Like it, but it would take 4 shakes to let out the first grain of rice, then another 2 for the next one, and then another 2 for the next, and then you'd get one for the next 2 shakes...

Could be - I was imagining it to be a square sieve with 10,000 holes in a 100x100 grid, but with some of the holes (i.e. the primes) blocked, in a "Sieve of Eratosthenes" pattern.

I have no idea what the Sieve of Eratosthenes is, but I hope the holes don't get blocked up as easily as they do on the one in my kitchen. Can you buy it in Steamer?

Just to be picky, the sieve of Eratosthenes is an algorithm for finding the primes, not the pattern of primes itself. A true SoEs ought to behave as [zen tom] first suggested.

Alternatively, with each shake a bit of metal could fall out into your cake mix, representing each composite as it is eliminated, and adding a fresh hole to the sieve.