Problems & Puzzles: Puzzles

Puzzle 344. Primes in Nature

In nature certain things happen suggesting very sharply the count of prime numbers. Not surprisingly, small primes are more abundant than larger ones, in nature, too.

For example, the prime number '2' is seen wherever bilateral symmetry is present. For example, in the human body, you will find two eyes, two ears, and so on.

Another example: we could say that we touch the outside world four times with the prime number 19 due to a delicate unbalance of our fingers & toes: 19=4+4+4+4+3; that is to say, four of our fingers/toes has 4 bones while the other has only 3 bones.

I invite you to send examples of prime numbers in nature. Specifically you are asked to send interesting links to photos or drawings available in the web, exemplifying the occurrence of primes in nature.

I just will start an increasing table with a few easy cases.

Prime Example By
3 Visible dimensions (height,width,length) Rick
5 Ribs in Astrophytum myriostigma (Bishop's cap): 1
Fingers in the human hand: 1
Arms in a Sugar Sea Star: 1
7 cervical vertebrae (common to humans, whales, and giraffes) Haga
11 pair of ribs in mongoloid children. Haga
19 Bones in human hand & fingers, after the wrist: 1
Bones in human foot & toes, after the knee : 1Pairs of chromosomes in cat and pig: 1


23 Pairs of chromosomes in Human and Hare: 1 Haga
31 Pairs of chromosomes in donkey: 1 Haga


During the first week after released this puzzle, contributions came from Enoch Haga and someone named 'Rick'.

Both pointed to the 'Cicadas' in nature. Rick sent the following link:

Rick added:

3: Visible dimensions (height,width,length)

Enoch pointed out the following primes in nature, but no links were sent.

7 cervical vertebrae (common to humans, whales, and giraffes.age 50)
5 lumbar vertebrae
1 person in 20 has a 13th pair of ribs
mongoloid children have 11 pair of ribs.


Patrick Capelle wrote (Feb. 07) an interesting note about his following observation:

Yesterday (10 Feb 2007) i went to the Royal Museum for Central Africa (RMCA, Belgium).
There was an important temporary exhibition about butterflies and moths (4 February 2006 - extended until 20 May 2007), a selection from the remarkable collection of the RMCA.
During the visit, I saw the following sentence in French (written with big letters) :
"Il existe 5 familles de papillons de jour, mais 29 familles de papillons de nuit et 73 familles de mites".
A translation to English (also written with big letters) was given :
"There are 5 families of butterflies, whereas there are 29 families of 'macro' moths and 73 families of small moths".
Incredible ! You can imagine my surprise. I did not change a word in these two sentences.
In my circle of friends nobody saw that 5, 29 and 73 are prime numbers ! In fact, they are the smallest prime numbers of the form 10n2 - 6n + 1 (see sequence A087348). Can somebody explain the origin of their presence here ?





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