell |first1=Chris K. |last2=Honaker, Jr. |first2=G. L. |url=https://primes.utm.edu/curios/page.php?short=666 |title=666 |website=PrimeCurios! |publisher=[[PrimePages]] |access-date=2023-07-12 }}
:{{nowrap|1=6<sup>6</sup> + 666 = 47322}}, and the 666th pair of twin primes is (47147, 47149).</ref> 

A [[Prime reciprocal magic square|prime reciprocal magic square]] based on <math>\tfrac {1}{149}</math> in decimal has a [[Magic constant|magic constant]] of 666. The twelfth pair of twin primes is ([[149 (number)|149]], [[151 (number)|151]]),<ref>{{Cite OEIS |A077800 |List of twin primes {p, p+2}. |access-date=2023-07-11 }}</ref> with 151 the thirty-sixth prime number.{{efn|1=149 and 151 also generate a twin-prime sum equal to [[300 (number)|300]], which is the 24th [[Triangular number|triangular number]].}}

666 is a [[Smith number]] and [[Harshad number]] in base ten.<ref>{{Cite OEIS |A006753 |Smith (or joke) numbers: composite numbers n such that sum of digits of n is equal to the sum of digits of prime factors of n (counted with multiplicity). |access-date=2023-07-11 }}</ref><ref>{{Cite OEIS |A005349 |Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits. |access-date=2023-07-12 }}</ref> The 27th indexed [[Unique prime|unique prime]] in decimal features a "666" in the middle of its sequence of [[Numerical digit|digits]].<ref>{{Cite OEIS |A040017 |Prime 3 followed by unique period primes (the period r of 1/p is not shared with any other prime) |access-date=2023-07-11 }}</ref>{{efn|1=It is the number '''11110...109877<span style="color:orange;">666</span>779011...011111''' (241 digits long), with an equal amount of digits (119) that precede and follow a central 666 ''string'' (that also contains all sixes in the number). It is the twenty-seventh [[Sequence|indexed]] member within the sequence of unique primes (where 3<sup>3</sup> = 27).}} 

The Roman numeral for 666, DCLXVI, has exactly one occurrence of all symbols whose value is less than 1000 in decreasing order (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1).<ref name="Wells" />

== In religion ==

=== Number of the beast ===
[[Image:DVinfernoLuciferKingOfHell m.jpg|thumb|666 is often associated with the [[Philosophy:Devil|devil]], who is illustrated here in an engraved interpretation by Gustave Doré.]]
{{Main|Unsolved:Number of the beast}}
In the ''[[Religion:Textus Receptus|Textus Receptus]]'' manuscripts of the [[Religion:New Testament|New Testament]], the [[Religion:Book of Revelation|Book of Revelation]] ({{bibleverse-nb||Revelation|13:17–18|}}) cryptically asserts 666 to be "the man's number" or "the number of a man" (depending on how the text is translated) associated with [[Unsolved:The Beast (Revelation)|the Beast]], an antagonistic creature that appears briefly about two-thirds into the apocalyptic vision. Some manuscripts{{Which|date=May 2019}} of the original [[Social:Koine Greek|Koine Greek]] use the symbols χξϛ chi xi stigma (or χξϝ with a digamma), while other manuscripts spell out the number in words.<ref name="gateway-stephanus">{{cite web|url=http://biblegateway.com/passage/?search=Revelation%2013:18;&version=69;|title=Revelation 13:18|work=Stephanus New Testament|publisher=Bible Gateway|access-date=2006-06-22}}</ref>

In modern popular culture, 666 has become one of the most widely recognized symbols for the [[Unsolved:Antichrist|Antichrist]] or, alternatively, the [[Unsolved:Devil in Christianity|devil]]. Earnest references to the number occur both among [[Unsolved:Apocalypticism|apocalypticist]] Christian groups and in explicitly anti-Christian subcultures.
References in contemporary Western art or literature are, more likely than not, intentional references to ''the Beast'' symbolism. Such popular references are therefore too numerous to list.

