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[PrimeNumbers] Re: Two factors of R(13860)

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  • Satoshi TOMABECHI
    David Broadhurst wrote. ... Where are factors of N-1? ( N=R(13860) ) Or please send me help file. I would like to test primality. I implmented all primality
    Message 1 of 16 , Oct 1, 2001
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      David Broadhurst wrote.
      > A bit of "if" statementing is needed when there is a pair
      > of complex roots, but Greg did not hit that case.
      >
      > However, I believe that Satoshi Tomabechi would we
      > an appropiate validator. Any chance, please, Satoshi?

      Where are factors of N-1? ( N=R(13860) )
      Or please send me "help" file.
      I would like to test primality.

      I implmented all primality tests which are described
      in Crandall and Pomerance's book. My code verified
      several results about GRU prime by Andy Steward.
      My code will give a verification by another implementaion.

      Phi Carmody wrote.
      >It looks quite simple from David's code though.

      My code may also look "too" simple:-)

      Satoshi Tomabechi
    • Satoshi TOMABECHI
      David Broadhurst wrote. ... Where is helper file? Or please send me helper file. I would like to test primality. But I have only 13.5% factors of N-1 now. My
      Message 2 of 16 , Oct 1, 2001
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        David Broadhurst wrote.
        > However, I believe that Satoshi Tomabechi would we
        > an appropiate validator. Any chance, please, Satoshi?

        Where is "helper" file?
        Or please send me helper file.
        I would like to test primality.
        But I have only 13.5% factors of N-1 now.
        My code may give a verification by another implementaion.

        Phi Carmody wrote.
        >It looks quite simple from David's code though.

        My code may also look "too" simple:-)

        Satoshi Tomabechi
      • d.broadhurst@open.ac.uk
        ... I put it in http://groups.yahoo.com/group/primenumbers/files/Factors/HD13860.fac ... Just what we need, thanks. ... I bet! This simple, uncombined, KP is
        Message 3 of 16 , Oct 1, 2001
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          Satoshi Tomabechi asked:
          > Where is "helper" file?
          I put it in
          http://groups.yahoo.com/group/primenumbers/files/Factors/HD13860.fac
          > My code may give a verification by another implementaion.
          Just what we need, thanks.
          > My code may also look "too" simple:-)
          I bet! This simple, uncombined, KP is easy, not so?
          Have you coded N+1?
          Have you coded 10/3*Max(F1,F2)+Min(F1,F2)>1 ?
          Best regards
          David
        • gchil0@pop.uky.edu
          Hi, ... I ve uploaded the factors to the files area. It can be downloaded at http://groups.yahoo.com/group/primenumbers/files/Factors/13860fac.zip Umm...looks
          Message 4 of 16 , Oct 2, 2001
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            Hi,

            > Where are factors of N-1? ( N=R(13860) )
            > Or please send me "help" file.
            > I would like to test primality.

            I've uploaded the factors to the files area. It can be downloaded at
            http://groups.yahoo.com/group/primenumbers/files/Factors/13860fac.zip

            Umm...looks like David did the same at about the same time :-) but his
            is missing the 2 new factors so I'll leave mine for now.

            David...could you also update hd1k.zip with the 2 new factors and
            Base10.zip with all 3 new factors?

            Thanks,
            Greg
          • d.broadhurst@open.ac.uk
            ... Sorry about that. I had uploaded an old file. Have now remedied that, with your 2 gems at the top:-) ... Sorry, my file management skills are minimal. It s
            Message 5 of 16 , Oct 2, 2001
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              Greg Childers wrote:
              > looks like David did the same at about the same time
              > but his is missing the 2 new factors
              Sorry about that. I had uploaded an old file.
              Have now remedied that, with your 2 gems at the top:-)
              > David...could you also update hd1k.zip with the 2 new factors and
              > Base10.zip with all 3 new factors?
              Sorry, my file management skills are minimal.
              It's already a minor miracle that I managed to
              get the previous version more or less OK.
              Please Greg, will you take over as Base10 DB manager?
              David
            • gchil0@pop.uky.edu
              ... OK, I ll delete mine. ... Sure. Delete the files you ve uploaded and I ll upload the updated versions. Greg
              Message 6 of 16 , Oct 2, 2001
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                --- In primenumbers@y..., d.broadhurst@o... wrote:
                > Sorry about that. I had uploaded an old file.
                > Have now remedied that, with your 2 gems at the top:-)

                OK, I'll delete mine.

