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17817[PrimeNumbers] Re: symmetrical primes

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  • Jens Kruse Andersen
    Mar 20, 2006
    • 0 Attachment
      Phil Carmody wrote:

      > 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 :-)

      I didn't like the fast growth of the minimal solution so
      I searched a non-minimal instead:
      Find 7 simultaneous primes in a specific chosen pattern
      with 6 symmetric around the center.
      Then see how far the symmetri extends.

      After 338 cases with 10 symmetric, a 12 finally appeared:
      3391781771953843 +/- 6, 24, 36, 66, 120, 126.

      In Phil's notation:
      3391781771953717 +6
      3391781771953723 +54
      3391781771953777 +30
      3391781771953807 +12
      3391781771953819 +18
      3391781771953837 +6
      3391781771953843 +6
      3391781771953849 +18
      3391781771953867 +12
      3391781771953879 +30
      3391781771953909 +54
      3391781771953963 +6
      3391781771953969

      Prp testing by the GMP library and primality proving by PARI/GP.

      --
      Jens Kruse Andersen
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