Cicada Mania

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April 1, 2012

Cicadas and Prime Numbers

Filed under: Anatomy | Magicicada | Periodical — Dan @ 8:51 pm

Last week io9 published an article titled Why do cicadas know prime numbers? The gist of the article is that cicadas developed long, prime-numbered, periodical life cycles to avoid gaining a predator that can synch up with the cicadas.

It’s an interesting read, but it’s a little thin on facts and references. Here is part of what the article is missing:

Only seven out of the hundreds of species of cicadas have 13 or 17-year life cycles, and they all belong to the genus Magicicada. Three species of cicadas have 17-year life cycles: M. septendecim, M. cassini, and M. septendecula. Four species of cicadas have 13-year life cycles: M. neotredecim, M. tredecim, M. tredecassini and M. tredecula. These are the periodical cicadas Stephen Jay Gould wrote about.

As one proof of the theory, there isn’t a wasp that specifically predates Magicicadas (the genus of cicadas with long, prime-numbered life cycles), but there is a Cicada Killer Wasp that predates Tibicen cicadas, which have shorter life cycles and emerge every year.

Although no animal predator has figured out their 17 & 13-year life cycle, one life form has: the Massospora cicadina fungus.

The book in which Stephen Jay Gould theorized about prime numbers and periodical cicadas is Ever Since Darwin: Reflections in Natural History. You can search through the book in Google Book Search, or just buy a copy (if you’re interested). I think I paid a cent for my copy (used).

Other species of cicadas also have life cycles of a prime number of years, but some do not. The Chremistica ribhoi is known for four-year life cycles, which coincide with the Fifa World Cup (association football event). The Raiateana knowlesi of Fiji has an 8 year life cycle.

Not all cicadas are periodical cicadas; the vast majority of cicada species appear every year even though their life cycles are longer than one year.

If you want to delve deeper into the subject of periodical cicadas and prime numbers, search for the paper Evolution of Periodicity in Periodical Cicadas by Nicolas Lehmann-Ziebarth et al.

This image is meant to be funny, but it’s a bit misleading…
A cicada counting prime numbers
It’s likely that periodical cicadas are counting in units of 4. 4+4+4+1 = 13. 4+4+4+4+1 = 17.

Prof. Douglas Galvao of the State University of Campinas has written a paper titled Emergence of Prime Numbers as the Result of Evolutionary Strategy. Download his paper from Cicada Mania.


  • Cicadas do not incubate underground. Cicada eggs hatch above ground; typically in grooves in the stems of plants created by female cicadas.
  • Cicadas rarely sing at night. In rare circumstances, like in the presence of artificial light, they will sing at night. If you hear an insect at night it is likely a cricket or katydid (or frog).
  • Here’s another article with a practical application for web design called The Cicada Principle and Why It Matters to Web Designers.
  • Mathematical “locusts” an mathematical explanation of the cicadas and prime numbers phenomenon.


  1. Joan T. Ferris says:

    I remember a major Cicada (17-yr.) event during 1972 in Glenview, IL., a Chicago suburb. Everything was covered with them. There were mature Oaks covering the yard. All small plant life was eaten. I found the event to be amazing yet depressing.

    1. Dan says:

      What? They don’t eat plants. They will drink their fluids though. 🙂

  2. Cameron says:

    Hello, within the past week or so I have been noticing cicada nymphs emerging from the ground in my yard. I don’t believe there periodical because they are black with sort of orange wings,and they’re not expecting them this year. I’ve watched some emerge from their shells and darken. After seeing the proto-periodical image of cicadas, I believe that is what they are.I live here in Monroe,New York and they’re starting to sing. They sound like Okangana. I haven’t noticed an emergence this heavy of them in about six years. During the day they almost from a chorus of a few dozen. I am fascinated with these insects and have been studying them ever since I was a kid.

    1. Dan says:

      Sounds reasonable. Send us a few photos and we can diagnose the species.

  3. j m rowland says:

    In the 3rd paragraph, I believe you say “species” when you meant to say “genus’. Magicicada is a genus, of which those mentioned are species.

    1. Dan says:

      You are correct!


    This is a link to a MySpaceMusic page where I have posted a good song about periodic cicadas set to a recognizable melody (hint: cicada emergence is like a “graduation”). Does anyone have video to go along with this song?


    Jeff “Dr Chordate” Moran

Leave a comment. Questions about plants or snakes are deleted.

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