Perfect Numbers

We all know that the word 'Perfect' means 'being complete of its kind and without defect'. You must have come across some people who are so perfect but did you know that there are numbers too which are complete that is perfect. Yes, long back, Pythagorus has defined a number to be Perfect if it equals to the sum of all of its divisors (factors), excluding the number itself . For example,
6 - divisors are 1, 2, 3; 1+2+3 =6 Perfect Number!
28 - divisors are - 1, 2, 4, 7, 14 ; 1+2+4+7+14 = 28 Perfect Number!

The major study on Perfect Numbers was done by Euclid , Nichomachus, Ibn al-Haytham, and Euler and some of the important conclusions drawn are
1. As per Euclid, perfect numbers can be generated by the formula 2ⁿ⁻¹(2ⁿ − 1)
2. As per Nichomachus, all Perfect Numbers are even. (a theory that is yet to be disproved).
2. As per Euler, all even Perfect numbers are of the form 2ⁿ⁻¹(2ⁿ − 1), where 2ⁿ − 1 is a Mersenne prime.

3. Every even perfect number ends with 6 or 8.

Now, that you know about Perfect Numbers, you must be curious to know some amazing facts associated with these numbers -
1. There is a belief of religious significance being associated with the Perfect Numbers 6 and 28. That is - 6 is the number of days taken by God to create the world, and it was believed that the number was chosen by him because it was perfect. Again God chose the next perfect number 28 for the number of days it takes the Moon to travel round the Earth. (http://www.gap-system.org/~history/HistTopics/Perfect_numbers.html).
2. There are only 4 (6, 28, 486, 8128) perfect numbers below 10,000.
3. As of September 2008, only 46 Mersenne primes are known, which means there are 46 perfect numbers known. Be first to find 47th.
4. Till date, people have not yet defined the benifit of Perfect Numbers in real time and also they could not find an Odd Perfect Number. Mathematicians are still working on these and if interested you can join them.

You can find more on Perfect Numbers at - http://en.wikipedia.org/wiki/Perfect_number and http://www-users.cs.york.ac.uk/~susan/cyc/p/perfect.htm