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Any help?

  1. Nov 9, 2008 #1
    The twin primes 5 and 7 are such that one half their sum is a perfect number. Are there any other twin primes with this property?

    It works for p=5. I think it should be of the form 1/2*(p+P+2). Is this true? How can I prove it?

  2. jcsd
  3. Nov 9, 2008 #2


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    I didn't find any. It's not too surprising, given how rare perfect numbers are.
  4. Nov 9, 2008 #3
    There aren't any more. An even perfect number (other than 6) is not divisible by three since it is the product of a power of 2 and a mersenne prime. Therefore one of P-1 or P+1 must be divisible by 3, and thus not prime.
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