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Topic: Pattern Found involving primes
Replies: 2   Last Post: Sep 24, 2017 12:51 PM

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 Graham Houston Posts: 2 From: N/Ireland Registered: 9/22/17
Pattern Found involving primes
Posted: Sep 23, 2017 5:10 PM

Hi .. I discovered a pattern that builds a structure using the natural
numbers.. I believe it to be the actual geometry of the numbers and not
linear as you might expect..

The reason I've come to this conclusion is because using my method you
can construct a simple natural structure that acts like a frame that
encompasses all the primes and "partitions them off in to incremental
sets". These sets or partitions as I call them are separated by
calculable lines that increment in distance.

The lines that create the frame are 100% void of prime numbers.. This
is a very useful property of the frame as you can use this to see if a
number is composite as if it belongs to the frame then its 100% not a
prime number! I call these numbers warden numbers but I think I'll be
changing that to something more intuitive such as frame numbers..

the sets or partitions between these frame lines are extremely dense in
prime numbers.. There is even a pattern that determines how dense these
are.. One of these lines in particular within the sets has given me
some amazing results with find primes that has a pattern based on the
index into the line... I'm assuming the same will be proven for the
other lines..

Some lines are sparse some are extremely dense..

I can even make simple observations regarding the distribution of the
prime number because of the structure.. Its clear to see that twin
primes will always occur due to the fact that frame lines always have
primes on the opposite sides when viewed in a direction.. The only
reason the twins would stop happening is if primes ran out and we know
this to be false..

For anybody interested in this I can explain how it works from
beginning to end and how to construct the structure..  its very simple
but is a little awkward to visualise what is going on until you actual
build a map of the structure!

I'm not a mathematician by any stretch of the imagination just a guy
with a obsession with patterns.. So don't expect any grand Maths talk
.. It will be in straight english

I believe the structure is 100% what Ulam's Spiral kind of hints
towards.. as I could see how it would create that if done the way it
was done..

There is a natural geometric that extends in both directions for + and
negative numbers .. I've been able to gather some unbelievable insights
into primes because of it.. I just feel it needs to be know so that
people with the skills can take it further..

It also explains the distribution discrepancy of the prime counting
theorem. It explains the connection 6-1 and 6+1 and primes..

Is there a way of uploading graphics and documents to the group?

I can even easy use this to find primes form the name digital patterns
as they grow based on the index also being the same digital pattern..

I believe I have something very important to number theory, yet after 8
years I've still not got a reply from anybody willing to look at my
finding! Infuriating stuff..

Date Subject Author
9/23/17 Graham Houston
9/24/17 David Hobby
9/24/17 mathedman@hotmail.com