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Discussion in '2003 Archive' started by Tim, Dec 26, 2003.
Double Yikes! KEEP AWAY FROM ME!
Odd facts about hitting 666
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.
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.
16661 is the first beastly palindromic prime, of the form 1[0...0]666[0...0]1. The next one after 16661 is
which can be written concisely using the notation 1 013 666 013 1, where the subscript tells how many consecutive zeros there are. Harvey Dubner determined that the first 7 numbers of this type have subscripts 0, 13, 42, 506, 608, 2472, and 2623 [see J. Rec. Math, 26(4)].
A very special kind of prime number [first mentioned to me by G. L. Honaker, Jr.] is a prime, p (that is, let's say, the kth prime number) in which the sum of the decimal digits of p is equal to the sum of the digits of k. The beastly palindromic prime number 16661 is such a number, since it is the 1928'th prime, and
1 + 6 + 6 + 6 + 1 = 1 + 9 + 2 + 8.
The triplet (216, 630, 666) is a Pythagorean triplet, as pointed out to me by Monte Zerger. This fact can be rewritten in the following nice form:
(6·6·6)² + (666 - 6·6)² = 666²
There are only two known Pythagorean triangles whose area is a repdigit number:
(3, 4, 5) with area 6
(693, 1924, 2045) with area 666666
It is not known whether there are any others, though a computer search has verified that there are none with area less than 1040. [see J. Rec. Math, 26(4), Problem 2097 by Monte Zerger]
The sequence of palindromic primes begins 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, etc. Taking the last two of these, we discover that 666 is the sum of two consecutive palindromic primes:
666 = 313 + 353.
A well-known remarkably good approximation to pi is 355/113 = 3.1415929... If one part of this fraction is reversed and added to the other part, we get
553 + 113 = 666.
[from Martin Gardner's "Dr. Matrix" columns] The Dewey Decimal System classification number for "Numerology" is 133.335. If you reverse this and add, you get
133.335 + 533.331 = 666.666
Do you mind explaining this one. It doesn't add up.
These two are the same. If you multiply out the second one you get the first.
Sorry -- it's the mathematician in me coming out.
And all these years I thought the identity of the beast was the only thing confusing about the number 666. Most of us can't even argue with the two of you. Most of us don't even want to try to understand, but more power to those of you who do.
I was starting to worry about Dr Bob for a minute then. He seemed to have WAY too much information on the topic...Thankfully he posted the URL at the end, now I will have to keep an eye on THEM
Although maybe someone should be keeping an eye on me. One boring arvo in my early teens I worked out that using a = 6, b = 12, c = 18, etc, my name adds up to...
hmmm I better resign from BB
I'm just guessing, but are you a friend of Louis Farrakhan?
Tim (thankfully past #666)
Tim I guess that makes you Nero.
Not personally, but boy that fellow has a way with clothes.
The late Senator Paul Simon was my mentor in how to "dress for success".
Where were you, when I need you back in 1997. I was in Bluefied, (I'm not sure if it was Va or WV) and stop at a reastuant for Breakfast. The bill came to $6.66, the young clerk would only point to the cash register, she would not tell me what the total was. Oh well
My goodness, does this mean that in 404 posts I have completed my initiatation for the BB?
You may NOW get your pix on your post. But when you hit 666, that pix will disappear and we get your firstborn.
Unless he's named Rumpelstilskin.
Yeah.... well I sent an updated photo of me to webmaster and his computer blew up!
I WONDERED what happend to herr Webmeister's computer. Now, the truth comes out.
I've decided that Dr. Bob has entirely too much free time on his hands.
Don't you have a honey-do list that needs attending?
Dan - the guy who ignores his honey-do list!