This embodiment teaches a variation of GCD-based sieving, building tables
of prime products, but intentionally restricting the size of table
entries to fit within a single machine word. This combination allows one
to mix advantages of the two most popular sieves, while retaining the
simple and straightforward structure of the simpler one. Divisor length
restriction can provide significant savings in the number of long
divisions, but may be implemented with only two very specific primitives.
The two primitives offer better optimization capabilities than a fully
generic multiword arithmetic library.