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> 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/



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.


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

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




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