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..