Tuesday, June 06, 2006

6-6-6 today

For all you superstitious types don't overlook that today is 6/6/6. This, of course, is only true if you follow the Julian calendar.

Made famous by the Book of Revelation (Chapter 13, verse 18) it has been studied extensively by mathematicians because of its many interesting properties.
Here are some interesting things about the number from Mike Keith and there are many more...

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

666 = 16 - 26 + 36.


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

666 = 6 + 6 + 6 + 6³ + 6³ + 6³.

There are only five other positive integers with this property. Exercise: find them, and prove they are the only ones!


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

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


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

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


The sum of the first 144 (= (6+6)·(6+6)) digits of pi is 666.

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