beeseven
May 13 2006, 09:22 PM
| | 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.
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unicornrose
May 14 2006, 02:14 AM
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. 
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Dooga
May 14 2006, 02:17 AM
Hey this is really interesting! I would show it to my math teacher, but then she'll shoot me for wasting my time...
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hulunes
May 14 2006, 03:57 AM
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.
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Plenoptic
May 14 2006, 10:30 AM
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.
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Florisjuh
May 15 2006, 04:59 AM
Sounds very interesting, but what's the use of it?
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Alissa
May 15 2006, 06:36 AM
That's really cool. Can you imagine being the person who first found these perfect numbers? It's insane. I could never. O.O
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leeleelee
May 15 2006, 09:58 AM
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.
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Plenoptic
May 15 2006, 11:23 PM
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.
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Justin S.
May 20 2006, 06:38 AM
What are you taling about perfect number?
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garbage
Aug 27 2006, 10:38 AM
I think this topic, is not for me since im not that good at the mathematics, but I was thinking the pefect number might have been zero.. I dont know why, but thats the number tyhat first popped into my head
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BhajunSingh
Aug 27 2006, 03:55 AM
I find this kind of pure mathematics very interesting personally - its also really amazing to me how people were able to come up with this stuff thousands of years ago. Also, in case anyone's interested further in perfect numbers, each number has a direct relation with a unique Mersenne Prime number. A Mersenne prime is a prime number in the form of (2^n - 1), where n is also a prime number. So, for example, the first Mersenne prime is 3, where n = 2, the second is 7, where n = 3, and so on. To find the directly related perfect number, you take the Mersenne prime (2^n - 1) and multiply it with (2^(n - 1)). So for example, with n = 2, the Mersenne prime is 6, and the perfect number is also 6: CODE
(2^n - 1)(2^(n - 1))
(2^2 - 1)(2^(2 - 1))
(4 - 1)(2^1)
(3)(2)
6
And when n = 3, the Mersenne prime is 7, and the perfect number is 28: CODE
(2^n - 1)(2^(n - 1))
(2^3 - 1)(2^(3 - 1))
(8 - 1)(2^2)
(7)(4)
28
Hope that makes some sense Anyway, so basically, since Mersenne primes are smaller and have more searching formulas, they're used to find more and more perfect numbers...and as there are only 43 known Mersenne primes, there are 43 known perfect numbers. Also, on an off note, Mersenne primes are also the largest primes known...the 43rd MPrime was about 2^30,400,000ish...just over 9 million digits long  Anyway, I ramble - I just find Mersenne primes especially, and the searching algorithms, very interesting. If anyone else wants to know more about then, http://www.mersenne.org is a good site - it runs the GIMPS (Great Internet Mersenne Primes Search) program that uses distributed computing to attempt to discover new Mersenne primes. 
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thewildmen2
Aug 26 2006, 04:56 AM
wow, so interesting, i want to show this to my brother..
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tdktank59
Aug 26 2006, 02:52 AM
well if we are doing that... i say the best number is still 42 but my ideal number would be a number that is NOT devisible by 1 lol figure that one out will ya?
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ProtoMan
Aug 26 2006, 02:30 AM
I think the perfect number is 3.141592653589793238462643383279502884197169399375105820974944592307816406286208 99862803482534211706798214808651328230664709384460955058223172535940812848111745 02841027019385211055596446229489549303819644288109756659334461284756482337867831 65271201909145648566923460348610454326648213393607260249141273724587006606315588 17488152092096282925409171536436789259036001133053054882046652138414695194151160 94330572703657595919530921861173819326117931051185480744623799627495673518857527 24891227938183011949129833673362440656643086021394946395224737190702179860943702 77053921717629317675238467481846766940513200056812714526356082778577134275778960 91736371787214684409012249534301465495853710507922796892589235420199561121290219 60864034418159813629774771309960518707211349999998372978049951059731732816096318 59502445945534690830264252230825334468503526193118817101000313783875288658753320 83814206171776691473035982534904287554687311595628638823537875937519577818577805 32171226806613001927876611195909216420198938095257201065485863278865936153381827 96823030195203530185296899577362259941389124972177528347913151557485724245415069 59508295331168617278558890750983817546374649393192550604009277016711390098488240 12858361603563707660104710181942955596198946767837449448255379774726847104047534 64620804668425906949129331367702898915210475216205696602405803815019351125338243 00355876402474964732639141992726042699227967823547816360093417216412199245863150 30286182974555706749838505494588586926995690927210797509302955321165344987202755 96023648066549911988183479775356636980742654252786255181841757467289097777279380 00816470600161452491921732172147723501414419735685481613611573525521334757418494 68438523323907394143334547762416862518983569485562099219222184272550254256887671 79049460165346680498862723279178608578438382796797668145410095388378636095068006 42251252051173929848960841284886269456042419652850222106611863067442786220391949 45047123713786960956364371917287467764657573962413890865832645995813390478027590 09946576407895126946839835259570982582262052248940772671947826848260147699090264 01363944374553050682034962524517493996514314298091906592509372216964615157098583 87410597885959772975498930161753928468138268683868942774155991855925245953959431 04997252468084598727364469584865383673622262609912460805124388439045124413654976 27807977156914359977001296160894416948685558484063534220722258284886481584560285 06016842739452267467678895252138522549954666727823986456596116354886230577456498 03559363456817432411251507606947945109659609402522887971089314566913686722874894 05601015033086179286809208747609178249385890097149096759852613655497818931297848 21682998948722658804857564014270477555132379641451523746234364 Thats how much I know...... Why do I like this number ? Because it is PI.It is very useful in mathematics.
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