                > > David...could you also update hd1k.zip with the 2 new factors and
                > > Base10.zip with all 3 new factors?
                > Sorry, my file management skills are minimal.
                > It's already a minor miracle that I managed to
                > get the previous version more or less OK.
                > Please Greg, will you take over as Base10 DB manager?

                Sure. Delete the files you've uploaded and I'll upload the updated
                versions.

                Greg
              • d.broadhurst@open.ac.uk
                ... Sure thing, Boss! That folder is now totally Broadhurst free. Thanks for taking over! David
                Message 7 of 16 , Oct 2, 2001
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                  Greg Childers commanded:
                  > Delete the files you've uploaded
                  > and I'll upload the updated versions.
                  Sure thing, Boss! That folder is now
                  totally Broadhurst free.
                  Thanks for taking over!
                  David
                • Satoshi TOMABECHI
                  Thank you, Greg and David. My program shows that 15793939750*R(13860)/R(10)+1 is prime, however I have little confidence in this result:-) I hope that the
                  Message 8 of 16 , Oct 2, 2001
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                    Thank you, Greg and David.

                    My program shows that 15793939750*R(13860)/R(10)+1 is prime,
                    however I have little confidence in this result:-)
                    I hope that the result is as same as David's.

                    The coefficients of cubic equation t3X^3 + t2X^2 + t1X + t0 = 0 are

                    t3 = 9499179946...9373462290 1400 digits
                    t2 = 2983442091...4520303837 2765 digits
                    t1 = -5786178299...9234821312 4165 digits
                    t0 = -8297037200...6079883289 2764 digits

                    The equation has three real roots r1,r2,r3.

                    r1=-1.433940810...*10^{-1401}

                    integral part of r2 246804372...4038770926 ( 1382 digits)
                    fractional part of r2 0.9565089129....

                    integral part of r3 -246804372...8946383526 ( 1382 digits)
                    fractional part of r2 0.5941852755....

                    Nearest integers of r1,r2 and r3 are not root of the equation.

                    # It was not easy to compute roots of the cubic equation.

                    Best regards.

                    Satoshi Tomabechi
                  • Satoshi TOMABECHI
                    ... Yes, of course. Furthermore I coded modified KP with additional square tests by you. http://groups.yahoo.com/group/primeform/message/2142 But I have not
                    Message 9 of 16 , Oct 2, 2001
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                      David Broadhurst wrote:
                      > Have you coded N+1?
                      Yes, of course.
                      Furthermore I coded modified KP
                      with additional square tests by you.
                      http://groups.yahoo.com/group/primeform/message/2142

                      But I have not coded combined KP.
                      http://groups.yahoo.com/group/primenumbers/message/1743

                      > Have you coded 10/3*Max(F1,F2)+Min(F1,F2)>1 ?
                      Sorry, I don't know such condition.
                      Please tell me reference or pointer to reference.

                      Satoshi Tomabechi
                    • d.broadhurst@open.ac.uk
                      ... By F1 and F2 I meant the fractions of N-1 and N+1. When F1 F2 this condition is what I used for Fib(25561), but it also works for F2 F1. Hence the Max and
                      Message 10 of 16 , Oct 2, 2001
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                        Satoshi TOMABECHI wrote:
                        > > Have you coded 10/3*Max(F1,F2)+Min(F1,F2)>1 ?
                        > Sorry, I don't know such condition.
                        By F1 and F2 I meant the fractions of N-1 and N+1.
                        When F1>F2 this condition is what I used for Fib(25561),
                        but it also works for F2>F1. Hence the Max and Min.
                        David
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