Talk:Superperfect number

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[edit] Infinitely many?

Is it known that there are infinitely many superperfect numbers? There's probably some elementary proof that there are, but nothing has occurred to me in the (admittedly brief) time that I have thought about this? In any event, if there are infinitely many, a pointer to such a proof would be useful for this article. --Craw-daddy | T | 18:04, 13 April 2008 (UTC)

I don't think it is known. If we knew there were infinitely many superperfect numbers then we could probably determine whether they were odd or even. It is not known whether there are any odd superperfect numbers, but an infinite number of even superperfect numbers would tell us that there were an infinite number of Mersenne primes, which is definitely not known. However, I don't have a source for this. Gandalf61 (talk) 18:43, 13 April 2008 (UTC)

Fair enough.  :) Thanks for the response. Number theory, while I find some parts interesting, isn't my bailiwick so that's why I asked. --Craw-daddy | T | 19:01, 13 April 2008 (UTC)