The details are unclear and the story may be legendary, but the great mathematician Alexander Grothendieck apparently once picked 57 as an example of a prime number. So a Grothendieck prime is a number that looks like it's prime but isn't. (And, by extension, a Grothendieck composite could be a number that looks like it's composite but is actually prime, like the 4999 mentioned.)
I told this story to Helen not long after she learned what a prime number was. It illustrates that checking primality is difficult — and when you're six that's actually true for 57, though I think she'll remember what 3x19 is now — it reinforces the idea that making mistakes is ok, and it gives a human face to mathematics, perhaps helping to stop the tedium of times tables memorisation killing any excitement about number theory.