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