It is common to see the symbolic role of the [[Integer|integer]] 666 transferred to the [[Numerical digit|numerical digit]] sequence 6-6-6. Some people take the Satanic associations of 666 so seriously that they actively avoid things related to 666 or the digits 6-6-6. This is known as hexakosioihexekontahexaphobia.

The Number of the Beast is cited as [[616 (number)#The Number of the Beast|616]] in some early biblical manuscripts, the earliest known instance being in Papyrus 115.<ref>''[[Religion:Novum Testamentum Graece|Novum Testamentum Graece]]'', Nestle and Aland, 1991, footnote to verse 13:18 of Revelation, page 659: "{{lang|grc|-σιοι δέκα ἕξ}}" as found in ''C'' [''C''=Codex Ephraemi Rescriptus]; for English see Metzger's ''Textual Commentary on the Greek New Testament'', note on verse 13:18 of Revelation, page 750: "the numeral 616 was also read ..."</ref><ref>{{Cite web|url=http://www.csad.ox.ac.uk/POxy/beast616.htm|archiveurl=http://archive.today/20000301070625/http://www.csad.ox.ac.uk/POxy/beast616.htm|archive-date=2000-03-01|url-status=dead|title=The Other Number of the Beast}}</ref>

=== Other occurrences ===
* In the [[Religion:Bible|Bible]], 666 is the number of talents of gold [[Biography:Solomon|Solomon]] collected each year (see {{bibleverse|1|Kings|10:14}} and {{bibleverse|2|Chronicles|9:13}}).
* In the Bible, 666 is the number of Adonikam's descendants who return to [[Place:Jerusalem|Jerusalem]] and Judah from the Babylonian exile (see {{bibleverse||Ezra|2:13}}).
* Using [[Unsolved:Gematria|gematria]], [[Unsolved:Number of the beast#Nero|Neron Caesar]] transliterated from Greek into Hebrew short-form spelling, '''נרון קסר''', produces the number 666. The Latin spelling of "Nero Caesar" transliterated into Ktiv haser Hebrew, '''נרו קסר''', produces the number 616. Thus, in the Bible, 666 may have been a coded reference to [[Biography:Nero|Nero]], who was the [[Social:Roman emperor|Roman emperor]] from 55 to 68 AD.<ref name="numberphile">{{Cite web |url=http://www.numberphile.com/videos/666.html |title=666 – professors explain Roulette and Nero in detail; numberphile.com |access-date=2013-04-06 |archive-url=https://web.archive.org/web/20130331120143/http://numberphile.com/videos/666.html |archive-date=2013-03-31 |url-status=dead }}</ref> Though historic protestants such as Andreas Helwig in 1612 proposed the application of the [[Unsolved:Isopsephy|Isopsephy]] principle to the papal name [[Religion:Vicarius Filii Dei|Vicarius Filii Dei]].<ref>{{Cite book |last=Helwig |first=Andreas |url=http://archive.org/details/antichristusromanus |title=Antichristus Romanus |date=1512 |publisher=VVttenbergae, Typis Laurentij Seuberlichs}}</ref>

== In other fields ==
[[Image:666parade.jpeg|thumb|A 666 float in a Paris street parade]]

