In this example, we wish to communicate our age in secret (we assume that we’re 18 years old). The public key of our recipient is used to encode this information. The public key consists of two numbers (the second number is generally 3, so we don’t need to send it). We perform an operation called “modulo exponentiation” using the public key. We can then sent the number 24 across any medium, and only by knowing the private key (I.e. the number 7), can the message be extracted.

The role played by prime numbers is when we generate the pair of numbers, 33 and 7. 33 can be factored uniquely into 3 and 11, which are used to generate 7. Of course, a real application would use much larger prime numbers, on the order of 200 digits.