Are there any other twin primes with this property?

  • Thread starter nikolany
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  • #1
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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?

Thx
 

Answers and Replies

  • #2
CRGreathouse
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Are there any other twin primes with this property?

I didn't find any. It's not too surprising, given how rare perfect numbers are.
 
  • #3
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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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