Imagine a pond that contains a long line of lily pads, each labelled with a number, starting with '2', '3', and so on.
A scary stork enters the pond, looking for frogs! Each turn, the stork will move to a new lily pad, starting with lily pad 2.
When the stork reaches a lily pad, it looks for frogs:
- If the lily pad has no frogs on it, the stork finds one in the water. Take a new frog token and write the lily pad's number on its back. Put it on the lily pad with the stork.
- If the lily pad already has frogs on it, the stork won't look in the water, so this lily pad does not get a frog of its own.
Stop after however many turns you like. When you're done, the numbered frogs represent all the prime numbers that you found (at least from numbers 2 to whatever lily pad you stopped at).
When a stork first reaches a lily pad, all the frogs there are the prime factors of that number. For example, when the stork reaches lily pad #20, the stork will find frogs 2 and 5 there. (20 = 2 x 2 x5.) Lily pad 19, however, is empty when the stork arrives arrives: the newly minted frog 19 indicates that 19 is a prime number, and there are no other prime factors (other than 1).
- Move the stork forward one lily pad (on the first turn, place it on lily pad 2).
- If the lily pad has no frogs on it when the stork gets there, make a new frog with the lily pad's number.
- All the frogs on the stork's lily pad jump forward a number of pads equal to their number.