Big news in bug math. This is the first year since 1803 when both 13-year cicadas and 17-year cicadas will emerge from the ground simultaneously in the US!

13 and 17 are both prime. It's believed cicadas evolved to have prime-number life cycles to avoid predators that emerge more frequently, like once every 4 years or 5 years or... whatever. By showing up infrequently, with a prime number life cycle, they can starve out those predators.

And since 13 and 17 are both prime and 13 × 17 = 221, both kinds of cicadas emerge simultaneously only once every 221 years. And

1803 + 221 = 2024

so now they'll both emerge simultaneously and we'll have 𝑙𝑜𝑡𝑠 of cicadas!

Also, this year the two kinds can interbreed!

The last time the Northern Illinois Brood’s 17-year cycle aligned with the Great Southern Brood’s 13-year cycle, Thomas Jefferson was president.

https://www.nytimes.com/2024/01/19/science/cicadas-emergence-broods.html

@johncarlosbaez 'Also, this year the two kinds can interbreed!' OK, that's too big a hook. Do we understand how the cycles happen - is it genetics? If so, how? If so what happens when they interbrede?

@penguin42 - I doubt we understand this, since Mendelian genetics wasn't a thing back in 1803. Maybe someone has been waking up cicadas prematurely and interbreeding them just to see what happens.... but that seems a bit unlikely.

@johncarlosbaez Hmm looks like people are trying but haven't got a conclusion; https://www.nature.com/articles/s42003-018-0025-7

@penguin42 @johncarlosbaez Nice. One thing to note (which I've also seen in other sources) is "life cycle regulation in periodical cicadas may not always be strict, because 4-year acceleration and/or deceleration of emergences have been observed in both groups of cicadas". So the mathematics may be beautiful but only an approximate description of what the cicadas do.