Chapter 10 Exercise 18, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

10.18 (Large prime numbers)
Write a program that finds five prime numbers larger than Long.MAX_VALUE.

public class StopWatch {

    private long mStartTime;
    private long mEndTime;
    private long mElapsedPause;
    private int mLastSecond = 0;

    private boolean mIsOn;
    private boolean mIsPaused;

    private int mSeconds;
    private int mMinutes;
    private int mHours;

    public StopWatch() {
        mStartTime = System.currentTimeMillis();
    }

    public long getStartTime() {
        return mStartTime;
    }

    public long getEndTime() {
        return mEndTime;
    }

    public void start() {
        mIsOn = true;
        mStartTime = System.currentTimeMillis();
    }

    public void stop(){
        mEndTime = System.currentTimeMillis();
        mIsOn = false;
    }

    public long getElapsedTime() {
        return mEndTime - mStartTime;
    }

    public long peek() {
        return System.currentTimeMillis() - mStartTime;
    }
    public void pause() {
        mIsPaused = true;
        mElapsedPause = System.currentTimeMillis() - mStartTime;
    }

    public void resume() {
        mIsPaused = false;
        mStartTime = System.currentTimeMillis() - mElapsedPause;
    }

    public boolean isOn() {
        return mIsOn;
    }
    public boolean nextSecond() {
        updateTime();
        if (mSeconds != mLastSecond) {
            mLastSecond = mSeconds;
            return true;
        } else {
            return false;
        }
    }
    public boolean nextFiveSeconds() {
        updateTime();
        return mSeconds % 5 == 0;
    }

    public int getHour(){
        updateTime();
        return mHours;
    }

    public int getMinute(){
        updateTime();
        return mMinutes;
    }

    public int getSeconds(){
        updateTime();
        return mSeconds;
    }

    private void updateTime() {

        long currentTime = peek() / 1000;
        mSeconds = (int)(currentTime % 60);
        currentTime = currentTime / 60;

        mMinutes = (int) (currentTime % 60);
        currentTime = currentTime / 60;

        mHours = (int)(currentTime % 24);

    }

    @Override
    public String toString() {

        updateTime();
        String hours = getTimeFormat(mHours);
        String minutes = getTimeFormat(mMinutes);
        String seconds = getTimeFormat(mSeconds);

        return hours + ":" + minutes + ":" + seconds;
    }

    private String getTimeFormat(int time) {
        return (time > 9) ? time + "" : "0" + time;
    }

    public void reset(){
        stop();
        mHours = 0;
        mMinutes = 0;
        mSeconds = 0;
        mStartTime = 0;
        mEndTime = 0;
    }


    public boolean isPaused() {
        return mIsPaused;
    }
}

import java.math.BigDecimal;
import java.util.ArrayList;
public class Exercise_18 {

    private static ArrayList<Long> primeArray;

    private static StopWatch time = new StopWatch();

    public static void main(String[] args) {

        System.out.println("First using Mersenne algorithm to finishes this exercise..");
        System.out.printf("%-10s%7s\n", "P", "2 * P -1");

        for (int i = 270; i <= 300; i++) {
            if (isPrime2(i)) {
                System.out.printf("%-10d%-10s\n", i, getMersennePrime(i));
            }
        }

        System.out.println("5 prime numbers larger than Long.MAX_VALUE above...");

        System.out.println("\nPlaying around with primes.");
        System.out.println("Loading prime array...");
        primeArray = new primeArrayClass().getPrimeArrayList();
        System.out.println("loading finished... array size: " + primeArray.size());

        System.out.println("Current biggest prime: " + primeArray.get(primeArray.size() - 1));
        System.out.println("Prime needed to accurate calculate primes about Long.MaxValue: " + (long) Math.sqrt(Long.MAX_VALUE));
        System.out.println("Looking for other prime numbers starting from:");
        BigDecimal n = new BigDecimal(Long.MAX_VALUE).add(new BigDecimal(2));
        System.out.println(n);

        time.start();
        for (int primeCount = 0; primeCount < 5; n = n.add(new BigDecimal(2))) {

            if (time.nextFiveSeconds()) {
                System.out.println("Primes above Long.Max found: " + primeCount);
                System.out.println("Current biggest prime: " + primeArray.get(primeArray.size() - 1));

                System.out.println("Currently checking if " + n + " is prime.");
            }
            if (isPrime(sqrt(n).longValue())) {
                primeCount++;
            }

        }

        System.out.println("DONE. Found 5 primes...");


    }

    public static boolean isPrime2(long n) {

        long square = (long) Math.sqrt(n);
        for (int i = 2; i <= square; i++) {

            if (n % i == 0) {
                return false;
            }
        }

        return true;
    }

    public static BigDecimal getMersennePrime(int p) {

        return new BigDecimal(2).pow(p).subtract(BigDecimal.ONE);
    }

    private static boolean isPrime(long n) {


        for (long i : primeArray) {

            if (n % i == 0) {
                return false;
            }
            if (i > n) {
                break;
            }
        }

        for (long i = primeArray.get(primeArray.size() - 1); i < n; i += 2) {
            if (n % i == 0) {
                return false;
            }
        }

        primeArray.add(n);
        return true;
    }


    // Karp's Tricks, this can be implemented without a loop in only two lines, giving 32 digits precision
    private static BigDecimal sqrt(BigDecimal value) {
        BigDecimal x = new BigDecimal(Math.sqrt(value.doubleValue()));
        return x.add(new BigDecimal(value.subtract(x.multiply(x)).doubleValue() / (x.doubleValue() * 2.0)));
    }

}