Real life uses of prime numbers (in physics/engineering) [closed]

Solution 1:

Clock making is a great example. Need a movement that moves at 23/83 ticks per second, anyone? In the olden-days, we'd approximate such a fraction using what's called the Stern-Brocot tree of rational numbers, which produces an ordered set of coprime ratios of integers which spans the rationals. See here for more.

Solution 2:

There are prime numbers in the biological world ... I assume for good evolutionary reasons.

For example, the Cicadas emerge every 13 or 17 years. Maybe this is to minimize the overlap with other species that also emerge only in certain years?

Here is what the Wikipedia article says about this:

The emergence period of large prime numbers (13 and 17 years) was hypothesized to be a predator avoidance strategy adopted to eliminate the possibility of potential predators receiving periodic population boosts by synchronizing their own generations to divisors of the cicada emergence period. Another viewpoint holds that the prime-numbered developmental times represent an adaptation to prevent hybridization between broods with different cycles during a period of heavy selection pressure brought on by isolated and lowered populations during Pleistocene glacial stadia, and that predator satiation is a short-term maintenance strategy.

Solution 3:

Prime numbers of turbine, fan and stator blades are very common in gas turbines (airplane engines), to push the fundamental frequency of air pulses through the wake of the stators away from each other. Of course, they need to be relatively prime - if you have seventeen blades behind seventeen stators, the whole disk is experiencing a pressure pulse every 1/17th of a rotation.

Whether you need to do this depends a bit on how highly loaded your components are and your other design decisions. This paper (end of p244, start of p245) talks about this.

Solution 4:

The NTSC timing frequencies are composed of small primes so that the color subcarrier didn't beat with the horizontal line frequency by being relatively prime. Part of the constraints on the choice was that the FM sound carrier frequency had a very tight tolerance and could not be changed and still maintain backward compatibility with black and white TVs. The horizontal line frequency could be altered however.

See:

Abrahams, I. C., "Choice of Chrominance Subcarrier Frequency in the NTSC Standards", Proceedings of the I-R-E, January 1954, pp 79-80

Abrahams, I. C., "The 'Frequency Interleaving' Principle in the NTSC Standards", Proceedings of the I-R-E, January 1954, pp 81-83