My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree2Thanks
Reply
 
LinkBack Thread Tools Display Modes
December 12th, 2016, 05:40 AM   #11
Senior Member
 
Joined: Mar 2015
From: England

Posts: 163
Thanks: 4

I found some new things.

1st row number = n

Last row number = n+(n*2+1)

/

Row position of Current P + 1 (if shift left) or + 2 finds next row position of Current P on next row.

/

Row position of Current P + 2 * x = row position of Next P on current row.

Here is the list of x starting from the first 0 http://oeis.org/search?q=0%2C2%2C2%2...lish&go=Search

Last edited by HawkI; December 12th, 2016 at 05:42 AM.
HawkI is offline  
 
December 12th, 2016, 08:12 AM   #12
Senior Member
 
Joined: Mar 2015
From: England

Posts: 163
Thanks: 4

Just realised the "Row position of Current P + 2 * x = row position of Next P on current row" is basically Current P + 2*n to next Prime so.

For example
3 + 2 = 5
5 + 2 = 7

etc
HawkI is offline  
December 15th, 2016, 04:10 PM   #13
Senior Member
 
Joined: Mar 2015
From: England

Posts: 163
Thanks: 4

I was looking into Pascal's triangle the other day and how if there's a Prime number after the number 1 on a row it can divide all the other numbers in that row. This inspired a new way of looking into this "Relative Fraction Trapezium" and what I found was interesting.

Not only is the next Prime number guaranteed to be in the finite row, but also now for the first time, it some times tells you what the next Prime number is through the use of finding the Average of Irrational rotations and or adding up the Integral values.

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

Last edited by HawkI; December 15th, 2016 at 04:15 PM.
HawkI is offline  
December 17th, 2016, 01:05 PM   #14
Senior Member
 
Joined: Mar 2015
From: England

Posts: 163
Thanks: 4

I just wanted to let you know that I am very close to finding how to do this Prime pattern automatically now and that if you want to be mentioned in this discovery (Rediscovery) then your time is running out.

I mention this because just now I realised I can manually find the value of "x" which divided by Pronic equals to round down 1 / Infinite round down. And then from there + OR - by n to get to the Prime in negative form.
HawkI is offline  
March 2nd, 2017, 09:29 AM   #15
Senior Member
 
Joined: Mar 2015
From: England

Posts: 163
Thanks: 4

On and off I have been looking at this and here are some new things I have found

You can consider each row of the trapezium as a set.

You can always find an intersection between the current set and the set below.

Find it to the right of the current Prime and the next Prime in the next set is directly below

Find it to the left of the current Prime and the next Prime in the next set is directly south west diagonal

Surely by now I have proved in some shape or form that Primes are a recurrence relation?

Last edited by HawkI; March 2nd, 2017 at 09:43 AM.
HawkI is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
pattern, prime, rediscovered



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
I've had a go at trying to find a pattern to prime numbers HawkI Math 5 June 27th, 2016 07:37 AM
Theory of variable prime pattern KenE Math 1 April 12th, 2016 01:05 PM
The Pattern in Pi! silvershell Applied Math 13 May 27th, 2015 03:19 PM
Is there a pattern here? alikn Elementary Math 5 November 29th, 2009 10:03 AM
The Pattern in Pi! silvershell Real Analysis 0 January 1st, 1970 12:00 AM





Copyright © 2017 My Math Forum. All rights reserved.