Calculus and my prime counting function

Discussion in 'Recreational Math' started by jstevh, Nov 19, 2006.

  1. jstevh

    jstevh Guest

    I've repeatedly emphasized the simple sieve form of my prime counting
    function to make a point that it is new, and unique in ways clearly
    seen to what was known before as you can just do a web search on "prime
    counting function" and easily see what math people already knew and
    find nothing close to the following.

    With natural numbers x and n, where p_i is the i_th prime:

    P(x,n) = x - 1 - sum for i=1 to n of {(P(x/p_i,i-1) - (i-1))}

    where if n is greater than the count of primes up to and including
    sqrt(x) then n is reset to that count.

    I don't think you can find another multi-variable prime counting
    function in the math literature at all. I know I haven't found one,
    and it's another crucial point to make against people posting against
    this research.

    But now things get a bit more complicated and I worry about making a
    more complicated post, but I need to address more directly just how
    important this research must be, and for that, there will need to be
    some calculus.

    Because my prime counting function recursively call itself you can go
    from the sieve form to a fully mathematicized form with the following.

    With natural numbers x and y, if y<sqrt(x) then

    P(x,y) = floor(x) - 1 - sum for k=2 to y of (P(x/k,k-1) -
    P(k-1,sqrt(k-1)))( P(k,sqrt(k) - P(k-1,sqrt(k-1))))

    else P(x,y) = P(x,sqrt(x)).

    That may look a lot more complicated but the main difference here is
    that because

    P(k,sqrt(k) - P(k-1,sqrt(k-1))

    will equal 0 if k is not prime, I can use the prime counting function
    itself as a switch which will zero out everything if k is not prime, so
    you only get non-zero values when k is prime, just like before.

    And now you have something never before seen at all with a prime
    counting function, which is a difference equation as part of it, and
    more specifically, what is being summed is a partial difference

    Not surprisingly, you can go from that to a partial differential

    P'y(x,y) = -(P(x/y,y) - P(y, sqrt(y))) P'(y, sqrt(y))

    and again find something never before seen with a prime counting

    So now to believe that my research is actually old you have to believe
    that no one bothered to go to a partial differential equation from the
    earlier form.

    In its sieve form my prime counting function can be related directly to
    other sieve prime counting functions and elements within them.

    Numerical integration of the partial differential equation can reveal
    if it is close to the prime count, and if it is, then it stands to
    reason also that it would be related to continuous functions that are
    close to that count as well, and more specifically if it is very close,
    to any functions that follow from the Riemann Hypothesis.

    The other possibility is that despite following directly from the prime
    counting function, the numerical integration of the partial
    differential equation is completely unrelated to the prime count.

    However, my own attempts at doing that integration show it to be closer
    than Li(x) but a bit further from the prime count than R(x), the
    Riemann function.

    If Legendres had my prime counting function but failed to figure out
    the fully mathematicized form and failed to figure out the partial
    differential equation, then he missed some obvious things, and not only
    him but mathematicians that followed him did as well, including Riemann

    Proper follow through on this research alone should make headlines
    around the world.

    It is just some of my number theory research.

    For instance, I have also proven Fermat's Last Theorem.

    James Harris
    jstevh, Nov 19, 2006
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  2. jstevh

    David Moran Guest

    I'm curious...How did you derive this equation? I'm not saying it's right or
    wrong, I'm just curious.
    I could be wrong, but wouldn't the numerical integration take a lot of the
    program's time? It seems to me if you could eliminate that, you could speed
    things up. But I don't see how you'd eliminate it.
    David Moran, Nov 19, 2006
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  3. But does your proof pass the null test? :)

    "All things extant in this world,
    Gods of Heaven, gods of Earth,
    Let everything be as it should be;
    Thus shall it be!"
    - Magical chant from "Magical Shopping Arcade Abenobashi"

    "Drizzle, Drazzle, Drozzle, Drome,
    Time for this one to come home!"
    - Mr. Wizard from "Tooter Turtle"
    Frank J. Lhota, Nov 19, 2006
  4. jstevh

    Dr. Doctor Guest

    this post has nothing to do with Calculus, nor your stinking counting

    Mau a big blac buck sit your ass down and read you math books while your
    Dr. Doctor, Nov 19, 2006
  5. jstevh

    Rupert Guest

    I don't believe this. I don't believe you've actually performed the
    numerical integration. Show me the code you used to do it.
    Rupert, Nov 19, 2006
  6. jstevh

    Rupert Guest

    Hey James, you didn't let me join your group. That's not being very
    friendly. After all the good times we've had together, too.
    Rupert, Nov 19, 2006
  7. jstevh

    Tonico Guest

    I knew it!! James Harris is Andrew Wiles in disguise...I knew it!!
    Tonico, Nov 19, 2006
  8. Why do you keep saying this? I mean even if it were true nobody
    sees why it would matter. And anyone can see that it's not true,
    just by looking up Legendre's formula, where there's that two-variable
    function phi right there on the page.
    For heaven's sake. Most of these things involve some sort of
    recurrence relation. And any recurrence relation is equivalent
    to a certain difference equation. The idea that this is a big deal
    is hilarious.
    Just because nobody ever wrote it down before. So what? You've
    never given any evidence that the solution to this PDE has
    anything to do with anything.
    Let's see, that might happen, and if that happens then this other
    might happen, which would say something unspecified about something.

