Use an array of 10000 Boolean values to represent the list of numbers. Initializ

Use an array of 10000 Boolean values to represent the list of numbers. Initialize all the array elements to true. To mark out a number reset the corresponding array element to false.You should write these functions and include them in your program:void initialize(bool primeList[]);void markOutComposites(bool primeList[]);void outputPrimes(ofstream &outFile bool primeList[]);The Sieve of Eratosthenes can be implemented with a simple brute force algorithm that works correctly but is very slow due to a lot of unnecessary marking out of values that have already been marked out. With some careful clever thought and clever coding you can reduce the redundancy to make your program much faster.