June 28th – which in Italy we write as 28/06 – is a mathematically perfect day. But what does it mean? In mathematics, a natural number is perfect if it is equal to the sum of its divisors (excluding the number itself).
From this point of view, therefore, June 28th is a doubly perfect date. Let’s see why and which other numbers are perfect.
First of all, natural numbers are those that are used to count, therefore trivially numbers like 1, 2, 3, … These are positive numbers, including zero, and among these there are some that are defined as perfect because they have the following property:
Perfect numbers are all those natural numbers that are equal to the sum of their divisors other than the number itself.
For example, the number 6 is a perfect number! This is because its divisors are 1, 2, 3 and 6, so if we add them all, except 6, we find
1 + 2 + 3 = 6
For the same reason the number 28 is also a perfect number: its divisors are the numbers 1, 2, 4, 7, 14 and 28 and if we add them all (excluding 28) we obtain
1 + 2 + 4 + 7 + 14 = 28
And here we are at why June 28th is a doubly perfect day: it is written as 28/06, that is, its numerical date is made up of two perfect numbers.
But how many numbers of this type are there? Although the definition does not involve particularly complex concepts, these numbers are not so easy to find. Suffice it to say that, after the number 28, the next perfect number is 496:
1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496
If we go back in time we even find a triply perfect day! In fact, June 28, 496 AD is written as 06/28/426, all three perfect numbers. The next triple perfect date, however, will happen in some time, having to wait until June 6, 8128.
It must be said that there is no precise rule that helps us identify all existing perfect numbers, a bit like what happens with prime numbers. In fact, the search for perfect numbers is an open mathematical problem that dates back to the times of Euclid – a Greek mathematician who lived around 300 BC – and which until now has led to the discovery of only 52 perfect numbers in total. These are 52 numbers, all even and all linked to the search for particular prime numbers called Marsenne primes.
