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theorems

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  • Jeremy
    What theorems/proofs exist of the form: If a
    Message 1 of 2 , Dec 18, 2005
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      What theorems/proofs exist of the form:

      If a<x<b, then there are at least z-many primes?

      I'm familiar with Bertrand's postulate, where:
      b=2a and z=1

      (a more formal definition is here:
      http://mathworld.wolfram.com/BertrandsPostulate.html )

      What others are there? I'll look into this myself... but in the
      meantime many people on this list might already have these tidbits
      memorized... :)

      Regards,
      Jeremy
    • Jeremy
      As a fun little exercise I wrote an algorithm that will give a minimum bound for pi(p(i)^2). I wish I could turn at least part of it into some sort of proof.
      Message 2 of 2 , Dec 26, 2005
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        As a fun little exercise I wrote an algorithm that will give a
        minimum bound for pi(p(i)^2).

        I wish I could turn at least part of it into some sort of proof.
        (For example, for all i>12, can it be proved that there are at least
        X many primes between p(i)^2 and p(i)?) But I'm not skilled at
        proofs, so the paper only highlights an algorithm.

        (Is there such a proof out there with that form, by the way? I tried
        to ask about that earlier, but I think my email got drowned in a
        flurry of other posts. Or maybe I asked the question poorly.)

        It's probably nothing significant... just a little trinket. But I
        wrote it up as I explored it if anyone wants some light reading:
        http://homepage.mac.com/bricolage1/primes/PatternsPSquared.pdf

        Hope everyone who's on holiday is having a pleasant and safe time.
        Regards,
        - Jeremy
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