What Is A Perfect Number?

A perfect number is a number with the property that all of its divisors (including 1 but excluding itself) add up to that number. Alternatively, if you want to include the number as a divisor, then all of its divisors add up to twice itself.

 

Some examples include:

6 (1+2+3)

28 (1+2+4+7+14)

496 (1+2+4+8+16+31+62+124+248)

8128 (1+2+4+8+16+32+64+127+254+508+1016+2032+4064)

It used to be thought that the fifth perfect number would have five digits since the others had 1, 2, 3, 4, but it turns out that the fifth is 33550336 which has eight digits. It was also thought that the endings would alternate between 8 and 6, but the sixth perfect number is 8589869056. There most likely aren't any odd perfect numbers, but if there are, they are extremely large (> 10^500).

 

Wikipedia has more, including the conditions which an odd perfect number must satisfy and the proof that all perfect numbers are also Ore's harmonic numbers.

Its not too surprising to me that when you got to the 6th number the amount of digets got larger. Math has alot of differant sequences that tend to do that. Just like nature sometimes math can throw you for a loop.

Hey this is really interesting! I would show it to my math teacher, but then she'll shoot me for wasting my time...

the perfect number remind me a former program in C,which is to carry out the procedure of quering the number of that kind during 10000.well.it is really a interesting math number IMO.

It's funny you made this post because in computer programming I was just told to make a program that will display the pefect numbers found between 1 and 1000. I think it is pretty interesting how it works. Of course it took me a while to get the equation right to have it find the numbers.

Sounds very interesting, but what's the use of it?

That's really cool. Can you imagine being the person who first found these perfect numbers? It's insane. I could never. O.O

It is not known when perfect numbers were first studied and indeed the first studies may go back to the earliest times when numbers first aroused curiosity. It is quite likely, although not certain, that the Egyptians would have come across such numbers naturally given the way their methods of calculation worked, see for example where detailed justification for this idea is given. Perfect numbers were studied by Pythagoras and his followers, more for their mystical properties than for their number theoretic properties.

Edited May 15, 2006 by leeleelee (see edit history)

Like lee said I think people have known about them they just weren't called Perfect Numbers. I am sure they figured it out soon enough. I wonder how many they have found so far and how many more they will find. I think it will turn out to be like the Largest Prime Number and people will start competing to see who can find one a million characters long unless they have already.

What are you taling about perfect number?

Beeseven, I honestly don't get what a perfect number is. It sounds very interesting thought, how you can have a perfect number, but then again, I'm just kurtis.If you have time please private message me, or we can talk on a messenger. Thanks for posting and making me think for the first time in my life.

Edited May 28, 2006 by kurtis (see edit history)

I have heard of perfect numbers before, but didn't really understand them until I viewed this topic on here.Now I've read this, I understand exactly what they are and how they work

Hmm pretty cool 'perfect number' hehe...I believe I learnt those in math class cause they seem to be familiar to me and etcGood and Informative post / Refresher hehe

Isnt this the same thing as a perfect square number? Correct me if I am wrong, im currious. I think that I did this in school a while ago.

Nice find man, i would like to know more about it.