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RE: Prime Puzzle with Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92732] RE: [mg92680] Prime Puzzle with Mathematica
  • From: "Tony Harker" <a.harker at ucl.ac.uk>
  • Date: Sat, 11 Oct 2008 06:47:36 -0400 (EDT)
  • References: <200810100835.EAA07106@smc.vnet.net>

]-> -----Original Message-----
]-> From: amzoti [mailto:amzoti at gmail.com] 
]-> Sent: 10 October 2008 09:35
]-> To: mathgroup at smc.vnet.net
]-> Subject: [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
]-> 
]-> 

  Here's a brute force method:

Select[Union[Map[Sort, Flatten[Outer[List, #, #, #], 2]]] &[
  Select[Range[10, 99], PrimeQ]], (Length[Union[#]] == 3) && 
   PrimeQ[(#[[1]] + #[[2]])/2] && PrimeQ[(#[[2]] + #[[3]])/2] && 
   PrimeQ[(#[[3]] + #[[1]])/2] && 
   PrimeQ[(#[[1]] + #[[2]] + #[[3]])/3] &]

  Tony 




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