Segmented Sieve of Eratosthenes?

Question

It\'s easy enough to make a simple sieve:

for (int i=2; i<=N; i++){
    if (sieve[i]==0){
        cout << i << \" is prime\" << endl;
           


        

Answer 1

There's a version of the Sieve based on priority queues that yields as many primes as you request, rather than all of them up to an upper bound. It's discussed in the classic paper "The Genuine Sieve of Eratosthenes" and googling for "sieve of eratosthenes priority queue" turns up quite a few implementations in various programming languages.