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11221Re: [PrimeNumbers] RE: Estimating log (B^pi(B))

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  • Markus Frind
    Feb 1, 2003
      Given the 1,2,15 seed, or 1,2,12 seed etc
      Couldn't we check for a 4th element using ECM, and a 5th element (e) such
      that we can form a 5-carm of the form N = e*1*2*15*ECMFactor

      Carms of that form

      5,7,13,193,439,9637697
      5,7,13,193,499,2657,42829
      5,19,37,547,1009,3211937
      7,19,37,541,601,58741
      7,79,157,2341,3541,9181
      13,19,37,541,631,2689
      13,19,37,541,739,811,1231
      13,19,37,541,1009,2311
      17,37,73,1093,2081,65521
      17,37,73,1093,93809

      With my dataset i will have 4 billion possible e values and 350 titanic
      seeds of whatever 3 part seed that is picked. Is it possible to create a
      carm by extending a "seed" at both ends. IE creating a custom formula for
      each e*1*2*15 which is then ecm'd. to get a prime that
      makes e*1*2*15*ECMFactor PRP


      Markus



      >But Markus is stuck with his NewPgen output and so
      >can't use CRT. So I thought it would be useful
      >to give {1,2,12} a proof in principle by beating the
      >4-Carmichael 4th factor record.
      >
      >In fact I did it twice over:
      >
      >2763260532*((1591638066432*3061#+19)^2-1)*3061#/
      >286610757607008951353515277095+1 3909 p44 03
      >4-Carmichael factor (4)
      >
      >757849549*((72753556704*3061#+19)^2-1)*3061#/
      >56731664597567983567442428202862519351615138+1 3891 p44 03
      >4-Carmichael factor (4)
      >
      >finding ECM factors at about twice
      >the rate for this seed as compared with
      >the other seeds in my plantpot.
      >
      >OK, it's a trivial [and suspect] use of Dickman.
      >
      >But it was funny that you should mention him
      >just after I had commented on another such seed
      >{1,2,15}. But Markus can't use that
      >Dickman-enhanced seed, since he
      >can't get x=1 mod 5 in
      >
      >? print(factor((1+x)*(1+2*x)*(1+15*x)-1))
      >[x, 1; 3*x + 2, 1; 10*x + 9, 1]
      >
      >because he used primorial mode in NewPgen.
      >
      >David
      >
      >
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      >The Prime Pages : http://www.primepages.org/
      >
      >
      >
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