Miért vannak, mire használják a prímszámokat?

Miert vannak? Nincs oka, egyszeruen vannak mert a matematika torvenyszerusegei miatt lenniuk kell.

Mire hasznaljak? Pl. kriptografiara (titkositasra).

[link]

Itt olvashatsz részletesen az RSA-kódolásról, melynek a prímszámok létezése jelenti az alapját. Ez egy nyilvános kulcsú titkosító algoritmus.

„The evolutionary strategy used by cicadas of the genus Magicicada makes use of prime numbers. These insects spend most of their lives as grubs underground. They only pupate and then emerge from their burrows after 7, 13 or 17 years, at which point they fly about, breed, and then die after a few weeks at most. Biologists theorize that these prime-numbered breeding cycle lengths have evolved in order to prevent predators from synchronizing with these cycles. In contrast, the multi-year periods between flowering in bamboo plants are hypothesized to be smooth numbers, having only small prime numbers in their factorizations.”

[link]

„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 1397.73 years.”

Théophile ( [link] ), Real-world applications of prime numbers?, URL (version: 2012-09-24): [link]

„Gas turbine and steam turbine shafts vibrate at low harmonics, such as 2,3,4,5 times the rotational frequency. As such, 60 blades, for example would be a very bad number, because the vibration from the blades would only enhance these low order vibrations. Much better to have 59 or 61 blades (both prime numbers) as this will give a blade-passing vibration at 59 or 61 times the rotational speed, and there will be no interactions with the low-order shaft vibrations.” [link] Steve Verrill, [link]

- jól jönnek egy csomó fejszámolásos esetben (amíg nincs a fejünkben chip, addig elő-előfordul ilyen eset)

- hadseregnél, ebédnél, amikor téglalap alakba akarunk rendezni valamiket (ekkor az összetett számokat használjuk)

- css háttér generálás: [link]

- DH publikus kulcscsere: [link] (ez olyasmi, mint az RSA, csak egyszerűbb)