A prime number is any integer greater than $1$ that's evenly divisible only by itself and $1.$ The Sieve of Eratosthenes is a method of finding prime numbers. It operates as follows:

a$)$ Create a Boolean array with all elements initialized to true. Array elements with prime indices will remain true. All other array elements will eventually be set to false.

b$)$ Starting with array index $2,$ determine whether a given element is true. If so$,$ loop through the remainder of the array and set to false every element whose index is a multiple of the index for the element with value true. Then continue the process with the next element with value true. For array index $2,$ all elements beyond element $2$ in the array that have indices which are multiples of $2($indices $4,6,8,10,$ etc.$)$ will be set to false; for array index $3,$ all elements beyond element $3$ in the array that have indices which are multiples of $3($indices $6,9,12,15,$ etc.$)$ will be set to false; and so on$.$

When this process is completed, the array elements that are still true indicate that the index is a prime number. These indices can be displayed. Write an application that uses an array of $1,000$ elements to determine and writes the prime numbers between $2$ and $999$ and the number of these prime numbers to a text file named "primes.txt$".$ Ignore array elements $0$ and $1.$ Include code to handle the FileNotFound exception and display "File Not Found" message to the console should the exception occur.

In the text file "primes.txt$",$ each prime number should occupy a single line. The total number of prime numbers should occupy the last line of the text file with one empty line from the last prime number. For example, if the requirement were to write the prime number between $2$ and $9,$ the primes.txt file should have the following content:java