    And the fact that all this _might_ happen proves you're a genius.
    Uh, yes, that's another possibility. Seems much more likely, given
    what happens with simple examples.
    Until you show that the pde has some connection with something, other
    than just looking kind of similar, you have no evidence that anyone
    missed anything. Here's why: If the solution to your de actually
    _does_ have something to say about pi() I'll be amazed - I see no
    reason why it should and I have very good reasons to think that
    it almost certainly doesn't.

    So maybe the de has no significance whatever. That seems very likely.
    If so then probably those guys didn't "miss" it.
    What research? You've written down a pde and actually _stated_
    absolutely nothing about it.

    Breaking JSH wrote down an equation! Didn't solve it,
    didn't prove anything about the solution. Wow.


    David C. Ullrich
    David C. Ullrich, Nov 19, 2006
  9. jstevh

    jstevh Guest

    Then show one.

    Readers should note that David Ullrich is a tenured math professor at
    Oklahoma State University, so his claim is not just a minor babbling
    from just some Usenet poster but goes to my charge that mainstream
    mathematicians are deliberately avoiding the truth about my research
    and deliberately misleading the public--lying about mathematics.

    Here the challenge to him is to show a difference equation with any
    other known prime counting function.

    His failure--as I know he can't--goes to the possibility of conspiracy
    on the part of established mathematicians at universities.

    James Harris
    jstevh, Nov 21, 2006
  10. jstevh

    gjedwards Guest

    Readers who note that he's a tenured math professor are more likely to
    also note that he has a clue what he's talking about, whereas you are
    just an idiot. That's basically the way readers have interpreted things
    for the last 11 years, but, hey, if you keep going for another 11 maybe
    one of your readers will eventually agree with your interpretation.
    Personally, I don't think 11 is enough. At least you've got the rest of
    your life to look forward to - doing this forever. Or you could get
    gjedwards, Nov 21, 2006
  11. jstevh

    Tim Peters Guest

    That's right. Everyone from amateurs with background in rigorous math, to
    tenured math professors, tells you you're wrong -- and, more, they all say
    the /same things/ about the specifics /ways/ in which you're wrong.

    "Get a clue" is far too weak to even scratch the surface of your delusions
    in response to this:
    See? For the most part, tenured professors don't bother replying to you
    anymore. The handful of us who still do aren't professors, but we tell you
    the same things. How do you work that into your paranoid delusions? You've
    tried selling the notion that we "worship" "top mathematicians", but I
    figured that sounded nuts even to you (as it certainly did to everyone
    else), because you rarely try to make that goofy pitch.

    Is it like having bees live in your head? Except for the honey, I suppose.
    Tim Peters, Nov 21, 2006
  12. jstevh

    jstevh Guest

    All Ullrich has to do is produce a difference equation with prime

    And how stupid do you really think the readership is?

    I make a simple challenge to Ullrich, and posters come in to try and
    rescue him with distractions?

    The question here is about conspiracy on the part of math professors at
    universities to mislead the public about mathematical research.

    That would help explain how I can have such dramatic finds and get

    A conspiracy is almost required as it's not enough to just insult
    someone on Usenet as people like you do. It takes a bit more than
    that--willful behavior on the part of university mathematicians to
    block this research, with Ullrich providing direct evidence of their

    Readers should see

    to verify for themselves that he is a math professor at Oklahoma State

    James Harris
    jstevh, Nov 21, 2006
  13. jstevh

    gjedwards Guest

    11 years and counting. You're still living on handouts and they're
    still not listening. Somebody's stupid I guess.
    gjedwards, Nov 21, 2006
  14. jstevh

    gjedwards Guest

    11 years and counting. You're still living on handouts and they're
    still not listening. Somebody's stupid I guess.
    gjedwards, Nov 21, 2006
  15. jstevh

    Tim Peters Guest

    [Tim Peters]
    Why? Just because you're too full of yourself to follow the simple
    explanations you've been given of exactly the same point across a span of
    friggin' /years/?
    Far less stupid than you need them to be to swallow your line of bull.
    Nope, just pointing out that you're an ignorant ass who has made the same
    "challenge" for years, and will likely continue making it until you're
    carted away or die. The alternate is learning something, but you seem to be
    too far gone for that. Sucks! You'd be better off addressing your real
    Nope, that's not "a question" to anyone else -- just your delusion.
    There are much simpler explanations, which have the additional virtue of
    being true. Like, no, you don't have any dramatic finds, at least none that
    you've talked about here. Those are overwhelmingly a mix of incoherent,
    wrong, or trivial. You did get a few things right over the last decade, but
    not even those were significant (your prime-counting formula, and I'm given
    to understand most of a proof of FLT for one exponent).
    I insult you after you insult me in response to giving you thorough
    technical explanations. Anyone can see that. Your continuing ignorance is
    solely your problem.
    And how stupid do you really think the readership is?

