It occurs to me that despite my putting it up a lot, few of you
understand how that partial difference equation I keep talking about
works.

Basically, for dS(x,y), where x and y are positive integers, if y is a
prime number p, dS(x,p) is the count of composites up to and including
x that have p as a factor but do NOT have primes less than p as a
factor. For instance, dS(10,3) = 1 because 9 is the only composite up
to 10 with 3 as a factor that doesn't have 2 as a factor.

While if y is not prime, dS(x,y) = 0.

That's it.

What happened is that when I looked for a way to count prime numbers,
I did it from scratch, having not checked any textbooks on the
subject. Going from scratch, I intuitively went for a way that works
differently from what mathematicians have been doing for over a
hundred years. So it was serendipity.

What mathematicians do is get a count of composites for a prime p, by
using floor(x/p) - 1. That is, they know that the count of numbers up
to and including x that have p as a factor is floor(x/p), and not
wanting to include p itself as it's not a composite, they subtract 1
for it. Trouble is, that you get a count that includes other primes
as well, so you correct. Like with 10, floor(10/3) = 3, and minus 1
is 2, which is the count for 6 and 9. But, when you get the count for
2, you have floor(10/2) - 1 = 5, which is 4, 6, 8, 10, so you have
overlap. So they subtract off floor(x/6)=1 to correct. Notice you
also need to already have a list of prime numbers.

That's Legendre's Method. It's been around for over a hundred years.
It's clunky and inelegant.

I didn't know Legendre's Method, as I didn't bother to read up on the
subject before thinking about it, so I came up with something more
complicated, but ultimately far more elegant, which is to use the dS
partial difference equation:

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.

And p(x, y) = floor(x) - S(x, y) - 1, and you get S as the sum of dS
from dS(x,2) to dS(x,y).

So what did I do when I made my discovery? I went to people in the
field, like Lagarias and Odlyzko, and basically got blown off.

So now I'm ****ed. I can see how mathematicians really behave. They
do a quick calculation trying to see how a discovery might promote
*their* personal careers. After doing the selfish calculation they
see my work as not helping them and couldn't care less about elegance,
or beauty or anything of value.

It's all about them. For people like Odlyzko, only they matter, not
the math.

I hate mathematicians.


James Harris

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

"James Harris" wrote in message
...
snip
So what did I do when I made my discovery? I went to people in the
field, like Lagarias and Odlyzko, and basically got blown off.

So now I'm ****ed. I can see how mathematicians really behave. They
do a quick calculation trying to see how a discovery might promote
*their* personal careers. After doing the selfish calculation they
see my work as not helping them and couldn't care less about elegance,
or beauty or anything of value.

It's all about them. For people like Odlyzko, only they matter, not
the math.

I hate mathematicians.


James Harris

Let me show you an analogy and see if this helps your understanding of
reality.

There's a farmer who raises corn for a living. He has a huge, fast combine
for harverting his corn. James Harris comes along, and knowing nothing
about corn, figures out a cool way to harvert corn by hand. It's simple,
cool, better than the old manual corn picking method, and has never been
thought of before in human history. However, it's thousands of times slower
than using the existing combine. The farmer blows James off because the
result, while unique, has no real value to him.

So what should James do? Something useful like going to aggie school to
learn modern corn farming methods? Find another hobby? Or whine endlessly
about how he's being ignored by corn farming society?

--Stan Gula

James Harris wrote:

It occurs to me that despite my putting it up a lot, few of you
understand how that partial difference equation I keep talking about
works.
[snip]

http://www.crank.net/harris.html
It's not every braying jackass that gets a whole page at crank.net

It has been more than amply posted that you have no idea what you are
doing. You define things to suit your psychosis and, when your
bull**** fails in practice, you ignore empirical fact and rave some
more - louder, more stupidly, and trolling more newsgroups with your
crap.

"alt.math.undergrad" Harris? If they can do algebra, they also know
you are an idiot. Try something in kindergarten to 12.

http://www.mazepath.com/uncleal/sunshine.jpg
http://w0rli.home.att.net/youare.swf

--
Uncle Al
http://www.mazepath.com/uncleal/qz.pdf
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)

James Harris wrote:

It occurs to me that despite my putting it up a lot, few of you
understand how that partial difference equation I keep talking about
works.


Prime Counting Function
http://mathworld.wolfram.com/PrimeCountingFunction.html

Prime Difference Function
http://mathworld.wolfram.com/PrimeDi...eFunction.html


Crank Information
http://www.crank.net/harris.html
http://www.crank.net/usenet.html
http://www.google.com/search?q=harri...Awww.crank.net
http://www.google.com/search?q=%22ja...s.pandora.b e

James Harris wrote:

It occurs to me that despite my putting it up a lot, few of you
understand how that partial difference equation I keep talking about
works.

Try pressing the CAPS LOCK key before posting. Surely you know that the
louder the message is shouted, the truer it is.

James, if you are posting in this newsgroup in order to tell everyone how
smart you are, go ahead. This is an unmoderated group and no one will stop
you.

If you are posting in this newsgroup in order to *convince* everyone how
smart you are, you must post material which is: 1) original, 2)
non-trivial, 3) useful, and 4) correct. Furthermore, the correctness must
be demonstrable by cogent arguments which are free of errors, gaps,
omissions, and ambiguities.

If you are posting in this newsgroup to further your aim of making lots
of money, maybe you should check your wiring. Something is loose
somewhere. When you find the problem and correct it, confirm to your own
satisfaction that this newsgroup is sci.math -- it is not PayPal or eBay.
There's no money here.


--
There are two things you must never attempt to prove: the unprovable --
and the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com

"C. Bond" writes:

If you are posting in this newsgroup in order to *convince* everyone how
smart you are, you must post material which is: 1) original, 2)
non-trivial, 3) useful, and 4) correct.

Not necessarily. He's already convinced me of how smart he is, and he's
done none of those things.

Doug

I hate mathematicians.


James Harris


Of course you do. They do math. And that
really ****es you off.

"James Harris" wrote in message
...
It occurs to me that despite my putting it up a lot, few of you
understand how that partial difference equation I keep talking about
works.

snipped what we have seen before

I hate mathematicians.

Didn't you say the same thing about them after they dismissed your FLT
proof? And your algebraic integer discovery?

Do you know anything about proof by induction?

On 25 Nov 03 17:23:30 GMT, Doug Norris wrote:

"C. Bond" writes:

If you are posting in this newsgroup in order to *convince* everyone how
smart you are, you must post material which is: 1) original, 2)
non-trivial, 3) useful, and 4) correct.

Not necessarily. He's already convinced me of how smart he is, and he's
done none of those things.

Doug


Zing!


--
Wolf Kirchmeir, Blind River ON Canada
"Nature does not deal in rewards or punishments, but only in consequences."
(Robert Ingersoll)

inductive proofs are one-to-one with deductive proofs,
as was shown in a 2-page proof in Mathematics Magazine;
can they prove it with categories?
I wouldn't know what to label Jimi's proofs,
other than "this site is under construction," or
"but the Internet was too small to contain it!"

"Richard Henry" wrote in message news:VKNwb.21473$m24.7860@fed1read02...

It occurs to me that despite my putting it up a lot, few of you
understand how that partial difference equation I keep talking about

Do you know anything about proof by induction?

--ils duces d'Enron!
http://larouchepub.com/other/2003/30...te_plmbrs.html