I used a product of primes for a real world work task to see who could FULLY, emphasis on FULLY, cover whose duties.
Employees skills were assigned a prime number.
For each employee a prime product was generated that represented their skill mix.
My work example involved about 40 different types of skills and from memeory around 80 or so employees, and I wanted to use the prime product to see who could COMPLETELY cover the duties of who.
So for a very simple example if we had skills :-
can serve - assign prime number of 2 (say)
can cook - assign a prime number of 3 (say)
can clean - assign a prime number of 5 (say)
can deliver - assign a prime number of 7 (say)
As an aside if you didn't want a manual list of prime numbers you could use Euler's formula of
p(n) = n^2 + n + 41
to generate primes on the fly.
So lets say
Joe can serve, cook and clean - prime product = 2 x 3 x 5 = 30
Ann can cook and serve - prime product = 2 x 3 = 6
Tom can serve and clean - prime product = 2 x 5 = 10
Sue can serve and deliver - prime product = 2 x 7 = 14
Ben can cook serve and deliver - prime product = 2 x 3 x 7 = 42
So to see who can cover who,
the prime product of the person covering needs to be
by the prime product of the person being covered.
Make sure its the right way round !
In other words there is no remainder , in many programming environments this can be checked using MOD.
So lets pose a question
Who can fully cover Sue ?
Sue's prime product = 14
Joe ? 30 / 14 = 2 r 2 So Joe can't fully cover
Ann ? 6 / 14 A fraction less than 1 so definitely cant cover
Tom ? 10 / 14 A fraction less than 1 so definitely cant cover
Ben ? 42 / 14 = 3 So Ben can FULLY cover Sue
This is a trivial example and doesn't amply demonstrate it's usefulness but imagine having a 100 employees with 40 or so skillsets and I think you can see then how useful this might be.
Hope this is of interest and even possible use.