Nature exploits prime numbers to ensure cicada survival

Article By : John Dunn

Nature exploits prime numbers to ensure the survival of two closely-related species and the magnitude of acoustic stress that gets imposed on us.

This year of 2021 is a mating year for 17-year cicadas during which time they can collectively make almost as much noise as a straight pipe motorcycle. I once read that cicada sound levels can reach the neighborhood of 90 dB sound pressure level (SPL).

We once discussed how noise canceling microphones work, and their properties might have particular significance this year.

The article in which I read about 17-year cicadas also mentioned a different cicada species which emerges and mates on a 13-year cycle with pretty much the same dreadful acoustics. We might ask why they emerge at those two different cyclic numbers of years; I suspect it is to reduce competition between the species.

When they both emerge in the same year, their mating calls will tend to drown each other out and interfere with each other. Ham radio enthusiasts would call that severe QRM. Also, there would be intense competition for perching space.

It would be to the benefit of both species if they came out at different years in order to minimize simultaneity and to maximize the time spans between simultaneous emergences.

We can examine that as follows.


Cycles Years
1 13 17
2 26 34
3 39 51
4 52 68
5 65 85
6 78 102
7 91 119
8 104 136
9 117 153
10 130 170
11 143 187
12 156 204
13 169 221
14 182 238
15 195 255
16 208 272
17 221 289


Figure 1 Here’s a basic look at cicada simultaneity interval.

Simultaneity will occur at 13 cycles of 17 years each and 17 cycles of 13 years each, which comes to simultaneity intervals of 13×17 , resulting in simultaneity every 221 years.

That would be the interval between years of simultaneous emergence of the two species, which is a very long time indeed. Ergo, there would be minimal competition between the two species.

It is helpful that 13 and 17 are prime numbers. If one species were five-year cyclic and the other species were 10-year cyclic, simultaneity could come in as little 10 years.

We should also note that there is no need for synchronization between the species. If, for example, we offset the 13-year species, simultaneity events still repeat at intervals of 221 years, as shown for several cases in Figure 2.

table of cicada simultaneity intervalsFigure 2 This is an extended view of the cicada simultaneity intervals.

We see that 663 – 442 = 221. We also see that 493 – 272 = 221 and that 544 – 323 = 221.

The pattern goes on and on and always retains the 221-year repetition rate.

This article was originally published on EDN.

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).

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