Alberto Monteiro wrote:
>
> David Hobby wrote:
> >
> >> Uh? Really? The last time I read about it, the only
> >
> > KNOWN
> >
> >> perfect numbers were the few that came from...
> >> 2^(n-1) (2^n - 1)
> >
> Right. I should have written the known part. It was
> yet unknown if there were odd perfect numbers.
>
> OTOH, IIRC the number of odd perfect numbers is
> infinite, as there are infinite prime Mersenne numbers.
You mean EVEN.
>
> >> What is the smallest known odd perfect number?
> >
> > Why it is:
> >
> > 235465427730240065113511519531(snip)
> >
> No, it isn't. Do you have any idea about it? Something
> like "it's between 10^10^100 and 10^10^... (100 times) ... 10^100"
Is too! You could prove me wrong? There is a
(large) lower bound, and no known upper bound.
But you did catch that I was joking?
> PS: I once thought about a computer contest, something like:
> given an extension of a computer language [like C] where
> the integer type is unbound and memory is unbound, write
> a set of functions that use only x charaters [or tokens] such
> that one of them returns the biggest number in a finite time.
>
> The first step would be the generalization of the power function
> to the next level: a *** 1 = a, a *** (n+1) = a ^ (a *** n). The next
> step would be a function that takes multiplication, power, and this
> superpower as members of a sequence of functions. The next
> step would be the next generation of this superfunction, and then
> the generalization of all these generalizations.
>
> really big numbers Maru
Well, the classic function along those lines is
Ackermann's function. See:
http://mathworld.wolfram.com/AckermannFunction.html
But given more than a few tokens, we would reach the
stage where it was unknown who won the contest. Suppose my
function returns the first odd perfect number, or loops
forever. Do I win?
---David
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