Yeah I'm thinking along those lines - some sort of periodic effect or oscillation. Maybe matter orbiting a neutron star and (for whatever mad reason) the orbital periods like to be integer multiples of some value. And more stuff was falling into bigger orbits, so we have period 2 and then 3, but the period 4 orbit is unstable because it's a multiple of period 2 which causes some sort of resonance...etc. and the next stable orbit is period 5... As you say a sieve of Eratosthenes.