The "Number of the Beast", 666, is of profound mystical and mathematical significance and is most famous for its appearance in the New Testament Book of Revelation, 13:18: "Here is wisdom: Let him that 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."
The number appears a total of four times in the Bible, however, the other three of which are in the Old Testament; two of these, in turn, say effectively the same thing. Only in Revelation does one find an explicitly negative association.
Here is Wisdom: Mathematical Properties of 666
The number 666 also appears in the 6x6 magic square of the Sun, which consists of numbers 1-36 arranged such that all rows, columns or diagonals add up to 111. Thus the square's 'magic number' is 666 because this is the sum of all numbers 1-36:
666 = 1 + 2 + 3 ... 34 + 35 + 36
The number of prime numbers preceding 666 is 121, or 11^2, and there are 11 primes occurring before 36. 36, as the sum of numbers 1-8, is the 8th triangular number; therefore 666 is the 36th. 36 is also the sum of the 5th and 6th triangle numbers, which are themselves the sums of numbers 1-5 and 1-6:
15 = 1 + 2 + 3 + 4 + 5
21 = 1 + 2 + 3 + 4 + 5 + 6
36 = 15 + 21
If these numbers are in turn plugged into Waring's Problem of "writing whole numbers as the addition of powers" (Crilly 39), it is revealed that
666 = 15^2 + 21^2 = 225 + 441
Furthermore, 666 is part of a Pythagorean quadruple: 320, 410, 416, 666, such that
666^2 = 320^2 + 410^2 + 416^2 = 102,400 + 168,100 + 173,056 = 443,556
21 and its square are highly significant symbolically and are related to the gematria of Genesis 1:1 (see below).
Mathematician and author Tony Crilly ("50 Mathematical Ideas") notes that various "unexpected properties" emerge when the number is examined according to Waring's problem. He writes: "In this setting the magic arts of numerology meet the clinical science of mathematics in the shape of primes, sums of squares and sums of cubes." Waring's Problem reveals that 666 is the sum of the squares of the first seven prime numbers:
666 = 2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2
He adds that "Numerologists will also be keen to point out that it is the sum of palindromic cubes and, if that is not enough, the keystone 6^3 is shorthand for 6 x 6 x 6:"
666 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 5^3 + 4^3 + 3^3 + 2^3 + 1^3
The intrigue does not stop here, as the "keystone 6^3," or 216, also happens to be the total number of letters that appear in all four verses containing 666.
There are other apparent relationships between said verses: if one chooses to ignore the modern chapter divisions, which were a later addition to the Bible, the following facts may be discerned:
v. 9,094 = 1 Kings 10:14 v.11,378 = 2 Chronicles 9:13 v.12,041 = Ezra 2:13 v.30,927 = Revelation 13:18
The sum of all OT verses is
32,513 = 41 x 793 = 9,094 + 11,378 + 12,041
And that of the NT is
30,927 = 39 x 793
(41 x 793) + (39 x 793) = OT (32,513) + NT (30,927) = 80 x 793 = 63,440
793 is the 11th centred and 12th dodecagonal ('12-gonal') number and consists of 12 triangles of 66 units each. The theomatician or numerologist would surely point out that the Bible consists of 66 books, and further that both Testaments often present the number 12 as central to a higher order under the 13th, as with Jacob and his sons, and later Jesus and His disciples. Both of these examples potentially reflect a certain knowledge of geometry, in that the Flower of Life consists of twelve circles orbiting a central 13th; or of calendrics, in which the twelve zodiac encompass the Sun.
Returning now to 216, a further allusion to this number is the fact that the verse following the Revelation occurrence, i.e. 14:1, reads: "And I looked, and, lo, a Lamb stood on the mount Sion, and with him an hundred forty and four thousand..."
144,000 / 666 = 216.2162162162162
6 x 6 x 6.
Most interestingly, 216 is also the standard gematria value of the fifth sephirah of the Qabalistic Tree of Life, at the heart of the Pillar of Severity: Geburah is interchangeably described as "Strength" and "Severity." The excerpts below are from Dione Fortune's The Mystical Qabalah, ch.19:
TITLE: Geburah, Strength, Severity MAGICAL IMAGE: A mighty warrior on his chariot
TITLES GIVEN TO GEBURAH: Din: justice. Pachad: fear.
ARCHANGEL: Khamael. Burner of God. ORDER OF ANGELS: Seraphim, Fiery Serpents.
VIRTUE: Energy. Courage. VICE: Cruelty. Destruction.
SYMBOLS: The Pentagon. The Five-petalled Tudor Rose. The Sword. The Spear. The Scourge. The Chain.
The pentagon and fiery serpents stand out as especially significant in relation to the Beast 666, who, as Satan, is represented as a serpentine ruler of a fiery realm and whose primary symbol is the pentagram. This is a remarkably fitting association for a number of reasons. Firstly, the pentagram itself betrays allusions to the number 666 in the ratios of the lengths of its line segments as approximations of phi (1.618), i.e. the Golden Section.