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17741Re: symmetrical primes

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  • Phil Carmody
    Mar 12 5:33 AM
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      From: "Mark Underwood" <mark.underwood@...>
      > Hi all,
      >
      > Six primes are symmetrically arranged around the number 12:
      > 5, 7, 11, (12) 13, 17, 19.
      >
      > Six primes are also symmtrically arranged around the number 15:
      > 7, 11, 13, (15) 17, 19, 23.
      >
      > Ten primes are symmetrically arranged around the number 30:
      > 13, 17, 19, 23, 29, (30) 31, 37, 41, 43, 47.
      >
      > Twelve primes are symmetrically arranged around the number 165:
      > 137, 139, 149, 151, 157, 163, (165) 167, 173, 179, 181, 191, 193.
      >
      > I looked up to 100,000 primes there are six cases of twelve primes
      > symmetrically arranged around a central number. Found nothing higher.
      > When is the first case of a symmetrical grouping of more than twelve
      > primes?


      A great puzzle Mark!

      Shame I misread it - I was trying to stick a prime in the middle...

      Some examples:

      6 primes symmetrically arranged around a central prime
      683747 683759 683777 683783 683789 683807 683819
      . +12 +18 +6 +6 +18 +12

      8 primes symmetrically arranged around a central prime
      98303867 98303873 98303897 98303903 98303927 98303951 98303957 98303981
      98303987
      . +6 +24 +6 +24 +24 +6 +24 +6

      10 primes symmetrically arranged around a central prime
      60335249851 +6
      60335249857 +12
      60335249869 +12
      60335249881 +60
      60335249941 +18
      60335249959 +18
      60335249977 +60
      60335250037 +12
      60335250049 +12
      60335250061 +6
      60335250067

      12 - well, that's a job for Jens :-)


      Quiz question:
      Why are my minimal examples so much larger than Mark's examples?

      I have the answer. It's quite elementary, but still took 30 seconds of head
      scratching before I worked it out. Award yourself a Carmody-approved pat on the
      back if you work it out more quickly.

      Yes, I appreciate this does not answer your original question :-P

      Phil

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