#1
You know, I have been wondering this for a while...

How do you demonstrate Euclid's method for finding perfect numbers?
His method is this:

"If (1+2+4+8+16+...+2^n) is prime-->(1+2+4+8+16+...+2^n)*2^n is a perfect number"

Perfect numbers are positive integers in which the sum of their positive divisors is said number (like 1+2+3=6 or 1+2+4+7+14=28, etc)


I think mathematicians only found like 6 or so even perfect numbers using this method (I don't know if this method can find all perfect numbers)

But how do you prove it to be true? How do you demonstrate it?
Surely it would be complete induction, and I would take a guess at it being a sumatory..
I think the problem would be the analitic expression for prime number, since there isn't only one analitic expresion to find them all (you can see most of the other ones here http://en.wikipedia.org/wiki/List_of_prime_numbers )...
And also another problem would be the analitic expresion of a perfect number, using "n" as a variable (so at least you can use induction with a sumatory)....

The method now used is 2^n-1(2^n - 1) for 2^n-1 being prime (the same thing really, but this one could be used in inductive reasoning)

How do you think it would be possible to demonstrate it?
Last edited by gonzaw at Jun 6, 2008,
#2
I can't be bothered to think all too much about that post

but I wrote a sieve program in C and have a file with 50 megabytes of prime numbers on my hard drive
#3
You can write a pretty simple program to find perfect numbers. Of course, there are limitations to this using a 32-bit computer because it can only go up to ~ 4.3 billion. However, using data structures like stack or queues, you can get it to perform calculations to unlimited lengths. There are probably programs on available on the internet that do this.
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Art & Lutherie
#4
Quote by darkstar2466
You can write a pretty simple program to find perfect numbers. Of course, there are limitations to this using a 32-bit computer because it can only go up to ~ 4.3 billion. However, using data structures like stack or queues, you can get it to perform calculations to unlimited lengths. There are probably programs on available on the internet that do this.


But don't those programs kind of "taunt" prime numbers for doing that method?
Isn't there a demonstration so you can't "taunt" them?