Re: Prime numbers, my find, and discovery

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


>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.

>I may have found that reason.

Nothing you've ever posted gives any explanation for this.

>Not surprisingly, a first-find in the area of prime numbers *should*
>be a big deal, but despite the ease with which I link my discovery to
>some of the biggest names and biggest issues in mathematics, there is
>the value to society of the discoverer.
>
>Since when has modern society decided that discoverers should be
>attacked instead of cheered?
>
>Now you may have seen a LOT of postings from people trying to attack
>the worth of my find, which can be a healthy process--if they stick
>with the facts.
>
>Unfortunately posters have shown a dismaying tendency to lie, but
>that's minor to the problem I've faced where mainstream mathematicians
>have tried to ignore or downplay my result.
>
>I have a first-find in the area of prime numbers, and my not being a
>mathematician does not mean that mathematicians can just deny the
>reality if it suits them.  While they may feel they have many reasons
>to attack the value of an important find from a non-mathematician,
>those reasons cannot be in the best interests of society.
>
>If Gauss were alive today, would he cheer me?
>
>I like to think he would, as he was someone interested in asking
>questions *and* in getting answers.  First and foremost I think he
>would have been driven to find out just where my discovery led, and if
>it was the answer to the question that intrigued him.
>
>As I've found a partial difference equation, it leads to a partial
>differential equation.  That partial differential equation may answer
>many questions.

"May" indeed. You've never shown why the solution to the 
"partial differential equation" has anything to do with pi(x),
and you've ignored explanations of why that seems unlikely,
based on analogy with other difference equations and the
"corresponding" differential equations.

>Or more importantly, it should raise many more.
>
>You should not allow mathematicians to continue to pervert a process
>that has helped humanity for so many thousands of years.  You must not
>show a loss of faith in the future of humanity, as if discoverers are
>no longer needed.
>
>Academic institutions can no more constrain who can make a major
>discovery, than they could limit who will be a great painter,
>composer, or architect.
>
>Maybe that's part of the problem as we know that architects require a
>lot of schooling beyond just art, as they need to know physics, like
>materials science, and engineering, among many other things.
>
>So it's easy to assume that a great building can only come from
>someone heavily trained in academia who can manage a huge structure.
>
>However, sometimes something a little smaller in terms of physical
>size can be huge in terms of social value, and the person who built
>it, might be someone from just around the corner, outside of academia.
>
>Maybe I'm pushing the analogy, but I hope that you'll agree that at
>the end of the day, what's important is the *information* and petty
>squabbles and personal attacks are irrelevant, and often forgotten
>over history anyway.
>
>It's the knowledge that remains--pure.
>
>dS(x,y) = [p(x/y, y-1) - p(y-1, sqrt(y-1))][ p(y, sqrt(y)) - p(y-1,
>sqrt(y-1))],
>
>S(x,1) = 0, p(x, y) = floor(x) - S(x, y) - 1, 
>
>and S(x,y) is the sum of dS from dS(x,2) to dS(x,y).
>
>And p(x,sqrt(x)) is the count of prime numbers up to and including x.
>
>That's pure knowledge.  Information discovered by me, and hey, it
>wasn't like it just jumped in my lap you know.  There's a value to
>cheering on discovery, and not attacking it.
>
>The value is hope for the future.  Hope that there may be answers out
>there from unlikely sources.  Hope that every person can be valuable.
>
>Maybe mathematicians want a reality that has them ordained as the only
>route for new mathematical knowledge.  Possibly they wish control over
>the creative process, and total dominion over mathematical discovery.

Or possibly you're just a megalomaniac idiot. Don't want to overlook
that possibility...

>But hey, they're only human.
>
>
>James Harris
>
>"My math discoveries, found for profit"
>http://mathforprofit.blogspot.com/

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

David C. Ullrich