666 (number)

This article is about the numerical value. For the year 666 AD, see AD 666. For other uses, see 666 (disambiguation).

"1010011010" redirects here. For the song, see 1010011010 (Cog song).

666 (six hundred [and] sixty-six) is the natural number following 665 and preceding 667.

← 665 666 667 →
List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	six hundred sixty-six
Ordinal	666th (six hundred sixty-sixth)
Factorization	2 × 32 × 37
Divisors	1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
Greek numeral	ΧΞϚ´
Roman numeral	DCLXVI
Greek prefix	ἑξακόσιοι ἑξήκοντα ἕξ hexakósioi hexēkonta héx
Latin prefix	sescenti sexaginta sex
Binary	10100110102
Ternary	2202003
Senary	30306
Octal	12328
Duodecimal	47612
Hexadecimal	29A16
Chinese numeral	六百六十六
Devanagari numeral	६६६

In Christianity, 666 is referred to in most manuscripts of chapter 13 of the Book of Revelation of the New Testament as the "number of the beast."^[1][2][3]

In mathematics

666 is the sum of the first thirty-six natural numbers, which makes it a triangular number:^[4]

${\displaystyle \sum _{i=1}^{36}i=1+2+3+\cdots +34+35+36=666}$.

Since 36 is a triangular number too, 666 is a doubly triangular number.^[5]

Also, 666 is the sum of two consecutive squares of Triangular numbers:

666 = 225 + 441 → 15² + 21²,

Which can be expressed

T(6²) = T(05)² + T(06)² → T(05)² + T(T3)².

While the secret value of 666 is:

36 = 15 + 21,

Which can be expressed

6² = T(05) + T(06) → T(05) + T(T3).^[6]

The difference of 21² and 15² is:

216 = 6 × 36 or 6 × 6 × 6,

Which can be expressed:

216 = T(3) × T(3)²

The number of integers which are relatively prime to 666 is also 216, ${\displaystyle \phi (666)=216}$;^[7] and for an angle measured in degrees, ${\displaystyle \sin {(666^{\circ })}=\cos {(216^{\circ })}=-{\tfrac {\varphi }{2}}}$ (where here ${\displaystyle \varphi }$ is the golden ratio).^[8][9][a]

666 is also the sum of the squares of the first seven primes (2² + 3² + 5² + 7² + 11² + 13² + 17²),^[8][11] while the number of twin primes less than 6⁶ + 666 is 666.^[12]

A prime reciprocal magic square based on ${\displaystyle {\tfrac {1}{149}}}$ in decimal has a magic constant of 666. The twelfth pair of twin primes is (149, 151),^[13] with 151 the thirty-sixth prime number.^[b]

666 is a Smith number and Harshad number in base ten.^[14][15] The 27th indexed unique prime in decimal features a "666" in the middle of its sequence of digits.^[16][c]

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).^[8]

In Christian religion

Number of the beast

666 is often associated with the devil, who is illustrated here in an engraved interpretation by Gustave Doré.

Main article: Number of the beast

In the Textus Receptus manuscripts of the New Testament, the Book of 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 the Beast, an antagonistic creature that appears briefly about two-thirds into the apocalyptic vision. Some manuscripts^[which?] of the original Koine Greek use the symbols χξϛ chi xi stigma (or χξϝ with a digamma), while other manuscripts spell out the number in words.^[17]

In modern popular culture, 666 has become one of the most widely recognized symbols for the Antichrist or, alternatively, the devil. Earnest references to the number occur both among 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 666 transferred to the 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 in some early biblical manuscripts, the earliest known instance being in Papyrus 115.^[18][19]

Other occurrences

• In the Bible, 666 is the number of talents of gold Solomon collected each year (see 1 Kings 10:14 and 2 Chronicles 9:13).
• In the Bible, 666 is the number of Adonikam's descendants who return to Jerusalem and Judah from the Babylonian exile (see Ezra 2:13).
• Using gematria, 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 Nero, who was the Roman emperor from 55 to 68 AD.^[20] However, historic protestants such as Andreas Helwig in 1612 proposed the application of the Isopsephy principle to the papal name Vicarius Filii Dei.^[21]

In other fields

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 constants of a six by six 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).^[20] This is a corollary of the fact that the number is a Triangular number, as mentioned earlier.
• 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.^[22]
• Was the original name of the Macintosh SevenDust computer virus that was discovered in 1998.^{[citation needed]} It is also the name of an extension that SevenDust can add to an uninfected Macintosh.^[23]
• The number is a frequent visual element of Aryan Brotherhood tattoos.^[24]
• Aleister Crowley adopted the title "the Beast 666".^[25] As such, 666 is also associated with him, his work, and his religious philosophy of Thelema.
• Molar mass of the high-temperature superconductor YBa₂Cu₃O₇.
• In Chinese numerology, the number is considered to be lucky and is often displayed in shop windows and neon signs.^[26][27] In China, 666 can mean "everything goes smoothly" (the number six has the same pronunciation as the character 溜, which means "smooth".^[28]
• Is commonly used by ISPs to blackhole traffic using BGP communities.^[29]
• 666 Fifth Avenue in New York City, which was bought for $1.8 billion in 2007, was the most expensive real estate deal in New York's history.^[30]

See also

• Mathematics portal

• Numerology

Notes

1. Other relevant trigonometric equalities include:^[10]

   • sin(6°) − sin(66°) = sin(666°),
   • cos(6°) − cos(66°) = cos(666°), and
   • tan(666°) × tan(216°) = −1.

   Where, sin(666°) = cos(216°) = −⁠φ/2⁠, also equivalently −cos(36°).
2. 149 and 151 also generate a twin-prime sum equal to 300, which is the 24th triangular number.
3. It is the number 11110...109877666779011...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 indexed member within the sequence of unique primes (where 3³ = 27).