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May1-11, 10:07 AM
P: 12
Quote Quote by baric View Post
While that may seem like a huge sieve, an additional 8% reduction (going from 79% to 81%) can be quite significant over a large range of numbers and justify the initial sieve setup.
One more point. Keep in mind that the sieve can be built dynamically as the prime number search continues. So you could start with a small sieve {30k+n...} and factor the primes to 210. From that point, you already have the sieve for {210k+n... } where 'n' is the series of primes up to 210, excluding the primes used to create the sieve (2,3,5,7).

Then when you've factored the primes up to 2310, you can easily switch to the sieve {2,3,5,7,11}.

This way, your sieve will automatically become more efficient as you progress through the primes, up to your computer's memory capacity to maintain the sieve.