what is the actual real-world application of prime numbers? Or is it just a math concept that’s neat to see and figure out but doesn’t have any actual use case?

Question

I read that they have some uses within online encryption, but to be honest I never really thought about why we learned them in school until this morning.

In: 20

Answer 1

Prime numbers and numbers which are “co-prime” to each other are important in engineering, as they minimize linkage between different components.

For example, if you have moving parts next to each other which might cause a vibration, then having the two parts each moving at a different prime number speed, minimizes the vibration between parts. This concept has been used in jet engines and other high speed machinery with multiple moving parts.

It can also be used to minimize electrical interference between different wires. A common way in modern electronics to transmit a signal is to use a pair of wires which are twisted together. The electromagnetic field from one wire cancels out the other, and the twisting keeps the wires close together. However, if you have two twisted pairs directly next to each other, then if the twists line up, you can have areas where the electromagnetic field doesn’t cancel fully and one pair’s signal can leak into the other pair. If you use different twist rates, and use prime numbers for the number of twists, then you minimize the number of points where the twists line up, and keep interference to the minimum – this type of construction is used in modern twisted pair cables, such as ethernet cables.

There are some uses in computer security, as one of the first public-key encryption systems (the RSA cryptosystem) was based on prime numbers. Public-key cryptosystems are important, because they allow you to have make a secure channel, without pre-arranging it. You can convert any communications channel into a secure channel at any time.

A symmetric cryptosystem (e.g. a password) requires that you first agree a password with whoever you want to communicate securely with – so you need to get your password to the other party securely – so you need a secure communications channel to get the password to them. Oh wait.

The use of RSA public-key encryption has largely fallen out of favor these days for internet security, although it is still by “chip” bank cards. There are more efficient public-key techniques available these days, and these tend to be preferred for internet security, and are now starting to be deployed in bank cards.