Is there a way to improve the Sieve of Eratosthenes by using wheel factorization? Or would using wheel factorization to sieve make it really not the Sieve of Eratosthenes anymore?
For example Rosetta Code states
Implement the Sieve of Eratosthenes...[without optimizations]
That means especially that you shouldn't optimize by using pre-computed wheels, i.e. don't assume you need only to cross out odd numbers (wheel based on 2), numbers equal to 1 or 5 modulo 6 (wheel based on 2 and 3), or similar wheels based on low primes.
If there's an easy way to add such a wheel based optimization, implement it as an alternative version.
What is meant by pre-computed wheel? I can see how one can not bother considering even numbers when doing the SOE but for larger primes (even 3) it becomes non-trivial to know which integer is the next non-multiple so you end up just doing SOE anyway.
There's also this question but I don't see how anything there could be considered SOE.