Re: Prime Puzzle with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg92705] Re: Prime Puzzle with Mathematica
• From: Peter Pein <petsie at dordos.net>
• Date: Sat, 11 Oct 2008 06:42:39 -0400 (EDT)
• References: <gcn48r\$74t\$1@smc.vnet.net>

```amzoti schrieb:
> Hi All,
>
> 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
>
> Thanks!
>
> ~A
>

Do you think of sth. like

In[1]:= Select[Subsets[Prime[Range[PrimePi[10] + 1, PrimePi[99]]], {3}],
And @@ PrimeQ /@ Mean /@ Subsets[#1, {2, 3}] & ]
Out[1]= {{11, 47, 71}}

?
Look for "Function" and "Select" in the documentation.

Peter

```

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