Number of the Beast (numerology)

666 is most famous as the Number of the Beast in the Book of Revelation of the Christian Bible. In the King James Version, Rev. 13:18 reads:

Here is wisdom: let him who hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.

In the Greek text of the New Testament it reads:

Ωδε η σοφια εστιν: ο εχων νουν ψηφισατω τον αριθμον του θηριου. Αριθμος γαρ ανθρωπου εστιν, και ο αριθμος αυτου εστιν εξακοσιοι εξηκοντα εξ.

Hôde hé sophia estin. Ho ekhôn noun psésiphatô hon arithmon tou thériou. Arithmos anthropou estin, kai ho arithmos autou hexakosioi hexékonta hex.

And in the Vulgate:

Hic sapientia est. Qui habet intellectum, computet numerum bestiae. Numerus enim hominis est, et numerus ejus est sescenti sexaginta sex.

There are various theories about the meaning of this verse, and there have been many attempts to show that a person is the Antichrist by relating his name to the number 666. For example, scholars who believe the Book of Revelation refers to real people and events argue that the number represents the value of Nero or Neron Caesar (נרון קסר, Nrwn Qsr*) in Hebrew letters, which also have numerical values (note that Hebrew is written from right to left):

                 r    S    q     n   w    r    n 
         666 = 200 + 60 + 100 + 50 + 6 + 200 + 50

Some early texts of the Book of Revelation use 616 instead, which would represent the alternative Hebrew spelling נרו קסר, Nrw Qsr:

                 r    S    q    w    r    n 
         616 = 200 + 60 + 100 + 6 + 200 + 50

*Note: Hebrew נרון קסר, Nrwn Qsr = Greek Νερων Καισαρ, Nerôn Kaisar, though קסר, qSr, should strictly speaking be כסר, kSr.

In Roman numerals 666 represents all the numbers from 1 to 500 in descending order, namely D (500) + C (100) + L (50) + X (10) + V (5) + I (1), or DCLXVI. Robert Graves suggests in his study of pagan symbolism The White Goddess that this is an acronym for the Latin sentence Domitianus Caesar Legatos Xti Violenter Interfecit, or "The Emperor Domitian violently killed the envoys of Christ".

Mathematics

Naturally enough, 666 also has many mathematical properties, some more interesting than others:

• 666 is the 667th natural number.

• 666 = 2 × 3² × 37 is the 333rd even number and the 544th composite number. (The 666th composite number is 806 = 2 × 13 × 31). 666 is the 260th non square-free number: {4, 8, 9, 12, 16, 18, 20, 24, ..., 648, 650, 652, 656, 657, 660, 664, 666, ...}. The 666th non square-free number is 1701.

• 666 is not a prime. The 666th prime is 4973. 666 is not a lucky number. The 666th lucky number is 5559.

• 666 has 12 divisors: {1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666}. The sum of its divisors is 1482. The first numbers in the interval [1, 10⁶] that have the same sum of divisors are 666, 1017, 1481. The sum of its proper divisors is 816>666, so 666 is the 162th abundant number. 666 has 3 distinct prime divisors {2, 3, 37} (ω(666) = ω(2 × 3² × 37) = ω(2) + ω(3²) + ω(37) = 1+1+1=3) and a total of 4 prime divisors (Ω(666)=...=4).

• By Euler's totient function φ(666) = 216. 666 is the 14th number with this value of φ: {247, 259, 327, 333, 351, 399, 405, 436, 494, 518, 532, 648, 654, 666, ...}

• The harmonic mean of the digits of 666 is an integer: 3/(1/6 + 1/6 + 1/6) = 6. 666 is the 54th number with this property.

• 666 is the 25th repdigit.

• 666 is the 76th palindromic number in base 10 and it is also the sum of two consecutive palindromic primes: 666=313+353. It is the 62th palindromic composite number.

• The sum of all the integers from 1 to 36 inclusive is 666. This means 666 is the 36th triangular number. (The 666th triangular number, on the other hand, (1+2+3+...+664+665+666) is 222111.)

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• A prime reciprocal magic square based on 1/149 in base 10 has a magic total of 666.

• 6^(6^6) or 6⁴⁶⁶⁵⁶ is 36,306 digits long. Its first 150 digits are:

26591197721532267796824894043879185949053422002699

24300660432789497073559873882909121342292906175583

03244068282650672342560163577559027938964261261109...

The sum of the digits 1 through 146 is 666, as is the sum of digits 2 through 148 and digits 2 through 149.

Culture and Psychology

The number 666 retains a peculiar significance in Western societies. Just as many people try to avoid the "unlucky" number 13 (sometimes going to the extent of having a floor "12A" in multi-storey buildings), so people find ways to avoid the "Devil's number", even in contexts that would seem on first sight to be far removed from superstition.

For example, when the giant CPU manufacturer Intel introduced the 666 MHz Pentium III in 1999, they chose to market it as the Pentium III 667 on the pretext that, since the actual clock speed was 666.666 MHz, 667 was the more accurate approximation—conveniently ignoring their own usual rounding practice: as examples, consider the earlier 66.666 MHz 486-66, the 466.666 MHz Celeron 466, or the later 866.666 MHz Pentium III 866.

Ronald Wilson Reagan has six letters in his first, middle, and last name.

In ancient Dacia, 666 was the number of those who returned to the right faith.

See also:

• Number of the Beast (alternative meanings)
• Numerology

External link

• Mike Keith's "Number of the Beast" (http://users.aol.com/s6sj7gt/mike666.htm) Collection of mathematics involving 666.