Re:Happy Prime Year
by alextgordon on Saturday January 01, 2011 @08:39PM
(#2059102)
Primes greater than 2 are always odd. So your first differences will always be even. Since the first differences are always even, then so will be the second differences, and the third, and so on. So the final value will always be an even number given any finite sequence of primes > 2.
Is there some interesting result in number theory that led you to take the absolute value of the differences?
I wish I could say I knew of some interesting result, but I did it only out of fascination. However, if you look closely at the two triangles, you can see some interesting pattens. For example, they each have a triangle of 0's on the right side of them, bordered by 2's. I think I remember reading about this occurrence (which I'm pretty sure appears in more places than just these two triangles I happened to choose), but I can't seem to remember where.
4 2 2 2 2 2
2 0 0 0 0
2 0 0 0
2 0 0
2 0
0 2 2 2 2
2 0 0 0
2 0 0
2 0
2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099
8 6 10 2 10 14 10 6 12 2 4 2 10
2 4 8 8 4 4 4 6 10 2 2 8
2 4 0 4 0 0 2 4 8 0 6
2 4 4 4 0 2 2 4 8 6
2 0 0 4 2 0 2 4 2
2 0 4 2 2 2 2 2
2 4 2 0 0 0 0
2 2 2 0 0 0
0 0 2 0 0
0 2 2 0
2 0 2
2 2
0
This does not always result in 0 at the end. For example, the differences of the first eight primes:
1 2 2 4 2 4 2
1 0 2 2 2 2
1 2 0 0 0
1 2 0 0
1 2 0
1 2
1
Here is what it looks like with better formatting: http://i.imgur.com/BuPij.png