import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.function.Predicate;
import java.util.function.Supplier;
import java.util.stream.Stream;

/**
 * Primes generator.
 */
public class Primes {

    private final Map<Long,Boolean> cache;
    private final Predicate<Long> isPrime;

    /**
     * Creates a new basic prime generator.
     */
    public Primes(){
        this.cache = Collections.emptyMap();
        this.isPrime = Primes::isPrime;
    }

    /**
     * Creates a memoized prime generator with a cache of
     * the provided size.
     *
     * @param cacheSize - the cache size.
     */
    public Primes(int cacheSize) {
        if(cacheSize < 1) {
            throw new IllegalArgumentException("The cache size must be a positive integer bigger than 0: " + cacheSize);
        }
        this.cache = new HashMap<>(cacheSize);
        this.isPrime = memoize(Primes::isPrime);
    }

    private Predicate<Long> memoize(Predicate<Long> source) {
        return x -> cache.computeIfAbsent(x, source::test);
    }

    private static boolean isEven(long n){
        return n % 2 == 0;
    }

    /**
     * Determines the smallest divisor of n starting at k.
     */
    private static long ldf(long n, long k) {
        while(true){
            if(n % k == 0) return k;
            else if(k * k > n) return n;
            else k = k + 2;
        }
    }

    private static boolean isPrime(long n) {
        return n==2 || ((n >= 2) && !isEven(n) && ldf(n, 3) == n);
    }

    /**
     * Infinite generator of prime numbers.
     */
    private static class PrimeGenerator implements Supplier<Long> {

        private long prime = 2;
        private final Predicate<Long> isPrime;

        PrimeGenerator(Predicate<Long> isPrime) {
            this.isPrime = isPrime;
        }

        @Override
        public Long get() {
            if(prime == 2) {
                return prime++;
            }
            do {
                prime = prime + 2;
            } while(!isPrime.test(prime));
            return prime;
        }
    }

    /**
     * Provides an infinite stream of prime numbers.
     */
    public Stream<Long> stream(){
        return Stream.generate(new PrimeGenerator(this.isPrime));
    }

}