If one lays out the numbers linearly, in contineous format, then looked at the distribution of primes, one does not see any emergent patterns.

Just like Matrices are used Mathematically, (one can in some way observe the format I used), I found out an interesting thing whilst reading a book on Born, it’s significance in the rule for density is paramount, I will try and provide further linkage.

What you notice is the the dimensions of the grids boxes, ie 10 rows x 10 columns are fixed and uniform. Now because of this uniform layout, the prime numbers fall in what appears a random number of rows, and random columns, obvious its the standard layout of the Eratosthenes sieve.

Now if one creates the prime grid thus:
http://homepage.ntlworld.com/paul.valletta/PRIME%20GRIDS.htm

(please ignore the simplistic and crudness of the pages, blame lazyness at the time)

Now, what happeans is all the randomness of the prime numbers are constrained into uniform certain criteria.

For instance, the second row starts beneath the number 2, so the first colume reading down from number 2 has 2 + 11.

You can do a number of things to reveal interesting factors when looking at the first 10 x 10 rows and columns, 100 numbers that are layered out like in my link.

Example in the colunm reading downwards form the starting number 6 (perfect number, nestled between primes 5 + 7), there are ZERO-PRIMES in this column, the same for the column starting from number 9.

Now you can read the grid in a number of ways that start to reveal the really interesting things about the distribution of primes.

Start at number 3, but in the diagonal adjoining boxes: 3, 13, 23,33..93.

What do you see?..it has the greatest number of primes, 6.
Read off the same starting from 7 and 9.

Diagonally, there are NEVER any prime numbers that occur when read off the numbers (diagonally) starting numbers [4-5-6].

There is a vast amount of other data(to much to place here) that I have discovered in producing the grid up to 5000 numbers (which is small I know, but I have physically drawn the boxes, and its time consuming!).

Interesting that, its how one looks and constructs the grid in order to observe the distribution of numbers contained.

I do have one question for the number theorists. It appears to me that the “mu” function is based on the primes but is also being used to make more “accurate” predicitions about their distribution. Isn’t that somewhat misleading? Using the primes to describe their distribution.

I was particulary fascinated by the apparent relationship between Quantum theory and Prime numbers. Very provocative.

Elliot

If I understood him correctly, the idea is that one’s first guess that the primes are distributed randomly is false. But the next guess, that they are distributed randomly with a kind of diminishing amplitude as you climb the integers, is just about right.

But it just raised this fascinating question for me: they look like they would look if they were distributed randomly (modulo that diminishing amplitude). But, there is only one throw of the dice here. I mean, in another number system, there would be another random pattern of primes? Boggle boggle. But what can ‘random looking’ mean in this context? Why is it that this particular ‘random’ pattern of primes exists? The notion of randomness, tho enlightening, raised as many questions as it answered.

I was also struck for the first time how odd it is that Eratosthenes sieve could yield a pattern like that. I mean, imagine pulling out the multiples of a given integer on a piece of tape…. pull out [.2.4.6.8....].. pull out [..3..6..9..12.....]. How more regular can those patterns be? So pull them all out, and look at the pattern of the residue. How can the complement of a set of perfectly regular patterns be so irregular?

So yeah, it clued me in to the magic of primes. I’m definitely going to go back and look at John Derbyshire’s commendable “Prime Obsession” again.

Last post on this topic.

Thanks

What holds my perspective is the fact that some method could be mapped, and if all the tragectories were traced back to a source in a collision processes, then how would information be mapped from that “point” outward, in a computational model? Is there such a thing.

We are given extra dimensional scenarios as possible problems with doing that? Why invoke it? Can you use superfluids to computational give information?

Quantum Algorithm for Hilbert’s Tenth ProblemTien D Kieu

We explore in the framework of Quantum Computation the notion of { Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert’s tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle–that is, if certain hamiltonian and its ground state can be physically constructed according to the proposal–quantum computability would surpass classical computability as delimited by the Church-Turing thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.

The last paragraph of the article doesn’t make sense to me, though.

This fact lies within the Quantum Mechanical Description of “pure” states

Here is a teaser/clue for those who like me like to solve a good mystery, think thus:It used to be False?..the False factor is never in the Future?

http://groups.msn.com/RelativityandtheMind/dynamictriangularaxions.msnw

if one puts the prime numbers into certain fixed grid forms;

http://homepage.ntlworld.com/paul.valletta/PRIME%20GRIDS.htm

then one can conclude that the ReimannZ :

http://www.freewebs.com/moorglade/riemannshypothesesthetru.htm

can be prooved?

But I do not want to place that there yet!..I have so much to learn, the programme has been a really amazing benefit to me, especiall in the understanding of the Prime Density Function by Gauss (which I had allready worked out but unknown to Guass’s work), and the fact that the first “perfect” Number is 6?

Amazing, I am going to continue to tease fro a while

-cvj

As a of layman status these things are interesting because of the underlying archetecture that such pure math is suppose to “explode of itself” onto the scenes of the day, as we go on with our lives.

Is it possible for lay people to be enamoured with this stuff? I am, because I know that all these fine people working in their respective areas, have to have this basis and the fortitude of conceptual developement towards the expression of said thoughts, held to these constraints? I watch the concepts to learn the math? It’s hard.

Are they others out there. I know there are, becuase it has held minds for sometime.

Tell me different please?

-cvj

Would be interesting to hear what non-mathematicians/physicists thought of it.