[giorgioz]

Prime numbers are used in cryptography. Public-private key cryptography is based on the fact that is hard to find the original two large prime numbers that were multiplied together from their result. Example you see written 721.000.165.331 . It's hard to calculate that is the product of the two prime numbers 730487 * 987013 So if they can calculate bigger prime numbers with a new faster method we can know larger prime numbers and have safer cryptography. (That's the simplified version that I remember as a software engineer)

[skissane]

> Prime numbers are used in cryptography. Public-private key cryptography is based on the fact that is hard to find the original two large prime numbers

That's true of one particular – albeit very popular – asymmetric cryptosystem, RSA. It isn't a property of asymmetric cryptography in general. There are other asymmetric encryption schemes which aren't based on the hardness of prime factorisation (e.g. DSA, elliptic curves, McEliece, NTRU)