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Re: Lucas super-pseudoprimes for Q <> 1

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  • djbroadhurst
    ... A few minutes later these turned up: 4013569, 4638985. If you will only think Chinese, such numbers may be found in GHz-minutes, rather than GHz-years :-)
    Message 1 of 46 , Oct 31, 2010
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      --- In primenumbers@yahoogroups.com,
      "djbroadhurst" <d.broadhurst@...> wrote:

      > > why only one non-Carmichael n (up to 1 million)
      >
      > Because 10^6 is a small number. Try these non-Carmichaels:
      > 1080905, 1739089, 1992641, 2110159, found in only a few minutes.

      A few minutes later these turned up: 4013569, 4638985.
      If you will only think Chinese, such numbers
      may be found in GHz-minutes, rather than GHz-years :-)

      The puzzle, with more than 70,000 (q,n) pairs
      and n not Carmichael, takes less than a GHz-hour
      to solve, by brute Chinese force, and only a second
      by judicious googling :-)

      David
    • djbroadhurst
      ... http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out gives my 116, in the format [n, factors, number of solutions] With n
      Message 46 of 46 , Nov 9, 2010
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        --- In primenumbers@yahoogroups.com,
        "mikeoakes2" <mikeoakes2@...> wrote:

        > > My revised count up to 2*10^10 is 116.
        > My (original) count up to 2*10^10 was 105.
        > So it must have missed 11, i.e. a bigger proportion.

        http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out
        gives my 116, in the format [n, factors, number of solutions]

        With n < 2*10^10, the record-holder for the number of solutions is
        [2214495361, [13, 17, 23, 29, 83, 181], 147407]
        which googles quite nicely, linking to
        http://www.cs.rit.edu/usr/local/pub/pga/fibonacci_pp

        David
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