Re: Prime numbers, my find, and discovery

David C. Ullrich <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> On 1 Dec 2003 19:13:39 -0800, [EMAIL PROTECTED] (James Harris) wrote:
> 
> >I should be a rather happy guy.  After all, over 18 months ago I found
> >this partial difference equation I call dS(x,y), and the sum of dS
> >from dS(x,2) to dS(x,sqrt(x)) is the count of primes up to and
> >including x.
> >
> >Afer talking with mathematicians all over the world by email and
> >Usenet, and searching math references, both bought and on the
> >Internet, I know that I have a first-find.
> >
> >Somehow, I am the first human being in recorded human history to find
> >a partial difference equation that sums to give the count of prime
> >numbers.  
> 
> Not true. Won't become true through repetition. See
> 
> http://mathworld.wolfram.com/LegendresFormula.html
> 

Are you saying David Ullrich that what's shown at the link you provide
is a partial difference equation that sums to give the count of prime
numbers?


> >This post is about some of the significance of that beyond
> >it being a first-find.
> 
> Really? Curious that it's such a long post, then.
> 
> >Prime numbers have fascinated people for some time, and mathematicians
> >especially.  The great mathematician Karl Gauss is credited with
> >making an important hypothesis in the field of prime numbers, as he'd
> >noticed something.
> >
> >Gauss noticed that the count of primes numbers could be approximated
> >by x/ln x, for instance, the count of primes up to 1000 is 168, and
> >1000/ln 1000 approximately is 144.76.  The count of primes up to 10000
> >is 1229, and 10000/ln 10000 is approximately 1085.73, which is a
> >closeness that continues as you go higher.
> >
> >Gauss wondered what the discrete count of prime numbers could have to
> >do with continuous functions like x/ln x, and while mathematicians
> >made progress in finding relations that gave limits, like Chebyshev's
> >use of the zeta function discovered by Euler, they never found a
> >reason why.
> 
> Not true. A reason why (that is, a proof of the Prime Number Theorem)
> was found long ago, I think in the 1890's. More or less simultaneously
> by two people, who I think are the people whose names I think are
> spelled something like Hadamard and de-Vallee Poisson.

That is false.  Can someone help David Ullrich out by *giving* the
Prime Number Theorem?  It's a boundary condition, and doesn't tell
why.

My discovery is a direct connection between the discrete and the
continuous because the partial difference equation I found has a
partial differential equation analog.

For you physicists, remember that in calculus integration is usually
discussed by considering *discrete* sums as approximations to a
solution.  Then you shrink your delta and consider the limit as it
goes to 0.

What I have is a first approximation, which shows that the *count of
primes numbers* is a first approximation in the integration of a
continuous function!!!

That has NEVER been shown before in recorded human history, and
offers, for the first time, a reason for *why* the prime distribution
is related to a continuous function like x/ln x.

Remember, Gauss noticed that the count of primes numbers could be
approximated by x/ln x, for instance, the count of primes up to 1000
is 168, and 1000/ln 1000 approximately is 144.76.  The count of primes
up to 10000 is 1229, and 10000/ln 10000 is approximately 1085.73,
which is a closeness that continues as you go higher.

You don't have to just trust me--some guy posting on Usenet--check the
literature on "partial difference equation", the "Prime Number
Theorem", and integration.

I'm putting in quotes phrases that needed to be put in quotes for
those who wish to do Google searches for maximum efficiency.

The Internet is important to me as it offers an independent source
that readers can quickly check.


James Harris

"My math discoveries, found for profit"
http://mathforprofit.blogspot.com/