You will be writing a program that takes two whole number $($without a decimal point$)$ between $0($inclusive$)$ and $1000,000($inclusive$)$ on the command line and find and prints out all prime numbers between those numbers. For instance, if your program is invoked with $1$ and $10,$ your program will print $[2,3,5,7].$

You must:

name your main class "PrimeFinder"

put all your program$/$classes in a package called "prime".

check for errors in command line arguments and handle it properly.

Example Run of the program

The red color indicates the program's output. The dollar sign $($$$)$ indicates your command line prompt and what follows is what the user types on the command line $($terminal$).$

Example $1($positive $-$ no error$)$:

$ java $-$cp $.$ prime.PrimeFinder $115$

$[2,3,5,7,11,13]$

Example $2($positive $-$ no error$)$:

$ java $-$cp $.$ prime.PrimeFinder $77$

$[7]$

Example $3($positive $-$ no error$)$:

$ java $-$cp $.$ prime.PrimeFinder $2426$

$[]$

Example $4($Negative $-$ bad input$)$:

$ java $-$cp $.$ prime.PrimeFinder $10050$

Error: Max must not be smaller than Min

Example $5($Negative $-$ bad input$)$:

$ java $-$cp $.$ prime.PrimeFinder $1$ abc

Error: Invalid argument$($s$)$

Example $6($Negative $-$ bad input$)$:

$ java $-$cp $.$ prime.PrimeFinder $-1100$

Error: Min out of range. Minimum must not be smaller than $0.$

Example $7($Negative $-$ bad input$)$:

$ java $-$cp $.$ prime.PrimeFinder $0100000000$

Error: Max out of range. Maximum must not be greater than $1,000,000$

Example $8($Negative $-$ bad input$)$:

$ java $-$cp $.$ prime.PrimeFinder $1\mathrm{.}422$

Error: Min and Max must be whole numbers.

Example $9($Negative $-$ missing an argument$)$:

$ java $-$cp $.$ prime.PrimeFinder $10$

Usage: PrimeFinder

Additional Instructions and Hints

You must validate the command line arguments passed in by the users. The examples above cover some of the error cases that you need to handle but there may be more. Big part of your grade will be about error detection and handling.

Command line arguments appear in your main method's argument as an array of Strings $($String$[]).$ You can check the number of command line arguments $($which is equal to the length of this array$)$ and read each of them as a String, and then perform validations on them or convert them to numbers or integers. You can use the method Long.ParseLong$($String s$)$ to convert a String to a long number.

A number is a prime if and only if it's divisible by $1$ and itself. To confirm that a number is prime, you need to make sure it is not divisible by any prime numbers that are smaller than or equal to the quare root of that number. For instance, to recognize if $13$ is prime, you keep dividing it by all prime numbers that are smaller than or equal to the square root of $13,$ i$.$e$.3,$ which are $2$ and $3.$ If the number is divisible by any of those primes, then it is not a prime. To test $101$ for primality, you must make sure it's not divisible by divide it by any prime smaller than or equal to the square root of $101,$ i$.$e$.,2,3,5$ and $7.$