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Re: [PrimeNumbers] Are these prime?

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  • Phil Carmody
    ... odd+/-1 = even ... Grab GP/Pari, it ll tell you in a trice. ... = ((3^9*2)^3) +/-1 = cube +/-1 x^3+1 = (x+1)(x^2-x+1) x^3-1 = (x-1)(x^2+x+1) ... Factoring
    Message 1 of 4 , May 29, 2006
      --- Roahn Wynar <rwynar@...> wrote:
      > Hello all,
      >
      > I have run accross the need to determine which, if any, of the following
      > eight numbers are prime:
      >
      > 3^30 +/- 1
      > 3^29 +/- 1

      odd+/-1 = even

      > (3^27 x 4 ) +/- 1

      Grab GP/Pari, it'll tell you in a trice.

      > (3^27 x 8 ) +/- 1

      = ((3^9*2)^3) +/-1
      = cube +/-1

      x^3+1 = (x+1)(x^2-x+1)
      x^3-1 = (x-1)(x^2+x+1)

      > I am not able to make the determination right now myself but I am working
      > hard to learn more advance factorization methods. I don't even have a good
      > sense of whether making the above primality determinations would be easy or
      > hard given the current state of the art. If anyone happens to have handy
      > answers I would be grateful, but I certainly do not expect anyone to make any
      > significant computation (if that is what it takes) on my behalf.

      Factoring anything under 60 digits is almost always instant.
      Primality testing anything under 500 digits is almost always instant.

      Phil

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