A # Beast Number (666)

The Beast Number, also known as the "Number of the Beast" or the Apocalypse Number, is 666 mentioned in the Bible's Book of Revelation, the relevant verse of which (Rev 13:18) is often quoted as:

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

Leaving aside the thorny issue of what this actually means, the number 666 does have some interesting mathematical properties. Most notably, it is the sum of the first 36 natural numbers (all the numbers on a roulette wheel): 1 + 2 + 3 + ... + 36, which makes it the 36th triangular number. It is also the sum of the squares of the first seven prime numbers, 22 + 32 + 52 + 72 + 112 + 132 + 172. Other curious representations of "the Beast" include:

 13 + 23 + 33 + 43 + 53 + 63 + 53 + 43 + 33 + 23 + 13 36 - 26 + 16 6 + 6 + 6 + 63 + 63 + 63

Furthermore, 666 is one member of a Pythagorean triplet, (216, 630, 666), which can be written in the remarkable form:

(6 × 6 × 6)2 + (666 - 6 × 6)2 = 6662.

In Roman numerals, 666 represents all the numbers from 500 in descending order, namely D (500) + C (100) + L (50) + X (10) + V (5) + I (1), or DCLXVI. In fact, it's been suggested that the Roman representation of 666 may have something to do with the Biblical reference. DCLXVI was often used as a generic way of referring to any unspecified or unknown large number – the Roman equivalent of our "zillion." Thus, the writer of Revelation might simply have been using "666" to mean "big but unspecified."