This appeals to my geeky sense of cool, but I'm afraid you'd be stuck with a small market (for clients and employees). People who can't make change in their heads might need some help figuring out prime factorization. And what happens when the party of 16 orders 903337795584000?

In my mind (as a computer techy), binary would be easier, but wouldn't accout for 2 or more of something.

And why wouldn't an '18' be three orders of '5' and an order of '3'? Or two orders of '7' and two orders of '2'?

<I> People who can't make change in their heads might need some help figuring out prime factorization. </I>

The register would do the factorization - after all, it's already calculating the change.

<I> And what happens when the party of 16 orders 903337795584000? </I>

In theory you get 16 number twos, 8 number threes, 3 number fives and 5 number sevens.

In practice the cashier punches in the wrong number and you get a confused look.

I'd bet that a party of 16 would actually give 16 different numbers though.

<I>And why wouldn't an '18' be three orders of '5' and an order of '3'? Or two orders of '7' and two orders of '2'?</I>

Because of the Fundamental Theorem of Arithmetic.(Hint - use multiplication, not addition.)

I love this idea. Why not offer it in the café of the mathematics department in a university first? People should be able to figure it out there...

I think you couldn't have a #1 on the menu. Otherwise,what would "give me a 1" mean? One order of #1 or many? Also, how would you distinguish 2 orders of #1 from one order of #2, etc.

Restaurants have a habit of screwing up orders as it is.. If they miskeyed one digit of a big order, all the food will be wrong.