Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Goldbach

Expand Messages
  • Phil Carmody
    ... I know it was a typo, which is why in the data below I correct that typo. And with the typo corrected I do find counterexamples. Check again please. Phil
    Message 1 of 45 , Jan 3, 2001
    View Source
    • 0 Attachment
      On Wed, 03 January 2001, Dick Boland wrote:
      > Sorry Phil,
      >
      > It was a typo. k*(k+1)/2 primes <= (p(k^2)+1)/2 and k*(k-1)/2 primes between ((p(k^2)+1)/2+1) and p(k^2). You won't find a counter example there.

      I know it was a typo, which is why in the data below I correct that typo. And with the typo corrected I do find counterexamples. Check again please.

      Phil


      > -Dick
      >
      >
      >
      >
      > Phil Carmody <fatphil@...> wrote:
      > On Wed, 03 January 2001, Dick Boland wrote:
      > > Yes I can. The distribution function is simply stated as follows,
      > >
      > > For any integer k>4, the first k^2 primes will be exactly distributed as follows:
      > >
      > > k*(k+1) primes between 1 and (p(k^2)+1)/2, and the remaining k*(k-1) primes will be distributed between ((p(k^2)+1)/2+1) and p(k^2).
      >
      > k*(k+1) + k*(k-1) == 2k^2
      >
      > So you seem to be out by a factor of 2 somewhere.
      >
      > Factoring in that factor of two...
      >
      > Table[{k,
      > k^2,
      > Prime[k^2],
      > (Prime[k^2]+1)/2,
      > PrimePi[(Prime[k^2]+1)/2],
      > k*(k+1)/2},
      > {k, 4, 8}]
      >
      > {{4, 16, 53, 27, 9, 10},
      > {5, 25, 97, 49, 15, 15},
      > {6, 36, 151, 76, 21, 21},
      > {7, 49, 227, 114, 30, 28},
      > {8, 64, 311, 156, 36, 36}}
      >
      > You seem to be saying the last two columns are the same.
      > I beg to differ.
      >
      > Let's look a bit further, at the data for k=100000-100005:
      >
      > {
      > {100000, 10000000000, 252097800623, 126048900312, 5141644677,
      > 5000050000},
      > {100001, 10000200001, 252103045511, 126051522756, 5141747035,
      > 5000150001},
      > {100002, 10000400004, 252108316073, 126054158037, 5141850524, 5000250003},
      > {100003, 10000600009, 252113577847, 126056788924, 5141953182, 5000350006},
      > {100004, 10000800016, 252118846391, 126059423196, 5142056263, 5000450010},
      > {100005, 10001000025, 252124112327, 126062056164, 5142159097, 5000550015}
      > }
      >
      > The last 2 columns really aren't that similar.
      >
      >
      > Phil
      >
      > Mathematics should not have to involve martyrdom;
      > Support Eric Weisstein, see http://mathworld.wolfram.com
      > Find the best deals on the web at AltaVista Shopping!
      > http://www.shopping.altavista.com
      >
      >
      >
      >
      >
      > eGroups Sponsor
      >
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
      > The Prime Pages : http://www.primepages.org
      >
      >
      >
      >
      >
      > ---------------------------------
      > Do You Yahoo!?
      > Yahoo! Photos - Share your holiday photos online!
      >
      > [Non-text portions of this message have been removed]
      >
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
      > The Prime Pages : http://www.primepages.org

      Mathematics should not have to involve martyrdom;
      Support Eric Weisstein, see http://mathworld.wolfram.com
      Find the best deals on the web at AltaVista Shopping!
      http://www.shopping.altavista.com
    • Kermit Rose
      From: Milton Brown Date: 12/21/05 16:35:16 To: Werner D. Sand; primenumbers@yahoogroups.com Subject: RE: [PrimeNumbers] Goldbach These messages about
      Message 45 of 45 , Dec 21, 2005
      View Source
      • 0 Attachment
        From: Milton Brown
        Date: 12/21/05 16:35:16
        To: Werner D. Sand; primenumbers@yahoogroups.com
        Subject: RE: [PrimeNumbers] Goldbach


        These messages about Goldbach's Conjecture are not
        supposed to be to this mailing list (also the Riemann Hypothesis).

        There are separate mailing lists for these.


        Kermit says.


        Milton! You surprise me.


        Goldbach's conjecture IS about prime numbers. It's doesn't matter that
        there exist mailing lists specifically about Goldbach's conjecture.

        [Non-text portions of this message have been removed]
      Your message has been successfully submitted and would be delivered to recipients shortly.