Evaluate the prime number by linear sieve (Euler's sieve)

I have been writing $ \ Text {o} \ left (n \ log {n }}\ right) $ for a long time, but I have never thought about its optimization. when I saw the linear screening method by chance, I thought it was a good optimization, so I learned it.

First, $ \ Text {o} \ left (n \ log {n }}\ right) the $ screening method must be slower than $ \ Text {o} \ left (n \ right) $, although it is not obvious on the current machine. do not set $ \ Text {o} \ left (n \ log {n }}\ right) $ to reliable. however, linear screening has its own purposes.

 

Evaluate the prime number by linear sieve (Euler's sieve)