For the year 666 AD, see 666.
← 665 666 667 →
Cardinal six hundred and sixty-six
Ordinal 666th
(six hundred and sixty-sixth)
Factorization 2 · 32· 37
Roman numeral DCLXVI
Binary 10100110102
Ternary 2202003
Quaternary 221224
Quinary 101315
Senary 30306
Octal 12328
Duodecimal 47612
Hexadecimal 29A16
Vigesimal 1D620
Base 36 II36
Greek numeral χξϛʹ[1]
Chinese numeral 六百六十六
Arabic numeral ٦٦٦

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

In mathematics

666 is the sum of the first 36 natural numbers (i.e.  1 + 2 + 3+ ... + 34 + 35 + 36 = 666), and thus it is a triangular number. Notice that 36=15+21; 15 and 21 are also triangular numbers; and 15^2+21^2=225+441=666. (In addition: the sum of the 15th triangular number (120) and the 21st triangular number (231) is the 26th triangular number (351).)

666 is part of a Pythagorean quadruple (320,410,416,666), since 320^2+410^2+416^2=102,400 + 168,100 + 173,056 = 443,556 = 666^2.

Since 36 is both square and triangular, 666 is the sixth number of the form n^2(n^2+1)/2 (sequence A037270 in OEIS) and the eighth number of the form n(n+1)(n^2+n+2)/8 (doubly triangular numbers) (sequence A002817 in OEIS).

The number of prime numbers up to 666 is 121, which is the square of 11, which is the number of prime numbers up to 36.

666 is an abundant number.

The harmonic mean of the decimal digits of 666 is (trivially – all repdigit natural numbers have this property) an integer: 3/(1/6 + 1/6 + 1/6) = 6, making 666 the 54th number with this property.

In base 10, 666 is a repdigit (and therefore a palindromic number) and a Smith number. A prime reciprocal magic square based on 1/149 in base 10 has a magic total of 666.

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).

(60 and 360 were used as bases in Babylonian mathematics, as in the degrees of a circle; 360=10×36 and 666 is the sum of the numbers from 1 to 36.)

666 is 1010011010 in the binary numeral system which is the same as its one’s complement in reverse digit order.

666 is a member of the indices of prime Padovan numbers: 3, 4, 5, 7, 8, 14, 19, 30, 37, 84, 128, 469, 666, 1262, 1573, 2003, 2210, … (sequence A112882 in OEIS).

The sum of the squares of the first seven prime numbers: 2² + 3² + 5² + 7² + 11² + 13² + 17² = 666.

In religion

The Number of the Beast

666 is often associated with the Devil.

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 number of a man,” associated with the beast, an antagonistic creature that appears briefly about two-thirds into the apocalyptic vision. Some manuscripts of the original Greek use the symbols χξϛ chi xi stigma (or ϝ digamma), while other manuscripts spell out the number in words.

In modern popular culture, 666 has become one of the most widely recognized symbols for the Antichrist or, alternatively, the Devil. The number 666 is reportedly used to invoke Satan. 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 not uncommon to see the symbolic role of the integer 666 transferred to the 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.

In some early biblical manuscripts, the number is cited as 616.

Other occurrences

  • In the Bible, 666 is the number of talents of gold Solomon collected each year (see 1 Kings 10:14, 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).
  • In the Bible, there may be a latent reference to 666 in the name of the great sixth-century BC king of Babylon. Commonly spelled Nebuchadnezzar, transliterating from the book of Daniel, the name is Nebuchadrezzar or Nebuchadrezzur in the book of Jeremiah (see Jeremiah 49:28–30). The number of each name can be calculated, since Hebrew letters double as numbers (see Hebrew numerals). Nebuchadrezzar is 663, and Nebuchadrezzur, 669. Midway between the two variants is 666. If the mysteries of Jeremiah are to be related to those of Revelation, Nebuchadrezzar, who came (though bidden by God) to crush God’s people, may prefigure the end-times beast.[2]
  • Using the same system in Hebrew of generating a number from the letters of a name, Neron Caesar written in Hebrew produces the number 666. Thus, in the Bible, 666 may have been a coded reference to Nero the Roman Emperor from 55 to 68 CE.[3]
  • In Kabbalistic Judaism, 666 is the number which represents the creation and perfection of the world. The world was created in 6 days, and there are 6 cardinal directions (North, South, East, West, Up, Down).

In other fields

666 float in a Paris parade

  • 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 (1 through 36).[3]
  • 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.[4]
  • was the original name of the Macintosh SevenDust computer virus that was discovered in 1998.
  • The number is a frequent visual element of Aryan Brotherhood tattoos.
  • Aleister Crowley adopted the namesake ‘the Great Beast 666’. As such, 666 is also associated with him, his work, and his religious philosophy of Thelema.
  • The most common carbon isotope (Carbon-12), the basis of all known life on Earth, consists of 6 protons, 6 neutrons and 6 electrons
  • Molar mass of the high-temperature superconductor YBa2Cu3O7
  • In China the number is considered to be lucky and is often displayed in shop windows and neon signs.[5]

See also

Portal icon Mathematics portal

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