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November 29th, 2016, 10:51 AM   #1
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Prime Pattern Rediscovered

https://drive.google.com/file/d/0B7M...ew?usp=sharing

Thanks to the discovery of the people who showed us that all Prime numbers except for 2 and 5 end in 1 or 3 or 7 or 9, and thanks to the Ancient Mathematicians such as Aristotle and Pythagoras for the discovery of Pronic numbers, and thanks to the support of this forum, here we are.

This isn't complete yet though, in order for this to be useful it would be good to find the formula.

The way it works is, as long as the irrational rotation is less then the Pronic, that guarantees you have the right configuration of the row. Then take the current Prime and keep subtracting 2 until you reach the next Prime number below.

Primes from 3 are reached by +2, Pronics are +2*n
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November 29th, 2016, 11:54 AM   #2
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Are you going to tell us what this "pattern" is? In the web page you link to I see a list of integers, some with red background, other with yellow. What do those mean? The yellow numbers appear to be primes, though it is not clear what "pattern" there is. Some of the red numbers are prime, others are not.
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November 29th, 2016, 12:03 PM   #3
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Right here's a demonstration, I apologize by the way for not putting the red and yellow numbers in black borders.

-16 -11
-19 -13

-11 - 2 = -13

from -11 taking away 2 each time leaves you with -13 first.

Down and left until you reach the first number along the second row. The yellow numbers are the Primes. The Red numbers are just to show you which number you would need to divide by if you wanted the next Prime, and to show you they are always in the row.


The downward triangle on the first page is a visual proof.
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November 29th, 2016, 12:24 PM   #4
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__________2 + -0.5 = 1.5
3 / 2 = 1.5

-11, -8, -5, -2, 1, 4, 7, 10

(+3)

5 is the 3rd Prime

Edit: 11 is less than 12, 10 is less than 12.

Edit: 1 * 3 = 3, - 2 * 2 = -1

Edit: at the bottom of the Google drive page there are three buttons Sheet1, Sheet2, Sheet3.

Last edited by HawkI; November 29th, 2016 at 12:35 PM.
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December 1st, 2016, 07:45 AM   #5
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As I used the On-Line Encyclopedia of integer sequences to try finding the formula, I realised I forgot to thank OEIS for getting this far. I would have been stumped if it wasn't for them.
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December 6th, 2016, 12:43 PM   #6
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Here are three new things I have found, I will use examples.


Row number starts at N then it's +1 * Pronic - 1.

-5,-3,-1,,1,,3,,5
,2,,3,,4,,5,,,6,7

3 2 -3
3 3

3 2 -1
4 3

This one is more experimental but I'll say it anyway. The smallest positive number's associated number becomes Prime as a result of this test. the two potential Irrational Rotations - current Prime.

3 - 2 = 1

1 - 2 = -1

And lastly Pronic + -0 column - N = 1st Irrational Rotation
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December 6th, 2016, 02:40 PM   #7
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Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by HawkI View Post
Here are three new things I have found, I will use examples.


Row number starts at N then it's +1 * Pronic - 1.

-5,-3,-1,,1,,3,,5
,2,,3,,4,,5,,,6,7

3 2 -3
3 3

3 2 -1
4 3

This one is more experimental but I'll say it anyway. The smallest positive number's associated number becomes Prime as a result of this test. the two potential Irrational Rotations - current Prime.

3 - 2 = 1

1 - 2 = -1

And lastly Pronic + -0 column - N = 1st Irrational Rotation
All you have shown so far is how to generate your spreadsheet. Clearly you believe it's generating all the primes but you haven't showed what any of it means. Are you trying to see/show how to anticipate where the prime is in the sheet? And what's this with the irrational rotations?? What is an irrational rotation?

-Dan
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December 7th, 2016, 01:08 PM   #8
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-0 column

- 1
_
Pronic



0 column

1
_
Pronic


Irrational rotation goes like this

3 2 -3
3 3

2*3-3*3 = -3

a b e
c d

b*c-d*a = e

Last edited by HawkI; December 7th, 2016 at 01:10 PM.
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December 9th, 2016, 07:53 AM   #9
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Quote:
Originally Posted by topsquark View Post
Are you trying to see/show how to anticipate where the prime is in the sheet?

-Dan

Yeah, that's what this is all about. I have found yet more things and for the first time have come up with a frame work which we can possibly modify into a predictable pattern for Prime numbers.

A - Round Down 1/Infinite Round Down, IR subset a - Current P - x, x OR y < x OR y = Next P
_________________________________IR subset b - Current P - y

IR subset a = (n * B subset 1 OR C subset 1) - (n + 1 * Current P)
IR subset a = (n * B subset 2 OR C subset 2) - (n + 1 * Current P)

If x < y, B subset 1 = n + n, B subset 2 = n + n - 1
If y < x, C subset 1 = n + n - 1, C subset 2 = n + n - 2

A - Round Down 1/Infinite Round Down = (n * z) - (n + 1 * Current P) = IR / (n * n + 1)

P means Prime
IR means Irrational Rotation

-P becomes P
Smallest positive number out of x and y becomes the next Prime

Last edited by HawkI; December 9th, 2016 at 08:05 AM.
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December 11th, 2016, 07:34 AM   #10
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Here's a direct quote from my Maths dictionary

"Other sequences are defined by a recurrence relation: a rule is given by which the nth term can be determined when one or more preceding terms are known. This is the case with the Fibonacci Sequence."


So excitingly it looks like the eventual formula for the Prime number pattern will have a recurrence relation.

Edit: here's what the trapezium of relative fractions look like

______________________-1/2,1/2
______________-3/3,-2/3,-1/3,1/3,2/3,3/3
__________-4/4,-3/4,-2/4,-1/4,1/4,2/4,3/4,4/4

Last edited by HawkI; December 11th, 2016 at 07:37 AM.
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