This problem will test your ability to convert a specification to a program as well as follow instructions. Read all

instructions carefully. Any deviation will count against you.

Problem Description

There is a set of base$-10$ numbers that are referred to as $$happy$$ numbers. There is also a set of numbers that are

referred to as $$prime$$ numbers. The intersection of those sets $($happy numbers that are also prime$)$ are called $$happy

prime$$ numbers.

$10-$Happy Numbers

A Happy Number n is defined by the following process. Starting with n$,$ replace it with the sum of the squares of its

digits, and repeat the process until n equals $1,$ or it loops endlessly in a cycle which does not include $1.$ Those numbers

for which this process ends in $1$ are Happy Numbers, while those that do not end in $1$ are unhappy numbers.

First few happy numbers are $1,7,10,13,19,23,28,31,32,44,49,68,70,79,82,86,91,94,97,100$

Example:

Assignment

Write a program to print the first N happy prime numbers where N is input from the user via the console. The numbers

should be printed one per line. Your program must consist of three classes named as follows:

$1)$ public class HappyNumber

a$)$ Contains the function

public static boolean isHappy$($int n$)$ throws IllegalArgumentException

Returns true if n is happy, false if it is not, throws an exception if n is less than $0$

b$)$ Contains any other private functions that you deem necessary

$2)$ public class PrimeNumber

a$)$ Contains the function

public static boolean isPrime$($int n$)$ throws IllegalArgumentException

Returns true if n is prime, false if it is not, throws an exception if n is less than $0.$ Note that $1$ is not a prime

number, by definition.

b$)$ Contains any other private functions that you deem necessary

$3)$ public class MainApp

a$)$ Contains the function

public static void main$($String$[]$ args$)$

Calculates and displays the first N happy$-$prime numbers where N is received from keyboard input. If the user

provides an invalid number for N $($e$.$g$.$ negative, floating point, character string...$)$ this function should throw an

exception explaining what went wrong.

b$)$ Contains no other functions.