our goal is to write a program to find $$good$$ prime numbers using the sieve of Eratosthenes. A

$$good$$ prime number is a number which:

$$ Is a prime number

$$ Is between a given lower and upper bound

$$ Does not contain a given digit

$2.$ Problem

You are to create a C$++$ project called sieve, a C$++$ source file called sieve.cpp$,$ and struct inside it

called PrimesEratosthenesSieve that finds $$good$$ prime numbers. The program asks the user for a

lower bound, an upper bound, and a bad digit, and then finds $$good$$ primes which are greater than

or equal to the lower bound and less than or equal to the upper bound and do not contain the bad

digit. When there is only one line of $$good$$ prime numbers in the output, the numbers should be

displayed with one space between each $($and no space at the end$).$ When there are multiple lines of

output, the numbers should be right$-$aligned to the width of the largest good prime. See below.

$3.$ Tips

$1.$ Use the template file found in Canvas. The framework for the program is there, and you will

need to fill in the methods. You MUST use the given members and methods to solve the

problem.

$2.$ You MUST dynamically allocate the primes$\_$ bool array. Don$$t forget to free any dynamically

allocated memory.

$3.$ If a function$/$method is inline, the compiler places a copy of the code of that

function$/$method at each point where it is called at compile time. inline is used for efficiency

with short $($one$-$line$)$ functions$/$methods

$4.$ Look up setw in the iomanip library to set the width of a field that is to be outputted.

$5.$ #include for the sqrt function.

$6.$ You may have up to $80$ characters on a line. If you cannot fit all the primes on one line, you

should wrap around to the next line. To find the width of the maximum prime value and how

many primes you can fit on a row, use the following code:

$7.$ const int max$\_$prime$\_$width $=$ num$\_$digits$($max$\_$prime$\_)$;

const int primes$\_$per$\_$row $=80/($max$\_$prime$\_$width $+1)$;

$8.$ Be sure to comment your code and put your name and Stevens pledge at the top.

$9.$ Make sure your code works with the test script.

$10.$ The algorithm for the sieve is found in the pseudocode below