That is quite a commonly useful technique (that I'm surprised more people don't know about).
Straying of topic a little...
You can use repeating patterns with prime periods to generate large tiling backgrounds that don't exactly repeat for a long time and so forth (the method is used in many games with procedurally generated landscapes to apply textures that don't repeat often enough to be noticable).
Even nature makes use of prime periods to avoid clashes.