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Divisibility and PrimesCicadas

Cicadas

North America is home to various broods of cicadas. These have the curious property that they only emerge every few years during the summer to breed – the remaining time they spend underground.

For example, the cicadas in Florida and Mississippi appear every 13 years. The cicadas in Illinois and Iowa only appear every 17 years. But there are no cicadas with 12, 14, 15 or 16 year cycles.

Both 13 and 17 are prime numbers – and that has a very good reason. Imagine that there are predators in the forest which kill cicadas. These predators also appear in regular intervals, say every 6 years.

Now imagine that a brood of cicadas appears every ${n} years (${isPrime(n) ? 'prime' : 'not prime'}). The two animals would meet every ${lcm(n,6)} years, which is the of 6 and ${n}.

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time until cicadas and predators meet, for various different cicada cycle lengths.

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