system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why are prime numbers important in cryptography?
gpt
They are mainly used in an encryption algorithm called RSA. RSA is a special encryption algorithm because it is *asymmetric*.

Normal encryption is symmetric, which means it uses some sort of secret key to encrypt the data, and the same key to decrypt it. However, this means that both sides need to know the same key, which can be difficult. Asymmetric encryption is one where the encryption and the decryption are done using *different* keys (the keys are mathematically related, but aren't easily derived from each other). This allow you to keep one key as the secret, *private* key, and publish the other one as a *public* key. Anyone can use the public key to encrypt data and send it to you, and you'll be the only one who can decrypt it using your private key. Alternatively, *you* can encrypt something using your own private key and anyone can decrypt it, proving that it was you who encrypted it (this is used for digital signatures). This is essentially the basis for all encryption on the internet today, and it's what allows you to communicate with any website securely. 

So what do prime numbers have to do with RSA? The math in RSA involves a large number. From this number you can derive two numbers - the encryption and decryption keys - but only if you know this number's prime factors (ie which prime numbers divide it evenly). 

The security in RSA revolves around the fact that taking a number and breaking it into its prime factors is *difficult* - if you have a number, and you want to know its prime factors, then you basically have to guess different numbers until you find one that divides it evenly. If the number has lots of small prime factors then it's relatively easy to find them, but if the number only has a few large prime factors, then it's difficult to find them (something a computer can't feasibly do). So the easiest way to come up with a number that has large prime factors is to multiply two random large prime numbers. 

If you want to know how RSA actually works, the Wikipedia article has a pretty good explanation, using a simple example.