On Mon, 01 Apr 2002 21:38:27 -0000, you wrote:

>I am looking for all twin primes such that their arithmetic mean is a

>perfect number.

>

>For example:

>

>If 5 and 7 are our primes then 6 is our arithmetic mean.

>

>Thank you for your help.

There aren't any others.

[Apologies to the real mathematicians for the standard of the proof. I

hope the logic is clear]

Given that these 3 numbers must be adjacent integers, then one of them

must be divisible by 3. Neither of the primes is 3 (because no number

adjacent to this is perfect), so it must be the perfect number that is

divisible by 3. It must be an even perfect number (because otherwise the

primes would both be even) and is therefore the product of a power of

two and a Mersenne prime. Obviously a power of two is not divisible by

three and so the Mersenne prime must be 3. And the only perfect number

of this form is 6, which gives you the solution you already have.

Regards

Steve nice but dim