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Fascinating pattern

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  • Adam <a_math_guy@yahoo.com>
    For those of you who don t like the wowee-gee-whiz side of mathematical investigations, I suggest you by-pass this post. I was reviewing a long list of
    Message 1 of 1 , Mar 1, 2003
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      For those of you who don't like the wowee-gee-whiz side of
      mathematical investigations, I suggest you by-pass this post.

      I was reviewing a long list of Carmichael numbers for ones that had
      relatively dense factors. That is, if C=prod(pi) is a the prime
      factorization of a Carmichael number, then I wanted min(pi)/max(pi)
      small. I choose arbitrarily to consider only a ratio at
      approximately 10 or less. (Off the cuff, the smallest I remember was
      around 4, but I am not done with the list.) The fascinating thing I
      saw happening often was that, given min(pi)=p, max(pi)=q=10p-9.

      Before you start hitting reply to razz me, consider first off that
      often was about once every 5 sheets of printed numbers. Consider
      also that I realize, given a min prime p and a max prime q, there are
      infinitely many formulas that connect p to q, q=f(p). The reasons
      why I saw 10p-9 was the (human) preference for base 10. For
      instance, if the minimum prime is p=151 then 10p-9=1501 and it just
      (kinda) sticks OUT because of the base 10 representation. (BTW 1501
      isn't prime, I realize this.)

      If I get any results relating to that (after I get done with what I
      am doing now), say a linear form pmax=f(pmin) with high correlation,
      or for relatively large subsets of the sample, I will post this.

      Adam
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