Examples of prime numbers in nature [closed]

Question

Finding primes in signals is seen as a sign of some kind of intelligence - see e.g. the role of primes in the search for extraterrestrial life (see e.g. here).
This is because there are relatively few examples of numbers that appear in nature because they are prime. One example of the use of prime numbers in nature is as an evolutionary strategy used by cicadas of the genus Magicicada (see e.g. here or here: [1])

My question:
Do you know of any other instances where prime numbers occur in nature? Could you please also give a source/link - and perhaps some background. Thank you.

[1] Goles, E., Schulz, O. and M. Markus (2001). "Prime number selection of cycles in a predator-prey model", Complexity 6(4): 33-38


Edit: Obviously many people misunderstood me. I didn't mean the occurrence of prime numbers just by coincidence - but because they are prime. The cicadas example - although being controversial - at least hints at some kind of evolutionary strategy.

Answer 1

Somewhat longish to be a comment, so here goes:

How about examples like:

• Polygons in nature? Unfortunately, the most famous one of them is a hexagon ;-)

But I am certain there are several chemical compounds, physical structures such as crystals, and so on that exhibit polygonal structures with prime number of edges / facets --- perhaps because the "primeness" there leads to a physically / chemically more stable configuration.

Is this an acceptable kind of primeness? Perhaps not. It seems to me that the question you pose is almost at a "meta" level!

Answer 2

Cicadas spend most of their lives underground, emerging to mate every $k$ years where the integer $k$ varies from species to species. Biologists have observed that $k$ tends to be a prime number -- for example, there are "13 year" cicadas and "17 year" cicadas. To the best of my knowledge, it is still controversial whether there is an evolutionary reason for this or whether it is just a coincidence.

Answer 3

I think this question is better asked as "are there examples of prime SEQUENCES in nature?"

The fact that a starfish has 5 points, or that a sunflower has 23 petals or whatever, proves very little about primes in nature. It could be complete coincidence that the number happens to be prime.

What if starfish are found to have either 3, 5, or 7 points? Does that imply a prime sequence? Maybe its just something about odd numbers > 1.

The Cicada example definitely implies a prime sequence, not just a single number which happens to be prime.

Answer 4

Nontrival primes: human chromosome number is 23, Sunflower chromosome number is 17, both of which are prime. Most flowers have an odd and often prime number of petals: five is a common number.

I assume you really meant non-trivial primes, where $p>2$ or $p>3$, but you didn't specify that, so let me point out some basic regions where 2 and 3 are prominent. And $2$ and $3$ are very prominent through-out nature, so these are not very special concepts.

Diploid genomes come in copies of 2, and 2 is prime. DNA chains come in duplicate copies, with one side reading in one direction as the sense and the other side being the "inverted carbon copy" and called the nonsense side. When DNA chains are copied, they split apart like a zipper and complementary copies are made on both, yielding two identical doubled-DNA chains.

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Three is also a prime number:

The human chromosomal set consists of 23 pairs of DNA chromosomes: $46$ in total, with $44$ of those being non-sex chromosomes, and $2$ of them being sex chromosomes: $XX$ for females and $XY$ for males.

Also, when you convert from 2 copies of these chromosomes to three, for example Trisomy 21, you can end up with Down's syndrome.

If, instead of having two sex chromosomes of the usual type, $XX$ or $XY$, you can have XYY syndrome or XXY syndrome also known as Klinefelter's syndrome. Technically, you could say that these types of sex-chromosome sets are not in the set of the usual two genders of male ($XY$) and female ($XX$), but are actually outside of the two genders. So to answer @vonjd's comment to the question, there are not just 2 genders.

Extra random point: the sunflower's spiral follows Fermat's spiral which at various points, is a prime number. So there must be some sunflowers which have a prime number of sunflower seeds.

Many flowers have five petals, five is prime.

Answer 5

Do you have any evidence of the higher incidence or prevalence of prime numbers in nature, other than happen-stance or co-incidence?

I believe you're mistaken in claiming that prime numbers are used in nature. I would simply state that prime numbers occur in nature; numbers occur in nature and must be used to describe natural phenomena and it is a mere coincidence that some numbers which occur are primes.

While it may be true that the cicada emergence cycle happens to be a prime number, is it always exactly so, or in some cycles is it an even number? What about other insects or varieties of cicadas that may use a non-prime number yearly cycle? As in the examples stated above, humans have twenty-three pairs of chromosomes, chimps have twenty-four. That chimps have 24 pairs does not make the human's 23 pairs less prime, just more likely to be co-incidental. It would appear that the majority of the comments and answers to this question are joke answers, and perhaps this question should be closed if joke answers are the only answers which mathematicians can provide.

If you could come up with a mechanism to collate all of the occurences of numbers in natural phenomena as a multi-set $S$, and then show somehow that the prevalence of prime numbers in this multiset $S$ is greater than would be expected by chance for another randomly selected multiset over the integers $\mathbb{Z}$, then perhaps I could buy the argument that primes are a sign of intelligence in nature.

The argument about SETI searching for prime number like signals from beyond is about the expectation that intelligent creatures would transmit a signal that would appear out of the ordinary and as a non-natural phenomenon. I think it's ridiculous to mix that up with looking for prime numbers in nature (and then jumping to the conclusion that some sort of intelligence or design might be behind it). Natural phenomena, even emergent evolutionary phenomena, have the statistical properties which they have.

Do you have any evidence of the higher incidence or prevalence of prime numbers in nature, other than happen-stance or co-incidence?

Answer 6

Here you go: The Holy Trinity, the Kremlin 5-pointed stars, the Magnificent Seven (and the Seven Samurai), the 7-11 convenience stores, the Devil's Dozen.

Edit 1 Of course, I forgot the 101 Dalmatians.

Edit 2 Also if $\alpha$ is the fine structure constant, then $\alpha^{-1}\approx 137$. But dalmatians are much cuter.

Edit 3 2011 is the year when this question is going to be deleted, I hope. Note that 2011 is prime.