## Thursday, 3 March 2011

### Perfect Numbers

This, truly is a definition of eloquence. One for its rarity and two for the fact that the numbers are in fact, perfect. But why are they perfect? They do not hold the key to the mysteries of the universe (as of 3rd March 2011!), they are just a phenomena that intrigues Mathematicians (an intrigue that started as early as 100AD). But, what is a perfect number? It is a number where all it's divisors (excluding the number itself) add to make the original number. They are incredibly rare however, and I believe that is the source of their intrigue.

Perfect Numbers and Mersenne Primes (I have touched on these before) go hand in hand, so hand in hand that the formula for finding Perfect Numbers requires Mersenne Primes. Euclid discovered that 2p−1(2p−1) where 2p−1 is prime, a Mersenne Prime in fact, will always reveal a Perfect Number. There is currently 47 Perfect Numbers known, the same amount as there is Mersenne Primes; obvious because Perfect Numbers rely on Mersenne Prime numbers.

Perfect numbers increase at a rather rapid rate, as you can see: 6; 28; 496; 8128; 33,550,336, 8,589,869,056; 137,438,691,328; 23,058,43,008,139,952,128. And the highest known perfect number has 25,956,377 digits, which is huge.

It is still unknown whether or not there is infinite Mersenne Primes and thus Perfect Numbers, it is also not known if there is any odd perfect numbers, if you would like to read more on this visit here: http://mathworld.wolfram.com/PerfectNumber.html