I'm preparing a talk on Mersenne primes, Perfect numbers and Fermat primes.
In trying to provide motivation for it all I'd like to provide an application of these things.
I came up with these:
Applications of Mersenne numbers: signed/unsigned integers, towers of Hanoi
Applications of Fermat numbers: relation to constructible polygons
But for perfect numbers the best I could find is: The earth was created in 6 days by God because 6 is perfect. Also, the cycle of the moon is 28 days.
For 6: $\log(1+2+3)=\log(1)+\log(2)+\log(3)$ This page (https://mathshistory.st-andrews.ac.uk/HistTopics/Perfect_numbers/) has a lot of history but no real applications.
Can anyone give application of perfect numbers?