* ''The Number of the Beast'', the 1982 album by English heavy metal band Iron Maiden, references 666 in its title and the album's title song.
* Is the magic sum, or sum of the [[Magic constant|magic constant]]s of a six by six [[Magic square|magic square]], any row or column of which adds up to 111.
* Is the sum of all the numbers on a roulette wheel (0 through 36).<ref name="numberphile"/>
* Was a winning lottery number in the 1980 Pennsylvania Lottery scandal, in which equipment was tampered to favor a 4 or 6 as each of the three individual random digits.<ref>{{Cite news|last=Baer|first=John|date=1980-09-20|title=Six Won $1.2 Million in Rigged Lottery, Pa. Says|language=en-US|newspaper=Washington Post|url=https://www.washingtonpost.com/archive/politics/1980/09/20/six-won-12-million-in-rigged-lottery-pa-says/f08e7f6e-577e-4a4e-8f4d-3862d80e9f17/|access-date=2021-03-18|issn=0190-8286}}</ref>
* Was the original name of the Macintosh [[Software:SevenDust (computer virus)|SevenDust]] computer virus that was discovered in 1998.{{Citation needed|date=January 2022}} It is also the name of an extension that SevenDust can add to an uninfected Macintosh.<ref>{{Cite web|title=Detailed Analysis - Mac/Sevendust-A - Viruses and Spyware - Advanced Network Threat Protection {{!}} ATP from Targeted Malware Attacks and Persistent Threats {{!}} sophos.com - Threat Center|url=https://www.sophos.com/en-us/threat-center/threat-analyses/viruses-and-spyware/Mac~Sevendust-A/detailed-analysis.aspx|access-date=2022-01-24|website=www.sophos.com}}</ref>
* The number is a frequent visual element of Aryan Brotherhood tattoos.<ref name="Brook-2011">{{cite book |last=Brook |first=John Lee  |title=Blood In, Blood Out: The Violent Empire of the Aryan Brotherhood |url=https://books.google.com/books?id=ZGe3vuePkxoC |access-date=10 January 2018 |date=June 2011 |publisher=SCB Distributors |isbn=978-1-900486-80-4 |oclc=793002272}}</ref>
* [[Biography:Aleister Crowley|Aleister Crowley]] adopted the title "the Beast 666".<ref>{{Cite web|title=Aleister Crowley {{!}} Biography, Teachings, Reputation, & Facts {{!}} Britannica|url=https://www.britannica.com/biography/Aleister-Crowley|access-date=2022-01-24|website=www.britannica.com|language=en}}</ref> As such, 666 is also associated with him, his work, and his religious philosophy of [[Philosophy:Thelema|Thelema]].
* [[Physics:Molar mass|Molar mass]] of the [[Physics:High-temperature superconductor|high-temperature superconductor]] [[Chemistry:Yttrium barium copper oxide|YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7</sub>]].
* In [[Unsolved:Chinese numerology|Chinese numerology]], the number is considered to be lucky and is often displayed in shop windows and neon signs.<ref name="China666">{{cite book |last=Mah|first=Adeline Yen|date=2009|title=China: Land of Dragons and Emperors|publisher=Random House Children's Books |url=https://books.google.com/books?id=nEcp5cFeVb0C&q=666+luck+china+smooth+flow&pg=PA7|isbn=978-0375890994|access-date=2013-12-07}}</ref><ref>{{cite web|url=http://au.ibtimes.com/articles/252918/20111121/know-meaning-numbers-chinese-culture.htm#.VFG7feelZeo|title=Know the Meaning of Numbers in Chinese Culture|website=au.ibtimes.com|access-date=2014-10-30|archive-date=2014-11-08|archive-url=https://web.archive.org/web/20141108104138/http://au.ibtimes.com/articles/252918/20111121/know-meaning-numbers-chinese-culture.htm#.VFG7feelZeo|url-status=dead}}</ref> In China, 666 can mean "everything goes smoothly" (the number six has the same pronunciation as the character 溜, which means "smooth".<ref>{{cite web|url=http://www.newsgd.com/culture/culturenews/200606090016.htm|title=666 – Good day, bad day or just another day?|website=www.newsgd.com|access-date=2014-10-30}}</ref>
* Is commonly used by ISPs to [[Black hole (networking)|blackhole]] traffic using BGP communities.<ref>{{IETF RFC|7999}}</ref>
*666 Fifth Avenue in {{wipe|New York City}}, which was bought for $1.8 billion in 2007, was the most expensive real estate deal in New York's history.<ref>{{Cite web|title=What you need to know about 666 Fifth Avenue|url=https://www.cbsnews.com/news/what-you-need-to-know-about-666-fifth-avenue/|access-date=2021-07-29|website=www.cbsnews.com|date=19 June 2017 |language=en-US}}</ref>

==See also==
* [[Unsolved:Numerology|Numerology]]

== Notes ==
{{notelist}}

== References ==
{{Reflist}}

== External links ==
* {{MathWorld|title=Beast Number|urlname=BeastNumber}}
<br />
{{DEFAULTSORT:666 (Number)}}
[[Category:Integers]]

{{Sourceattribution|666 (number)}}