The World as I see it.

Following up on my post yesterday on Hexakosioihexekontahexaphobia, apart from the film I am going to watch today, my interest in the number is purely mathematical.

For those of you not mathematically inclined, I expect this to sail over your heads, but as I always assert, you lose nothing by knowing 1 or 2 impractical facts.

1. The number 666 is a simple sum and difference of the first three 6th powers:

2. 666 = 1⁶ - 2⁶ + 3⁶.

3. It is also equal to the sum of its digits plus the cubes of its digits:

4. 666 = 6 + 6 + 6 + 6³ + 6³ + 6³.

5. 666 is related to (6² + n²) in the following interesting ways:

6. 666 = (6 + 6 + 6) · (6² + 1²)
   666 = 6! · (6² + 1²) / (6² + 2²)

7. The sum of the squares of the first 7 primes is 666:

8. 666 = 2² + 3² + 5² + 7² + 11² + 13² + 17²

9. The sum of the first 144 digits of pi [22/7, Π] is 666.
10. And from the number theorist, Carlos Rivera, the number 20772199 is the smallest integer with the property that the sum of the prime factors of n and the sum of the prime factors of n+1 are both equal to 666:

There exists more attributes of this popular number but I think I have reached my mathematical limit.