666

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666
Cardinal Six hundred sixty-six
Ordinal 666th
Factorization \begin{smallmatrix} 2 \cdot 3^2 \cdot 37 \end{smallmatrix}
Greek numeral χξϛʹ[1]
Roman numeral DCLXVI
Chinese numeral 六百六十六
Binary 1010011010
Octal 1232
Hexadecimal 29A
Base12 476, i.e. 04 07 06
Base32 KQ
Base36 II
Base60 11 06

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

Contents

In mathematics

666 is the sum of the first 36 natural numbers (i.e.  1 + 2 + 3+  ... + 34 + 35 + 36 = 666), and thus a triangular number.

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 (D=500, C=100, L=50, X=10, V=5, I=1).

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

The sine of the angle 666° multiplied by -2 is equal to the golden ratio:

-2 \sin 666^\circ = 2 \sin 54^\circ = 2 \cos 36^\circ = \varphi\, = \frac{1 + \sqrt{5}}{2} = 1.61803\,39887\ldots\,

The Number of the Beast

666 is often associated with the Devil.

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.

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 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 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 to 36).
  • 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.[2]
  • 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 band Genesis' masterpiece, Supper's Ready, contains the lyric, "666 is no longer alone"

See also

References

External links


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Officer 666 (1914 Film)