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Re: Primes again

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  • djbroadhurst
    ... But, sweet William, you seem to have mised the main point: http://factordb.com/index.php?id=1100000000464436687 was factorized by Bernardo. Moreover there
    Message 1 of 199 , Nov 14, 2011
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      --- In primenumbers@yahoogroups.com,
      "elevensmooth" <elevensmooth@...> wrote:

      > > Since Robin likes factors, I have listed in
      > > http://physics.open.ac.uk/~dbroadhu/cert/robinfac.txt
      > > complete factorizations of ((25^n-9)/4)^2-5 up to n = 82,
      >
      > One of my favorite features of the factordb is the ease
      > with which you can create customized tables of factorization.

      But, sweet William, you seem to have mised the main point:
      http://factordb.com/index.php?id=1100000000464436687
      was factorized by Bernardo. Moreover there is now
      no unfactorized composite for any of the cases with n <= 82.

      Your undoubted web skills may have corrupted mathematical knowlege?

      David
    • mikeoakes2
      ... That was 9 months ago. Since then, this learning process by David, Kevin and me has continued, and if you visit that link you will find that those 18
      Message 199 of 199 , Sep 1, 2012
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        --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
        >
        > > http://physics.open.ac.uk/~dbroadhu/cert/mwrank9.txt
        > > is growing rather slowly
        >
        > This continues, with merely 18 curves currently in that rank-9 file.
        > However, I hope that Mike may soon add to these, since in
        > the case y^2 = x^3 + k with k < 0 his systematic methods
        > may be more powerful than anything that Kevin or I have contrived.
        >
        > In any case, this continues to be a learning process for us,
        > so thanks again to Cino:
        > http://tech.groups.yahoo.com/group/primenumbers/message/20404
        > and then Robin:
        > http://tech.groups.yahoo.com/group/primenumbers/message/23589
        > for getting us started.
        >
        > David
        >

        That was 9 months ago.
        Since then, this "learning process" by David, Kevin and me has continued, and if you visit that link you will find that those 18 elliptic curves have grown somewhat in number! And there are related pages, if you replace "9" by "8" thru "12" in the URL (that signifying the rank of the curves).

        We have recently ventured into the rather scary territory of the Tate-Shafarevich group, which is currently not deeply understood by the number theory community. (It is a famous open problem to prove that it is always of finite order.)

        You may be interested in our today's post to the NMBRTHRY list:
        https://listserv.nodak.edu/cgi-bin/wa.exe?A2=nmbrthry;8f3b553f.1208
        which describes a nontrivial result from our researches in this area.

        Mike
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