Mathematicians had all but given up hope of ever understanding prime numbers. The last time there was a brief flurry of excitement was when it was discovered that the periodicity of zeros from the Riemann-Zeta function closely matched the spacing of energy levels in high-Z nuclei [1]. Prior to that, Gauss and others [2] had showed a relationship between Pi, Logs and prime number density. You then have to go back to Euclid some 2,300 years ago for his proof of an infinity of prime numbers [3].

Number theory sits at the centre of the mathematics world and despite a massive effort to understand prime numbers, little is known about them. A number of important conjectures (Riemann’s Hypothesis [4], Goldbach’s Strong Conjecture [5] and others) lie unsolved and perhaps unsolvable.

The mathematicians working on prime numbers are very smart people who are able to manipulate a group of abstract concepts in their heads which leaves myself and others wondering which world they come from. But having adopted a unique problem-solving method in my own software company that proved highly successful, I decided to dabble in mathematics as an exercise to see if this approach to solving complex problems could find answers when other approaches were clearly not delivering. What ensued was an adventure of discovery and obstacles that lasted over six years.

The first project I started on was to look at the Four-Colour Map Theorem and discovered a way of simplifying it but failed to convince a local mathematician and a professor from my old university of Otago of its relevance. This was my first experience of mathematicians discounting simplicity and this was repeated many times. Looking back at this problem after six years made me realise that there is an even better was of simplifying that should lead to a simple proof but I sense that it will be ignored.

Undeterred, I started working on Fermat’s Last Theorem and Goldbach’s Conjecture and that is when I observed a pattern in the pairs of primes that combine to form all even integers according to this latter conjecture. Driven by a need to understand this observation, I spent almost two years getting to grips with this before I demonstrated this to a local professor and a senior colleague. They were intrigued but again dismissed it as not relevant, believing that the French mathematician Dirichlet already covered this.

At this stage most people would have accepted the advice of those considered to be much more knowledgeable but my trusted intuition said they were wrong. History will show that I was right to persevere with two papers on prime numbers now published on the internet [6,7] that reveal a number of facts about numbers in general and prime numbers and all are based on simple mechanisms requiring nothing more than high school mathematics to understand.

In my first paper, I discovered that multiples of 3 and 5 form a palindromic pattern, leaving all higher prime numbers and multiples of those prime numbers, evenly distributed between eight channels I called the Prime Number Channels. This provides a basis for understanding Goldbach’s Conjecture in terms of why some even integers are more likely to have more pairs of primes than others, something that over 200 years of research failed to produce.

In my second paper, I describe simple attributes of prime numbers and show a remarkable graph that presents a powerful and convincing argument that groups of prime numbers occur between boundaries.

My scope of research also included looking at Riemann’s Hypothesis and the nature of the multiple of 3 and 5 strongly suggested that this problem was probably not worth pursuing as it didn’t take into account that all other prime numbers need to be treated as a separate group. It also made me wonder why researchers were using a manipulation of logic to prove this hypothesis when in reality they were trying to prove that the behaviour of prime numbers, which is unknown, matches this model.

In my papers I make many suggestions for further research and want to start a new period of interest in prime numbers. As to my secret method of problem solving and the reasons why I believe that mathematicians have failed where I have succeeded, you’ll have to wait until my book ’Simplicity for a Competitive Advantage’ is published. The draft is ready and and I am looking for a publisher to pick it up.

My papers are not written in an orthodox terminology, a result of my limited knowledge of mathematics convention, but in the end I wanted to write them in a way that opened my ideas to an audience that is wider than mathematicians. The mechanisms of number interaction were not designed by mathematicians and belong to everybody. Finally, I have held back two papers which I will release in the future and these will be sure to create some surprises.

*References*

1. The stability of electron orbital shells based on a model of the Riemann-zeta function.

2. Prime Number Theorem

3. Euclid’s Proof of an Infinite Number of Primes

4. Riemann’s Hypothesis

5. Goldbach Conjecture

6. Paper 1

7. Paper 2

*Phil Jackson runs his own small software company, Concept Patterns Limited. He can also be found on the Simplicity Instinct website.*