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

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  • 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 1 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 2 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 3 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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