Embarrassing Moments

Had this conversation with my girlfriend:

My girlfriend:  If each menu item were assigned a different prime number, you could communicate your entire order in one number, which would be the multiple of all the items you want to order.

Me:  That system wouldn't work, because there could be more than one order that would result in the same number.

My girlfriend:  No there couldn't.  You just factor the number and you know exactly what was ordered.

Me:  But what if the number could be factored in different ways?  Like, how can the waiter tell if you wanted two "4's" or one "8"?

My girlfriend:  That's why you use prime numbers, none of the numbers is a factor of another.  Neither of your numbers is prime.

Me:  But what if one of the prime numbers is a factor of another prime number?  What will the restaurant do then?

My girlfriend:  If a number has factors other than itself and one, it's not a prime number.

By that point she was embarrassing herself so much that I had to stop the conversation.  Apparently she's never heard of the "no true Scotsman" fallacy.  In this case, she might as well have said:  "No true prime number has factors other than itself and one."  Yes, dear.  [Nodding dutifully.]  Whatever you say.  I sometimes wonder whether two people, like us, who are so different in terms of intelligence, can really be happy together.