Prime number encryption works as soon as a consumer inputs a credit card number online. The RSA algorithm uses a public key and a private key to hide information from possible thieves. The public key is available to the public, but it is hard to break because it is a product of two very large prime numbers. The private key, known only to the merchant, is a product of two smaller prime numbers.

The reason this RSA algorithm encryption works is because the number used to encrypt the data with a public key is a very large number that is hard to factor into prime numbers. The University of California at Berkeley states that it is simple to multiply two very large prime numbers together but difficult to break that figure down unless someone has a powerful computer to do the work.

The overall encryption program works using the example "x=yz" where x is the public key, while y and z are the private keys. These private keys are very large prime numbers multiplied together, sometimes to the order of 100 or 200 numeric places. The two private keys unlock the public key and decode the information sent through the transmission.

A prime number is a numeral that has just two factors: itself and one. Small prime numbers include two, three, seven, 11, 13, 17 and 19.