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

Primes factorization is a really simple way of explaining the “one-way” processes that underpin encryption.

The property of primes you have to know is that every single number has only one so called “prime factorization” which just means that if you only multiply prime numbers, there is only one combination of those prime numbers that gives you your original number.

Example 1: 17*47=499. The only way you can get 499 from prime numbers is by multiplying 17 and 47.

Example 2: 2*2*2*19=152 is the only way to multiply prime numbers and get 152.

Etc. You can do that for every number.

The trick is that while it’s “easy” to multiply numbers together, it’s incredibly hard to reverse it. Like, try to find the prime factorization of 2455. (Actually don’t try, it’s not going to work, it’s 5*491)

You basically have to go through every prime number one by one, and multiply them to find out what it might be.

So you have an operation that’s easy in one direction and hard to reverse.

You have, a basic encryption algorithm.

There are thousands of applications of prime numbers otherwise, but this one is incredibly simple to explain despite being quite a powerful observation.