In an ideal world every tooth on the gear is exactly the same, but in the real world they have slight differences that wear each tooth differently. So by having

In an ideal world every tooth on the gear is exactly the same, but in the real world they have slight differences that wear each tooth differently. So by having a prime number of teeth, the teeth of two gears don't mesh with the same teeth on the opposite in a short repeating pattern. The gear teeth wear more evenly this way and imperfections are worn off over time instead of worn in.