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11216RE: Estimating log (B^pi(B))

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  • David Broadhurst <d.broadhurst@open.ac.u
    Feb 1, 2003
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      Phil:

      > That's a completely sideways way of looking at things!
      > I like it!

      Thank ye, kind sir.

      > I think one of my results was a {1,4,6} wasn't it?

      Yep. I said you didn't need to bother, not that you
      didn't bother.

      > I'm surprised it works, because the factors need to
      > be of a particular residue in order to make the thing
      > carmichael

      \begin{explanation}

      lcm{1,2,12}=3*4

      We get the 3 from 4*x+3, since
      x=0 mod 3, because of the primorial.

      We get the 4 from (1+1/d).
      All possible d's are odd.
      So half of the combinations of ECM primes work.
      But we double these using the 5 from 6*x+5,
      since x=0 mod 5, because of the primorial.

      So {1,2,12} is as rich as {1,2,3}.
      Except that it's twice as fast
      as {1,2,3} for ECMing.

      \end{explanation}
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