Re: Prime numbers, my find, and discovery

On 3 Dec 2003 06:03:06 -0800, [EMAIL PROTECTED] (James Harris) wrote:

>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?

Uh, yes.

>> >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?  

Everyone but you _knows_ the PNT.

>It's a boundary condition,

Huh? Exactly how is the statement that pi(x) is asymptotic to
x/log(x) a "boundary condition"?

> and doesn't tell
>why.

No it doesn't - I didn't say it did. The _proof_ of the PNT is what
explains why it's true.

Duh.

>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.

Except that you've never shown that the solution to what you
insist on incorrectly calling that pde has anything whatever to
do with pi(x).

>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.

Uh, no, the reason why was given over a century ago.

Otoh _you_ have never given any explanation for the connection.
Just _saying_ that your difference equation has an analogous
"pde" does not prove that pi(x)/(x/log(x)) tends to 1 as x tends to
infinity.

Unless maybe I missed it. How does your proof of that fact
go again?

>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.

You know, when you equate Google with the mathematical
literature you sound like an idiot. Just a hint.

>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/

************************

David C. Ullrich