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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