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Re: q | L(2^n * p^m)?

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  • David Broadhurst
    L2738 (2,74) 70531186979083.P543 settles the matter, in my mind. I cannot believe that Blair Kelly missed a p18*p544 split at a smaller index. Please see:
    Message 1 of 12 , Oct 30, 2002
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      L2738 (2,74) 70531186979083.P543

      settles the matter, in my mind.

      I cannot believe that Blair Kelly

      missed a p18*p544 split at a smaller index.

      Please see:

      http://home.att.net/~blair.kelly/mathematics/fibonacci/status3000.html

      And you have *no* composite to appeal to
      larger than these

      L2687 C562
      L2692 (4) C562
      L2731 3371665291.C562

      as far as I can tell.

      David
    • Shane
      ... Then I agree, any of these composites, would not have a prime larger than p543. Hats off to David! I will be silent now, while I try and redeem myself.
      Message 2 of 12 , Oct 30, 2002
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        "David Broadhurst" wrote:
        > L2738 (2,74) 70531186979083.P543>
        > settles the matter, in my mind.
        > I cannot believe that Blair Kelly>
        > missed a p18*p544 split at a smaller index.


        >
        > L2687 C562
        > L2692 (4) C562
        > L2731 3371665291.C562



        Then I agree, any of these composites, would not have a prime larger
        than p543.

        Hats off to David!
        I will be silent now, while I try and redeem myself.
        Shane F.
      • David Broadhurst
        ... Yes, but that *idiot* Broadhurst overlooked the fact 2738=2^2*37^2 and you had cunningly included this type of limited cyclotomic disadvantage when the
        Message 3 of 12 , Oct 30, 2002
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          Shane:

          > Then I agree, any of these composites,
          > would not have a prime larger than p543.

          Yes, but that *idiot* Broadhurst overlooked the fact

          2738=2^2*37^2

          and you had cunningly included this type of
          "limited cyclotomic disadvantage"
          when the two odd primes are not distinct!

          So you can survive the p19 squeeze from

          p543|L(2^2*37^2)

          because of your get-out clause "p^m" in the title.

          However there are at least three
          "severely cyclotomically disadvantaged"
          aspiring largest-yet record holders:

          p609|L(2*29*53)
          p913|L(2*43*53)
          p1793|L(67*131)

          needing some ECM work to rule out
          already highly implausible splits
          of a few nearby composites with no
          more than 31 extra digits

          P.C. warning : Anyone found to be running extra ECM on
          a few carefully selected composites 30 digits larger
          than one of these putative paraplegic record holders,
          in the *very* remote hope of extracting a W.A.S.P.
          prime that might displace it, will be reported to
          the suitable authorities for politically incorrect
          persecution of a severely disadvantaged minority :-)
        • Shane
          Doomed, from the start anyway. counterexample: q | L(0) q=2 lol Shane F.
          Message 4 of 12 , Oct 30, 2002
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            Doomed, from the start anyway.
            counterexample:
            q | L(0)
            q=2


            lol
            Shane F.
          • David Broadhurst
            ... If you omit the requirement that the index be a natural number, then a much funnier thing than that happens: 2|L(0) is not a record because 3|L(-2) ?
            Message 5 of 12 , Oct 30, 2002
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              Shane:

              > q | L(0)
              > q=2

              If you omit the requirement that the index
              be a natural number, then a much funnier
              thing than that happens:

              2|L(0) is not a record because 3|L(-2)

              ? L(n)=if(n,fibonacci(2*n)/fibonacci(n),2);
              ? if(L(-2)%3==0,print(ok))
              ok

              3|L(-2) is not a record because 7|L(-4):

              ? if(L(-4)%7==0,print(ok))
              ok

              and so on, showing that *no* record exists :-)

              > lol
              loss of logic?

              David
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