# The number 666

(You might also wish to view 666 in context on my numbers page.)

## 666

The mother of all cult numbers, as described below — but first I will list some mathematical properties of 666:

666 is the sum of the squares of the first 7
primes: 2^{2} + 3^{2} + 5^{2} + 7^{2} + 11^{2} +
13^{2} + 17^{2}.

Another similar sum: 666 = 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} +
6^{3} + 5^{3} + 4^{3} + 3^{3} + 2^{3} + 1^{3}. Such sums could be
called "hyper-octahedral" numbers, based on a 4-dimensional polyhedron
analogous to the octahedron. Perhaps when Christian numerologists go
to heaven, instead of a one-mile cube, their new Jerusalem will be a
6-mile hyperoctahedron.

It is the 36th triangular number: 1+2+3+...+36
= 666, which seems more significant because 36=6×6. (This also makes
it the sum of all the numbers in a 6×6
magic square or the 6^{th} member of sequence
A37270). 666 is the largest triangular number that is a
repdigit.

666 = 3^{6}-2^{6}+1^{6}.

Φ(666), the number of integers less than and relatively prime to 666, is 6×6×6 = 216.

If you take the prime factors of 666 = 2×3×3×37 and add their
digits, you get 18 = 6+6+6. That makes 666 the 34^{th}
Smith number. That's not too special — it's true
for 49 of the first 1000 composite numbers.

### 666 as a Cult Number

666 has attracted more attention than nearly any other number in numerology, for at least several hundred years if not longer. This makes it the greatest cult number in recent history. It is the "number of the beast" mentioned in the book of Revelation (the only apocalypse in the Christian canon, attributed to the apostle John). The relevant verse is Rev 13:18; in the original Greek it reads:

ωδε η σοφια εστιν. ο εχων νουν
Πηφισατω τον αριθμον του θηριου͵
αριθμοΣ γαρ ανθρωπου εστιν͵ και ο
αριθμοΣ αυτου εξακοσιοι εξηκοντα εξ.

Phonetically:
Ode E sophia estin o echOn. noun
psEphisatO ton arithmon tou thEriou,
arithmos gar anthrOpou estin, kai o
arithmos autou exakosioi exEkonta ex.

Translations vary because they attempt to make passages sound natural and avoid cumbersome constructions. However, the most accurate translations resemble this (from the 1958 Amplified New Testament):

Here is [room for] discernment [a call for the wisdom of interpretation]. Let anyone who has intelligence (penetration and insight enough) calculate the number of the beast, for it is a human number [the number of a certain man]; his number is six-hundred sixty six.

εξακοσιοι εξηκοντα εξ is "six-hundred sixty six". Notably, some
early Greek texts^{2} read "six-hundred ten six", that is,
616. Why was the specific number 666 (or 616) chosen
for this passage? The wording clearly indicates that some effort and
calculation will be needed, and that something isn't directly obvious
without applying this "wisdom". Since it says "calculate this number"
in one place, but then goes on to say "[the] number is 666", there is
a contradiction: what would the reader have to calculate if the writer
gives away the answer in the next phrase? There are two ways to
interpret the contradiction:

- The number itself is unspecified (and 666 is just a metaphor), or

- 666 (or 616) is indeed the answer but that the method of calculation to produce it (and/or perhaps the identity of the "certain man") is the unspecfied mystery.

David Wells^{1} suggests the first interpretation, when he points out
the fact that 666 in Roman numerals (DCLXVI) was often used as a
generic way of referring to any unspecified or unknown large number.
(616 would have been similar, DCXVI). "DCLXVI" is a Roman slang way of
saying "any big long number", like our colloquial slang
zillion, because big numbers in Roman numerals
always end up being long unmanagable strings with lots of different
letters in them. Thus, the writer of Revelation might have been using
"666" to mean "an unspecified or unknown large number". This makes
sense because of the fact that the writer says wisdom is needed to
calculate the number: if he were giving the number explicitly, you
wouldn't need any wisdom to calculate it. He is saying that the number
of the beast is large, unknown and unspecified, but if you have wisdom
or insight you might be able to figure out what it is.

Supporting this general idea, numerologists like to point out that any of our common numbers (telephone, license plate, credit cards, tax ID numbers, etc.) would have appeared very large to someone living 2000 years ago. Indeed, they are too large to represent in most of the ancient number systems, so it would have been impossible to know or to specify such numbers. A very great wisdom indeed would have been required to calculate one!

