[fyhn]

Isn't this only relevant for fixed gear bikes, where you can skid the rear wheel to brake, and you want maximize the number of possible "skid patches", or orientations of the rear wheel while the pedals are in a fixed position?

[analog31]

It could also apply to the wear on the chainring and cog if their teeth are in a perfect proportion to one another, but without thinking too hard about it, I'm guessing that's actually rare. For instance a 2:1 ratio would be awkward for most cyclists riding on pavement (too low) and 3:1 too high, if they had to choose exactly one ratio.

I ride 46:19, because those are the parts that were in my bin when I built the bike, and it's a pretty good all-round ratio for city riding unless you're a lot more athletic than I am.

Also, those components wear out soon enough anyway -- a chain lasts 2 to 3 thousand miles, and a cog lasts a few chains.

[namdnay]

"I suppose this only applies to single sprocket bike."

[jstanley]

It applies to any bike. Ideally the number of links in the chain would be coprime to the number of teeth on every sprocket. The easiest way to achieve this is to make the number of links in the chain prime.

It'll still work just fine if you ignore this idea, but it might wear out more quickly. If you're a hobbyist just trying to make something work, you can safely ignore it and do whatever is most convenient. If you're a bicycle engineer trying to make things reliable and long-lasting, then there's no downside to making the number of links prime if you can arrange it.

I don't know whether bike companies actually do choose prime-numbered chains, maybe they have other constraints that are more important.