It doesn't matter much anyway, because as I understand it, all of the local bug-eating animals absolutely gorge themselves whenever the cicadas come out! EDIT: I should have refreshed my memory before posting. I just re-read the article, and the cicadas do not hibernate underground.
They apparently "suckle on tree roots". The article has a few other mild corrections to my answer, as well. The most popular example I know comes from Cryptography, where many systems rely on problems in number theory, where primes have an important role since primes are in a sense the "building blocks" of numbers. When I was some 20 years old and living by myself for the first time, I designed a little racetrack with numbered squares on it, along with a handful of coloured tokens that would race along the track at the speed of one square per day.
Each token had a household chore and a prime number on it; when a token hit its number, I had to carry out the given task, and it would get reset to zero.
So, I washed the dishes every two days, watered the plants every three, vacuumed the carpet every five, It was a good system. It made cleaning fun, it provided variety and structure at the same time, and I was obliged to devote the entire day to chores only once every Intensity of green colour for each pixel was calculated using a function, which can be described with this pseudocode snippet:.
Just to add one more: Primes are also useful when generating Pseudo-Random Numbers with the computer. A few formulas use them to avoid patterns in the output. Prime number are used in developing machine tools. Utilizing primes you can avoid setting up harmonics which "eat" your very expensive tools. Tools chatter, bounce up and down , as they are being used.
Allowing those vibrations to propagate intensifying the chatter and the wear. You ever wonder how the metal racks in a microwave get designed? Again they use primes to assure that there are no harmonic possibilities, and you don't get the light show you would on an older microwave.
It was only when I was refining my Ada coded program to get the highest number of primes that I could get from a bit machine that I came across the offset logarithmic integral. I needed to reserve enough - but not too much - memory for my holding array for the primes. The array, of course, had to be declared prior to making any assignments to it.
All I'm saying here is that this equation made me wonder about primes in the context of a number of other things that use related functions.
That led me on to thinking about entropy calculations, particularly about selecting compositions more likely to give rise to metastable crystal forms - possibly even glasses - than other compositions using the same constituent elements. The Arecibo message consisted of a rectangle with prime width and height. This guarantees that aliens can only interpret the image in 2 ways modulo rotations and excluding a flat 1 x N image. Another application in the alien communication vein: in the 's documentary series Cosmos , Carl Sagan proposes that we use a signal like:.
The rationale is that this is likely to catch their attention, since there are no? A simple answer is finding GCF and LCD for whole numbers which allows us to efficiently manipulate fractions, both arithmetic and algebraic. Another is rationalizing and simplifying radical expressions. Prime number manipulation is a basic and not-so-basic tool of mathematics.
Quadratic Reciprocity is stated in terms of the residues modulo primes. This "Golden Theorem" as called by Gauss, is one of the main threads leading up to Langlands program and eventually to the geometric Langlands Program.
This later area of research has been shown to have ties with S-duality in string theory. String theory is just now being proven useful in understanding phenomena in condensed matter physics. Also it is the techniques that are used to prove results about prime numbers that have applications rather than a particular theorem about specific families of primes. Prime numbers are often test beds for more general results used in other areas of mathematics. Thought I'd mention an application or more like an explicit effect, rather than a direct application that prime numbers have on computing fast Fourier transforms FFTs , which are of fundamental use to many fields e.
It turns out that most algorithms for computing FFTs go fastest on inputs of power-of-two size and slowest on those of prime size. This effect is not small; in fact, it is often recommended, when memory is not an issue compared to time, to pad one's input to a power of 2 increasing the input size to earn a speedup. Papers on this have been written: e. And github issues like this suggest it is still an issue.
Very specific algorithms e. There may be some applications other than to cryptography, already mentioned in Manfred Schroeder's book, Number Theory in Science and Communication. Yes indeed modern cryptography is a useful branch which requires extensive use of prime numbers. Now when I say real world I don't mean the physical world. Primes numbers use is only in the computer world, in which we use computers in our physical world; if that makes any sense at all.
Primes number had little use until about the 19th century, when mathematicians experimented with them in hopes to uncover some breakthrough with their use. When the times of the war came around, the U.
Encryption was used, and to make the process of using primes numbers to encode information, computers came into play to create more complex and longer codes that would be much harder to crack by anyone. Primes can also be used in pseudorandom number generators and computer hash tables. In that book, aliens choose to send a long string of prime numbers as proof that their message is intelligent and not natural in origin, since primes are one thing that cannot change due to differences of psychology, lifestyle, or evolutionary history.
No matter what an advanced alien life -form looks or thinks like, if it understands the world around it, it almost certainly has the concept of a prime.
Home Extreme What are prime numbers, and why are they so vital to modern life? This site may earn affiliate commissions from the links on this page. Terms of use. This newsletter may contain advertising, deals, or affiliate links. Subscribing to a newsletter indicates your consent to our Terms of Use and Privacy Policy. You may unsubscribe from the newsletter at any time. Dividing 24 by 6 gives a result of 4, so each person gets 4 brownies.
Exchanging money is another common function that relies on factoring. You probably already know that 4 quarters make a dollar. Looking at this in terms of factoring, 2 factors of are 4 and Similarly, you can exchange a twenty-dollar bill for 20 one-dollar bills factors 1 and 20 , 2 ten-dollar bills factors 2 and 10 or 4 five-dollar bills factors 4 and 5. You also use factoring while shopping to compare prices per unit. For example, there are two cans of an expensive coffee blend on sale.
Using factors, you can compare the price per ounce without using a calculator or notepad. Dividing 36 by 12, the factors of 36 are 3 and Dividing 24 by 6, the factors of 24 are 4 and 6.
Time is another opportunity to use factoring in the real world. An hour divides into 60 minutes. Factors are also useful when traveling.
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