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Curious 3's

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  • JohnKemeny
    The folowing is just a curio, and of no great import, but anyway... Motivated by the fact that the integer part of (3^33/33^3) is prime, I looked at the
    Message 1 of 1 , Apr 19, 2002
      The folowing is just a curio, and of no great import, but anyway...

      Motivated by the fact that the integer part of (3^33/33^3) is prime,
      I looked at the integer part of (33333333/3^3)^3+k.(333/3^3), and
      found it prime when k=4. The left part of the equation is just the
      integer part of repunit(n)^3/(3^6), and the right part is just 12.k.

      So here is the curio: between 8 an 18, whenever the left part was not
      even, I could find a small k such that the equation was prime, viz.,

      n k
      8 +4
      9 -5
      11 -4
      13 -7
      15 +4
      17 +5
      18 -6

      I didn't look beyond 18. Seems like a curiously high density of
      prime numbers to me, but then again...

      John
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