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Re: [PrimeNumbers] Carol/Kynea-related forms

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  • Cletus Emmanuel
    Rob, In 1995, I did check Carol Kynea for powers of 3 and greater, but found that they were not poppulated enough as far as I was concern. They may be of good
    Message 1 of 2 , Feb 24, 2004
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      Rob,
      In 1995, I did check Carol\Kynea for powers of 3 and greater, but found that they were not poppulated enough as far as I was concern. They may be of good interest, because they are more easily proven prime compared to powers of 4 and greater. I felt that K= (2^n+1)^4 - 2 was more interesting that C/K = (2^n +/- 1)^3 - 2. Although the former is more easily proven prime, I had a greater interest in the latter, as a result I found the largest known PRP.

      Just like we've found (6^n-1)^2 - 2 to be interesting, So is (2^n-1)^6 - 2. If one wants to beat my record PRP, I suggest that they search using (2^n-1)^6 - 2. I've toyed Carol/Kynea Numbers in severall generalized ways, but abondoned a lot of the results because I didn't think that a particular form was dense enough for me. Again, once I can prove my conjecture then most of these numbers will be of great importance because they would be readily proven prime if they pass a PRP test.
      ----Cletus Emmanuel

      Rob Binnekamp <robdine@...> wrote:
      Steven et al.,

      I propose to introduce the Carol-rel. form (2^k-1)^3+2
      and the Kynea-rel. form (2^k+1)^3-2.

      These forms produce provable primes, powers > 3 prp's.

      I tested both forms nearly up to k=50000 and will send you the results.

      Rob



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