There is also the segmented Sieve of Eratosthenes. It has a simlar performance but uses much less memory: the number of prime numbers from 2 to sqrt(n). For example, for n = 1000000, the RAM has to store only 168 additional numbers.
I use this algorithm here https://surenenfiajyan.github.io/prime-explorer/
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Yep, this is the natural way to go, especially considering the possibility of parallel computing and the importance of cache locality, etc.