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14306Re: [PrimeNumbers] Re: Modification of PFGW

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  • Cletus Emmanuel
    Dec 31, 2003
      Ok then. Now, Who's willing to act? We need a 1M digit Carol/Kynea

      (I tried to join the PFGW group, but that site is blocked from work. I will try to log on outside of work and try to join...)

      Paul Underwood <paulunderwood@...> wrote:
      --- In primenumbers@yahoogroups.com, Cletus Emmanuel <cemmanu@y...>
      > Guys,
      > Again, this is why I love this group. I live to learn(and
      especially when it is math). You guys have a wealth of information
      which I don't have and it is great to learn from all of you. I
      hearing from Mike that testing for Carol/Kynea can be improved by 50%.

      As Phil ( the silent ) pointed out this won't be 50%, it will be
      approxiamately 0% :-(

      > And hearing from Paul that we can even save more time. I can't
      implement these changes in PFGW. Can anyone of you do it?

      The best place to lobby for these changes is the primeform Yahoo
      group at:


      and probably the best people to make the changes are the OpenPFGW
      developement team. Perhaps we could have a switch instead of relying
      on the application to recogonise these forms.

      > I think that it will be worth it considering that there are 40
      Kynea, 32 Carol for k<= 100,000 and 52 Generalized Carol Primes
      (273*2^k-1)^2 - 2 for K<= 100,000 (but not all k-values checked).
      These are more dense than Mersenne and the number of digits are twice
      as large.

      Yes, but the Mersennes are counted over the primes.

      > Isn't this incentive enough to modify PFGW and coordinate a search?

      I think a lot of people would benefit from the changes:
      You: Carol/Kynea (+ generalisations)
      Mike: Gaussian Mersennes
      Jiong: AP3 searches
      Me: generating loads of trinomials of the form 2^n-2^k-1 ;-)

      I programmed something like this in C long before I got on the Net
      and ... During exponentiation a number is squared ( and sometimes
      multiplied by the base of the Fermat depending on whether is a one or
      a nought in the binary representation of N. ) This results in a
      number that is twice as long in computer memory. Modular reduction is
      performed to reduce this size back down. Using O(N) shifts, adds and
      mults, it should be possible for any trinomial of the form A*2^n-
      B*2^k-C, where A,B and C are small, much more quickly modularly
      reduced than PFGW does it now.

      Paul ( hardly capable of RTFS )

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