This is no particular interest but here is some code that uses the “execute around” pattern to build a timer to time the “primes generator”, as well as a second primes generator that uses a self-modifying stream filter, a closure that accumulates all the primes found so far so as to perform divisibility testing, which is evidently faster than the “try to divide by every x between 2 and sqrt(n)”.

import org.junit.jupiter.api.Test;

import java.util.*;
import java.util.function.Predicate;
import java.util.function.Supplier;
import java.util.stream.IntStream;
import java.util.stream.Stream;

import static java.util.stream.Collectors.toList;
import static org.junit.jupiter.api.Assertions.assertEquals;

class SimpleTimer {

    public final long duration_ms;
    public final List<Integer> result;

    private SimpleTimer(List<Integer> result, long duration_ms) {
        this.result = Collections.unmodifiableList(result);
        this.duration_ms = duration_ms;
    }

    public static SimpleTimer timeIt(Supplier<List<Integer>> supplier) {
        long start = System.currentTimeMillis();
        List<Integer> result = supplier.get();
        long stop = System.currentTimeMillis();
        return new SimpleTimer(result, stop - start);
    }

}

class Primes {

    public static boolean isPrime(final int number) {
        return number > 1 &&
                IntStream.rangeClosed(2, (int) Math.sqrt(number))
                        .noneMatch(divisor -> number % divisor == 0);
    }

    private static int primeAfter(final int number) {
        if (isPrime(number + 1)) {
            return number + 1;
        }
        return primeAfter(number + 1);
    }

    public static List<Integer> primes(final int fromNumber, final int count) {
        return Stream.iterate(primeAfter(fromNumber - 1), Primes::primeAfter)
                .limit(count)
                .collect(toList());
    }

}

class PrimesSieveNoDoubles {

    private enum What {found_divisor, surpassed_sqrt, possibly_prime}

    // This is actually a little bit *slower* than a version that computes sqrt(x)
    // to determine whether to stop instead of using integer division to check whether
    // the dividend has become smaller than the divisor.

    public static List<Integer> primes(int limit) {
        final var store = new LinkedList<Integer>();
        Predicate<Integer> p = x -> {
            What what = What.possibly_prime;
            Iterator<Integer> iter = store.iterator();
            while (what == What.possibly_prime && iter.hasNext()) {
                int somePrime = iter.next();
                // it is faster to compute remainder and divisor next to one another always
                // than compute the divisor inside the "else", apparently due to compiler optimizations
                int remainder = x % somePrime;
                int dividend = x / somePrime;
                if (remainder == 0) {
                    // System.out.println(x + " = " + somePrime + "*n, not a prime");
                    what = What.found_divisor;
                } else {
                    // int divisor = x / somePrime;
                    if (dividend < somePrime) {
                        what = What.surpassed_sqrt;
                    }
                }
            }
            if (what == What.surpassed_sqrt || what == What.possibly_prime) {
                // System.out.println(x + " is prime");
                store.addLast(x);
                return true;
            } else {
                return false;
            }
        };
        List<Integer> result = Stream.iterate(2, x -> x + 1).
                filter(p).
                limit(limit).
                collect(toList());
        // add the end of the collect, the result and the store have the same content
        // this comparison takes a few ms
        assertEquals(store,result);
        return result;
    }

}

public class Primality {

    private final static int limit = 1_000_000;

    @Test
    void runBookPrimes() {
        List<Integer> l1 = Primes.primes(1, 10);
        List<Integer> l2 = Primes.primes(100, 5);
        assertEquals(List.of(2, 3, 5, 7, 11, 13, 17, 19, 23, 29),l1);
        assertEquals(List.of(101, 103, 107, 109, 113),l2);
        System.out.println("10 primes from 1: " + l1);
        System.out.println("5 primes from 100: " + l2);
    }

    @Test
    void runBookPrimesWithTimer() {
        // not an actual test, just printout
        final SimpleTimer timeIt = SimpleTimer.timeIt(() -> Primes.primes(2, limit));
        final List<Integer> result = timeIt.result;
        final String range = (result.isEmpty()) ? "" : "in range [" + result.get(0) + "," + result.get(result.size() - 1) + "] ";
        System.out.println("Using book code: finding " + result.size() + " primes " + range + "took " + timeIt.duration_ms + " ms");
    }

    @Test
    void runPrimesSieveWithTimer() {
        // not an actual test, just printout
        final SimpleTimer timeIt = SimpleTimer.timeIt(() -> PrimesSieveNoDoubles.primes(limit));
        final List<Integer> result = timeIt.result;
        final String range = (result.isEmpty()) ? "" : "in range [" + result.get(0) + "," + result.get(result.size() - 1) + "] ";
        System.out.println("Using primes sieve w/o doubles: finding " + result.size() + " primes " + range + "took " + timeIt.duration_ms + " ms");
    }
}