Last month I
wrote about happy numbers and sexy numbers so I thought I’d complete a
little hat trick and talk all about perfect numbers.
A number is
said to be perfect if it equals the sum of its divisors. The second perfect
number (28) is divisible by 1,2,4,7,14. 1+2+4+7+14=28
Perfect numbers
are rare. At the last count only 48 have been discovered. It is not known whether there are an infinite number of perfect numbers
or that if there are any odd ones (Every one found so far is even) and these remain open questions to be solved
Perfect numbers are also entwined
with prime numbers as every even perfect number can be represented by the form
2n − 1(2n − 1),
where 2n − 1 is a prime number (otherwise known as
a Mersenne prime). In order for 2n − 1 to be a
prime number n must be a prime number. This is known as the Euclid–Euler theorem.
Just to get my retaliation in early this time there are no uses
whatsoever for perfect numbers (It doesn’t mean one won’t be found, prime
numbers were nothing more than a curiosity for centuries) but who says
everything we do in life has to be utilitarian? Let’s just marvel at the
beauty, interesting nature and perfectness of a small list of numbers.
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