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April 1, 2012

Cicadas and Prime Numbers

Filed under: Cicada 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 a 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. A species belonging to the genus Chremistica is known for four-year life cycles, which coincide with the World Cup (association football event). Okanagana rimosa is said to have a 9-year life cycle (and to be proto-periodical).

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.

A cicada counting prime numbers

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.



    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

    Comment by Jeff "Dr Chordate" Moran — April 19, 2012 @ 12:42 pm

  2. Excellent!

    Comment by Dan — April 22, 2012 @ 8:10 am

  3. […] 1) Avian Predation Pressure as a Potential Driver of Periodical Cicada Cycle Length by Walter D. Koenig and Andrew M. Liebhold, The American Naturalist. This is a newly electronically published paper about what drives the long, prime-numbered lifecycle of Magicicada periodical cicadas. […]

    Pingback by Cicada Mania: Two new cicada publications worth reading — January 20, 2013 @ 2:28 pm

  4. […] speculate that one reason why these cicadas emerge in 17 or 13 year cycles is because those are prime numbers, which makes it difficult for predators to synchronize with […]

    Pingback by Cicada Mania: The most interesting 17 year cicada facts — April 2, 2013 @ 5:31 am

  5. 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.

    Comment by j m rowland — May 21, 2013 @ 9:20 am

  6. You are correct!

    Comment by Dan — May 21, 2013 @ 10:32 am

  7. 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.

    Comment by Cameron — May 16, 2015 @ 8:53 pm

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

    Comment by Dan — May 16, 2015 @ 9:11 pm

  9. […] you’re interested in prime number stories, check out this page at cicadamania and skim Gould’s Ever Since […]

    Pingback by Talk about Back Yard Science! Wooo Boy! — May 21, 2015 @ 7:46 pm

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