PL> The last time I looked at these numbers is a looong time ago, but at 
least 
PL> the following questions were unsolved:
PL> - given X, is there a quick way to determine its perfectness ?
PL> - is the number of perfect numbers finite ? If not, what is its 
distributio
PL> - are all perfect numbers even ?
    (finite?) Since you are dealing with an infinite range,
    x - a goes to infinity as x goes to infinity. (where x is the
    range of numbers and a is the number of non-perfect numbers)
    (not a proof, but a logical assumption)
    (quick determination?)
    Are any odd numbers perfect? Can you represent the definition
    of "perect" using a formula? Do all perfect number end in a 6 or 8?
    
    p(x) = (Ex) a + b + c +...+ n = x
           (Ex) a % x = 0, b % x = 0, c % x = 0,...,n % x = 0
    where p(x) = perfect nuber
    (Ex) = there exists an x (variable)
    a,b,c,...,n = constants
    % = modulo
    This PLF does not explicity state that a,b,c,...,n are the only
    divisors of x.
--- GEcho 1.00
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