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DrWatson · 70-79, M
There are so many different criteria one could use.
Six is the first "perfect number". It is the sum of all it's divisors (other than itself).
That is, 6 is divisible by 1, 2, and 3, and
6 = 1 + 2 + 3
Apart from my thinking that being perfect is a pretty property for numbers to have, what I also find beautiful is the doorway this opens to other mathematical questions.
There are about 50 numbers that are known to be perfect. ( The next one after 6 is 28. You can check for yourself that it is perfect.) Nobody knows whether the list of perfect numbers goes on forever or whether there is a greatest perfect number.
All the known perfect numbers are even. Does an odd perfect number exist? Nobody knows.
And there is a beautiful connection between perfect numbers and certain prime numbers known as Mersenne primes, but I won't go into that here.
Six is the first "perfect number". It is the sum of all it's divisors (other than itself).
That is, 6 is divisible by 1, 2, and 3, and
6 = 1 + 2 + 3
Apart from my thinking that being perfect is a pretty property for numbers to have, what I also find beautiful is the doorway this opens to other mathematical questions.
There are about 50 numbers that are known to be perfect. ( The next one after 6 is 28. You can check for yourself that it is perfect.) Nobody knows whether the list of perfect numbers goes on forever or whether there is a greatest perfect number.
All the known perfect numbers are even. Does an odd perfect number exist? Nobody knows.
And there is a beautiful connection between perfect numbers and certain prime numbers known as Mersenne primes, but I won't go into that here.
