Amos, I'm not completely sure what you mean with your question but if it is what I think you mean the proof goes roughly like that:

Imagine there is a largest prime number (idea: start with an assumption and if you can show that this assumption leads to a contradiction the assumption must be wrong). Then the number of prime numbers must be finite. You multiply all of them and add one. The resulting number is not dividable by any of the prime numbers on you list, therefore it must be a new prime number which contradicts your assumption.

Wolfgang