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• Mar 20, 2006
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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
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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