It's a secret (19)

So, PPK - you start with two really (really, really) big prime numbers - call them p and q.  You multiply them together and end up with a ginormous number which we call "n".  Then, using mathematical techniques which we needn't go into here (which is just a clever way of saying - I don't really understand, so don't ask) from these three numbers - p, q and n, we derive two other smaller numbers - x and y.  We now choose one of those numbers to be our private key - let's say we choose x.  We now lock this number away and don't divulge it to another living soul.  We can now dispose of p an q and the other two numbers (n and y) now become our public key - we can broadcast these to the world at large and anybody using a particular openly-known method and these two numbers can encrypt a message.  But here's the clever part - a message encrypted using our public key can only be decrypted using our private key, so it's useless to anyone other than us.  So message passed without any key passing.  Success, yes?  But is it secure?