Re: OT: Re: Sieve of Erastosthenes optimized to the max

Am 02.09.2024 um 05:40 schrieb Tim Rentsch:

This is a brainless statement (and incidentally illustrates why I
was motivated not to read postings from BM).  In fact no primes need
be pre-calculated to determine whether any given number is prime.
The point of using a sieve is the sieve method is much faster than
not using one.  For example, suppose we want to determine all primes
less than a trillion.  Taking the approach of pre-computing only
those primes less than a million (the square root) and then testing
numbers individually takes more than 100 times as many operations as
using a sieve.  Furthermore the operations used are more expensive
for the non-sieve approach - simply setting a bit in the case of a
sieve, versus computing a remainder in the non-sieve case.

I don't wanted to say that each numbe is indivually sieved against all
primes up to the square root but a range. I do that myself to speed up
the computation.