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Re: [PrimeNumbers] GFPS

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  • 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 1 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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