The other possible interpretation, namely that the answer actually is 666 but that you have to discover what calculation will yield that answer (or which "certain man" owns the number), is the one that has drawn the most attention. An incredible variety of attempted calculations, connections, interpretations, hidden meanings, etc. have been found for the number 666, and a fair number for 616 as well. They have plenty to go on, given the availability of no less than four relevant contemporary languages (Hebrew, Aramaic, Greek, Latin) each with a variety of different numerical and numerological systems. There is clear evidence (in the grammar and vocabulary) that Revelation was translated from Hebrew to Greek, or written by someone for whom Greek was a second language.

Numerology connects a number or multiple numbers with something else, such as a person's name or an important word, phrase or passage of text. The determination of which number(s) to use generally follows some type of letter-value system. For example, the Greek system is shown here; each letter is turned into a number and then added together.

In Hebrew culture this type of numerology is part of Gematria. The numbers reveal otherwise-hidden meanings and connections between one name, phrase, etc. and another. The Hebrew alphabet has 22 letters, and there are many different systems for assigning numbers to the letters for Gematria purposes. There is also one numbering system (shown here) used for everyday purposes. Using that system, here is an example:

Saddam = םאדאס (samex, alef, dalet, alef, mem(final))
= 60 + 1 + 4 + 1 + 600 = 666

Hussein = נהששוה (he, vau, shin, shin, he, nun)
= 5 + 6 + 300 + 300 + 5 + 50 = 666

The name "Saddam Hussein" has been spelled as it would be in Hebrew and the values of the letters are added to get the sums. The second line is sort of cheating, because the נ (nun), being the final letter, should be a final nun ן, and its value would then be 700, not 50. (Or alternately, change the mem at the end of Saddam to a non-final mem מ with value 40). Such "cheating" is widespread in numerology particularly when a connection to 666 is being shown, and the numerologist always finds a reason to justify bending the rules.

Another example, possibly connected to the appearance of 666 in the Bible, is רסק נורנ (Neron Kaisar, the Greek name of the Roman emperor Nero rendered in Hebrew writing) equal to 200+60+100+5+6+200+50. Nero was contemporary to the early Christians and would have been considered evil by them, but such an accusation could not be made openly, thus the gematriatic riddle. There is also the nice fact that if the final נ is left off, giving the more familiar name Nero Kaisar, the number becomes 616.

An equivalent letter-numbering system, adapted to English, would go

something like this:

A=1 B=2 C=3 D=4 E=5 F=6 G=7 H=8 I=9 J=10 K=20 L=30 M=40 N=50 O=60 P=70 Q=80 R=90 S=100 T=200 U=300 V=400 W=500 X=600 Y=700 Z=800

Some examples:

FOX = 6 + 60 + 600 = 666

BUSINESS = 2 + 300 + 100 + 9 + 50 + 5 + 100 + 100
= 666

GUTENBERG = 7 + 300 + 200 + 5 + 50 + 2 + 5 + 90 + 7
= 666

NEWARK = 50 + 5 + 500 + 1 + 90 + 20
= 666

Naturally, our high-tech age has given numerologists plenty of new ways to compute these sums. Computers give each letter, digit and symbol a number according to their ASCII code. For example, "MS-DOS 6.21" = 77 + 83 + 45 + 68 + 79 + 83 + 32 + 54 + 46 + 50 + 49 = 666.

Simpler techniques have been used as well, such as counting the number of letters in each word: "Ronald Wilson Reagan" (6 letters each) = 6 6 6.

Many numerologists like to prove things based on more
pure-mathematical properties (that is, not depending on words or
alphabets). For example, if you take 666^{7} =
58,119,196,856,185,328,256 and add the digits in groups of 3, the
total is 1998. The same is true for a few other powers of 666. (This
was used as part of an elaborate and somewhat illucid discussion on
this web page, which for a while
was titled Proof That the World Will End In 1998. It features
lots of really amusing detail, such as poetry allegedly translated
from Aramaic but which rhymes in English, and of course an update
appropriately titled Why the World Did Not End In 1998 (the
short answer: the world is ending, you just didn't notice!).) As
it happens, all powers of 666 (starting with 666^{2}) are multiples of
999, and therefore, because of the
casting out 9's property applied to
999, all sums of 3-digit groups of powers of 666 are
multiples of 999. Thus, many powers of 666 all have the same
3-digit-group sums; the same thing happens for powers of 333 and 999
for the same reasons.

The claim that 39 is uninteresting goaded one numerologist into showing that 39 is related to 666 in the following way:

39^{2} = 1521

15^{2} + 21^{2} = 666

See also 10^{(6.65565×10668)}

Footnotes

**1 :**
Wells, David, The Penguin Dictionary of Curious and
Interesting Numbers. (Original edition 1986; revised and expanded
1998).

**2 :**
Holy Bible, New Revised Standard Version. Revelation 13:18,
footnote g. Available at
Biblos.com.

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2018 Jan 06. s.11