- #1

- 1,559

- 0

Over the last couple of years I've spent some time on a pseudo-mathematical investigation the primes. I feel the results of this investigation are important, but I cannot be sure of this since I know so little about mathematics. I have written, emailed and phoned a number of senior mathematicians and called in a few favours in the hope of interesting someone in my notes but none have even replied. Recently I've been trying to tidy up these notes with a view to submitting them for publication. Not because they are likely to be published, I've no idea how to write on this topic, but because this would at least get my notes read by someone competent and establish some sort of priority.

Just this week, however, I was horrified to discover that a new website is under construction called 'The Orbits of the Primes'. It claims that the content, once the site is up and running, will revolutionise number theory. I suspect, from the few clues given, that this site will present the same conclusions about the primes that I have reached. This is very annoying, to put it mildly. A year ago I constructed a virtual 'observatory' in Excel showing the orbits of the primes and how these orbits allowed us to predict the postion and distribution of the primes. I think I'm onto something but do not know how to express it in a way a mathematician would immediately grasp, and am trapped in complete (mathematical) obscurity.

So, I'd like to ask for some help and advice. I need to reframe my ideas in mathematical language, and I need to find out whether or not my approach to the primes is mathematically interesting.

Using my approach it is possible, I think, to prove that there are infinitely many twin primes. Also, this approach seems to shed some light on why there is a correlation between the pattern of the primes and the pattern of energy levels in a random quantum drum. I already have a rough function for pi(x). More importantly, for I need the money, I think that at least in theory this approach would allow a proof of the Riemann hypothesis, or at least a proof of its decidability.

Whoever proves that Riemann's hypothesis is true (or false) would win fame, a bright future in mathematics and a million dollars. If I am right about the primes then such a proof need not be beyond the average graduate mathematician, and not beyond some of the mathematicians here. I know how unlikely this will seem, but it seems likely to me that a proof, if one is possible, will come from an unusual source. After all, all the obvious methods have been tried and have so far failed.

I am not interested in fame or a bright future in mathematics, but I am interested in a share of a million dollars. This gave me an idea. Suppose I post my ideas here. Then you could rip them to shreds if that is what they deserve and I can forget all about number theory. However, if by some miracle I am right and some interesting new proofs can be derived from these ideas, then as mathemticians you would be in a position to develop and exploit them. As you would be able to express them properly you might even be able to create something publishable out of them. If so, I hope I'll get a credit.

Also if, by some miracle, I am not mad after all but have found a not-too-difficult route to a proof of RH (or of its decidability) then someone here might be able to construct such a proof, or pass on some ideas to someone capable of doing so. This is almost certainly not going to happen, but sometimes truth is stranger than fiction. You will all have connections in the mathematics world, I have none.

If anyone here can make use of these ideas then feel free to do so. All I ask is for a mention, or for a mention of this discussion. If they lead to a proof of RH then all I ask for is for 25% of the prize.

What I would like to do is post chunks of notes and ask for your comments, for some help in expressing them properly, and for your opinion on whether they are interesting or trivial. I'll explain all the principles and work towards my thoughts on RH. The notes are quite long so I wanted to generate some interest before inflicting them on you. Shall I start posting them or shall I go back to philosophy?

The million dollar question would be: Can you prove the Riemman hypothesis by using my methods? If so, you've won $1,000,000 less my cut.

To start things off here is one 'result'. All numbers at 6n+/-1 are prime unless they can be written in the form 6np+/-p. From this 6np+/-p rule the behaviour of the primes is entirely predictable.

Shall I post more? My notes are long and incompetently expressed so I don't want to start posting them unless someone's interested in trying to understand them.

Regards

Peter Jones (Canute)