Suppose you are sorting all of the prime numbers between $1$ and some large number $N$, from smallest to largest; into buckets which correspond to their residue classes modulo some prime $p_i$.
Now suppose you actually had two copies of the prime numbers between $1$ and some large number $N$; one to be sorted by residue classes modulo prime $p_i$, and the other to be sorted by residue classes modulo prime $p_{i+1}$.
At each step in time you place the smallest prime number and its copy into the two buckets as instructed above.
At what point in time can you be sure that, all of the buckets that correspond to residue classes of $p_i$ (excluding bucket $[0]_i$) contain more prime numbers than any of the buckets corresponding to residue classes of $p_{i+1}$.
Or can you never be sure?