Conference rusure::math

    I don't know why, but I seem to remember that it is 33,550,336
    but then again, I may be wrong.....                           
    
    						matt
    (then again, it may have been the combination to a gym locker, 
    the number sticks in my head for some reason....)

    
For what it is worth....

       	       8128 = 2 ^ 6 * (2 ^ 7 - 1)
       
     Since 2 ^ 7 - 1 is prime, 8128 is perfect.  (This is easily proved 
by someone who is suitably awake.)

     All of the known perfect numbers are of the form 
2 ^ (p - 1) * (2 ^ p - 1)  where p is prime and (2 ^ p - 1)
is prime.
       
isprime(2^11 - 1);
                                     false

isprime(2^13 - 1);
                                      true

evalf(2^12 * (2 ^ 13 - 1));
                                   33550336.

quit;

       	       	       	       	       	       	    matt

btw, for grins try the above commands to MAPLE in a batch job 
without the quit command at the end.... i.e. the following...

$ maple -q
isprime(2^11 - 1);
isprime(2^13 - 1);
evalf(2^12 * (2 ^ 13 - 1));
convert(2^12 * (2 ^ 13 - 1),  binary);
    

The next few perfect numbers are 2^(k-1) * (2^k-1) for 
k=17	8589869056
k=19	137438691328
k=31	2305843008139952128
k=61
k=89
k=107
k=127
k=521
k=607
k=1279
k=2203
k=2281
k=3217
k=4253
k=4423
k=9689
k=9941	(5985 digits)

The primes of the form 2^k-1 are the corresponding Mersenne primes.

The information above is taken from Beiler's *Recreations in the Theory of 
Numbers*, p19.