In this publication I add some examples related to compound integers, perhaps some of these may be considered partly unrelated to physics for some person, and after asking about the relevance or importance of compound integers in physics. To know what happens to integers and physics, I have read the conversation notes (1). I also know other good YouTube videos (see the comment).
We consider integers greater than or equal to $ 1 $.
Example 0 One can think of prime numbers as a strip of unit paper squares that cannot be arranged in a pretty rectangle $ c = a times b $, where $ a> $ 1 Y $ b> 1 $ are integers This example It seems Of course it is not related to physics. For example the integer $ c = $ 8 or $ c = $ 9 They can be organized in beautiful rectangles. The importance, density and open problems related to prime numbers are known. In particular I mean (2).
Example 1. For the design of the Arecibo message, a rectangle was considered as a format $ a times b $, for those specific integer values $ a> $ 1 Y $ b> 1 $ which refers to Wikipedia Message from Arecibo. Therefore, physicists or people who designed this format did not choose a first $ p $let's say like a rectangle $ p times 1 $, as a format / frame for that message. Here I emphasize that the interesting thing is that to transmit certain information a format was chosen.
Example 2 For example, on YouTube you can search and see examples of how to make a hologram in your home, using different materials and some devices, say a phone or TV that projects a certain amount of photos / files in order to create the hologram. My belief (I think it's obvious) is that each of these identical photos / files is a rectangle $ a times b $ with $ a> $ 1 Y $ b> 1 $, a compound integer.
Question. I would like to know if compound integers have any relevance or importance in physics. What are the problems or those scenarios that exemplify and motivate that compound numbers are important in the theories that explain our physical world? Thank you.
In this post, I ask from an informative point of view, and as a soft question. If there are examples, and you know it from the literature, refer it, do not hesitate to answer this question as a reference request, and try to find and read it in the literature.
(1) David Tong, Physics and the integers, University of Cambridge, Trinity Maths Society (2010).
(2) Barry Mazur and William A. Stein, Prime numbers and the Riemann hypothesis, Cambridge University Press (2016).