[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.

[dmurray]

> It applies to any bike

On a bike with derailleur gears, every time you change gears the derailleur will add some slippage so you won't get this effect.

> The easiest way to achieve this is to make the number of links in the chain prime

The chainring is fixed, but you might need to add or remove a link in the chain. In practice it seems more common to make the chainring have a prime number of teeth (53 or 47).

[jstanley]

Good point about the derailleur, I hadn't thought of that!

[1-more]

> then there's no downside to making the number of links prime if you can arrange it.

Bike chains always have to have an even number of links because they come in inner and outer pairs. But this has an effect on chainrings as well. When the tooth on a chainring or sprocket is in between two inner plates it's in a narrow gap. When the tooth is in between outer plates that's a wide gap. If you have a chainring with an even number of teeth then you can have the teeth match the narrow and wide profiles (called a narrow-wide chainring) which is supposed to make it less likely that you drop your chain off the chainrings. I'm not sure if it works, tbh. It seems to only be a thing in mountain or gravel bikes with a single chainring. I can't find any track chainrings that have the profile but I only looked for a second.

For chains themselves there's usually a pretty narrow number of links that work on a road drivetrain. I think I can live with one fewer or more pair of links on mine.

https://www.firstcomponents.com/narrow-wide-chainring/

[et-al]

Just to add on:

Track chainrings don't need a narrow-wide profile because there's very little slack in the system for the chain to come off. Saint Sheldon warns of the possibility of losing a finger also for this reason.

[jstanley]

> Bike chains always have to have an even number of links

D'oh! Of course, you're right.

[et-al]

Yeah, chains and cassettes are considered wear items, so I doubt manufacturers put much thought into patterned wear. Avoiding chain drop and crisp shifting are higher priorities.