       RE: Prime Puzzle with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg92700] RE: [mg92680] Prime Puzzle with Mathematica
• From: "Harvey P. Dale" <hpd1 at nyu.edu>
• Date: Sat, 11 Oct 2008 06:41:45 -0400 (EDT)
• References: <200810100835.EAA07106@smc.vnet.net>

```Amzoti:

okQ[l_]:=Module[{l2=Subsets[l,{2}]},And@@PrimeQ[Mean[#]&/@l2]]

Select[Select[Subsets[Prime[Range[PrimePi,PrimePi]],{3}],PrimeQ
[Mean[#]]&],okQ]

This yields: {{11,47,71}}

Best,

Harvey

-----Original Message-----
From: amzoti [mailto:amzoti at gmail.com]
Sent: Friday, October 10, 2008 4:35 AM
To: mathgroup at smc.vnet.net
Subject: [mg92700] [mg92680] Prime Puzzle with Mathematica

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

```

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