Doing a lot of math isn't what destabilizes a system. Unrestrained consumption of system resources will.
I can consume just as many CPU cycles as the hardest math problem with a simple infinite loop. But so long as the system schedules my loops time on the CPU so that the OS still gets the time it needs your mouse pointer will glide along fine.
If I eat up memory or file handles or any other limited resource it doesn't mater how little math got done in doing it, the system is now starved for resources. In this state it's hard to get it to do anything new.
Your biggest problem is that it takes a long time to do your math. Most software only has to come up and be stable for a few hours before someone will close it. Your stuff will be up for weeks. That's not client level coding. That's server level coding.
Code that can be stable for a long time is what you need here. Make sure you close everything you open and free everything you allocate when your done with it. Otherwise you'll leak resources, crash, and burn.