I am preparing for an interview on Distributed Systems. I have gone through a lot of text and understand the basics of the area. However, I need some examples of discussions on designing a distributed system given a scenario.

For example, if I were to design a distributed system to calculate if a number N is primary or not, what will the be design of the system, what will be the impact of network latency, CPU performance, node failure, addition of nodes, time synchronization etc. If you guys could present your in-depth thoughts on this example, or point me to some similar discussion, that would be really helpful.