Odd Perfect numbers?

[Syntho-sis]

Does such a thing exist? I think the highest perfect number so far was calculated at 10^300 and mathematicians are currently moving towards 10^500.. so far all perfect numbers are even... Do you think odd perfect numbers exist?

 

I did a few calculations of my own... and thought about it quite a bit and I think it could be done.... it would take an infinite amount of time to calculate the exact number but maybe if you could figure out "about" where it is.. the perfect-number pattern which is....(after the main number of course) "6,8,6,8" adds to itself every consecutive, but it also jumps around a bit to. Another question I have is, are numbers themselves capable of period doubling?

[Shadow]

Wiki says no:

 

http://en.wikipedia.org/wiki/Perfect_number#Odd_perfect_numbers

 

Personally, I wouldn't be all that surprised by either the existence or absence of odd perfect numbers.

Edited February 28, 2009 by Shadow

[the tree]

Wiki says no:

No it doesn't.

It is unknown whether there are any odd perfect numbers.

 

Personally my bet is with no. Though not based on any particularly rigorous reasoning.

[Shadow]

I meant this:

 

Carl Pomerance has presented a heuristic argument which suggests that no odd perfect numbers exist. Also, it has been conjectured that there are no odd Ore's harmonic numbers (except for 1). If true, this would imply that there are no odd perfect numbers.

 

But I agree, my sentence was incorrectly phrased. Sorry about that.

[Syntho-sis]

What about Period-doubling? Are vast numbers capable of falling into this kind of pattern? Chaos theory and integers?

[Syntho-sis]

wow...no replys... thats lames