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#1 Re: Help Me ! » Strange Prime number pattern » 2007-01-04 07:40:18

But can it be proven to grow infinitely? :-)

#2 Re: Help Me ! » Strange Prime number pattern » 2007-01-03 14:08:58

Thanks! Those look great.

I think we can see the pattern, for lack of a better word, want to continue.  However, is there anyway to turn this visual pattern into a proof?

#3 Re: Help Me ! » Strange Prime number pattern » 2007-01-03 12:31:38

Great to hear Ricky!

I'm going to describe it similar to text processing. I'm sure there is a much more efficient way to do it, but this will be easier to describe. My algorithms are less than text-book quality so I'll leave them out.  This is a bit of a repeat from above but I'll post it that way for clarity.

1. Create (or read from) a list of prime numbers starting at 3

      (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61...)


2. Make a list of the differences between on number and the next.

      3 -> 5 = 2
      5 -> 7 = 2 ...

      (2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6 ...)

3. Take the first two numbers in the list (n1 and n2) and plot them as coordinates.

4. Do the same for either a. (n3 and n4) or b. (n2 and n3), I've found both produce interesting results.

   That is take... 
      (2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2)

   And plot points
      (2,2) (4,2) (4,2) (4,6) (2,6) (4,2)

    OR. plot to points
      (2,2) (2,4) (4,2) (2,4) (4,2) (2,4) (4,6) (6,2) (2,6) (6,4) (4,2)

5. Since all numbers are even,optionally divide all numbers by two to collapse the resulting shape of negative empty areas.

Let me know if you have any questions if I have not been clear.  I'd post my Python but eek do I have to show the world what a horrible coder I am???  :-)

#4 Re: Help Me ! » Strange Prime number pattern » 2007-01-03 05:17:10

krassi_holmz wrote:

Intersting.
There's a conjecture, that for every even n, there exists infinitely many prime couples (p,q), such that p-q=n.
Intersting pattern.
Does your avatar has some connection with this?

My avatar and the now posted image show prime couples everywhere that one of the coordinates is 2.

Since the origin is at the bottom left, the left and bottom most sides of the image represent (2,x) and (x,2) of the coordinate system.

This pattern has always grown in this way and would really love to see it pushed into the billions if possible (my avatar shows about 80,000 primes or the primes from 3 to 1 million). I know it's not a 'proof' but it's an interesting map to show new pairs of all sorts consistently growing.

Are there any interested C programmers who could take pseudo code and optimize it?

#5 Re: Help Me ! » Strange Prime number pattern » 2007-01-03 04:54:18

Ok I've figured out how to post images, I'll edit this post and put up a more interesting one.
While this post is up, the picture below is much like my avatar but color and height coded to show repeated "hits" on that spot.

Higher and brighter = more repetition.

#6 Re: Help Me ! » Strange Prime number pattern » 2007-01-02 08:02:47

Regarding prime pairs.  There is a way to plot this info in 2D that makes that prime pairs visible.

Take the list of differences (2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6 ...)
and plot them (n1,n2) (n3, n4)
basically take each pair and turn them into coordinates.

This will show that not only do prime pairs (primes 2 aparts) continue to happen over and over, but so do many other combinations (minus certain holes).  These holes in the scatter graph that forms are very constant as the graph fills.

You can also start "late" in the sequence and find it fills in both directions.

It's as if to say "all distances between primes exists at all sizes" minus of course the holes I originally posted about.
I have images, is there a way I could post them?

In a scary form of ascii art, here is the pattern as it seems to fall, all odd spaces are removed so this grid represents even numbers only with the origin in the lower left.

ooooooooooooooooooooo
o oo oo oo oo oo oo o
 oo oo oo oo oo oo oo
ooooooooooooooooooooo
o oo oo oo oo oo oo o
 oo oo oo oo oo oo oo
ooooooooooooooooooooo
o oo oo oo oo oo oo o
 oo oo oo oo oo oo oo
ooooooooooooooooooooo
o oo oo oo oo oo oo o
 oo oo oo oo oo oo oo
ooooooooooooooooooooo
o oo oo oo oo oo oo o
 oo oo oo oo oo oo oo

The actual scatter graph looks more like this....

oo 
o o
 oo     o
oooo
o oo 
 oo oo     o (very random placement)
ooooooo
o oo oo o
 oo oo oo o
oooooooooooo     o
o oo oo oo oo
 oo oo oo oo oo
oooooooooooooooooo
o oo oo oo oo oo  
 oo oo oo oo oo oo oo

^
Here at origin, pattern gets very solid very quickly.

Aha! Posted image as my avatar!

#7 Re: Help Me ! » Strange Prime number pattern » 2006-12-31 16:03:09

Thanks Pi man.  The rest of the pattern (of non-pairs) is 4,16,28,...(intervals of 12) and   8,20,32,... (also intervals of 12).
These all seem to follow what you've described.

I'm running this into the millions for the first time with python and glad to know what they show.
I'll post some pictures when I can.

#8 Help Me ! » Strange Prime number pattern » 2006-12-31 15:04:29

BluemanSteele
Replies: 28

Hi everyone.  This is my first post so I hope this is the right place.
I started a project in 1993 with prime numbers and recently picked it back up.
The first time I did this I worked in QBasic.  Now I'm doing it in Python.
I'm only a hobbyist in programing and math, so I'd like to see if someone
with more knowledge than me in both can let me know if I've found something
new or if I'm just seeing a side effect of known properties of primes.

Here are the steps to my findings.

1. Take a list of prime numbers starting at 3

      (3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61...)


2. Make a list of the differences between on number and the next. 

      3 -> 5 = 2
      5 -> 7 = 2 ...

      (2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6 ...)

3. Note the pair of 2s and 6s, but no pair of 4s

I noticed this in 1993 but the numbers I was working in had to stay in the tens of thousands and thus my hunch had no "proof".

I tried various ways of graphing this and found a pattern of "holes" missing from the gaps between primes.
I was told this was just a side effect of sieve of eratosthenes, but the pattern is so regular and predictable that I wanted to find out more about it.

I'm not a mathematician nor a programmer, just a very curious person.  So I'd love to find out more, but worry I might not understand the answer.  If anyone is patient and curious, I'd love to share my findings and see what can be discovered.

Thanks in advance.

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