Re: Prime Puzzle with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg92708] Re: Prime Puzzle with Mathematica
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 11 Oct 2008 06:43:15 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <gcn48r\$74t\$1@smc.vnet.net>

```amzoti wrote:

> trying to find an efficient way to this in Mathematica.
>
> I found the answer - but it was a manual list manipulation - and it
> was ugly!
>
> Any suggestions?
>
> 3 Nice Primes:
>
> Find three 2-digit prime numbers such that:
>
>     * The average of any two of the three is a prime number, and
>     * The average of all three is also a prime number

Select[Subsets[Table[Prime[n], {n, 5, 25}], {3}],
PrimeQ[1/3
Plus @@ #] && (And @@ (PrimeQ[1/2 Plus @@@ Subsets[#, {2}]])) &]

The above expression returns the unique solution to the problem
(assuming I have correctly understood it, of course :-)

Regards,
-- Jean-Marc

```

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