Primality testing

From Lenka:

I tell Abi: a number is prime if, after I give you that many coins, you can't arrange them in several rows of equal length. Now guess if this is prime...

She "guessed" a corect answer for every set of pennies that I gave her (I tried everything from 4 to 16), just by looking at it and shifting some coins. Having given the answer, she would construct the rows for composite numbers to prove her "guess". Rows were not always on the shorter side: for 12, she used rowlength=4. After a few games, she stopped caring about aligning coins, of even about keeping them "row-like".

She can still occasionally miscount, or skip (say) 17 when counting to 20