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GFPS

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  • Andrey Kulsha
    Hello! There are some questions about GF(n,b). 1) Why GFNSieve doesn t remove b s which are odd powers of even numbers (e.g., 216)? Why doesn t Proth
    Message 1 of 2 , Jan 4, 2002
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      Hello!

      There are some questions about GF(n,b).

      1) Why GFNSieve doesn't remove b's which are odd powers of even numbers (e.g.,
      216)? Why doesn't Proth immediately report them composite?

      2) Do all GFPS contributors take this into account?

      3) Do all GFPS contributors take into account that the most of b's which are
      perfect squares are already tested (with smaller n), and enough small b's may
      also be already tested (with bigger n)?

      Thanks for comments,

      Andrey
    • Yves Gallot
      ... The test was not implemented in GFNSieve or in Proth. I considered that the proportion of GFN, with b s which are odd powers, and which have no small
      Message 2 of 2 , Jan 4, 2002
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        > There are some questions about GF(n,b).

        > 1) Why GFNSieve doesn't remove b's which are odd
        > powers of even numbers (e.g., 216)?
        > Why doesn't Proth immediately report them composite?

        The test was not implemented in GFNSieve or in Proth.
        I considered that the proportion of GFN, with b's which are odd powers,
        and which have no small factor, is so small that this optimization was
        not needed.

        > 2) Do all GFPS contributors take this into account?

        I think that none takes this into account.

        > 3) Do all GFPS contributors take into account that the
        > most of b's which are perfect squares are already tested
        > (with smaller n), and enough small b's may also be
        > already tested (with bigger n)?

        No. The small b's are double-checked because of your remark and I think that
        it's a good point. In a first step, the numbers are tested with small b (for
        example 262144 and b < 1000). When 131072 is completed, this range will be
        double checked. But the proportion of numbers that will be tested twice is
        only 1/1000.

        Yves
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