November 23, 2011

Prime numbers in nature

I found this on Wikipedia, reading about prime numbers:

“Inevitably, some of the numbers that occur in nature are prime. There are, however, 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.These insects spend most of their lives as grubs underground. They only pupate and then emerge from their burrows after 13 or 17 years, at which point they fly about, breed, and then die after a few weeks at most. The logic for this is believed to be that the prime number intervals between emergences make it very difficult for predators to evolve that could specialize as predators on Magicicadas. If Magicicadasappeared at a non-prime number intervals, say every 12 years, then predators appearing every 2, 3, 4, 6, or 12 years would be sure to meet them. Over a 200-year period, average predator populations during hypothetical outbreaks of 14- and 15-year cicadas would be up to 2% higher than during outbreaks of 13- and 17-year cicadas. Though small, this advantage appears to have been enough to drive natural selection in favour of a prime-numbered life-cycle for these insects.

There is speculation that the zeros of the zeta function are connected to the energy levels of complex quantum systems.

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Biology, Number Theory, Philosophy of Nature