    Anyone can read your arguments, my arguments, David's arguments, and anyone
    else's arguments here. Oops. Nothing's hidden, but everyone /still/ says
    "you're wrong". Why is that? Oh, I see: all the tenured professors are
    deliberately lying, while everyone else is just trying to insult you.
    Couldn't be that your attempts at math /are/ wrong, eh? Na, that's
    impossible -- you yourself say they're correct.

    You need help, James. You really do. You can't get it here. Take a trip
    down memory lane 4 years back, to a post you surely wish you /could/ delete.
    That's too bad, because it's the closest you ever got to making real
    progress here (and despite that you may have thought that it too was just
    another cynical ploy):
    Tim Peters, Nov 21, 2006
  16. Show one what?
    What I said was that any recurrence relation is equivalent to
    some difference equation. This is incredibly clear.

    Say (a_n) is a sequence that satisfies some recurrence:

    a_{n+1} = f(a_n, n).

    Then (a_n) also satisfies the difference equation

    a_{n+1} - a_n = g(a_n, n),

    where g is defined by g(x,y) = f(x,y) - x.
    That's the way it seems to you. To everyone else it's clear that
    your comments in this direction go to the possibility that you're
    a raving lunatic.


    David C. Ullrich
    David C. Ullrich, Nov 21, 2006
  17. Thanks for sharing that link. It was so pleasing to see James with a
    clear understanding of his problem, and with some resolve to overcome
    it. It is a shame that he backslid and wasted another few years of his
    life with the Narcissistic rants. Hopefully, he'll see the wisdom of
    what he wrote on Christmas 2002, and get the help he needs. If he were
    to get treatment, these newsgroups would lose Jame Harris as we know
    his, the raving buffoon. But I for one would welcome a new James Harris,
    one who is humble, polite, and here to share the fun he has with
    Frank J. Lhota, Nov 21, 2006
  18. jstevh

    Dave Guest

    James has a fungal brain infection. Whenever the fungi bodies start
    fruiting, James starts posting.
    It is not JSH talking anymore, but the millions of spores infecting his ripe
    brain material.
    Dave, Nov 21, 2006
  19. jstevh

    Scot Guest

    you know, im no biologist but i kind of doubt that fungi could survive
    on such limited resources. lol.

    conspiracy?!?! c'mon.
    Scot, Nov 22, 2006
  20. jstevh

    jstevh Guest

    A recurrence relation equivalent to a difference equation.

    But it'd be especially nice if you did so in relation to prime counting
    with the recurrence relation for phi(x,a).
    But the context is with prime counting.

    Still it will be nice for you to just give a recurrence relation and a
    difference equation that follows from it, as I'll show in a bit.
    Ok, so you know what a difference equation is.

    Now then, demonstrate with the recurrence relation for phi(x,a), which
    readers can see at MathWorld using the following link:

    Show the corresponding difference equation, if one exists.

    Or do so with ANY function previously known related to prime counting.
    Crucial to my claims is the point that no previously known prime
    counting function recurses by calling itself, as being able to do so
    allows one to use a difference equation instead of sieve functions.

    The history of prime counting is full of sieve functions, not
    difference equations.

    Now either you don't know that, or you're lying.

    If you did not know that, then now you do, and should correct your
    previous statements, especially any disagreement with the simple fact
    that my prime counting function in the form that uses a difference
    equation is a first in the history of counting prime numbers.

    If it is not, then show another difference equation with prime

    If you fail to do so, your position as a tenured math professor opens
    up the possibility that the refusal to acknowledge my research is not
    just some odd-ball thing on the fringes of Usenet but instead may be a
    conspiracy on the part of established mathematicians at universities.

    Now then, show a difference equation with prime counting.

    To see the difference equation form of my prime counting function,
    readers should look at my new paper, which can be found using the
    following link:

    And readers should ask themselves, if it is true that no other prime
    counting function or even helper functions used with prime counting
    functions like phi(x,a) can be written using a difference equation, why
    would a tenured math professor at a state university publicly lie about
    such a thing and try to convince people one could?

    James Harris
    jstevh, Nov 22, 2006
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